Leibniz: What Kind of Rationalist? (Logic, Epistemology, and the Unity of Science, 13)

LEIBNIZ: WHAT KIND OF RATIONALIST?

LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 13

Editors Shahid Rahman, University of Lille III, France John Symons, University of Texas at El Paso, U.S.A.

Editorial Board Jean Paul van Bendegem, Free University of Brussels, Belgium Johan van Benthem, University of Amsterdam, the Netherlands Jacques Dubucs, University of Paris I-Sorbonne, France Anne Fagot-Largeault, Coll`ege de France, France Bas van Fraassen, Princeton University, U.S.A. Dov Gabbay, King’s College London, U.K. Jaakko Hintikka, Boston University, U.S.A. Karel Lambert, University of California, Irvine, U.S.A. Graham Priest, University of Melbourne, Australia Gabriel Sandu, University of Helsinki, Finland Heinrich Wansing, Technical University Dresden, Germany Timothy Williamson, Oxford University, U.K.

Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light no basic issues in the discussion of the unity of science. This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity.

For other titles published in this series, go to www.springer.com/series/6936

Leibniz: What Kind of Rationalist? Edited by

Marcelo Dascal Tel Aviv University, Tel Aviv, Israel

123

Editor Prof. Marcelo Dascal Department of Philosophy Tel Aviv University 69978 Tel Aviv Israel [email protected]

ISBN: 978-1-4020-8667-0

e-ISBN: 978-1-4020-8668-7

Library of Congress Control Number: 2008931198 2008 Springer Science+Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

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Published with the financial support of the Van Leer Jerusalem Institute, the Cohn Institute for the History and Philosophy of Sciences and Ideas at Tel Aviv University, and the S. H. Bergman Center for Philosophical Studies at the Hebrew University of Jerusalem. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com

Gottfried Wilhelm Leibniz, Varia physica: Sketch drawing. Without date. Gottfried Wilhelm Leibniz Bibliothek-Nieder¨as¨achsische Landesbibliothek: LH XXXVII,IV Bl. 3v

The pulleys of thought? Referring to manuscript XXXVII, the art historian Horst Bredekamp (2004: 194; see below, Introduction, p. 12) writes: “If ever there was a window into Leibniz’s thinking world, it is offered by these Mir´o-reminding scribbles inscribed in cardboard, which in their confusion of clashing and reflecting lines seem to faithfully mirror Leibniz’s mental theater”. He further suggests that these, along with other features of his thought, grant Leibniz a particular actuality in our days, as a thinker who permits to escape the dichotomy calculation vs. intuition. “Leibniz – Bredekamp writes – immunizes against the theologians of the computer as well as against those who are disenchanted by looking for meaning in the digital world” (ibid.). Whatever one’s view about its nature and consequences, Leibniz’s thought is certainly pulled by forces, pulleys, and connecting lines whose interaction is still far from our comprehensive grasping. Marcelo Dascal Tel Aviv, May 2008

Contents

A puzzling Leibniz manuscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi The pulleys of thought? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marcelo Dascal

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Part I Reinterpreting Leibniz’s Rationalism? 1 Leibniz’s Rationalism: A Plea Against Equating Soft and Strong Rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Heinrich Schepers 2 Leibniz’s Two-Pronged Dialectic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Marcelo Dascal 3 Leibniz’s Rationality: Divine Intelligibility and Human Intelligibility Ohad Nachtomy

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Part II Natural Sciences and Mathematics 4 De Abstracto et Concreto: Rationalism and Empirical Science in Leibniz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Philip Beeley 5 Leibniz Against the Unreasonable Newtonian Physics . . . . . . . . . . . . . . 99 Laurence Bouquiaux 6 Some Hermetic Aspects of Leibniz’s Mathematical Rationalism . . . . . 111 Bernardino Orio de Miguel vii

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7 Symbolic Inventiveness and “Irrationalist” Practices in Leibniz’s Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Michel Serfati 8 The Art of Mathematical Rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Herbert Breger Part III Epistemology 9 Ramus and Leibniz on Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Andreas Blank 10 Locke, Leibniz, and Hume on Form and Experience . . . . . . . . . . . . . . . . 167 Emily Rolfe Grosholz 11 Leibniz’s Conception of Natural Explanation . . . . . . . . . . . . . . . . . . . . . . 183 Marta de Mendonc¸a 12 The Role of Metaphor in Leibniz’s Epistemology . . . . . . . . . . . . . . . . . . 199 Cristina Marras 13 What Is the Foundation of Knowledge? Leibniz and the Amphibology of Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Marine Picon Part IV Law 14 Leibniz: What Kind of Legal Rationalism? . . . . . . . . . . . . . . . . . . . . . . . . 231 Pol Boucher 15 On Two Argumentative Uses of the Notion of Uncertainty in Law in Leibniz’s Juridical Dissertations about Conditions . . . . . . . . . . . . . . . . . . 251 Alexandre Thiercelin 16 Contingent Propositions and Leibniz’s Analysis of Juridical Dispositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Evelyn Vargas 17 Leibniz on Natural Law in the Nouveaux essais . . . . . . . . . . . . . . . . . . . . 279 Patrick Riley Part V Ethics 18 Authenticity or Autonomy? Leibniz and Kant on Practical Rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 Carl J. Posy 19 The Place of the Other in Leibniz’s Rationalism . . . . . . . . . . . . . . . . . . . 315 Noa Naaman Zauderer

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20 Morality and Feeling: Genesis and Determination of the Will in Leibniz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Adelino Dias Cardoso 21 Leibniz and Moral Rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Martine de Gaudemar Part VI Decision Making 22 Leibniz’s Models of Rational Decision . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Markku Roinila 23 The Specimen Demonstrationum Politicarum Pro Eligendo Rege Polonorum: From the Concatenation of Demonstrations to a Decision Appraisal Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 J´er´emie Griard 24 Declarative vs. Procedural Rules for Religious Controversy: Leibniz’s Rational Approach to Heresy . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 Fr´ed´eric Nef 25 Apology for a Credo Maximum: On Three Basic Rules in Leibniz’s Method of Religious Controversy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 Mogens Laerke Part VII Religion and Theology 26 Convergence or Genealogy? Leibniz and the Spectre of Pagan Rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Justin E.H. Smith 27 “Paroles Enti`erement Destitu´ees de Sens”. Pathic Reason in the Th´eodic´ee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Giovanni Scarafile 28 The Authority of the Bible and the Authority of Reason in Leibniz’s Ecumenical Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 Hartmut Rudolph 29 Leibniz on Creation: A Contribution to His Philosophical Theology . . 449 Daniel J. Cook Part VIII The Metaphysics of Rationality 30 For a History of Leibniz’s Principle of Sufficient Reason. First Formulations and Their Historical Background . . . . . . . . . . . . . . . . . . . 463 Francesco Piro

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31 Innate Ideas as the Cornerstone of Rationalism: The Problem of Moral Principles in Leibniz’s Nouveaux Essais . . . . . . . . . . . . . . . . . . . . . 479 Hans Poser 32 Causa Sive Ratio. Univocity of Reason and Plurality of Causes in Leibniz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Stefano Di Bella Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

Abbreviations

1 Leibniz’s Works A = S¨amtliche Schriften und Briefe. Edited since 1923 by various Leibniz Research Centers in Germany. Currently published by Akademie Verlag, Berlin. B = Der Briefwechsel von G. W. Leibniz mit Mathematikern. Edited by C.I. Gerhardt. Berlin, 1899 (repr. Hildesheim, 1962). C = Opuscules et fragments in´edits. Edited by L. Couturat. Paris, 1903 (repr. Hildesheim, 1966). D = Opera Omnia. Edited by L. Dutens. Gen`eve, 1767 (repr. Hildesheim, 1989). E = Opera Philosophica quae exstant latina gallica germanica omnia. Edited by J.E. Erdmann. Berlin, 1840. FC = Oeuvres de Leibniz. Edited by A. Foucher de Careil. Paris 1859–1875 (repr. Hildesheim, 1969). GM = Leibnizens Mathematische Schriften. Edited by C.I. Gerhardt. Halle, 1849– 1863 (repr. Hildesheim, 1962). GP = Die Philosophischen Schriften von G. W. Leibniz. Edited by C.I. Gerhardt. Berlin, 1875–1890 (repr. Hildesheim, 1965). GR = Textes in´edits. Edited by G. Grua. Paris, 1948. K = Die Werke von Leibniz. Edited by O. Klopp. Leipzig, 1864–1884. LH = Leibniz-Handschriften, Nieders¨achsischen Landesbibliothek Hannover. M = Rechstfphilosophisches aus Leibnizens ungedruckten Schriften. Edited by G. Mollat. Leipzig, 1885. NE = Nouveaux essais sur l’entendement humain. In A VI 6 and in GP 5.

2 English Translations A&G = Philosophical Essays. Translated by R. Ariew and D. Garber. Indianapolis, 1989. CH = The Early Mathematical Manuscripts of Leibniz. Translated by J.M. Child. Chicago, 1920. DA = The Art of Controversies. Translated by M. Dascal, with the cooperation of Q. Racionero and A. Cardoso. Dordrecht, 2006. xi

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Abbreviations

L = Philosophical Papers and Letters. Translated by L.E. Loemker. Dordrecht, 2nd ed., 1969. P = Logical Papers. Translated by G.H.R. Parkinson. Oxford, 1966. R = The Political Writings of Leibniz. Translated by P. Riley. Cambridge, 1972. R&B = New Essays on Human Understanding. Translated by P. Remnant and J. Bennett. Cambridge, 1996. SR = De Summa Rerum – Metaphysical Papers 1675-1676. Translated by G.H.R. Parkinson. New Haven, 1992.

Contributors

Philip Beeley, a former member of the Leibniz-Forschungstelle at M¨unster and lecturer in History of Science at the University of Hamburg, is Fellow of Linacre College and researcher on the Wallis Project at the Centre for Linguistics, University of Oxford. He is co-editor of the projected eight volumes of the Correspondence of John Wallis (1616–1703) (Oxford 2003ff.) and author of numerous studies on Leibniz and the history of early modern science and philosophy, including Kontinuit¨at und Mechanismus (Stuttgart 1996). He is currently preparing in collaboration an edition of Wallis’s Treatise of Logick. Andreas Blank has been Lecturer at the Philosophy Department of the Humboldt University in Berlin, Visiting Fellow at the Center for Philosophy of Science at the University of Pittsburgh, USA, and Visiting Fellow at the Cohn Institute for the History and Philosophy of Science and Ideas at Tel Aviv University, Israel. He is currently a researcher at the Herzog August Bibliothek in Wolfenb¨uttel, where he investigates the late medieval background of Leibniz’s thought. He also pursues research in metaphysics, early modern philosophy, and analytic philosophy. He is the author of Der logische Aufbau von Leibniz’ Metaphysik (2001), Leibniz: Metaphilosophy and Metaphysics, 1666–1686 (2005), and of numerous articles on Leibniz, early modern thinkers, and Wittgenstein. Pol Boucher teaches philosophy in Rennes, France, and is Associate Researcher at the Institut de l’Ouest, Droit et Europe (IODE). His scholarly work spans the history of law and jurisprudence in Europe, particularly in late Scholasticism, the Renaissance, and early modern thought. Leibniz’s juridical work and ideas occupy a special place in Boucher’s research and publications. He has translated into French, with enlightening introductions and notes, a series of fundamental juridical writings by the young Leibniz, including so far the Doctrina Conditionum (1995), the De Conditionibus (2002), the De Casibus Perplexis in Jure (2008). The Acad´emie des Sciences Morales et Politiques awarded him the “Lucien Dupont Prize” for the second of these publications, and the “Emile Girardeau Prize” for the third. From the city of Rennes he received in 2008 the “Prix de la Ville de Rennes” for the ensemble of his already published work. We should expect soon the publication of his translations of Leibniz’s Specimen quaestionum philosophicarum ex jure xiii

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collectarum and of the comprehensive juridical treatise of 1667, the Nova Methodus Discendae Docendaeque Jurisprudentiae, a new edition of which Leibniz began to prepare in the 1690s. Laurence Bouquiaux is Professor of Philosophy and department chair at the University of Li`ege, Belgium. She specializes in the history of modern philosophy and the philosophy of physics. She is the author of several papers on Descartes, Spinoza and Leibniz. Herbert Breger is director of the Leibniz Archive in Hanover, Germany, and ausserplanm¨aßiger Professor at the Institute for Philosophy at the University of Hanover. He is editor of the journal Studia Leibnitiana. His areas of interest are Leibniz, philosophy of mathematics, history of science. A joint research project with Emily Grosholz resulted in the book The Growth of Mathematical Knowledge (2000). Adelino Dias Cardoso is a researcher at the Centre of Philosophy of Lisbon University, Portugal. In addition to his work on Leibniz and his contemporaries, he is the director of a research project on “Philosophy, Medicine and Society”. His authored books include Leibniz segundo a express˜ao (1992), Fulgurac¸o˜ es do eu (2001), O Trabalho da mediac¸a˜ o no pensamento leibniziano (2005), Vida e percepc¸a˜ o de si. Figuras da subjectividade no s´eculo XVII (2008). He cooperated with Marcelo Dascal in the publication of the collection of Leibniz’s texts The Art of Controversies (2006), co-edited Descartes, Leibniz e a Modernidade (1998), and published several Portuguese translations of Leibniz’s works. Daniel J. Cook is Professor Emeritus of Philosophy from Brooklyn College of the City University of New York. He has been a visiting Professor at the Hebrew, Tel Aviv, and Bar-Ilan Universities in Israel. He published extensively in comparative philosophy and the history of modern philosophy, primarily on Hegel and Leibniz. His books include Language in the Philosophy of Hegel and G.W. Leibniz: Writings on China (co-edited with Henry Rosemont). He is currently co-editing Leibniz’s Relation to Jews and Judaism and an English translation of Leibniz’s correspondence with Joachim Bouvet, the French missionary in Beijing. Marcelo Dascal is Professor of Philosophy and former Dean of Humanities at Tel Aviv University, Israel. He is president of the New Israeli Philosophical Association and of the International Association for the Study of Controversies. His research activities include pragmatics and the philosophy of language, epistemology and the philosophy of science, cognitive sciences and the philosophy of mind, controversies and the history of ideas, with special interest in Leibniz and his contemporaries and followers. In addition to several edited and co-edited volumes, his books include La S´emiologie de Leibniz (1978), Pragmatics and the Philosophy of Mind (1983), Leibniz. Language, Signs, and Thought (1987), Interpretation and Understanding (2003), G. W. Leibniz: The Art of Controversies (2006, 2008). He is the founder

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and editor of the journal Pragmatics & Cognition and of the book series “Controversies”. For his research achievements he was awarded the Humboldt Prize (2002) and the Argumentation Award of the International Society for the Study of Argumentation (2004). Stefano Di Bella is research fellow in the Scuola Normale Superiore, Pisa, Italy. His main areas of interest are history of philosophy, early modern philosophy (especially Descartes and Leibniz), and metaphysics. He has published Le Meditazioni metafisiche di Cartesio, Introduzione alla lettura (1997) and The Science of the Individual. Leibniz’s Ontology of Individual Substance (2005). Martine de Gaudemar graduated in philosophy (Ecole Normale Superieure, Paris), in sociology, economics, mathematics (Institut d’Histoire des Sciences et des Techniques, Paris-Sorbonne, and Institute Henri Poincar´e). She obtained her Doctorat d’Etat (1989) with a dissertation on The notion of power in Leibniz, after which she studied and practiced psychopathology. To her early interest in logical form she added a concern with forms of life. At present she works on the constitution of individuality on both sides of a material living body and of forms of life in language. She uses Leibniz’s philosophy as a tool-box, which enables her to develop the notion of a living person and a cultural character as united in the leibnizian concept of “persona”. In 1994 she was appointed Professeur des Universit´es, teaching first at the Universit´e de Strasbourg and thereafter at the Universit´e de Paris-Ouest (Nanterre). She is a Senior Member of the Institut Universitaire de France (Chair: Philosophy, Ethics and Humanities). J´er´emie Griard, PhD in History of Philosophy, Universit´e de Paris-Sorbonne (2003), held a post-doctoral position as a researcher at the Department of Philos´ ophy and the Centre d’Etudes et de Recherches Internationales of the Universit´e ´ de Montr´eal (CERIUM), Canada. Since 2007, he has been a research fellow of the Alexander von Humboldt Foundation at the Leibniz-Archiv in Hanover. His research areas include Leibniz’s political thought, the concept of sovereignty, and the notion of Europe, with special interest in the stakes of a quasi-contractual social theory for the European Union project. He co-edited with Franc¸ois Duchesneau Leibniz selon les Nouveaux essais sur l’entendement humain (2006). Emily Grosholz is Professor of Philosophy and Fellow of the Institute for Arts and Humanities at the Pennsylvania State University; Corresponding Member of REHSEIS / Centre National de la Recherche Scientifique / University of Paris 7; Life Member of Clare Hall, University of Cambridge; and Associate of the Center for Philosophy of Science, University of Pittsburgh. She is author of Representation and Productive Ambiguity in Mathematics and the Sciences (2007) and Cartesian Method and the Problem of Reduction (1991), and co-author, with Elhanan Yakira, of Leibniz’s Science of the Rational (1998), as well as co-editor, with Herbert Breger, of The Growth of Mathematical Knowledge (1999).

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Mogens Laerke, PhD in History of Philosophy (University of Paris–Sorbonne, 2003), is currently a Harper Fellow at the University of Chicago. He was awarded a post-doctoral scholarship by the Carlsberg Foundation (2004–2007) and worked as a post-doctoral researcher in the Leibniz-Locke Research Project at Tel Aviv University (2007). He is the author of Leibniz lecteur de Spinoza. La gen`ese d’une opposition complexe (2008). Apart from extensive work on Leibniz and Spinoza, Laerke has written on Biblical exegesis and theological politics in the 17th Century. He has published a book in Danish on the influence of Jewish Mysticism on early modern philosophy, and written several articles on the contemporary French philosopher Gilles Deleuze. Cristina Marras, PhD in philosophy (Tel Aviv University, 2004), ‘Laurea’ in aesthetics and in pedagogy (University of Cagliari, Italy), is currently a researcher at the Instituto per il Lessico Intelletuale Europeo e la Storia delle Idee (ILIESI-CNR, Roma), where she is a member of the project Discovery (Digital Semantic Corpora for Virtual Research in Philosophy). She also teaches “Theory of Communication” at the Faculty of Philosophy, University “La Sapienza”, Roma. Her main research interests include philosophy of language, early modern philosophy, rhetoric and mediation, controversies, and Leibniz. Her recent research has addressed the relations between metaphor and philosophy. She wrote the entry “scientific metaphors” for the Enciclopedia Italiana di Filosofia (2005) and published several articles in journals and collective volumes. Marta Mendonc¸a is a Professor at the Department of Philosophy of the New University of Lisbon, Portugal. Her PhD dissertation, on The Doctrine of Modalities in the Philosophy of Leibniz, is scheduled to be published in 2008. She is a member of the National Council for the Ethics of the Sciences of Life, a member of the Centre of the History of Culture (New University of Lisbon), and a member of the International Association for the Study of Controversies. She has published articles on modalities, particularly on the Aristotelian and Leibnizian doctrines of modalities and their relations with determinism. Noa Naaman Zauderer, PhD in philosophy (Tel Aviv University, 2002), is a Lecturer in the Department of Philosophy, Tel Aviv University, Israel. Her main research interests are early modern philosophy (especially Descartes, Spinoza, and Leibniz), the history of ideas, the epistemology of error, and early modern conceptions of rationality. She published several papers in journals and collective volumes and her book Descartes: The Loneliness of a Philosopher has been published in Hebrew by Tel Aviv University Press in 2007. Ohad Nachtomy, PhD Columbia University (1998), is a Senior Lecturer in the Department of Philosophy, Bar-Ilan University, Ramat Gan, Israel. He also teaches at Tel-hai Academic College, near the Lebanese border. Before concluding his doctoral dissertation, which discusses Leibniz’s approach to possibility, he spent a year of research (1996–1997) on Leibniz and Spinoza at the Ecole Normale Sup´erieure,

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Paris. His recent publications include the book Possibility, Agency and Individuality in Leibniz’s Metaphysics (2007) and several articles on Leibniz in journals and collective volumes. ´ ´ Fr´ed´eric Nef is Directeur d’Etudes at the Ecole des Hautes Etudes en Sciences ´ Sociales, Paris, and is a member of the Institut Jean-Nicod (Ecole Normale Sup´erieure/CNRS). His philosophical research touches on several fields, some of which he deals with in an interdisciplinary way. They include, among others, philosophical logic, philosophy of mind, metaphysics, formal and social ontology, and history of philosophy, with a special interest in Leibniz and Austrian philosophy. Among his recent books: L’Objet Quelconque (1997), Leibniz et le langage (2001), Qu’est-ce que la m´etaphysique? (2004), Leibniz et les Puissances du Langage (coedited with Dominique Berlioz, 2005), and Les Propri´et´es des Choses (2006). Bernardino Orio de Miguel has been a teacher of philosophy in Spanish secondary schools from 1974 to 2001. His interest in Leibniz’s thought and its connection with hermetic thought developed and deepened thanks to research grants at the Herzog August Bibliothek, Wolfenb¨uttel (1980) and at the Leibniz-Archiv, Hanover (1984), and culminated with his PhD dissertation (Universidad Complutense de Madrid, 1988) on “Leibniz y la tradici´on teos´ofico-kabbal´ıstica: F.M.van Helmont”, published in two volumes and containing unpublished Leibniz’s texts on van Helmont. With a grant of the March Foundation (1996–1998) he has published Leibniz y el pensamiento herm´etico: a prop´osito de los “Cogitata in Genesim” de F.M. van Helmont (2 vols., 2002) and edited Lady Conway’s “Principia Philosophiae”: La Filosof´ıa de Lady Anne Conway: un ‘Proto-Leibniz’ (2004). At present, he is working on Leibniz’s correspondence with the Bernoulli brothers, with B. de Volder and with Jacob Hermann. Marine Picon is a former student of the Ecole Normale Sup´erieure de la Rue d’Ulm, Paris. She has taught philosophy at the University of Paris-Sorbonne and at the Ecole Normale Sup´erieure. In 2002, she was awarded a research scholarship by the Fondation Thiers (Institut de France, CNRS). Her current research bears on Leibniz’s early metaphysics and epistemology. Francesco Piro is a Professor of Philosophy at the University of Salerno, Italy. His main research interests are the philosophy and psychology of action, practical reason, the philosophy of language, and the history of philosophy, especially the early modern philosophical controversies in the domains mentioned. His works on Leibniz include two books, Varietas identitate compensata (1990) and Spontaneit`a e ragion sufficiente (2002). He edited an Italian translation of Leibniz’s philosophical and scientific dialogues, G. W. Leibniz: Dialoghi Filosofici e Scientifici (2007), co-edited Monadi e monadologie. Il mondo degli individui in Bruno, Leibniz, Husserl (2005), and published several papers on Leibniz in collective volumes and journals. He worked also on the psychology of imagination and its history, and he has published Il retore interno. Immaginazione e passioni all’alba dell’et`a moderna (1999).

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Hans Poser is Professor Emeritus of Philosophy at the Technische Universit¨at Berlin and currently (Spring 2008), visiting professor at the Humanities Research Center of Rice University, Houston, USA. His areas of research include the philosophy of science and technology and the history of philosophy, and he has contributed much to Leibniz research. He served for nearly three decades as the Vice President of the International Leibniz Society, besides being a former president of the German Philosophical Society. Poser’s books on Leibniz include a classical study on Leibniz’s modal logic, Zur Theorie der Modalbegriffe bei G. W. Leibniz (1969) and a recent introduction to his thought, G. W. Leibniz zur Einf¨uhrung (2005). Carl J. Posy is a Professor of Philosophy at the Hebrew University of Jerusalem, Israel. He holds a B.A. in Mathematics and Philosophy and a PhD in Philosophy from Yale University. Before coming to Israel in 1998 he taught philosophy in the United States. He is a well-known Kantian scholar, as well as a philosopher and historian of mathematics and logic. His current research includes Leibnizian influences on Kant’s pre-critical as well as his critical period. Patrick Riley is Professor of Political Philosophy in the Department of Government, Harvard University. He was formerly Oakeshott Professor of Political and Moral Philosophy at the University of Wisconsin, Madison (1972–2007). He has made Leibniz’s political and juridical views known throughout the English speaking world thanks to his selection and translation of The Political Writings of Leibniz (1972, 1988); his more recent volume, Leibniz’s “Universal Jurisprudence”: Justice as the Charity of the Wise (1996), provides a synthetic and well argued view of the universalistic side of Leibniz’s theory of justice. Markku Roinila, PhD University of Helsinki (2007), has done research on Leibniz’s theory of rational decision-making and philosophy of mind. He is currently studying Leibniz’s views on emotions and the perfectibility of man, and is a Research Doctor in the research unit Philosophical Psychology, Morality and Political Theory, led by Simo Knuuttila and funded by the Academy of Finland. His dissertation, Leibniz on Rational Decision-Making (2007), is volume 16 of the series Philosophical Studies of the University of Helsinki. Roinila is also editing a collection of translations of Leibniz’s texts into Finnish (forthcoming in 2009) and maintains a web-page of Leibniz resources and a discussion forum on Leibniz at http://www.helsinki.fi/∼mroinila/leibniz.htm Hartmut Rudolph, Dr. theol. (University of Heidelberg), published monographs on the history of the Prussian military church from the 18th century to World War I, about the German Protestant churches and their meaning for the integration of the refugees into the West-German society 1945–1972, several articles on the history of the Reform period in early modern Germany, on the relation of public and church law, on Leibniz, and on subjects of contemporary German church history. He collaborated with the historical-critical edition of the works of Paracelsus (since 1976) and Martin Bucer (since 1983). From 1993 to 2007 Hartmut Rudolph was Director

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of the Leibniz Edition Potsdam of the Berlin Brandenburg Academy of Humanities and Sciences, and since his recent retirement he continues to contribute to the edition of the theological and political writings. Giovanni Scarafile, PhD in philosophy (Lecce, 2001) is a Lecturer of philosophy at the University of Salento (Lecce, Italy), where he is in charge of the discipline Ethics of Communication. Co-founder of Sapere aude!, a research community concerned with the relation between faith and reason, he is also a member of the International Association for the Study of Controversy. His research interests include Leibniz’s theodicy, the philosophy of languages (pragmatics, rhetoric, cinema), and the relation between pathologies and theories of language. He is the author of the monographs Proiezioni di senso. Sentieri tra cinema e filosofia, (2003), La vita che si cerca. Lettera ad uno studente sulla felicit`a dello studio (2005), and In lotta con il drago. Male e individuo nella teodicea di G.W. Leibniz (2007), as well as the co-editor of La governance dello sviluppo: etica, economia, politica, scienza (2004), Libert`a e persona (2004), Libert`a e comunit`a (2005), Libert`a, evento e storia (2006), and Libert`a e dialogo tra culture (2007). Heinrich Schepers, Professor Emeritus of Philosophy at the University of M¨unster, Germany, was for many years head of the Leibniz Forschungstelle M¨unster, responsible for the edition of the philosophical writings. His contribution to the Academy Edition is invaluable, both for his profound familiarity with the manuscripts and ability to decipher them and for the technical and substantive innovations he introduced in the laborious procedure of edition. From 1982 to 1991 he made available to a group of Leibniz scholars a printed pre-edition (in 10 volumes) of volume 4 of the Philosophical Writings, whose final edition was published only in 1999. In this way he not only enlarged the worldwide scholarly collaboration with and interest in the editorial work, but also allowed a new generation of researchers to advance Leibniz research at a pace and quality that wouldn’t have been possible otherwise. Besides his incomparable devotion to Leibniz scholarship, Schepers is also a philosopher and historian of ideas whose work is widely acknowledged. Michel Serfati is Honorary Professor holding the Higher Chair of Mathematics in Paris. He has been for many years the head of the seminar on epistemology and history of mathematical ideas held at the Institut Henri Poincar´e, Universit´e de Paris 7. He has organised many conferences on the history and philosophy of mathematics, and is the author and editor of works in both disciplines. His most recent books are La R´evolution symbolique. La constitution de l’´ecriture symbolique math´ematique (2005) and De la M´ethode (2003), as well as the co-edited volume Math´ematiciens franc¸ais du XVII`eme si`ecle. Descartes, Fermat, Pascal (2008). He holds doctorates in mathematics and philosophy. In mathematics, his research concerns the algebraic support of multiple-valued logics (i.e, Post algebras). In philosophy, his work focuses on the philosophy of mathematical symbolic notation as a part of the philosophy of language. His research also deals with various aspects of the history of mathematics, especially in the 17th century, as a specialist in Descartes and Leibniz.

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He also worked in the history and philosophy of contemporary mathematics (e.g., Category Theory and Stone’s theorem). Justin E. H. Smith, PhD Columbia University, is Associate Professor of Philosophy at Concordia University in Montreal, Canada. His main research interest is the intersection and interconnection between the rise of the empirical sciences and that of ‘modern’ philosophy in the 17th century. He is the author of numerous articles on Leibniz and early modern philosophy, and is the editor of the recent volume The Problem of Animal Generation in Modern Philosophy (2006) in Cambridge Studies in Philosophy and Biology. Alexandre Thiercelin is a graduate student at the University of Lille 3, where he works on the relationship between logic and law. He organized with Professor Shahid Rahman the international conference “Argumentation and Law”, which was held in Lille on November 2005. The doctoral dissertation he is preparing bears the title “Meaningfulness of the expression ‘juridical logic’ in the perspective of Leibniz’s works concerning the use of conditions in law – mainly his Disputationes juridicae de conditionibus (1665) and his Specimen certitudinis seu demonstrationum in jure exhibitum in doctrina conditionum (1667–1669)”. Evelyn Vargas is Professor of Philosophy at the University of La Plata, Argentina, and a researcher in epistemology and the history of science for the National Council of Scientific and Technological Research (CONICET). She has written articles on Leibniz’s natural philosophy as well as on Peirce.

Introduction Marcelo Dascal

Gottfried Wilhelm Leibniz (1646–1716) was perhaps the last polymath who contributed significantly to such diverse fields of human thought and activity as metaphysics, epistemology, logic, law, history, politics, mathematics, natural science, theology, linguistics, and technology. Traditional historiography of philosophy has tagged Leibniz as one of the early modern “rationalists” – a label that no doubt has a sound basis in his own pronunciamientos, as well as in the Rezeption of his work by his contemporaries and by later centuries. Yet, different historians of ideas, different schools of thought, and different times have endowed this label with substantively different meanings – each according to their own bias and emphasis on one or another strand of Leibniz’s thought. Although every commentary, generic or specific, on Leibniz’s immense oeuvre cannot but illuminate some aspect of his “rationalism”, there has been no individual or collective effort focused mainly on this notion – itself a main focus of reflection by Leibniz, as well as undoubtedly the underlying motive of his theoretical and practical activities. The purpose of this book is to fill, at least partly, this lacuna. Our individual and collective aim is to investigate and analyze as precisely as possible the nature of Leibniz’s “rationalism”. This is, no doubt, quite an ambitious aim. But it is certainly apposite at this particular point of time, when the nature and role of reason and rationality in all human endeavors is under thorough examination in the light of stern criticism of modernity’s reading of these notions. It is also apposite regarding Leibniz scholarship, within which some voices have been arguing for a substantive revision of Leibniz’s rationalism as predominantly logic-oriented – an image that prevailed in the twentieth century. And it is, furthermore, fundamental for shedding light on the transformations the concept of rationality underwent in its path from early modern thought to late eighteenth century Enlightenment – a path, currently under intense study,1 in which Leibniz occupies a pivotal position. Of course, a possible outcome of bringing together several Leibniz scholars, many of whom specialize in different domains of his work, is to highlight rather the fact that the presupposition of the title question of this volume is false. That is to say, that there

M. Dascal Tel Aviv University, Tel Aviv, Israel

M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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is not one rationalism in Leibniz, but a variety of rationalisms; that he is not, therefore, a rationalist of a single kind, but of many kinds. It might even be the case that the different contributions to this book, based on different approaches, interpretations, and perspectives, as well as on research on different parts of Leibniz’s oeuvre, turn out to reveal, if not inconsistencies between the kinds of rationalism the contributors to this collective enterprise attribute to him, at least a pluralism that cannot be reduced to a common “rational” denominator. Were this the case, we would be in a position similar to that of those who, having searched for the underlying unity of Leibniz’s “system”, came up with different answers, one of which consists in viewing it as “plural”, i.e., irreducible to any single major component. We owe Leibniz, however, the charity of trying to find out whether and how the unquestionable variety and plurality of his thought is indeed guided, unified, and systematized by some overarching concept of reason and rationality, albeit different from the one customarily attributed to him. After all, he insisted that, if we are to understand the rationality of the world, we must take as global as possible a perspective as we can, so as to approach as much as humanly possible the creator’s point of view. Only if we face this challenge head on, as required by the title question of this book, we are entitled – eventually – to reach, as far as we can reach a decision (quoad nos, as Leibniz would put it), a negative conclusion to our search for the particular kind of Leibniz’s rationalism. One difficulty that has so far hampered attempts such as the one undertaken in this book is the fact that Leibniz scholarship displays often the property of being divided into a set of, so to speak, windowless monads. This is understandable, given the sheer magnitude of the oeuvre and the fact that roughly half of Leibniz’s writings still remain to this day either fragmentarily published or altogether unpublished. Furthermore, when in the 1920s, it was decided to begin a complete critical edition of all the manuscripts, the task had to be organized in such a way that different editorial teams were each in charge of a “Series” corresponding (roughly) to thematic clusters of Leibniz’s production in what for us – but not necessarily for him – amount to different “fields”. At present four such teams are active in Germany – in Hanover, M¨unster, Potsdam, and Berlin – respectively in charge of the mathematical, philosophical, theological-political and scientific-technological writings.2 The result of this division of labor, without which of course the editorial work could not advance, has been however to entrench the thematic divisions: normally, whoever focuses his attention on one “field”, tends to concentrate on the writings of the “relevant” series, largely disregarding the other ones. In order to remove this obstacle and to open windows across the subdivisions of Leibniz scholarship – a must if one’s aim is to understand such a fundamental concept for Leibniz as that of rationality – the present volume contains contributions from leading experts in several of the most important areas of Leibniz’s activity, some of whom are also responsible for the editorial work for the Academy Edition performed in the above mentioned Research Centers. This, I trust, corresponds to the only way of attempting some sort of synthesis of Leibniz’s rationalism as manifested in his multi-thematic and multi-perspective thought – namely, through a concerted cooperative effort of scholars familiar with different aspects of the oeuvre.

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By “cooperative” and “concerted”, I do not mean, of course, that criticism and disagreement are banned from this volume – as the reader will soon realize. Quite on the contrary, in the spirit of Leibniz’s anti-sectarianism, discussion is rather strongly encouraged, since – unlike other of his rationalist fellows – he believed that it is only through a tireless attempt to critically understand each other’s contribution that human minds can contribute together to the growth of knowledge.3 Consequently, no artificial uniformity is sought by attempting to hide the divergences and controversies underlying the different interpretations of Leibniz’s “rationalism”. The diversity of opinions is amply expressed in this volume not only through head on confrontations between some of the chapters, but also through the choice of different domains of Leibniz’s work, which require differential approaches to the rationality, both theoretical and practical, that informs each of them. Obviously, not all of Leibniz’s multifarious fields of activity can be covered in a single volume, especially if one wishes to attain some interpretive fidelity to the texts as well as argumentative cogency. Yet, the eight parts of the book deal with the fields Leibniz himself treated as the most important – judging from the amount of his research, production, and correspondence in each of them. In any case, these are areas in which rationality, however specific the meanings it may wear, is of paramount importance. I believe that, together, the contrast of opinions and the diversity of domains stand a good chance of shedding non negligible light (as Leibniz would say) on what kind or kinds of rationalist he was. In what follows, I attempt to provide brief introductory remarks on each of the chapters, following the order of the parts, and suggesting threads that connect them. Naturally, the chapters’ stand on the hard–soft rationalism divide (or union) will be often mentioned, but it is certainly neither the only nor the major theme that this introduction dwells in. Part I launches the discussion in medias res, by offering Heinrich Schepers the floor to defend his conception of Leibniz as a “radical”, “hard” rationalist, holding a unitary view of Reason (Chapter 1). This conception had been challenged by Marcelo Dascal, who argued that another, “soft” strand in Leibniz’s rationalism must be also identified and its importance duly acknowledged, if the comprehensiveness of his rationalism is to be properly accounted for.4 Schepers here undertakes to rebuke one by one Dascal’s (2001, 2003, 2004a) arguments for and examples of rational softness in Leibniz, developing considerably his earlier (Schepers 2004) reply to him.5 Instead of directly replying to Schepers, Dascal (Chapter 2) takes the indirect route of providing an elaborate example of soft–hard opposition-cuminteraction in an extremely important topic, in which Leibniz’s position is usually considered o be clearly and exclusively “hard” – namely, the art of conducting and resolving controversies. According to him, Leibniz’s sui generis “dialectic” instantiates well the relationship between the hard and soft components of rationality. For, he argues, this dialectic is both one and two-pronged – thus accommodating both the unity of reason with the deep difference between its soft and hard branches. Dascal argues his case with abundant textual evidence and explores its implications for understanding not only Leibniz’s rationalism, but also the fundamentally tolerant ethos of his thought. Ohad Nachtomy (Chapter 3) concludes Part I by suggesting

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a solution to the hard–soft clash. He proposes to consider rationality in terms of intelligibility, and equates “hard” and “soft” with two types of intelligibility, each belonging to a different domain: the former, divine; the latter, human. He argues that these two kinds of rationality-intelligibility do not exclude each other, but hold intrinsic, complementary connections. Nevertheless, he defines them as being each subordinated to one of the two main principles of Leibniz (the principle of contradiction and the principle of sufficient reason, respectively), whose inter-relations are a notorious problem in the interpretation of Leibniz’s thought. Nachtomy’s attempt at conciliation would, however, probably please both Schepers and Dascal (albeit for different reasons), though both would probably not be entirely satisfied with it (again, for different reasons). Rather than settling the controversy it directly deals with, Part I in fact fosters its continuation and deepening. In so doing, it sets the stage for an open and broader debate, in which other aspects of Leibniz’s conception and uses of reason emerge and shed light on his rationalism. Thus, although across the other parts, hard vs. soft aspects of Leibniz’s rationalism are put in evidence, analyzed, confronted, further explored, and explained, whether directly relating to the above controversy or not, it becomes clear in the volume as a whole that softness is not the only new dimension to be added to our understanding of the particular kind of rationalism he professed. The results of this broadening of perspectives are sometimes surprising. Part II, for example, reveals a mathematician that, far from adopting geometry as his methodological paradigm and Euclid as his undisputable hero, explores a variety of other ways of developing mathematical knowledge, i.e., of using reason within mathematics. A case in point is Leibniz’s use of mathematical notation, analyzed by Serfati (Chapter 7). As a combinatorial system, mathematical symbolism permits the generation of formulas “blindly”, i.e., independently of their meanings. This practice, which frees the mathematician from the traditional enslavement to a pre-ordained semantics, contributes powerfully to the modern idea of formalization. It also provides a new method of discovery, whose results are not submitted beforehand to semantic or logical “rational” constraints, and can therefore lead to innovative breakthroughs. As shown by Breger (Chapter 8), mathematical rationality unfolds at different levels of abstraction, the higher ones relying on a less explicit, tacit kind of knowledge, a know-how or “art” of a pragmatic nature, whose legitimacy lies not in its complete semantic analysis and logical justification but in the fact that “it works”. Although the know-how in question, as Breger stresses, cannot be deductively proved, it is not only essential, but also sometimes the only available “reason” a mathematician can give. This is in fact the only ground of legitimacy of the differential calculus Leibniz (or any other mathematician) could provide in the 17th century, as his standard reply to the Newtonians’ demand (accepted by the Leibnizians) of a fuller, metaphysical justification (what kind of entity are these dx and dy?) shows. If this is the case within mathematics, what about the applications of mathematics to other domains? In natural science, mathematical results must be in harmony with experimental and observational data. Yet, according to Beeley (Chapter 4), this requires a complex, sometimes pragmatic in nature, process of “accommodation”, for

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which Leibniz has recourse to a varied set of strategies. Deduction, he points out, is but one of them; and a narrow, deductive interpretation of his rationalism is incompatible with the methodological plurality of his approach. Bouquiaux (Chapter 5), discussing Leibniz’s critique of Newtonian physics as “barbarian” and “unreasonable”, also considers this problem of “accommodating” experience to theory: What seems to Newton to be unequivocal experimental proof of the existence of absolute space (for it requires the distinction between relative and absolute motion), can for Leibniz be interpreted without Newton’s theoretical construct, thus yielding a more parsimonious dynamics and metaphysics. Their disagreement, therefore, is not resolvable by “proof”, since it is a matter of harmonizing in the best possible way experimental findings with theoretical assumptions – which is where “reasonableness” lies. If we move a step further, with Orio (Chapter 6), who has done much to demonstrate the hermetic sources of Leibniz’s metaphysics, mathematical equations gain a “semantic cosmic content” that, though an essential part of their meaning, is not deducible from them; rather, it is an “overdimension” they have, which can only be reached via analogical thinking – a fundamental component of Leibniz’s rationalism, no doubt. The key Leibnizian notion of “blind thought”, upon which rests the importance he attributes to signs and their role in knowledge (not only mathematical), is also central in Picon’s (Chapter 13) argument against the thesis that interprets his epistemology as based in a pre-symbolic intuition of thought-contents. She thereby provides additional support to Belaval’s (1960) radical distinction between Cartesian “intuitionism” and Leibnizian “formalism”. This distinction is, no doubt, intimately connected with the two philosophers’ quite different conceptions of rationality. But, per se, it does not permit to determine whether they oppose each other also concerning the soft vs. hard distinction.6 Another chapter of Part III deals with Leibniz’s “formalism”. Grosholz (Chapter 10) claims that Leibniz overstates the power of formalization, even in mathematics. She argues that this exaggeration might be mitigated with the help of Locke’s nominalism and the mediation of a notion of “formal experience” she elicits from Hume. By comparing how this notion fares in mathematical and in legal contexts, she shows how a rational method can be developed that overcomes the gap between abstract principles and particular cases.7 The notion of “natural explanation” Leibniz applies to the natural, as analyzed by Mendonc¸a (Chapter 11), inserts itself nicely in a hierarchical scale of kinds of explanation, viz. of rationality, he appears to use. For example, he ranks his hypothesis of the pre-established harmony as the only natural explanation of nature, for it is neither arbitrary nor appeals to miracles; for this reason it is more than a mere hypothesis, although it is not certain either. The epistemological role of “natural explanations” – now in connection with the uses of natural language – also figures in Chapters 9 and 12, where Blank and Marras discuss, respectively, Leibniz’s conception of philosophical “analysis” and the use of metaphor as a cognitive tool in his philosophical writings.8 With Part IV, we enter domains concerned, in one way or another, with practical rationality, beginning with law – the field in which Leibniz the jurist first established a solid reputation. While Chapters 14, 15, and 16 focus on his early legal writings,

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Riley (Chapter 17) concentrates on a passage of the Nouveaux essais, and inquires why Leibniz has found it fit to express his views on law and justice in a chapter that deals with maxims, principles, and axioms. In consonance with his well known “hard” interpretation of Leibniz’s theory of justice (see, e.g., Riley 1996), he replies that it is because, like mathematics and logic, universal jurisprudence belongs to the domain of “truths of reason”, i.e., of necessary, not contingent truths. By stressing, in particular, Leibniz’s claim that the fundamental maxims of law itself, which derive from “pure reason”, are those that “constitute natural law” (NE 4.7.19; A VI 6 425), Riley implicitly highlights a radical contrast between this strong sense of “natural” and the weaker sense of this term analyzed by Mendonc¸a – a contrast that deserves to be reflected upon. The three other chapters in this part plunge deep into the technicalities of young Leibniz’s juridical work. Jointly, they reveal a concern for rigorous definitions and demonstrations, as well as for the solution of “hard cases” traditionally considered as unsolvable. Both Thiercelin (Chapter 15) and Vargas (Chapter 16) analyze specific types of legal reasoning Leibniz employs and undertakes to provide a solid logical foundation for. Boucher’s (Chapter 14) endeavor is more general: He seeks to single out the originality of the young Leibniz’s juridical rationalism against the background of a long tradition of legal thought he shared. With a wealth of details and examples, Boucher shows that Leibniz’s originality lies in his ability to look at concrete cases and positive law from the perspective of a logician who seeks to discern in them fundamental logical patterns.9 This distinguishes Leibniz from his predecessors, whose viewpoint yields the equivalent of “statements worded by pure lawyers, wishing only to report on the data of positive legislation”, although they phrase them in a logic sounding terminology, where the words “definition”, “axiom”, and “demonstration” loom large. Boucher’s conclusion is that, at least in this early period, the fundamental characteristic of Leibniz’s legal thought is “the constant search for the immanent order of institutional rights and mechanisms”, and that his legal rationalism is “particularistic, exhaustive and theorising”. The four chapters of Part IV present thus a Leibniz whose “legal rationalism” is inspired by the ideals of hard rationality. A more complete picture of his brand of legal rationalism, however, should include its “soft” version – the one where weighing reasons supersedes counting them, uncertainty is the rule, and the typical kind of inference is presumptive rather than deductive. These are the features of “juridical logic” to which Leibniz usually alludes when he speaks of the “new logic” which other disciplines ought to imitate, a logic yet to be done, which the jurists – though able practitioners of this art – have not yet been able to formulate adequately.10 Maybe the need to account for the complementary relationship between the hard and the soft strands of Leibniz’s juridical rationalism is already announced in Boucher’s formula, which juxtaposes particular and universal, casuistic and theoretical, substantive and logical, piecemeal and complete. The chapters of Part V emphasize those aspects of Leibniz’s “moral rationality” that have a distinct “soft” flavor. All of them point out the role of some type of feeling in Leibniz’s account of moral action, which cannot indeed be reduced to the result of pure rational or intellectual deliberation. In this connection, it is

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convenient to recall that, for Leibniz, the mind is not acted upon “as the weights act on a balance” by any privileged set of motives for action, whatever their pedigree; as an agent, it is the mind that “acts by virtue of the motives, which are its dispositions to act”; and – he takes care to stress – these motives “include all the dispositions the mind may have in order to act voluntarily, since they include not only the reasons but also the inclinations which come from the passions or from other previous impressions” (Leibniz’s Fifth Paper to Clarke; GP 7 392).11 Therefore, regardless of their actual weight, the “Balance of Reason” cannot overlook the agent’s feelings’ influence in inclining the agent towards one rather than another choice of action – an influence that, furthermore, may be decisive in assessing the action’s morality. The formation and operation of the will – as points out Cardoso (Chapter 20) – is a “striving of the intelligent” (conatus intelligentis), which requires a continuous and close interaction between reason and feeling. Consequently, it is neither determined by reason nor indifferent to it. Furthermore, choice, i.e., the exercise of free will, requires also an ongoing awareness by the moral agent of his motives and of the situation within which his action is embedded. Such awareness is, however, severely restricted by the Leibnizian doctrine of the “petites perceptions”, which applies to both, external and internal perception. Given all these uncertainties, Leibnizian moral life, on Cardoso’s analysis, can hardly be a matter of simply applying the “hard” rules of a strict moral code, and demands much more from the subject’s moral feelings and judgment. Posy too (Chapter 18) focuses on the moral agent’s self awareness and the role of feeling therein. Employing a very interesting and useful comparative Kantian grid for analyzing the Leibnizian conception of the self, he argues that the complete concept of an individual substance and its analytical, conceptual “unpacking” cannot be the whole story, as far as morality is concerned. According to Posy, in addition to its logically and sequentially organized predicates, the seamless Leibnizian self comprises “endemic qualities”, which confer to it more than “artificial unity”. These are qualities such a Hamlet’s brooding nature or Cassius’s (as distinct from Iago’s) jealousy, “themes that run through the sequence of stages, a sort of leitmotif (or several) within the overall symphony that is a life, [. . .] tendencies in the sum of [an individual’s] deeds”. Posy does not intend by these poetic descriptions, I gather, to attribute to the Leibnizian self something like the momentary, phenomenological “qualia” of the “moods” that are in favor in today’s philosophical psychology, but some more enduring quality, a sort of “style” of the individual that “gives an internal rhythm and order to [his] appetites and inclinations” and whose desires “project forward”. Using the strange (for Leibniz) notion of maturation of a concept, he claims that “each mature individual concept” has such endemic qualities and that they are not “revealed by any ordinary conceptual containment”, i.e., that in order to grasp them “it is not enough to work through the concept sequentially”. Yet, he concludes that, however problematic it may be to pack into a complete individual concept yet another set of properties not derivable from it,12 however dim or confused is the individual’s grasping of these underlying qualities, and however obviously “soft” their inclining without necessitating effects are, they must be taken into account in Leibniz’s theory of self and action, for

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Leibniz considers them essential for judging an action as worthy of praise or of condemnation. Naaman (Chapter 19) and Gaudemar (Chapter 21), by choosing the “place of the other” principle as the pivot of their analyses, focus on the interactive, social nature of the Leibnizian moral self. Both stress the altruistic, feeling dimension (namely, love, empathy, charity) that this principle brings to the fore. Naaman points out, in particular, the close connection between the human and the divine “other” in this respect: loving God, she argues, has a necessary formative role in loving “thy neighbor”, i.e., in the constitution of ethical norms. Gaudemar, in a rather ambitious paper, undertakes to reconstruct Leibniz’s entire ethics from the viewpoint of its natural and rational underpinnings. Addressing the soft–hard rationality issue, she argues that, in the light of Leibniz’s “perfectionist thesis”, calculative rationality can become an efficient tool of moral rationality, provided it is viewed from the outset as nothing but a tool that ought to be “moralized” for that purpose. This intriguing thesis, which stresses the unity of reason and the gapless continuity – hence the possibility of cooperation – between its modalities, does not rule out, however, the recognition of important differences between their natures and modi operandi. Furthermore, the “adaptation of the tool” to a new set of tasks, in which the “moralizing” operation consists, is not unidirectional, for it brings about, as Gaudemar herself acknowledges, modifications of both, morality and rationality. In Part VI, still along the practical axis, rationality is envisaged from the point of view of rational decision making and problem solving. The object of study here is thus the variety of specific models, methods, techniques, procedures, strategies, etc. into which rationality unfolds in order to be able to perform its more down to earth, universally recognized task of providing a rational, reliable base for our choices in any domain. Ideally, these tools ought to be applicable independently of the field of application – which is what ensures their validity. This is supposed to be the case for the two Leibnizian decision-making models (the balance and the vectorial models) analyzed by Roinila (Chapter 22); for the “surjective deduction” and combinatorial comparison of properties – which Leibniz employs in his “demonstrative” tract, analyzed by Griard (Chapter 23), on the best candidate in the forthcoming election for King of Poland, a method he hails as “a type of mathematics with respect to the evaluation of reasons” (A I 13 551); and for Nef’s (Chapter 24) distinction between “declarative” and “procedural” rules, appeal to which can of course be made in the analysis of debates other than the Leibniz-Pellisson debate on heresy. To this list of ideally content-independent rational methods, at least part of Leibniz’s “dialectic” should be added, of course (Chapter 2). In practice, however, not all the above mentioned and similar rational tools are entirely content-independent, for their application may depend on domain-specific assumptions. Mogens (Chapter 25), for example, discusses the principles used by Leibniz in theological controversies. He singles out three rules, all of which deserve the Christian names he gives them, “Pauline”, “Augustinian”, and “Jesuit”. Consequently, they cannot be taken as rules of a universal method of conducting controversies, because they assume that the opponents, engaged in an intra-Christianity controversy, share (or should share) certain

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Christian commitments. This cannot be assumed, however, when the disputants belong to deeply heterogeneous backgrounds, e.g., different cultures or religions – a fact that prevents the universalization of the rules as expressions of “rationality” (or, in the case at hand, of “morality”) as such.13 Nevertheless, on closer examination, one can observe differences in the ease with which each of Laerke’s rules generalize – which suggests that some are perhaps closer to “universal” standards of rationality or morality than others. This context- and content-dependent “gradation” is worth exploring further, for it can contribute to the eventual de-dichotomization of the hard–soft debate. With Parts VII and VIII we return to the more abstract spheres of theology and metaphysics – although, in some of the chapters, not entirely detached from their political and historical contexts. Smith (Chapter 26) in fact offers a historicalethnographical panorama of Early Modern Europe’s attitudes vis-`a-vis nonEuropean peoples, in view of the attempts to somehow accommodate their very existence with the Holy Scripture’s story. This serves as a useful background for situating Leibniz’s position on the many issues the encounter with the pagans, of the West and of the East, raised. The theological debate (on which this chapter focuses) about whether they – “savages” as well “civilized” pagans – could have a true religion not derived from Christian revelation was conducted with an eye on its political implications, especially regarding the missionary enterprise. But it also led, in Leibniz’s case, to the development of a pluralistic view, which granted both raw nature and a different but sophisticated civilization a well deserved share in religiosity and morality, as well as in rationality and wisdom. Politics is certainly not absent of Leibniz’s irenic endeavors, and the issue of the Bible’s irrefutable authority – an essential Protestant contention – is not free from it. As shown by Rudolph (Chapter 28), Leibniz’s ecumenical efforts, which require mutual concessions from Protestants and Catholics, lead him even to be ready to mitigate considerably Bible’s authority, in spite of his faithfulness to Lutheranism. He does not go as far as subordinating that authority to reason – an unneeded step for someone who believed in the harmony between revelation and reason; but he does place above it the criterion that excludes whatever is contrary to reason, even as far as biblical exegesis is concerned. Scarafile (Chapter 27) tackles the theodicy in its usually neglected phenomenological aspect: The incommensurability of the suffering caused by evil. What kind of rationality, he asks, can face this “scandal”? He comes up with an interesting candidate, which he calls “pathic reason”. I don’t dare to summarize this rather dense notion, except for pointing out threads that connect it to Chapters 18, 20, and 25: Pathic reason has a constitutive individuating role, but is not conceptual in nature; it is based on the living experience of feeling; and it shares with the mysteries of faith the fact that its language contains a non-eliminable ambiguity, being thus fit for expressing what is, ultimately, unintelligible – namely, evil. Part VII concludes with a chapter that should perhaps open it, for it deals with Creation. Cook (Chapter 29) launches a defense of Leibniz’s philosophical-theological view of Creation, against those critics who either dismiss it as nonsense or as a mere allegiance to Christian orthodoxy. He analyzes the range of arguments used by Leibniz in this connection, which cover a variety of strategies, from hard to soft reasoning.

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As we move finally into metaphysics, the reader is familiar to its close connection with Leibniz’s rationalism. But the chapters of Part VIII dwell on not so familiar details of this connection and reveal unsuspected aspects thereof. Poser (Chapter 31) elaborates upon the peculiar nature of Leibniz’s innatism, which he views as the epistemological and metaphysical cornerstone of Leibniz’s rationalism. Poser stresses in particular the role of the neglected notion of “instinct” therein. As applied to morality, he claims, Leibniz’s use of this notion yields a dispositional theory of “moral instincts” which we naturally obey; but these instincts can be clarified by means of the process of reflection, yielding “moral laws”, which the vir bonus understands not as instinctive but as having the more elevated status of conditioned moral necessities. Piro (Chapter 30) undertakes to reconstruct the evolution of Leibniz’s Principle of Sufficient Reason. Tracing the influence of Scholastic and Early Modern sources such as Hobbes, he identifies in very early Leibnizian writings an initial version which defines “sufficient reason” as the sum of all necessary conditions or “requisites” involved in the existence of something. Between this formula and the mature, better known ones, several intermediate versions can be found – as pointed out by Piro – and the evolution he discerns and analyzes is extremely interesting, because it is directly connected to (if not responsible for) the evolution of his logic, theory of truth, and metaphysics (especially the doctrines of universal expression, of individual identity, and of freedom). It is also linked to many of his polemics – in particular those in which he defends himself against the charges of necessitarian Spinozism. “This last point – says Piro – is probably the most important in comprehending the overall sense of the evolution which intervenes in Leibniz’s rationalist metaphysics and the peculiar equilibrium between “strong” and “soft” rationalism which occurs there”. Di Bella (Chapter 32), dealing with similar issues, reaches a different conclusion. Like Piro, he rejects the view, often expressed by commentators, that Leibniz confused “cause” and “reason”. Instead, he shows that Leibniz was well aware not only of the difference between them, but also took part in the reshaping of the Aristotelian theory of causes. From the two remaining models of causality, the “eidetic” and the “efficient” or “productive”, he restates the primacy of the former, without depriving the latter from a measure of irreducibility and variation. This choice yields “a surplus of reason with respect to cause”, as Di Bella puts it. Thanks to it, causes can be viewed as a subset of reasons and conceptual dependence can explain causal dependence. As a result, Di Bella contends, the unity of reason can be preserved, leaving plurality to be accounted for by the multiplicity of causes. Acknowledgments The vast majority of the chapters of this book are revised versions of papers presented at the 20th International Workshop on the History and Philosophy of Science, held in Tel Aviv and Jerusalem, from 30 May to 2 June 2005. I wish to thank the generous support of the Van Leer Jerusalem Institute, of the Cohn Institute for the History of Science and Ideas (Tel Aviv University) and of the S.H. Bergman Center for Philosophical Studies (The Hebrew University of Jerusalem). My thanks go also to my colleagues, Israeli and visiting Leibniz scholars, who collaborated in the organization of the Workshop. Special thanks are due to Rivka Feldhay, then academically in charge of the series of Workshops: Rivka accepted with enthusiasm the idea of Leibniz’s rationalism as deserving a special Workshop and gave it unrestricted support. And, last

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but not least, the participants as well as myself are profoundly grateful to Shulamit Laron, from the Van Leer Jerusalem Institute, for her efficacy and sympathy before, throughout, and after this memorable Leibnizian encounter of minds.

Notes 1. See, e.g., Haakonssen (2006), Himmelfarb (2004), Israel (2001, 2006), McMahon (2001). 2. More precisely, the Edition is divided in eight series (I. General, Political and Historical Correspondence; II. Philosophical Correspondence; III. Mathematical, Natural Science and Technical Correspondence; IV. Political Writings; V. Linguistic and Historical Writings; VI Philosophical Writings; VII Mathematical Writings; VIII. Writings in Natural Sciences, Medicine and Technology). Hanover is responsible for series I, III and VII, M¨unster for series II and VI, Potsdam for series IV (which includes also theological writings), Berlin for series VIII, and series V has not yet been assigned. So far, about half of the planned roughly 100 volumes (averaging 870 pages per volume) of the Academy Edition have been published, and the expectation is that the publication will be completed by 2050. 3. For the dialectical nature of the cooperative construction of knowledge, see Dascal (2006). 4. For a characterization of “hard” and “soft” rationalism, see Dascal (Chapter 2). 5. Here is a brief description of the moves in this controversy. Dascal (2003) is an extended critical review of the four volumes of A VI 4, which contains mainly Leibniz’s philosophical writings of the 1680s – arguably the decade in which his thought matured and took its definitive shape. Schepers, chief editor of this impressive contribution to Leibniz scholarship, added to it also a long interpretive Introduction, which was the main target of Dascal’s criticism. Schepers’ reply (2004) followed suit, along with Dascal’s response (2004a). The present chapter by Schepers, delivered as the opening lecture at the “Leibniz: What Kind of Rationalist?” conference in Tel Aviv (2005) was the next installment in their controversy, the spirit of which can be traced also in Schepers (2006), a lecture at the concluding plenary session of the VIII Internationaler Leibniz-Kongress in Hanover, as well as in Dascal’s lecture on the same occasion (which was not ready for publication in the Congress Proceedings and will be published elsewhere). Earlier presentations of the “soft rationalist” face of Leibniz include Dascal (2005; Spanish version published in 1996) and Dascal (2001; lecture at the concluding plenary session of the VII Internationaler Leibniz-Kongress in Berlin). 6. Lucy Prenant (1946) argues that the thought of both Leibniz and Descartes comprises “hard” as well as “soft” elements (in my terminology). They differ in that, whereas Descartes’s starting point is softer and as it develops incorporates harder components, Leibniz’s development runs in the opposite direction, from a harder beginning to a softer conception of rationality that includes reasonableness. 7. A notion of “formal experience” is not alien to Leibniz, certainly not in mathematics and presumably also not in law. Something of this sort is the experience – mentioned above and analyzed in Chapter 7 – of a symbolism whose combinatorial mechanism generates new formulas regardless of whether they can be assigned a meaning. Furthermore, when Leibniz elaborates upon the merits of his project of a “numerical characteristic” (see, e.g., DA 119–127, 275–283, etc.), he usually stresses its foolproof character by referring to tests such as the casting out of nines, which he describes as an “easy experience” and contrasts with experiences in physics, which “are difficult and expensive” and with those in metaphysics, which are “impossible” (A VI 4 4). 8. Gensini (1991) stresses the role of this notion, especially in accounting for natural languages as non-arbitrary phenomena. 9. This interpretation is convincingly supported by the fact, pointed out by Boucher, that the De Arte Combinatoria, roughly contemporary to the legal texts under consideration, contains, as examples of “problems” to which it can be applied, detailed analyses of legal cases.

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10. Texts emphasizing this soft strand in his legal rationalism were written by Leibniz throughout his life. For some examples, see DA, Chapters 5, 9, 10, 11 and 36, among others. In section 3.9 of his contribution to the present volume, Schepers belittles the significance of this soft juridical model for Leibniz, and interprets his comment to the effect that nobody has so far invented the scales with which to weigh reasons as an ironical remark. Given the co-texts where the remark is made, this seems to me to be a remarkable misinterpretation. With his remark, Leibniz is simply pointing out that the fact – which he admits – that the jurists themselves have not elaborated “this method of judging and weighing opposed reasons, as if in a balance” does not “render the new investigation here proposed superfluous”, but quite on the contrary, should stimulate us to perform it (cf. DA 39). Dascal (Chapter 2, section 6.6) refers to the significance of a Leibniz’s writing which contains this remark, in the context of the hard-soft rationality divide. 11. For a discussion of the Leibniz/Clarke polemics to which this passage belongs, see Dascal (2005: 36–39). 12. For example, a claim of this sort runs, prima facie, against emphatic assertions such as: “Whenever we find some quality in a subject, we ought to believe that if we understood the nature of both the subject and the quality we would conceive how the quality could arise from it” (Et toutes les fois qu’on trouve quelque qualit´e dans un sujet, on doit croire que si on entendoit la nature de ce sujet et de cette qualit´e, on concevroit comment cette qualit´e en peut resulter; NE, Preface; GP 5 59; A 4 6 66; R&B 66). 13. For the distinction between intra- and inter-religious controversies and the use of rational argumentation therein, see Dascal (2004b). See also Dascal (Chapter 2), for a more general discussion of Leibnizian “dialectic”.

References Belaval, Y. 1960. Leibniz critique de Descartes. Paris: Gallimard. Bredekamp, H. 2004. Die Fenster der monade: Gottfried Willhelm Leibniz’ theater der Natur und Kunst. Berlin: Akademie Verlag. Dascal, M. 1996. La balanza de la raz´on. In O. Nudler (ed.), La racionalidad: su poder y sus l´ımites. Buenos Aires: Paid´os, pp. 363–381. Dascal, M. 2001. Nihil sine ratione → Blandior ratio. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress). Berlin: Leibniz Gesellschaft, pp. 276–280. Dascal, M. 2003. Ex pluribus unum? Patterns in 522+ texts of Leibniz’s S¨amtliche Schriften und Briefe VI 4. The Leibniz Review 13: 105–154. Dascal, M. 2004a. Alter et etiam: Rejoinder to Schepers. The Leibniz Review 14: 137–151. Dascal, M. 2004b. On the uses of argumentative reason in religious polemics. In T.L. Hettema and A. Van der Kooij (eds.), Religious Polemics in Context. Assen: Royan Van Gorcum, pp. 3–20. Dascal, M. 2005. The balance of reason. In D. Vanderveken (ed.), Language, Thought and Action. Dordrecht: Springer, pp. 27–47 [Revised, translated version of Dascal 1996]. Dascal, M. 2006. Die Dialektik in der kollektiven Konstruktion wissenschaftlichen Wissens. In W-A. Liebert and M-D. Weitze (eds.), Kontroversen als Schl¨ussel zur Wissenschaft? Bielefeld: Transcript Verlag, pp. 19–38. Gensini, S. 1991. Il naturale e il simbolico: saggio su Leibniz. Roma: Bulzoni. Haakonssen, K. (ed.). 2006. The Cambridge History of Eighteenth-Century Philosophy. Cambridge: Cambridge University Press. Himmelfarb, G. 2004. The Roads to Modernity: The British, French, and American Enlightenments. New York: Alfred A. Knopf. Israel, J. 2001. Radical Enlightenment: Philosophy and the Making of Modernity 1650–1750. Oxford: Oxford University Press. Israel, J. 2006. Enlightenment Contested: Philosophy, Modernity, and the Emancipation of Man 1670–1752. Oxford: Oxford University Press.

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McMahon, D.M. 2001. Enemies of the Enlightenment: The French Counter-Enlightenment and the Making of Modernity. New York: Oxford University Press. Prenant, L. 1946. Le ‘raisonnable’ chez Leibniz: la revanche du jugement sur la forme. Revue ´ Philosophique de la France et de l’Etranger 137: 486–512. Riley, P. 1996. Leibniz’ Universal Jurisprudence. Cambridge, MA: Harvard University Press. Schepers, H. 2004. Non alter, sed etiam Leibnitius: Reply to Dascal’s Review Ex pluribus unum? The Leibniz Review 14: 117–135. Schepers, H. 2006. Perzeption und Harmonie. Das Viele im Einen, die Welt in der Monade. In H. Breger, J. Herbst, and S. Erdner (eds.), Einheit in der Vielheit, Nachtragsband (VIII. Internationaler Leibniz-Kongress). Hanover: Leibniz Gesellschaft, pp. 200–216.

Part I

Reinterpreting Leibniz’s Rationalism?

Chapter 1

Leibniz’s Rationalism: A Plea Against Equating Soft and Strong Rationality Heinrich Schepers

1 Introduction I am grateful to Marcelo Dascal for the opportunity to formulate my arguments against some of his theses and so to continue the controversy, which he enjoys so much. It is completely uncontroversial that historians are at liberty to subsume phenomena that interest them under terms that they have defined themselves. Of course the acceptance of these terms by the scientific community is necessary as well. This acceptance is forthcoming if historians are able to give plausible reasons for their use of the new term, for example to demonstrate previously undetected interconnections. It is, however, problematic to create terms, which are in conflict or even in contradiction with the intentions of the author of the phenomena subsumed by them. Although it is interesting to subsume many of Leibniz’s activities under the heading ‘soft rationality’, it is nevertheless essential to keep in mind that Leibniz can only be called a rationalist because he demands a rigorous use of reason for reaching metaphysical conclusions, as well as a metaphysical foundation of physics. The only properties that should be called characteristic are those that can only be found in a single author (or in a single group), but not anywhere else. We therefore have to consider whether those activities of Leibniz which are classified under the heading ‘soft rationality’ cannot also be detected in the case of empiricists, in which case they could not be labelled ‘rationalistic’. If it is problematic to split Leibniz’s rationality into two, it is even more difficult to classify fields of activity as soft rationality, which have to be considered to belong to the proper domain of strong rationality. In a variety of papers and talks Marcelo Dascal has drawn our attention to what he calls the ‘other Leibniz’. Dascal investigated those of Leibniz’s arguments where strict argumentation is replaced by reasoning with the help of metaphors. Given that even such an eminent logician as Leibniz was not so narrow-minded to present

H. Schepers University of M¨unster, M¨unster, Germany

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his entire arguments in forma (since purus putus logicus est putus asinus), it is not difficult to come up with a variety of arguments, which present such a ‘different Leibniz’. Dascal, however, aims further than that. He intends to demonstrate that logic and metaphysics, and in particular the logic of probabilities, cannot be tackled by strong rationality on its own, but always remain dependent on what he likes to describe as weak rationality. I, on the other hand, am of the opinion that, even if we admit that many of his activities can be subsumed under the label of weak rationality, it only makes sense to speak of Leibniz’s rationalism because he was a rationalist in the strict sense. If we therefore draw this distinction at all, strict rationality has to be regarded as primary. The very fact that Dascal’s description of weak rationality is exclusively phrased in negative terms (Dascal 2004: 138f.) suggests that strict rationality, which can be positively described, should be assigned primacy. Dascal wants to inquire into the different meanings of the notion of ratio in the works of Leibniz. In doing this, however, he neglects to give due consideration to the important abstract notion of rationality, which he frequently employs. Leibniz’s ratio can mean reason as the ground for something, less frequently cause or proof, and also method, way of representation or proportion; above all, nevertheless, it means reason as power of cognition. There is an important difference to be made between metaphysical reasons and actual reasons admissible in a court of law, as well as between the perfect rationality of God or the perfectible rationality of man.

2 General Remarks Regarding the Notion of Rationality As he himself said, Leibniz studied mathematics for the sake of theology; he demanded the exercise of reason as a step on the way towards salvation; he developed his metaphysics to justify freedom, discussed the problem of evil to demonstrate divine justice, and, more generally speaking, always developed a theory with its practical application in mind. I take all of these to be immediately evident support for Leibniz’s disposition to solve problems using strict rationality. The term ‘rationalist’ can be applied to a thinker by others either objectively or pejoratively, and his rationality will be judged accordingly. Although I did not employ this term, I have always intended to describe Leibniz as a philosopher who regarded his strength in all fields to consist in ‘a radical use of reason beginning at the very roots of a problem’ (A VI 4 xlvii). Leibniz always intended to get to the bottom of things, to defuse controversies by pointing out the existence of common roots, of principles both disputing parties shared. This is not supposed to mean that the ‘predominantly logical notion of reason’ in the period of the writings published in A VI 4 is characterized by ‘analyze!, demonstrate!, formalize!, calculate!’, without due regard for the qualification ‘weigh carefully’ (Dascal 2003: 118; Dascal 2004: 138–139). As long as the scientia generalis and the characteristica universalis it is based on are not completed, the calculemus remains Leibniz’s

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guiding principle as a future programme. Up to this point all that is important is to ensure the truth of the premises by demanding and presenting arguments in forma. That logic is not able to solve any problems on its own does not mean that it is dispensable. Its aim is to draw implications from a set of principles by a set of truthpreserving rules, as well as to determine which principles lead to contradictions and must therefore be discarded. This is the sole intention of the calculemus and the demand to argue in forma whenever matters are controversial. Nobody will seriously dispute that only a strict and intersubjectively confirmable demonstration is able to eliminate the last remnants of doubt. Leibniz himself demonstrated syllogistically in his correspondence with Denis Papin (wir triebens u¨ ber den 12ten prosyllogismum) (GP 7 522) what he took a demonstration in forma to be: a method, which is always demanded in cases where persistent doubts and counterarguments prevent the settling of a debate. There are pragmatic reasons for the fact that arguments are generally not presented in forma; this is not in itself evidence for an unavoidably weak rationality. In the really important cases, only rigorous proof counts as any evidence at all. Where proof is impossible, we have to propose plausible hypotheses. Then we also need rigorous arguments for establishing their plausibility. There is no abstract ratio for Leibniz, unless we understand it as a compendium loquendi. In concrete terms, it is first of all Leibniz’s own rationality, an innate ability present in everybody, even though it has to be developed to a greater or lesser extent in individual cases. But ratio is eminently divine rationality, which, according to Leibniz, is structurally identical with ours, even though it is defined as perfect, as containing all truths, not just the eternal ones. Perfect rationality is what distinguishes God from man. Leibniz, however, is not so much concerned with the difference; he is much more concerned with establishing that human and divine reason have an identical structure. That is what makes him a rationalist. Considered abstractly, rationality is the use of reason to achieve an end. Considered in concrete terms, rationality is Leibniz’s own use of reason, which he also recommends to others. This recommendation in turn makes it general, and allows us to treat it in abstract terms. Rationality is strict if it obeys particular rules established by reason itself. It is softer if it allows itself (or is forced to) disregard these rules in particular cases. Strong rationality covers everything that can be derived by strict reasoning from a set of assumed principles, that is, all those propositions that have to be affirmed if we do not want to contradict these principles. This implies that everything that is not compatible with the principles and their implications has to be rejected. Both, affirmation and rejection can only be carried out by strong rationality. The intellectual landscape of 17th century Europe was determined on the one hand by the rise of the natural sciences, and on the other by a period of stagnation in the humanities. This stagnation also applied to the universities more generally, which were basically limited to teaching and disputing scholasticism and a variety of Aristotelianisms, apart from occasional references to Plato and Epicurus and a more general interest in humanistic pursuits. After Descartes’ methodical doubt cleared away the scholastic disputations pro et contra and established the sum cogitans as

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an unshakeable foundation, Leibniz stressed the importance of reason being aware of itself. This reason is the only one he regarded as being able to provide a way out of the intellectual difficulties of the times. Leibniz is not to be regarded as a rationalist because of his work on the development and application of logic, but rather because of his strong conviction in the power of logic and in its indispensability for solving problems. Nobody but a strict rationalist could comfortably propose a bet that no two exactly identical leaves can ever be found. The weak rationalist would perhaps doubt that, after searching through an infinitely big pile of leaves, we might after all hit upon two exactly identical ones, presupposing we have an infinite amount of time at our disposal for conducting the search. The confidence of the strict rationalist depends on the universal truth of the principle of the indiscernability of identicals, together with the principle of individuation which claims that each individual is determined by the sum of its – and only its – properties. Only a strict rationalist can put himself – and even God – in a situation where a decision between maxima and minima has to be made, since for him there is no third alternative. This is true even if he has to admit that only God can know what really is the best, whereas man can only choose what appears to him to be the best and to avoid the worst. Even though ‘rationalism’ is a common collective term, which subsumes approaches that are as different as metaphysical and theological rationalism, we should nevertheless inquire into the reasons of such a subsumption. We should further take into account that it is possible to be called a rationalist in one discipline but not in others.

2.1 Rationality and the Establishment of Principles To restrict strong rationality to that of the provable means to misjudge the meaning of establishing principles which provide the basis for further deductions. It is of course possible to come up with such principles on the basis of experience and accepted theories. But this does not mean that they can be acquired by induction. These principles have to prove themselves by the higher plausibility of their implications. For a rationalist like Leibniz who regards these principles as a habitus of reason, there is no doubt about this at all. Leibniz is a rationalist not because he uses deductions, but because he establishes principles and definitions based on trust in the power of reason and the rationality of the world and its creation, and because he will not accept anything which does not follow from these principles, yet accommodates everything which does so follow. Here are a few examples:

r r

He establishes action as the characteristic of substances, which has the final consequence that only monads exist. He maintains that substances cannot act on one another, which implies that a monad’s action has to be regarded as an emanation remaining inside the monad, even though it encompasses the world and its past and future history.

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r r

r

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He regards the possible as not just what has been, or will be in the future, but as the merely possible besides the contingent, which is either actually present, or past, or future. Based on this, he develops his theory of possible worlds, which is then used to argue for human freedom and divine justice. He assumes that all our concepts can be analyzed into basic, undefined concepts, as long as they are not primitives themselves. In this way, he can define truth as containment of the predicate in the subject, determine the distinction between necessary and contingent truths, and finally define an individual in terms of its complete concept, thereby explaining its own constitution as the free acquisition of its attributes. An individual thereby turns into a monad mirroring the entire world from its unique perspective. He is convinced that he can establish his characteristica as an alphabetum cogitationum humanarum and as a lingua rationis which ‘unifies and abbreviates all the works of mind in a marvellous manner’ (A V 3 456). In a scientia generalis based on this the entirety of knowledge, as long as it can be expressed in universal propositions (since all scientific knowledge for Leibniz as for Aristotle is knowledge of the universal) can be phrased, analytically assessed and synthetically combined.

Only a strong rationalist can postulate principles of this kind and develop them cum rigore in the way Leibniz did! Of course, this list could be extended. I am tempted to assume that even the astrologically inspired notion of incliner sans necessiter is nothing but a means for the exoteric exposition of the principle of the best. The sequence of reasons that is demanded by the nihil sine ratione cannot be infinite. The final reason consists in the knowledge that acting in a specific way is acting in the best way, at least for God, who knows what is best. For all other rational substances, it consists in acting according to what appears to them as the best. Establishing such a principle, which cannot be obtained inductively, is clearly evidence of strict rationality. This principle gives reason, which knows (even though it is deficient when compared with divine reason), priority over the will, which acts, thereby excluding the possibility of a mere random choice by the reversal of the maxim stat pro ratione voluntas. It is in general not possible to deduce principles. Principles can be made plausible, however, for example – by demonstrating the deficiency of the opposite; – by demanding a reason for the principle, and by demanding an ultimate reason as a starting-point for the chain of reasons; – in terms of incomprehensibility, as for example in the case of the influence of one substance on another one; – by the maxim of harmony, which allows us to comprehend the many in the one, as in the case of the multiplicity of sounds in pieces of music; and finally – by the pseudo-Hippocratic maxim of universal sympathy connecting everything with everything else, despite the direct influence, which has to be rejected, of one substance on another one.

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Even the analysability of concepts and the implied analytic nature of thinking, concerning both human and divine calculating reason, is one of the principles or presumptions, if you like, which is valid only as long as it is replaced by a better alternative. A rationalist is characterised by only accepting what can be derived from such principles by formal means. The rationalist differs from the dogmatist by acknowledging that the principles (apart from the law of contradiction and the law of sufficient reason) are hypotheses, hypotheses the rationalist believes are true, but hypotheses nevertheless. These principles established by reason can be supported by our own and by other peoples’ experiences, but they cannot be undermined by them. They do not require these as a support, nor are they based on it. This is what Leibniz means when he defends the innateness of the principles against Locke and when he describes them, to use his own terminology, as habitual, since they are part of the nature of reason. Rationalism is the opposite of empiricism. Both together are answers to scepticism. Concerning those questions where we cannot base our answers on experience in any substantial manner, i.e., in the case of the questions of metaphysics, Leibniz believes that the only way forward is to follow the principles of reason strictly. The laws of contradiction and sufficient reason remain the touchstone for the implications of the assumed theses. A strong rationalist will necessarily have to define and make an instrument of God as the perfection of that which the philosopher conceives under reason, power and goodness. Furthermore he assumes an isomorphism between thinking and being, as well as between thinking and creating. Calculating reason and the calculating God require one another, but calculating reason is not dependent on soft rationality in the way in which the actual and pragmatic use of reason doubtlessly is. Human rationality, on the other hand, has to be developed, and the means for this development should be the newly conceived logic. This requires on the one hand the development of new calculi and the further investigation of logical relations, and on the other hand the systematization of the totality of human knowledge by the yet to be developed characteristica universalis on which the scientia generalis will be based.

3 Consideration of Some Particular Arguments In a single overwhelming attempt Dascal tried to argue in Berlin (Dascal 2001) that Leibniz was forced to rely on soft rationality in virtually any discipline. Apart from the disciplines of logic, mathematics, and metaphysics I am tempted to agree with this. But I would now like to consider some of his arguments given there more specifically. Leibniz’s Egyptian proposal (A IV 1 N. 10–18) (which in fact never reached Louis XIV nor was at any time deposited in French archives) is not developed more geometrico. Moreover, Leibniz wrote a brilliant literary fabula politica in support

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of his proposal, imagining and describing the success of the enterprise on the Nile a hundred years hence (A IV 1 N. 11). This is certainly evidence for the claim that Leibniz did not want to deduce absolutely everything based on strict reason alone. The fact that his irenic activities present Leibniz to us not as a stubborn logician but rather as a versatile diplomat should not let us forget that his grand visionary aim consisted in employing his scientia generalis (no doubt an instrument of strict rationality) to settle both political as well as religious disputes and activities. The Systema theologicum was really meant to establish a solid platform for further approximation of the confessions, but Leibniz never showed it to anyone. Already during his time in Mainz the young Leibniz was working on the fact that the mysteries of faith cannot be proved by strong rationality, but that it is nevertheless possible and necessary to use strong means to refute arguments against their credibility. Moreover, this is not a switch from demonstrability to defensibility and thereby to soft rationality (Dascal 2001: 277). By this he kept pursuing a strategy which he upheld up to the time of the Th´eodic´ee, a strategy which, unlike scholastic disputations, can be put into practice with strong rationality.

3.1 Exoteric vs. Esoteric and the Use of Metaphors As far as the distinction exoteric vs. esoteric is philosophically important it was already drawn by Leibniz in the preface to his edition of Nizolius in 1670, where he contrasts the exoteric manner of philosophizing with the esoteric or, as he prefers to call it, acroamatic manner. When working in an exoteric manner many ideas can be presented without proof, being supported only by similes and topical arguments or explained in terms of examples. The acroamatic manner, on the other hand, has to proceed rigorosissime and exactissime. This implies that nothing is to be admitted apart from definitions, divisions, and proofs, in order to rule out all unclarities altogether. The use of allusions, similes, metaphors, examples, subtleties and anecdotes is allowed, as long as an excess of obscurity and confusion is avoided, in order to revitalize the tired spirits of the reader by including some pieces of intellectual amusement (A VI 2 426f.). The distinction is important for our purposes because it allows us to distinguish Leibniz’s strict esoteric metaphysics from its exoteric expositions, where in fact metaphors are liberally employed. This metaphoric way of speaking is now taken by Dascal as evidence for Leibniz’s dependence as a metaphysician on soft rationality. When looking at the writings where Leibniz operates cum rigore, however, it is completely clear that the metaphors are only there to present the very abstract implications in a more accessible manner. We encounter a dependence on weak rationality if strictly defined concepts, which can be analyzed in turn and which have to be used in proofs, are replaced by metaphors. In order to demonstrate this, Dascal enumerates a set of metaphors, some of which are indeed frequently employed by Leibniz, others, which have been so well devised that it appears as if we encounter them again and again. But if we can show that each of these metaphors corresponds to some precisely defined concept

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and that it does not have any conceptual content over and above the concept which it presents in a more accessible manner, it becomes clear that these instruments of weak rationality only have a rather limited role. The metaphors are not more important than the concepts they elucidate, in fact they are not even equally important. Leibniz’s attempts to explain his spectacularly new metaphysics not just to newcomers to philosophy, but to seasoned philosophers of all persuasions (primarily to Cartesians and Scholastics) are also to be regarded as exoteric. He more or less explains matters to them using their own terminology (however, not without having made these terms successively more precise in the workshop of his rationality), mainly to make matters as accessible as possible. But this does not turn his exoteric attempts into popular philosophy. We would not even want to apply this pejorative term (if it is indeed one) to his bestselling Th´eodic´ee, which he himself regarded as a popular work. Nevertheless, we have to note that the so-called Monadology, despite its richness of content, and even more so the piece written for Prince Eugenius have to be regarded as exoteric treatments, and not as the legacy of his thoughts, or of a big metaphysical work which remained unwritten in its entirety.

3.2 Reasons for Leibniz’s Esoteric Works Leibniz frequently voices the concern that his revolutionary rational metaphysics would fail to be understood and that it might attract the Inquisition’s attention. This might have endangered the prospects for his grand project of a scientia generalis. He attributed these potential problems to a lack of mathematical sophistication, of tinctura matheseos (A VI 4 1650) in most of his contemporaries, as well as to their unwillingness to follow through difficult and abstract arguments. Nowadays, some people mistake Leibniz’s popular exoteric treatment for his real intention and disregard the less straightforward material. Thus, we encounter frequent references to the fact that monads have no windows, but only infrequently to the notion of emanation, which that fact is supposed to represent. In other places (GP 3 193f.) Leibniz distinguishes the certitudo metaphysica from the certitudo moralis amongst the theological truths. Whilst metaphysical certainty is supposed to be based on definitions, axioms, and theorems from ‘true philosophy and natural theology’, moral certainty is taken to be based on history, facts, and the interpretation of texts. In order to access both kinds of certainty, Leibniz argues, we have to refer back to the veritable philosophie. That is to say, we here encounter another instance of the primary role of strict rationality.

3.3 Metaphysics Without Metaphors We can disprove the argument that Leibniz could not have developed his metaphysics without metaphors by showing that the theory of monads can be constructed in its entirety cum rigore metaphysico without using a single metaphor. This could be done as follows.

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Consider monads. They are possible subjects (possibilia) made existent. A possible subject (not object! because of subjects being conceived as essentially acting ones, whereas objects are not able to act) is one of the infinitely many possibilities in the mind of God, who can conceive of the world with all its possible histories without leaving out a single possibility. Possible subjects that are compatible form a possible world in which they accomplish a certain degree of reality. Every possible subject belongs to exactly one of these worlds. It is made existent in and together with the world that accomplishes the highest degree of reality, which is the best of all possible worlds. This is a rough version of an exposition cum rigore metaphysico. It does not even use the notion of a point de vue that Leibniz employs frequently in order to give us a first idea of the multitude in the mind of God. The principle of identity of indiscernibles and the completeness of the conceivable in God’s mind entail that every change in a possible subject between one moment and the next will necessarily cause changes in all other possible subjects. Every possible subject is connected with every other one; two identical possible subjects would coincide. In order to describe this fact we do not have to use the metaphorical talk of mirrors at all. The possible subjects are to be taken as individuals, that is, as single, acting essences (substances) which aspire to existence by freely constituting themselves. Leibniz considers this process of self-constitution as an instantaneous perceiving, together with a successive move from perception to perception by the appetitus. In harmony with the maxim that one substance cannot influence another one, as there would be no rational explanation of such an influence, all the activities of possible subjects, including monads, stay restricted within them. Leibniz conceives of this in terms of the Plotinian emanatio, which claims by definition that the effect remains in the cause, and explains this difficult idea by using the handy metaphor of monads being without windows. It is obvious that the basis of abstract concepts, not just of the metaphysical ones, is (or originally has been) a set of metaphors, which still point to a great extent towards their own connotation, but cannot replace them. Leibniz uses metaphors whenever he addresses a larger audience, when he appeals to potential sponsors or collaborators, or when he tries to direct another thinker, such as Locke, towards his ideas. Metaphors are also used when difficult concepts have to be made accessible. Leibniz does not, however, employ metaphors when developing his metaphysics cum rigore. That his metaphors were part of the exposition of his metaphysics, but not of its development, should be beyond dispute. They are only used when abstract consequences of the principles postulated have to be made less difficult to be understood. Summing up, we realize that Leibniz developed his metaphysics cum rigore metaphysico in an esoteric way. He only used metaphors for explaining his complex thoughts. In the end many readers of his works used these to replace the original concepts. Even when Leibniz speaks of blandior tractandi ratio (A VI 4 342) he is concerned with exposition, he tries to explain the results achieved by strict mathematical reasoning in a more accessible way. ‘To explain’ here means neither ‘to understand’ nor ‘to prove’, but rather presupposes both of them.

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3.4 Inclination Understood in a Different Way The statement inclinans, non necessitans is primarily directed against Spinoza’s determinism and is only later used as a criticism of indifferentism. Leibniz mainly uses it as a means for the exoteric explanation of the principle of the best. For if the best was given as a binding rule for actions there would be no freedom allowing us to act against it. From a theological perspective this would mean that there is no sin, or that God himself has to be regarded as the creator of sin. If, however, the best is what appears to be best to the agent then he is inclined to act in such a way as to bring it about without being forced to do so. This is another case where Leibniz does not take refuge in a weaker type of reason. He rather uses the above sentence to explain the actions of substances. He already conceived of their actions as free and not threatened by the dilemma of indifferentism by conceiving of them as possible subjects ante creationem. We therefore have to regard it as a fundamental assumption for the interpretation of the self-constitution of individuals. For Leibniz, this is a doctrine (A VI 4 1460). The fact that God’s decision to make this world actual is a free decision, and thereby due to an inclinatio, not a necessitatio, does not deny that he is guided by the principle of the best. His rational demand that this world, compared to all other worlds, turned out to be the best was a sufficient but not a necessary reason for its creation. Inclinare does not mean to be completely at liberty to do something different from what one is inclined to do. It rather means to know which of two options is preferable. Had Buridan’s ass acted according to an inclinatio he need not have starved. It is possible that human beings decide against the best, due to a lack of knowledge. This is not possible for an omniscient God. Leibniz claims that God also made his creatures in such a way that they would never act without following the rationes praevalentes seu inclinantes (A VI 4 1651; GR 305). It is only due to the fact that possible beings have acted differently from the way proper knowledge of the best would have demanded that there are incompatible possible subjects, and therefore they belong to other possible worlds. This fact, however, is not evidence for a weaker form of rationality, but is caused directly by the imperfection of created beings, which distinguishes them from their perfect maker. Leibniz distinguishes necessitating and inclining reasons (A VI 4 1650). This means that free will has the ability to decide to choose what reason has decreed to be the best, or to decide not to choose it. This applies to God’s act of creation as well as to the actions of possible subjects, whether they are merely possible or actualized ones. This does not imply that we have to accept a weak form of rationality. Leibniz asserts that inclining reasons do not conflict with the existence of freedom or contingent facts (GP 2 228; GP 7 110). This sounds very different from Dascal, who claims that they serve as a reason for contingent facts (Dascal 2001: 278). To derive contingent facts and freedom from incliner sans necessiter means to regard the creation of the world as the product of a mere divine whim. Leibniz explains his inclining reasons as rationes convenientiae seu optimi (GP 5 550) and reminds us that our insight is only based on an exigua pars seriei rerum, which is, however, sufficient until we viatores mundi move from faith in and love

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for God to the state of visio, when our souls are raised ad sublimiorem perfectionis gradum. This is the metaphysical and religious dimension of Leibniz’s thought.

3.5 Inclination and the Scales of Reason Only by a clever interpretation and compilation of Leibniz’s metaphors is it possible to compare inclination with a set of scales and the set of reasons with the weight causing one side to descend (Dascal 2003: 138–140). Apart from this, however, the textual evidence for this comparison is rather thin. To be inclined but not forced means that one could equally do the opposite of what one is in fact doing (GP 2 359; GP 7 109). What is at issue here is not the degree of inclination, but its direction. Apart from the metaphor connecting them there is nothing which the trutina rationis, the scales of reason, and the inclinatio mentis, the natural inclination of the mind have in common. One is a means for finding truth, the other a means for the metaphysical foundation of free action. Appealing to the trutina rationis also gives us no evidence for soft rationality. As Leibniz explained in great detail already in his youth (A VI 1 N.22) it employs the ‘true logic’ (§ 61), initially identified by him with syllogistics (§ 65), even though he made clear already then (in 1671) that the true logic had hitherto been neither described nor applied. It is not possible to disregard the decision made by the inclining part of the scales. The scales are therefore the ideal instrument of strong rationality. If we weigh possibilities successfully there is no further need for mere estimation. The heaviness of the weights corresponds to the truth (not to the probability) of those propositions which Leibniz was already hoping to be established in a public liber definitionum during his time in Mainz, which corresponds to his later project of a ‘demonstrative encyclopaedia’, another name for scientia generalis.

3.6 The Place of the Contingent in the Leibnizian Square of Modalities We can hardly regard highly enough the rational achievement of the young Leibniz, when he set out (against the weighty tradition ranging from Diodorus via Wicleff up to Descartes, Hobbes, and Spinoza) to define the notion of the possible (A VI 1 465–466; A VI 2 528). He managed to distinguish the possible from the contingent by taking the latter to be what is, was or will be actual, and therefore not just what happens to be. Contingency is hypothetical necessity. It is hypothetical because it was only brought into existence by God’s decision, as opposed to all other possible subjects, which remain merely possible, because they lack the essential property of being brought about by a divine act of actualization. Necessity and impossibility were already precisely fixed concepts since the time of Aristotle, possibility and contingence, on the other hand, remained ambiguous. It was only Leibniz’s new definition of the contingent, which superseded Diodorus’ concept of possibility, which Leibniz regarded as the origin of Spinoza’s determinism. Leibniz’s new definition

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considered the contingent to be that which could have been different, but is the way it is due to specific conditions, and the possible in a seemingly paradoxical way as that which is not but could have been, since it is free of contradictions. Even though contingent truths can only be checked in infinitely many steps, this does not mean that they are the object of weak rationality. The verification of contingent truths is not something Leibniz considered to be the task of philosophy, as Dascal seems to think (Dascal 2003: 140). By drawing an explicit parallel with mathematics, he found a way of making the distinction between the necessary and the contingent explicit. Leibniz’s achievement consists in the structural identification of truths of fact and truths of reason, which determines the truth of either in terms of the containment of the predicate (or rather of all predicates) in the subject by finitely many or, respectively, infinitely many steps. Furthermore his rational achievement consists in the creation of the concept of the individual, the notio completa substantiae singularis, a concept which nobody before or after Leibniz was able to think of and to define with the same amount of rigour and comprehensiveness. Contingence is defined by its conditional actuality, which depends ultimately on a divine decision, not by an infinitely long analysis or the impossibility of providing proofs for the reasons in turn. Furthermore, infinite analysis does not just remain a metaphor. For Leibniz, it is an analogy. The assumed containment of the predicate in the subject is the principium infallibilitatis in omne veritatum genere (A VI 4 1654). This principle, which is presupposed by the notion of an infinite analysis is, as Leibniz puts it ‘wonderfully illustrated and illuminated’ by the analogy with mathematical proportions (A VI 4 1657; see also A VI 4 N. 327). All this analogy is supposed to do is to make its explanation more accessible.

3.7 All Scientific Propositions Are Hypothetical It is a cogent implication from Leibniz’s rational perspective to realize the hypothetical nature of all sciences (which nowadays even applies to mathematics, given the conflicting accounts of its foundations). This realization goes back to De Conditionibus, which he composed during his student days. Even his metaphysics is not excluded from this. Leibniz proposed his hypothesis of concomitance or pre-established harmony as a more plausible hypothesis than those of the monist Spinoza or the occasionalist Malebranche, or indeed Suarez’s theory of influxus. What is implied by the hypothesis, however, is not arbitrary, but is the subject of rigorous proof, as this is the only way of supporting the hypothesis’ claim to truth. But we should not interpret Leibniz’s insight of the hypothetical nature of all human knowledge as claiming that nihil scitur absolute, since Leibniz should not be regarded as an unwilling sceptic.

3.8 The Principle of Sufficient Reason It is absurd to subsume the principle of sufficient reason and thereby the principle of the best under the notion of weak rationality (Dascal 2001: 279). The idea of

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a multiplicity of fully complete worlds in the mind of God, out of which one is chosen by the divine will according to the principle of the best is a rationalistic one par excellence. Without the strong support of a rigorous deductive framework, it would be impossible to keep it in its place. Dascal takes the distinction between radical rationality and soft rationality to be theoretically fundamental, as he considers them to correspond to the principle of the excluded contradiction and the principle of sufficient reason, respectively. In this way, he intends to include the notion of contingence within the domain of soft rationality (cf. Dascal 2004: 143f). I think that to consider the principle of sufficient reason in this way to be a general presumption of rationality means to rob Leibniz’s rationalism of its strongest support; its very foundations are thereby put in question. Dascal directs our attention to the ‘ominous cautionary phrase’ to the extent to which we can penetrate things (GR 304; Dascal 2001: 280) and considers this to be a limitation of the principle of sufficient reason, which perhaps would lead Voltaire to revise his interpretation of the principle. Leibniz, however, means that our knowledge of the principle is limited, not the principle itself. For Leibniz the principle of sufficient reason holds without any exceptions. It is a fundamental part of our mind, divinitus, i.e., placed there by God (GR 304). It also applies to God’s own actions. The reason that God actualized precisely this world is its greater perfection in comparison with other possible worlds. The reason for the perfection of individual possible subjects is their freedom to constitute themselves according to their insight into what is best for them. This is possible whenever there is no conflict with another possible which wants just the same and which as such would coincide with it. As human beings we do not know the reason for the incompatibility of different possible subjects (A VI 4 1443). If the possible subjects had no inherent desire for existence, nothing would exist at all (ibid.). This is because possible subjects (possibilia) are not logical abstractions, but substances which have the ability to act as a basic property. Even though the actions of those which remain merely possible are never going to be actual in this world, they still contribute to the existence of the actual world. According to Dascal, in order to make a clear distinction between necessity and contingence we, as rational beings, would have to be able to examine an infinite chain of reasons (Dascal 2001: 278). It is indeed true that we cannot verify contingent truths in a finite number of steps via demonstrationis. But Leibniz’s great discovery was to realize that truths of reason and contingent truths of fact have the same internal structure. Leibniz furthermore recommends that we should not follow the philosophers, who like to conceal this deficiency, but rather the mathematicians who declare the principles they use, so that everyone knows that everything following from them can only be established hypothetically (A VI 4 804; L 225). The principle of sufficient reason is not a principle of epistemology but a principle of metaphysics (A VI 4 530). Leibniz does not inquire how we realize what the reasons are, or whether we know of their existence at all, but he only postulates that these reasons exist. To put it more precisely, he claims that nothing is without a reason, and nothing is the way it is without a reason. There is a difference between wanting to know that everything has a reason and wanting to recognize these reasons. This knowledge allows us to draw rational consequences from them. The

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vain thirst for such cognition leads to scepticism, which cannot even be countered by postulating a God as the only one knowing these reasons. The first belongs to the province of metaphysics, the second to that of epistemology. The first is the basis of rationalism put up in defence against scepticism. Many of Leibniz’s remarks, which appear to pertain to matters of epistemology, are really just put in place to counter hypothetical objections. That reasons incline (GR 303) in contingent propositions is due to the free actions of self-constituting individuals. Dascal regards freedom as essentially dependent on weak rationality (Dascal 2001: 279). It remains beyond dispute that the ability to act freely is a constitutive property of substances. The fact that, as Leibniz admits, our search for reasons depends on experience and the testimony of authorities does not really get to the heart of the matter. This is because Leibniz argues at the same time that each accidental sequence of reasons reaches up to infinity and that for this reason no accidental sequences but only the essential sequence will get us what we want (as was already realized by the medieval Scholastics). This is the insight that the first or ultimate reason for the existence of any being must be outside of this world, namely a necessary being essentially distinct from accidental, created beings, which is God, who created all things. But this is the same God who thought of these beings, thereby preferring the thoughts later actualized to all his other thoughts. In this respect, Leibniz uses the principle of sufficient reason as a proof of the existence of God (GP VII 302–308; Monadology, § 38). Leibniz thinks that the question why God created individuals in the way they are and not in some other way (for example an Adam who would not have been tempted by the fateful apple), is wrongly put. In this case, he claims, Adam would not have been Adam and would not have existed in our world. God did not create Adam, but a world in which Adam sinned, even though (or because) it presented itself therefore to him as the best of all possible worlds. Leibniz here uses the traditional theological notion of a felix culpa. That Adam took the apple was a completely free choice. Had this just been a trick played by God on mankind, in order to present his only son as a saviour, there would have been no grounds for speaking of freedom at all. It is not the case that these actions take place in different domains, one being ante creationem, which determines our existence, the other being in the world in which we live, which would be a determined re-enactment of earlier events. We can be eyewitnesses of the first domain by taking up the divine point of view, which includes knowledge of the future (praevisio). This knowledge is not anything we could actually obtain, we can only know by rational means that it exists. In order to construct this and other metaphysical theories in a convincing way, Leibniz necessarily needed the rigor metaphysicus. That this rigor would not withstand later criticism does not provide any reason for us (who want to understand Leibniz from a historical perspective) to replace it by soft rationality. Rationality is necessarily only a feature of higher creatures. Only they have insight into the actions emerging (spontaneously) from their own power, and are therefore responsible for these. This insight is free because it is connected with an inclination, a fact that does not weaken or even destroy its rationality. In fact it is a precondition of this rationality, because rationality without inclination would be

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meaningless. For Leibniz, freedom means the ability to follow one’s own nature, which means one’s natural inclination without any restrictions from the outside. One must not conduct an argument at different levels. There is no point in using probabilistic reasons (for example those used by a judge to settle a particular case) against metaphysical reasons, that is, against the actions of substances which result in the existence of the world, which cannot be divided into strong and weak reasons.

3.9 The Maxim Rationes non esse numerandas, sed ponderandas and the Theory of Probability Dascal (2001: 278) wants to turn the memorable maxim rationes non esse numerandas, sed ponderandas into a guiding principle for interpreting Leibniz’s thought, even though it is manifestly not suited for this job. It is nothing but a fac¸on de parler amongst lawyers, which Leibniz only quotes in two letters to Gabriel Wagner (GP 7 521) and a short time later to Thomas Burnett (GP 3 194), each time explicitly identifying it as a manner of speaking. In this context, Leibniz uses the term rationes only for what physicians call ‘indications’ (indicantia et contraindicantia), and uses an ironic way of limiting it at the same time, saying ‘that nobody has up to now shown the scales on which we are to measure them’. He himself hopes to solve this problem ‘at some time in the future’ by constructing a theory of probabilities. Aged 50, he declares that if God gave him health and some more years he would at least develop an important part of what is required, and give others the opportunity of building on this. His theory of probability would also be applicable to theological hermeneutics, and would also be a general means for settling disputes based on matters of fact. The ars judicandi he is about to construct was supposed to provide the sole arbiter of disputes about universal truths, which constitute the subject-matter of the sciences. First of all, he would be looking for a m´ethode des e´ tablissements, which made it possible to distinguish more from less secure pieces of knowledge. Before this method could be applied in theology, however, it would be necessary to construct a demonstrative metaphysics and a natural theology, a moral dialectic and a natural jurisprudence, par laquelle on apprenne demonstrativement la mani`ere d’estimer les degr´es des preuves (GP 3 194), so that the degrees of proof could be determined in a demonstrative fashion. Does this mean that the ‘new logic’ must provide non-calculative means for this balance of reason (Dascal 2004: 142)? Or does it rather mean that the metaphor of the scales stands for the real project of a rational technique for calculating probabilities? Already in 1682, Leibniz announced that once his Elementa veritatis aeternae were available ‘he could show that manifest demonstrations, which are equivalent to arithmetical calculations or geometrical diagrams, could be carried out in every kind of learning’ (palpabiles demonstrationes, calculi Arithmeticorum, aut Geometrarum diagrammatis pares, in omni genere confici possint). In this, he explicitly includes a method for deducing the highest degree of probability in an infallible way from the data present (A VI 4 892).

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3.10 Truths of Fact and Their Metaphysical Background The truths of fact, which are primarily the concern of those who are interested in practical applications, such as lawyers, physicians, politicians or even historians are regarded as structurally identical with contingent truths, which are the concern of the metaphysician, even though he is interested in them in a completely different way. Whilst those concerned with practical applications will have to settle even for mere probabilistic knowledge, in order to decide pressing cases, the metaphysician wants to tackle contingent truths as such, in order to draw universal conclusions about God, the world, and all things in it. For practical applications it is necessary to develop and employ suitable instruments of so-called soft rationality. The metaphysician, however, will only be able to defend his arguments if they have been obtained by strict rationality. He cannot afford to act against commonly accepted rules. This does not make soft rationality an inferior pursuit, but it means that we have to distinguish different interests and abilities.

3.11 La place d’autruy ‘Assuming another one’s point of view’, does not mean to leave one’s own in a conciliatory manner, but trying to understand which reasons support the opponent’s argument, in order to defend oneself more effectively against it (A IV 3 N. 137). For example, in the Systema theologicum Leibniz is not arguing from the point of view of a Catholic in order to become one himself. The closest modern equivalent to this mindset is presumably that of the profiler employed in criminal investigation.

3.12 Presumption or Principle? Is the dependence on presumptions really an argument for soft rationality? The phrase ‘the possible should be presumed true as long as the opposite has not been proved’ (possibile (verum) praesumitur donec contrarium probetur), which Leibniz uses repeatedly (e.g., A VI 1 522; A VI 3 631; A VI 4 136), means for the lawyer that the uncertain is to be tolerated for reasons of legal certainty. The notion of presumption gives us a general method for turning the uncertain into the modal, thereby allowing us to introduce it into strictly deductive inferences without having to compromise deductive standards of rigour. Dascal considers being a presumption as a sufficient condition for including it in the domain of weak rationality. But would we not want to say that rationalism in itself is not conceivable without presumptions (or principles, as I prefer to call them)? Leibniz also bases the distinction between the certain (certum) and the necessary on the square of modalities, which allows him to distinguish the contingent from the merely possible by treating it as hypothetically possible. This, however, is the case only to the extent to which God’s decision or, more precisely, His decree to create

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the actual world as the best of all possible worlds is the precondition for all contingent subjects. We obscure the fact that only this hypothesis is referred to by talking generally about decrees ‘which are violated in other possible worlds’ (Dascal 2003: 138). This is because God’s decrees, unlike his commandments, cannot be violated at all. They relate to existent subjects, or, to put it more precisely, to existiturientia, to ‘things which have to be brought into existence’.

3.13 Was Leibniz an Eclectic? Dascal only points at a general eclectic trait in Leibniz’s work to use his eclecticism as evidence for weak rationality. Had Leibniz uncritically and eclectically adopted concepts and corresponding theories, we might indeed regard this as a manifestation of weak rationality. However, as it is the case that Leibniz wants to underline the truth constantly present in rational thought in the sense of a philosophia perennis, we are here talking about a positive, not a polemical understanding of eclecticism. This is presumably the sense Diderot had in mind, although this does not have force as an argument. Nowadays, ‘eclectic’ is generally used as a pejorative term. Moreover, the evidence from Diderot’s use of the term is not very strong, since his knowledge of Leibniz’s writings was very restricted, although he held him in high esteem.1 I do not regard Leibniz’s letter to Placcius from 28 April 1695 (D VI 1 53) as an ‘eclecticist manifesto’ (Dascal 2004: 145). Leibniz’s primary goal is to politely decline Placcius’ request to review his latest publications. The general reason Leibniz gives for this is the need to recognize good points found in every piece of writing, which of course does not mean that one would have to take them all on board. When Leibniz claims that in his readings he is mainly concerned to look for profectus meos, quam defectus alienus, this means that he is primarily looking for whatever coheres with his own ideas, rather than others’ mistakes. It does not mean that he is merely looking for what ‘contributes to his own improvement’, because it is useful to him – as one would expect in the case of an eclectic.

3.14 Plurality – No Argument for Soft Rationality I also do not think that plurality constitutes an argument for soft rationality. For Leibniz, plurality demands harmony; the definitions of harmony as varietas in unitate redacta or as diversitas identitate compensata (A VI 1 484; A VI 2 283; A VI 3 116), or unitas in multis (A VI 3 122) are well known, but are rarely carefully considered in their consequences. Leibniz takes this essentially rationalist maxim not just to be a definition of harmony, but also as a guiding principle for his thoughts and actions. For him, establishing harmony means to bring whatever drifts apart together again, following the example of nature, the harmonia rerum. This is done by explicating the reasons connecting things, which have to be identified by rationality. He attempts to reduce the plurality of natural languages by reducing them to root

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words (the etyma) and the plurality of logical structures by reducing them to the lingua mentis or lingua philosophica or to a grammatica rationis, applicable to all languages. In both cases Leibniz follows a rational principle of reduction. He aims to preserve and to overcome at the same time the plurality of confessions, religions, and cultures by pointing out their individual features and emphasizing their underlying common rationality. He particularly recommends Christianity as a highly rational religion.

4 Concluding Remarks I had to disregard the mutual influence of research in the natural sciences and metaphysics in this essay. Let me just note that Leibniz was always looking for a metaphysical basis of physics, rather than for a physical or biological basis of metaphysics. Nothing gives us a stronger indication of his strong rationality than his rigorous distinction between monads and their phenomena. I would like to add that it does not appear right to me to disregard Leibniz’s monadology (which some might regard as strange) in favour of only those parts of his work which correspond closely to contemporary interests heavily influenced by the natural sciences. Even if the model of strict rationality, which Leibniz uses in an esoteric manner to construct his metaphysical system, will find few proponents nowadays (mainly due to assumptions no longer acceptable and the consequences of these), the historian at any rate must base his conclusions on the evidence available in Leibniz’s extant writings and letters. He must certainly not allow himself to cook up his own Leibniz according to his particular tastes, in order to pitch then this creature against different ones of the same breed. Numerous interpreters tend to search the works of the great philosophers (not just that of Leibniz) for mistakes, or for what they consider to be mistakes, in order to reduce them to their own mediocrity, hoping to tackle the problem more easily in this way. To regard soft rationality as an equal competitor or even to regard it as representative, in order to avoid Voltaire’s criticism, means to give up Leibniz’s well-founded, if difficult, rationalism on the flimsiest of grounds. The author of the Candide could hardly have had any knowledge of Leibniz’s metaphysics, which is the basis of his Th´eodic´ee. Even if he had wanted to get to know it, it is unlikely that he would have been granted access to Leibniz’s papers kept in Hanover. We have to interpret Leibniz’s rationalism according to what he himself was aiming to achieve and expecting to bring about, not according to what he would have had to prepare for this aim without already possessing the desired means to bring it about, and certainly not according to what he had to do when carrying out the daily tasks his offices obliged him to. As he calls himself a nominaliste par provision (A VI 4 996), I would like to call him a rationaliste par intention, and to consider his strong rationality as a conditio sine qua non for any sort of rationality which we might call weak.

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Acknowledgments I thank Jan Westerhoff for translating this paper into English and Philip Beeley for his critical comments on the final version.

Note 1. Diderot’s excellent entry in the Encyclop´edie came out in 1767; Dutens’ edition only in 1768, but Raspe’s edition of the Nouveaux essais appeared already in 1765.

References Dascal, M. 2001. Nihil sine ratione → Blandior ratio. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress). Berlin: Leibniz Gesellschaft, pp. 276–280. Dascal, M. 2003. Ex pluribus unum? Patterns in 522+ texts of Leibniz’s S¨amtliche Schriften und Briefe VI 4. The Leibniz Review 13: 105–154. Dascal, M. 2004. Alter et etiam: Rejoinder to Schepers. The Leibniz Review 14: 137–151.

Chapter 2

Leibniz’s Two-Pronged Dialectic Marcelo Dascal

D’o`u vient l’union dans un mˆeme esprit de la hantise d’une philosophie enti`erement m´ecanis´ee ou logicis´ee, o`u la discussion serait remplac´ee par le calcul, et d’une consid´eration si attentive des opinions de tous? ´ Emile Br´ehier (1946: 385)

1 Introduction In a number of papers,1 I have argued that, in addition to the “hard” rationality through which Leibniz’s rationalism is most familiar, it is imperative to acknowledge the existence and centrality in his thought of another form of rationality, which I proposed to dub “soft”. Several prominent Leibniz researchers – some of them present in the meeting from which the present book originates – have contested, on a variety of grounds, my suggestion, giving rise to an interesting and productive debate.2 The purpose of this chapter is not to respond directly to these criticisms. Its contribution to our ongoing discussion consists rather in scrutinizing an important instance of the hard-soft distinction in Leibniz’s work. Focusing on this instance will permit not only a better understanding of its seeming paradoxical nature but also, at the meta-level, to realize the rational power of softness as an argumentative strategy. I believe these two results will sharpen and deepen the debate and lead us together, if not to its solution, at least to clarifying the issues at stake. The central, and prima facie most problematic case, of Leibniz’s conception and use of rationality I will examine is his sui generis “dialectic”, which comprises what may be properly called his “art of controversies”. In the vast territory of rationality, Leibniz’s “art of controversies” occupies a peculiar position. He conceives it sometimes as a calculus that decides rigorously and unquestionably which of the opposed positions is true and which is false, and sometimes as a negotiation strategy leading to a conciliation of the adversaries’ positions, which cannot therefore be logically contradictory. While the former is a typical “hard” rationality approach, the latter is typically “soft” in nature. A question that immediately arises is why, instead of treating these two forms of handling controversies as two fundamentally different Leibnizian approaches to quite distinct kinds of debate-generating opposition, should one insist in subsuming M. Dascal Tel Aviv University, Tel Aviv, Israel M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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them under one single label. Doesn’t one thereby generate the alleged paradox one will have to struggle to solve, namely, how can hard and soft rationality live peacefully, conceptually united under the same roof? For, having pointed out this distinction and having stressed the profound character of the opposition in question, it is up to me, if I undertake to defend the one-dialectic thesis, to show what is actually shared by this dialectic’s so diverging manifestations. Furthermore, by defending such thesis, I am contributing to the suspicion as to how radical and profound their opposition can be if they are in fact united at a deeper level – a suspicion it is also up to me to dispel. Why should I create with my own hands a situation that puts upon my shoulders such a heavy burden? I confess that when I decided to analyze the particular case of Leibnizian dialectic in the context of the hard-soft debate I intended, through it, to shed light on the difference between these two kinds of rationality. That is, I sought thereby to further support my earlier arguments in favor of their distinction and hopefully also deepen their separation. Rather than giving up the alter and contenting myself with an etiam, as had been intimated by Schepers (2004), the contrast between the two dialectics would provide additional evidence in support of the irreducibility of Leibniz’s soft rationality to its hard counterpart, thus reinforcing my rejoinder to Schepers (Dascal 2004b).3 To be sure, neither Schepers nor me contested the fact that both varieties of rationality somehow exist side by side in Leibniz, but we viewed this coexistence quite differently: Whereas his etiam was an unwilling concession, mine was an emphatic assertion; whereas for him it was to be accounted for by the different contexts of use of the one and only rationality – the hard or, as he put it, “radical” one – admitted by Leibniz, for me its sources were to be found in the irreducible difference between his two fundamental metaphysical principles; consequently, whereas for him the unity of dialectic was hardly a problem, for me it was on the verge of the impossible. If I wanted to hold both, the full force of the otherness of soft rationality and the possibility of its coexistence and cooperation with its hard sister in one and the same rational task, it was clear that the burden of proof was on me. I would have to show that the one could not subsist without the other, and that togetherness ought to be given no less attention than otherness. Once I realized this, I also realized why Br´ehier’s quote struck me as the nearly perfect motto for this chapter. Choosing to commemorate Leibniz’s 300th birthday by focusing on his dialectic and especially on the inner conflict between its two trends, he highlighted perhaps the fundamental problem of Leibniz’s rationalism; asking “whence comes the union, in one and the same mind” of these opposed tendencies, he demanded an explanation for how can coherence be preserved in uniting what, on the face of it, is incommensurable – as a well known 20th century historian of science would put it. Besides the intrinsic value of solving this puzzle, I further realized the windfall benefit that would ensue, as far as the aim of establishing the indispensable role of soft rationality in Leibniz’s thought is concerned, from achieving such a solution and thus discharging the above mentioned burden of proof. For it became clear to me that the only way to reconcile the hard and soft branches of Leibnizian dialectic

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required construing their opposition as soft, rather than hard, of course without thereby underestimating their deep differences. Consequently, answering Br´ehier’s question about the coherence of Leibniz’s dialectic would – at one and the same time – show the need for a dialectic’s soft component, demonstrate the effectiveness of this component in resolving an apparent but thorny incompatibility, and provide a paradigmatic example of its workings! I am not sure that the textual evidence I present in this chapter provides a complete solution to the puzzle – an achievement upon which all the far-fetching consequences I mentioned rests, of course. But I am fairly well persuaded that this non-conclusive evidence convincingly shows that the rationality of Leibniz’s dialectic cannot be confined to the resources of calculative deductive procedures, even when what is at stake is the understanding of its own nature.

2 One Dialectic? First of all, one must ask whether lumping together in a presumed “dialectic” components that are radically opposed in their aims and procedures, and allegedly stem from different strands of Leibniz’s rationalism, is justified. This is not a simple question, for it requires some criterion for discerning – in Leibnizian terms – what binds together different elements so as to form a “discipline” or “field” or even a “project”, endowing it with a distinguishable conceptual unity or “identity”. Choosing such a criterion is particularly difficult in the case of a philosopher that has been rightly described as a pluralist and who abides in each domain, as well as in his work as a whole, by a principle of continuity that abhors gaps. Obviously, the choice of a criterion is closely linked to the characterization of what is to be called “dialectic” in a Leibnizian context and how does it differ from other endeavors or approaches in the history of thought that bear this name; it will also depend on the identification of its major components and their functions, of offshoots, spin-offs and other derivatives, as well as of the inter-relations between all of them. Taken together, these tasks amount to no less than providing the expression Leibniz’s dialectic with a well-grounded definite meaning:4 at the very least, with a “nominal definition”, based on whatever “distinct knowledge” of what it refers to is available; this should hopefully lead, in its turn, to a “real definition”, i.e., to a demonstrably noncontradictory complex concept; thereby its existence qua “idea”, rather than as a mere, possibly meaningless psychological compound (a “notion”), would be established.5 Evidently, if we had to wait for the complete analysis and subsequent synthesis of this cluster of concepts, which would yield the fulfillment of the definitional requirements mentioned above, in order to begin our task, our inquiry would never take off, since each of these steps would surely involve fierce dispute. In fact, given the declared positions of the contenders in the hard-soft debate concerning the components of the presumed dialectic, the demand of a “real definition” would mean forestalling that debate, either by begging the question or by obviating any alternative solution. So, in order to begin to discuss the nature of Leibniz’s dialectic without unduly prejudging or barring this or that solution, we should avoid over-demanding

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pre-conditions that would suppress rather than foster the debate. Instead, regardless of the suspicion that the present author is not exactly neutral in this debate, let us focus on the Art of Controversies, where the contrast between the two components is most explicit and dramatic, and examine in it whether and how the hard and soft varieties of dialectic differ, coexist, share some content, and are used within what seems to be a division of labor pattern.

3 Difference Let us recall first the distinction I have proposed between hard and soft rationality and observe how it is markedly reflected in two instances of Leibniz’s dialectic. By “hard” rationality I understand a conception of rationality that has standard logic and its application as its fundamental model. This conception views logical inconsistency as the paradigmatic expression of irrationality and regards certainty as the principal aim and sign of knowledge. Since mathematics is the most successful implementation of this ideal of rationality, hard rationality privileges what it takes to be the basic reasons of this success. Accordingly, it considers, as conditions of rational thinking and praxis or as their preferred manifestations, such parameters as: uncompromising obedience to the principle of contradiction; precise definitions formulated in terms of necessary and sufficient conditions; conclusive argumentation modeled upon deduction; formalization of this procedure by means of a symbolic notation; quantification and computability; axiomatization of domains of knowledge; and the like. By “soft” rationality I understand, broadly speaking, a conception of rationality that seeks to account for and develop the means to cope with the host of situations – theoretical as well as practical – where uncertainty and imprecision are the rule. Although acknowledging the applicability and usefulness of the high standards of hard rationality in certain fields, it rejects the identification as “irrational” of all that falls short of them. It deals with the vast area of the “reasonable”, which lies between the hard rational and the irrational. The model underlying the idea of soft rationality is that of scales where reasons in favor and against (a position, a theory, a course of action, etc.) are put in the scales and weighed. But there is a deep difference between “weighing” reasons and “computing” them. For, except for a handful of cases, the weights of reasons are not precisely quantifiable and context-independent; hence, weighing them does not yield conclusive results whose negation would imply contradiction. Unlike deduction, weighing reasons in this “balance of reasons”, “inclines without necessitating” – in Leibniz’s felicitous phrase. Even so, if the weighing is properly performed, the resulting inclination toward one of the plates provides reasonable guidance in decision-making. Soft rationality’s logic is, thus, non-monotonic and cannot be reduced to standard deductive logic. It is the logic of presumptions that rationally justify conclusions without actually proving them, of the heuristics for problem-solving and for hypothesis generation, of pragmatic interpretation, of negotiation, and of countless other procedures we make use of in most spheres of our lives.

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The best known instance of a hard rationality approach to dialectic by Leibniz is his project of applying the Characteristica Universalis to the definitive solution of disputes.6 He formulated and collected a large number of definitions of important concepts, which might have served as the raw material for the conceptual analysis required by the Characteristica; yet, he did not pursue the analysis systematically so as to yield a set of primitive concepts – which he called “the alphabet of human thoughts” – that would form its rock bottom basis. Nor was the vast majority of the many drafts and fragments of logical calculus found in his manuscripts specifically formulated for use with such a conceptual “alphabet”.7 Furthermore, as far as I know, there are no attempts by Leibniz, even fragmentary, to apply the “hard” project to the solution of actual controversies, although he heralded it as one of his top priorities. Perhaps it is the successful advertising that led later generations to view this project as emblematic of Leibniz’s conception of rationality and as his privileged, virtually sole method for dealing with controversies. The key idea of this method is that of a calculus, which Leibniz defines as follows: “A calculation or operation consists in the production of relations by means of transformations of formulae, performed according to certain prescribed laws”.8 A formula is composed of one or more characters, which are “visible signs that represent thoughts”.9 The ars characteristica is the “art of forming and ordering characters in such a way that they refer to thoughts, i.e., so that the characters have among themselves the relation that the thoughts have among themselves”.10 This art thus ensures that a strict correspondence between the level of signs and that of thoughts is established. Therefore, once properly applied, the art guarantees that formulae, relations and operations at the former level represent so-to-speak transparently notions, statements, and syllogisms, at the latter.11 This in turn prevents the occurrence of mistakes or confusion, i.e., provides the certainty of the method based upon the ars characteristica, which Leibniz considers the “True Organon of the General Science”, applicable to “everything that falls under [the label] ‘human reasoning”’.12 And it is this method, of course, that Leibniz advertises as sufficient for the contenders in a debate to easily resolve their dispute by calculating: We will present here, thus, a new and marvelous calculus, which occurs in all our reasonings and which is not less rigorous than arithmetic or algebra. Through this calculus, it is always possible to terminate that part of a controversy that can be determined from the data, by simply taking a pen, so that it will suffice for two debaters (leaving aside issues of agreement about words) to say to each other: Let us calculate! . . .In short what will be expounded is a method of disputing formally that is adequate for the treatment of questions, free of the tedium of scholastic syllogisms, and capable of overcoming those distinctions through which in the schools each party eludes the other.13

But is this “new and marvelous calculus” the only appropriate way of dealing with, and eventually solving every dispute? The answer is clearly hinted at in the very texts we have just been quoting. Consider first the provisos in the preceding quotation: (a) “that part of a controversy that can be determined from the data”; (b) “leaving aside issues of agreement about words”. Both clearly refer to controversial issues which the calculative method is unlikely to resolve. Consider next the proviso following the claim that the calculative method applies to “everything

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that falls under [the label] ‘human reasoning”’, namely: “provided it is clothed with the continuous chain of demonstrations of an evident calculus . . .our Characteristic itself, i.e., the art of using signs by means of a certain kind of exact calculus”.14 Here it is emphasized that the hailed method applies only to reasoning that has already undergone the process of formalization. Consider, finally, the opening sentence of the text we have been quoting from, which states peremptorily: “All human reasoning is performed by means of certain signs or characters”.15 This is an expression of Leibniz’ semiotic credo, namely, the indispensable role of signs in thought (see Dascal 1978). While this credo does not limit the semiotic dependence of mental life to the case of reasoning alone, the present statement does not restrict the kind of semiotic means employed in human reasoning to those of a transparent calculus. Therefore, insofar as controversies of course comprise argumentative moves, the possibility of semiotic means other than calculative ones for conducting our reasoning in such moves is left open by Leibniz even in the opening statement of a text devoted to the foundations of a calculus for reasoning. But there are more than indirect hints. In his annum mirabilis of 1686, characterized by great achievements in logic and other epistemological projects, in metaphysics, and in theology (see Dascal 2003: 132–152), Leibniz carefully indicates an important limitation – and this is not the only one – of an ars characteristica or standard logic inspired dialectic: It must be noticed, however, that this language [i.e., the Universal Characteristic] can function as a judge of controversies, but only regarding natural matters and not revealed ones, because the terms of the mysteries of revealed theology cannot be subjected to an analysis up to the minimal details, for if they did they would be perfectly understood and there would be no mystery in them. In so far as it is necessary to make use of ordinary words in matters of revelation, these words are endowed with another, superior meaning.16

Let us turn now to a clear instance of Leibniz’s soft approach to dialectic. In Des controverses, written in 1680 (A IV 3 204–212; DA 201–208), Leibniz reports a conversation with Duke Johann Friedrich of Hanover, where he presents to his patron “a very peculiar method” of handling controversies, which would advance the cause of the reunification of the Church. This method, he boasts, “had two great advantages: first, it could not be disapproved by anyone; second, it would lead to the end, furnishing a sure means to reach a conclusion”.17 This brief advertisement, along with the reference in the immediately preceding lines to his earlier interrupted work concerned with “an exact discussion of some controversies”,18 and the following comparison with the method of “a Geometer who understands true analysis”,19 might suggest a rather “hard” method endowed with universality, a decision procedure, and exactness. However, as Leibniz – prompted by the Duke’s skepticism vis-`a-vis such marvels – unfolds the main features of the new method, it turns out that its peculiarity is quite far from the properties of the calculative model. The visible sign that makes this method “one of a kind” is moderation: . . .there is nothing that makes a dispute more commendable than the moderation of the disputants; . . .this moderation will be manifest here in a quite special and indisputable way . . .[for] the nature of the dispute forces people to speak moderately in spite of themselves.20

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Moderation is achieved, in Leibniz’s method, thanks to a moderator or expounder whose neutrality is apparent to all, someone who would “write down controversies in such a way that the reader cannot know which party is favored” by him. This would not be due to some property of the moderator’s character, but rather to the very “form of the undertaking” which, as “everyone would have to admit”, would “impose moderation” on the performance of his task.21 The presence and example of this figure restrains eruptions of emotion, irrelevant and ungrounded arguments, purely eristic moves and other forms of ill faith, and mistakes – though it will not eliminate them altogether. Specifically, Leibniz lists five common defects that plague disputes,22 and claims: I dare say that the method that I purport to employ reduces these difficulties at once, and excludes them formally. For one will actually see a representation of the reasons of both sides which is so faithful that every reader will need only common sense in order to judge, without depending upon the moderator’s [expounder’s] expression of his inclination.23

All of this is achieved by a moderator who operates according to a few rules and aiming not at judging, reconciling or taking sides in a controversy, but only at carefully reporting it – neutrally, orderly, concisely, unambiguously, taking into account all the relevant arguments of both sides, and in a way that is sufficient for “a man of common sense to make his judgment based on the report”.24 It is quite evident that this method is concerned with removing or attenuating those factors that disturb the good will and the understanding, for, if the latter were universally shared, disputes would be prevented and the need for a method of solving them would be obviated.25 In this respect, it sets the stage for the eventual resolution of controversies, but does not actually purport to solve them – a task that the moderator is in fact barred from undertaking. This is a task left for the “man of common sense”, whose capacity of judging is, to be sure, helped by the moderator’s or expounder’ preparatory work, but certainly not replaced by an infallible decision procedure such as that allegedly provided by the “hard”, calculative method. Therefore, in terms of the parameters I have proposed for characterizing “cognitive technologies”, the method adumbrated in Des controverses is a “partial” rather than “integral” cognitive technology (it provides only “helps” for achieving a cognitive purpose), as well as a “weak” rather than a “strong” one (it does not provide a decision procedure yielding certainty).26 Taken together, these two parameters, along with the other features of the method, clearly characterize a “soft” rationality approach to the handling of controversies. It is important to stress that the method described in Des controverses was not the mere expression of a momentary enthusiasm with no sequel. Some of its key elements – e.g., the idea of the moderator or rapporteur – are elaborations of earlier ideas, such as that of a “director” of a controversy, already present in the Vices of mingled disputes of the late 1660s (A VI 2 387–389; DA 1–6); others, such as the very idea of moderation, were considerably developed in later writings’ elaboration of strategies of reconciliation (e.g., Methods of Reunion, 1687; A I 5 10–21; DA 247–262); and some – e.g., the idea of a visibly neutral report as capable of leading to an objective solution – were actually implemented in Leibniz’s dialectic praxis.

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A notorious example of the successful implementation of this idea and its corollaries is the Examination of the Christian Religion, one of Leibniz’s most ingenious efforts to mitigate the Catholic-Protestant doctrinal as well as political feud and thus to advance the irenic project.27 The Examination opens with a clear statement of the neutral and objective stance of its not named author, which is worth quoting: After having prayed much and at length for divine help, and leaving aside as much as humanly possible any partisanship, I have meditated about religious controversies as if I had just arrived from a new world, alien to all sects and uncommitted to any party. Everything considered, I have reached the conclusions I will expound, which I have decided to adopt because the Sacred Scripture, the authority of pious antiquity, right reason itself and the testimony of the facts appear to recommend every mind free of prejudice to believe in.28

The fact that the author declares what are the conclusions of his careful weighing of the issues examined does not detract from the neutral and objective stance, for his conclusions do not amount to siding, overall, either with the Protestant or with the Catholic position. Quite on the contrary, the basic neutrality of the stance makes room for an evaluation of each particular controversial point on its own merits – which leads to particular conclusions that are sometimes palatable to one side and sometimes to the other. That is to say, such conclusions embody not one-directional concessions, but bi-directional ones. This not only confirms the rapporteur’s neutrality, but grants it the visibility it must have according to the Des controverses method. That in this particular text the method worked is demonstrated by the surprise and enthusiasm of the Catholic theologians who discovered and translated the text:29 upon seeing how far Leibniz the Lutheran was ready to concede many points held by the Catholics, including points adopted in controversial decisions of the Council of Trent, they wondered whether Leibniz had secretly converted to Catholicism and began to praise and trust him!

4 Concomitance A fact worth noticing is that Leibniz’s concern with controversies begins very early and continues during his whole life, until his very last days. Throughout all these years, the “soft” and the “hard” approaches coexist, sometimes within the same text, as viable ways of handling controversies – ways that he applies, theorizes about, and is constantly concerned to develop. Leibniz’s first academic publication was his B.A. thesis, the Disputatio Metaphysica de Principio Individui (A VI 1 3–19), which he defended in December 1662 and published in May 1663 in Leipzig. Though the disputatio was at the time the standard form of writing and defending a dissertation for obtaining an academic degree, its subject matter was not necessarily a controversy. Nevertheless, the young Leibniz chose as his theme the “very difficult and prolix controversies” about the principle of individuation.30 As usual in the academic disputationes of the time, Leibniz begins by surveying the state of the issue (status quaestionis), by distinguishing between the various meanings attributed to the key terms in

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the controversy, and by identifying the main points of contention and the various positions held in the debate. Having complied with this formality, he soon takes sides, dismissing those positions that don’t satisfy the “general argument” that “every individual is individuated by its whole entity” – an opinion “held by the most serious scholars”.31 Among those who accept this axiom, neither Thomas Aquinas nor Duns Scotus are included; and Scotus, “known as an extreme realist because he put the true reality of universals outside the mind”,32 becomes the target of Leibniz’s critique in the rest of the text, where, leaning on nominalist counter-arguments, he refutes the arguments of Scotus himself and of several of his followers. The syllogistic form of the argumentation, typical of the genre disputatio, might suggest that this is strictly a “hard” rationality text; nevertheless, it deals with a classical metaphysical debate in which disagreements usually handled by “soft” rationality tools, such as questions of interpretation, basic assumptions and presumptions, and the very issues at stake have a fundamental role – a role the young Leibniz does not overlook. The Specimen Quaestionum Philosophicarum ex Jure Collectarum (A VI 1 71–95) is a text written for a disputatio held in December 1664, in which Leibniz – bearing since February the title of Master of Philosophy – presides over the proceedings, the younger Johannes Matthaeus Menzelius being the respondent. It marks the beginning of Leibniz’s shift to juridical studies, while at the same time stressing the continuity between them and his philosophical interests. The text deals with a variety of questions, from logic to metaphysics, through the philosophy of mind, mathematics, physics, the liar paradox, and the nature of animals and humans. Of particular interest to our topic here is Question II (A VI 1 76–77), which deals with the issue of who bears the charge of the proof in a dialectical confrontation. Leibniz points out the inconsistency between two rules, the one observed by philosophers, the other, he seems to imply, by jurists – respectively, “The person who affirms a thesis is responsible for proving it” and “The opponent is held responsible for proving his statements”.33 The solution to the conflict that may arise as to which of the rules to apply in a given case is solved by the presumption that the latter is more “natural” than the former, whence follows the recommendation: “When in doubt, the second rule prevails”.34 This is justified by pointing to the “tacit contract” between the participants in a disputation: Whoever has taken upon himself the role of respondent in a disputation has thereby only accepted the obligation of defending [his] thesis against the opponent’s objections, which must be proved by the latter.35 Leibniz further argues that the “philosopher’s rule” would render the phenomenon of debate unexplainable, since – he asks – “what is easier than to transmute a negative word into a positive one and vice-versa?” Such a move, he contends, “would virtually eliminate all disputes, since, before a dispute could begin, endless debates would be needed in order to establish whether a given proposition is, in itself, of an affirmative or of a negative nature”.36 It seems to me that he is clearly suggesting that the issue of who bears the charge of the proof in a dispute is neither a syntacticmorphological, nor a semantic-logical “hard” issue, but a pragmatic one, having to do with the proper performance of the role of each disputant in each context. He indeed insists on the context sensitivity and consequent “flexibility” of the assignment of onus probandi. In a court of law, for example, the aim being to

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decide a case on the basis of true, reliable evidence, “it is necessary by all means to extract, from the deeds and from what has been proved, the truth, so as to be able to decide the matter at hand”; from which it follows – he argues – that “the charge of the proof must be imposed upon whoever can discharge it most ably, so as not to leave the matter without a decision”.37 Furthermore, “the same need to prevent that the inquiry of the truth be interrupted” mandates that the charge be transferred to the other contender, if the one that was presumed to discharge it is unable to do so. Ultimately, this flexibility is possible precisely because it is not a “hard”, but rather a “soft” rule that guides the assignment of the charge of the proof: “it is not universally established whether it is the plaintiff or the defendant that is required to prove, since neither a tacit contract concerning this matter obtains between the parties, nor – as happens in contemplative philosophy – it is possible to give up a sentence and a decision without damaging the other party”.38 Leibniz’s next disputation, the Disputatio Juridica De Conditionibus, was defended in two installments, in July and August 1665 (A VI 1 98–150). In a brief Preface, he defends the conciseness of this very dense demonstrative structure of 160 definitions and 375 theorems, whose aim is to provide a general systematic account of the types and of the validity of conditional dispositions and contracts, especially in Roman law, by comparing his method to that of the Ancients, who made use of “very certain and almost mathematical demonstrations”.39 While my comment on this text would perhaps be to point out that it instantiates “hard rationality at its best”, Yvon Belaval would probably go further. In accordance with his stress on the central role of formalism in Leibniz’s thought (Belaval 1960), he might describe the De Conditionibus by emphatically repeating what he wrote about the Confessio Philosophi of 1673: “The love of formalism is not new: it is a constant in our philosopher. The most sublime method is the one that deduces from first principles. These principles? Definitions. As for the form of reasoning, it is taught to us by syllogistics, natural theology, and jurisprudence” (Belaval 1961: 18). Pol Boucher, at least in part, would follow suit, for he discerns in the De Conditionibus’ attempt to put in logical form the informal demonstrations of the Justinian corpus a glimpse of “the project of reducing knowledge to a chain of definitions” (Boucher 2002: 11–12). As an outstanding connoisseur of this text, however, he warns that the kind of juridical rationality it actually displays is not that of the standard logical-mathematical model. Since it has to cope with a “polyphonic complexity” of sources and constraints (ibid., pp. 10, 19), its formalism at times violates “standard” logical requirements. For example, the necessity of some propositions (e.g., theorems 264, 288, 298) “is not strictly logical even though their contraries imply contradiction”, because “in spite of their mathematical or logical components, their evidence depends first of all upon the acceptance of fundamental norms concerning the origin and the balance of rights” (ibid., pp. 19, 20). The combination of independent and complex reasons in what Boucher calls a “composite logic” yields the peculiar phenomenon of “apparently circular demonstrations” (ibid., p. 47), i.e., demonstrations based on theorems posterior to the one being proved (see, for instance, the demonstrations of theorems 23 and 29). The solution Boucher proposes for this apparent breach of deductive linearity is based on the observation that the “circular” theorems40 refer to legal properties of conditional

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dispositions “that are not consequences of a single fundamental norm but of several independent norms” (ibid., p. 56). The picture of this deductive text that emerges, therefore, is not that of a single linear logical thread, but rather that of a crisscrossing series of independent deductive chains, such that within each of them logical linearity is respected and at the nodes where two or more of them meet the resulting combination of the logically independent legal properties is validated by positive law (ibid., pp. 57–58). Regardless of whether a structure such as this is “hard” or “soft”, its form is certainly not a conventional one – in either of these two types of rationality. In the last of his formal disputations, which granted him the doctoral degree in November 1666, the Disputatio Inauguralis de Casibus Perplexis in Jure (A VI 1 233–256), Leibniz addresses one of the most difficult issues in legal theory and practice, the so-called “hard cases”. His opening exploration of the meaning of casus perplexus points to metaphors (Gordian knot, squaring of the circle, blind intestine), proverbs (for a hard knot a hard wedge), and concepts (doubt, problem, antinomy, impossibility, insolubility) that suggest conundrums for which a way out is indeed very hard to find, if at all. But he also points out that there are all sorts of knots, not all which are Gordian, and that etymologically “perplexity”, which derives from the verb plecto, a frequentative of plico (“to fold”), refers to the pliability of things that are “simultaneously flexible and tenacious”,41 so that the entanglement of hard cases involves a peculiar mix of soft and hard properties. Nevertheless, after examining the contemporary attitudes of jurists towards how to decide these cases – attitudes including the refusal to decide, the appeal to lots, the granting of complete freedom of decision to the judge, and the restriction of such freedom through the reliance on non-juridical criteria (e.g., charity, equity, humanitarian considerations) – Leibniz adopts a rather strict position, according to which “all the cases can be decided by the law alone”.42 To those who, like Bachovius, argue that the interpretation of positive law is uncertain, he retorts by appealing to natural law and natural reason, upon which positive law, if it is to be reliable, must be grounded. In this way, he hopes perhaps to shuffle aside the problem of interpretation, as well as other “soft” elements, such as the “natural” presumptions he himself mentions, that challenge the certainty of the decision procedure for hard cases he is proposing.43 This casts doubt on the basis of the confidence he expresses in the capacity of the three rules he formulates (and whose use the rest of his dissertation illustrates) to decide at least all hard cases stricto sensu (A VI 1 255). In discussing the above examples of Leibniz’s early work, especially those pieces explicitly defined as disputations, I have been trying to show that some of them are mostly “hard” in nature, others rather “soft” (at least in some of their parts), and others comprise both types of rationality. The effort I had to spend in putting together the evidence to argue this point would have been considerably reduced had I noticed before that Leibniz himself had already done it! In 1669, Leibniz compiles in one volume three of his disputations: De Conditionibus, De Casibus Perplexibus, and Quaestiones Philosophicae Ex Jure Collectae.44 The way he orders them and slightly modifies their titles in this volume indicate his own assessment of their “soft” and “hard” characteristics. This is neatly posted in the title page of the Specimina Juris (A VI 1 367–430):45

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Notice first that each of the pieces is presented as an example (specimen) of a different aspect of law: the fact that the law does involve serious practical and theoretical difficulties, the fact that its formulation and application is related to a broad range of knowledge in a variety of domains, and the possibility of formalizing it rigorously. Notice also that the order of presentation is not that of composition (which is II, III, I), and observe the different size of the fonts employed for each piece: It is as if, taken together, order and font indicate their relative importance – II and III being perhaps represented as illustrating the kinds of considerations or tools capable of contributing to eventually solving difficulties such as those discussed in I. And notice, finally, the addition of the word amoeniores (“more pleasant”) in the title of II. This addition explicitly calls attention to the element of “softness”, whose presence we noticed in our analysis of the Second Question of text II.46 The ensemble of this carefully crafted composition shows Leibniz’s care in making explicit that his juridical work makes use of both a hard, formal method and a soft, persuasive one and that it would be a grave mistake to consider the former as capable to solve all juridical problems and, therefore, as privileged vis-`a-vis the latter. Let us turn now to another domain in Leibniz’s early work, his writings on theological controversies, intended to advance his irenic views.47 Here too we find the concomitant presence of markedly different “hard” and “soft” approaches, as well as a certain “polyphony” that reminds the one Boucher detects in the early juridical writings. The Catholic Demonstrations project is explicitly “hard” – as indicated by its general title as well as by those of the pieces it comprises; the first part of the Short Commentary on the Judge of Controversies, with which the early theological production ends, is, as we will see, of a “soft” nature.48 The Catholic Demonstrations begins with a synoptic table of the demonstrations it planned to contain (Demonstrationum Catholicarum Conspectus, 1668–1669; A VI 1 494–500). It follows a quasi-axiomatic order, beginning with demonstrations of God’s existence and of the immortality and immateriality of the soul, followed by a long set of demonstrations of the possibility of the mysteries of the Christian faith and refutations of the alleged proofs of their impossibility, and ending with no less than demonstrations of the authority of the Catholic Church and of the Sacred Scriptures. The dialectic strategy of the part devoted to the mysteries, which includes actual refutations of various objections to their rationality, consists simply in: Let us decide this controversy by proving the possibility of the mysteries! This is clearly expressed, for example, in “On the demonstration of the possibility of the mysteries of the Eucharyst”: . . .the vindication of the truth against the insults of atheists, infidels, and heretics in claiming the impossibility and contradiction [of the mysteries] demands not only denouncing but also exposing them, and nothing is more correct and deeper than doing this by means of a demonstration of possibility; for, as a single clear definition saves a thousand distinctions, so too a single clear demonstration saves a thousand responses. Once the possibility is thus clearly shown, it appears immediately that all the alleged impossibilities derive from using a false hypothesis and a contested sentence which is ill-understood and belongs to something else.49

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In the Short commentary, written roughly at the same time as the above quoted text, Leibniz’s strategy in theological controversies, especially those regarding the mysteries of faith, undergoes a remarkable shift. It is no longer through logical demonstration that he seeks to defend the Christian dogmas, but rather through scriptural hermeneutics. The “judge of controversies” in “questions of faith necessary for salvation” is not conceptual analysis and definition, but explicit textual presence in the Sacred Scripture: “Regarding these questions, no proposition is to be accepted as belonging to faith unless it is expressly contained in the Sacred Scripture, taken literally from the sources”.50 This criterion, however, does not amount to a decision procedure, for one must believe not in the words, but in their meaning, which the presence of these words in the Scripture still leaves to be determined: But it remains a non-negligible difficulty. Since one has faith not in words, but in their meanings, it is not enough for us to believe that the person who uttered the sentence ‘This is my body’ said the truth unless we know also what he said. However, we do not know what he said if we only have the words and ignore their meaning.51

But how to determine the appropriate meaning, if not through a process of interpretation that may involve a measure of arbitrariness, which might lead us far away from the proper or literal meaning? In order to avoid this danger and keep as close as possible to narrow “textualism”, Leibniz adopts a strange compromise. He goes as far as admitting that the content of a belief – even in “questions necessary for salvation” – need not be semantically determined and may consist in favoring one proposition, out of a set of available alternatives, albeit without having a precise criterion for justifying such a preference: This is a very hard knot. But it can be solved. My reply is that it is not always necessary for faith to know that a particular sense of the words is true; [it suffices that] we understand that sense and reject it positively, but rather leave it under doubt even though we might be inclined towards some other [sense]. Furthermore, it is sufficient that we believe in the first place that whatever is contained in the meanings be true; this is clearly the case in those mysteries, where practice does not vary whatever the meaning turns out [finally] to be.52

This largesse grants legitimacy to figurative interpretations too, provided these are not systematically favored at the expense of literal ones: But what about the improper sense? In this case, I think that, upon listening to the words of the text, Christians have to take them as true under the proper sense. Yet [they should do so] with the pious candor that knows it can deceive itself and that perhaps the proposition is true in a figurative sense, thus acting in a surer way. This faith will be disjunctive, although it inclines towards one of its parts. And indeed this is what most Christians do in practice, if you look at it carefully.53

Under the semantic conditions the passages quoted above describe, it is evident that a great deal of philological and historical knowledge, as well as hermeneutic skill are required for choosing the appropriate interpretation. This is, obviously, fertile ground for interpretative controversy, which the Short Commentary suggests to deal with by means such as the presumptions these passages spell out – e.g., that all the different meanings evoked by a Scriptural passage are true or that one should

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give priority to the literal sense over the figurative senses. Presumptions are typically “soft” inferential devices, like all other appeals to the textual norm, since they only incline the balance of reason towards one of its scales without thereby providing the judge of controversies with logically compelling, unquestionable solutions.54 This section has highlighted the concomitance of hard and soft dialectic strategies in Leibniz’s early writings pertaining to different domains. Boucher has pointed out, with respect to the relationship of the different approaches present in Leibniz’s early juridical writings, that neither can be viewed as either evolving from or reducible to the other, though there is an undeniable connection between them. He suggestively calls this non-linear and non-reductive link “fragmented continuity” (Boucher 2002: 21). And, without giving up altogether the evolutionary perspective, he stresses both, the concomitance and the difference of approaches that range from a privileged focus on positive law to a quasi-axiomatic natural law based model.55 He refers to this state of affairs as a “polyphonic development”, where the intimacy of the presence of the “analytic, architectonic and natural law approaches” is so marked that “one can feel in each line the attenuated action of the two others” (Boucher 2002: 22). A similar polyphony, though perhaps not as intimate and harmonious, characterizes most phases of the development of Leibniz’s thought, as far as the undeniable copresence and mutual irreducibility of hard and soft rationality in general, and in the theory and practice of dialectic in particular, are concerned.

5 Content Sharing It is now time to inquire whether, beyond the fact that the two kinds of dialectic appear concomitantly in Leibniz’s writings and play a virtually simultaneous role in the development of his thought in several domains, they also share some content. If they do, while at the same time preserving their profound differences, this may count as evidence in favor of the one dialectic thesis (see Section 2). Of course, for this to be the case the sharing ought not to be merely circumstantial or domaindependent, but should rather consist in or be derived from essential features of his conception of dialectic, which manifest themselves, albeit differently, in its “hard” and “soft” dialectic branches. The concept of “form” and its associates is a good example. The opening paragraph of the Vitia disputationis confusanae (A VI 2 387–389, DA 1–6) defines a confused dispute as “a dispute in which the form of reasoning is not respected”;56 the final paragraph of this sharp analysis of the types of disputations and their problems ends with a list of “firm and solid rules” that would put an end to endless disputes with a ban on informal inferences: “nothing should be said without proof and nothing should be inferred except formally”.57 Prima facie, these opening and closing lines should suffice for locating this writing in the category of “hard” contributions to Leibniz’s meta-dialectic reflections, since it seems to insist clearly on formal logic as the means to put controversies in the right track. On closer inspection, however, a rather different picture emerges. Except for the initial and final statements quoted in the preceding paragraph, there is virtually no

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trace of formal logic (or of mathematics) in the Vitia. Neither are mistakes in logical inference or other faults of reasoning singled out as causes of confusion in disputes, nor are the strictures of reasoning in forma specifically mentioned as the means of preventing and curing any of the confusions discussed in the text.58 And for good reason, since the causes – hence the treatment – of the type of confusions this text is concerned with are of an entirely different kind. They have to do not with how the contenders think but with how they argue with each other, not with the reasons they have but with when and how they are presented and what persuasive power they have, not with the validity of their reasonings but with the dialectical interaction that takes place in the dispute. Confusion arises in a dispute when the lack of a clear structure prevents participants and audience alike from keeping track of the argumentation lines, from reaching a conclusion, and from succeeding in their persuading efforts: If one continues to reply, then either this is done through alternating turns of speech or through a continuous peroration. If the reply allows for alternation or permits interpolations by the other, the following problems arise: (a) each [participant] is not able to complete his line of reasoning; (b) we forget the preceding reasons when discussing the present one; . . .(d) the hearers of these disorganized repartees end up forgetting them [all] or becoming confused. In these ways it becomes hopeless both to convince the adversary – who can always jump from one topic to another, to elude the reasoner, and to pursue the matter ad infinitum – and to persuade an audience that has been confused or bored.59

Overcoming this kind of problems cannot be achieved by intervening merely at the level of logical form. For Leibniz, it requires the introduction of a new factor at the level of dialectic interaction, which turns out to be our familiar moderator or rapporteur (see Section 3), who in the Vitia’s earlier impersonation is endowed with enough powers to bring the dispute to a successful end: If there is a director, with the power to formulate questions adequately and to interrupt or terminate the dispute whenever appropriate, then, assuming that this director is prudent and good, the dispute may have a [successful] end. For the director either formulates from the beginning preliminary questions, or else he formulates them in view of the discrepancies between the parties. . . .In this way, he can completely avoid leaving arguments without refutation . . .thus avoiding the omission of anything. Therefore, if such a good and smart director is available, there is hope that the majority [of disputes] can be handled correctly.60

The introduction of the director no doubt contributes to reducing the danger of confusion, but it is not enough to yield a reliable structure to disputes. Directors, after all, are human beings: not all of them are as clever and skillful as their function requires, and sometimes they make use of their power for nothing but advancing their personal interests;61 and the contenders too: their original reasons and beliefs “tend to remain tenaciously fixed in the mind, thereby escaping the power of the director and of any other person”.62 An additional element is therefore needed in order to reach a structure comparable to that of logical form, namely that set of “firm and solid rules” which contenders as well as directors must obey.63 Once this is provided, one can claim to be able to eradicate confused disputes thanks to a strict “dialectical form” that, if enforced, will allow such an eradication for those disputes that respect the “argumentative order” their confused counterparts lack.64

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Notice, however, that such a form need not be instantiated by a version of “hard” logical form (see Section 7). This is apparent in the Vitia, where, in spite of Leibniz’s initial and closing statements, the “firm and solid rules” he proposes are nowhere near the rules of logical inference as far as their “hardness” is concerned. This is due to the fact that the “dialectical form” shared by the two branches of Leibnizian dialectic represents the general theoretical level of pragmatic organization of adversarial communication, whereas “logical form” – in the context of the present analysis – refers to one of the available means for implementing such an organization – the one exemplified by the hard “Let us calculate!” project. But dialectical form can as well be implemented by other, soft means, such as those instantiated by the Vitia’s Director or the Des Controverses’ Moderator (see also DA 66, 146). That these two levels – say, of theoretical meta-conceptualization and implementation of dialectical form – are indeed distinguished by Leibniz is shown by an attempted implementation of some of the dialectical principles that the Vitia formulates through the use of “hard” looking numerical and semiotic means. In the mid-1680s Method of Disputing until the Completion of the Subject Matter,65 Leibniz formulates a method for ensuring “dialectic relevance” and preventing “dialectic redundancy”. The formalism employed consists in a tree-like diagram, where arguments, objections, replicas, retorts, etc. are represented numerically and displayed in such a way that one can easily see the relations between them. The structure, being purely syntactical, is formal precisely in the same sense as the symbolic representation of a Modus Ponens inference as “p → q, p;  q” is. And, in both cases alike, this is what is supposed to ensure the possibility of using this method in all sorts of disputation, regardless of their domain and content, as Leibniz correctly stresses.66 Nevertheless, whereas the syntactic hardness of the second formalism is a necessary consequence of the semantic hardness of the logical relations it expresses, this is not the case with the formalism that expresses dialectical relations, for these are not semantic but rather pragmatic in nature, and could also be expressed satisfactorily by softer means. Just as “form” is a theoretical meta-concept shared by both branches of Leibnizian dialectic, so too are other meta-concepts that are closely related to that of form, such as “order”, “rule”, “method”, and “proof”. It is this sharing that allows for the same text or neighboring ones to make claims or implement models based on both, the soft and the hard senses of these terms. The phenomenon is not limited to dialectic and extends to other domains where Leibniz employs the meta-concepts in question alternating between their two senses. For instance, when describing his plan of creating a German society of scholars whose task would be the systematization of research, Leibniz defines the “form or order” of this society”s objectives in terms of his cherished hard projects: “the conjunction of the two most important arts of discovery, the Analytic and the Combinatory”.67 However, the fourteen canons that are to spell out the conditions for the plan’s implementation specify soft rules concerning division of labor, how to thank the authors for their work, the discursive form and order of the written output, the use of definitions and experiments, etc.68 Another example, of particular interest for dialectic purposes, is the alternation between a hard, strict sense of “proof” (probatio) virtually equivalent

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to demonstration, and softer senses of this term and its cognates. This softening of the meaning is sometimes expressed through quasi-synonyms or hedges of “proof”, which quite explicitly weaken the demonstrative force conveyed by its usual sense. For example, when something is said to be proved or determined “as far as permitted by the data” or when the degree of probability of a “proof or conjecture” is estimated, regardless of how precise the resulting estimation, it “cannot serve us for reaching certainty, which is impossible”, but only “for acting in the most reasonable way possible on the basis of the facts or knowledge available to us”.69 Hard and soft proofs can thus be lumped together, at a certain level of abstractness, in a scale of “degrees of proof”, which provide reasons with different weights, each corresponding to the “degree of hardness (or softness)” of the proof that supports it – as Leibniz the jurist was well aware of.70 Perhaps the most convincing textual evidence of content sharing between the two modalities of Leibnizian dialectic is revealed by following a terminological thread he himself provides: the fact that two key dialectical expressions – “judge of controversies” and “balance” – are employed by Leibniz for referring, alternatively, to the soft and to the hard dialectic projects of his. As we have seen (Section 4), Leibniz sides with the “textualists” in claiming that the judge of substantive religious controversies must be the Biblical text itself (cf. Short Commentary, §§5, 34); yet, he admits that, since the meaning of the Scripture is not always determinable with certainty, this textual judge is not a hard, infallible one, but rather a softer one: its interpretive decisions are based on presumptions that incline the balance towards some meaning without necessitating, however, its choice (§§24, 32, 35). Nevertheless, as in §36 the Short Commentary moves from religious to secular controversies, both judge and balance undergo a radical shift in meaning and function. The former is now Right Reason (§52), rather than a text, however sacred it may be; the latter, a perfectly built and calibrated balance, whose precise mechanism prevents any mistakes (cf. §65a,b ). To be sure, Leibniz points out, humans and social groups, influenced as they are by interests and passions, may deviate from reason and commit mistakes (cf. §§36–47); but this is not the case for “Right Reason abstractly taken”, which therefore – he concludes – “must be, in my opinion, the judge of controversies in the world”.71 The art of this judge, which Leibniz compares with the “fabulous science of making gold” (§60), is nothing but “the True logic, endowed with a certain exact and rigorous form of proceeding that excludes all sophisms”.72 The ideal judge and the ideal balance are thus in fact equivalent, at least when controversy arises about questions “amenable to calculation”. For, in this case, there is no need for a judge, since if one numbers everything diligently and attentively, without omitting anything, the necessary conclusion emerges with maximum evidence . . .In such a way, it is clear that what is evidently demonstrable should be withdrawn from the judge’s decision and trusted to the balance of reason.73

Obviously, we have landed in the hard domain of calculative dialectic, and the shift from the soft judge and balance to their hard counterparts has not required even a warning.

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If such radical shifts are possible within one text, no wonder one can find them across texts written twenty years apart, such as the Short Commentary (1669) and the Exhortation (1688), which includes among the tasks of the General Science project the development of a judge of controversies, which Leibniz describes as follows: On the judge of human controversies or Method of infallibility; and on how it can be achieved that all our mistakes be no more than errors of calculation that can be corrected by an easy examination.74

The only noticeable differences between this quote and the corresponding version in the Short Commentary are (a) the broader scope of the Exhortation judge, whose jurisdiction spans all human controversies and mistakes, rather than only those “amenable to calculation”, and (b) the omission of the image of the balance, which becomes redundant due to the extended scope.75

6 Division of Labor In the light of the evidence so far presented, hard and soft dialectic hold a rather complex relationship of deep difference and radical separation along with concomitance and content sharing. While the evidence provides reasonable support for the one dialectic thesis, the question remains why this one dialectic should unfold into two markedly different branches along a hard/soft divide. In this concluding section, I will explore an answer to this question that seems to me to have a high degree of likelihood: division of labor. 6.1 Division of labor is obviously necessary when different domains of research and action intrinsically require different forms of rationality. In Dascal (2001), where my aim was to highlight the importance of soft rationality for Leibniz, I have stressed the essential role of this kind of rationality in fields such as law, politics, theology and church politics, science and scientific policy, epistemology, and metaphysics, arguing that no proper account of them is possible without acknowledging this role. In the present study of Leibniz’s two-pronged dialectic, however, what must be stressed are the diverse needs of different fields, which leads some of them to tend more towards hard means and others towards soft ones. For example, logic and mathematics, the paradigms of hard rationality, function also as a general paradigm of hard dialectic – although Leibniz surprisingly points out that even in mathematics a “blandior ratio tractandi” is required.76 Leibnizian ethics, on the other hand, has clearly soft requirements, characteristic of the deliberations involved in deciding between the relative weight of conflicting values in specific situations. For example, a generally condemned action such as lying “ceases to be an evil by being used for the good”, provided “it cannot be proved, either by reason or by the authority of the sacred scriptures” that it is, “by its very nature, sinful” – which, according to Leibniz, indeed cannot be proved.77 Even in domains such as politics and legal practice, both inclined towards the soft branch of dialectic, marked differences between the strategies of argumentation employed are pointed

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out by Leibniz. For example, while in a court of law where to win the case is what matters most, “hardly anybody will shift from his own opinion to that of the other in public discussions”, in princely courts where political power depends upon alliances and broad support, “interest itself demands at times that one abandon one’s opinion and cease to insist on it”.78 6.2 Division of labor is also intimately connected with the basic nonconfrontational attitude underlying Leibnizian dialectic. When his friend Vincent Placcius asks him to read and criticize a manuscript he is about to send to him, the polite but firm reply is: . . .you should not doubt that I will be an eager and, as far as possible, a studious reader of whatever emanates from you. Nevertheless, to exercise criticism requires more work, and it should not be expected from me, for by nature and education I am prepared to look for, in the writings of others, what contributes to my own improvement rather than the others’ failure.79

He stresses that this is no idiosyncratic attitude, nor an attempt to escape the burden of attentive reading required by criticism. It is rather a matter of policy, whose implementation demands even more attention and effort than criticism itself: My long experience has taught me not to disdain anything easily. There are profound reflections in every kind of doctrine, each with its own usefulness, even though they are not so obvious. Therefore, what has been reflected upon in various kinds of interpretation, I usually consider as deserving applause for its precision, rather than contempt; in this way, I stimulate the learned to explore those deeper notions rather than being deterred by them.80

This eclectic epistemological policy is mandatory once one realizes the multiplicity and variety of often contrary opinions on every possible subject matter. Metaphysically, this is a result of the different perspectives from which each monad reflects the whole universe.81 Consequently, knowledge cannot be built by solitary individuals as in the Cartesian paradigm, but only through a multi-perspective, cooperative strategy – for which dialectic turns out to be a fundamental tool:82 There are comfortable and uncomfortable, good and bad aspects in all things, sacred and profane; this is what disturbs men, this is what gives rise to the diversity of opinions, everyone considering each thing from a particular side. There are only few persons who have the patience of making a tour around the thing, up to the point of putting themselves on the side of the adversary. That is to say, there are very few who undertake to examine the pro and the con with equal application, in the spirit of a disinterested judge, in order to see to which side the balance should incline.83

The young Leibniz began very early to elaborate detailed plans for the institutional organization of the required cooperation, which at last culminated with the creation of the Academy of Sciences in Berlin. These plans, as we have seen (cf. Section 5), included specific rules for the social aspects of the division of labor; they also included provisions for coordinating the divided labor in order to yield results whose “hard” status would thus be ensured – e.g., agreed upon definitions: “The definitions will be communicated to the members, who will establish them through joint deliberation; this will avoid the cause of confusion that consists in using, in the same encyclopedia, one word with various meanings”.84

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6.3 A non-confrontational dialectic implies an eclectic perspective and a cooperative division of labor, as we have just seen. Does it also imply the fusion between the two branches of Leibnizian dialectic? The temptation to answer “yes” is great, especially if one recalls that the satisfaction of the non-confrontational drive presupposes the possibility of conciliation between apparently contrary positions: What will Leibniz do? Notice that he lives among scholars who believe in the incompatibility of the two methods. Will he reject the ancients’ method? Not at all; for such exclusion does not fit his method, which tends to conserve everything by reconciling things that seem to be contrary to each other (Boutroux 1948: 78–79).

This is however, a reply to a rather different question, which has to do not with the two branches of Leibnizian dialectic, but with two variants of one of them – the hard one. Leibniz’s dilemma, as presented by Boutroux (1948: 78), was whether to abandon entirely syllogistic logic once he realized the immense advantages of modern mathematics and the possibility of its generalization into a symbolic logic. But from the viewpoint of the hard-soft opposition, this is a false dilemma, as Boutroux himself promptly points out. Since syllogistic inferences can be brought to a degree of mathematical precision and validity not inferior to that of a logical calculus,85 there is no opposition between them in this respect; hence no need of conciliation. Where there seems to be the need of some sort of “conciliation” – be it in the form of division of labor or some other form of modus vivendi – is between the hard and soft modalities of dialectic, whatever their variants. But can such conciliation be achieved under the tutelage of the overarching “principle of conciliation” Boutroux considers to be an essential piece of Leibniz’s method? I doubt it: if this is indeed a principle of Leibniz’s method – and I agree that it is a strategy cherished by him – it must be a principle of soft dialectic (and rationality), rather than of dialectic (and rationality) tout court; for the simple reason that in hard dialectic exclusion is not ruled out, but quite on the contrary, it is the ruling principle! To elevate the “principle of conciliation” to the status of a governing dialectic principle would amount, therefore, to reducing the hard branch to the soft one, just as to place a formal “principle of calculability” in the position of the overarching dialectic principle would amount to reducing soft to hard dialectic. Instead of either of these blunders, the evidence we have been collecting suggests a non-reductive relationship between the horns of the two-pronged Leibnizian dialectic. It points to a coexistence and cooperation that preserve the difference between these horns because it is thanks to it that the work done by each of them complements that done by the other. Theirs is a harmony that must be itself dialectic – i.e., grounded not in the axiomatic similarity of siblings who stem from a single principle, but in the complementary talents of partners whose shared aims converge. In a letter to Burnett of 1697, Leibniz describes a “Method of Establishments” for overcoming endless disputes and thereby contributing to the advancement of knowledge, which is perhaps the best illustration in his writings of this kind of complementary partnership. It brings together under the same roof two kinds of propositions: those that “can be demonstrated absolutely with metaphysical necessity” and those “that can be demonstrated morally, i.e., in a manner that provides

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moral certainty – as when we know that China or Peru exist, even though we have never seen them and have no absolute proof of it”;86 the co-habitation of these hard and soft kinds of truth in any given field, e.g. theology, requires a method capable of handling harmoniously a hodgepodge of disciplines as varied as, e.g., philosophy, history, hermeneutics, mathematics, jurisprudence, and others. 6.4 A complementarity of this kind between soft and hard dialectic is especially needed in cases such as metaphysics where the highest degree of certainty – which is the obvious desideratum – cannot be reached because the matter at hand does not admit it.87 Therefore, whenever the issue is such that the certainty of necessary truth – the highest possible degree of certainty – is unattainable, means softer than strict demonstration should be used in order to enable the inquiry to reach at least that degree of certainty it is capable of, rather than giving up the quest for certitude altogether. This is why in crucial paragraphs of the Discours de m´etaphysique, Leibniz appeals to soft notions such as reasonableness, presumption and moral necessity in order to justify metaphysical truths fundamental for his system. Important as they are, these truths involve contingency and thus cannot be proved by deductive methods alone; therefore, they must be supported by reasons that “incline without necessitating”, i.e., by reasons that are weaker than deductive proof.88 Even so, the support they provide to metaphysical truth is effective because these reasons occupy the highest rank in the continuum of soft reasons, namely “moral certainty” or “moral necessity”, which – Leibniz stresses – is neither “based upon induction alone”89 nor is equivalent to “mere probability”.90 A physicist, on the other hand, can combine the hard means at his disposal with even softer means than those required by the metaphysician: [He] can account for experimental data by employing sometimes simpler experiments already performed and sometimes geometrical and mechanical demonstrations, with no need of general considerations, which belong to another sphere; and if he makes use of God’s help or of some soul, muse, or the like, he exaggerates as much as someone who, in an important practical deliberation, would wish to engage in grand reasonings about the nature of destiny and of our freedom . . .91

6.5 It is well known that the task of the first of the Essais de Theodic´ee, titled “Preliminary Discourse on the Conformity of Faith and Reason”, is to establish a common ground between these two key domains in Leibniz’s thought. What has not been sufficiently noticed and emphasized, however, is that this task is performed by showing how hard and soft dialectic can and must work together in a non-reductive complementary way in order to achieve the desired conformity. A close look at a few paragraphs of the Discourse should suffice here as a reminder of this important fact. In §30, he claims that good definitions and basic logic alone would be sufficient for determining precisely the borderline between reason and faith, thus resolving once and for all the debate about their respective territories: There wouldn’t be anything as easy as to terminate the disputes about the rights of faith and reason if men wanted to make use of the most vulgar rules of logic and to reason with the minimum of attention. Instead, they get mixed up by oblique and ambiguous expressions . . .92

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In §31 he continues this line of argument, stressing the sufficiency of standard logic for tackling issues that can be solved through necessary inferences. This logic, however, is insufficient in “important deliberations” on matters that need a logic that “goes beyond”, capable of performing such soft reasoning tasks as estimating probabilities: Precision causes us discomfort and rules seem to us childish. This is why vulgar logic (which more or less suffices, however, for the examination of reasonings addressed towards certainty) is left for pupils; and we haven’t even noticed those rules that must govern the weight of probabilities, which would be so needed in important deliberations. The source of most of our mistakes lies in the disregard or imperfection of the art of thinking, for there is nothing more imperfect than our Logic, when one goes beyond necessary inferences; and the best philosophers of our time, such as the authors of the Art of thinking, of the Research of truth, and of the Essay on the understanding,93 are very far from having indicated the appropriate means for helping this faculty of weighing the estimations of truth and falsity . . .94

Such an extension of logic to cover also non-necessary inferences is a sine qua non for deliberation in important matters, especially those discussed in “human tribunals, which are not always able to reach the truth, being often forced to rely upon clues and verisimilitudes, and above all upon presumptions or prejudgments”.95 Yet, although soft considerations of this kind are also needed in the discussion of metaphysical and theological issues such as whether God is an accomplice of the evil he allows for in the world he created, they cannot be automatically transferred to this more complex and subtle domain without further refinement – which Leibniz provides in §33. Here, he points out that, in addition to legitimizing the use of presumptions, their proper dialectic use must also take into account that they are not equal in “strength” and that the possibility of finding reasons against them is not equally accessible for all presumptions. These nuances are what, ultimately, rescues God from the charge of complicity mentioned above. They also illustrate how sophisticated may have to be the logic and dialectic of soft rationality in order to be able to deliver its share in the division of labor discussed in this section. 6.6 But the need for the division of dialectical labor goes deeper. Its source lies in fact in the great metaphysical divide between the necessary and the contingent, which is essential not only for Leibniz’s ontology, for his accounts of creation, of liberty, of truth and rationality, and for epistemology and logic. It is also essential for his practice as well as theory of dialectic. On the side of praxis, it is thanks to this divide that Leibniz can successfully refute the accusations of spinozistic determinism often leveled against him; furthermore, it is by resorting to the distinction between the two branches of dialectic that he can keep at bay the skeptics’ and rationalist theologians’ attacks against his way of conciliation between reason and faith. On the theoretical side, besides the fact that it provides the ground for the distinction between a soft and a hard dialectic, the necessary/contingent divide provides also the basis for their co-habitation and division of labor. It is worth taking a look, however brief, at this Leibnizian tour de force.

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Recall first the dividing points. First, two separate realms correspond to the necessary vs. contingent divide: the set of all possible worlds vs. the one existing actual world. Second, two kinds of truth: the truths of reason and the truths of fact (Monadology §§33, 34). Third, two great principles upon which our reasonings are based: the Principle of Contradiction and the Principle of Sufficient Reason (§§ 31, 32). Fourth, two logics: “Just as the mathematicians have excelled above the other mortals, in the logic, i.e., the art of reason, of the necessary, so too the jurists did in the logic of the contingent”.96 And fifth, the split these distinctions build up seems to be so sharp that dialectic cannot escape it. This calls into question not only the possibility of cooperative division of labor between its two branches, but even the plausibility of the one-dialectic thesis. However, in spite of the sharpness of the divide, it would be a mistake to think the two sides do not share a significant number of features. First, although contingent and necessary truths differ in kind, they must share a concept of truth, just as God and Creatures, being both existents, however different, must share a concept of existence.97 Second, although the PC’s jurisdiction is over necessary truths and it cannot account for contingent ones (otherwise they would all be necessary),98 and although without the PSR “there would be no principle of truth in contingent things”,99 both principles apply in fact to both realms. The contingent realm cannot contain true propositions that violate the PC, for they would be impossible and therefore necessarily false; furthermore, since the actual world is also a possible world, those truths – the necessary ones – that are true in all possible worlds, are also true in it. The PSR, on the other hand, posits that every true proposition must have a reason – and this is precisely the concept of truth shared by necessary and contingent truths. It is “one of the first principles of all human reasoning and after the principle of contradiction it has the greatest use in all the sciences”.100 Third, the difference lies in that a reason for the former is a demonstration that “necessitates”, whereas a reason for the latter merely “inclines”.101 This is what the difference between the “two logics” – the mathematician’s and the jurist’s – amounts to: a different kind of “validity” of their inferences. We are thus back to the hard/soft rationality divide, that stresses the modus operandi of these two kinds of rationality as that which basically characterizes each of them. The impressive metaphysical, epistemological, and logical aura they acquired in this last leg of our corresponding dialectic tour no doubt deepens the significance of the divide, which is confirmed by Leibniz’s tracing it back to God’s own decision: . . .just as God himself decided never to act unless he hast true reasons of knowledge, he created rational creatures so that they never act unless they have prevalent or inclining reasons.102

Nevertheless, the deeper philosophical ground from which the two-pronged dialectics now is seen to flow does not broaden the gap between its soft and hard horns, as we have seen. Rather, it explains why they must be both, substantially different and capable of cooperating in covering the needs of that deepened and broadened ground.

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7 Concluding Remarks Ultimately, I admit that this method of judging and weighing opposed reasons, as if in a balance, has not been elaborated by jurists in such a way as to render the new investigation here proposed superfluous.103

This is but one of the many occasions in which Leibniz acknowledges that one of the “two logics” (see Section 6.6), whose importance and need he had discerned, was far from having been satisfactorily developed. On other occasions, he laments the fact that he himself didn’t do his share in accomplishing this – a plan he had entertained since his youth, and still envisages achieving in his late years, time and health permitting: . . .no one has as yet given us the scales that would serve to weigh the force of reasons. This is one of the greatest defects of our logic whose effect we indeed experience in the most important and serious matters of life . . . It is almost thirty years ago that I made these remarks publicly, and since then I have performed much research in order to lay the foundations of such an undertaking, but a thousand distractions have prevented me from spelling out the philosophical, juridical and theological elements I had planned. If God grants me further life and health, I will make it my main endeavor.104

But his concern with the logic of the contingent, the soft logic the jurists ought to have developed and systematized, is only part of his concern with the creation of a comprehensive “new logic”. He expresses this desideratum already in 1677, in a writing explicitly titled After so many logics, the logic I want has not yet been written.105 The topics the desired logic should contain, according to this text, form a mixed list, including themes treated in Scholastic as well as “modern” treatises, traditional problems not yet satisfactorily handled, according to Leibniz (e.g., “oblique inferences”; cf. DA: Chapter 31C), and also issues dealt with in the contemporary “dialectics” literature (e.g., a variety of loci, including “argumentative loci, which can also be called “means of arguing”106 ). Other references, direct or indirect, to the needs of the new logic vary in content, usually mentioning probabilities (e.g., DA: Chapter 23), methods for resolving controversies (e.g., DA: Chapter 28), presumptions (e.g., DA: Chapters 36, 38), juridical logic (e.g., DA: Chapter 45), as well as formalization. Formalization is no doubt his main objective in the impressive logical work he performs in the annum mirabilis of 1686 (e.g., the Elements of Reason, A VI 4 713–729; and especially the General Inquiries, A VI 4 739–788): “This is precisely what I am presently working at – to devise formulae or general laws applicable to all kinds of reasoning”; but the other targets in the expansion of logic are not forgotten, as Leibniz’s mentioning – immediately after the above statement – of our familiar balance, albeit in its hard version, shows: “as if we were to make use of an arithmetical calculus or to weigh the truth in a balance, with the help of an evaluative table”.107 Although stressing, in these writings, that correct form (recta forma) is that which is present in every reasoning whose conclusion is reached by the force of form (vis formae), Leibniz makes clear that this is not the case only in mathematical reasoning. Any kind of argumentation that is systematic enough

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to “prevent the mind from wandering and tottering”, including “the art of human language” as practiced by good orators, preserves form and ensures its conclusive power (ibid.). It is tempting to extend this broadening of “form” even more, making it cover also those cases where structure and order are methodically respected and prevent “wandering and tottering”, even though “the force of form” that yields the conclusion inclines without necessitating. This would be the case with at least some instances of “dialectical form” (see Section 5). This move, perhaps barely hinted at in the Elements of Reason, might help to explain the wandering and tottering of Leibniz’s search for an encompassing new logic, sometimes separating and sometimes putting together hard and soft rationality, as well as for a unified one-dialectic with non-reducible-to-each-other hard and soft horns. “For ultimately”, he writes, what is a judicial process if not the form of disputing transferred from the schools to life, purged of vacuousness and limited by public authority in such a way that it is illicit to wander about or to twist or to omit whatever can be shown to be relevant for the search of truth?108

Leibniz, who depicts in a moving auto-biographical report (K 4 452–454; see DA i–ii) his main motivation for his studies of hard rationality as being his interest in the solution of controversies, particularly the theological ones, would presumably have agreed to the suggested move. He sincerely regretted not having developed neither a hard nor a soft dialectic, nor some combination of both, nor even a blueprint for his disciples to develop a sufficiently rich dialectic capable of achieving this major aim. At times he felt the irenic negotiations in which he so intensely participated were close to success, and he may have attributed their failure to the lack of method he himself might have avoided. But he should not be so sad, after all. For, as someone who left so many writings unpublished entrusting to posterity the making of good use of them, he deserves to be acknowledged, as far as his contribution to rationality and dialectic is concerned, not as the author of this or that particular method, but rather as what Foucault calls a “fondateur de discursivit´e”. By these he means “authors who are not only the authors of their works, of their books. They have produced something more: the possibility and the rule of formation of other texts . . .they have established an infinite possibility of discourses” (1969: 832–833). In the case of Leibniz, the title “fondateur de discursivit´e” is perhaps even more justified than in the cases of Freud or Marx, to whom Foucault attributes it. For the simple reason that the rule of possibility he proposes for the infinite set of discourses is a rationality and a dialectic of tolerance, not of exclusion, a readiness to attend to all discourses and to try to learn from them, and a varied set of means and reasons that permit one to do so. Leibniz’s thus opened dialectic of tolerance may be precisely the space of discursivit´e that we need in order to restore to a world where argument has given room to invective, threat and violence, the ethical and communicative basis through which we can find again a reasonable course. Having initiated this chapter with a motto by Br´ehier, to which I hope to have done justice, permit me to conclude with the last

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words of his article, leaving for another occasion the special attention his pregnant sentence deserves: . . . la discussion reste donc le seul moyen humain d’assurer la communication et finalement la communion des esprits; la raison n’est pas intol´erante; la tol´erance a, au contraire, un fondement rationnel (Br´ehier 1946: 390). Acknowledgments I wish to express my warm thanks to Varda Dascal, for the profound interest and patience she showed in listening to and discussing with me the interpretation of Leibniz’s texts, for making very useful suggestions, and for accompanying me with perseverance and unrestricted enthusiasm in completing the writing and preparation of this chapter for publication.

Notes 1. See Dascal (2001, (2003, 2004b, 2005) 2. See Schepers (2004), Goldenbaum (2004), for example. 3. I am referring to the titles of Schepers’ and Dascal’s papers, which indicate their respective stances in the debate, at that point in time. 4. I am deliberately restricting in this chapter the term “dialectic” to “art of controversies”, thereby focusing on a rather narrow part of the broad range of argumentation-related phenomena this term traditionally covered. Though Leibniz himself didn’t use this term for referring to controversy or other forms of debate, my terminological choice fits his more general concern with an ars inveniendi (“art of discovery”) for the advancement of knowledge. Leibniz in fact extended considerably the Ciceronian and Renaissance Topics or Dialectics, conceived as an “art of finding arguments”, to a whole set of tools useful for discovery, ranging from mathematics and semiotics to museums and the encyclopedia, and arguably including the art of properly conducting disputes and solving controversies. 5. The expressions in inverted commas in this paragraph are key notions in Leibniz’s important article “Meditationes de cognitione, veritatis et ideis”, of November 1684 (“Meditations on knowledge, truth, and ideas”; A VI 4 585–592; L 291–295), to which he often refers. 6. For typical expositions of the project, see, e.g., Chapters 14, 21, 28 and 30 of DA. 7. To be sure, some of the “numerical” calculi (e.g., A VI 4 221–227; 228–236; 242–250), in which the validity of syllogistic as well as non-syllogistic inferences was checked by using numbers, might be adapted for this purpose with relative ease, by matching the “alphabet of human thoughts” and its “syntax” (once available) with numbers and arithmetical operations. 8. “Calculus vel operatio consistit in relationum productione facta per transmutationes formularum, secundum leges quasdam praescriptas factis” (Fundamenta calculi ratiocinatoris, 1688; A VI 4 921; English transl. in Dascal 1987: 183). 9. “Characterem voco, notam visibilem cogitationes repraesentantem” (De characteribus et de arte characteristica, 1688; A VI 4 916). 10. “Ars characteristica est ars ita formandi atque ordinandi characteres, ut referant cogitationes, seu ut eam inter se habeant relationem, quam cogitationes inter se habent” (ibid.). 11. “Patet igitur, formulas . . ., relationes, et operationes se habere ut notiones, enuntiationes, et syllogismos” (Fundamenta calculi ratiocinatoris, 1688; A VI 4 920; English transl. in Dascal 1987: 183). 12. “. . .Verum Organon Scientiae Generalis omnium quae sub humanam ratiocinationem cadunt” (Fundamenta calculi ratiocinatoris, 1688; A VI 4 920; English transl. in Dascal 1987: 182). 13. “Calculus quidam novus et mirificus, qui in omnibus nostris ratiocinationibus locum habet, et qui non minus accurate procedit, quam Arithmetica aut Algebra. Quo adhibito semper terminari possunt controversiae quantum ex datis eas determinari possibile est, manu tantum ad calamum admota; ut sufficiat duos disputantes omissis verborum concertationibus sibi

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14.

15. 16.

17.

18.

19. 20.

21.

22.

23.

24. 25.

26. 27.

M. Dascal invicem dicere: Calculemus. . . .Ostenditur etiam modus disputandi in forma, conveniens tractationi rerum, a taedio Scholasticorum syllogismorum vacuus, et supra distinctiones illas positus, quibus in scholis alter alterum eludit” (Synopsis libri cui titulus erit: Initia et Specimina Scientiae novae Generalis pro Instauratione et Augmentis Scientiarum ad Publicam Felicitatem, 1682; A VI 4 443; DA 216–217). “. . .sed perpetuis calculi evidentis demonstrationibus vestitae contineatur . . .Characteristica nostra, seu ars signis exacto quodam calculi genere utendi” (Fundamenta calculi ratiocinatoris, 1688; A VI 4 920; English transl. in Dascal 1987: 181). “Omnis humana ratiocinatio signis quibusdam sive characteribus perficitur” (Fundamenta calculi ratiocinatoris, 1688; A VI 4 917; English transl. in Dascal 1987: 182). “Notandum autem est linguam hanc esse judicem controversiarum, sed tantum in naturalibus non vero in revelatis, quia Termini minuscule mysteriorum Theologiae revelatae non possunt recipere analysin, alioqui perfecte intelligerentur, nec ullum in illis esset mysterium. Et quoties vocabula communia ex necessitate quadam transferuntur ad revelata, alium quondam induunt sensum eminentiorem” (Analysis grammatica ad characteristicam seu linguam generalem condendam, 1686; A VI 4 800–801). “Je m’estois propos´e une methode tout a` fait particuliere, qui avoit deux grands avantages, premierement en ce qu’elle ne pouvoit estre desapprouv´ee de qui que ce soit, et en deuxi`eme lieu, parce qu’elle conduisoit a` la fin, et donnoit un moyen asseur´e de conclure” (Des controverses, 1680; A IV 3 204–205; DA 202). “La variet´e d’´etudes que j’ay est´e oblig´e de cultiver, ayant interrumpu il y a longtemps le dessein que j’avois de travailler a` une discussion exacte de quelques controverses” (ibid., p. 204). Presumably, this reference is to the series of papers belonging to the Demonstrationes Catholicae of the late 1660s (A VI 1 489–559). See Sections 6.3, 7. “. . .un Geometre qui entend la vraye analyse . . .” (Des controverses, ibid., p. 205). “. . .qu’il n’y a rien qui rende la dispute plus recommendable que la moderation de ceux qui disputent: or je pretends que cette moderation paroistra icy d’une maniere toute particuliere et incontestable . . .parce qu’icy, dis-je, la nature de la dispute oblige les gens a` parler moderement malgr´e eux” (ibid., pp. 205–206). “. . .je pretends en un mot d’ecrire des controverses en sorte que le lecteur ne puisse point juger quel party l’auteur peut avoir e´ pous´e. . . .On sera oblig´e de reconnoistre que la forme de mon dessein m’obligeoit a` la moderation” (ibid., p. 206). 1. Each disputant chooses his own order and orders as he pleases both the adversary’s reasonings and his own; 2. disputes tend to thicken and inflate themselves; 3. disputants hide or weaken the adversary’s arguments when they report them; 4. repetition of the reasons adduced, without taking into account the adversary’s replies; 5. digression, as when one engages in a discussion of some lateral difficulty, where one believes one is able to obtain some advantage over the adversary (ibid., pp. 209–210). “J’ose dire que la methode dont je pretends me servir retranche tous ces embarrass a` veue d’oeil et les exclut formellement. Car on verra une representation si fidele des raisons de part et d’autre, que tout lecteur n’aura besoin que de bon sens pour juger sans que le rapporteur soit oblig´e de declarer son panchant” (ibid., p. 210). “il sera ordinairement ais´e a` un homme de bon sens de juger sur le rapport qui a est´e fait sans que le rapporteur ait besoin de se declarer” (ibid., p. 212). “Si tous les hommes avoient la bonne volont´e que j’ay, et si tous ceux qui ont de la bonne volont´e avoient les lumieres penetrantes de Vostre Altesse, nous n’aurions pas besoin de Methode dans les disputes” (ibid., p. 208). For this terminology and typology, see Dascal (2002: 160–161; 2004a: 40–41). Examen Religionis Christianae (A VI 4 2355–2455). This long and detailed text, virtually complete, written in the anus mirabilis of 1686, remained unpublished until it was “discovered’ about a century later by Catholic theologians, who published and divulged it under the title “Systema Theologicum’, along with a French translation. For some additional information and comments on its dialectical nature and strategy, see Dascal (2003: 134–137).

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28. “Cum diu multumque invocato divino auxilio sepositique, quantum forte homini possibile est, partium studiis perinde ac si ex novo orbe neophytus nulli adhuc addictus venirem controversias de religione versaverim; haec tandem mecum ipse statui, atque expensis omnibus sequenda putavi, quae et Scriptura sacra, et pia antiquitas, et ipsa recta ratio et rerum gestarum fides homini affectuum vacuo, commendare videntur” (Examen, ibid., pp. 2356– 2357). 29. The text (and the method) obviously did not and presumably would not work in the context of negotiation for which it was probably written a century earlier – which is presumably why Leibniz, aware of the fact that the minds in both sides were not yet mature for his approach, decided not to publish nor use it in that context, leaving its worthwhile ideas, like those of many others of his writings, for posterity. 30. This is how Jacob Thomasius describes the task his young pupil took upon himself, in the preface, titled “The origin of the controversy on the principle of individuation”, in which he is full of praise for the way Leibniz fulfilled his job of respondens and actually went beyond it. That Thomasius was absolutely right about the complexity of the medieval debate about individuation can be grasped from the excellent systematic analysis provided in Gracia (1988). Thomasius, by the way, published in 1670 an introduction to logic, which includes a treatise on the “process of disputation’, where – unlike Leibniz’s insistence on the importance of a “director’ or “moderator’ – he suggests that this third “agent’ in a disputation (the “president’) is perfectly dispensable, for his task can be performed by the Respondens; he also suggests that the ancient practice of “interrogation’ has been succesfully dispensed in modern disputations and replaced by the use of formal syllogisms (Thomasius 1670: 139– 140). 31. “. . .omne individuum suˆa totˆa Entitate individuatur” (Dissertatio Metaphysica de Principio Individui, 1663; A VI 1 11). 32. “Notum autem est Scotum fuisse Realium extremum, quia universaliaa veram extra mentem realitatem habere statuit . . .” (ibid.; A VI 1 16). 33. “Affirmanti incumbit probatio . . .opponens teneatur, ad probationem” (Specimen Quaestionum Philosophicarum ex Jure Collectarum, 1664; A VI 1 76). 34. “In dubio igitur praevalere posterior debet; ex contractu, ut ita dicam tacito” (ibid.). 35. Lest one would be tempted to say that the second rule is simply a particular case of the first, Leibniz points out that “if, contrary to the order of things, it were up to the one who affirms to prove, the Respondent would adduce proofs, which the Opponent would deny”; consequently, “since most theses are affirmative”, the Opponent would be not an affirmer but a denier, i.e., he would not abide by the first rule. 36. “Quid enim qu`am facile mutatis vocibus negativa in affirmativam et contra transmutari potest? Hˆıc plan`e tolleretur omnis pene disputatio, et antequam inveniri posset, sitne aliqua propositio ex ipsa rei natura affirmative, an negative, infinitis litibus opus esset” (ibid.). 37. “Quare necesse est, quomodocumque licet, erui ex actis et probatis veritatem, ut decidi res possit. Ex hoc sequitur, ut ei imponatur onus probandi qui commodissim`e potest, ne res sine probatione habeat (ibid.). 38. “Apud partes ver`o in foro litigantes non est determinatum universaliter, Actor, an reus teneatur ad probationem, quoniam neque tacitus inter partes de eo contractus intercessit, neque etiam, ut apud Philosophos contemplantes, potest a` sententia et decisione supersederi sine alterius partis praejudicio” (ibid.). 39. “. . .in certissimas ac pen`e mathematicas demonstrationes” (Disputatio Juridica de Conditionibus, 1665; A VI 1 101). 40. Which abound in the De Conditionibus: Out of the 188 explicitly demonstrated theorems, 60 are of this sort, according to Boucher’s count. 41. “Perplexitas autem propri`e dicitur de plicabilibus, quales sunt res flexiles simul et tenaces” (Disputatio Inauguralis de Casibus Perplexibus in Jure, 1666; A VI 1 236). 42. “Nos speramus ex mero jure decidi omnes casus posse” (ibid.; A VI 1 239).

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43. “If occasionally the interpretation is uncertain, one should employ natural reason’s rules of interpretation, and even though these rules and presumptions provide equal support for both parties, the decision should be against the one that relies on some positive law which, though instituted, cannot be sufficiently proved” (Quod si jam interpretatio incerta est, adhibendae regulae interpretandi rationis naturalis, et etsi pro utraque parte aequales regulae et praesumtiones militant, judicandum contra eum, qui se in Lege aliqua positive, quam tamen introductam satis probare non potest, fundat; ibid., A VI 1 240). 44. Of these, only the De Conditionibus was substantially revised and was published under the title Doctrina Conditionum, being reproduced in the Academy edition of the Specimina Juris. The revisions, for the most part minor corrections, of the other two disputations are indicated in footnotes of the Academy’s edition of their original editions (A VI 1 231–256; 69–95). 45. The picture in the title page, which I am not going to comment upon here, is also very rich in its allusions and deserves careful study. I should only mention that it is also a tool Leibniz uses for helping the reader to understand some of his points in text I, the De Casibus Perplexis (see A VI 1 243). 46. The questions treated in II may be also considered “more pleasant” (i.e., less technical, hence more easily readable) than the difficulties of I and the chains of definitions and demonstrations of III. In any case, amenity refers to a kind of pleasantness that is related to softness and softness is related precisely to this kind of pleasantness. Amenior, therefore, is here conveying roughly the same idea as blandior (“softer”, “more caressing”) conveys in a text where Leibniz argues that the “asperity” of mathematical demonstration which compels the mind should be mitigated by a “softer” mode of treating problems that is also able to persuade (mathematicarum asperitas blandiore quadam ratione . . .mitiganda est; A VI 4 342; translated in DA 133). This parallel between two texts written ten years apart, both referring to the Leibnizian idea of encyclopaedia, and one of them deliberately highlighting softness seems to me far from casual. 47. Examples of Leibniz’s argumentation strategies in theological debates and Church politics other than the two instances discussed in this section can be found, e.g., in DA (Chapters 7, 8E, 27, 32–35, 40, 41). 48. For an analysis of the special position of this text among Leibniz’s argumentative strategies in theological controversies, see Dascal (1987: Chapter 6); for its epistemological dimension in the second part of the Short Commentaries, where the “balance of reason” model becomes “hard”, see Dascal (2005). On the presence of two different interpretations of the balance metaphor in this text, see Section 5. 49. “. . .ad vindicationem veritatis contra insultus Atheorum, infidelium, haereticorum quibus impossibilitates et implicatam contradictionem non crepantibus tant`um sed etiam exponentibus, neque rectius neque profundius occurri potest qv`am demonstratione possibilitatis; ut enim unica clara definitio compendium est mille distinctionum, ita unica clara demonstratio compendium est mille responsionum. Possibilitatis enim modo semel clar`e exposito, apparet statim omnes objectas impossibilitates falsa hypothesi sententiaqve oppugnata non intellecta niti et aliorsum pertinere” (De demonstratione possibilitatis mysteriorum Eucharistiae, 1671; A VI 1 515). 50. “In his nulla propositio admittenda est tanquam sit de fide, quae non in terminis Scriptura Sacra ad verbum ex fontibus versa continetur” (Short Commentary on the Judge of Controversies, or the Balance of Reason and the Textual Norm, §12; A VI 1 549; DA 9). 51. “Sed superset non modica difficultas. Nam fides est sensˆus, non vocum, non sufficit igitur nos credere verum locutum esse qui hanc propositionem dixit, hoc est corpus meum; nisi sciamus etiam quid dixerit. Non autem scimus quid dixerit si verba tant`um teneamus, ignorata vi et potestate” (ibid., §20; A VI 1 550; DA 11). 52. “Durissimus hic nodus est. Sed solubilis tamen. Respondeo enim non semper esse opus ad fidem, ut sciamus quis sensus verborum sit verus, dummodo eum intelligamus, nec rejiciamus positive sed circa eum nos habeamus dubitative, etsi ali`o inclinemus. Im`o sufficit interdum quod credamus: quicunque in iis sensus contineatur eum esse verum, idque inprimis in

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53.

54. 55. 56. 57. 58. 59.

60.

61.

62. 63.

64.

65.

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mysteriis in quibus praxis non variat, quisquis tandem sit sensus” (ibid., §21; A VI 1 550; DA 11). “Sed quid de sensu improprio? Eo casu id officium Christiani puto: audiendo verba textus: ea arripere tanquam vera sub sensu proprio, cum pia tamen simplicitate, quae cogitet posse se falli, et fortasse veram esse propositionem sub sensu tropico, sed tamen sic tutius agere. Et ita fides ista erit disjunctiva, inclinans tamen in unam partem. Et hoc revera si attendas in praxi plerique Christiani faciunt” (ibid., §24; A VI 1 551; DA 12). I have italicized here expressions used either in the passages quoted above or in the title of the Short Commentary. Compare, for example, the De Conditionibus of 1665 with the Elementa Juris Naturalis of 1669–1671 (A VI 1 431–485). “Confusanae disputatio est in qua forma ratiocinandi non servatur” (Vitia Disputationis Confusanae §1; A VI 2 387). “. . .nihil sine probatione dicatur et nihil nisi formaliter concludatur” (ibid., p. 389). When Leibniz wishes to emphasize the power and advantages of formal logic, he usually talks of reasoning “in forma”. See Dascal (1978: 212–214) and DA 19, 125, 180, 226, 379. “Si igitur huius rei causa replicatur tunc vel replicatur interruptis verbis vel continuis quasi perorationibus. Si replicatur interruptis verbis, seu interpellare alterum licet tunc haec mala sequuntur (1) quod non licet pertexere telam rationis suae, (2) quod obliviscimur aliarum rationum dum de hac altercamus, . . .(4) auditores in illa inordinate reciprocatione omnium hinc inde tandem obliviscuntur, aut confunduntur; et ita cessat fructus tum convincendi adversarium, qui ab uno ad aliud transsilire, eludereque ratiocinantem, et rem in infinitum protrahere licet; tum persuadendi caeteros confusos aut taedio affectos” (Vitia Disputationis Confusanae §8; A VI 2 388; DA 3). “Si quis director adest, id est in cujus potestate est quaestiones formare ut lubet et disputationem interrumpere et finire ubi lubet (etiamsi autoritatem alios movendi non habeat, de hac enim nollo hic locui) tunc posito quod is director sit prudens et bonus, res exitum reperire possunt. Director enim vel ab initio format quaestiones praeliminares, vel eas format ex disceptationibus partium. . . .Et omnino cavere potest ne ulla ratio sine refutatione relinquatur . . .Si quis igitur detur director bonus et sagax, tunc spes est pleraque recte confici posse” (ibid. §11, p. 389; DA 4). “Sed directores plerumque sunt parum sagaces et periti; interdum vero sagaces se mali, et utuntur arte illa formandi quaestiones . . .tantum in rebus sibi utilibus” (§11, ibid., p. 389; DA 4). “Nam plerumque rationes aut ultimae aut primae aut peculiari quadam circumstantia prolatae solent potissimum animis infixae manere, et a directore aliisve arripi” (§12, ibid., p. 389). These rules would, among other things, permit to conduct a dispute “without omitting or repeating anything, without there being a reason without a response nor a response without its reply, without shifting to another theme before concluding the preceding one, without anything being said without proof, and nothing being concluded except formally” (“. . .et nihil possit omitti, et nihil possit bis dici, et nulla ratio sine responsione, et nulla responsio si patitur sine replicatione praettermitatur, et a nulla re nisi confecta ad aliam transsiliatur, et nihil sine probatione dicatur, et nihil nisi formaliter concludatur”; ibid. §14, p. 389). The manuscript of the Vitia contains in §1 another, erased definition of confused dispute, which has been replaced by the one with which we opened the present section. This erased definition says: “[Confusanea Disputatio est] in qua ordo argumentandi non est” (“in which there is no order of argumentation”; §1, ibid., p. 387). Methodus disputandi usque ad exhaustionem materiae (A VI 4 576–578; DA 155–157). Leibniz made sure the dialectic element would not be overlooked by adding to the title the German Kunst ausszudisputieren “art of disputing”, as the proper way of understanding “methodus disputandi”, thus stressing the difference between disputing with an adversary (ausszudisputieren) and merely disputing an issue (disputieren). I am grateful to Gerd Fritz for this philological information.

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66. “[This method will ensure] that no party can say anything that is not at least pertinent to the matter at hand or that has already been affirmed or refuted. The same method serves in every deliberation, in replying in judicial proceedings, in terminating philosophical or theological controversies, and, in general, wherever many things are said in a misleading way” “Ut scilicet nihil amplius utrinque dici possit, quod non vel parum ad rem pertineat, vel jam sit dictum aut refutatum. Eadem Methodus prodest in omni deliberatione, in referendo ex Actis judicialibus, in finiendis controversiis philosophicis aut theologicis, et omnino ubicunque utrinque multa speciose proferuntur” (ibid., p. 577). 67. “Forma sive ordo ipse consistet in conjunctione duarum maximarum inveniendi atrium, Analyticae et Combinatoriae” (Consultatio de naturae cognitione, “Advice on the knowledge of nature”, 1679; A IV 3 871). 68. For example: “II. The work is divided among the members according to the preferences and commodity of each; . . .IV. The contribution of each member will be acknowledged publicly and privately by the society; . . .VII. Everyone collects the explored experiments pertinent to his topic; VIII. Everything is to be expressed not through dissertations or narratives, but through [concise] positions; . . .XIV. No experiment is to be reported that is not acknowledged as either performed by the writer himself or as communicated to the writer or to a friend of his by a reliable person” (“II. Labor inter socios pro gustu et commoditate cujusque dividatur; . . .IV. Quod quisque praestiterit, societas grata publice privatumque agnoscet; . . .VII. Unusquisque colligat experimenta explorata quae rem suam tangunt. VIII. Omnia exprimantur non per dissertationes seu narrationes, sed per positiones; . . .XIV. Nullum scribatur experimentum, quod non sit in confesso, aut factum ab ipso scribente, aut communicatum ab alio admodum fide digno, sive scriptore sive amico”; ibid., pp. 871–872). 69. “. . .les logiciens n’ont pas encore examin´e les degr´es de probabilit´e ou de vraisemblance qu’il y a dans les conjectures ou preuves qui ont pourtant leur estimation aussi asseur´ee que les nombres; cette estimation nous peut et doit servir non pas pour venir a` une certitude, ce qui est impossible, mais pour agir le plus raisonnablement qu’il se peut sur les faits ou connoissances qui nous sont donn´ees” (Nouvelles Ouvertures, 1686; A VI 4 689; DA 233). 70. See, for example, the concluding passage of On controversies on sacred matters of 1677: “Reasons are either proofs, or presumptions, or semi-proofs or probabilities. For them to provide a sensible sign, they must be arranged in a certain form so that the evidence of the truth becomes apparent. Above all one needs this form when what is in question is establishing the mute or oral authority of the judge himself. For the final judge regarding the judge is reason” (“Rationes sunt aut probationes, aut praesumptiones, aut semiprobationes seu probabilitates. Quae ut faciant notam sensibilem certa forma proponendae sunt; ut appareat evidentia veritatis. Et hac forma inprimis opus est, cum de ipso judice vel autoritate muta vel vocali stabilienda agitur. Ultimus enim de judice judex ratio est”; De controversiis sacris generalibus; A VI 4 2163–2167, DA 49–56; p. 2167). 71. “. . .est ipsa Recta Ratio in abstracto sumta, hanc ego judicem controversiarum in mundo esse debere ajo” (Commentatiuncula de Iudice Controversiarum seu Trutinˆa Rationis et normˆa Textus, §52; A VI 1 555, DA 18). 72. “Ea autem Ars est vera Logica, et adhibita qvaedam forma procedendi plane exacta et rigorosa, omnia sophismata excludens” (ibid., §61; DA19; p. 556). 73. “ Nam cum qvaestio est de calculo subducendo, non est opus judice, qvia si tant`um diligenter id est attent`e nihil transsiliendo numeretur, evidentissim`e emergit necessaria conclusio . . .manifesto judicio ejusmodi evidenter demonstrabilia esse arbitrio judicis eximenda et relinqvenda trutinae rationis (ibid., §58; DA19; p. 556). In the second part of this quotation Leibniz is referring to judges in a law court whose verdicts contradict the terms of the law and must, therefore, be “mechanically” corrected. 74. “De judice controversiarum humanarum seu Methodo infallibilitatis, et quomodo effici possit, ut omnes nostri errores sint tantum errores calculi, et per examina quaedam facile possint justificari” (Paraenesis de Scientia Generali Tradenda; A VI 4 975). 75. A few lines before the quotation above, a balance is mentioned: “On the degrees of probability, or the balance of verisimilar reasons” (“De gradibus probabilitatis, seu Libra rationum verisimilium”; ibid.). It seems significant that, in different contexts, Leibniz makes use of

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76.

77.

78.

79.

80.

81.

82. 83.

84.

85.

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different Latin words for “balance”, namely “trutina” (in DA: Chapter 2), “statera” (in DA: Chapter 5), and “libra”, as well as of a compound expression that seems to be a neologism of his own coinage, “logometric balance” (DA 38). Although basically synonymous, each of the Latin terms refers to different properties or conditions of use of a balance – respectively, general daily use; precision, as required by jewelers; instrument of measure. “. . .just as the other sciences have to access certainty following the example of mathematics, so too the asperity of mathematics must be mitigated by a softer mode of proceeding that follows the example of the other sciences . . .” (“. . .quemadmodum aliae scientiae exemplo mathematicarum ad certitudinem eniti debent, ita vicissim mathematicarum asperitas blandiore quadam tractandi ratione caeterarum exemplo mitiganda est . . .”; Project of a New Encyclopedia to be written following the method of invention, 1679; A VI 4 342, DA 133). “. . .saepe mala esse cessant per usus bonos; . . .Omne autem falsiloquium sua natura esse peccaminosum neque ratione neque Sacrarum Scripturarum autoritate demonstrari potest” (Saying a falsity is not condemnable, 1700; GR 702; DA 152). “. . .neque enim quisquam facile in publica ejusmodi collatione nisi accedant secretae rationes aut singularia insueta artificia, ab opinione sua ad opinionem alterius transit, praesertim in juridicis; . . .quod secus plerumque est in deliberationibus politicis, ubi proprium interesse necessitate saepe ad deserendam opinionem suam et mittendam pertinaciam” (Vitia Disputationes Confusaneae §7; A VI 2 388; DA 3) “. . .sim lecturus avid`e, et, quantum licebit, studios`e, quidquid a te proficiscitur, dubitare non debes. Sed censuram exercere, majoris operae est, nec a me exspectandae, qui natura atque instituto ita comparatus sum, ut in aliorum scriptis poti`us quaeram profectus meos, quam defectus alienos” (Letter to Placcius, 17 April 1695; D VI 1 53, DA 297). “Ego diuturno usu didici nihil facile spernere. Profundae illiae meditationes in omni doctrinarum genere habent et ipsae usus suos, etsi non tam obvios. Itaque quod de variis interpretationum generibus meditatus est, majore solito akribeia mihi applausus poti`us, qu`am contemtum mereri videtur, excitandosque poti`us doctos ad notiones illas enucleatiores prosequendas, qu`am deterrendos” (ibid.). None of these perspectives should be a priori discarded as worthless. This includes, contrary to the attitude of many of Leibniz’s “modern” contemporaries, paying due attention to ancient books as sources of valuable knowledge. Locke, for example, manifests his satisfaction that, given the effort necessary “to find out the true meaning of ancient authors”, we need only to care about the ancient books that “contain either truths we are required to believe, or laws we are to obey”, so that “we may be less anxious about the sense of other authors” (Essay 3.9.10). To which Leibniz replies that, besides the fact that in order to understand the Sacred Scripture and Roman law many other books must be consulted, there is valuable knowledge on other matters and in other ancient sources as well: “Once the Latin, the Greeks, the Hebrews and the Arabs will have been used up”, ancient books of other cultures, e.g., Chinese, Persian, Armenian, Coptic, Indian, will be unearthed and be worth our curiosity and study (NE 3.9.9-10; A VI 6 336). On the combination of a cooperative and a dialectic approach to science, see Dascal (2006). “Il y a des commodit´es et des incommodit´es, des biens et des maux dans toutes les choses du monde sacr´ees et profanes, c’est ce qui trouble les hommes, c’est ce qui fait naistre cette diversit´e d’opinions, chacun envisageant les objets d’un certain cost´e: il n’y en a que tres peu qui ayent la patience de faire le tour de la chose jusqu’`a se mettre du cost´e de leur adversaire; c’est a` dire qui veuillent ave une application e´ gale, et avec un esprit de juge desint´eress´e examiner et le pour, et le contre afin de voir de quell cost´e doit penser la balance” (Conversation du Marquis de Pianese et du Pere Emery Eremite, 1679–1681; A VI 4 2250, DA 173). See also Dascal (2000). “Definitiones communicentur sociis, ut communi deliberatione constituantur, vitandae confusionis causa, ne scilicet in eadem Encyclopaedia idem vocabulum diversimode sumatur” (Consultatio de naturae cognitione, 1677; A IV 3 873). “Aristotle has reasoned with mathematical rigor in establishing his theory of the syllogism” (Boutroux 1948: 79).

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86. “. . .les unes se peuvent demonstrer absolument par une necessit´e metaphysique et d’une maniere incontestable; les autres se peuvent demonstrer moralement, c’est a` dire, d’une maniere qui donne ce qu’on appelle certitude morale, comme nous sc¸avons qu’il y a une Chine et un Perou, quoyque nous ne les ayons jamais vˆus, et n’en ayons point de demonstration absolue” (Letter to Burnett, 1 February 1697; GP 3 193, DA 365). 87. And this is the case because the degree of certainty achievable depends upon the object of inquiry, so that “only that degree of certainty is to be had which a given matter admits”(“Sola certitudinis ratio habenda est, quantam materia capit”; Preface to Nizolius, 1670; A VI 2 409, L 122). 88. Cf. Discours de m´etaphysique §§6, 7, 13, discussed in Dascal (2003: 137–140, 142–143; 2004: 142–143). See also Theodic´ee, Disc. Prel. §2 (GP 6 50). 89. “Sed haec moralis certitudo non fundata est in sola inductione” (Preface to Nizolius, ibid., p. 431). 90. “. . .non tantum probabile, sed et certum est” (On how to distinguish real from imaginary phenomena, 1685–6; A VI 4 1501). 91. “De mˆeme un Physicien peut rendre raison des experiences se servant tantost des experiences plus simples d´eja faites, tantost des demonstrations geometriques et mechaniques, sans avoir besoin des considerations generales, qui sont d’une autre sphere; et s’il employe le concours de Dieu ou bien quelque ame, Arch´ee ou autre chose de cette nature, il extravague aussi bien que celuy qui dans une deliberation importante de practique voudroit entrer dans des grands raisonnemens sur la nature du destin et de nostre libert´e . . .” (Discours de m´etaphysique, §10; A VI 4 1543–1544). 92. “Il n’y auroit rien de si ais´e a` terminer que ces disputes sur les droits de la foy et de la raison, si les hommes vouloient se servir des regles les plus vulgaires de la Logique, et raisonner avec tant soit peu d’attention. Au lieu de cela, ils s’embrouillent par des expressions obliques et ambigues . . .” (Theodic´ee, Disc. Prelim. §30; GP 6 68). 93. A. Arnauld and P. Nicole, La logique ou l’art de penser (1662); N. Malebranche, De la Recherche de la Verite (1674); J. Locke, An Essay Concerning Human Understanding (1689). 94. “L’exactitude nous gˆene, et les regles nous paroissent des puerilit´es. C’est pourquoy la Logique vulgaire (laquelle suffit pourtant a` peu pr`es pour l’examen des raisonnemens qui tendent a` la certitude) est renvoy´ee aux ecoliers; et l’on ne s’est pas meme avis´e de celle qui doit regler le poids des vraisemblances, et qui seroit si necessaire dans les deliberations d’importance. Tant il est vray que nos fautes pour la plupart viennent du mepris ou du defaut de l’art de penser; car il n’y a rien de plus imparfait que nostre Logique, lorsqu’on va au dela des argumens necessaires; et les plus excellens philosophes de nostre temps, tels que les Auteurs de l’Art de penser, de la Recherche de la verit´e, et de l’Essai sur l’entendement, ont et´e for eloign´es de nous marquer les vrais moyens propres a` aider cette facult´e qui nous doit faire peser le apparences du vray et du faux . . .” (Theodic´ee., Disc. Prelim. §31; GP 6 68). 95. “. . .dans les Tribunaux des hommes, qui ne sauroient tousjours penetrer jusqu’`a la verit´e, on est souvent oblig´e de se regler sur les indices et sur les vraisemblances, et surtout sur les presomptions ou prejug´es . . .”(Theodic´ee, Disc. Prelim. §32; GP 6 69). 96. “Ut Mathematicos in necessariis, sic Jurisconsultos in contingentibus Logicam, hoc est rationis artem, prae caeteris mortalibus optime exercuisse” (Towards a Balance of Law concerning the Degrees of Proofs and of Probabilities, 1676; C 211, DA 36; italics in original). Immediately following this statement there is a detailed list of typically soft dialectic tools that can be learned from jurists as “logicians of the contingent’. 97. “Nihilominus, quia tam Deum quam Creaturas existere dicimus, et necessarias non minus quam contingentes propositiones dicimus esse veras, necesse est ut communis aliqua sit existentiae notio et veritatis” (On Contingency, 1686; GR 303). 98. “Veritates contingentes non possunt reduci ad principium contradictionis, alioqui omnia forent necessaria . . .” (ibid.).

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99. “Nisi daretur tale principium, nullum daretur principium veritatis in rebus contingentibus, quia principium contradictionis utique in illis locum non habet” (ibid., p. 305). 100. “Et hoc est inter prima principia omnis ratiocinationis humanae, et post principium contradictionis, maximum habet usum in omnibus scientiis” (Introduction to a Secret Encyclopedia, 1683; A VI 4 529, DA 222). 101. “Commune omni veritati mea sententia est ut semper propositionis reddi possit ratio, in necessariis necessitans, in contingentibus inclinans” (ibid., p. 303). 102. “Et quemadmodum Deus ipse decrevit nunquam agere, nisi secundum sapientiae rationes veras, ita sic creavit creaturas rationales, ut nunquam agant nisi secundum rationes praevalentes seu inclinantes” (ibid., p. 305). 103. “Postremo fateor hanc quam ego profero dijudicandi, et ratione[s] inter se conflingentes velut in bilance expendendi methodum, nec apud Jurisconsultos in traditam esse, ut novo studio nostro non fuerit opus” (Towards a Balance of Law; C 214, DA 39). 104. “. . .personne ne nous a donn´e encore cette balance qui doit servir a` peser la force des raisons. C’est un des plus grands defauts de nostre Logique, dont nous nous ressentons mˆeme dans les matieres les plus importantes et les plus serieuses de la vie . . .Il y a presque trente ans que j’ay fait ces remarques publiquement, et depuis ce temps j’ay fait quantit´e de recherches, pour jetter les fondemens de tels ouvrages; mais mille distractions m’ont empech´e de mettre au net ces Elements Philosophiques, Juridiques et Theologiques que j’avois projett´e. Si Dieu me donne encor de la vie et de la sant´e j’en feray ma principale affaire” (Letter to Burnett, 1 February 1697; GP 3 194, DA 366–367). 105. Post tot logicas nondum logica qualem desidero scripta est (A VI 4 8–11). 106. “Loci dialectici sunt loci argumentorum, possunt et vocari media argumentandi” (ibid., p. 9). 107. “Atque hoc ipsum est, quod ego nunc agito, excogitare formulas quasdam sive leges generales, quibus omne ratiocinationis genus astringi possit, perinde ac si calculo arithmetico uteremus, aut tabula quadam aestimatoria, veritatem quasi in bilance expenderemus . . .” (Elements of Reason, 1686; A VI 4 719). 108. “Postremo quid aliquid est processus judiciarius quam forma disputandi a scholis translata ad vitam, purgata ab inaniis, et autoritate publica ita circumscripta, ut ne divagari impune liceat, aut tergiversari, neve omittatur quodcunque ad veritatis indagationem facere videri possit” (Towards a Balance of Law; C 211, DA 36).

References Belaval, Y. 1960. Leibniz critique de Descartes. Paris: Gallimard. Belaval, Y. 1961. “Pr´esentation”. In G.W. Leibniz (1961), pp. 9–21. Boucher, P. 2002. “Introduction”. In G.W. Leibniz (2002), pp. 9–66. ´ 1948. La Philosophie Allemande au XVIIe Si`ecle: Les Pr´ed´ecesseurs de Leibniz: Boutroux, E. Bacon, Descartes, Hobbes, Spinoza, Malebranche, Locke. Paris: Vrin. ´ 1946. Leibniz et la discussion. Revue Philosophique de la France et de l’Etranger ´ Br´ehier, E. 137: 385–390. Dascal, M. 1978. La s´emiologie de Leibniz. Paris: Aubier-Montaigne. Dascal, M. 1987. Leibniz: Language, Signs, and Thought. Amsterdam: John Benjamins. Dascal, M. 2000. Leibniz and epistemological diversity. In A. Lamarra and R. Palaia (eds.), Unit`a e Molteplicit`a nel Pensiero Filosofico e Scientifico di Leibniz. Firenze: Leo S. Olschki, pp. 15–37. Dascal, M. 2001. Nihil sine ratione → Blandior ratio. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress). Berlin: Leibniz Gesellschaft, pp. 276–280. Dascal, M. 2002. Leibniz y las tecnolog´ıas cognitivas. In A. Andreu, J. Echeverr´ıa, and C. Rold´an (eds.), Ciencia, Tecnolog´ıa y Bien Com´un: La Actualidad de Leibniz. Valencia: Editorial Universidad Polit´ecnica de Valencia, pp. 159–188.

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Dascal, M. 2003. Ex pluribus unum? Patterns in 522+ texts of Leibniz’s S¨amtliche Schriften und Briefe VI 4. The Leibniz Review 13: 105–154. Dascal, M. 2004a. Language as a cognitive technology. In B. Gorayska and J.L. Mey (eds.), Cognition and Technology: Co-existence, Convergence and Co-evolution. Amsterdam: John Benjamins, pp. 37–62. Dascal, M. 2004b. Alter et etiam: Rejoinder to Schepers. The Leibniz Review 14: 137–151. Dascal, M. 2005. The balance of reason. In D. Vanderveken (ed.), Logic, Thought and Action. Dordrecht: Springer, pp. 27–47. Dascal, M. 2006. Die Dialetik in der kollekiven Konstruktion wissenschaftlichen Wissens. In W-A. Liebert and M-Denis Weitze (eds.), Kontroversen als Schl¨ussel zur Wissenshaft? Wissenskulturen in sprachlicher Interaktion. Bielefeld: Transcript, pp. 19–38. Foucault, M. 1969. “Qu’est-ce qu’un auteur?”. Bulletin de la Soci´et´e Franc¸aise de Philosophie 63(3): 73–104 [Repr. in Dis et e´ crits I, 1954–1975. Paris: Gallimard, 2001, pp. 817–849]. Goldenbaum, U. 2004. Reason Light? Kritische Anmerkungen zu einer neuen Leibnizinterpretation. Studia Leibnitiana 36: 2–21. Gracia, J.E. 1988. Introduction to the Problem of Individuation in the Early Middle Ages, 2nd ed. M¨unchen/Wien: Philosophia Verlag. Leibniz, G.W. 1961. Confessio Philosophi / La profession de foi du philosophe. Transl. Y. Belaval. Paris: Vrin. Leibniz, G.W. 2002. De Conditionibus / des conditions. Transl. P. Boucher. Paris: Vrin. Locke, J. 1967. An Essay Concerning Human Understanding. J.W. Yolton (ed.). London/New York: Dent/Dutton. Schepers, H. 2004. Non alter, sed etiam Leibnitius: Reply to Dascal’s Review Ex pluribus unum?. Leibniz Review 14: 117–135. Thomasius, J. 1670. Erotemata Logica pro Incipientibus. Accessit pro Adultis Processus Disputandi. Leipzig: G.H. Frommann.

Chapter 3

Leibniz’s Rationality: Divine Intelligibility and Human Intelligibility Ohad Nachtomy

1 Introduction My primary purpose in this paper is to account for the presence of and the relations between two pictures of rationality – termed by Marcelo Dascal and Heinrich Schepers “radical” and “softer” reason (Dascal 2003) – in Leibniz’s metaphysics. In his reply to Schepers in the Leibniz Review, Dascal has written: The issue at stake [. . .] is not the existence of ‘soft rationality’ or ‘something like it’ in Leibniz’s writings, which Schepers, in spite of this attempt to downgrade its specificity, does in fact acknowledge. Nor is it the existence of a ‘radical picture’, which Schepers, in spite of his attempts to confine it to the SG mega-project, actually upgrades to the role of the paradigm of recta ratio. The issue is to what extent these pictures differ and how they are related (Dascal 2004: 143).

I fully agree with the last line of the passage above, namely, that a major challenge facing Leibniz’s interpreters is to describe adequately the relations between these two pictures or rather modes of rationality. Accordingly, I will suggest that Leibniz’s two modes of rationality do not exclude one another but rather play complementary roles in his metaphysics. In doing so, I will also attempt to shed some light on Leibniz’s view of possibility, which is an indispensable aspect of his rationalism and plays a crucial role in his philosophy. I will argue that some of the differences between Leibniz’s two pictures of rationality and their complementary roles stem from his supposition of two different contexts of rationality: on the one hand, divine rationality that defines all intelligible concepts formally, and, on the other, human rationality that seeks to represent and discover these concepts by particular examples and pragmatic means. My suggestion is that Leibniz’s two modes of rationality partly correspond to two contexts of rationality, divine intelligibility and human intelligibility, both of which play an essential role in his philosophy. If adequate, this mapping clearly speaks against the attempt to ascribe primacy to Leibniz’s hard or radical rationalism, defended by Schepers

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(2004 and this volume). Rather, I will argue that Leibniz’s two modes of rationality are essential aspects of his logic and metaphysics.1 In the first section, I present Leibniz’s notion of rationality as intelligibility. In the second section, I present the notion of intelligibility in its divine context, which also corresponds to Leibniz’s presuppositions about the notion of possibility. In the third section, I present Leibniz’s notion of intelligibility in its human context. I conclude by pointing out some of the intrinsic connections between these two contexts of rationality in Leibniz’s philosophy.

2 Leibniz’s Rationality as Intelligibility Let me begin with a brief reminder of Leibniz’s two principles of reason and their role: while the principle of contradiction defines the space of logical possibilities and necessities, the principle of sufficient reason is used for choosing the best (and allowing non-deductive deliberation) among logical possibilities. It goes without saying that Leibniz’s notion of rationality itself can be partly characterized through his employment of his “two great principles of reason”. Leibniz is very clear in using the principle of non-contradiction (or self consistency) to characterize the realm of the intelligible, which he equates with the possible. As he writes, “all truths that concern possibles or essences and the impossibility of a thing or its necessity rest on the principle of contradiction . . .” (On Freedom and Possibility (1680–1682); A&G 19). Accordingly, the possible is what can be conceived, that is so as not to make the word ‘can’ occur in the definition of ‘possible’ what is understood clearly by an attentive mind; the impossible—what is not possible (Confessio; A VI 3 126–127).

“What is understood by an attentive mind” is defined by the principle of contradiction, so that, in this sense, any (and only) consistent thought is deemed intelligible or possible. As Leibniz says, “the possible is that which does not imply a contradiction” (A VI 2 475).2 is clear that by “attentive mind” Leibniz refers primarily to God’s mind. As he writes, “God is that which perceives perfectly whatever can be perceived” (A VI 3 519; SR 79). While this view of intelligibility might seem all too familiar, I would like to draw attention to a number of non-trivial features of Leibniz’s rationality that are closely related to it: (1) The scope of rationality is more extensive than that of truth and validity. If intelligibility is defined in terms of self-consistency, it follows that the realm of the rational is more extensive than the realm of truth, as well as of valid inferences. This also extends considerably the traditional scope of logic. Indeed, in Leibniz, logic is not limited to inferential relations between concepts (syllogistics); it also includes the content and structure of concepts. In other words, as Leibniz’s examples amply show, he is not interested only in the formal aspect of concepts but also in their content and semantics. Likewise, logic is not limited to examining the truth value of propositions but also examines their intelligibility and the intelligibility of their

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constituents, that is, the terms from which they are made up. This notion of logic and rationality is intrinsically related to Leibniz’s combinatorial theory of intelligibility, which I shall sketch in Section 3. (2) Leibniz sees logic as intrinsically related to what he calls “Divine Combinatorics” and the human attempt to model it. He considers his logic as a part of a combinatorial activity, which he ascribes both to God and to humans. According to Leibniz, combinatorics is the most general science and, accordingly, its objective is to capture the most general laws of thought.3 In this way, the scope of Leibniz’s logic includes all possibilities or all intelligible concepts in the sense of capturing how they are formed in God’s understanding. This has been his conception of logic since his early work, De Arte Combinatoria (1666), which consists both in the art of discovering new concepts and propositions and in the art of ascertaining their truth value. (3) As we have seen, intelligible concepts are defined in terms of consistent combinations of terms, which imply complex concepts or propositions. Leibniz’s position implies that his notion of truth presupposes that of possibility and intelligibility.4 And indeed, since his Paris years Leibniz is clear that assessing the truth of propositions requires real definitions, which show that the concepts used in propositions are possible or self-consistent. The paradigmatic and formative example of this approach is his attempt to provide a real definition of the notion of (and thus to prove the possibility of) the Ens Perfectissimum as a precondition for asserting its existence. As he writes, A real definition is one according to which it is established that the defined thing is possible, and does not imply a contradiction. For if this is not established for a given thing, then no reasoning can be safely taken about it, since if it involves a contradiction, the opposite can perhaps be concluded about the same thing with equal right. And this was the defect in Anselm’s demonstration, revived by Descartes, that the most perfect or the greatest being must exist, since it involves existence. For it is assumed without proof that a most perfect being does not imply a contradiction; and this gave me occasion to recognize what the nature of real definition was (A Specimen of Discoveries, circa 1686; cited from Leibniz 2001: 305–307).

The truth (or falsity) of the claim “God exists” presupposes the possibility or intelligibility of the notion of “God”, defined as “the greatest or most perfect being”. It is interesting to observe that Leibniz’s paradigmatic example of an impossible notion is a very similar notion, namely, that of “the greatest number”.5 Why did Leibniz think that “the greatest being” constitutes a paradigm of possibility and “the greatest number” a paradigm of impossibility is a fascinating question that I address elsewhere (Nachtomy 2005). (4) Leibniz’s celebrated theory of truth as the inclusion of a predicate in a subject also follows from his analysis of intelligible notions in terms of the principle of contradiction. This can be presented along the following lines: Anything that can be said – either truly or falsely – presupposes a proposition. A proposition presupposes predication, that is, an ascription of a predicate-term to a subject-term. As part of his compositional view of concepts, Leibniz presupposes that all complex concepts have logical predicates, which he identifies with its logical constituents – the various

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conceptual elements that make it up. Thus, if an ascription of a predicate to a subject picks out one of the subject’s constituents, the proposition is true; otherwise, it is false. (5) Leibniz’s notion of possibility is also logically prior to his notion of existence. Anything that can exist must be conceived as a possibility in the mind of God, who may create it or not. This is true of the actual world and it is consistent with Leibniz’s metaphysical account of creation, according to which the actual world is selected among many possible worlds, according to the principle of the best. However, note that, in applying the principle of the best, one goes beyond the principle of contradiction into questions that involve moral considerations as well as non-deductive reasoning.

3 Intelligibility in the Divine Context Let me now present in some more detail (yet still very briefly) Leibniz’s presuppositions about possibility.6 As I already noted, for Leibniz, possibilities are conceived in God’s mind. More specifically, possibilities are conceived as consistent or intelligible thoughts in God’s mind. The definition of possibility in terms of the consistency relation implies that the notion of possibility applies to complex thoughts alone. This is the case, since, thus defined, possibilities require a (consistency) relation between terms. For this reason, complex thoughts or concepts presuppose simple constituents.7 Leibniz indeed presupposes absolutely simple constituents or forms. He writes that, “there are necessarily simple forms” (A VI 3 514; SR 69), and that “nothing can be said of forms on account of their simplicity” (ibid.). He also stresses that these simple forms are unanalyzable and indefinable (A VI 3 572; A VI 3 590) and that humans cannot know what they are – a point to which we shall return.8 Interestingly, Leibniz identifies the simple forms with the attributes of God. He writes that “God is the subject of all absolute simple forms” (A VI 3 519; SR 79) and that “[a]n attribute of God is any simple form” (A VI 3 514; SR 69). As we shall see, this accords with his view of the production of possibilities as consistent thoughts in God’s mind. It is also significant that God’s simple forms are unique, so that each differs from all others. This difference constitutes what Fichant (1998: 85–119) has called the “source of negation”. In Leibniz’s words, There are necessarily several affirmative primary attributes; for if there were only one, only one thing could be understood. It seems that negative affections can arise only from a plurality of affirmative attributes (A VI 3 572–573; SR 93).

He also writes: “I cannot explain how things result from forms other than by analogy with the way in which numbers result from units – with this difference, that all units are homogeneous, but forms are different” (A VI 3 523; SR 85). The postulation of unique simple forms would allow Leibniz to account for negations and the incompatibility relations among predicates of complex concepts. As Fichant

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argues convincingly, unless a variety of simple forms are supposed, it would be impossible to account for exclusion relations among complex concepts (“L’origine de la n´egation”, reprinted in Fichant 1998: 117). Without such a supposition, it would be impossible to account for the variety of possible individuals and the compossibility relations between them, which are necessary for the formation of possible worlds. Thus, without grounding his theory of the production of possibilities in unique simple forms, Leibniz would not be entitled to his doctrine that each individual has a complete concept (Discours de M´etaphysique 13) and that they are distributed in possible worlds in God’s mind. As the “subject of all perfections” and as an active (thinking) agent,9 God thinks the various combinations among his simple forms, so that complex concepts or possibilities arise in his mind (see A VI 3 514; SR 71). As Leibniz puts it, “God thinks out infinitely many things in infinitely many ways” (A VI 3 515; SR 71). Thus, Leibniz’s notion of possibility presupposes simple forms and their mental combination in various ways. All the consistent results of these mental compositions are seen as logical possibilities and inconsistent ones are seen as impossibilities. In addition, according to Leibniz, God’s thinking implies reiterative reflection. This point can be put briefly thus: For Leibniz, thinking implies reflection, and reflection implies reiterative reflections. Regarding the first point, he writes, “[a] necessary being acts on itself, or, it thinks. For to think is nothing other than to sense oneself” (A VI 3 587; SR 113). “Thinking is internal action on itself, reflection and perception” (A VI 2 493). He even goes as far as claiming that “God understands because he acts on himself” (A VI 3 463; SR 11). Regarding the second point, if God reflects or acts on himself, what is he reflecting on? What is he perceiving in perceiving himself? I suggest that God reflects on his simple forms and that he reflects on his reflections. In fact, he may further reflect on these resulting reflections to infinity. As Leibniz interestingly notes: The mind never forgets anything since the mind is indestructible. Motion, once given, is necessarily continued. Thought, or the sensation of oneself, i.e., action on oneself, is necessarily continued (A VI 3 588; SR 113).

Leibniz draws an interesting analogy between the reflection of reflections and the relations of relations, both of which, as Leibniz’s example shows, go to infinity (A VI 3 399; SR 115). His explicit fascination with the notion of reflection of reflections comes out clearly in passages such as this: The following operation of the mind seems to me to be most wonderful: namely, when I think that I am thinking, and in the middle of my thinking I note that I am thinking about my thinking, and a little later wonder at this tripling of reflection. Next I also notice that I am wondering and in some way I wonder at this wonder . . .(A VI 3 516; SR 73).

This remarkable passage testifies to Leibniz’s iterative view of reflection. Leibniz continues with the following example: When it happens that he cannot sleep, let him begin to think of himself and of his thinking and of the perception of perceptions . . .and so the perception of a perception to infinity is perpetually in the mind, and in that there consists its existence per se, and the necessity of the continuation (A VI 3 517; SR 73–75).

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Here we see that the reflection of reflections to infinity is clearly on Leibniz’s mind. Let us connect his view of reiterative reflection with his view of possibility. Given that God thinks all possibilities as complex, self-consistent thoughts, God’s reflections may be seen as all the combinations among his simple forms and the relations among them. There is one more component in Leibniz’s presuppositions regarding the composition of concepts or possibilities in God’s mind that is worth noting here: God’s reflections have what Leibniz calls a natural ordering – from the simple to the complex. He recalls having given the following definition: “naturally prior involves the more simple” (VE 132).10 “Prior by nature is a term which consists of terms less derived. A term less derived is equivalent to one [which includes] a smallest number of primitive simple terms”(VE 100).11 However, as Rauzy remarks, this natural order constitutes a general matrix to which one can refer in considering the order of things rather than the order of human discoveries (Rauzy 1995: 40). One reason for this is that the simple forms are unknowable to humans.12 As Leibniz makes clear, “[a]n analysis of concepts by which we would arrive at primitive notions, i.e., at those which are conceived through themselves, does not seem to be in human power”(A VI 4 530).13 In concluding this section, let me summarize Leibniz’s presuppositions presented above. First I noted that possibilities are situated in a conceptual realm and are seen as thoughts in God’s mind. More precisely, possibilities are seen as consistent thoughts in God’s mind. Consistent thoughts are explicated in terms of complex thoughts or complex concepts, whereas complex concepts presuppose simple elements so that consistency relations hold between the terms of complex concepts. We have seen that Leibniz presupposes logically simple elements that are indefinable and unanalyzable. Furthermore, Leibniz identifies these logically simple elements with God’s attributes or God’s simple forms. At the same time, God is seen not merely as “the subject of all simple forms” but also as an active, thinking mind. More precisely, God is seen as the most perfect mind whose primary activity is thinking and self-reflection. In addition, Leibniz sees God as reflecting on his simple attributes or forms. God’s reflections on his simple attributes may be seen as mental combinations of his simple forms that produce complex forms. Likewise, God’s reflective operations are iterative, implying that he reflects upon his reflections. In this way, God thinks the combinations among his simple forms, so that more and more complex concepts arise in his mind. This implies that God combines the simple forms in a natural order – from the simple to the complex – and, in this sense, Leibniz’s system of possibility is recursive. These suppositions agree with Leibniz’s (and his generation’s) assumption that any complex concept is composed of simple ones and can, at least in principle, be analyzed into its constituents. The very simple constituents, though, cannot be analyzed and constitute the basic elements, which are at the foundation of this combinatorial approach to possibility. Since the basic elements are seen as the attributes of God, both God’s simple attributes and his mental operations constitute the actualist aspect of Leibniz’s approach to possibility.

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Leibniz’s approach to possibility is, thus, conceptualist in the sense that possibilities are thoughts of God, not entities or potential states of existing things; it is logical in the sense that it is divorced from the temporal notion of potentiality and inherent capacities of existing things; and it is actualist (in Adams’ 1979 sense) in that it presupposes an actual basis, viz., God’s mind and his simple attributes.

4 Divine Rationality and Human Rationality While divine rationality can be seen as producing all intelligible concepts by composing all simple forms in all ways, that is, as a purely formal combinatorial scheme, the human attempt to discover and partly represent these concepts constitutes a different context of rationality. One sharp difference between human rationality and divine rationality is that humans must employ symbols and a language in order to represent and use concepts. Humans must use symbols and signs (to represent pure concepts) and they must also use examples to substantiate the purely formal (and empty) universal structure. It is worth recalling here that, according to Leibniz, the discovery and formulation of concepts is, as we noted earlier, a necessary condition for ascertaining the truth and falsity of propositions. There are two additional constraints on human rationality: (1) humans cannot grasp the very simple forms, and (2) they cannot grasp very complex notions. As we have seen, both simple and complex notions are postulated in Leibniz’s combinatorial scheme, which is presupposed to be operative in God’s understanding. The first constraint, the difficulty of grasping the simple ideas, is intrinsically related to Leibniz’s view of symbolic representation. Since we cannot perceive the true simple elements directly, we have to assign simple symbols or characters to stand for them. Like letters of the alphabet or the natural numbers, such simples constitute the basis of any representational system.14 At the same time, the possibility of representation depends, according to Leibniz, on a structural resemblance (isomorphism) between the concept and the symbol (see, e.g., Quid sit idea). The method and the order of constructing a symbol must correspond to the method and the order of the production of the complex idea in God’s mind. However, since this view of representation requires structural resemblance, the simples cannot be represented. By definition, the simple elements lack any structure. The limit on complexity derives from the finitude of our minds, which also makes the indispensability of using symbols evident. Given these constraints on human rationality, Leibniz’s early schemes, the Universal Language and the Real Characteristics are best seen as human projects that presuppose divine rationality of absolute intelligible concepts, on the one hand, and reflect the human attempt to represent and approach these concepts, on the other. In this sense, these projects reflect different but intrinsically related kinds of rationality. The consistency assumption of the intelligibility of concepts is of course common to both contexts of rationality. However, whereas in the divine context it is self evident, in the human context it presents itself as a task that must be approached by means of symbols and characters.

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It seems to me that the connection between these two contexts of rationality can be seen clearly through Leibniz’s supposition of the combinatorial nature of concepts, which is common to both contexts. The combinatorial nature of concepts serves as the formal and universal structure of all concepts by stipulating a calculus of all the consistent combinations among all simple forms in God’s mind. The combinatorial nature of concepts applies to human thought as well. However, humans must substitute the variables – and the simple elements and the combinatorial rules – with notations, including the “alphabet” and the syntax of actual sciences, practices, and applications, such as written languages, geometry, music, chemistry etc (see, e.g., Leibniz’s letter to Tchirnhaus of 1678). In this sense, the universal language serves as a necessary instrument for humans to represent the purely intelligible realm of concepts in God’s mind. And, in this way, Leibniz’s project of a universal language is intrinsically related to his notion of possibility. In fact, it is arguable that Leibniz’s project of a universal language derives its inspiration and raison d’ˆetre from his conception of possibility. The universal language complements Leibniz’s view of possibility by devising the means for representing concepts and possibilities to human beings. In this sense, Leibniz is both a hedgehog and a fox, to borrow the terminology made famous by Isaiah Berlin. On the one hand, he supposes a unifying formal basis for all concepts and possible objects of knowledge; on the other hand, this thin structure can only be realized if it is applied to a variety of domains and disciplines. It thus admits both unity and multiplicity in the sense that all particular notations and domains have a common and universal foundation. Therefore, the project of a universal language calls for the design of particular notations for its very realization. This picture explains Leibniz’s usage of a variety of specimens and models from different domains and disciplines. As he writes, [t]he pure sciences such as mathematics are seen as the source of a river, a rather dry and meager source, but from it water descends continuously into the most fertile rivers of mixed sciences like acoustics, optics, and mechanics, which in turn flow out into a sea of various uses and applications (Beeley 2003: 83; De rationibus motus, 7; A VI 2 160).

5 Conclusion I have argued that the presence of Leibniz’s two modes of rationality (hard and soft) partly derives from his understanding of rationality in terms of intelligibility and from his supposing of two different contexts of intelligibility – divine and human – which complement rather than exclude one another. The source of hard rationality is the formal structure of concepts in God’s mind. The source of soft rationality is the need of humans to represent and employ such concepts in practical and scientific contexts. If this is right, the question whether Leibniz was a hard or a soft rationalist is misguided. His particular kind of rationalism clearly presupposes and requires both modes of rationality. I have tried to show that each mode of rationality to some

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extent requires the other and that their mutual usage typifies the complexity and subtlety of Leibniz’s rationality. Acknowledgments I would like to thank Marcelo Dascal for initiating the discussion on Leibniz’s rationality and thus providing the stimulation for writing this article. I would also like to thank Andreas Blank, Dan Garber, Francesco Piro, and Heinrich Schepers for useful comments and discussion.

Notes 1. Schepers (2004: 126) writes that “for Leibniz human and divine reason function in accordance with the same principles. They concern the same reality, so that everything follows just one reason. Everything obeys the principle of contradiction”. While, strictly speaking, this is correct, I will argue that the context of human rationality requires a different mode of rationality to represent divine rationality for itself – one which essentially depends on the use of symbols and some pragmatic considerations and constraints. 2. Possibile est, quod non implicat contradictionem. Possibile est quicquid clare distincteque cogitabile est (A VI 2 475). 3. Combinatoria agit de calculo in universum, seu de notis sive characteribus universalibus (quales sunt a, b, c, ubi promiscue alter pro altero sumi potuisset) deque variis legibus dispositionis ac processus seu de formulis in universum. Calculus algebraicus est species quaedam certa calculi generalis, lex verbi gratia multiplicationis est, ut quaevis pars multiplicantis, cuivis parti multiplicandi combinetur (A VI 4 511; C 556). See Couturat (1901: 299–300). 4. “That which can be understood clearly, however, is not always true, though it is always possible; and it is also true, in addition, whenever the only question is that of possibility” (Elements of Natural Law; L 207). 5. “The number of all numbers is a contradiction, i.e., there is no idea of it; for otherwise it would follow that the whole is equal to the part, or that there are as many numbers as there are square numbers” (A VI 3 463; SR 7). 6. My presentation of Leibniz’s view of possibility in this section draws on the first chapter of Nachtomy (2007). 7. “Car les pens´ees simples sont les e´ l´ements de la caract´eristique et les formes simples sont les sources des choses” (GP 4 296). 8. Nihil a nobis cogitari simplicissimum (GP 1 272). 9. “There is a uniquely active thing, namely, God” (A VI 2 489; Mercer 2001: 347). 10. Definiveram alicubi natura prius esse involutum simplicius (cited from Rauzy 1995: 37 n. 18). 11. “Sed si sic definias: Natura prior est terminus qui constat ex terminis minus derivatis. Terminus autem minus derivatus est, qui paucioribus simplicibus primitivis aequivalet” (VE 100). See also, A VI 3 475; SR 27; and A VI 3 465, 480, 495, 509, 515–517, 518. 12. Leibniz often remarks in his Paris notes that the simple elements are unanalyzable and indefinable (A VI 3 572); that “there are necessarily simple forms” (A VI 3 514); and that “nothing can be said of forms on account of their simplicity” (A VI 3 514; SR 69). 13. Non videtur satis in potestate humana esse Analysis Conceptuum, ut scilicet possimus pervenire ad notiones primitivas, seu ad ea quae per se concipiuntur (A VI 4 530; C 514). 14. As Fichant noted, “l’alphabet des pens´ees humaines ne co¨ıncide pas avec l’alphabet divin des notions absolument premi`eres: il n’est que le recensement des notions premi`eres secundum nos, dont toutes les autres sont compos´ees, quoique peut-ˆetre elles ne soient pas absolument les premi`eres” (C 220; cited from Fichant 1998a: 112).

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References Adams, R.M. 1974. Theories of Actuality. Noˆus 8: 211–232. Reprinted in Michael J. Loux (ed.), 1979. The Possible and the Actual. Ithaca, NY: Cornell University Press, pp. 190–209. Beeley, P. 2003. Leibniz on the limits of human knowledge. With a critical edition of Sur la calculabilit´e du nombre de toutes les connaissances possibles and English translation. The Leibniz Review 13: 83–101. Couturat L. 1901. La Logique de Leibniz. Paris: Presses Universitaires de France. Dascal M. 2003. Ex pluribus unum? Patterns in 522+ texts of Leibniz’s S¨amtliche Schriften und Briefe VI 4. The Leibniz Review 13: 105–154 Dascal, M. 2004. Alter et etiam: Rejoinder to Schepers. The Leibniz Review 14: 153–167. Fichant, M. 1998. Science et m´etaphysique dans Descartes et Leibniz. Paris: Presses Universitaires de France. Fichant, M. 1998a. L’origine de la n´egation. In M. Fichant (1988), pp. 85–119. Leibniz, G.W. 2001. The Labyrinth of the Continuum. Writings on the Continuum Problem, 1672–1686. Ed. by R. Arthur. New Haven, CT: Yale University Press. Leibniz, G.W. 1982–1991. Vorausedition zur Reihe VI – Philosophische Schriften. M¨unster: Leibniz Forschungstelle der Universit¨at M¨unster [= VE]. Mercer, C. 2001. Leibniz’s Metaphysics: Its Origins and Development. Cambridge: Cambridge University Press. Nachtomy, O. 2005. Leibniz on the greatest number and the greatest being. The Leibniz Review 15: 49–66. Nachtomy, O. 2007. Possibility, Agency and Individuality in Leibniz’s Metaphysics. Dordrecht: Springer. Rauzy J.B. 1995. Quid sit Natura Prius? La conception leibnizienne de l’ordre. Revue de M´etaphysique et de Morale 1: 31–48. Schepers H. 2004. Non Alter sed etiam Leibnitius: Reply to Dascal’s Review Ex pluribus unum? The Leibniz Review 14: 117–137. Schepers, H. This volume. Leibniz’s rationalism: A plea against equating soft and hard rationality.

Part II

Natural Sciences and Mathematics

Chapter 4

De Abstracto et Concreto: Rationalism and Empirical Science in Leibniz Philip Beeley

1 Introduction Conflicts are sometimes best resolved by unorthodox means. It was, as Leibniz often tells us,1 his reading of the row between Christiaan Huygens and Christopher Wren on the question of the publication of their very similar laws of motion which originally prompted him to undertake his own investigations on the topic. If he had wanted to be more accurate, Leibniz would have said that it was a row between Huygens and his friend Henry Oldenburg, who had neglected to publish the Dutch mathematician’s laws at the same time as those of Wren in what many people already then incorrectly considered to be the official organ of the Royal Society, the Philosophical Transactions.2 But his response was no less remarkable because of this slight inaccuracy. The two authors were, he suggested, quite mistaken in thinking they had discovered the laws of nature at all, even if they had provided accurate accounts or descriptions of natural phenomena. Huygens and Wren had quite simply failed to distinguish between the rational and the empirical level, between what can be deduced rigorously from precise definitions and the objects which are presented to us by our senses. According to the position Leibniz puts forward at that time, the true laws of nature can only be discovered by pure reasoning and must therefore properly be allocated to the rational as opposed to the phenomenal level.3 This was a distinction of enormous consequence, since it provided him with a model which would serve him well throughout his philosophical career (Beeley 1995, 1999). As a solution to the problem at hand, however, it had in many ways outserved its purpose by the time it was published in the Hypothesis physica nova and the Theoria motus abstracti of 1671. Huygens and Oldenburg rapidly put their quarrel behind them once the secretary of the Royal Society had consented to publish the Dutch mathematician’s paper in the Philosophical Transactions with an account of the background to the disagreement.4 Ironically, it was this issue of the journal which Leibniz saw at the spa town Bad Schwalbach, where he accompanied his patron Baron von Boineburg in late summer 1669. Just two years later and on

P. Beeley University of Oxford, Oxford, UK

M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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the basis of the exceedingly positive reception of the Hypothesis physica nova by the Oxford mathematician and theologian John Wallis (Beeley 2004a), Oldenburg sent Huygens a letter introducing his rather talented fellow countryman,5 thereby preparing the groundwork for Leibniz’s illustrious mathematical career which, as is well-known, began in Paris soon thereafter. But such biographical details, fascinating though they may be, are not the subject of this chapter. Instead, I shall look at one of the central questions with which Leibniz’s philosophy from the early 1670s up to his death is concerned, what might be called the relation between pure and applied science, but in his day was more generally termed the relation of mathematics to mixed sciences such as acoustics, hydraulics, optics, and pneumatics. I will consider how he adapted his philosophy to meet the needs of contemporary science and how this played a central role in lending credence to the position he was putting forward at any one time. In this way, I will argue that careful reading of Leibniz’s papers and letters, when they are taken in their whole breadth, shows that orthodox views on his rationalism, which have recently been espoused with a new vehemence, are too narrow and cannot be upheld. These views, I will suggest, have been based on a highly selective reading of available texts and have largely ignored his more scientific writings, i.e., those generally not contained in the philosophical series of the Academy Edition. I will close the chapter by referring to a number of passages in Leibniz which provide substantial evidence for the position I argue for and which show in particular that he recognized that often pragmatic or accommodating solutions and approaches constitute the most reasonable course to be taken.

2 Beyond Phenomena Although the young Leibniz was convinced that the true laws of nature could only be discovered by ratiocination, this did not entail that from a phenomenal point of view nature was for him somehow divorced from a rational approach to understanding. Such a severance was of course precluded in his metaphysics by his conception of the creator as a perfect geometer. Just as the young Leibniz conceives the geometrical continuum to be the foundation of divine reason, so, too, does he hold the passage from pure theory to physics with the aid of well-chosen concepts to be thoroughly explicable. An essential part of this conception finds its expression in remarks to the effect that there are traces of God to be found everywhere in the order of nature.6 The one conviction was therefore joined by another of equal importance: that any deviation between the true laws of nature and the phenomena must itself be accessible to rational explanation. While this meant that the two levels could be reconciled with each other, it did not imply the extension of procedures such as those of deductive reasoning to the contingent truths of this world. To have denied this distinction would have been to deny the existence of the problem of explaining the application of mathematics in the first place. In words similar to those of the river metaphor he employed to explain the role of mathematics in our understanding of

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nature in one of his preliminary studies on the abstract theory of motion, the De rationibus motus of 1669, he writes to Antoine Arnauld in November 1671: I truly claim to have found certain, I almost say necessary, concepts which connect mechanics to physics, reason to experience, effect the passage from abstract laws of motion to concrete phenomena of bodies and which if plenty of well-ordered experiments are added suffice to explain all varieties of natural things (A II 1 (1926) 179 / (2006) 285).7

It is not necessary here to go into the details of how the passage is effected or the modifications to the proposed solution in subsequent years. Suffice it to say that the decisive concept for Leibniz in 1671 is that of ether, an all-embracing invisible medium, whose existence he infers from perceived effects on the phenomenal level. In going beyond the level of what was directly perceivable in itself in order to explain certain phenomena, Leibniz was of course doing no more than what atomists since classical antiquity had done. But by introducing an intelligible principle as a complementary element to his mechanistic model he achieved two important results. First, he was able to remove the explanatory defects of the model itself, and, second, he was able to bring about its harmonization with pure theory.8 In doing this, Leibniz not only anticipated the strategy he would employ in his mature metaphysics but also showed us his willingness to adopt pragmatic solutions when faced with problems which could not be solved by more direct means. In the case in hand, harmonization is achieved by summoning a hypothetical principle. His new hypothesis, he writes to the custodian of the royal library in Paris, Pierre de Carcavy, in June 1671 applies abstract to concrete things, geometry to physics and shows that the phenomena of this world can only be harmonized with the abstract laws of motions and that experience can only be harmonized with reason, if a certain universal spirit or quintessence or ether is summoned (A II 1 (1926) 126 / (2006) 209).9

As is well known, he often speaks in similar terms in his mature thought, but there it is not a question of reconciling rational laws of motion with phenomena but rather of explaining the source of the admittedly different, contingent laws of motion themselves. To be more precise, in later years he sees the principles of mechanism and the laws of motion as being founded on a higher level than that provided by mechanism, namely on the level of metaphysics, thus enabling the day-to-day task of scientific explanation to be carried out without the intrusion of metaphysical considerations. This was of enormous importance to him, for, like no other philosopher in his time, Leibniz recognized in his later years the need to take account of the growth of knowledge. Expressed in mechanistic terms, this meant that we can always push the limits of our analysis further, corresponding to the infinite actual division of everything in nature. Nevertheless, this does not help us on the fundamental issue: we are on Leibniz’s view obliged to take recourse to principles which, as he sets out in a polemical tract he wrote against the Cartesians around May 1690, “are not subject to imagination even if they are exceedingly intelligible, that is to say it is necessary to join metaphysics to geometry, the doctrine of cause and effect to the doctrine of whole and part” (Leibniz to unknown correspondent, LH IV 1 4k, Bl. 23v).10 At no time, it appears, did Leibniz ever conceive mechanism to provide a wholly

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sufficient conceptual means to explain natural phenomena. Conversely, the defects in mechanism always served to confirm his fundamental views on metaphysics in respect of final causes. There is more than a passing similarity in the way in which Leibniz describes the relation of metaphysics and geometry in his mature writings to the role of ether in the early philosophy, but I do not focus on that here. Instead, I look at the distinction Leibniz introduces in this context between general and particular physics. In the former, foundational metaphysical principles such as God and substantial forms are concerned, whereas in particular physics, phenomena are explained exclusively in terms of the mechanical principles of magnitude, figure, and motion on the basis of mechanical and mathematical laws considered as established. He sets out his view particularly clearly in the tract from which I have just quoted: However, just as I hold in respect of particular phenomena that it is useless to take recourse to metaphysical principles once one has successfully established the laws of mechanics, so, too, am I persuaded of the contrary in respect of general physics, which consists in the laws of nature or the principles of mechanics themselves. For I have found proofs which make it apparent that there is something else in bodies besides magnitude, shape, and motion and that not one of these three constitute the essence of body [. . .] Thus one will not employ substantial forms when it is a question of explaining colours, sounds, tastes, medicinal qualities, chemical reactions, but one will certainly employ them, and indeed cannot do without them, in explaining the essence of body. It is a little like how it is useless to dispute the concurrency of God, the composition of the continuum and other similar matters when it is a question of special physics (Leibniz to unknown correspondent, LH IV 1 4k, Bl. 23v).11

At first glance this appears to be a radical distinction, far more radical than that between pure theory and phenomena in his first philosophy. Repeatedly, Leibniz tells us that consideration of forms serves no purpose whatsoever in the details of physics.12 Indeed, if this were not the case, his strongest criticism of scholasticism, the particular implementation of metaphysical principles, would scarcely be credible. In the Discours de m´etaphysique (§ 10; A VI 4 1543),13 as in the later Monadology (§ 79; GP 6 620), he describes the metaphysical principles as being altogether of a different sphere. This is of course highly understandable in terms of his response to what he sees as being materialistic currents of thought within the mechanistic approach. But where such intentions do not stand in the foreground, Leibniz is keen to point out that there are certain conceptual commonalities between the two levels which allow us to consider the transition from the one to the other to be in some way continuous and therefore accessible to reason. As he writes in Elementa rationis, in the first laws of mechanics there is, alongside geometry and numbers, something metaphysical concerning cause and effect, force and resistance, change and time, similitude and determination “through which the passage from mathematical things to real substances is effected” (A VI 4 722).14 For most purposes, the means supplied by mechanistic philosophy suffice, Leibniz tells us, for the explanation of colours, sounds, tastes and visual phenomena, even if, following ancient tradition, he finds the employment of optimal principles exceedingly useful in investigations in optics. But precisely because a transition to

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metaphysics is conceivable which is itself not outside the bounds of rationality, the question of scientific explanation turns out to be a question of defining limits. We see this approach already in Leibniz’s early philosophy where he justifies the employment of the conciliatory concept of ether on the mechanistic level by appealing to a sensible limit “in the various progressions of degrees in fineness and power into infinity” within which it can reasonably be considered to fall, this being the limit, he tells us, “at which the philosopher and equally the empirical scientist must call a halt” (Hypothesis physica nova § 60; A VI 2 256).15 What goes beyond this limit, one might add, is the subject of metaphysical speculation, even if the supposition is that the proposed mechanistic structure is infinitely replicated. In later years the distinction is, as I have said, rather more radical, but nevertheless Leibniz clearly talks in terms of limits: And this is the true harmonization of ancient and modern philosophy: that it is always necessary to philosophize mathematically and mechanically as far as we can, when particular phenomena are concerned, but that one must take recourse to metaphysical principles in order to provide the foundation for mechanism itself, or for general physics (Leibniz to unknown correspondent, LH IV 1 4k, Bl. 23v).16

It is important to note that in determining limits Leibniz does not appeal to some or other elevated standard of rationality, but rather to the possibilities provided by mechanism itself. He is not concerned to extend the application of deductive reasoning or of an algorithm beyond the fields in which these are typically applied, such as in logic, mathematics, and in part of the projected Ars inveniendi. How far we proceed in our investigations is, on his view, a function of the instrumental and material means available to us. But as we shall see, it is also a function of the purpose we set out to achieve, with everything being decided ultimately according to the aim, not of establishing a rigorously deduced philosophical system, but rather of improving the human condition, this being what already the young Leibniz described as the sole aim of philosophy.17 The course which Leibniz follows here has a two-fold context. It is, first, a response to what he sees but for good reason seldom describes as the dogmatism of Descartes whose hypotheses, “all too far removed from practice” (Elementa rationis; A VI 4 721),18 are unable to take account of modern developments in the mathematical and natural sciences. And, second, it is grounded in the belief that the truth value of the position he puts forward is supported by the fact that it is able to accommodate different views not only in the sciences, for example Robert Boyle’s work on the vacuum or Marcello Malpighi’s results in microscopy, but also in theology. Indeed, Leibniz sees his infinitesimal calculus as an example of how growth in science is accommodated by his philosophy, “since it has given us the means of combining geometry and physics”, while his dynamics “has furnished us with the general laws of nature” (NE 4.3.26; A VI 6 389).19 In later years, Leibniz scarcely describes his position as a hypothesis, but what he writes in 1671 of his Hypothesis physica nova remains valid for his conciliatory philosophical approach throughout his life: “a by no means small indicator of the truth of my hypothesis is that it harmonizes all” (A VI 2 252).20

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In many ways it is the architectonics of his model of nature – and this applies both to his earlier and to his later thought – which guarantees the very possibility of this conciliatory approach or harmonization. Admittedly, Leibniz often reverses the genuine dependency and speaks of divine economy or divine benevolence as having assured that this agreement “to the benefit of human life” (Hypothesis physica nova § 59; A VI 2 255)21 would come about. But let us be under no illusion here. It is precisely because he takes contemporary scientific developments and needs into account and because he has seen the trap of dogmatism into which Descartes “whose ideas were removed from the senses” (Notata quaedam G.G.L. circa vitam et doctrinam Cartesii; A VI 4 2058)22 and others had fallen that he often departs from the strict rationalism which recent commentators have ascribed to him as an exclusive position which he either holds or to which he strives. Accommodation and agreement go right to the heart of Leibniz’s philosophy. It is not just a question of making concessions in order to initiate or enable debate – although such considerations clearly often do play an important role – it is rather that the architectonics of his model of nature lends itself from the outset to pragmatic solutions, to the pushing back of limits, and to the adaptation to and harmonization with the results of others working in the fields of science and technology. He expresses this concept using a favourite metaphor about the task of an architect in a letter to Gilles Filleau des Billettes of [15]/25 March 1697: “I believe that just as the architects have no need to push the analysis of materials beyond a certain point, so likewise are the physicists able to arrive at a certain analysis of sensible bodies which serves practical purposes” (A I 13 656).23 Similarly, he points out to the theologian Friedrich Wilhelm Bierling in his letter of [1]/12 August 1711 that there are “degrees of inquiry”. He then proceeds to explain this in terms which make clear how, according to his view, different modes of investigation can be accommodated without prejudice to metaphysics: The architect or builder is content to distinguish sand, clay, stones, and similar things, and does not need to proceed as far as the chemist, who examines the salts and sulphurs and other things contained in the earth. And the physicist inquires more after the constitution of these salts and sulphurs and detects the mechanical causes of phenomena. Even if we have not yet proceeded sufficiently forwards, there is no reason therefore for the mind to be despondent, because the figures of the salts themselves lead to the mechanism. In the meantime we discover interior and invisible causes, but not therefore the most interior and not all causes. We employ not only induction but also reasoning (GP 7 500).24

As Leibniz recognizes, procedures differ according to the nature of the investigation to be carried out. Neither a purely inductive nor a purely deductive method would suffice in the natural sciences, but it is not this which he especially seeks to emphasize. Rather, it is that the techniques we employ are a function of the aims we set out to achieve. The scientist investigating nature typically adopts a pragmatic approach to his inquiries and Leibniz sees it as incumbent upon him as a philosopher to develop a position which takes this on a very fundamental level into account.

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3 Beyond Strict Rationalism The final line in the passage of the letter to Bierling just quoted takes up the topic of the approach to inquiry which for recent commentators provides some of the strongest evidence for the strict rationalist reading of Leibniz.25 I should like to devote the next part of this chapter to making some remarks on the role of visualization and imagination in his philosophy and to show how these add further weight to the critique of orthodox views on his rationalism. Again, at first glance the evidence would appear to be fairly comprehensively against a constructive role for the faculty of imagination in Leibniz’s thought. Famously in Phoranomus, the tract on motion which he wrote during his stay in Rome in July 1689, but also in other pieces, he places blame on the imagination for having led him astray philosophically during his youth, for his brief adherence to atomism and for his various attempts at composing the continuum from final elements (Robinet 1991: 803). Both the infinite divisibility of the continuum and the actual division of bodies into infinity conflict, as he suggests, with the need of the imagination to grasp composition finitely. Throughout his so-called middle years he wrestled with the problem of continuity. As is well-known, part of the solution to the labyrinth of the continuum in his mature philosophy consists in taking extension on the material level to be purely a product of the imagination, thus entirely removing the question of physical composition from the field of inquiry. Similarly, Leibniz considers overcoming reliance on the imagination as being an important achievement in the development of his new infinitesimal method of analysis. In this respect, the rigorousness of deductive reasoning is played out against the defects of inductive proof, including the employment of incomplete induction by his friend and correspondent Wallis. In very general statements he tells us that the senses alone do not suffice to explain the nature of necessary truth.26 It is true, he writes in June 1702 to the Queen of Prussia, Sophie Charlotte, that the mathematical sciences “would not be demonstrable and would consist in a simple induction or observation,” which would never give us the assurance of the perfect generality of truths, as we find in them, if something higher, which only the intellect can supply, “did not come to support the imagination and the senses” (GP 6 501).27 But more than this, Leibniz often identifies rigorous proof with pushing back the role of the imagination and when for example he contrasts his treatment of curves such as the cycloid or the quadratrix, which he calls transcendents, with their treatment in Descartes, he emphasizes that by using means provided by his calculus he is able to discover the properties rigorously by calculation without the inconvenience of having to employ the imagination.28 Part of the argument Leibniz here puts forward is that reason is able to go beyond the limits which the imagination seeks to impose on it. Thus he tells us we should not rebuke truths concerning incommensurables “on the pretext that the imagination cannot attain to them” (Leibniz to Lady Masham, [19]/30 June 1704; GP 3 357).29 At the same time, traditional geometry, with extension as its subject, is often contrasted with metaphysics precisely because the principles of the latter, although exceedingly intelligible, are not accessible to the imagination. In one of

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many pieces which he produced in the context of his projected Scientia generalis, he writes: I have remarked that the reason why we err so easily outside mathematics and geometers have been so successful in their argumentation is that in geometry and in other parts of abstract mathematics one can verify and demonstrate continually not only at the conclusion but at all times and at every step one makes from the premises by reducing the whole argument to numbers. In physics, however, even after conducting much reasoning experience often refutes the conclusion and nevertheless it does not put this reasoning straight and does not show the place where one has committed the mistake. In metaphysics and in moral philosophy it is even worse: often one cannot verify conclusions except in a very vague manner and in the core of metaphysics verification is sometimes absolutely impossible in this life (Projet et Essais pour arriver a` quelque Certitude pour finir une bonne partie des disputes, et pour avancer l’art d’inventer; A VI 4 964).30

In many ways this corresponds to the distinction between general physics and particular physics. On the one side, there is the highly intelligible doctrine of cause and effect and, on the other, the highly imaginable doctrine of whole and part.31 But the point Leibniz attempts to make in this context is that reason, too, can easily go astray in the sense of empty metaphysical speculation and thus often requires sense or imagination in order to provide it with some kind of hold. Whereas mathematicians can fix their ideas by means of figures, all that is available in metaphysics, he tells us on one occasion, is the “application of rigorous reasoning” and the “observation of logical form” (Leibniz to Bourguet, [23 March]/3 April 1716; GP 3 592).32 Similarly, in the Nouveaux Essais he sees mathematics as having a distinct advantage not only over metaphysics but also over physics on account of the immediacy of its relation to the senses: It is easier to argue demonstrably in mathematics, and this is to a large extent because sense experience can there guarantee reasoning at each moment, as this is also the case with syllogistic figures. But in metaphysics and morals this parallelism of reason and experience no longer occurs; and in physics experiment requires effort and cost (NE 4. 2.12; A VI 6 371).33

Leibniz often puts the failure of contemporaries to take sufficient account of physical experiments down to the expense and the practical difficulties involved, but nevertheless he emphasizes that without this approach one “searches in vain for detailed knowledge of natural bodies” (Remarques sur la doctrine Cartesienne; A VI 4 2050).34 And this connects up in many ways with the positive role he ascribes to visualisation and experience in general. Just as his proposed universal character will promote thought and investigation by so to speak enabling us to “fix and paint our ideas” (Leibniz to Tschirnhaus, end of May/beginning of June 1678; A III 2 450)35 – thus easing the burden on our senses –, so too experience has a decisive benefit for Leibniz in providing “a sensible thread through the labyrinth of thought” (Elementa rationis; A VI 4 715).36 Indeed, without the Ariadne thread of universal character, our understanding is only of “fluctuating reliability” and as soon as it turns away from experience it is “immediately confused through the darkness and variety of things, is controlled by false conjectures and pure opinion and without prompting can scarcely progress” (Elementa rationis; A VI 4 717).37 In respect of

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combinatorics he points out in the Nouveaux Essais that starting out from simple principles or definitions it would be “like drinking an ocean” (NE 4.2.7; A VI 6 369)38 if we did not employ a principle of exclusion to prevent us from considering all possible combinations. Here the method of analysis can provide us with the thread in the labyrinth, he tells us. But there are cases “where the nature of the question itself demands that one feels in all directions and short cuts are not always possible” (ibid.). As an example of a shortcut he could have mentioned the method of synthesis: deductive reasoning from previously established principles. The point that he seeks to make is that a plurality of approaches needs to be considered. The strict rationalism of deductive reasoning which some commentators have primarily associated with Leibniz is just one of these. In fact, for Leibniz, it is not a question at all of turning away completely from visualisation and experience. Not only does he recognize the valuable role which the inspection of empirical or mathematical data can play, both in the formulation of rules and, more generally, in questions of human inventiveness. Examples of this abound from Drˆole de pens´ee of 1675 to Leibniz’s lifelong interest in Wallis’s techniques of deciphering as a means of promoting the rather neglected analytic side of the Ars inveniendi. And in Elementa rationis he tells us that concepts which are abstracted from the concretion of images are “the most powerful which occupy reason” (Elementa rationis; A VI 4 722),39 precisely because in these concepts the principles and the bonds of imaginable or sensible things are contained. Experience is a guide to reason, and so also to scientific practice. Leibniz’s own approach to developing physical hypotheses reflects this. Advances in contemporary science and technology gave him decisive nods and winks for creating his various models of nature from early youth up to his maturity. Examples range from Georg Christoph Werner’s hydraulic pump to Antony van Leeuwenhoek’s discoveries of micro-organisms. The truth of the hypotheses with which he seeks to explain phenomena in the widest possible sense is forged precisely out of systematic internal coherence and through agreement with the theories and results of others. Leibniz would have been much less of a philosopher had he adopted dogmatically what those who adhere to the strict rationalist interpretation propose.

4 Conclusion Many of Leibniz’s descriptions of various ways of approaching problems involve the analogy of various routes one might take in order to get from one place to another. Already in his youth he compares the relation of mathematics to the physical sciences with the course of a river, emphasizing the role which the former plays in our understanding of nature and in promoting scientific and technological developments to the benefit of mankind. Mathematics, whose truth rests on what is demonstrated from definitions, is the rather displeasing “dry and meagre source”. But from it water descends continuously into “the most fertile rivers” of mixed sciences which in turn flow into “an ocean of various uses and applications” (De rationibus motus

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§ 7; A VI 2 160).40 In later years, the question is more often which route to take when a choice is available. He describes, for example, the use of algebra in geometry as “an assured route”, which although not the best, has to be preferred until a suitable geometrical characteristic has been developed (Projet et essais pour arriver a` quelque certitude; A VI 4 970).41 This was how Leibniz saw the growth of scientific knowledge in general. Different approaches are possible, and are indeed sometimes necessary, both in investigation and in discourse. In his letter to Nicolas Malebranche of [22 June]/2 July 1679 he describes his own approach to philosophical problems in this way. Here, while emphasizing the unquestionable importance of rigorous demonstration in his thought, he makes clear the importance, too, of adopting unorthodox strategies such as the one he chose for the solution of the problem of the laws of nature in 1671. Leibniz was well aware of the dangers of falling into a dogmatic position such as that which he found in the philosophy of Descartes and his followers. It is thus no coincidence that he uses the opportunity of writing to the Cartesian Malebranche to set out his own views on philosophical method. The argument he provides is one advocating a richness of approach which is irreconcilable with the strict interpretation of Leibniz’s rationalism: Nevertheless I am persuaded of all the truths quoted above despite the imperfection of ordinary proofs, in place of which I believe I am able to give rigorous demonstrations. As I started to deliberate on these things, I was not yet imbued with Cartesian opinions, this allowed me to enter the interior of things by another door and to discover new countries, just as strangers do who make a tour of France following the footsteps of those who have preceded them, learning practically nothing new, even if they be very precise and very felicitous; but those who take a path cross country, even at the risk of getting lost, can more easily meet with things unknown to other travellers (A II 1 (1926) 479 / (2006) 726).42 Acknowledgments I should like to thank Heinrich Schepers for numerous discussions on the theme of Leibniz’s rationalism and Marcelo Dascal for having initiated the broader discussion in the first place as well as for organizing the congenial meeting on the topic in Tel Aviv and Jerusalem in 2005. My travel expenses for taking part in that meeting were generously funded by the Deutsche Forschungsgemeinschaft.

Notes 1. See Leibniz, De rationibus motus, A VI 2 160; Leibniz to Oldenburg, [13]/23 July 1670, A II 1 (1926) 59 / (2006) 95; Leibniz to Oldenburg, [18]/28 September 1670, A II 1 (1926) 62 / (2006) 101; Leibniz to Oldenburg, [16]/26 April 1673, A III 1 85; Fichant 1994: 32–33. 2. Together with John Wallis’s Summary Account of the General Laws of Motion (Wallis 1669), Wren’s laws (Wren 1669) were published in the January 1669 issue of Philosophical Transactions. On seeing these publications without mention of his own contribution, Huygens sent a summary of the rules of motion which he had discovered (and which basically agreed with Wren’s) to Gallois for the Journal des Sc¸avans, where it was published in the issue for 18 March 1669, N.S, 22–24. 3. Leibniz to Oldenburg, [13]/23 July 1670, A II 1 (1926) 59 / (2006) 95: “Nam de veris Motus rationibus Elementa quaedam condidi, ex solis terminorum definitionibus Geometrica methodo demonstrata [. . .] atque illud etiam ostendisse, Regulas illas, quas de motu incomparabiles viri Hugenius Wreniusque constituerunt, non primas, non absolutas, non liquidas esse, sed per

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accidens, ob certum globi Terr-aq-a¨erei statum, evenire [. . .], non axiomata, non theoremata demonstrabilia, sed experientias, phaenomena, observationes, at felices, at praeclaras (ultra quas hactenus nemo processerit) esse”. Huygens’s laws of motion and Oldenburg’s account, both printed in Latin, appeared in the April issue of Philosophical Transactions (Huygens 1669). Oldenburg to Huygens, 28 March/[7 April] 1671, Hall and Boas Hall 1970: 537–538, 538– 540. See for example Leibniz to the Duchess Sophie, [23 October]/2 November 1691: “[. . .] et sur tout a` cause des traces de l’infini qu’on y decouvre, qui sont des ombres d’une substance infinie” (A I 7 48). “Ego vero videor reperisse quasdam ac pene dixerim necessarias notiones, quae Mechanicam physicae, rationem experientiae connectant, quae ab abstractis motus legibus transitum ad concreta corporum phaenomena faciant, quae, si experimentorum copia et ordinatio accedat, sufficiant explicandis omnibus varietatibus naturae rerum”. It was certainly not his intention, as has recently been suggested by U. Goldenbaum, to bring about “eine methodisch gesicherte Ausweitung der Gewißheit versprechenden und bew¨ahrten Verfahren des exakten Schließens und des Algorithmus auf alle kontingenten Wahrheiten” (Goldenbaum 2004: 17). Leibniz’s aim, as he makes clear on many occasions, was the harmonization of experience and theory, not to make the one subordinate to the other. “Hoc (sc. Hypothesis physica nova) abstracta Concretis, Geometriam Physicae applicat ostenditque non posse aut aegerrime posse Phaenomena Mundi cum abstractis motus Legibus, Experientiamque cum ratione conciliari, nisi adhibito quodam Spiritu universali, vitae motusque velut ␲␳␻␶ ´ ␻˛ ␦␧␬␶␫␬␻˛` quem sive aethera sive quintam essentiam, sive animam Mundi, sive materiam subtilem voces perinde est”. “Car voulant rendre raison des loix du mouvement, j’ay trouv´e que la grandeur et la figure, et en un mot, l’etendue ne suffisent point, et qu’ayant pouss´e l’analyse au bout, on est oblig´e de recourir a` des principes qui ne sont pas sujets a` l’imagination, quoyqu’ils soyent tres intelligibles, c’est a` dire qu’il faut joindre la Metaphysique a` la Geometrie; doctrinam de causa et effectu, doctrinae de toto et parte”. “Mais autant que je soˆutiens a` l’egard des phenomens particuliers, qu’il est inutile de recourir a` des principes Metaphysiques, lors qu’on a une fois bien e´ tabli les loix de mecanique, autant suis je persuad´e du contraire a` l’egard de la physique generale, que consiste dans les loix de la nature ou dans les principes de la mecanique mˆeme. Car j’ay trouv´e des demonstrations qui font voir, qu’il y a quelque autre chose dans les corps, que la grandeur, la figure et le mouvement et que pas un de ces trois la ne constitue point l’essence du corps. [. . .]Ainsi on n’employera pas les formes substantiales lors qu’il s’agira de rendre raison des couleurs, des sons, des gousts, des vertus medicinales, des operations de chymie; mais on les employera tres bien, et mˆeme on ne pourra pas s’en passer, los qu’il s’agira d’expliquer l’essence du corps. A peu pr´es comme il est inutile de disputer de concursu Dei, de compositione continui, et autres choses semblables, lors qu’il s’agit de la physique speciale”. See Discours de m´etaphysique (§ 10; A VI 4 1543): “Je demeure d’accord que la consideration de ces formes ne sert de rien dans le detail de la physique et ne doit point estre employ´ee a` l’explication des phenomenes en particulier”, and Leibniz to Arnauld 4/[14] July 1686 (GP 2 131). §10: “De mˆeme un Physicien peut rendre raison des experiences se servant tantost des experiences plus simples d´eja faites, tantost des demonstrations geometriques et mechaniques, sans avoir besoin des considerations generales, qui sont d’une autre sphere”. “In ultima certe analysi deprehenditur, Physicam principiis Metaphysicis carere non posse. Etsi enim ad Mechanicam reduci possit debeatve, quod corpuscularibus philosophis plane largimur, tamen in ipsis primis Mechanicae Legibus praeter Geometriam et numeros, inest aliquid Metaphysicum, circa causam, effectum; potentiam et resistentiam; mutationem et

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P. Beeley tempus; similitudinem et determinationem, per quae transitus datur a rebus mathematicis ad substantias reales”. Hypothesis physica nova § 60: “Etsi enim possint in subtilitate et virtute dari graduum progressus in infinitum, dantur tamen summi gradus sensibiles, ita ut quod ultra est, ne virtute quidem, nedum forma sensibili ad nos pertingat; in hoc ergo limite Philosopho pariter atque Empirico subsistendum”. “Et c’est l`a la veritable conciliation de la philosophie ancienne et Moderne, qu’il faut tousjours philosopher mathematiquement et mecaniquement, autant qu’on peut, lors qu’il s’agit des phenomenes particuliers, mais qu’on doit recourir a` des principes Metaphysiques pour etablir la mecanique mˆeme, ou la physique generale”. See also Discours de metaphysique (§ 18 ; A VI 4 1559). Hypothesis physica nova, concl. (A VI 2 257): “[. . .] ac denique de translatione inventorum ad usum vitae augendamque potentiam et felicitatem generis humani, qui unus Philosophandi finis est”. “hypotheses [. . .] attamen nimis ab usu remotas adhuc sterilesque, ut de incertitudine nihil dicam”. “[. . .] depuis que l’analyse infinitesimale nous a donn´e le moyen d’allier la Geometrie avec la physique et que la dynamique nous a fourni les loix generales de la nature”. See also Leibniz to Wallis, 28 May/[7 June] 1697 (GM 4 26). § 59: “Hypothesis nostra non parvo veritatis indicio omnes conciliat”. “[. . .] atque ita incredibili Die beneficio [. . .]”. “Dogmata ejus [sc. Cartesius] metaphysica, velut circa ideas a sensibus remotas [. . .]”. “Mais comme les Architectes n’ont besoin de pousser l’analyse des materiaux qu’`a un certain point, je crois que les Physiciens de mˆeme peuvent arriver a` une certaine analyse des corps sensibles, qui serve a` la practique”. “Sunt quidam in inquirendo gradus. Ex. gr. architectus contentus in terra distinguere sabulum, argillam, saxa et similia, non habet opus, ut tam longe procedat, quam chymicus, qui etiam salia, sulphura aliaque in terra contenta examinat: at Physicus in ipsorum salium sulphurumque constitutiones amplius inquirit, et rationes phaenomenorum mechanicas vestigat. Etsi autem nondum satis sic profecerimus, non ideo tamen animus est despondendus, cum ipsae salium figurae ducant ad mechanismum. Eruimus interdum causas interiores et invisibiles, sed non ideo intimas et omnes. Non sola inductione, sed etiam ratiocinatione utimur”. For a more extensive discussion of the implications of this passage see Beeley (2004b). See H. Scheper’s Introduction to volume A VI 4 of the Academy Edition, as well as Schepers (2004) and Goldenbaum (2004). NE 1.1.5; A VI 6 80: “les sens peuvent insinuer, justifier, et confirmer ces veritez, mais non pas en demontrer la certitude immanquable et perpetuelle”. “Il est vray que les sciences mathematiques ne seroient point demonstratives, et consisteroient dans une simple induction ou observation, qui ne nous asseureroit jamais d’une parfaite generalit´e des verit´es qui s’y trouvent, si quelque chose de plus haut, et que l’intelligence seule peut fournir, ne venoit au seccours de l’imagination et des sens”. Leibniz to La Loub`ere, 17/27 October 1692 (A I 8 485): “[. . .] sans me gˆener l’imagination”. See also Leibniz to Molanus (for Eckhard), beginning of April 1677 (A II 1 (1926) 307–308 / (2006) 479–480); Leibniz to Gallois, end of 1675 (A III 1 358); Leibniz to Koch´anski, [10]/20 August 1694 (A I 10 513). “[. . .] car mˆeme les mathematiques nous fournissent une infinit´e de choses qu’on ne sauroit imaginer, temoin les incommensurables dont la verit´e est pourtant demonstr´ee. C’est pourquoy on ne doit pas se rebuter des verit´es sous pretexte que l’imagination ne les sauroit atteindre”. “J’ay remarqu´e que la cause qui fait que nous nous trompons si ais´ement hors des Mathematiques, et que les Geometres ont est´e si heureux dans leurs raisonnemens n’est que parce que dans la Geometrie et autres parties des Mathematiques abstraites, on peut faire des experiences ou preuves continuelles non seulement sur la conclusion, mais encor a` tout moment, et a` chaque pas qu’on fait sur les premisses en reduisant le tout aux nombres; mais dans la

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physique apr`es bien des raisonnemens, l’experience refute souvent la conclusion et cependant elle ne redresse pas ce raisonnement, et ne marque pas l’endroit o`u l’on s’est tromp´e. En Metaphysique et en morale, c’est bien pis, souvent on n’y sc¸auroit faire des experiences sur les conclusions, que d’une maniere bien vague, et en Matiere de Metaphysique l’experience est quelques fois tout a` fait impossible en cette vie”. See also Systeme nouveau (GP 4 472). See the beginning of Leibniz’s tract against the philosophy of Descartes, dated May 1702: “[. . .] principia Mechanismi, quae non ex solis mathematicis atque imaginationi subjectis, sed ex fonte metaphysico [. . .] deduci debent” (GP 4 398). “Car comme en Metaphysique on n’a pas l’avantage des Mathematiciens de pouvoir fixer les id´ees par des figures, il faut que la rigueur du raisonnement y suppl´ee, laquelle ne peut gueres etre obtenue en ces matieres, qu’en observant la forme Logique”. See also Remarques sur le livre de l’origine du mal, publi´e depuis peu en Angleterre (GP 6 400): “Car il faut savoir que la rigueur du raisonnement fait dans les matieres qui passent l’imagination, ce que les figures font dans la Geometrie, puisqu’il faut tousjours quelque chose qui puisse fixer l’attention; et rendre les meditations li´ees”. “Ce qui a fait qu’il a eˆ t´e plus ais´e de raisonner demonstrativement en Mathematiques, c’est en bonne partie parce que l’experience y peut garantir le raisonnement a` tout moment, comme il arrive aussi dans les figures des syllogismes. Mais dans la Metaphysique et dans la morale ce parallelisme des raisons et des experiences ne se trouve plus; et dans la physique les experiences demandent de la peine et de la depense”. See also NE 4.3.30 (A VI 6 391). “[. . .] mais il est vray aussi que c’est une temerit´e d’esperer la connoissance du detail des corps naturels sans faire, ou sc¸avoir beaucoup d’experiences.”. “Ipsam autem Combinatoriam seu Characteristicam generalem longe majora continere, quam Algebra dedit, dubitari non debet; Ejus enim ope omnes cogitationes nostrae velut pingi et figi, et contrahi atque ordinari possunt”. See also De natura numerorum primorum et in genere multiplorum (A VII 1 598). “Hoc vero beneficium perpetui per experimenta examinis, filumque sensibile in labyrintho cogitandi, quod oculis percipi et quasi manibus palpari possit [. . .], in aliis humanis ratiocinationibus hactenus defuit”. See also GP 7 21; NE 4.2.7; A VI 6 368–369. “Intellectus autem noster nisi superna luce illustretur, aut filo quodam Ariadnaeo ducatur, quali solae hactenus usae sunt Mathematicae, fluxae fidei est, et ubi primum ab experimentis recessit, statim rerum tenebris et varietate perturbatur, et conjecturis fallacibus, opinioneque vana regitur vixque sine offensa progredi potest”. “On arrive souvent a` des belles verit´es par la Synthese, en allant du simple au compos´e, mais lors qu’il s’agit de trouver justement le moyen de faire ce qui se propose, la Synthese ne suffit pas ordinairement, et souvent ce seroit la mer a` boire, que de vouloir faire toutes les combinaisons requises; quoyqu’on puisse souvent s’y aider par la methode des exclusions, qui retranche une bonne partie des combinaisons inutiles, et souvent la nature n’admet point d’autre Methode”. “Et tamen abstractas a concretione imaginum notiones sciendum est, omnium quibus ratio occupatur esse potissimas, iisque contineri principia vinculaque etiam rerum imaginabilium et velut animam cognitionis humanae”. “. . .nam fontes artium, ut ariditate quadam et simplicitate delicatis displicere solent, ita decursu perpetuo in uberrima scientiarum flumina, denique quoddam velut mare usus ac praxeos excrescunt”. “La voye de l’Algebre en Geometrie est asseur´ee, mais elle n’est pas la meilleure, et c’est comme si pour aller d’un lieu a` l’autre on vouloit tousjours suivre le cours des rivi`eres”. “Cependant je suis persuad´e de toutes les verit´es susdites non obstant l’imperfection des preuves ordinaires a` la place des quelles je croy de pouvoir donner des demonstrations rigoureuses. Comme j’ay commenc´e a` mediter lors que je n’estois pas encor imbu des opinions Cartesiennes, cela m’a fait entrer dans l’interieur des choses par une autre porte, et decouvrir des nouveaux pays. Comme les estrangers qui font le tour de France suivant la trace de ceux qui les ont preced´es, n’apprennent presque rien d’extraordinaire; a` moins qu’ils soyent fort

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References Beeley, P. 1995. Les sens dissimulants. Ph´enom`enes et r´ealit´e dans l’Hypothesis physica nova. In: M. de Gaudemar (ed.), La notion de nature chez Leibniz. Stuttgart: Steiner, pp. 17–30. Beeley, P. 1999. Mathematics and nature in Leibniz’s early philosophy. In: S. Brown (ed.), The Young Leibniz and his Philosophy (1646–1676). Dordrecht: Kluwer, pp. 123–145. Beeley, P. 2004a. A philosophical apprenticeship: Leibniz’s correspondence with the secretary of the Royal Society, Henry Oldenburg. In: P. Lodge (ed.), Leibniz and His Correspondents. Cambridge: Cambridge University Press, pp. 47–73. Beeley, P. 2004b. In inquirendo sunt gradus – Die Grenzen der Wissenschaft und wissenschaftliche Grenzen in der Leibnizschen Philosophie. Studia Leibnitiana 36: 22–41. Fichant, M. (ed.) 1994. G. W. Leibniz, La r´eforme de la dynamique. De corporum concursu (1678) et autres textes in´edits. Paris: Vrin. Goldenbaum, U. 2004. Reason Light? Kritische Anmerkungen zu einer neuen Leibnizinterpretation. Studia Leibnitiana 36: 2–21. Hall, A. R. and Boas Hall, M. (eds). 1970. The Correspondence of Henry Oldenburg. Vol. 7. Madison, Milwaukee, London: University of Wisconsin Press. Huygens, C. 1669. A summary account of the laws of motion. Philosophical Transactions 46 (12 April 1669): 925–928. Robinet, A. (ed.) 1991. G. W. Leibniz, Phoranomus seu de potentia et legibus naturae. Part 2. Physis 28: 797–885. Schepers, H. 2004. Non alter, sed etiam Leibnitius: Reply to Dascal’s Review Ex pluribus unum?. Leibniz Review 14: 117–135. Wallis, J. 1669. Summary account of the general laws of motion. Philosophical Transactions 43 (11 January 1668/9): 864–866. Wren, C. 1669. Dr. Christopher Wren’s theory concerning the same subject. Philosophical Transactions 43 (11 January 1668/9): 867–868.

Chapter 5

Leibniz Against the Unreasonable Newtonian Physics Laurence Bouquiaux

1 Newtonianism as a Doctrine “Foreign to Reason” At the beginning of his Anti-barbarus physicus, Leibniz writes: It is, unfortunately, our destiny that, because of a certain aversion toward light, people love to be returned to darkness. We see this today, where the great ease for acquiring learning has brought forth contempt for the doctrines taught, and an abundance of truths of the highest clarity has led to a love for difficult nonsense (A&G 312).1

Leibniz does not make any explicit reference to Newton in this text, but he clearly aims at the Principia mathematica when he writes, “It is astonishing that there are those who now, in the great light of our age, hope to persuade the world of a doctrine so foreign to reason” (A&G 312). The Correspondence with Clarke bears ample witness that Leibniz regarded Newtonian physics, later to be considered as one of the most brilliant demonstrations of the power of human reason, as a doctrine which threatened to return us to the dark ages. In his Fifth Paper, §114, Leibniz returns, in similar terms, to the theme of the Anti-barbarus physicus: In the time of Mr. Boyle, no one would have ventured to publish such chimerical notions (such as attraction and other inexplicable operations). But “it is men’s misfortune to become disgusted with reason itself and to be weary of light” (A&G 344). Newtonianism is “foreign to reason”, as Leibniz says, first of all, because it gives up mechanical laws, which alone are intelligible, and introduces an “attractive force”, which turns the motion of bodies into a “perpetual miracle”. A free body naturally recedes from a curve in the tangent. “If God wanted to cause a body to move free in the aether round about a certain fixed center, without any other creature acting upon it, it could not be done without a miracle” (Leibniz’s Third Paper §17; A&G 327). And this recourse to miracles to explain natural things, “is reducing a hypothesis ad absurdum, for everything may easily be accounted for by miracles” (Leibniz’s Second Paper §12; A&G 324). Attraction requires a means of communication that is “invisible, intangible, not mechanical”. He might as well have added, L. Bouquiaux University of Li`ege, Li`ege, Belgium

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Leibniz writes, “inexplicable, unintelligible, precarious, groundless, and unprecedented” (Leibniz’s Fifth Paper §120; A&G 345). Furthermore, it is not enough for God to preside over the Newtonian world; he must constantly adjust it. God needs to wind up his watch from time to time, otherwise it would cease to move. [. . .]. The machine of God’s making is so imperfect, according to these gentlemen, that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it, as a clockmaker mends his work, who must consequently be so much the more unskillful a workman as he is more often obliged to mend his work and to set it right (Leibniz’s First Paper; A&G 320–321).2

In the absence of divine intervention, the quantity of motion and force in the world would perpetually decrease. There is much to say (and indeed much has been said) about the different ways in which Leibniz, on the one hand, and Newton and Clarke, on the other, conceived of the role of divine intervention in the world. Leibniz accuses Newton and Clarke of minimizing God’s power. Clarke, for his part, claims that Leibniz leaves no place for Divine Providence, adding: As those men, who pretend that in an Earthly Government things may go on perfectly well, without the King himself ordering or disposing of any thing; may reasonably be suspected that they would like very well to set the King aside: So whosoever contends, that the Course of the World can go on without the Continual direction of God [. . .]; his doctrine does in effect tend to exclude God out of the World (Clarke’s First Reply; LC 31).

According to Leibniz, Newton’s God lives from day to day, operates without reason, which is contrary to divine wisdom, and wills things without any motive, which is chimerical, contradictory and inconsistent with the definition of the will. In Leibniz’s opinion, Newton believes that nothing is quite divine enough unless it is opposed to reason. According to Clarke, Leibniz’s God, whose will alone is not sufficient reason for him to act in one way rather than in another, is devoid of freedom and spontaneity. He simply weighs motives and he is no more a free agent than would be a balance. Leibniz’s God is under obligation “never to bring about any thing in the universe, but what is possible for a corporeal machine to accomplish by mere mechanick laws, after it is once set a going” (Clarke’s Fifth Reply; LC 209). In Newton’s opinion, Leibniz excludes God’s actual government of the world. The end of the story, as told by A. Koyr´e, is well known: “Every progress of Newtonian science brought new proofs for Leibniz’s contention: the moving force of the universe, its vis viva, did not decrease; the world-clock needed neither rewinding, nor mending” (Koyr´e 1957: 276). And “the force of attraction which, for Newton, was a proof of the insufficiency of pure mechanism, a demonstration of the existence of higher, non-mechanical powers, the manifestation of God’s presence and action in the world, ceased to play this role, and became a purely natural force, a property of matter, that enriched mechanism instead of supplanting it” (Koyr´e 1957: 274). God had thus less and less to do in the world, until Laplace, a hundred years after Newton, told Napoleon who asked him about God in his System of the World: “Sire, je n’ai pas eu besoin de cette hypoth`ese”.

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As for attraction, the introduction of void and atoms constitutes, according to Leibniz, an offense against reason. More precisely, those who believe in atoms prefer imagination to reason. Leibniz writes that, when he was young, he accepted the void and atoms (To Thomas Burnett, May 1697; GP 3 205). But, after much reflection, he recovered from his error and understood that void and atoms are a consequence of “lazy philosophy, which does not sufficiently carry on the analysis of things and fancies it can attain to the first material elements of nature, because our imagination would be therewith satisfied” (Leibniz’s Fifth Paper §24; A&G 334). Because of attraction and atoms, Newton’s philosophy is, according to Leibniz, unreasonable, absurd or, at least, as he writes somewhat more diplomatically to Princess Caroline “a little bit extraordinary” (LC 17). Moreover, those who are in favor of Newton affirm the existence of an absolute space and an absolute time, which proves that they refuse the important principle, that nothing happens without a sufficient reason why it should be so rather than otherwise. This point is very important. Leibniz even wrote to Remond that the whole controversy could be reduced to this principle, which, according to him, Newton grants only in words but denies in reality. This question is of great interest for another reason: some commentators (Hans Reichenbach, for example), think that, on this topic, Leibniz is particularly clearsighted, since he anticipates the objections Ernst Mach addressed at the end of the nineteenth century to the foundations of classical physics, objections which were vindicated a few years later by the theory of relativity. Nearly two centuries before Mach, Leibniz is supposed to have understood that Newtonian space and Newtonian time are purely imaginary, that the unobservable absolute motion has no place in a scientific theory, and that the principle of relativity can be extended to all frames of reference, even accelerated ones. Hans Reichenbach (1957: 210) even says that the Correspondence between Leibniz and Clarke is a dispute between relativists and antirelativists, and that “whoever reads those letters today finds in them many of the arguments and objections which are known from modern discussions of the problem of motion”. Reichenbach adds that, from the principle of the identity of the indiscernibles, Leibniz derived a theory of the relativity of motion which even today forms the basis of the theory of relativity. In the 1960s and 1970s, this thesis of a direct filiation between Leibniz, Mach and Einstein was questioned by different authors, among others, by John Earman who maintained that it is based on a confusion between a relational conception and a relativistic one (relativistic in the sense of the special and general theories of relativity). Today, a century after Einstein discovered the theory of relativity, it’s not illtimed to revisit briefly this question.

2 Space, Time and the Principle of Sufficient Reason One of the questions raised by the contemporary discussions is whether it would have been possible, at the beginning of the eighteenth century, to settle the controversy (positivists tend to stand up for the position that Newton made an

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epistemological mistake, and Leibniz rightly corrected it) or if it was only after two hundred years of scientific progress had added scientific arguments to philosophical ones that it became possible to know who was right and who was wrong.

2.1 The Leibniz-Clarke Correspondence When reading the Leibniz-Clarke Correspondence, one gets the feeling that it would have been very difficult to end the controversy at that time: two consistent but incompatible systems confront each other, and it cannot be said that either has managed to defeat the other. Objections formulated on both sides require premises the adversary refuses, so that the two authors can rightfully accuse each other of petitio principii. For example, in his Third Paper §5, Leibniz asserts that the existence of an absolute space is incompatible with the principle of sufficient reason: Space is something absolutely uniform, and without the things placed in it, one point of space absolutely does not differ in anything from another point of space. Now, from hence it follows (supposing space to be something in itself, besides the order of bodies among themselves) that it is impossible there should be a reason why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise – why everything was not placed the quite contrary way, for instance, by changing east to west (A&G 325).3

If space were something in itself, no reason could be given why matter was not placed otherwise in space. And the same is the case with respect to time. If time were anything distinct from things existing in time, there could be no reason why God did not create everything a year sooner. To this argument, Clarke answers, in his Third Reply, that he does not deny the principle of sufficient reason, but that God’s mere will can be itself a sufficient reason for acting in any place, when all places are indifferent. Leibniz’s argument is in fact harmless for somebody who believes that God manifests his freedom by acting without external reason. Clarke also insists that getting rid of absolute space will not be enough to save the (very strong) Leibnizian version of the principle of sufficient reason: Even if space were nothing real, but only the mere order of bodies, “it would still be absolutely indifferent, and there could be no other reason but mere will, why three equal particles should be placed or ranged in the order 1,2,3 rather than in the contrary order” (LC 68). Leibniz acknowledges that it is an indifferent thing to place three bodies, equal and perfectly alike, in any order whatsoever, but what he concludes from that is that no such things will be produced by God, and, consequently, that there are no such things in nature. It is Clarke’s argument, this time, which is made innocuous: It is inadmissible for somebody who recognizes the principle of the identity of indiscernibles. Other examples could be added to show that the controversy makes no progress: each opponent repeats his arguments over and over again and charges the other with petitio principii but fails to demonstrate the inconsistency of the opposing doctrine.

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It is possible, without inconsistency, to follow Leibniz and to assert the principle of indiscernibles, to maintain a strong version of the principle of sufficient reason, and to define space and time as orders between things. But it is also possible, with Newton and Clarke, to refuse the principle of indiscernibles, to prefer a weaker version of the principle of sufficient reason (allowing the mere will of a free agent to be a reason) and to posit the existence of an absolute space and an absolute time, beside the order of bodies and events. Should we, then, consider that these two conceptions have equal validity? In his Fourth Reply, Clarke tells us that we are bound by observation to side with Newton: the reality of space is not a supposition; it is proved by the existence of observable effects, like centrifugal forces. In his Mathematical Principles, Newton has shown from real effects how it is possible to distinguish between real and relative motions. And, Clarke adds, his arguments are not to be answered simply by asserting the contrary. Speculation leaves us in a state of uncertainty, but observation allows us to decide, and it proves Newton right.

2.2 The Bucket Experiment Clarke refers to the famous scholium in the beginning of Mathematical Principles of Natural Philosophy where Newton says that “[w]e may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects”. “The effects which distinguish absolute from relative motion are”, Newton writes, “the forces of receding from the axis of circular motion” (MP 10). The example he puts forward is also well known. Hang a bucket full of water to a strongly twisted cord. When you release the bucket, it begins to spin. “The surface of the water will at first be plain, as before the vessel began to move; but after that, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede little by little from the middle, and ascend to the sides of the vessel” (MP 10). Newton regards this real and observable centrifugal effect as the consequence and the proof of a real motion, i.e., a motion with respect to absolute space. It does not appear when the rotation is only relative (at the beginning, the relative motion of the water in the bucket produces no endeavor to recede from the axis). It has been shown that the bucket experiment was directed against the definition of motion Descartes gives in the Principles of Philosophy (II §25), according to which “motion is the transfer of one piece of matter, or one body, from the vicinity of the other bodies which are in immediate contact with it, and which are regarded as being at rest, to the vicinity of other bodies”. Against Descartes, the bucket experiment proves that the true rotation of a body cannot be defined by its motion relative to the adjacent bodies, but has to be measured by the endeavor of its parts to recede from the axis. But Newton intends to prove that real rotation is different not only from motion relative to adjacent bodies, but also from any relative motion. So, at the end of the scholium, he proposes another example: the rotation of two globes, connected by a

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cord and revolving about their common center of gravity. In this case, the quantity of the circular motion can be measured by means of the tension of the cord: from the increase or decrease of the tension of the cord, we may infer the increment or decrease of the motions of the globes. And Newton makes clear that this effect depends only on rotation relative to space itself, and not on the presence of other bodies: “We might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared”. The question whether a body isolated in the universe is in rotation or not is meaningful. Those who are in favor of Newton think that inertial effects (centrifugal effects, for instance) prove the existence of what causes them: absolute space. These effects are due to motion relative to space and would remain even if all bodies disappeared. That is what Clarke objects to Leibniz in his Fifth Reply: It is affirmed, that motion necessarily implies a relative change of situation in one body, with regard to other bodies: and yet no way is shown to avoid this absurd consequence, that then the mobility of one body depends on the existence of other bodies; and that any single body existing alone, would be incapable of motion, or that the parts of a circulating body (suppose the Sun) would lose the vis centrifuga arising from their circular motion, if all the extrinsick matter around them were annihilated (LC 191–192).

We know that Leibniz was prevented by death from answering Clarke’s last Reply. However, he treats the question of centrifugal effect in other writings. Arguing from an extract of the Dynamica, Reichenbach asserts (rather doubtfully, as we will see) that Leibniz was eager to supplement relativistic kinematics with a relativistic dynamics, and that he tried to reach this aim by attributing inertia to the motion of masses relative to the surrounding ether. “He would argue”, Reichenbach (1957: 212) writes, “that the appearance of centrifugal forces on a disk isolated in space proves its rotation relative to the ether and not relative to empty space”. If Reichenbach is right, Leibniz has clearly anticipated Ernst Mach’s developments. For, according to Mach, Newton’s experiment with the rotating vessel of water simply informs us, that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of earth and the other celestial bodies (Huggett 1999: 174).

This experiment does not prove that the centrifugal effects are due to a rotation with respect to a hypothetical absolute space. According to Mach, it is rather because of its motion relative to all the bodies in the universe that water tends to recede from the axis. If he had to answer the objection Clarke ironically made to Leibniz in his Fifth Reply, Mach would no doubt maintain that, if all the extrinsic matter around a circulating body were annihilated, the body would actually lose its vis centrifuga. Inertial effects do not provide any foundation for the notions of absolute space and absolute motion. According to Mach (as well as to Leibniz), space and time are nothing else than a set of relations between bodies and events. A lot of people, and, at least for a time, Einstein himself, believed that Relativity vindicated Mach’s (as well as Leibniz’s) views on space and time.

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Newton was wrong, in Mach’s opinion, to introduce an absolute time “without relation to anything external”, which is beyond all measures of duration by means of motion. Newton was also wrong, in Mach’s opinion, to introduce an absolute space and an absolute motion, which are “pure things of thought, pure mental constructs, that cannot be produced in experience” (Huggett 1999: 174): it is impossible to say anything about the motion of a body K unless the other bodies A, B, C, are present with reference to which the motion of the body K can be estimated. It makes no sense to talk about the motion of a body in an empty space. Newton was wrong, according to Mach, to conceive of space and time as “autonomous entities existing independently of things”. On all these points, Relativity seems to prove Mach right. Indeed, Einstein himself often pointed to the debt owed by his theory to the positivist notion that only observables have a place in physical theory. In 1916, Einstein wrote that Mach had perfectly understood the defects of classical mechanics, and that he was not far from asserting the necessity of a theory of general relativity. Speaking of the untenable privilege that Newton grants to inertial frames, Einstein affirms that the inconsistency of this concept was very clearly brought to light by Mach, and that it had already been recognized (although less clearly) by Huygens and Leibniz. Shall we say, without further ado, that Leibniz was the hero who anticipated the Machian (and then the Einsteinian) conception of space and time? In fact, we know that both parts of this thesis are questionable. It is doubtful whether Leibniz can be viewed as Mach’s precursor, and it is doubtful whether Mach’s conception is similar to Einstein’s.

2.3 Did Leibniz Anticipate Ernst Mach’s Developments? Let us begin with the first point. Leibniz’s conceptions have unquestionably a lot in common with Mach’s: they both support a relational view of space and time; they both reject a space or a time existing independently of things, both maintain that all motion (even rotation or any accelerated motion) is the relative motion of bodies and that Galilean relativity has to be extended to all frames of reference. However, we have to be careful when looking for Machian theses in Leibniz’s texts – more careful, at least, than Reichenbach when he claims to have discovered the Machian interpretation of the bucket in the Dynamica. As a matter of fact, Reichenbach acknowledges that Leibniz does not precisely formulate the Machian view, but he thinks it “may legitimately be extrapolated” from proposition 19 of the Dynamica (Reichenbach 1957: 212). This proposition tells us that the law of the equipollence of hypotheses holds not only for rectilinear motions, but also universally. Let’s have a look at this text: Motion by its nature is relative [. . .] Thus, when a ship is borne on the sea in full sail, it is possible to explain all the phenomena exactly, by supposing the ship to be at rest and devising for all the bodies of the universe motions agreeing with this hypothesis [. . .] I remember, indeed, that a certain illustrious man formerly considered that the seat or subject of motion cannot (to be sure) be discerned on the basis of rectilinear motions, but that it can on the basis of curvilinear ones, because the things that are truly moved tend to recede

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from the centre of their motion. And I acknowledge that these things would be so, if there were anything in the nature of a cord or of solidity, and therefore of circular motion as it is commonly conceived. But in truth, if all things are considered exactly, it is found that circular motions are nothing but compositions of rectilinear ones, and that there are in nature no other cords than these laws of motion themselves (GM 6 508; Stein 1977: 42).4

Howard Stein (1977: 4–7) proposes a convincing interpretation of this text: If there were any real solids in the world, it would not be true that all motions are composed of uniform rectilinear ones; rather, there would be real circular motions. But, in actuality, all bodies have a certain degree of fluidity, so that, “when a body rotates, its particles not only strive to go off on the tangent, but actually begin to go off, and are then turned aside by the medium”. I think Howard Stein is right to assert that what the ambient medium is responsible for is the cohesion of the body, and not (as Reichenbach maintains) the inertial effects. His interpretation is confirmed by a similar text from the Specimen dynamicum: (Nothing is really solid or fluid, absolutely speaking, and everything has a certain degree of solidity or fluidity; which term we apply to a thing derives from the predominant appearance it presents to our senses.) For if we assume something we call solid is rotating around its center, its parts will try to fly off on the tangent; indeed, they will actually begin to fly off. But since this mutual separation disturbs the motion of the surrounding bodies, they are repelled back, that is, thrust back together again, as if the center contained a magnetic force for attracting them, or as if the parts themselves contained a centripetal force. Thus, the rotation arises from the composition of the rectilinear nisus for receding on the tangent and the centripetal conatus among the parts. Thus, all curvilinear motion arises from rectilinear nisuses composed with one another, and at the same time, it is understood that all solidity is caused by surrounding bodies pushing a body together; if matters were otherwise, then it could not happen that all curvilinear motion is composed of pure rectilinear motions [. . .] From this we can also understand why, on this matter, I cannot agree with certain philosophical opinions of certain important mathematicians, who, beyond the fact that they admit empty space and don’t seem to shrink from attraction, also take motion to be an absolute thing, and strive to prove this from rotation and the centrifugal force that arises from it. But since rotation also arises only from a combination of rectilinear motions, it follows that if the equivalence of hypotheses is preserved in rectilinear motions, however they might be placed in things, then it will also be preserved in curvilinear motions (A&G: 135–137).5

It seems rather risky to extrapolate from these texts to the Machian explanation of centrifugal forces. In fact, I do not think that Leibniz gives a convincing explanation of these effects. Furthermore, Leibniz, like Descartes, maintains the principle of inertia: a free body naturally remains in rectilinear uniform motion. Only a miracle can prevent a body from receding from a curve in the tangent. Thus, Leibniz introduces into his dynamics an objective distinction between a rectilinear uniform motion and an accelerated motion. But this distinction is incompatible with the universal (very strong) principle of relativity Leibniz also asserts. It is not certain that Leibniz was, as Reichenbach suggests, eager to supplement relativistic kinematics with a relativistic dynamics. All of this invites us to be cautious in considering Reichenbach’s enthusiastic evaluation of Leibniz’s objections to Newton. I think Robert Disalle is right to contest the thesis according to which Einstein was only saying what philosophers ought

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to have known, and a few (as Leibniz) had already suspected, on purely philosophical grounds. In fact, absolute acceleration is required by Newton’s physics. Newton has managed to give this notion a well-defined empirical content. For example, absolute rotation can be empirically defined (and measured) by centrifugal forces. (In this perspective, the point is not to prove that centrifugal forces on the water are caused by absolute rotation, but, as Disalle (2002: 45) says, “to define a theoretical quantity, absolute rotation, by exhibiting how it is detected and measured by centrifugal effects.”). Absolute acceleration is not an arbitrary metaphysical notion, whose introduction into the theory shows that “Newton has acted contrary to his expressed intention only to investigate actual facts”; its definition is well founded, at least as well founded as Newton’s laws of motion. And this is why, in spite of all the traditional philosophical objections to it, it could only be overthrown by Einstein’s introduction of new fundamental physical laws. Several of Newton’s spatio-temporal concepts are postulated by classical physics. And by “classical physics”, we do not only mean Newtonian physics, but also Cartesian and Leibnizian physics. Instead of charging Newton with an offense against empiricism, we should rather recognize that, as Disalle says, he has offered a conceptual analysis of what is presupposed about motion by Descartes, Leibniz, and every other seventeenth-century mechanist who asserts the principle of inertia and thinks that a physical cause is required to modify a motion. Still, we must not concede too much to Newton. As we have just mentioned, absolute time and absolute acceleration are required by his physics, and it is possible to give these notions an empirical content. But the case is quite different as long as absolute motion and absolute velocity are concerned. Newtonians were wrong to conclude from the significance of absolute acceleration to the existence of a “quasisubstantial” space, existing independently of things, and able to give a foundation to the notion of absolute motion (or absolute rest). Centrifugal forces allow us to define absolute rotation, but not absolute space. The bucket experiment, for instance, does not allow us to distinguish a unique frame of reference, at rest in absolute space; it leads to an infinite collection of inertial frames. Of course, the existence of an absolute space can be postulated, but, doing that, one must be conscious of going beyond what observation can provide. Newton’s dynamics does not prove that Leibnizian relationism is untenable. In fact, had Newton remained faithful to his program of only studying observable facts, he would have adopted Galilean space (which does not allow the definition of absolute rest), and he would have left open the possibility that space and time were not structures pre-existing to things, but rather (as Leibniz suggested) a set of relations between bodies and events. Let us sum up what we have said so far. Leibniz’s strength lies in the judiciousness of his objections to Newtonian substantivalism: he is quite right to assert that the existence of an absolute space is not proved. In fact, Galilean relativity (which is an integral part of Newtonian physics) would rather suggest that substantivalism has to be given up. Leibniz’s weakness lies in his incapacity to provide a dynamics compatible with the very strong principle of relativity he states. Newton’s strength lies in the fact that, for his part, he managed to elaborate a dynamics, which accounts for

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the observations, and in particular for the existence of centrifugal forces. Newton’s weakness is that he stated more that what his physics would support: absolute rest has, according to his dynamics, no empirical meaning and the quasi-substantial character of space remains, as Leibniz stated, a petitio principii. Mach showed that it is possible to give a non-substantialist interpretation of spatio-temporal relations within Newtonian physics, but he goes perhaps too far when he suggests that this interpretation is the only one. After all, no classical experiment proves that a body’s inertia is fully determined by the presence of other masses (but it is true, on the other hand, that no classical experiment proves the contrary).

2.4 Did Relativity Vindicate Mach’s (as Well as Leibniz’s) Views on Space and Time? It would remain to determine to what extent the theory of relativity proves that Mach (and Leibniz before him) were correct. Does Einstein validate relationist ideas? This is an interpretation that has been widely held, at least until the 1970’s. Several arguments can be formulated to support this thesis. First of all, general relativity does away with the preferential treatment of inertial frames. Acceleration is no longer an absolute notion, and Galilean relativity can be universally extended, as Leibniz and Mach had foreseen. Moreover, general relativity states that the presence of masses modifies the structure of space-time and that the distribution of masses determines the gravitational field and, consequently, inertial effects. This seems to provide a spectacular confirmation of Machian (and, more generally, relationist) conceptions. It can also be added that several solutions to Einstein’s equations (Lense-Thirring, for instance) underscore typically Machian effects. Can we then conclude, with Hans Reichenbach, that Einstein’s theory of relativity means the fulfillment of Mach’s philosophical program? Probably not (as John Earman and Michael Friedman have shown). As a matter of fact, it can be pointed out that, although certain solutions to Einstein’s equations appear to support Mach, others, like the solutions describing an empty space, for example, appear to argue against him. It is worth noticing that, initially, Einstein thought that such solutions would not be found. He was convinced that a (physically) empty space should not imply a (mathematically) structured space. Thus, in 1916, Einstein wrote in a letter to Schwarzschild, that, according to his theory, inertia is only an interaction between masses, and not something which space in itself could take part in. He added that the main characteristic of his theory is that no property can be attributed to space in itself. If all the things were to disappear, Einstein concluded, according to Newton inertial space would remain in existence but according to his own theory nothing would be left. Later, however, Einstein distanced himself increasingly from Mach. In fact, Einstein’s position with respect to “Mach’s principle” and to Machian conceptions in general changed considerably between 1910 and 1915 and the end of his life. In 1913, Einstein wrote enthusiastically to Mach that general relativity perfectly supports his research and

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his objections to the bucket experiment. But in 1954, he would affirm that Mach’s principle could best be forgotten. In the preface Einstein wrote to Max Jammer’s Concepts of Space in 1953, one can gauge the distance from Machian ideas, but also the evolution in the way Einstein considers the Leibniz-Newton controversy: The concept of space was enriched and complicated by Galileo and Newton, in that space must be introduced as the independent cause of the inertial behavior of bodies if one wishes to give the classical principle of inertia (and therewith the classical law of motion) an exact meaning. To have realized this fully and clearly is in my opinion one of Newton’s greatest achievements. In contrast with Leibniz and Huygens, it was clear to Newton that the concept [of a purely relational space, inconceivable without a material object] was not sufficient to serve as the foundation for the inertia principle and the law of motion. He came to this decision [. . .]: space is not only introduced as an independent thing apart from material objects, but also is assigned an absolute role in the whole causal structure of the theory. This role is absolute in the sense that space (as an inertial system) acts on all material objects, while these do not in turn exert any reaction on space [. . .] Today one would say about that memorable discussion: Newton’s decision was, in the contemporary state of science, the only possible one, and particularly the only fruitful one (Einstein 1953: xvi). Acknowledgments I want to thank Yves de Rop for helpful comments on various parts of this paper.

Notes 1. “Fato sinistro accidit, ut homines quodam lucis fastidio ad tenebras reverti ament. Id hodie experimur, ubi magna discendi facilitas doctrinae contemptum peperit; abundantia clarissimarum veritatum amorem difficilium nugarum reduxit” (GP 7 337). 2. “Dieu a besoin de remonter de temps en temps sa montre. Autrement elle cesseroit d’agir [. . .] Cette Machine de Dieu est mˆeme si imparfaite selon eux, qu’il est oblig´e de la d´ecrasser de temps en temps par un concours extraordinaire et mˆeme de la raccommoder comme un horloger son ouvrage; qui sera d’autant plus mauvais maistre, qu’il sera plus souvent oblig´e d’y retoucher et d’y corriger” (LC 23). 3. “L’espace est quelque chose d’uniforme absolument, et sans les choses y plac´ees un point de l’espace ne diff`ere absolument en rien d’un autre point de l’espace. Or il suit de cela, suppos´e que l’espace soit quelque chose en lui mˆeme outre l’ordre des corps entre eux, qu’il est impossible qu’il y ait une raison pourquoi Dieu, gardant les mˆemes situations des corps entre eux a plac´e les corps dans l’espace ainsi et non pas autrement; et pourquoi tout n’a pas e´ t´e mis a` rebours (par exemple) par un e´ change de l’orient et de l’occident” (LC 53). 4. “Motus sua natura est respectivus [. . .] Itaque cum navis plenis velis in mari fertur, possibile est omnia phaenomena exacte explicare, navem quiescere supponendo atque affingendo omnibus Universi corporibus motus ad hanc hypothesin congruentes [. . .] Memini quidem, viro cuidam praeclaro olim visum ex motibus quidem rectilineis non posse discerni sedem subjectumve motus, posse tamen ex curvilineis, quoniam quae revera moventur, recedere conantur a centro motus sui. Atque haec fateor ita se haberent, si ea esset natura retinaculi seu firmitatis atque adeo motus circularis, quae communiter concipi solet. Verum omnibus exacte consideratis reperi, motus circulares nihil aliud esse quam rectilineorum compositiones, neque alia in Natura esse retinacula quam ipsas motuum leges” (GM 6 508). 5. “Nam si ponamus aliquod ex iis quae firma dicimus (quanquam revera nihil sit absolute firmum fluidumve, sed certum habeat firmitatis fluidibilitatisque gradum, a nobis autem ex praedominio respectu nostrorum sensuum denominetur) circulari circa suum centrum, partes per tangentem

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conabuntur avolare, imo avolare incipient re ipsa, sed quoniam hic ipsorum a se invicem discessus turbat motum ambientis, hinc repelluntur seu rursus contruduntur ad se invicem, quasi centro inesset vis attrahendi magnetica, aut quasi ipsis partibus inesset vis centripeta, et proinde circulatio ex nisu rectilineo recedendi per tangentem et conatu centripeto inter se compositis orietur. Manetque adeo omnem motum curvilineum ex nisibus rectilineis inter se compositis oriri, simulque intelligitur hanc contrusionem ab ambiente esse causam omnis firmitatis. Alioque fieri non posset, ut omnis motus curvilineus ex meris rectilineis componeretur [. . .] Ex his quoque intelligi potest, cur magnorum quorundam Mathematicorum sententiis quibusdam philosophicis hac in re stare non possim, qui praeterquam quod vacuum spatium admittunt et ab attractione non abhorrere videntur, etiam motum habent pro re absoluta, idque ex circulatione indeque nata vi centrifuga probare contendunt. Sed quoniam circulatio quoque non nisi ex rectilineorum motuum compositione nascitur, sequitur si salva est aequipollentia Hypothesium in motibus rectilineis suppositis utcunque, etiam in curvilineis salvam fore” (GM 6 252–253).

References Descartes, R. 1985. The Philosophical Writings of Descartes. Translated and edited by J. Cottingham, R. Stoothoff, and D. Murdoch. Cambridge: Cambridge University Press. Disalle, R. 2002. Newton’s philosophical analysis of space and time. In I.B. Cohen and G.E. Smith (eds.), The Cambridge Companion to Newton. Cambridge: Cambridge University Press, pp. 33–56. Earman, J. 1989. World Enough and Space-Time. Cambridge, MA: The MIT Press. Einstein, A. 1953. Foreword for Max Jammer’s Concepts of Space. The History of Theories of Space in Physics, 3rd ed. [1993]. New York: Dover, pp. xii–xvii. Friedman, M. 1983. Foundations of Space-Time Theories. Princeton, N.J.: Princeton University Press. Huggett, N. (ed.). 1999. Space from Zeno to Einstein. Classic Readings with a Contemporary Commentary. Cambridge, MA: The MIT Press. Koyr´e, A. 1957. From the Closed World to the Infinite Universe. Baltimore, MD: The Johns Hopkins University Press. Newton, I. 1729. Isaac Newton’s Mathematical Principles of Natural Philosophy. Translated by A. Motte. Repr. Berkeley, 1947 [= MP]. Reichenbach, H. 1957. The Philosophy of Space and Time. New York: Dover. Robinet, A. (ed.). 1957. Correspondance Leibniz-Clarke. Paris: Presses Universitaires de France [= LC]. Stein, H. 1977. Some philosophical prehistory of general relativity. In J. Earman, C. Glymour, and J. Stachel (eds.), Foundations of Space-Time Theories. Minneapolis, MN: University of Minnesota Press, pp. 3–49.

Chapter 6

Some Hermetic Aspects of Leibniz’s Mathematical Rationalism Bernardino Orio de Miguel

1 Introduction Perhaps one way to clarify the problem of the plurality or the unity of Leibniz’s rationalism would be to analyze the use he makes of mathematical reasoning in his proofs of dynamics. As is known, and generally admitted, Leibniz works simultaneously on three epistemic levels: (1) the metaphysical level of simple substances, in which the entelechy and the prime matter, as primitive forces, constitute respectively the action and the counter-action in the preservation of the equilibrium of the monad’s activity in the real world; (2) the physical level of the second matter or organic mass of phenomenal bodies, which, as a result of such inner activity, individualizes, divides or diversifies itself into the actu infinite division by means of elasticity and the natural inertia or resistance, as derivative forces in the impact of bodies; (3) the mathematical level, in which, solely by means of the ideal division done by calculus, we can imaginatively measure these phenomena. This three-level intelligibility contains, according to many scholars, a gap or ␹␻␳␫␴␮´o␵ between an ontology of the essential, absolute individuality of substances and a physics as a universal hypothetical science of phenomena, in which the substances express themselves. In fact, if phenomena become real only in monads, then there will only be individual phenomena; that is, a phenomenon is every successive perception of every perceived substance from every perception of the other substances. Every phenomenon, then, is as individuated as every perception and as every substance. But, with these premises, what function does abstract mathematics have to fulfil in order to generalize these phenomena in Leibniz’s science? It is not enough to appeal, as Leibniz does on countless occasions, to the utopian ideal of the Universal Characteristic, according to which reasoning would be the same thing as calculating; nor is it right to say that the calculus “deals with the possible and with the real as possible”, since this would always imply taking for granted that an important problem has been solved, namely that of the incommensurability between the actu B. Orio de Miguel Madrid, Spain

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infinite – that of the monads and their phenomena – and the ideal infinite – that of the possible, with which the calculus deals. The dilemma of Leibnizian science, from the present standpoint, is to choose between two imperfect options. First, we could abandon the intimate relationship between monads-phenomena, on the one hand, and calculus, on the other, and limit ourselves to studying his physical system mechanically and mathematically, comparing it then to Descartes’, Huygens’, and Newton’s systems. They believed that the phenomenal and the mathematical coincide and that there is nothing scientifically treatable beyond the phenomenon. In this case, however, what we are doing is not Leibnizian science. The second option would be to examine such a correlation and to try to find out what happens in the spirit and matter and in the spirit-matter and calculus relationships, respectively. This could be a Leibnizian approach, but it would not be science, or, at the very most, it would be another science furnished with different parameters than those of Descartes, Huygens and Newton. Leibniz’s famous sentence: “let us study the mechanical science as if there were no monads, and let us study the monads beyond the mechanism” (GM 6 134ff., 242ff.; 4 434ff.; GP 7 343) is not quite a Leibnizian sentence. It is not consistent with his way of doing science; it was only a “politically correct” strategy to walk a middle road between two other stances (“they who have introduced life everywhere” and “the materialists, who make nature consist only in the pure impact of bodies”). Leibniz’s science is something different, so it must be treated as such. His physics seeks to be, without any doubt, a universal science but, at the same time, it is an ontology of the real, the concrete. Leibniz’s intention was precisely to avoid the gap between the concrete and the abstract, between the actual and the ideal, between the real and the apparent. In a word, he sought to avoid the gap between morality and science, which was the poison contained, according to him, by the new mechanical science. During the last few years, my aim has been to investigate where Leibniz could have found the transversal thread with which he tried to give unity to the three levels of his science. For this reason, I have studied some of his biological, vitalistic and cabbalistic sources, which I am obviously not going to be able to discuss here. In my opinion, Leibniz gives to the theory of expression and to the principle of continuity a hermetic cosmic meaning, which we should examine in order to understand him fully. I will just briefly state my hypothesis and later I will point out some examples taken from dynamics.

2 Leibniz’s Hermetic Rationalism 2.1 Hermetic Tradition The manifold and variety of expressions of the Hermetic Tradition can be summarized and unified in three statements: 2.1.1. Being is inner activity, “potentia sive conatus agendi”. All things in nature – all of them, the so called organic and non-organic, the minerals, plants,

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animals, and the humans, equally – are internally active, down to their very minute particles or action centres. So the external side or phenomenal view of things is the result of this internal activity. The world is, in essence, symbolic in a strict sense. 2.1.2. All things are related to each other in different degrees and ways according to their proximity or type of activity, and they are transformed into others, so that they constitute a holistic organism, whose knowledge is governed by the principle of analogy. That is, the variety of our experiences inside the macro- and microcosm is subsumed in this organic unity. 2.1.3. Harmony is the base-concept of this wide organism; it is the unity in plurality as an expression of the Common Cause. These three statements unfold that basic concept which the Hermetic Tradition symbolized by the anagram “the all the one”.

2.2 Leibniz’s Hermetic Analogy The metaphysical-physical-mathematical system that Leibniz wanted to construct may be subsumed under these hermetic parameters. Maintaining this perennial Tradition – the philosophia perennis – and adding to it the discoveries of the new science was his essential aim. For this purpose, he used – he had to use – the same terms and concepts as his masters and colleagues did, but he had to provide them with a semantic-cosmic content, which was required by his strong belief in the divine-organic unity of being. Substance, body, inertia, resistance, elasticity and atoms in physics, and continuity, infinitesimals and imagination in mathematics are all concepts that acquire, in Leibniz’s thought, certain transversal, specular, convoluted connotations among the above mentioned three levels. Such concepts invite us to analyze these levels from the perspective of analogical reasoning. Obviously, Leibniz’s adversaries could not share this perspective, though all of them, from the ancient Hellenic metalworkers to the Arab alchemists and the medieval Christians through the Renaissance theosophists and Gnostics, had made use of it. That is what I call “hermetic analogy”, and it is, if I have understood it correctly, what Leibniz formulates in his theory of expression and uses recurrently in his scientific reasoning.

2.3 Expression as Hermetic Analogy The theory of expression as “hermetic analogy” goes beyond a semiotic treatment of the composition of concepts and signs. It deals with a way of reasoning that corresponds to an ontological insight, which understands the mutual specular relationship of the different orders of being in virtue of their previous pertaining to the same organic universe. That is to say, the absolute metaphysical principles or axioms and the hypothetical natural laws which derive from them are each other different but

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equipotent: they illuminate from different points of view, each one from its own language, the coherence of the whole system as a “state of reversible things’, “like the streets and the squares in a city, from which we can start and to which we can arrive coming from everywhere”. These principles or laws are not independent from one another or deductively irreversible, as a contemporary logical system would demand. In Leibniz’s view, physics is in no way an irreversible deductive science, but a repeatedly specular one. For example, the entelechy/prime matter equilibrium in primitive forces means the same as living forces/the resistance or natural inertia in derivative forces; the mathematical continuity in calculus means the same as the bodies’ elasticity in the impacts; the metaphysical principle of equipollence between the full cause and the entire effect means the same as the physical impossibility of the mechanical perpetual motion, and both of them express in their own languages the same equilibrium of the activity of the monad. A comparative study of the texts in which Leibniz states his dynamics shows how he sometimes demonstrates elasticity by means of the continuity principle, but in other passages it is the other way around. The subtlety or the infinite folds of matter leads him to deny physical atoms, but on other occasions he makes such a denial because the principle of the identity of the indiscernibles demands it. In both cases, the instrument of the infinitesimal calculus is used as a method of approach. In a word, elasticity, continuity, subtlety, resistance, infinitesimal, conservation of forces, etc. are concepts that surround each other, forming a convolute, and all of them express, in the language of phenomena, the same thing that occurs in the universe of monads. In a very important letter to Johann Bernoulli, dated November 1703, commenting on Huygens’s physics, Leibniz argues that the principle according to which ‘motions diversely composed produce the same’ is established more by the result than by a necessary demonstration, and that is why those who look for its cause will not find more than the harmony or perfection of things, on which motion’s laws, as a whole, really depend like effects of the supreme Mind, and not on a deaf necessity as geometric necessity is. [. . .] [N]either will anyone easily prove a priori this hypothesis nor will anyone demonstrate it by geometric or metaphysical necessity (GM 3 728).

And he adds: As you will see from that, you must not think that I just make use of a unique principle, that one of the reduction to perpetual motion like something absurd, although I certainly used it in the Acta in order to adapt the problem to everyone understanding. In truth, you will scarcely find a method that I have not used to obtain the same, as I made with the study of the graves, with the elastic property of bodies, with the equality of the effect and the cause, the equality between the action and the reaction of the concurrent bodies, the hypothesis of indiscernibility, the absence of jumps and the presence of dead forces, the composition of motions and especially the oblique impact (GM 3 729).

And he concludes his letter asking his friend Bernoulli to share it with Mr. de Volder, who, I suppose, will not find unpleasant these things about laws of nature, which must not be derived from geometric necessity, but from the principle of wisdom and harmony [. . .], so that nature, in its own general laws, bears witness to the supreme Author, what would not happen if a mere geometric demonstration took place (GM 3 730; my italics).1

So – he will add in the Theodicy – “the absence of necessity of these principles is what expresses the beauty of laws that God has chosen, where many beautiful

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axioms are together, being impossible to say which one of them is the most primitive” (GP 6 320ff.; my italics).2 If the results of my investigation are confirmed, we will have to state that, actually, Leibniz constructs a specular science among the above mentioned three levels, and that the notion of repraesentatio (perceptio multorum in unum, “perception of the many in the one”) is not only the definition of the monad, but also the structure and working mechanism of the whole cosmic organic universe. The metaphor of the “substance” as “active living mirror”, which Leibniz takes from the Hermetic Tradition, defines his entire system. What for the old alchemists, doctors and botanists was an animistic transformation of some substances into others, for Leibniz is a “repraesentatio” in each one of all the others (and vice-versa) and, consequently, the “repraesentatio” of an ontological level in another. This is the hermetic analogy. We must draw all the consequences of this theory. An idea, Leibniz says, is not a trace in some part of the brain; nor is it a thinking act. An idea, for Leibniz, is a disposition or a permanent faculty of our mind: that there is in our mind an idea of things is not but the fact that God, the author of things as well as of the mind, has impressed in this one a faculty of thinking which corresponds perfectly to what happens in things [. . .], provided that a certain analogy is kept in the relationships [. . .]. So, the whole effect represents its full cause, and the world itself represents God in a way (GP 7 264; my italics).3

Accordingly, the analogy between the inside (the monad) and the outside (phenomena), between the non-extended (activity itself) and the extended (derivative forces), between the discrete (monads and their modifications) and the continuum (extension, space, time, number), between the complete actual/active things (substances) and the incomplete, the ideal (differential calculus), and, generally, the analogy between motion and rest, between the large and the small, between a geometric angle and an angle of contact, between the right line and the curved one, between a mathematical equation and its “cosmic meaning”, and so on, is by no means a mere similarity between two different objects or the translation of the formal into the extended, or a mere gnoseological strategy for the production of concepts, but is the ontological fact of their mutual specular relationship by means of their previous belonging to the one and the same organic universe. So, the traditional mirror metaphor of the infinite mirrors or mercury balloons, which was used for centuries to explain the infinite replication of subjects as well as its representative singularity, is converted by Leibniz into a universal scientific principle.

2.4 Leibniz’s Hermetic Rationalism We could describe this cosmic view of Leibniz’s expression, his hermetic rationalism, in four propositions: 2.4.1 Specular Harmony Between Minds and Things That is, the principle of harmony-perfection has two convergent symmetrical sides: (1) the world is an ensemble of infinite actu existing, alive, active beings, which

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are all related among themselves: it is the harmony of things; (2) every rational act (experience plus theoretical reason) is specular by definition, that is, every one seeks to reflect as a mirror, in a more or less perfect way according to their own inner coherence, the other rationalities: it is the harmony of minds. In this way, the specular relationship between things and human reason is a hermetic fact, a holistic, intellectual intuition, which is not demonstrable by empirical reason or necessary in the sense a mathematical equation is, but is a contingent fact, a product of the divine free choice. The universal harmony and our intellectual expression are the two symmetrical sides of one and the same reality. (Leibniz never seeks to demonstrate this specular harmony: he always presupposes it and uses it like an axiom.) 2.4.2 Not Empirical or Mathematical, but Hermetic Rationality Although our mathematical rationality cannot exceed the limits of phenomenal abstract science, the specular relationship – by virtue of the expression – assures the validity of our knowledge in the real world of substances. Indeed, even though these are in themselves unknowable, the expression establishes a bond between us and them. The expression guarantees that the more coherent and manifold the intellectual representations we manage to establish among the observed phenomena are, the more real our knowledge will be. Leibnizian rationality is characterized by this increasing and asymptotic approach to the real. The foundation of that rationality is not demonstrable or refutable either from sceptical phenomenalism or from pure mathematical deductive rationality. So, it is a hermetic rationality. It is Rational because it involves only the rigorous use of our reason and because it is not an emotional impulse or a mystical theophany; being a part of nature, it performs the function of expressing our rapprochement to the infinitely real. But, at the same time, it is a hermetic rationality, because the intelligibility of the real, which the mathematical formulates abstractly, reveals itself not as a “caeca necessitas” (which would exclude the contrary), but as an effect of God’s free will, a will that chooses the most perfect (although the less perfect is still possible). Although the optimum is also calculated as a maximum, it does not exist as a maximum but as an optimum.4 2.4.3 Analogy and Reversibility Between Principles and Laws Since the expression guarantees the link of our rationality with being, we can argue a posteriori (by the experience, like an empiricist) with the most perfect guarantee of truth without any reference to the principle of harmony (“that all bodily phenomena can be deduced from the efficient mechanical causes”; GM 6 242); but, for the same reason, we can also use the principle of harmony as much as to confirm the validity of the laws of nature that experience and calculus reach as to adjust them to it (“but the laws themselves of mechanism are to be derived from higher reasons”, ibid.). In turn, metaphysical principles that govern phenomenal laws of nature, because they are not really based on our logical deductive reasoning but on the harmony of things, on the optimum or the architectonic realm, do not depend on this reasoning

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(even though we can only grasp them and formulate them by means of it). In other words, the reversibility or equipollence of metaphysical principles does not imply their scientific invalidity; on the contrary, their mutual convergence, as well as the convergence of our phenomenal experience with them, is the guarantee of rationality. Leibniz’s science is a specular or convolute science. 2.4.4 Practical Reason Therefore, human reasoning is in no way an abstract construction detached from the harmony of the world; it is, on the contrary, the expression of the same universal harmony in the process of becoming. It is therefore a practical rationality. As the Hermetic Tradition taught, man is both a “microcosm” and a “co-creator” of the world, a co-worker with the sovereign Architect in transforming nature by transforming himself. This cooperation of man both with things and with the author of things implies that, although knowledge and action are different operations, both of them must cooperate in the limitless progress, in the “increase of truth and mercy”. Any rupture between science and morality is, for Leibniz, an assault on reason. There is no epistemic subject without a moral subject. The hermetic theory of expression leads Leibniz to the most radical anti-Cartesianism, to the dream of a different enlightenment, which unfortunately did no come to pass. This view of world activity, as the unfolding of the infinite divine activity, formally overflows any mathematical describable mechanism or rationality, either Cartesian, Newtonian or our own. Leibnizian rationalism is only intelligible from the cosmic unity of all the orders of being and from the transversal universal value of analogy as an ontological and epistemic structure. I have tried to suggest here that this is the essential common denominator of the Hermetic Tradition, which Leibniz provided with a new technical line of argument. He would be an “enlightened hermeticist”, if I can be allowed to use such an expression.

3 Some Examples of Hermetic Reasoning We will now seek to uncover specular proofs in Leibniz’s texts and describe their hermetic dimension. There are countless examples. In my last book and in earlier articles I have outlined some such proofs, and now I am working on others, extracted from the correspondence with Johann Bernoulli, B. de Volder and Jacob Hermann. As it is not possible to outline them in full here, I will only refer to some of them.

3.1 Activity of Substance The first is whether or not the activitas may be proved a priori as a definition of substance. This was the key problem in the correspondence with de Volder. The Dutch mathematician accused Leibniz of petitio principii: “but you, in order to

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prove unity, posit first the entelechies” (GP 2 254ff., 259, etc). Leibniz rejects angrily this claim and answers that the activity and the unity of substance can be proved only a posteriori, namely, from the subjective consciousness of our I and by means of the subsequent application of the principle of uniformity and variety of nature, which makes us understand that our human condition is not an exception in the world, and therefore it is reasonable that there are other Is in it (GP 2 264, 270, 275, 282; GM 3 756, etc). Nevertheless, neither this principle nor the other ones, Leibniz repeats tirelessly, are principles a posteriori: “every modification requires something durable” and “if there is nothing truly one no true thing exists” (GP 2 251).5 Moreover, the concept of unity that Leibniz deals with implies and actually contains the subject, which neither from the mathematical nor from the physical pluralities is logically deducible, as he himself had taught in the Specimen Dynamicum, in the Syst`eme Nouveau, and elsewhere (GP 4 478ff.; GM 6 241ff.). All this leads to the conclusion, then, that Leibniz presupposes the identification of unities with active living subjects, as it is very easy to compare with many other texts (for example, De vera methodo phil. et theol.:) the body is therefore an extended agent, provided that we admit that every substance acts, and that every agent is a substance. It can well be shown from the inner principles of the metaphysics that what does not act does not exist, because the power of acting without any start putting into action is nothing” (GP 7 326).6

The Plotinian origin, which is hermetic, of this theory is evident.

3.2 The Principle of Continuity A second very important example of specular reasoning is the treatment Leibniz gives to the principle of continuity. Continuity was a hermetic belief, which alchemists, botanists, physicians and “philosophers” had always used in order to understand and to “put at work” the universal transformation of minerals and organisms. The fact is that Leibniz did not understand it as an abstract or ideal truth of mathematical origin but as a truth of fact, a practical truth, which derives from the principle of perfection or the divine order law (GP 2 168ff.). This allowed him to use it as a universal analytic-analogical tool and to make it convoluted with the different ontological orders of the world. He employed it “in a manner that nobody had previously used it”, says a proud Leibniz (GP 3 52; GM 6 129ff.; GM 3 544s, 549, 553, etc). Let us remember some cases: (a)

Following the Hermetic Tradition, Leibniz establishes, in a convoluted way, the continuity in transforming organisms (GM 3 544ff.) and minerals (Protogaea), to the point that the famous distinction between “machines of art” and “machines of nature” (GP 4 481) – a very important distinction in Leibniz’s system – seems to be almost vanished into the continuity: “organism of the living beings is nothing else but a more divine mechanism, which goes in its subtlety into the infinite” (C 16).

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(b)

In the controversy with Locke and Bayle about primary and secondary qualities, Leibniz points out the continuity between “distinct” and “confused” perceptions through the petites perceptions of the united unconsciousness of the subject (NE 4.6.7, GP 5 383–385).

(c)

There is elasticity in all bodies, and therefore there are no physical atoms because of the continuity both in the motion of bodies and in all degrees of perfection of beings. Otherwise, Leibniz says, “none of our dynamic theorems would be valid at all” (GP 2 158ff.); thus, elasticity and continuity, the first in the natural system and the second in the metaphysical realm, are two principles which surround each other, forming a circle: they are two different but equipotent principles; in short, they do this by virtue of the principle of perfection, “tout va a` l’infini dans la nature”. The ddifferential calculus (i.e., the understanding rest and equality as a motion or an inequality smaller than any given) is a technical strategy of the mathematical approach, whose cosmic meaning goes beyond the value of the equations as such. Indeed, the differential calculus is only a particular case of the universal world continuity.

(d)

3.3 Overdimension of the Mathematical Equations This last proposal leads us to a third example of specular reasoning, which runs through all of Leibniz’s dynamics. If I may coin a new phrase, I would like to say that Leibniz “overdimensions” all his mathematical equations, that is, he gives them a cosmic meaning, which they themselves, though formally well constructed, do not have. The reason, in my opinion, is that Leibniz starts from a hermetic concept of inertia very different from Descartes’ or Newton’s. Opposing Newtonian inertial inactivitas (inactivity), Leibniz stresses the active conservation of the force-plusresistance of every body as an expression, in the derivative forces, of the entelechyplus-prime matter of simple substances. It is worth distinguishing these concepts. Leibniz understands by ␶o␦␷␯␣␮␫␬´o␯ two things: the entelechy or activitas (which expresses itself phenomenally in the living force of bodies) and the prime matter or extensionabilitas (which expresses itself in the resistance of bodies). There is, therefore, a perfect correlation between the inside equilibrium – between entelechy-plus-prime matter – of the simple substance (primitive forces) and the outside equilibrium – between the elasticityplus-resistance – of the impacts of bodies (derivative forces). The problem of the “self-convolution” of this system consists in not knowing whether the derivative forces are deduced from the primitive forces (which does not seem to be possible, as the extended cannot be deduced from the non-extended), or whether, on the contrary, the empirical study of the impacts of the bodies raises us to the realm of active substance (which leads us to another concept of science, where the “suprageometric”, that is, what is the very real, is something essential to construct our science). In his innumerable texts, Leibniz just says that “phaenomena (sive materia secunda)

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resultant ex entelechiis”7 (GP 2 250, 251, 256, 264, 268, 275, 282), but he never explains precisely how we should understand such “results”. Only the expression remains, the hermetic expression, that is, the specular relationship between both levels, without any empirical or mathematical proof. When Leibniz expounds his a priori and his a posteriori arguments, he implicitly takes for granted this specular structure, he does not prove it, and it is embodied in the conclusion of his equations. This is what I would call the “overdimension” of the Leibnizian equations of dynamics. Let us see some of his suggestions. In Dynamica de Potentia (1690, p. II, sec.2, cap.2, prop.17 (16); GM 6 502), Leibniz wrote that he suspected that by means of some secret procedure, nature effectively maintains its efforts, and the particulars of every body.8 In the correspondence with Johann Bernoulli, with de Volder and with Papin, Leibniz repeats the same idea in another more explicit manner. In search of the way to reduce the measure of forces to an arithmetic calculus, Leibniz says that, when repeating the standard measure, a modal repetition (when only velocity is repeated) is not enough, but a real repetition (when the body, that is, the resistance, also has to be repeated) is necessary. “I understand,” Leibniz says, “that we must repeat the real potentia, namely, that one which includes the subject”.9 A body twice A moved with a velocity e, that is, Ae + Ae, is not the same thing as a body A moved with a velocity twice e, that is, Ae + e, because, although in the latter case the velocity has been duplicated (modal repetition), the body has not been repeated at the same time (this would be the real, complete repetition). Leibniz writes to de L’Hospital: “Between two bodies with the same quantity of motion, the one which is smaller will develop more force, because it resists less” (GM 2 305–311); and, to Bernoulli, “I suspect that the other things that still arouse in you some doubts only come from not having noticed that, which is for me the prime principle of the Universal Art of the Measure, namely, the Science of Quantity in general” (GM 3 221). Following his much admired Kepler, Leibniz transformed the old notion of inertia sive tarditas naturalis into a new concept of materia and resistentia. Leaving aside whether Leibniz was right or not (he probably was not), the truth is that his physical approach goes beyond the kinematics of his masters. He maintains almost literally Galileo’s and Huygens’ equations, but he inserts us, with them, into the interior of the bodies. Huygens understood that the three conservation equations (that of the respective velocities, v − y = z − x; that of the common centre of gravity or conservation of the direction of progress, av + by = ax + bz; and that of the living force, mv 2 ) showed different aspects of the relativity of motion in a kinematic universe constituted by particles which impact among themselves by inertia. On the contrary, Leibniz, with the same equations, understood that the two relative conservations (that of the respective velocities, and that of the quantity of forces-progress) were the specular and full expression of the absolute (mv 2 ) in the relative. With these tools in his hands, Leibniz outlined in 1686 his Brevis demonstratio erroris memorabilis Cartesii, which is well-known and thus there is no need to reproduce it here. However, it is worth recalling the comment Leibniz sent to Bayle. It deals with an a posteriori argument: we have to measure forces by the quantity of the effect.

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This requires two things: first, knowing that the whole effect has been produced; second, knowing that the whole effect produced is the whole effect that can be produced; this presupposes a new metaphysical principle, that of the equivalence between the full cause and the entire effect. It is worth remembering that this principle was, of course, well known by the scholars of that time and was already implicitly used by Descartes and Newton (in the third law of the Principia). Nevertheless, Leibniz, using an apparently neutral language, gives it a different meaning. He describes it to Bayle in this way: “This law says, not only that the effects are proportional to their causes, but something more, that every effect is equivalent to its cause” (GP 3 46; my italics). With these words, Leibniz moves us into the bodies, into the inside of each body, namely, into the ␦␷␯␣␮␫␬´o␯ or the inner equilibrium of “entelechy-resistance” which the body already has. That is why he adds: I have shown that force is not to be measured by the composition of the velocity with the magnitude, but by the future effect. Nevertheless, it seems that the force or power is something real already from the present, while the future effect is not. Hence it follows that it will have to be admitted that there is inside the bodies something different from the magnitude and the velocity, unless we want to deny to bodies all power of acting (GP 3 48; my italics).10

This last belief, stressed by a strong “unless” (`a moins que), is for Leibniz a presupposition about which he has no doubt, but which Bayle, Huygens, Newton and Descartes refused to admit, because it introduced a disturbing indemonstrable element into science. It is obvious that Leibniz works in another world, not merely the phenomenal one. Only by supposing, before the proof, that the body already has its force (that is, its activity and its own resistance) which could not be cinematically acquired from another body, could we conclude that cette chose de different (this different thing) is precisely ␶o␦␷␯␣␮␫␬´o␯, its force, and that the future effect is not produced by any other inertial mechanism, as his opponents thought. So, Leibniz’s conclusion is logically mistaken; it is wrong, it is a petitio principii, it is a convoluted argument, a hermetic argument.

3.4 The “In-esse” Principle Finally, I would like to refer to a fourth example: the “in-esse” principle. In his reply to Dascal, Schepers rightly says that the chasm between necessary and contingent truths cannot be bridged. The ‘inexpectata lux’ (1686) allowed Leibniz to transfer the analyticity from the necessary to the contingent truths: the inclusion of the predicate in the subject. Otherwise, there would be no way of using the notio completa to ground the metaphysics of possible worlds [. . .], which cannot be achieved by mere metaphors [. . .]. In any case it is more than a handy and suggestive analogy, viz. a metaphor (Schepers 2004: 126).

I have no objection to this, and I suppose that neither would Dascal. No doubt, the “in-esse” principle was a brilliant Leibnizian invention for saving his metaphysics from Spinoza’s necessitarianism. Nevertheless, to my mind, the “living mirror”

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metaphor, as I suggested earlier, is in no way a mere metaphor, but an ontological structure of universal representation, as it had been used by the Hermetic Tradition. The main question to be elucidated in the correspondence with Arnauld is the reason why Leibniz affirms the continuous and spontaneous production of thoughts in the mind, and why the present thoughts are predetermined by the preceding ones and, in turn, prefigure the future ones, and why, therefore, “the nature of an individual substance is in fact to have such a complete concept, that it may be deduced from it all that can be attributed to it” (GP 2 41), and why, at the same time, it represents in itself all that happened, happens and will happen in the universe (GP 2 39). This reason, the reason of the permanence of this identity, Leibniz says, must be a priori: “my attributes of time and previous states and my attributes of time and following states are both predicates of the same subject (insunt eidem subjecto)” (GP 2 43). But it will not be necessary to study Hume in order to understand that, beyond the subjective consciousness of our I, we try to assert that the different attributes of time and present state, as well as that of time and future state, are ontological predicates of one and the same subject. Thus, we take for granted, but do not prove, the existence of the subject. That is, there is in no way an a priori argument, specifically, an analytic one, which could give the reason for the facts of the world and about the existence of subjects. Leibniz compares demonstratively the analyticity – or logical completeness – of true propositions with the spontaneity – or ontological completeness – of the individual substances. He says: “It is true that the results from such a manifest dogma are paradoxical, but I want to say nothing more but what all philosophers understand when they say that “the predicate is in the subject of a true proposition”.11 However, this is not the truth; logicians taught something very different than he did: a logician cannot speak about ontological subjects. This paragraph of the correspondence with Arnauld is a significant example of specular reasoning; even the subtle irony of Leibniz’s phrase shows it: “It is a lack of the philosophers, who do not carry through the clearest notions” (ibid.). Leibniz is establishing infinitely much more than what the logical “in-esse” principle contains; here it is an “overdimensioned principle”. He is convinced that nature is full of subjects, that it is already constituted of real, active, alive, complete subjects, or of “living mirrors” as the Hermetic Tradition taught. Leibniz makes the ontology of spontaneity semantically slide into the logic of analyticity, and he works on the specular characteristic of the “in-esse” principle. In other words, the analyticity of logical truth and the ontological spontaneity of the individual substance are two very different but equipotent principles, which express by analogy, each one in its language, one and the same world: the inner activity of every substance and, as a result of this primitive activity, the inner activity of every body and of every particle of matter in the derivative forces of the phenomenal world. So, it is obvious that there is no a priori reason other than the fact that [t]hese [ontological] principles were laws enclosed inside the subject or inside my complete notion, which makes what is told I, and which is the connecting ground of all my different states, and what God understood perfectly from all eternity (GP 2 43; my italics).

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It is clear that in Leibniz’s thought “representing” and “being” are for a monad the same thing, that is, two different but equipotent principles in the analogical unity of the universe. This is, in my opinion, the hermetic meaning of “living mirrors”, which are not, in fact, as Schepers states, “a handy and suggestive metaphor” (ibid., 126), or “a striking and picturesque formula”, as Jolley puts it (2004: 133). Indeed, they are much more than that, as Leinkauf proved in the 1990s.

4 Provisional Conclusion Galileo pointed out that mathematics exhausts all the physical intelligibility of the world, and following his lead until now mathematicians and scientists have done the same. The only exception has been Leibniz. Why? My hypothesis is that only the adherence to an organic and holistic Tradition, which the new ontology of mathematics and of physics came to destroy, inspired Leibniz’s very original position, which still today amazes us and, perhaps, still confuses us. For Leibniz, mathematics only exhausts the phenomenal intelligibility of our measures. All the other, that is, the very real, monads, cannot be measured, they enveloppent l’infini (NE 3.3.6; GP 5 268). Nevertheless, Leibniz argues that monads and their metaphysical principles are the foundation without which all empirical science remains empty and consists of pure appearance. My suggestion is that maybe expression as a hermetic analogy could help us to understand better the mystery of Leibniz, which is perhaps our mystery: no matter how strange it might seem today, without the monads, without inner life, there is no possibility of science in the strict sense!

Notes 1. “Eventu magis quam demonstratione necessaria, hoc principium varie compositi motus idem efficiens stabiliri fatendum est, neque causam quaerentibus aliam occurrere, quam Harmoniam sive perfectionem rerum, a qua in universum verum est pendere leges motus, tanquam effectus supremae Mentis, non a surda quadam necessitate, qualis geometrica est [. . .]; quam hypothesim a priori non facile demonstrabit aliquis, aut geometricae vel metaphysicae necessitatis esse ostendet [. . .]. Ex his vides, etiam non esse cur putes, uno tantum me usum principio, nempe reductionis ad motum perpetuum tamquam absurdum: quamquam adhibui in Actis, ut rem intellectui omnium accommodarem. Caeterum vix ulla excogitabitur Methodus, qua non sim usus ad idem efficiendum, nempe non tantum ope gravium, sed et elasticorum deprimendorum, aequalitatis effectus et causae; aequalitatis inter actionem et reactionem concurrentium, indiscernibilitatis hypothesium, evitandi saltus et interventus virium mortuarum, compositionis motuum, et speciatim concursus oblicui [. . .]. Cui [Voldero] haec puto non ingrata erunt de legibus Naturae, non ex geometrica necessitate, sed Sapientiae et Harmoniae principio plene derivandis [. . .], ut de Supremo Autore in ipsis Legibus suis generalibus Natura testetur, quod cesaret, si geometriae demonstrationi locus foret” (GM 3 727–730; my italics). 2. “C’est ce defaut mˆeme de la necessit´e qui releve la beaut´e des loix que Dieu a choisies, o`u plusieurs beaux axiomes se trouvent reunis, sans qu’on puisse dire lequel y est le plus primitif” (Th´eodic´ee, 347; GP 6 320ff.).

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3. “Ideam itaque rerum in nobis esse, nihil aliud est, quam Deum, autorem pariter et rerum et mentis, eam menti facultatem cogitandi impressisse, ut ex suis operationibus ea deducere possit, quae perfecte respondeant his quae sequuntur ex rebus [. . .], modo habitudinum quaedam analog´ıa servetur (. . .). Omnis effectus integer repraesentat causam plenam [. . .] et mundus ipse quodammodo repraesentat Deum” (Quid sit idea: GP 7 263ff.). 4. “Dei cognitio non minus est principium scientiarum, quam essentia ejus et voluntas principia sunt rerum [. . .], ut ex consideratione Mentis potiora Physicae dogmata deducantur”, (Principium quoddam generale: GM 6 134); “ita ut simul et regno potentiae maximum et regno sapientiae optimum obtineatur” (my italics) (Specimen Dynamicum I: GM 6 243; my italics). Fichant (1994: 286) says: “Mais au-del`a de cet aspect cat´egorique [of the idea of cause, effect, power, action as universal notions a priori], le ‘Nouveau Principe de la mechanique g´en´erale’ [the leibnizian principle of equivalence between the full cause and the entire effect] offre une voie pour reconnaˆıtre que la condition de possibilit´e de la math´ematisation ne rel`eve pas elle-mˆeme de l’intelligibilit´e math´ematique dont elle fonde la pertinence”. 5. “Omnis modificatio aliquid durabile supponit” and “Quodsi nullum vere unum adest, omnis vera res erit sublata” (GP 2 251). 6. “Corpus ergo est agens extensum, modo teneatur omnem substantiam agere, et omne agens substantiam appellari. Satis autem ex interioribus metaphysicae principiis ostendi potest, quod non agit non existere, nam potentia agendi sine ullo actus initio nulla est” (GP 7 326; cfr. also NE 2.23.72; GP 5 195; De ipsa natura, n. 9, 13, 15; GP 4 508, 512). 7. Phenomena (i.e., second matter) result from entelechies. 8. “Suspicor autem Naturam arcanis quibusdam modis omnes suos conatus etiam particulares conservare et ad exitum perducere”. 9. “Intelligo autem potentiam suum subjectum includentem seu realem repeti [. . .], non vero sufficit aliquid modale repeti, verb. gr. gradum velocitatis repetitum corpore non repetito” (GM 3 220; GM 6 208ff.; GP 2 150ff.). 10. “J’ay montr´e que la force ne doit pas s’estimer par la composition de la vitesse et de la grandeur, mais par l’effect futur. Cependant, il semble que la force ou puissance est quelque chose de r´eel d`es a` present, et l’effect futur ne l’est pas. D’o`u il s’ensuit qu’il faudra admettre dans les corps quelque chose de different de la grandeur et de la vitesse, a` moins qu’on veuille refuser aux corps toute la puissance d’agir” (GP 3 48; my italics). 11. “. . .praedicatum inesse subjecto verae propositionis” (GP 2 43).

Chapter 7

Symbolic Inventiveness and “Irrationalist” Practices in Leibniz’s Mathematics Michel Serfati

1 Inventiveness and Rationality This paper is devoted to Leibniz’s practices – whether rationalist or not – with respect to mathematical invention and the creation of new mathematical objects. These two features were deeply-rooted in the completely new mathematical symbolic writing, which had appeared at Leibniz’s time. More precisely, they were organized around the (then new) possibilities of substitution within that symbolism. Detailed study brings to light an epistemological scheme involving two stages, substitution and control, which embody a tension between inventiveness and rationality.1 The conclusions will be presented in two final sections, “ ‘Ars Combinatoria’ and ‘natural selection’ ” and “The Leibnizian ‘paradox’ ”. Various effective and important Leibnizian examples could be used to illustrate the mechanism, for instance the so-called “Leibnizian” exponential of sign az , or the formula for the n-th differential of a product of two functions, or the discovery in 1673–1676 of the Leibnizian “New Calculus”. I examine the second example below. As to the first one, recall briefly that, by means of an exponential which originally lacked any signification (z is the sign of an arbitrary number – real in modern terms), Leibniz hoped to go further than both Descartes’ a3 and Newton’s am/n (cf. Serfati 2005: 325–343; Breger 1986). However, I chose to illustrate the process via the third example, the elaboration of the Leibnizian “New Calculus”.

2 Leibniz and the Establishment of Symbolic Notation With respect to the establishment of mathematical symbolic writing, Leibniz’s role is specific. He did not invent the general structure of the symbolic apparatus: rather, he inherited it from Vieta, Descartes and Newton – even if he supplemented it with a lot of signs of his own – but he was actually the first to grasp and exploit its

M. Serfati Institut Henri Poincar´e, Universit´e Paris 7, Paris, France

M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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outstanding power, and to develop, in a very modern fashion, some applications inconceivable for his predecessors. First, faced with a lack of general comprehension – especially from Tschirnhaus – Leibniz put into circulation dozens of new signs, which he could test, in order to select the most appropriate. But above all, equipped with an outstanding symbolic imagination and an inveterate optimism, Leibniz developed the new symbolic system in such an optimistic way and across such various contexts that he enriched it, simply by making it work, especially by the repeated use of the so-called technique of “metamorphosis”. In Leibnizian terminology, this term denotes some systematic, blind trials of successive substitutions – originally irrelevant for the most part to any questions of meaning and rationality. Here is, for instance, a quotation from Leibniz’s correspondence about his Arithmetic Quadrature of the Circle: But, the ordinates of the circle being irrational, I have endeavored to transform the circle in another figure of those I call rational, i.e., those whose ordinates are commensurable to their abscissas. For this purpose, I have enumerated many metamorphoses, and having tested them by means of a quite easy combination (for I could thereby write in one hour a list of more than 50 plane or solid figures, different and yet dependent upon the circular one), I soon found the means that I will explain. However, I thought it is useful to note this en passant in order to justify what I had once said about the utility of combinations for discovering things that algebra and, if you wish, even analysis – as known to us today – would not be able to discover. It turns out that the means provided by the combinations allows one to find an infinite number of figures that are commensurable to a given figure.2

This methodological standpoint, by using the rich possibilities of “combinatorial” substitutability, is a very important epistemological feature of the new formalism, and was not enforced by Vieta or Descartes – though they paved the way – but rather by Leibniz who made everyday use of it. For instance, he discovered what he called first “Algorithme”, then “New Calculus” – which turned out to be the core of his infinitesimal calculus – by a systematic use of “metamorphosis” inside some originally organized symbolic forms. This scheme – theorized by Leibniz under the name of Ars Combinatoria – was radically novel. Hence, for Leibniz and his successors, the mere synoptic survey of some symbolic forms or formulas was often at the origin of ideas governing their manipulation, sometimes in ways linked to their interpretation, but often in ways far removed from any initial consideration of rationality.

3 Leibniz’s “New Calculus” 3.1 Leibniz’s Conception of His Calculus One of the epistemological lessons drawn by posterity from Descartes’s conclusion as to the representation of “powers” was Leibniz’s analogical creation of his “New Calculus”, following an approach that one can trace for instance from Consid´erations sur la Diff´erence qu’il y a entre l’Analyse Ordinaire et le “Nouveau

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Calcul” des Transcendantes.3 This is a text in which Leibniz explains his conception of his “Calculus”, as compared to those of Vieta and Descartes, focusing only on their “five operations”: in this old “Calculus”, the mutual relations of signification between the five operations had long since been exhaustively analyzed (sums of products, products of sums, roots of quotients, etc.). However, with the advent of the symbolic notation, this inventory was carried over to the so-called “combinatorial field”,4 by a survey, also exhaustive, of various substitutions in “forms”, organized around the existing assemblers, “cross”, “linear absence”, “line”, “bar”, “vee” (for these terms, cf. Serfati 2005: 12–13). Leibniz then considered that he had extended the list  by the adjunction of two prehensors (one place-assemblers) with signs d and (hereafter designated as “dee” and “esse”) interpreted as differentiation and summation. Thus, these signs were assemblers with one  place only (down the line) which was firstly occupied by a “letter” such as “dx” or z. Afterwards it transpired, within the new calculus, that Leibniz had to re-examine combinatorially – that is, primarily regardless of any signification – all the “forms” that he could obtain by all possible substitutions, so that they involved both old and new signs for operations, and examine only afterwards their possible significations.

3.2 The Nova Methodus With respect to the “dee”, Leibniz undertook an exhaustive exploration of the possibilities of symbolic manipulation in the first part of the Nova Methodus of 1684,5 the text which, as is well known, marked the official creation of the Calculus. In fact, with respect to the combinatorial aspects, Leibniz explored all the possible “forms” that he could get by substituting in place of x inside dx five of the forms previously organized in the Calculus of Vieta and Descartes, so that he could obtain:   v d(xa ) d(x + y) d(x − y) d(xy) d y the meanings of which forms he interpreted afterwards as so many open questions, thereby wondering about the value of the differential of a sum, a difference,6 a product, a quotient7 or a power.8 As to the differential of a product, for instance, one has, as he observed, d(xy) = xdy + ydx, which is a formula that did not spontaneously occur to him, and which he had difficulty in proving.9 It is also a result which became – and remains – important under the name of integration by parts.10 Such a system of rules of operation, completed by adding the five properties above, Leibniz at first called the differential algorithm (GM 5 222). It included the new concept of the differential within the field of significations, as well as the “dee” on the combinatorial side. The algorithm also contained the old “Calculus”.

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And one can easily understand from this example to what extent the study of the combinatorial generation of all possible collections of signs contributed to mathematical invention. Since, for instance, the very idea of seeking a formula for the differential of a product could hardly have arisen naturally within the conceptual structure of the “Old Calculus”, it had no immediate geometric meaning (one cannot directly represent an ordinate on a geometric figure as the product of two ordinates). Therefore, the Ars Combinatoria contributed here, not so much to finding proofs, but to suggesting ideas of some properties to be proven, thus exploring a new area of the Ars inveniendi.

3.3 The Ars Combinatoria Since then, Leibniz never ceased proclaiming the virtues of his Ars Combinatoria. He dealt therefore with a crucial chapter of pure invention in mathematics, for which, even now, no treatise of method had at that point been written. Beyond these wishful proclamations – though very clear – Leibniz unfortunately did not explain himself in any detail concerning his own mathematical practice, nor what should be the actual modalities of application of his Ars Combinatoria to his algorithm, as proposed supra. The “algorithm” is abruptly presented without any explanation or proof but only ironically preceded by “Here are the rules of the Calculus” (“His positis, calculi regulae erunt tales”; ibid., p. 220). Therefore, unsurprisingly, despite the impassioned proclamations of its author, this systematic approach was misunderstood by his colleagues, especially John Bernoulli who, in the beginning, considered the Nova Methodus as “an enigma rather than an explanation”.11 Nevertheless, this methodological stance constituted the active principle of Leibniz’s research.

3.4 Representing Repetition: The Scheme Since the “Old Calculus” was wholly contained in the new one, it naturally allowed the substitution of more complex “forms”, such as d(6x2 − 3xy + 5), or12  x3 x4 x x.x + + + + etc. d 1 1.2 1.2.3 1.2.3.4 

Later on, Leibniz noticed that “dee” was a one-place assembler, so that some “forms”, such as d(dx)

and

d(d(dx)),

were also combinatorially legitimated.13 In a natural way, Leibniz interpreted these as the repetition of the differential which he named the second and third differential, and represented in symbols14 by d2 x or d3 x.

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Thus the Cartesian exponent found in Leibniz a new interpretation for which it had never been intended, namely to indicate repetition. This role, established by Leibniz, is now quite common in the representation of iteration by composition.15 Quite naturally, Leibniz also made the same substitutions in the “forms” organized in this new way and hence obtained for instance d3 (2x2 − 4x + 5). Later on, once more, he introduced summation, another operation symbolically represented by a second one-place assembler, the “esse”. As a next step, repeating summation was allowed,16 yielding, for instance,17  

   × or

×

which he represented once more with Cartesian exponents (cf. Jean Bernoulli to Leibniz, April 20th, 1695; GM 2 171) and thus got 2

3 z or

z

which he named naturally “second sum” and “third sum”. Afterwards, substituting in place of x in these “forms” lead him to new and more complex examples, such as 3 (5x4 − 6x + 7) In many papers – the Consid´erations are one example – Leibniz expressed his great satisfaction at having brought to light a scheme involving doubling and repetition, which for short may be hereafter termed the Leibnizian Scheme.18

3.5 Representing Duality Moreover, since   both “dee” and “esse” were one-place assemblers, such “forms” as dx or d x, were legitimized and interpreted by the successive execution of differentiation and summation, performed in both possible directions. By that move, Leibniz “established” the two formulas:   dx = x and d x = x valid whatever the value of the “ordinate” of sign x. As Leibniz wrote to Jean Bernoulli (October 3, 1696; GM 3 802): “Ita et d conjuncta se mutuo tollunt”. This was a double formula of considerable importance which Leibniz proved (or believed that he had proved) by geometric methods inspired by analogy with some properties of sequences of integers which he had studied in Paris – they are now

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called “finite differences”. In a somewhat artificial manner, he reconstructed the genesis of his proof in 1713 in “Historia et Origo Calculi Differentialis” (GM 5 392–411), an appropriate text in the context of the priority dispute with Newton. However that may be, differentiation and summation, like “power” and extraction of roots, were in turn considered by their discoverer as two opposing operations, insofar as their successive execution might lead to identity, in whatever direction they are performed. They formed a second epistemological scheme, of another nature, hereafter called Duality to which Leibniz also attached great importance. Amazed by his own discovery, Leibniz even showed that the analogy between the two pairs, “power”-root on the one hand, and differentiation-summation on the other hand, could be further extended with respect to effectiveness, since in each of the two pairs there is one of the two terms which can be explicitly performed (“power” or differentiation) while the other (root or quadrature, that is summation) cannot, generally speaking. Here is Leibniz’s quotation: For, this method, or this differential calculus, serves not only for the differences, but also for the summations, which are the reciprocal of the differences, more or less as the ordinary calculus does not serve only for the powers, but also for the roots, which are the reciprocal of the powers. And the analogy goes even further. In ordinary analysis it is always possible to perform a computation by freeing it from hindrances and roots by means of the powers. But the public doesn’t have as yet the method to free it from implied powers by means of pure roots. Likewise, in our analysis of transcendents, it is always possible to free the computation from hindrances and summations by means of the differences. But the public doesn’t have as yet the means to free the implied differences by means of pure summations or quadratures; and since this is not ordinary arithmetic, nor is it always possible to effectively provide summations or quadratures in order to yield the ordinary or algebraic magnitudes of ordinary analysis [. . .]. And I have thereby provided a general way in terms of which all problems, not only of differences or summations, but also of difference-differentials or summations of summations and beyond, can be constructed sufficiently in so far as practical matters are concerned [. . .]. Finally, since our method is indeed the part of mathematics that deals with the infinite, it is the method which one needs in order to apply mathematics to physics, given that the character of the infinite Author is normally involved in the operations of nature.19

So, Leibniz wrote, “il n’est pas toujours possible non plus de donner effectivement les sommes ou quadratures” (GM 5 308), i.e., summations are not always performable. However, to state that a summation represented by some “form” was not performable meant that one could not provide any symbolic representation of the “form” other than the “form” itself. In other words, that it had no possible interpretation other than a certain summation (cf. Serfati 1996). However, since then, some “forms” which initially lacked any geometric signification, having been obtained only by the pure combinatorial play of a succession of substitutions, such as  5

x3 + 2x2 − 1 4x + 1

or (Jacques Bernouilli to Leibniz, 28 February, 1705; GM 2 97):

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131

 mx + n, dx3 hx3 + ixx + kx + 1

or else (Jean Bernouilli to Leibniz, April 20 1695; GM II 171): 

 ze dm n

+e

ze−1 dm−1 n dz

now appeared as combinatorially legitimate, and were actually proposed by Jean Bernoulli and Leibniz, so bringing to light a whole list of new problems and concepts. That any new symbolic structure had to be open to substitutions turned out to be an essential requirement, which one can find illustrated in every page of Leibniz’s practice. Leibniz took a legitimate pride in his “New Calculus” which, after 1690, he also called Analysis of transcendents.

3.6 New Calculus and Old Geometrical References This class of new problems created in the late seventeenth century had definite and deep roots in the practice of substitutions, that is to say it had a combinatorial origin, which did not involve the significations. Actually, in the example above (from 1695) of a certain “form”, there was no longer any referent that really could be represented on a geometrical figure, but only some implicit possible remote linkage to Geometry, operating as a warrant. Therefore, Leibniz and Bernoulli could only mechanically weaken the field of significations. So, in Leibniz the symbolic text itself has sometimes taken first place, chronologically and conceptually. At the end of the seventeenth century, the ancient geometrical reference, weakened by this development, sometimes completely disappeared, which paved the way for algebraic and more modern methods, conceptually distinct from all previous ones.

3.7 Leibniz and the Historical Commentary Finally, one must rectify the idea of Leibniz as a “master-builder of mathematical notations” (Cajori 1925) or “Begr¨under der symbolischen Mathematik” (Mahnke 1926). As already noted, Leibniz did not invent the symbolic system, which was definitely set up before him by Vieta, Descartes, and Newton (assemblers with open places, signs of aggregation and constitution, substitutions “in the place of the exponent”).

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4 Ars Combinatoria and “Natural Selection” 4.1 Field of Significations and Combinatorial Field: Substitutability Consequently, the field of knowledge to which Leibniz gave the name Ars Combinatoria may from then on be briefly described as a set of directions for the substitution of symbols. To repeat: For Leibniz and his successors, the mere synoptic survey of some symbolic forms or formulas could often be at the origin of ideas governing their handling, sometimes according to their interpretation, sometimes far removed from any such initial consideration of rationality. Before Leibniz, when the two aspects – combinatorial and conceptual – were first recognized and distinguished, the sole direction for any movement of thought which could be legitimately accepted between them was that of representation, that is, from signification to symbolism. Neither Descartes nor indeed Cardan thought it possible and legitimate to receive any conceptual suggestion from the sheer symbolic text! In contrast, Leibniz allowed the reception of direct information from the symbolism, that is, information not primarily correlated to any signification, and used it in turn to manipulate the same symbolism. In other words, he acted before understanding what the action meant; it was of course understood that a test of reality would afterwards ratify the process. To repeat: Leibniz was the first (and sole) mathematician in history who claimed the right of free action in this specific way, even if this practice became afterwards, and up to the present day, widely used by other scholars. By this action, he granted to the symbolic text this crucial capacity of “essentially conveying combinations of informations involving their own structure” (“v´ehiculer [. . .] des combinaisons d’informations portant sur leur propre structure”), as Granger (1968: 22) rightly stressed.20 While doing this, Leibniz obviously had to take into account the symbolic field in its own right, that is, as endowed with an existence per se; thus, the autonomy of the symbolic text and the enlargement of the practice of the Ars Combinatoria were historically linked in an indissoluble way. Once translated into the field of significations, this Ars Combinatoria, which Leibniz trusted so deeply, led him both to some fruitful and unsuspected results, which could not have been otherwise obtained at the time, or to some (temporary) aporias, such as his early formula for the differential of a product, or his differentials 1 with rational exponents such as d 2 x (GM 3 228).

4.2 Natural Selection So, the Ars Combinatoria in Leibniz involves two necessary stages, namely genesis and ratification. In the first stage, one produces automatically (literal) formulas without regard to their signification, a procedure Leibniz highly esteemed; one recognizes here to what extent he was methodologically opposed to Descartes. In the second stage, the author himself or, alternatively, the mathematical community,

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will afterwards ratify, decide, select or eliminate, having surveyed the “blind” productions coming from the combinatorial system. The whole procedure can thus be described as a sort of “natural selection”; the unexpected character of some results must then be ascribed to the resistance displayed by some mathematical traditions and habitual practices. Some of these results, long established, enforced a fossilized view of the relations between existing concepts. Precisely because of its blindness, this kind of “combinatorial play” can free the mathematician from some of these constraints. At least Leibniz hoped so.

4.3 Leibniz’s Formula The outcome of the combinatorial substitution may therefore sometimes appear astonishing, even for its author, disclosing properties which he would never have thought of – one can here cite the well-known example of Leibniz and John Bernoulli, amazed by their discovery of the n-th differential of a product of two terms. This development can be found in the Leibniz-Bernoulli correspondence in 1710.21 Leibniz wrote dn (xy) = dn x d0 y + ndn−1 x d1 y +

n(n − 1) n−2 2 d x d y + · · · + . . . usque ad d0 x dn y. 2

He indicated that the coefficients involved in the formula are the combinatorial ones; also that, following the “law of homogeneity”, he wrote d0 y in place of y, in order to establish what he calls a “harmony”. One must stress the introduction of d0 y, actually a meaningless “form”, which appears as an absurdity if one describes it in natural language, but an expression whose constitution is however rightly presented by Leibniz as necessary to achieve and state the result (cf. Serfati 2001).22 On the other hand, according to the two geometers, the formula was obtained by pure substitution from the n-th power of a binomial, that is, from Newton’s formula in a very simple case. In order to further justify the structural analogy between the two formulas, Leibniz writes pn (x + y) in place of (x + y)n . He then obtains pn (x+y) = pn x p0 y+npn−1 x p1 y+

n(n − 1) n−2 2 p x p y+· · ·+. . . usque ad p0 x pn y. 2

This instance of Leibnizian metamorphosis operating on the symbolic text is quite remarkable. It is made up of two simultaneous substitutions, involving the two assemblers only, completely irrelevant to any signification: the “point” (multiplicative) substituted for the “cross” (additive) at the same time as the “dee” (differentiation) replaces the “pee”, the Leibnizian sign for the product. Nevertheless, the computation provided some valid and very important ratification, which has long since been taught in university first year courses under the name of the “Leibniz formula”. The correspondence between Leibniz and Bernoulli depicts a quite comical exchange between these mathematicians, amazed with their own boldness and

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discovery: “Et puto nescio quid arcani subesse” (“I think I don’t know what secret remains hidden”) writes Leibniz (GM 3 175).23 “Haud dubie aliquid arcani subest” (“There is no doubt that something secret remains hidden”) answers Bernoulli (GM 3 179).24 Thus, the combinatorial game may appear to run counter not only to habitual practices, but also, in a way, to rationality itself.

5 The Leibnizian Paradox 5.1 The Evolution of Leibniz’s Mathematical Conceptions (1672–1684) Now, a brief comment about the evolution of Leibniz’s mathematical conceptions. Newton’s two Epistolae of 1676 proposed to Leibniz two outstanding and distinct extensions of Cartesian exponentials, so as to imbue him with this staunch trust in the power of mathematical symbolic writing, which, though he had not previously shown any peculiar interest in it, he thenceforth never abandoned. Here is my analysis, from Serfati (2005: 334): By the end of 1676, Leibniz’s situation was the following one: having just ‘graduated’ from the Greek and scholastic rhetorical writing of mathematics of his youth, he had met (only two years earlier) the new mathematical writings in Descartes’s Geometry, as well as the recently introduced Cartesian exponent – and I have stressed to what extent it had been important for the Cartesian conception that a simple number be written in the place of the exponent. Leibniz, thus, had to familiarize himself – rapidly and globally – with the new symbolism, quite distant from the considerations that guided him in his youth. And then, two years after his meeting with the Geometry, and in less than four months (July-October 1676), this time due to Newton, he faced the need to integrate in his considerations two new exponential ‘forms’. These were obtained from the same initial Cartesian ‘form’ (which Newton had, in addition, literalized) by two successive extensions of the field. The fact that the first, broken version of the Newtonian exponential (in the Epistola Prior) was correctly and completely defined, while the second, surd, was far from it, was not a reason for Leibniz to worry.25 In fact, he drew from this a two-fold conclusion: On the one hand, that the Cartesian exponential ‘form’ was not combinatorially fixed, contrary to what the weight of a quite recent tradition might lead one to believe. On the other, that all the questions of meaning were in fact subaltern vis-`a-vis the power of the combinatorial realities (the primacy of the exponential ‘form’).

On the other hand, both Epistolae also brought a huge corpus of coherent and very effective formulas about powers series, a subject that Leibniz hardly knew at the time. The Epistola Prior, though not overshadowing Leibniz’s result on the Arithmetic Quadrature of the Circle, nevertheless dissuaded him for a while from working any longer in this direction. For all these reasons combined, Leibniz, back in Hanover, devoted himself to a new project, for the first time in a symbolic field, namely the elaboration of the Geometric Characteristic which he communicated to Huygens who was staying in Paris. My claim – “The Epistola Prior or Leibniz’s meeting the “forms” without substance” (Serfati 2005: 325) – is that the origin of

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all these symbolic preoccupations on Leibniz’s part is to be found in the Epistola Prior of June 1676.26

5.2 Leibniz and the Adepts I described already how, in 1683–1684, Leibniz developed his general “algorithm” of the calculus of differences, via his Ars Combinatoria, that is, primitively, regardless of any issues of signification. Recall that the Nova Methodus does not contain any proof of the results it states, important and true as they may be. Finally, I will evoke the essential paradox that Leibniz had to face from that point which remained with him all his life and which constituted the background of his quarrel with Newton: On the one hand, he was unable to give to his “New Calculus” any kind of “reasonable” ontological foundation (by “reasonable” is not intended the contemporary anachronistic meaning; rather, it is to be understood with respect to the mathematical ontology in force among the XVIIth century scholars for whom Leibniz’s so-called “explanations” about his infinitesimals, made via comparisons and analogy (for instance with the mechanism of imaginary quantities), turned out to be widely inadequate by the criteria of the time). On the other hand, once Leibniz himself, or his correspondent, had admitted its confused and even contradictory prerequisites, the “Calculus” developed into an extraordinarily productive machinery. Moreover, it led to a wide field of various applications, the obvious authenticity and effectiveness of which one could easily check. From the 1690s onwards, more and more mathematicians naturally wrote to Leibniz so that he could enlighten them as to the actual matter of the “New Calculus” which he had invented and of which they wanted to become adepts. These included young geometers such as De l’Hˆopital,27 Varignon28 or Grandi,29 but also wellknown scholars such as Wallis30 and above all Huygens,31 the ancient master, whose support for the Calculus was so much appreciated by Leibniz. The paradoxical exchanges of correspondence with the adepts underline the somewhat apparent uncomfortable situation of Leibniz. He was actually unable to provide any firm meaning to his fictions of “infinitesimals”, which were supposedly at the foundations. Nor did he think it possible, as did De Morgan (1849) and Babbage (1827) much later for instance, to ask willing followers, who would have agreed for the most part (for reasons of effectiveness), simply to make use of the rules of calculation, regardless of ontology.32 In responding to such correspondents, Leibniz contented himself with a ritual discourse where he started by evoking the analogy with imaginary quantities already established as a paradigm; afterwards he made them check, on the basis of more and more various examples, the faultless working of a machinery that he had erected with the perfect formal play of his Ars Combinatoria (cf. Serfati 2005). From a situation which appears retrospectively rather uncomfortable to us, Leibniz, on the contrary, drew very positive conclusions with his usual optimism. He strengthened his belief in the absolute capacity of symbolic writing per se – actually the sole theoretical strength of his “New Calculus” – a belief which became so firm

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as to constitute the crux of his vision of the mathematical world33 and of which his “principle of continuity” became one of the most perfect achievements.

Notes 1. Some of these conclusions were previously published in Serfati (2005). 2. Mais les ordonn´ees du cercle e´ tant irrationnelles, j’ai tˆach´e de transformer le cercle en une autre figure, du nombre de celles que j’appelle rationnelles, c’est-`a-dire dont les ordonn´ees sont commensurables a` leurs abscisses. Pour cet effet j’ai fait le d´enombrement de quantit´es de M´etamorphoses, et les ayant essay´ees par une combinaison tr`es ais´ee (car je pourrais par ce moyen e´ crire en une heure de temps une liste de plus de 50 figures planes ou solides, diff´erentes et n´eanmoins d´ependantes de la circulaire) j’ai trouv´e bientˆot le moyen que je m’en vais expliquer. J’ai cru cependant a` propos de remarquer ceci en passant pour justifier ce que j’avais dit autrefois de l’utilit´e des combinaisons pour trouver des choses que l’alg`ebre, et si vous voulez, l’analyse mˆeme telle que nous l’avons ne saurait donner. Or le moyen que les combinaisons m’ont offert sert a` trouver un nombre infini de figures commensurables a` une figure donn´ee (GM 5 90). 3. Journal des Sc¸avans 1694 (GM 5 308). 4. I suggested a conceptual distinction between “registre des significations” and “registre combinatoire”, i.e., “field of significations”, as opposed to “combinatorial field” (combinatorial does not coincide with formal; see Serfati 2005: 402–405). 5. “Nova Methodus pro Maximis et Minimis, itemque Tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus”. Acta Eruditorum, 1684 (GM 5 220). 6. Leibniz writes additio and substractio (addition and subtraction): “Jam Additio et Substractio: sit z − y + w + x aequ. v, erit dz − y + w + x seu dv aequ. dz − dy + dw + dx. Multiplicatio: dxv aequ. xdv + v dx, seu posito y aequ. xv, fiet dy aequ. xdv + vdx” (GM 5 220). 7. Leibniz writes divisio. I will deliberately omit here the ambiguities of signs proposed by Leibniz:   v v dy - y dv d = y yy 8. Idem, 222. Potentiae: d(xa ) = axa−1 dx. In Leibniz’s terminology, it was therefore a canon. From the context, it is clear that a is the sign of an indeterminate relative integer, that is positive or negative. Afterwards, Leibniz considered two numerical instances, first a = 3, then: d(x3 ) = 3x2 , then another one, with a = −3. 9. Between 1675 and 1677, Leibniz found a somewhat empirical proof of this fundamental property. It was a toilsome work, scrupulously analyzed by CH 83, 91, 97, 124, 130. Leibniz also tested the validity of the formula by taking simple monomial expressions for x and y. Therefore one could use induction. In a letter to Oldenbourg (June 21 1677 (B 241)), Leibniz also provided a so-called “ general “ proof using explicitely “infinitely small differences”, which he probably did not dare to copy in print. He wrote for instance: “Hinc nominando imposterum d¯y differentiam duarum proximarum y (. . .) et d¯x(. . .) differentiam duarum proximarum x (. . .) patet dy2 esse 2ydy et dy3 esse 3y2 dy etc. et ita porro. Nam sint duae proximae sibi (id est differentiam habent infinite parvam) scilicet [. . .]” (B 241). Finally, Leibniz did not give any valid proof. 10. My remark corresponds to Leibniz’s original idea, namely, proving the result under its “ summatory “ aspect:  x.y =

 ydx +

xdy

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by means of a bi-partition of a rectangle, according to the following drawing (cf. CH)

11. However the same Jean Bernoulli, once he understood the full interest of the Leibnizian discovery, drew an outstanding profit from it. One must rightly consider Bernoulli as one of the discoverers of the practice of differential and integral calculus. 12. Jean Bernoulli to Leibniz, December 1, 1696 (GM 2 340). In modern conceptions, one must find a differential equation satisfied by the sum of a power series. 13. Obviously, this property of one-place assemblers is no longer valid for usual two-placed assemblers which cannot be consecutive. 14. In the memoir Historia et Origo Calculi Differentialis (GM 5 392) Leibniz explained how he found the ideas of differentials and sums, then of successive differentials, firstly in 1674– 1675, while he studied some sequences (series) of natural integers. Following the so-called epistemological scheme of the “harmonical triangle”, Leibniz actually claimed (GM V 397) that, if y denotes the “term of an initial series”, it was possible (licebit) to denote by dy the term of the line difference (or first difference), by ddy the second difference, by d3 y the third difference, and so on. 15. Let E be an arbitrary set and f any mapping from E to E. One now usually denotes f(2) = fO f, f. This symbolism is therefore Leibniz’s (cf. Serfati 2001). and by induction, f(n) = f(n−1) O 16. Leibniz situated once again the origin in some x le terme  sequences of integers: “appelant  d’une autre series, il est possible d’appeler x la somme de celle-ci et x la somme des 3 4 sommes ou somme seconde, x la somme troisi`eme et la somme quatri`eme x (GM 5 397). 17. Cf. for instance, the letter from Leibniz to  Jean Bernoulli, December 28, 1696 (GM II 352), where one can find: y = 12 xx + 16 x3 + ydxdx 18. Cf. “Consid´erations sur la diff´erence qu’il y a entre l’analyse ordinaire et le nouveau calcul des transcendantes”. Journal des Sc¸avans. 1694. (GM 5 306–308). 19. “Car cette m´ethode, ou ce calculus differentialis, sert non seulement aux diff´erences, mais encore aux sommes qui sont le r´eciproque des diff´erences, a` peu pr`es comme le calcul ordinaire ne sert pas seulement aux puissances, mais encore aux racines, qui sont le r´eciproque des puissances. Et l’analogie va plus loin qu’on ne pense. Dans l’analyse ordinaire on peut toujours d´elivrer le calcul a vinculo et des racines par le moyen des puissances : mais le public n’a pas encore la m´ethode de le d´elivrer des puissances impliqu´ees par le moyen des racines pures. De mˆeme dans notre Analyse des transcendantes, on peut toujours d´elivrer le calcul a vinculo et des sommes par le moyen des diff´erences : mais le public n’a pas encore la m´ethode de le d´elivrer des diff´erences impliqu´ees par le moyen des sommes pures ou quadratures : et comme il n’est pas toujours possible de tirer les racines effectivement pour parvenir aux grandeurs rationnelles de l’Arithm´etique commune, il n’est pas toujours possible non plus de donner effectivement les sommes ou quadratures, pour parvenir aux grandeurs ordinaires ou alg´ebriques de l’analyse commune [. . .] Et j’ai donn´e par l`a une voie g´en´erale, selon laquelle tous les probl`emes, non seulement des diff´erences ou sommes, mais encore des diff´erentiodiff´erentielles ou sommes des sommes et au-del`a, se peuvent construire suffisamment pour la pratique [. . .]. Enfin notre m´ethode e´ tant proprement cette partie de la Math´ematique g´en´erale, qui traite de l’infini, c’est ce qui fait qu’on en a fort besoin, en appliquant les Math´ematiques a` la Physique, parce que le caract`ere de l’Auteur infini entre ordinairement dans les op´erations de la nature” (GM 5 308).

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20. “[. . .] l’espace informationnel offert par la chaˆıne parl´ee telle qu’elle est perc¸ue se prˆete mal a` la r´eception et a` la transmission de messages qui doivent v´ehiculer essentiellement des combinaisons d’informations portant sur leur propre structure” (Granger 1968: 22). This point is crucial in Granger’s philosophical conception (his “contenus formels”) of the functions of language in science (and especially in mathematics). 21. “Symbolismus Memorabilis Calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum et de lege homogeneorum transcendentali”. In Miscellanea Berolinensia, 1710 (GM 5 377–382). 22. In this paper, I analyzed in some detail the function of the so-called “conventions” – a term coined, after Leibniz, by the mathematical community. 23. Leibniz wrote to Bernoulli (GM 3 175): “Multa adhuc in istis summarum et differentiarum progressionibus latent, quae paulatim prodibunt. Ita notabilis est consensus inter numeros potestatum a binomio, et differentiarum rectanguli; et puto nescio quid arcani subesse. Exempli gratia [. . .] 4x + y = 1x4 + 4x3 y + 6x2 y2 + 4x y3 + 1y4 d4 , xy = 1d4 x + 4dy d3 x + 6d2 y d2 x + 4d3 y dx + 1d4 y. 24. Bernoulli answered: “Nihil elegantius est, quam consensus quem observasti inter numeros potestatum a binomio et differentiarum rectangulo; haud dubie aliquid arcani subest. Nondum satis vacavit examinare an quid inde pro summationibus elici possit” (GM 3 179). 25. At the time, a “broken” (rompu) number was a rational √ number (e.g., 2/3), while a “surd” (sourd) number was a quadratic irrational number (e.g., 2). 26. Neither Child, nor Hofmann, nor Knobloch – who drew up an inventory of Leibniz’s manuscripts in Paris – mentions any work in the symbolic area prior to 1676. Cf. CH, Hofmann (1974), and Knobloch (1978). 27. Leibniz to De l’Hˆopital, April 28, 1693 (GM 1(2) 236–241). 28. Leibniz to Varignon, February 2, 1702 (GM 4 91–99). This well-known letter was the object of an abundant commentary. In my opinion however, one must not search in it any possible foundation of Leibnizian infinitesimals no more than of his untraceable “science of infinite”. In Freud’s “principe du chaudron” style, Leibniz was actually satisfied with heaping up and juxtaposing some irrelevant or even contradictory arguments. 29. Leibniz to Grandi, July 11, 1705 (GM 4 210–212). 30. Leibniz to Wallis, June 1697 (GM 4 11–14). 31. Leibniz to Huygens, July 11, 1690 (GM 1(2) 41–44). The correspondence between Leibniz and Huygens, interrupted from 1680 up to 1690, went on again continuously since February 1690, within the frame of the Leibnizian “Nouveau Calcul”. 32. As to this point, cf. the following quotation from De Morgan (1849: 98–99) : “The next and second step [. . .] consisted in treating the results of algebra as necessarily true, and as representing some relation or other, however inconsistent they might be with the suppositions from which they were deduced. So soon as it was shewn that a particular result had no existence as a quantity, it was permitted, by definition, to have an existence of another kind, into which no particular inquiry was made, because the rules under which it was found that the new symbols would give true results, did not differ from those previously applied to the old ones”. Cf. my commentary of this text in Serfati (2005: 224–225). 33. Following a parallel approach, Leibniz then produced a theory of simple substances able to take into account the paradox: as soon as the concept of every substance was supposedly containing definitely its past as well as its future, its accidents and harmonies, the legitimacy of the mean which one could use to bring it to light was actually irrelevant, however inadequate to be founded it might be.

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References Babbage, C.1827. On the influence of signs in mathematical reasoning. Transactions of the Cambridge Philosophical Society 2: 325–375. Breger, H. 1986. Leibniz Einf¨urhung der Transzendenten. 300 Jahre “Nova Methodus” von G.-W. Leibniz (1684–1984). Studia Leibnitiana 14: 119–132. Cajori, F. 1925. Leibniz, the master-builder of mathematical notations. ISIS 23: 412–429. De Morgan, A.1849. Trigonometry and Double Algebra. London: Taylor, Walton & Maberly. Granger, G-G. 1968. Essai d’une philosophie du style. Paris: Armand Colin. Hofmann, J. 1974. Leibniz in Paris. 1672–1676. His Growth to Mathematical Maturity. Cambridge: Cambridge University Press [Engl. transl. of Die Entwicklungeschichte Mathematik w¨ahrend des Aufenthalts in Paris (1672–1676), M¨unchen: Oldenbourg, 1949]. ¨ Knobloch, E. 1978. Falsch datierte Handschriften mit Doppel-und Mehrfachindizies in Ubersicht u¨ ber die unver¨offentlicheten mathematischen Arbeiten von Leibniz (1672–1676). Studia Leibnitiana, Supplementa 17: 34–39. Mahnke, D. 1926. Leibniz als Begr¨under der symbolischen Mathematik. ISIS 30: 279–293. Serfati, M. 1996. Naissance de l’´ecriture symbolique math´ematique de Descartes a` Leibniz. In J. Echeverr´ıa, J. de Lorenzo, and L. Pe˜na (eds.), Calculemos . . .Homenaje al Profesor Miguel S´anchez-Mazas. Madrid: Trotta, pp. 55–74. Serfati, M. 2001. Math´ematiques et pens´ee symbolique chez Leibniz. In M. Blay et M. Serfati (eds.). Math´ematiques et physique leibniziennes (1`ere partie). Revue d’Histoire des Sciences 54(2): 165–222. Serfati, M. 2005. La r´evolution symbolique. La constitution de l’´ecriture symbolique math´ematique. Paris: P´etra.

Chapter 8

The Art of Mathematical Rationality Herbert Breger

1 Preliminary Remarks “Ma metaphysique est toute mathematique pour dire ainsi, ou la pourroit devenir” (A III 6 253), Leibniz writes to L’Hˆopital in 1694. And in a letter to Bouvet, Leibniz states that with the help of others, he could derive his whole philosophy from a few axioms (A I 19 411). Moreover, Leibniz’s various proofs for the existence of God, his conception of God’s reason as the region of eternal truths, the characteristica universalis (which includes his conviction of the existence of fundamental notions which cannot be reduced to other notions), the analytical theory of truth and finally his programme to prove all axioms are indicative of a strong rationalism in the centre of Leibniz’s philosophy. But in addition to this emphatic role played by reason, it also has an everyday role; in addition to triumphant, successful reason, there is also a doubting reason, one that is questioning and searching. Leibniz did not reject Descartes’s classical definition “la raison est un instrument universel, qui peut servir en toutes sortes de rencontres” (Descartes 1637, 5`eme partie, §10). Different opportunities, different problems, different levels require reason to adopt different procedures. 17th century reason, of course, always tries to proceed methodically, but, as I would like to show, method is also a notion which comprises quite a range of different procedures. There is a continuum of various procedures, ranging from a clever artifice, which may sometimes be applied and not at other times, to a rather formalized method. Different contexts require different ways of applying reason. Is Leibniz’s rationalism logic-oriented? I would like to make three preliminary comments on this question. Firstly, under the influence of Couturat, Russell and analytical philosophy, we are inclined today to overemphasise the role of logic in Leibniz’s thought. Jaenecke (2002) has at least shown that it is a one-sided approach to interpret the characteristica universalis entirely in logical terms, and Fichant (2004) has pointed out that after the 1680s Leibniz appears to have renounced the idea of substance as an individual concept – an idea that plays such a dominant role in Leibnizian research; in so far as we can judge it on the basis of the philosophical

H. Breger University of Hanover, Hanover, Germany

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works left in Leibniz’s literary estate, as yet only partially published, logic played a much more minor role in the metaphysics of the more mature Leibniz than is often apparent in modern research. I shall not dwell any further on this topic. Secondly, even where Leibniz does focus on calculating, demonstrating reason, he does not understand it in such a narrow sense as the present-day logicians sometimes think. For logicians, understanding takes place on a meta-level outside of logical calculation; for mathematicians, understanding and insight are important components of mathematics. Leibniz spoke out on various occasions against a purely deductive view of mathematics: Euclid’s style coerces the mind rather than enlightens it; the reader is forced into concurring and he does not learn how one arrives at the proof (A VI 4 341). This is not to be understood as a call for didactics, for a mathematics without tears, as one would now express it; it is a result of Leibniz’s appreciation of the power of insight, understanding and the active capacity to solve new problems instead of passively being able to follow existing proofs logically and step by step. The inventionis lux needs to be combined with the stringency of proof (A VI 4 342). Thirdly, we need to ask what we should understand by logic. If logic is defined as a deductive theory, as we know it today, and nothing else, then Leibniz’s rationalism is not or at least not exclusively logic-oriented. But in the famous letter to Gabriel Wagner, Leibniz defines logic as the art of using one’s reason; this implies the art of finding things which are concealed (GP 7 516). Therefore art, and in particular the art of finding something new, is intimately connected with reason. In recent decades, the claim has been made (Dreyfus and Dreyfus 1986: Chap. 1) that experts act neither rationally nor irrationally, but arationally. This claim evidently presupposes that rationality is something which can be made completely explicit, that is, rationality is considered to be capable of being formalized in rules, or, in other words, this meaning of rationality does not include any tacit knowledge in the sense of Polanyi, according to whom our entire faculty of knowing is rooted in tacit knowledge (Polanyi 1958). Leibniz’s conception of rationality may well be worthy of further investigation; at least in the aforementioned passage in the letter to Gabriel Wagner, the domain of reason is not just scientia, but also ars, even if ars strives to establish and to enlarge scientia. For an art, no set of fixed rules exists. An art can be learnt, but it is one thing to learn a formalized theory and something very different to learn an art. In the following text, three types of the art of using one’s reason are discussed, namely analysis, levels of abstraction and pragmatic decisions.

2 Analysis The difference between analysis and synthesis was well established in 17th century mathematics, and is an important element of its particular “atmosphere”. Admittedly, Euclid’s deductive structure was not only admired, it was also considered to be an example of philosophy as well as of mathematics. Nevertheless, the ardent desire of the best mathematicians of this period was not to write a deductive textbook, but rather to find new solutions, new theorems and, in particular, new methods. Analysis

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was exciting, whereas synthesis was considered to be a little boring and somewhat trivial. One can see this, for example, in Descartes’s G´eom´etrie: he exposes an analysis, he solves problems, but he does not bother to give demonstrations, because they would be more or less trivial. Leibniz explicitly states that he loves mathematics because in mathematics he finds “les traces de l’art d’ inventer en general”, and, as he continues, true metaphysics is hardly different from this art of making new inventions (A II 1 1st edition: 434, 2nd edition: 662; see also A I 13 554). True metaphysics, in this sense, would clearly have no deductive structure; it would be a method, to be sure perhaps a partially formalized method. Leibniz regretted that the mathematics of antiquity was constructed on exclusively deductive principles: ancient mathematicians appear to have withheld their arts; we do not know how they arrived at their results (A III 5 366). Vi`ete and Descartes had put forward essentially new ways of conducting mathematical analysis, and Leibniz (as well as Newton) made another big step, namely the introduction of an analysis infinitesimalis. As yet I have found no passage where Leibniz uses an expression such as “synthesis infinitesimalis”. So analysis infinitesimalis is the art of solving problems by the use of infinitesimals. Leibniz does not claim that infinitesimal analysis is a formal theory with a deductive structure like Euclid’s Elements (for details see Breger 1999). The following quotations serve to confirm this role of infinitesimal analysis. Leibniz calls his solution of the isochrone problem (finding the curve of a body falling without acceleration) an analysis. Having solved the problem by the use of infinitesimals, he adds a formal demonstration without using infinitesimals (GM 5 241–243). As for the catenary, he provides the analysis using infinitesimals and then adds that a formal demonstration would be long-winded and not really necessary for experts (GM 5 247). In a commentary on the problem of the catenary, Leibniz remarks that the problem will be difficult to understand for those unfamiliar with infinitesimal analysis, but on the other hand, he continues, once the solution is found and published, it is easy to prove without infinitesimal analysis that this particular curve is the solution (A III 5 118). Furthermore, Leibniz was told that de la Hire had used the methods of ancient mathematicians to prove certain results which Leibniz had discovered by infinitesimal analysis. Leibniz comments that de la Hire did a laborious job without producing really new results (A III 6 317, 517; GM 7 391). And in a letter to Varignon in 1702, Leibniz argues that it is not a useless task justifying infinitesimal calculus, but it would be a pity if Varignon spent too much time on it, because Varignon would otherwise be capable of making new discoveries (GM 4 95). In connection with the dispute about scepticism, Leibniz remarks in a letter to Foucher (GP 1 402) that mathematicians had sought the solutions of problems and the proof of theorems, although the deductive structure of geometry could have been improved if one had first demonstrated some of the axioms and postulates. It would have been unfortunate if the mathematicians had proceeded differently; but it is certainly of much benefit that several scholars later finished off what had previously been skipped over for the sake of making rapid progress. The meaning of the word “analysis” in mathematics has changed significantly since the 17th century, while during the same period the difference between analysis and synthesis fell into oblivion. So, sometimes the claim has been made that

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Leibniz’s calculus lacks a rigorous foundation. But this is a misunderstanding. The art of analysis does not require a deductive structure. Of course, a mathematical achievement is only an achievement if deductive proof can be given. But once the solution of a problem is known, the deductive proof is a matter of routine. Leibniz provides a general strategy for this: if someone claims that there is an error equal to any positive number, then it can be shown that the error must be smaller than that number, therefore the error equals zero (GM 4 92). Thus, it would not be difficult to convert infinitesimal calculations into rigorous demonstrations (GM 7 391). Such argumentation had been more or less familiar, even before Leibniz, to those mathematicians who used infinitely small or indefinitely small quantities. In the 19th century, Cauchy introduced the Greek letter “epsilon” as an abbreviation of the French word “erreur”. By the way, Cauchy also preferred to use infinitesimals because they are more convenient, the difference to Leibniz being that Cauchy had no problem with using infinitesimals in his formal proofs. With the strategy just mentioned, Leibniz transforms Archimedes’s pattern of apagogical proof into a strategy of controversy between two opponents. The application of this general strategy to a particular problem requires some expertise; to use one’s power of reasoning is still an art. On the general level – is the use of infinitesimals legitimate or not? – Leibniz does not need to give proof; it is sufficient to convince the experts. On the lower level of abstraction, i.e. when looking at a particular problem, synthesis can always be given. And it is exactly this fact – the possibility of a formal synthesis in each particular case – that convinces the experts. Mathematicians, historians of mathematics and philosophers of mathematics from the period after Leibniz until the present day have tended to question the legitimacy of infinitesimal calculus on the higher level of abstraction. Both the shift in meaning of “analysis” as well as the gradual but clear increase in the 18th and 19th centuries (and certainly in the 20th century) in the degree of abstraction in mathematics have contributed to this reassessment (both factors being of course mutually dependent). It was then decided that Leibniz had no answer on the higher level of abstraction and it was deduced from this that infinitesimal calculus provided an unreliable foundation. But Leibniz had not intended to give an answer on the higher level of abstraction nor had he any reason to give one on the higher level. He used infinitesimals as part of the art of finding something, but his problems and results were expressed on the lower level of abstraction. At this level, however, it is no longer a question of infinitesimals; it is simply one of whether a certain result expressed without infinitesimals is the correct solution for a certain problem expressed without infinitesimals. Using Archimedes’s apagogical method, or, rather, what is today called “epsilontics”, this is easy to demonstrate in every individual case (and on the lower level of abstraction one is only dealing with such cases). Modern day mathematicians may ask themselves why Leibniz used infinitesimals at all, if he refrained from using them in the proofs. The answer is that the infinitesimals are more appropriate for grasping a problem and solving it intuitively – at least in a continuum as Leibniz and his successors used it, i.e. in a continuum that did not consist of points (for details see Breger 1992).

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So analysis and synthesis are different ways of using one’s reason; they are complements of each other, but neither of them is irrational or less rational than the other. If you want to find a difference in rationality between analysis and synthesis, then you might say: It is not rational, at least for an expert, to prove lots of trivial statements; it is more rational to find interesting results (which could be proven, if someone considers this necessary). That providing mathematical proof as just discussed was of lesser importance to Leibniz can be concluded from a remark from 1678 on Spinoza’s Ethics: “in mathematics one can easily guard against errors and therefore it is sometimes useful to deviate from mathematical stringency, but in philosophy one must definitely adhere to the stringency of proof” (A III 2 451; see also A II 1 1st edition: 478, 2nd edition: 725). The further development of mathematics abolished the difference between analysis and synthesis and led to higher levels of abstraction. Today’s non-standard analysis differs from Leibniz’s use of infinitesimals in several ways; one of the differences is that non-standard analysis is a formal theory on a higher level of abstraction, whereas Leibniz argued on the level of the particular problem. Another example of a procedure designed to solve problems is “analysis situs”. Leibniz wanted to amend some imperfections of Cartesian analysis. In La G´eom´etrie, Descartes presents an algebraic procedure more or less systematically, in order to find constructions for geometrical problems. Leibniz claims that Cartesian analysis does not always lead to the best or the most elegant solution. Sometimes the solution is awkward, although a simple and beautiful construction exists; in particular, this is true of the problem of finding the tangent to the conchoid (A III 2 237–238; GM 5 178). To find an aesthetically pleasing construction, “ingenium” and “felicitas” are required (A VI 3 420), and this clearly demonstrates that up till then a method had been lacking. The method aimed at was not only to be used in pure geometry, it should also be useful in its application: for example, it should assist in inventing machines (GM 5 143, 183). The analysis situs is concerned, in particular, with transforming geometrical intuition and a sense of beauty into a method of invention, and with using it to solve problems. In the long run, such a method, once it had been developed, would presumably also be able to serve to construct a deductive theory for these questions, but as far as I know Leibniz does not mention such an aim. The importance of the analysis situs may be seen from a remark made in 1678: “Je ne cherche presque plus rien en Geometrie, que l’art de trouver d’abord les belles constructions” (A III 2 566). Leibniz was not successful, but his analysis situs is one facet of his rationality. One last example is that of the problems of integral calculus. For differential calculus, there are a number of rules which help to find the differential quotient. But for integral calculus, there are only a number of artifices (including integration by parts, clever substitution of variables, reducing to fractions, expansion of series) which sometimes work and sometimes do not work. Leibniz comments that these are things requiring ars; for these things no perfect method yet exists (A III 5 672: “daß sind dinge, so kunst erfordern, und noch nicht ad perfectam methodum gebracht”). In fact, in today’s mathematics these things still require art; even today there is no formalized method, no theory for them on a higher level of abstraction.

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3 Levels of Abstraction Leibniz mentions a simple example of different levels of abstraction – or of different levels of rationality – when he compares an empiricist to a judicious man. Whereas the empiricist bases his action only on experience, the judicious man tries to understand the reasons for the empirical facts in order to be able to foresee when an exception from the rule of experience might occur (A VI 6 51). In other words, the judicious man strives to achieve a higher level of rationality. According to Leibniz, a way of thinking is more perfect the more objects there are that can be referred to by this act of thinking (A VI 4 1360: “Hinc jam perfectior ille est cogitandi modus, per quem fit ut unus cogitandi actus ad plura simul objecta porrigatur”). So, abstract thought – provided the abstraction has not been made arbitrarily – is more perfect. But this does not imply that an argumentation on a lower level of abstraction is irrational. As Leibniz points out, people may be rational, even if they are not explicitly aware of the principle of contradiction, the principle of sufficient reason or the axiom that the whole is greater than the part (GP 7 523; A VI 6 428, 449). On the other hand, people will achieve more if they have explicit knowledge of logical principles, that is, if they have knowledge on a higher level of abstraction. Another example is a remark Leibniz made about the Italian mathematician Viviani (A III 5 365–366). Leibniz says that Viviani knows more than he knows. That means he does not understand how to put his knowledge into a methodical form. People like Viviani lack the art of creating arts; they have a certain routine of inventing something in their own particular manner, but they are often not aware of this and therefore make little progress therein. They have, Leibniz continues, a natural analysis just as a farmer has a natural arithmetic. What Leibniz is demanding of Viviani is what he had done himself, when he realized that the infinitely small triangle used by Pascal could be applied in many more examples, thus constituting a method; Leibniz tells us that a truth dawned upon him that Pascal had failed to see. Pascal had veiled eyes (so to speak) and had failed to recognise the general benefit of the infinitely small triangle. Leibniz reports further that he communicated his discovery to Huygens, who had also employed the infinitely small triangle as a special trick, but who had not made it the basis of a new method for determining the tangents and surface area (GM 5 399, 232; GM 3 72–73). It is one thing to possess a certain skill and it is another to understand the theory of this skill. Many people can sing, even though they lack knowledge of music (GP 7 523). On the other hand, it may happen that someone cannot sing or play an instrument, though he can read all the important books on the theory of music (GP 7 522). Naturally, for Leibniz, theoretical knowledge is of a particular perfection, but this theoretical knowledge must have a solid foundation. Therefore, just as fencing cannot be taught with words alone, logic should not be taught without examples and exercises (GP 7 526). The same is true of mathematics; you would not understand mathematics without examples and exercises. So the higher level of rationality sometimes only develops its potential if know-how or artful knowledge exists on the lower level. In the current discussion on tacit knowledge, one occasionally hears the opinion voiced that tacit knowledge or know-how are only to be found combined

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with skill, not with knowledge. In reality, the difference between knowledge and skill is anything but sharply defined; one aspect of being able to grasp a mathematical theory entirely is that one can solve the problems and exercises related to this theory, just as the ability to solve all, rather than just a few, tasks is only reached when the mathematical theory has been thoroughly understood. If the understanding of a mathematical theory can only be developed on a higher level, the same can be said of the concept of beauty and of the concept of simplicity. Mathematicians know very well what is meant by beauty or simplicity in one case or another, but neither Leibniz nor any other mathematician has succeeded in expressing a sense of mathematical beauty and simplicity. Nevertheless, this aesthetic sense exists, and mathematicians, as a rule, agree about this sense. Beauty and simplicity are guiding stars of mathematical development; they show that in mathematics not only is deductive reason at work. Leibniz expresses his interest in mathematical beauty and simplicity outside of the analysis situs again and again (Breger 1994); I simply mention several examples selected at random. While talking about the formula for a quarter of ␲, nowadays called the Leibniz series, Leibniz says that there is no more aesthetically pleasing and simpler expression for the surface of a circle in rational numbers (A III 3 37, 243). Vi`ete had developed a very beautiful method to solve equations in rational numbers (GM 7 143). And Leibniz’s study of a theory of determinants is crowned by a theorema pulcherrimum (Leibniz 1980: 10). The concept of different levels of abstraction is not the same as the logician’s concept of logical calculus and meta-level or of the difference between procedural and declarative knowledge. In mathematics, it is typical to find an interplay between different levels of abstraction. To be more precise, an art or a method may typically develop later into formal knowledge on a higher level, and the formal knowledge may later become the starting point of a new art of solving problems. In fact, different levels of abstraction play an important role in the development of mathematics. We all presumably learned at school how to solve a system of linear equations with several unknowns. The procedure we learned is not difficult, but it is not completely formalized. It may happen that a wrong decision is made, then the calculation leads to something like 0 = 0 and has to be started anew. By inventing the theory of determinants (cf. Leibniz 1980), Leibniz established a formalized procedure on a higher level of abstraction. By using more abstract notions, you can at once recognize whether a solution exists and you can find the solution by following the formalized procedure. It is by no means irrational if you use the procedure you learned in school, but from an intellectual point of view, the higher level is more satisfying. The mathematical progress achieved by the introduction of determinants is twofold: Problem solving is facilitated, and, in addition, it produces a new mathematical theory on the higher level, namely a theory of determinants. This new theory could also be made a deductive one, but it is remarkable to see that Leibniz is not really interested in that. A further example is that of transformations. It is precisely the fact that Leibniz, on the one hand, does not know the term of mathematical transformation, but, on the other, uses transformations again and again in specific contexts of physics and mathematics (Breger 1989; Breger 1990: 226–229) that is of interest. One could say that

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he possesses an intuitive feeling for the modern term of transformation. To recognise the existence of a transformation means to see similarities and connections between specific problems and objects from a higher level of abstraction. On the higher level of abstraction, a formal theory of transformations can then be erected; one can then talk, for example, of symmetries in the sense of group theory, of Euclidean transformations in geometry or of permutations in combinatorics. Leibniz either fails to reach the higher level of abstraction or only partially arrives there, but in many individual instances he recognises the superiority of argumentation based on transformations. This is of course most obviously the case when dealing with combinatory contexts, i.e., where the unknown behaves in the same (“se eodem habent modo”) or in a similar manner (“se similiter habentium”) (A III 2 442). Such combinatory relations are, according to Leibniz, one of the greatest secrets of algebra; such relations are also the way of finding beautiful and elegant constructions in geometry (A III 2 443); indeed, Leibniz tried to construct the analysis situs as a method of finding beautiful constructions on the basis of the terms of congruency and similarity (and thus on the basis of the corresponding transformations). It is the aspect of transformations that causes Leibniz to subordinate algebra as the science of magnitude to combinatorics as the science of forms and similarities (A VI 4 545). Leibniz occasionally speaks of an “ars formularia” as well (A VI 4 346), which is concerned with the same and the different, with the similar and the dissimilar, thus with the forms of things, independent of size, position and action. With the help of this ars formularia, Leibniz obviously intends to try to develop a method and theory of transformations and their applicability. The similarity of geometric positions and geometric figures, important for the analysis situs, is for Leibniz a special case of regarding forms or qualities in metaphysics (GM 7 179). In making the geometric term of similarity into a more general notion (Breger 1990) – Leibniz claims to be the first to have found the true definition of similarity (A VI 6 157; GM 5 179–180) – he attempts to create the foundation of a theory of qualities on a higher level; this would be, at the same time, the basis for applying transformations, which means that similar circumstances and problems might be converted into each other. Firstly, Leibniz underlines the fact that his definition of similarity was more natural and simple in mathematics (A III 2 228; GP 2 62); secondly, this simplicity can be arrived at by more strongly emphasising the factor of intuition: something that Euclid had proved in a roundabout manner was immediately obvious, “primo statim intuitu”, when using the new definition of similarity (GM 7 275). From the point of view of a cogitatio caeca (A VI 6 185), Leibniz’s definition of similarity is a step backwards when compared to Euclid’s. Again, this demonstrates that Leibniz’s rationality is closer to that of a mathematician, who thinks highly of understanding and insight, than to that of a logician.

4 Pragmatic Decisions There is also a pragmatic aspect to Leibniz’s mathematical rationality. Decisions about the legitimacy of objects and methods of proof permissible in mathematics can clearly not themselves be derived deductively, they are rather decisions made by

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the mathematical community. That does not in any way imply that these decisions are irrational; they are based on the mathematical community’s expertise, whereby tacit knowledge, as defined by Polanyi, may also be part of this expertise, that is, a type of knowledge not explicated by the experts and one that they would perhaps only be capable of explicating at a much later date. These decisions were made by means of pragmatic rationality. It may well be that the decisions were reached tacitly in many cases, rather than being consciously and expressly voiced by the community. Most of the mathematicians certainly proceed as if the decision has been made, and if someone one day explicitly voices the decision, it generally meets with no protest. The transition from the view that either the Euclidean or one of the non-Euclidean geometries must be true to the opinion that there are a number of theories of equal standing is a well known example of this; the acceptance of negative numbers would be another one. A similar, albeit less spectacular shift, took place in the second half of the 17th century, whereby Leibniz was the one who expressed the decision taken by the mathematical community. It concerned the question of which mathematical objects and which geometric means of construction were legitimate. Magnitudes which could be constructed with a ruler and compass were legitimate in Euclid’s Elements; Descartes made the decision that all algebraic magnitudes were legitimate in geometry. He considered transcendental magnitudes and curves not to be constructible in an exact manner and therefore to be part of mechanics. Leibniz extended the border of mathematics once again by introducing transcendental magnitudes and curves (for details cf. Breger 1986). In order to do so, he had to change the criteria hitherto accepted for mathematical legitimation and for mathematical exactitude and, above all, he had to convince his fellow mathematicians. Leibniz referred to three arguments for his decision. The first argument was the applicability of mathematics. Most problems in physics were transcendental; therefore mathematics should include calculations with transcendental magnitudes. This argument was not very convincing, because the application to physics would not be impeded if part of the calculation were to be done outside of a strictly defined geometry. The second argument was the claim that it was possible to find new means of construction. Leibniz toyed with the idea of establishing new methods of construction with the help of evolutes, the catenary, even by means of the relation between logarithms and friction, so that the transcendental curves could then also be constructed (GM 5 243–244, 265, 295). Since these curves could be described with a precise and continual movement, they must also be considered mathematically legitimate objects (GM 5 229). Descartes had, admittedly, argued against the precision of such a movement: in constructing cycloids, the two generating movements stand in a transcendental and thus, for Descartes, not an exactly definable ratio (Descartes 1902 VI 390). Leibniz presupposes the exactitude and mathematical legitimacy of this ratio; his reasoning ignores Descartes’s objection completely. I know of no contemporary mathematician who reproached Leibniz for the circularity of his argument. Nevertheless, Leibniz does appear to have dropped this second argument later; presumably because it proved to be difficult to show that all transcendental curves really could be arrived at from a few simple means of construction. In addition, it may have been the case that the mathematical community – perhaps contrary to Leibniz’s

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original expectation – did not express any interest in further construction methods. So Leibniz – and with him the mathematical community – were finally content simply to use an equation as the basis for the legitimation of a curve. This is all the more remarkable in that at the same time the actual way of writing formulae was also being revised: not only were variables permitted in exponents, ways of writing formulae for individual transcendental functions, such as l or log for the logarithm (A III 6 121, 166), now came to be regarded as legitimate. The third argument was derived from the new calculus which Leibniz sometimes called “l’Analyse des Transcendants” (GM 5 278): the derivative of an algebraic curve is again algebraic, but the integral of an algebraic curve is in many cases a transcendental curve. In order to have a closed domain for the reciprocal operations of differentiation and integration, it would be useful to include transcendental curves in the realm of mathematics. This third argument can be extended in a natural way: If sequences, convergent series and limits become important parts of mathematics, the strict difference between algebraic or constructible magnitudes and transcendental or non-constructible magnitudes loses its persuasive force. The mechanistic ideas of 17th century mathematics, exemplified in points moving along lines, etc., tend to make the inclusion of the continuum as a whole plausible (and not just those points which can be constructed with ruler and compass or by the Cartesian means of construction). By using expansions of series, Gregory and Newton had already gone in the same direction, although they did not explicitly argue for a change in the criteria for mathematical admissibility. In any case, Leibniz’s arguments were not cogent, but they were plausible and they were accepted without any real debate. Another example of a pragmatic decision is Leibniz’s use of imaginary quantities. Like infinitesimals, they are fictions and they should not occur in the final result. But like infinitesimals, they are useful fictions. With their help, Cardano’s formula for an equation of the third degree makes sense even in the casus irreducibilis: the sum of two complex numbers may be a real number (A VII 2 683; A III 1 282, 284; GM 4 92, 93). So, although Leibniz considered these quantities to be impossible, he decided to allow for a restricted use of them in order to have an efficient algebraic calculus. Leibniz does not aim at a deductive calculus for imaginary or complex numbers; these numbers are only the means of solving equations. Seen from this angle, permitting imaginary numbers is also an example of analysis as the skill of finding, one that genuinely benefits from imaginary expressions as well. There are, Leibniz continues (GP 1 405–406), certain falsehoods from which one can benefit when in search of truths. At the place cited, Leibniz states that extremes coincide as a further example; one should not of course take the theorem literally, but it could be a useful heuristic principle.

5 Postscript My examples have been taken from mathematics and to a lesser degree from philosophy. But there are more facets to the art of using one’s reason. I just wish to mention two examples selected arbitrarily from history and philology, both taken

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from the Academy Edition volume that has appeared recently (A I 19); it may be useful to compare these examples to mathematics. The historian cannot state in every case what he is looking for. Even if someone else tells him that the house of Brunswick or the house of Este are not mentioned in a particular bundle of medieval documents, he has to read the documents if at all possible. “Car une circomstance, un mot, decouvre quelques fois beaucoup a` un homme qui possede son sujet; ce qu’un autre ne sc¸auroit voir ny remarquer. Et mˆeme quelques fois le simple silence de tels auteurs est de poids” (A I 19 80). It is rational for the historian to acquire through arduous study a feeling for the atmosphere of his topic and of the documents pertaining to his topic, and the rationality of the historian is to a certain extent based upon such tacit knowledge. Something immediately comparable would no doubt be regarded as invalid in mathematics, but a loose analogy is perhaps permitted. To be able to solve a given mathematical problem, it might well be rational to start by making various attempts. The mathematician is well aware of the fact that these attempts will later prove to be na¨ıve, and he certainly does not entertain the hope that one of these first attempts will chance upon the solution. With these attempts he is trying to gain a feeling for the particular problem. The mathematician will only find the right solution if he bases his investigation on the tacit knowledge that plausible attempts at a solution arise from thorough knowledge of the problem’s difficulties, as well as from knowledge of the reasons why his first attempts go wrong. The second example is taken from the controversy between Bentley and Boyle on the so-called epistles of Phalaris. Bentley had given a number of plausible, though not cogent arguments to show that the epistles were not authentic. Boyle tries to refute each of these arguments separately. Leibniz comments: “Mais leur force consiste dans l’assemblage” (A I 19 448). In other words: for a set of arguments it can be true that the whole is more than the sum of its parts. For the rationality of a logician, it is inconceivable that one argues in this manner. But it is entirely conceivable when arguing pragmatically in a meta-mathematical dispute: We have noted Leibniz’s three arguments for introducing transcendental magnitudes. No doubt, in philosophy and mathematics (though not in history and philology) a deductive theory (as well as the intuitive understanding of this theory and the capacity to solve problems within this theory) would be Leibniz’s final aim. To be more precise: a deductive theory is desirable for those parts of human knowledge where, according to Leibniz, a deductive theory would be possible. Everywhere where something individual is involved, in history for example (incidentally every material object and every living being is individual, cf. A VI 6 744), a deductive theory is impossible, for the individual implies an infinity of determining elements (A VI 6 289), and even God can definitely not apply infinite analysis and even less so produce infinite proof (A VI 4 1656, 1658). The characteristica universalis cannot therefore relate to individuals. Nor can it extend to encompass empirical natural sciences as a whole, for in the individual and in the best world, infinity is implied in many ways (laws of nature too are, as we know, contingent according to Leibniz). But even in those areas in which a deductive theory might be possible, such a theory has not been, or, at most, has only partially been attained. And as long as there is still

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much to discover, invention is an important and interesting task for reason. Leibniz expresses his wish that a capable mathematician would write an extensive book on the theory of games; this would be very useful for the art of invention, “l’esprit humain paroissant mieux dans les jeux que dans les matieres les plus serieuses” (A VI 6 466; see also GP 4 570; GP 3 639). Acknowledgments I would like to express my gratitude to Dr. Catherine Atkinson for the translation.

References Breger, H. 1986: Leibniz’ Einf¨uhrung des Transzendenten. In A. Heinekamp (ed.), 300 Jahre Nova Methodus von G. W. Leibniz (1684–1984) (= Sonderheft 14, Studia Leibnitiana). Stuttgart: Franz Steiner, pp. 119–132. Breger, H. 1989: Symmetry in Leibnizian Physics. In The Leibniz Renaissance. International Workshop Firenze, 2–5 giugno 1986. Firenze: Leo S. Olschki, pp. 23–42. ¨ Breger, H. 1990: Der Ahnlichkeitsbegriff bei Leibniz. In A. Heinekamp, W. Lenzen, and M. Schneider (eds.), Mathesis rationis. Festschrift f¨ur Heinrich Schepers. M¨unster: Nodus, pp. 223–232. Breger, H. 1992: Le continu chez Leibniz. In J.-M. Salanskis and H. Sinaceur (eds.), Le Labyrinthe du Continu. Paris: Springer France, pp. 76–84. Breger, H. 1994: Die mathematisch-physikalische Sch¨onheit bei Leibniz. Revue Internationale de Philosophie 48: 127–140. Breger, H. 1999: Analysis und Beweis. Internationale Zeitschrift f¨urPhilosophie: 95–116. Descartes, R. 1637: Discours de la methode. Leiden: Maire. Descartes, R. 1902: Œuvres. Edited by Ch. Adam and P Tannery, vol. VI, Paris: L´eopold Cerf. Dreyfus, H.L. and Dreyfus, S.E. 1986. Mind over Machine. New York: The Free Press. Fichant, M. 2004: Introduction. L’invention m´etaphysique. In M. Fichant (ed.), G. W. Leibniz: Discours de m´etaphysique suivi de Monadologie et autres textes. Paris: Gallimard, pp. 7–140. Jaenecke, P. 2002: Wissensdarstellung bei Leibniz. In F. Hermanni and H. Breger (eds.), Leibniz und die Gegenwart. M¨unchen: Fink, pp. 89–118. Leibniz, G.W. 1980: Beginn der Determinantentheorie. E. Knobloch (ed.). Hildesheim: Gerstenberg. Polanyi, M. 1958: Personal Knowledge. London: Routledge and Kegan Paul.

Part III

Epistemology

Chapter 9

Ramus and Leibniz on Analysis Andreas Blank

1 Introduction In a recent article, Stephen Daniel suggests that retrieving the Ramist context of Leibniz’s philosophy allows one to appreciate how reasoning, for Leibniz, is modeled on discursive and legal strategies (Daniel, forthcoming). As Daniel points out, in marginal notes and early works such as the Dissertation on the Art of Combinations (1666) and the New Method of Discussing and Teaching Jurisprudence (1667), Leibniz occasionally invokes Ramist themes by name, usually in order to highlight the link between logic and discourse.1 Daniel argues that Ramus’ portrait of the art of reasoning as “the art of discourse” (virtus disserendi) implies that in terms of the rhetorical character of discursive strategies, logic is said to reveal the structure of thought and reality. Daniel indicates that, with respect to Leibniz’s description of a universal language, according to the first (two volumes) Latin edition of Ramus’ Dialectical Institutions (1543), reality is structured according to a natural dialectic by which God communicates the order found in things themselves.2 Furthermore, he proposes that Leibniz recognized how this reorientation towards the ontological potential of a logic of discourse informs Nizolius’ On the Principles and the True Reason of Doing Philosophy,3 and that this caused Leibniz to reprint it in 1670. In the present chapter, I argue for two claims: (1) In the 1547 edition of the Dialectical Institutions – the first three volumes Latin edition that came out under his own name4 – Ramus explicitly dissociates human discourse from truth in the Divine mind. Rather, he holds that dialectics is founded on innate, natural capacities of the human mind which function as a substitute for insight into Divine truth. According to his view, analysis has the task of disentangling the elements of common human discourse, thus providing us with examples, which subsequently, in the process of genesis, fulfill the function of models for forming new discourses. (2) Leibniz’s attitude towards Ramus is not a matter of simply accepting or rejecting such an account of the role of analysis in the constitution of discourse. On the one hand, Leibniz does not accept Ramus’ views about the connection between analysis and the function of

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examples as models for constructing new discourses. According to Leibniz, rather, analysis provides us with the concepts and truths that function as starting points for demonstrative arguments. On the other hand, he shares with Ramus the view that philosophical analysis can only explicate what implicitly already is known. As for Ramus, for Leibniz analysis has a purely descriptive starting point in the common usage of language.

2 Ramus on Analysis In the 1547 edition of the Dialectical Institutions, Ramus is explicit about the natural origin of dialectics. He writes: Dialectics is made available, like the ability to other arts, by nature, doctrine, and exercise. For nature endows us with the principle of discourse, doctrine shapes what we are endowed with through its own and appropriate precepts, exercise puts what is taught by art into work, and thus accomplishes it (DI 1).

Moreover, he claims that instruction in dialectics brings to light natural inclinations: If this boy is to be instructed, he is naturally inclined to reason: and he would, even if less strongly, achieve this on his own: in a much more certain and constant way, however, by the application of the known precepts and exercises of the art (ibid.).

According to his view, the art of dialectics, therefore, has to consider the limits of the natural inclination towards discourse, and has the task of giving precepts that are in accordance with the natural use of reason (DI 1–2). In the 1543 edition already, Ramus maintains that examples belong essentially to the natural use of reason, such that other – demonstrative – forms of reasoning cannot replace examples: I want art, and the exercise of art, to be conjoined with nature: and since the whole life of a human being should be nothing but the use of reason, that is, the exercise of natural dialectics: let us think about and exercise the art of reason, or natural dialectics [. . .] during our whole life in all things; in this way [. . .] we will realize that an art is known not so much by means of precepts but by means of exercise, and that much of what as schoolboys we thought to be idle and dry we admire as old men, when we are most diligently versed in this use; and sense itself informed by custom and examples shows something that quiet thought, even the most acute one, was unable to understand (Ramus 1543: fol. 54).

Whereas in the 1543 edition, Ramus characterizes natural capacities of discoursing as mirroring the discourse in the Divine mind,5 in the 1547 edition, he understands the natural use of examples as a substitute for the insight into Divine truths. It becomes clear that human discourse, according to Ramus’ modified view, is unable to provide insight into the eternal order of things when, in the 1547 edition, he writes about the sublime nature of philosophy: This all appeared to Plato, so that he said that it is not an invention of human beings but of gods [. . .] But if the access to this artful path is barred, he makes another way by means of the force of intelligence and prudence, and employs all help of nature, custom, use, life, and examples, since he is deprived of the benefits of doctrine: and as if thrown into the tempest

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in the Ocean (since he cannot keep his course) he changes his navigation, and with whatever winds he is able to use, he directs his vessel undamaged to the port (DI 133–134).

As we shall see here, the dialectical use of examples plays a crucial role in Ramus’ account of analysis. The logical structure of the use of examples is also one of the central topics in his account of invention in the first book of the Dialectical Institutions. According to Ramus, “Invention is the doctrine of thinking and finding an argument, i.e., a reason suitable to explicate a question” (DI 3). Invention takes place by using concepts that make such an explication possible. In this sense, he regards categorical concepts as loci fulfilling this function in the constitution of discourse. He differentiates them by using the traditional distinction between innate (insita) and conventional (assumpta) concepts (ibid.). Among the innate, non-conventional concepts, he counts causal concepts such as those of final, formal, efficient, conserving, and spontaneous cause (see DI 3–11). These concepts are not characterized as something derived from juridical contexts. In this sense, it is misleading to claim, as Daniel does, that for Ramus reasoning is “modeled on discursive and legal strategies”. Rather, he describes concepts such as those of different causes as applied to, but not formed in a juridical context: “This kind of causes of spontaneous and non-spontaneous agents is of great use. This kind, namely, in the first instance, is taken into consideration in the estimation of praise and blame, punishment and reward” (DI 13–14). Legal discourse provides us with examples of the application of causal concepts, not because of generating them, but because applying them in a particular clear way. In this sense, passages from rhetorical works provide perfect examples of the ordinary use of these concepts. Ramus claims, “We can derive from the common use [communis usus] of simple prudence all the testimonies of all the merits of dialectics” (DI 172). That is why he points out that, when using examples from literary and rhetorical works, he understands poets and orators as “famous and illustrious witnesses of this common sense [communis sensus], and of human prudence” (DI 172–173). He also puts it thus: “The art of dialectics has as its subject and aim to explicate the natural use of reason as it is impressed on great minds, in a certain custom, in perfect examples” (DI 21). Passages from juridical and rhetorical works function as examples because they represent a conceptual structure common to all human discourse. Because they represent natural, innate, concepts, juridical examples fulfill a logical function by defining what the correct use of expressions in the formation of a new discourse consists in. Insofar as these examples represent innate, non-conventional concepts, the invention of new arguments is based on something that implicitly is known already. This has interesting consequences for the logical structure of arguments, which use one or several particular instances. According to Ramus, arguments using examples are non-syllogistic in character, as are those using induction. Walter Ong, who holds that induction and examples, like enthymemes, are “all merely syllogisms for Ramus, with one or another part suppressed or understood” (Ong 1958: 186–187), misses this crucial point. Ramus holds that induction and examples have a function different from that of syllogisms. He writes: “Induction is not the name of an argumentation [argumentatio]: but of an argument [argumentum] taken from the locus

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of distribution: For when parts are enumerated in order to conclude something about the whole, this is called induction [. . .]” (DI 112–113). And again: [E]xample is the name of an argument, not of an argumentation, and it is almost an image of the things that are dealt with: and it differs only in this from induction, that induction either collects all, or most parts. An example takes only one [. . .] Thus, induction and examples do not pertain to judgment but to the locus of invention having to do with parts (DI 113).

Thus, induction and examples are not enthymemes, i.e., imperfect syllogisms that by addition of a further proposition could be turned into perfect syllogisms. In this sense, arguing by means of particular cases as in the use of examples and induction, in Ramus’ view, has an irreducible, non-demonstrative, logical form. Ramus’ discussion of syllogisms in the second book of the Dialectical Institutions, too, prepares the account of the nature of analysis in the third book. What is of interest to Ramus in syllogisms is not that they provide us with a form of demonstrative reasoning involving logical necessity. Rather, he emphasizes the pragmatic role of a syllogism as an answer to a given question: The syllogism, like the other precepts of this art, has to be derived from the common use [usus communis] [. . .] A syllogism will be the constant & firm combination of an argument with a question, from which the question itself is judged to be true or false (DI 78).

According to his view, even if a syllogism is given as an answer to a question, the judgment about truth or falsity is not a matter of logical necessity. Rather, he ascribes to the syllogism a function in the weighing of reasons. This is why he thinks that the term “ratiocination” has a metaphorical connotation derived from what happens in calculating sums: A syllogism is the common rule of judging about all things. In Latin, it is called an argumentation [argumentatio] and a ratiocination [ratiocinatio]. An argumentation, because it is a combination of an argument . . .with a question. It is called a ratiocination and a syllogism for one and the same reason [. . .] [B]oth terms seem to be transferred from numerical reasoning: or from there the similitude is transferred here: as good calculators find out by adding and subtracting what sum remains, dialecticians by adding and subtracting parts, explicate the sum of some reasoning (DI 78–79).

As he indicates, what is crucial for the weighing of reasons is not the correct expression of the logical form of a syllogism. Rather, he ascribes to the human mind a capacity of weighing reasons, which works independently of the formal correctness of a syllogism: We would render the art ridiculous, if we stated that human beings did not posses any stable judgment unless it were expressed by means of three terms: a belief has to be weighed [ponderanda], not that terms have to be counted [numeranda].6 And since the seat of the natural judgment is not in the tongue and hand but in the intellect and mind: the reason of the artificial judgment can be got not from words that are expressed by the voice or scripture but from the inner sense of speech (DI 84).

Hence, even given formal correctness, the validity of syllogisms derives from the sense of the concepts expressed by signs, and which underlies the natural capacity of judgment, whether or not formal connections between signs are established. That

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is why syllogisms are described as an instrument in the process of weighing reasons, a process that can take place even without formal tools. Ramus’ pragmatic conception of syllogism is connected with his views on analysis. Obviously, using a syllogism in weighing reasons presupposes a clear grasp of the reasons to weigh. Indeed, later in the Dialectical Institutions, Ramus ascribes a further pragmatic function to syllogisms, namely, the function of making the parts of a complex discourse perspicuous: [T]he main utility of the syllogism lies in unweaving [retexendis] longer discourses, which frequently happen to be rather obscure: such that when you distinguish many syllogisms in the parts of continuous and long speech, you embrace its sum total in one piece minus all amplifications, but [. . .] with a succinct grasp of the headings of arguments (DI 159).

“Unweaving” the parts of complex discourse lies at the heart of Ramus’ conception of analysis. The function of syllogisms in unweaving a complex discourse therefore is part of what analysis has to accomplish. Ramus discusses analysis in the third book of the Dialectical Institutions, devoted to the role of exercises in acquiring the art of dialectics. Analysis, as a part of the exercises of the dialectician, is related to innate, natural, human capacities in a direct way: Of the three parts that are necessary for discoursing, nature & art are now briefly [. . .] outlined: now we have to treat exercise (which still is left over) equally with a few words: which puts nature, instructed by art, into act (DI 136).

As in the case of syllogisms, the function of analysis is to enable the survey of the elements of a complex discourse: Dialectical analysis [. . .] is a given art unweaved [retexta] [. . .] Thus, at first, analysis unweaves the whole work it undertakes to explicate from the headings: it distinguishes the question that is proposed to the interlocutor: it inspects the arguments by means of which it is treated: and it specifies where the loci are taken from, and their law and nature: and finally it spells out the disposition given to the proposed topic (DI 136–137).

In this way, analysis contributes to defining the elements of the art of discoursing. The place of definition in analysis, however, is a somewhat specialized one, which should be recognized in order to understand correctly Ramus’ notion of analysis. Ramus distinguishes two kinds of definition. A definition in the proper sense “explicates what the thing itself is by means of the causes that constitute the proper and true nature of a thing [. . .]” (DI 68–69). In addition to this kind of causal definition, he acknowledges the importance of another kind of definition: “[W]hen we also use other arguments to explicate what it is that is asked, we call it a description [. . .]” (DI 69). Analysis can be understood as providing the second kind of definition – a description of the elements of discourse. Ramus characterizes the aims of description as follows: And in this way, whole volumes in good authors are filled with definitions that are more perspicuous than short. And the reason of this whole kind of definition lays not so much in brevity as in perspicuity [perspicuitas]. Since not only for the sake of memory alone (which brevity supports), but much more for the sake of understanding, which perspicuity brings about, the route of giving definitions is demanded (DI 71).

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In this sense, analysis provides the practitioner of dialectics with an understanding of the elements of discourse by representing them in a way that makes their survey easier. Subsequently and complementing analysis, it is the task of genesis to use examples in the formation of new discourses: Genesis is not the inspection of a proposed example like analysis but the production of a new work; which meditation follows exactly the same way as writing and teaching. In writing the first and easiest way is imitation; in which we have to observe carefully the one we imitate: to whom we want to be similar [. . .] Then we will have to make endeavors for ourselves, and set out a free argument about ordinary and popular affairs, and what pertains to everyday life [. . .] when we take causes, effects, and other kinds of (acceptable) arguments from the sources of invention; finally we make use of all modes of disposition with equal diligence [. . .] (DI 161–162).

Thinking about analysis and genesis in this way ascribes a logical function to examples taken from the ordinary use of language: due to the similarity of relations between examples and elements in new works, they function as norms for judging the parts of new discourses. At the same time, the function of analysis is detached from the task of constructing demonstrative knowledge.

3 Leibniz on Analysis The claim that analysis is detached from constructing demonstrative knowledge is the main point where his 16th and 17th century critics departed from Ramus.7 Leibniz’s views on analysis relate to 16th and 17th century debates about Ramism through his response to Hermann Conring’s preface to the centenary edition of Bartolomeo Viotti’s On Demonstration (1561). Leibniz’s response should not simply be seen in terms of accepting or rejecting claims made in the Ramist tradition. Rather, his response should be seen as an attempt at positioning his own view of the nature of analysis in the broader context of theoretical alternatives developed in the controversy between Ramus and his critics. As it turns out, Leibniz’s views on analysis are much closer to Viotti’s than to Conring’s. Although he shares some of Viotti’s and Conring’s objections to Ramism, he also shares some views that are common to Ramus and Viotti. In On Demonstration, Viotti takes the following line of critique against Ramus and Ramism: [I]f it is true that we have knowledge of something, and not only an opinion, it suffices that this can be derived from the fact that it is impossible that things could stand otherwise; however, this we get through a proof, not through some other kind of reasoning [. . .] Hence, if the necessary medium is that which establishes a connection such that we attain knowledge, it connects by way of some kind of argumentation, not by means of examples or enthymemes, since these are instruments of the orators, not of the philosophers; they are invented for the purposes of persuasion, not for the search after truth (Viotti 1561: Book I, Chapter 5).

Subsequently, he discusses a possible line of attack against this proof-oriented conception of knowledge:

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That nothing is deduced but from known principles is admitted by all sects, as well as those who defend the claim that everything can be demonstrated, as well as those who defend the claim that nothing or only something can be demonstrated. But they prove that the principles cannot be known, as follows: What is known is known by means of proof. But the principles cannot be known by proof. Hence, they are not known [. . .] (Viotti 1561: Book I, Chapter 6).

Viotti responds by rejecting the assumption that everything that is known is known by means of proof. He argues that “the first beginnings of demonstrating, which are assumed as perspicuous [perspicua] beyond proof from the senses & the intellect, are not only known, but more known than those that are proved by means of them” (ibid.). Viotti is non-committal as to the metaphysical status of concepts and principles accessible by the light of the intellect, and only investigates their logical role in the formation of proofs (Viotti 1561: Book II, Chapter 3). He gives the following account of how knowledge of definitions that serve as the starting point of definitions can be acquired: There is a paved and easy way open for us, on which we get to the essential definition: this is by means of the term associated with the given concept. When, e.g., you want to investigate the essence of pulse or fever, it is necessary to begin with the term in order to grasp the concept all human beings have of pulse [. . .] The interpretation of the term brings all accidents to light, from the knowledge of which we proceed to the knowledge of the substance and nature of the thing [. . .] Insofar as you, by examining and interpreting the common concept which all human beings have about this term “moon”, you could say that everyone understands by “moon” some heavenly body which appears at the heavens at some determinate time in the night and illuminates the earth in various forms [. . .] But this I want to be eternal: for investigating essential definitions, the mentioned interpretation of terms is a big help (Viotti 1561: Book II, Chapter 11).

In his preface, Conring objects that “all argumentation gains true and certain knowledge solely from that which is necessary in itself”. In particular, he applies this view to jurisprudence and political science: I have validated extensively the Civil science and its proofs in my book entitled On Civil and Political Prudence8 [. . .] But moral philosophy differs in nothing with respect to certainty or the way of proving from the Civil one [. . .] (Conring 1661: [xxi]–[xxii]).

Apart from this strategy, Conring applies a type of proof based on the interpretation of revealed precepts in the Holy Scripture. As he points out, “even this kind of reasoning is a true demonstration, gaining knowledge, however not absolutely, but only hypothetically” (Conring 1661: [xxiii]). Accepting such a hypothetical type of demonstrative knowledge modifies Conring’s overall views on the role of proofs in political and juridical matters. Nevertheless, it is clear from these remarks that Conring tries to defend the view that, apart from cases of revealed truths, demonstrative knowledge requires definitions and axioms which are necessary in themselves rather than the outcome of the analysis of ordinary concepts. In his letter of January 3, 1678, Leibniz rejoins to Conring: With what you say about that in all disciplines and even in particular cases there are proofs, I perfectly agree. Since even in matters of fact, when both sides fight with presumptions and conjectures, it is possible to define accurately, on which side, seen from the given

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circumstance, the greater probability lays. Hence, the probability itself can be proved, and its degrees can be estimated [. . .] (GP 1 187).

Thus, Leibniz takes sides with Ramus’ critics in defending the distinction between probable opinion and demonstrative knowledge. Moreover, he tries to extend the realm of demonstrative knowledge by rendering probabilistic calculations demonstrative – conditional on a given estimation of degrees of probabilities. However, he adds a serious objection: I regard axioms not, as you say, as something apodictic but only as something that in most cases does not require a proof. Yet that they are demonstrable, I believe to be certain. Whence does it come that we are certain about their truth? As I believe, not from induction, since in that way all sciences would be rendered empirical; thus, from themselves, i.e. from their terms, which happens when the same is said of the same (e.g., A is A, everything is equal to itself, and similar identical propositions) or when only from the signification of terms or, what is the same, from the understood definition the truth of the proposition is apparent [. . .] (GP 1 187–188).

Hence, according to Leibniz, the axioms used in demonstrations are not self-evident or revealed, as in the conception of Conring. Rather, they are themselves accessible to demonstration. The kind of demonstration Leibniz has in mind in this passage is a demonstration based on the analysis of the concepts contained in the axioms. However, in the subsequent letter to Conring (March 19, 1678), Leibniz expands his view on the non-apodictic nature of axioms: I have only said what I have found out in this matter through the experience of many years and through the examples of my own reasoning and that of others, and, moreover, something that is in accordance with what human beings daily do, even if they are not always aware of it, something that is efficient for inventing and judging, and not, as the methods and precepts of some others, sterile and remote from use and examples (GP 1 193).

Leibniz here criticizes the methods of other theoreticians for being detached from use and examples. This critique suggests that he assigns a positive function to common usage and examples for providing an analytic foundation for axioms, such as principles of reason or principles of jurisprudence. As the letter to Conring quoted above made clear, the role of examples cannot be one of inductive reasoning. Rather, as the present passage explicates, the relevant examples are samples of our everyday reasoning. Moreover, these samples are portrayed as containing, in an implicit way, something that is constitutive in forming new judgments. This emphasis on samples of everyday reasoning, Leibniz shares with Ramus and Viotti. To be sure, Leibniz does not give up the distinction between the method of the Topics and demonstrative knowledge. As Giovanna Varani has pointed out, in New Method of Learning and Teaching Jurisprudence (1667), Leibniz explicitly distinguishes between the application of the method of the Aristotelian Topics and the demonstrative method of a theory of universal jurisprudence (Varani 1995: 99–100). According to Leibniz, “Johannes Felden and other Aristotelians want that the rules of law are contingent truths [. . .] They don’t seem to have considered the matter sufficiently” (A VI 1 308). “The science of law, by its nature, does not belong to the conjectural sciences. Conjectures are allowed in the realm of facts but not in the

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realm of law” (A VI 1 309). Varani understands these claims only in the perspective of an “axiomatic jurisprudence” having an affinity with axiomatic geometry (Varani 1995: 100). Certainly, this corresponds to a project Leibniz formulated very early.9 However, the role of the project of axiomatic jurisprudence has to be complemented by the role Leibniz ascribes to the method of analysis in the formation of a demonstrative science. Varani (1995: 106–116) gives a detailed exposition of Leibniz’s remarks about the limits of the “ars analytica”.10 Nevertheless, it is important to see in which respect exactly Leibniz locates the limits of the applicability of analysis. Interestingly, these limits closely correspond to the limits he draws for the feasibility of the project of a universal characteristic. According to his view, analysis does not work for disentangling the simple components of the experiences of the physical world, both for reasons of the limitation of our experimental capacities and for the unknowability of simple properties understood as attributes of the Divine mind (see A VI 3 404). Nevertheless, the applicability of the method of analysis exactly matches the applicability of a universal characteristic for categorical concepts. That is why Leibniz, despite the serious limitations of the applicability of analysis, in On the Imperfection of Analysis and Its Supplementation by Synthesis (Spring– Summer 1673) defends the view that analysis can be applied to metaphysics, ethics, and jurisprudence: Invention takes place by means of analysis, wherever for inventing nothing else is assumed than the given problem or theorem, which, if it is analyzed into its first elements, provides us with the solution. Invention by means of synthesis is a kind of invention, in which other already known things are required [. . .] Analysis in physical things is impeded, because we do not know the experiments, and find them only by chance or a big effort of time [. . .] In practical action analysis in general cannot, in most cases, be applied, because it would require an exceeding amount of time, and there are infinitely many factors that would have to be taken into account [. . .] In general political questions, but above all in questions of law there is a most certain and perfect analysis, and the same holds for some issues in metaphysics. Concerning arithmetic and geometry, there are some topics that are not accessible to analysis, in the one due to the multitude, in the other due to the infinity of things to be considered [. . .] (A VI 3 404).

Thus, Leibniz understands ethics and jurisprudence as more than conjectural disciplines which, nevertheless, are built up not only in an axiomatic-deductive way. Rather, in spite of the limitations of an analytic methodology in other fields, he characterizes the theory of justice, along with some metaphysical topics, as accessible to analysis. Leibniz also holds that definitions are capable of expressing the nature of the defined. In particular, the importance of this claim makes itself felt in the context of his view of the role of definitions in practical philosophy. According to him, in this area, the nature of what is defined coincides with the nature of mind. In this sense, Leibniz writes in the Appendix to the Dissertation on the Art of Combinations (1666): Although each method can be applied in each discipline; so that we follow in our research either the traces of our own investigations or productive nature; it nevertheless happens in the practical disciplines that the order of nature and the order of knowing coincide, because here the nature of the thing has its origin in our thought and production. Since the goal moves us to produce the means, and at the same time leads us to recognize them; which is

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not the case for objects that we only know but cannot produce. Apart from this, even if each method is permissible, not every one is useful (A VI 1 229).

In New Method of Learning and Teaching Jurisprudence, Leibniz takes up the idea that concepts such as thought and causation are expressions of the nature of the mind, and extends this idea to definitions in ethics and jurisprudence: Sensible qualities are of two kinds: some perceived in the mind alone, others in fantasy or by means of mediating bodily organs. In the mind, only two sensible qualities are perceived: thought and causality. Thought is a sensible quality either of the human intellect or of something ‘I know not what’ within us, which we observe to be thinking. But we cannot explain what thinking is any more than what white is or what extension is. [. . .] Logic is built on the sensible quality called thought [. . .] The other sensible quality found in mind alone is causality – when it can be proved demonstratively from an effect that it has some cause, even though latent. This quality, abstracted from others such as motion and figure, is in the cause of the world or God [. . .] and in our own minds as the cause of bodily motion. But we cannot explain the method of causality. This is the subject matter of pneumatics, which deals with the external actions of incorporeal beings, as logic deals with their internal actions, or thought. Here belongs also practical philosophy, or the doctrine of the pleasant and the useful, and of justice or what is of common value in a community (A VI 1 286–287).11

Because according to Leibniz’s view, the axioms of a theory of justice belong to the nature of rational beings, these axioms are accessible by means of a comparative method. In the fourth MS of the Elements of Natural Law (1670–1671), Leibniz describes this method as follows: The method of our investigation is to gather the more important and distinctive examples of the use of these terms and to set up some meaning consistent with these and other examples. For just as we construct a hypothesis by inductions from observations, so we make a definition by comparing propositions; in both cases we make a compendium of all other instances, as yet untried, out of the most important given cases. This method is necessary whenever it is not desirable to determine the use of terms arbitrarily for oneself (A VI 1 461).

Thus, the common conceptual equipment of rational beings guarantees that the definitions of concepts of reason are not arbitrary. Moreover, a few lines after the passage just quoted, Leibniz refers the reader to what he said in his Preface to Nizolius. About logical concepts, he writes there: True logic is not only an instrument, but also contains in some way the principles and the true reason for doing philosophy, because it hands down those general rules, through which the true and the false can be discerned, and by means of which, through the mere application of definitions and experiences, all conclusions can be proven. But neither are these rules the principles of philosophy, or of the propositions themselves, and they do not make the truth of things, but rather show it; nevertheless they make the philosopher, and are the principles of the right way of doing philosophy, which – as Nizolius has observed – is enough (A VI 2 408).12

Here, Leibniz does not regard the principles of reasoning as something that is constitutive of philosophy as a particular theoretical discipline. Principles of reason, in his opinion, are not a tool of theory construction. Rather, they are something that in philosophical analysis is only made explicit. In this sense, making principles of reason explicit only “shows” the truth which our ordinary way of thinking about

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things already contains. In the Preface to Nizolius, this view of the descriptive nature of philosophical knowledge leads Leibniz to claim that philosophers do not know other things than ordinary people but rather the same things in a different way: And it is very true that there is nothing that cannot be explicated in popular terms, only using more of them. Therefore, Nizolius rightly urges at various places that what does not possess a general term (i.e., as I understand him, what, conjoined with other general terms, can in particular express a thing) in common language should be regarded as nothing, as a fiction, and as useless. For philosophers do not always surpass common men in that they sense different things, but that they sense them in another way, that is with the eye of the mind, with reflection or attention, and comparing things with other things (A VI 2 413).

Although the example of “comparing things with other things” mentioned here concerns Joachim Jungius’ attempt at classifying birds through a comparison of their external features, the point Leibniz has in mind here seems to be more general. The function of comparing things with each other in this context does not have the function of arriving at empirical generalizations based on an inductive procedure. Rather, using a comparative method leads to an insight into a conceptual structure that, due to its commonly shared nature, can be regarded as a kind of implicit knowledge that only has to be made explicit.

4 Conclusion I set out to argue that, in the 1547 edition of the Dialectical Institutions, Ramus dissociates the logical use of examples from insight into Divine truth. In his view, using examples from rhetorical and poetical works conveys insight into common, innate concepts that play a formative role in the constitution of human discourse. Analysis, for him, like the use of syllogisms, has the task of making the elements of discourse perspicuous. According to his view, by making elements of a complex discourse perspicuous, syllogisms enhance natural capacities in weighing reasons. Analysis provides us with perspicuous examples which, due to the similarity or dissimilarity between them and elements of new discourses, function as norms in the formation of new discourses. By contrast, Leibniz shares with Ramus’ critics the view that analysis is connected with the task of providing definitions underlying demonstrative arguments. Yet, he also shares with Ramus the view that analysis is directed towards the everyday usage of language and, thus, makes concepts common to rational human beings explicit. In this sense, Leibniz shares with Ramus the view that what is accessible to analysis belongs to a kind of knowledge that is established on descriptive grounds. Acknowledgments Research for this article was carried through during my time as a Visiting Fellow at the Cohn Institute for the Philosophy and History of Science and Ideas at Tel Aviv University during the academic years 2004–2005 and 2005–2006. I would like to acknowledge a debt of gratitude to the Alexander von Humboldt Foundation for having granted me a Feodor Lynen Fellowship for the two years in Israel.

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Notes 1. See De reductione hypothesium ad demonstrationes ac phaenomenorum ad theoremata (1669–1670; A VI 2 476–477); Marii Nizolii De veris principiis et vera ratione philosophandi libri IV, Dissertatio praeliminaris (A VI 2 462); Specimen demonstrationum de natura rerum corporearum ex phaenomenis (1671; A VI 2 301). For the role of Ramism in Leibniz’s academic education, see Bruy`ere (1984: 364–367). 2. Daniel refers the reader to Ramus 1543: fol. 57. See also Daniel (2001). 3. See Nizolius 1553. 4. For the history of the three-book Latin editions of the Dialectical Institutions, see Ong 1958: 200–201. In what follows, I refer to the 1547 edition of the Dialectical Institutions as “DI”. All references are to page numbers. 5. See the passage pointed out by Daniel; see above note 2. 6. This conception of weighing reasons foreshadows Leibniz’s conception of a “balance of reason”. For Leibniz’s views, see Dascal (1996). 7. For an overview over early Aristotelian responses to Ramus, see Robinet (1996: Chapter 2). 8. See (Conring 1662: Chapters 8 and 10). 9. See, e.g., Nova methodus discendae docendaeque jurisprudentiae (A VI 1 311); Dissertatio de arte combinatoria (A VI 1 189). 10. See, e.g., Desiderata Analytica (1674; A VI 3 410). 11. As I have argued elsewhere, much of Leibniz’s theory of universal justice is based on a descriptive, bottom-up strategy that begins with the analysis of the nature of our thought. See Blank (2004 and 2005: Chapter 2). 12. For Nizolius’ metaphilosophical views, see Marras and Varani (Forthcoming).

References Blank, A. 2004. Definitions, sorites arguments, and Leibniz’s M´editation sur la notion commune de la justice. Leibniz Review 14: 153–166. Blank, A. 2005. Leibniz: Metaphilosophy and Metaphysics, 1666–1686. Munich: Philosophia. Bruy`ere, N. 1984. M´ethode et dialectique dans l’œuvre de La Ram´ee. Paris: Vrin. Conring, H., 1661. Herman[nus] Conringus Andreae Fr¨olingio logices in Academia Julia professori collegae sui, in B. Viotti, De demonstratione libri quinque ante hos centum annos Parisiis primum editi, ed. A. Fr¨oling, Helmstedt, pp. [xvii]–[xxxi]. Conring, H. 1662. De civili prudentia liber unus. Helmstedt. Daniel, S.H. 2001. The Ramist context of Berkeley’s philosophy. British Journal of the History of Philosophy 9: 387–412. Daniel, S.H. Forthcoming. Ramist dialectic in Leibniz’s early thought. In M. Kulstad (ed.), The Young Leibniz. Stuttgart: Franz Steiner. Dascal, M. 1996. La balanza de la raz´on. In O. Nudler (ed.), La racionalidad: su poder y sus l´ımites. Buenos Aires/Barcelona: Paid´os, pp. 363–381. Marras, C. and G. Varani. Forthcoming. I dibattiti rinascimentali su retorica e dialettica nella ‘Prefazione al Nizolio’ di Leibniz. Studi Filosofici. Nizolius, M. 1553. De veris principiis et vera ratione philosophandi contra pseudophilosophos. Parma. Ong, W.J. 1958. Ramus: Method, and the Decay of Dialogue. Cambridge, MA: Harvard University Press. Ramus, P. 1543. Dialecticae institutiones. Paris. Ramus, P. 1547. Institutionum dialecticarum libri III. Paris. [= DI] Robinet, A. 1996. Aux sources de l’esprit Cart´esien. L’axe La Ram´ee-Descartes. De la Dialectique de 1555 aux Regulae. Paris: Vrin. Varani, G. 1995. Leibniz e la “Topica” Aristotelica. Milano: Istituto di Propaganda Libraria. Viotti, B. 1561. De demonstratione libri quinque. Paris.

Chapter 10

Locke, Leibniz, and Hume on Form and Experience Emily Rolfe Grosholz

Locke, Leibniz, and Hume had no admiration for “enthusiasm”, a kind of dogmatism grounded in alleged religious revelation. Enthusiasm is a self-reinforcing subjectivity that refuses to examine its own grounds by objective methods; the enthusiast is above reproach, or criticism. All three philosophers, in different ways, offer an epistemology where improvement and correction are always possible and indeed required, where the one who knows must always be interested in the correction of moral and scientific knowledge. Locke and Hume believe that methods for assessing, criticizing, and improving knowledge claims must be empirical in order to be objective, though their accounts of experience differ; Leibniz believes such methods must be formal in order to be objective. In order to compare the relative merits of their positions, I will appeal to realms of human endeavor that all three of them take as paradigmatic: the legal system as essential to rational morality, and mathematics as essential to rational science. I will argue that a successful legal system requires empiricism in its management of evidence, and formalism in its principles and rules of inference to guarantee impartiality; and that successful mathematics also requires formalism at the level of principle as well as inference, and empiricism in the sense that structures must be tested and revised by application to mathematical individuals. Yet Locke misunderstands the virtue of formality, and Leibniz overstates it, or does so at least in the New Essays; Hume’s doctrine of “formal experience” can be used to find common ground between them.

1 Locke on Formal Reasoning For Locke, the formal schema for finding new knowledge is the discovery of “middle terms”. This vocabulary comes variously from the theory of ratios and proportions found in Eudoxus and Euclid, and from Aristotle’s theory of the syllogism. If we know A and C, and assert the proportion A : B :: B : C, then “B” is the middle term to be discovered, which brings A and C into rational relation. If we assert the standard valid syllogism, “All P is M and All M is S, then All S is P”, then “M” is E.R. Grosholz Pennsylvania State University, State College, Pennsylvania, USA M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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the middle term to be discovered, bringing the minor term P and the major term S into rational relation. Towards the end of Book Four: Of Knowledge and Opinion in An Essay Concerning Human Understanding (sections that begin with Chapter 12: Of the Improvement of Our Knowledge), Locke asserts that the improvement of knowledge depends on two things. First is the development of a good taxonomy: “determined ideas of those things whereof we have general or specific names”. As Descartes urged, our complex ideas should be complete concatenations of clear and distinct simple ideas; and the spelling out of complex ideas in terms of simple ideas is what leads to good taxonomy. Second is the “art of finding out those intermediate ideas, which may show us the agreement or repugnancy of other ideas, that cannot be immediately compared” (Locke 1959: 341–356). Locke begins Chapter 12 with the claim, “Knowledge is not from Maxims”. That is, a satisfactory account of truth cannot simply be deduction from first principles which serve as “foundations”. It has appeared to some thinkers, he allows in Section 2, that this way of proceeding is successful in mathematics; but in Section 3 he disputes this appearance. He claims instead that even advances in mathematics were not made by derivation from maxims laid down in the beginning, but rather from the clear, distinct, complete ideas their thoughts were employed about, and the relation of equality and excess so clear between some of them, that they had an intuitive knowledge, and by that a way to discover it in others; and this without the help of those maxims (Locke 1959: 342).

We might take the celebrated proof of the Pythagorean Theorem in Book I of Euclid’s Elements as an example of what Locke means here. Our understanding of the truth of the proof depends on the use of a specific right triangle representing “any” right triangle, with squares constructed on its two legs and hypotenuse, and lines connecting the original triangle and those squares so that the equality of the area of the two squares on the legs with the area of the square on the hypotenuse is apparent. Later on, in Chapter 17: Of Reason, Section 2, Locke argues that we need reason “both for the enlargement of our knowledge and regulating our assent”, and therefore must not identify it with the use of formal logic. For Locke as for Leibniz, whose common inspiration was Descartes, the work of reason must involve procedures that discover and at the same time improve knowledge. Good discovery procedures not only exhibit new knowledge but also explain it, that is, they articulate and organize our reasons for believing it. In Section 4, he asserts, “Syllogism not the great Instrument of Reason”, and argues for this claim in two ways. On the one hand, the formal system of syllogistic does not show us how to find the middle terms we seek; it only gives us a convenient way of arranging them once we have them in hand, setting a series of middle terms in order as a kind of bookkeeping. The ability to find middle terms depends on acquaintance with the peculiar nature of the given subject matter (in the case of the Pythagorean Theorem, lines, triangles, trapezoids, and circles), as formal rules of inference do not. Indeed, formal rules of inference, to carry out their proper role, should not express the peculiar nature of any subject matter. On the other hand, the formal system of syllogistic is awkward and limited even in the way it represents the rules of inference we do use in thinking

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(about anything). Locke writes, “[i]f we will observe the actings of our own minds, we shall find that we reason best and clearest, when we only observe the connexion of the proof, without reducing our thoughts to any rule of syllogism” (Locke 1959: 386–400). Locke develops his arguments against the hegemony of syllogistic by making use of both Cartesian intuitionism and his own nominalism. Descartes’ epistemology begins from intuitions, the seeing of things that must exist due to their intelligibility: God, the soul, figures and numbers. The thinker encounters them as unified things of a certain kind. Thus Locke writes, God has not been so sparing to men to make them barely two-legged creatures, and left it to Aristotle to make them rational . . .He has given them a mind that can reason, without being instructed in methods of syllogizing; the understanding is not taught to reason by these rules; it has a native faculty to perceive the coherence or incoherence of its ideas, and can range them right, without any such perplexing repetitions.

The better way of attaining knowledge, he sums up, is “not by the forms themselves, but by the original way of knowledge, i.e., by the visible agreement of ideas” (Locke 1959: 391). Descartes’s and Locke’s intuitionism stands in uneasy tension with the strongly reductive account of knowledge they offer; Locke borrows from Descartes the view that every complex object of knowledge ought to be “led back” to the simples that compose it. Descartes’ simples are, e.g., God, the soul, geometrical figures and numbers in the Meditations; straight line segments in the Geometry; and particles of matter in inertial motion in the Principles (Grosholz 1991). Locke’s simples are simple ideas of perception and reflection. Both of them, however, use the term “intuition” to assert a “seeing” that is more fundamental than and prior to any formalization of discursive reasoning. In Section 14 of Chapter 17, Locke argues, Our Highest Degree of Knowledge is intuitive, without Reasoning. Some of the ideas that are in the mind are so there that they can be by themselves immediately compared one with another; and in these the mind is able to perceive that they agree or disagree as clearly as that it has them. In this consists the evidence of all those maxims which nobody has any doubt about, but every man [. . .] knows to be true, as soon as ever they are proposed to his understanding (Locke 1959: 407).

If we refer this claim to the proof of the Pythagorean Theorem, Locke is here asserting that our ability to see the equality of the area of the square raised on the hypotenuse of the right triangle with the areas of the two squares raised on the legs is prior to any formalization of the proof in terms of maxims and rules of inference. This entails, of course, that we be able to “see” a triangle as a triangle, an intelligible, unified, existing shape. Whether this triangle-vision can be explained in terms of a reconstruction out of simple ideas of sense or reflection (Locke) or straight line segments (Descartes) is another question, which I here leave aside. Locke also invokes nominalism in his attack on the hegemony of syllogistic, which is also, of course, an attack on Scholasticism. In Section 8 he announces, “we reason about particulars”, and goes on,

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it is fit [. . .] to take notice of one manifest mistake in the rules of syllogism: viz. that no syllogistical reasoning can be right and conclusive, but what has at least one general proposition in it. As if we could not reason, and have knowledge about particulars; whereas, in truth, the matter rightly considered, the immediate object of all our reasonings and knowledge is nothing but particulars [. . .] Universality is but accidental to [our reasoning], and consists only in this, that the particular ideas about which it is are such as more than one particular thing can correspond with and be represented by (Locke 1959: 403–405).

Once again, this reflection may be referred to the proof of the Pythagorean Theorem. This proof proceeds by the combined use of an icon, the diagram; of symbols, e.g. lines and figures tagged by concatenations of letters (which refer to points on the diagram), and conjoined in ratios and proportions; and of natural language that explains the combination of the icon and symbols. The icon denotes a specific right triangle, which can stand as a representative of all right triangles because its symbolic handling does not make use of any of its peculiar features, features that distinguish it from other right triangles. The denotation of a particular, dependent on the use of an icon, is essential to the proof. If the proof holds for this right triangle, then it must hold for any other; yet it must hold for this triangle or the proof has no content. As I would say, the proof requires the triangle both to be an icon of a particular triangle, and to represent symbolically, in conjunction with the ratios and proportions, all other right triangles. The natural language exposition is therefore also needed to guide the reader in dealing with the ambiguity of the diagram, that is, to distinguish and relate its iconic and symbolic roles (Grosholz 2005). I can sum up Locke’s arguments against “truth as derivation from maxims” and “syllogistic as the key to reason” in the following way. When we re-write our best efforts to attain knowledge, like the proof of the Pythagorean Theorem in mathematics, in the formalism of maxims and syllogisms, we substitute a mode of representation that exhibits correct inference quite well for a combination of modes of representation that exhibits geometrical knowledge quite well, allowing for denotation and successful problem solving by displaying the kinds of things we are dealing with, their characteristic unity, and the reasons why they are the kinds of things they are (the middle terms). Moreover, even if our main concern were exhibiting correct inference, the formalism of syllogistic is defective, since there are many forms of inferring that we cannot capture in that idiom.

2 Leibniz on Formal Reasoning Leibniz had a much deeper and richer understanding of the nature of formalism than Locke. He understood that “formalism” meant not just logic as the canon of forms of inference about anything at all, but also algebra – indeed algebras of different kinds that represent formally the peculiar features of different subject matters. In the New Essays on Human Understanding, he sees syllogistic as embedded in a broader enterprise that he calls a kind of universal mathematics or “art of infallibility” in his commentary on Locke’s Chapter 7: Of Reason. He explains that he means by formal arguments, “any reasoning in which the conclusion is reached by virtue of the form, with no need for anything to be added”. He also includes

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a sorites, some other sequence of syllogisms in which repetition is avoided, even a well drawn-up statement of accounts, an algebraic calculation, an infinitesimal analysis – I shall count all of these as formal arguments, more or less, because in each of them the form of reasoning has been demonstrated in advance so that one is sure of not going wrong with it.

He further adds to this list the Euclidean use of ratios and proportions: Euclid’s invertings, compoundings and dividings of ratios are merely particular kinds of argument-form which are special to the mathematicians and to their subject-matter; and they demonstrate the soundness of these forms with the aid of the universal forms of general logic (R&B 479).

Leibniz saw something about formal languages more clearly than anyone else in the 17th century, and certainly more clearly than Locke. He understood the “algebraic” virtue of form: It can be (provisionally) detached from its applications or instances – allowed to take on a life of its own – and then its rules of procedure may be considered infallible. According to the algebra of arithmetic, a(b + c) infallibly produces ab + ac, no matter what integers we plug into the formula. We can rely on the formalism; in this case, we do not have to perform the operations of adding b + c and then multiplying the result by a, but can instead multiply a and b, then a and c, and finally add the products. The algebraic form insures that we will arrive at the same result. Another example will make the point even more emphatically. In the first few pages of Descartes’ Geometry, the construction of the products of line segments is quite a bit more difficult than the construction of sums; we can save ourselves the trouble of constructing both the product of ab and ac (and then constructing their sum) by first constructing the sum of b + c and then, one time only, constructing the product of a and b + c. The algebraic form guarantees the infallibility of this alternative. Moreover, Leibniz understands very well (better than anyone else at the time) that the mathematical study of forms independent of their applications is rewarding mathematically. He rightly chastises Locke for thinking that the relation between a formal expression and its instances is abstraction or induction from instances. It is not abstraction, because abstraction begins with a range of instances and subtracts what makes them different, leaving only what they have in common. But on the contrary, “in so far as you conceive the similarities amongst things, you are conceiving something in addition to the things themselves, and that is all that universality is” (R&B 485). Discovery of significant form adds something to the furniture of the universe, that is, intelligible structure conceived in addition to the things compared. Algebra adds its own truths to those of arithmetic and geometry. And the relation is not induction from instances, because the selection of what counts as the instances in induction presupposes that we already have a grasp of the additional “something” of significant form. “The instances derive their truth from the embodied axiom, and the axiom is not grounded in the instances” (R&B 449). The use of algebra in Descartes’ Geometry shows that the truth of the algebraic rule given above is not grounded in arithmetical facts any more than it is grounded in facts about line segments.1 Leibniz was understandably enchanted by his novel insight into autonomous and detachable form, and its importance for both the criticism and the growth of knowledge, an enchantment heightened by his polemic against Cartesian intuition. But

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the enchantment and the polemic led him to overstate the virtues of form. Locke’s protests against syllogistic have weight after all, even for mathematics, and we must take them into account. For example, Leibniz writes, [i]t is by no means always the case that ‘the mind can see easily’ whether something follows: in the reasoning of other people, at least, one sometimes finds inferences which one has reason to view initially with skepticism, until a demonstration is given. The normal use of ‘instances’ is to confirm inferences, but sometimes this is not a very reliable procedure [. . .] (R&B 481).

His claim echoes the early critique of Descartes, that one’s subjective conviction that an idea is clear and distinct may lead to error. He makes the point by referring to two geometric examples, and warns against using images in proof, because the faculty of imagination, drawing on sense-experience, must be prone to the confusions attendant on sensation. The first example shows that Leibniz understood that the parallel postulate in Euclid has a status different from some of the other first principles. (Many pages in Leibniz’s Nachlass are spent examining the logical structure of Euclid’s Elements.) Euclid, for instance, has included in his axioms what amounts to the statement that two straight lines can meet only once. Imagination, drawing on sense-experience, does not allow us to depict two straight lines meeting more than once, but this is not the right foundation for a science. And if anyone believes that his imagination presents him with connections between distinct ideas, then he is inadequately informed as to the source of the truths, and would count as immediate a great many propositions which really are demonstrable from prior ones (R&B 451).

Leibniz faults the definition of a straight line given by Euclid. The second example is that of the asymptote to a curve: It is likely too that by allowing our senses and their images to guide us we would be led into errors; we see something of the sort in the fact that people who have not been taught strict geometry believe, on the authority of their imaginations, that it is beyond doubt that two lines which continually approach each other must eventually meet. Whereas geometers offer as examples to the contrary certain lines which they call asymptotes (R&B 452).

Here I argue, in defense of Locke, that Leibniz misunderstands the roles of instances and of images in proof. I begin with the assumption that mathematical representation serves the aim of problem-solving, so that (a) problem-solving is often enhanced, or only possible, when a variety of modes of representation are combined; (b) icons and the iconic aspects of symbols are necessary to the denotation required for representation; and (c) some modes of representation are better than others for certain kinds of problem-solving and others better for others. So, as I argued earlier, in the celebrated diagram that accompanies the symbolic ratios and proportions and natural language (Greek) of the Pythagorean Theorem, the diagram exhibits, and must exhibit, this right triangle in order to show that the theorem holds for any right triangle. Due to the irreducibility of shape, in order to denote this triangle we have to present a shape; due to the nature of mathematical induction, the anchor case must be exhibited in its particularity in order to generate what Poincar´e calls the “cascade” of other cases. Algebraic symbols and numbers can be correlated

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with shapes in the service of solving geometrical problems, but successful problemsolving requires both denotation and apt representation, representation that exhibits aspects of the things denoted pertinent to solving the problem (Grosholz 2007). The diagram does in fact successfully and correctly help to exhibit the relation between the squares on the legs of the triangle and the square on its hypotenuse; there is nothing misleading about its contribution to the proof. Given the problem, then, the diagram, the symbolic notation of ratio and proportion, and the explanatory natural language that links them provide a combination that leads to a satisfactory proof. Leibniz reproaches Euclid for offering a definition of the line that does not articulate what happens to parallel lines at infinity. But this frame issue arises from problems that interested Leibniz in the seventeenth century; it does not impugn the truth of the Pythagorean Theorem for the cases to which it was intended to apply, or the cogency of Euclid’s definition of a straight line, which must be taken in conjunction with its representation by a straight line. Both diagrams and symbols are found to be “incorrect” when they are applied to cases not envisaged by their original authors. Some of Descartes’ algorithms for the hierarchy of algebraic curves, for example, were disproved when more information was gleaned about algebraic curves higher than the conics and cubics, as were Leibniz’s own attempts to formulate algorithms for infinite series. The use of symbols – as opposed to icons – in mathematics is no guarantee of infallibility; and the use of icons does not doom an argument to confusion, or to a lack of reliability and rigor. Leibniz is, however, right on one point. The genius of algebra is not only the way in which it allows us to combine reasoning about numbers and figures, but also the way in which it allows us to move between the finitary and the infinitary (and the infinitesimal) in our reasoning. Leibniz was right to celebrate the “blindness” of his new characteristics because they allowed him to assert rational structural relations between finitary things and things that are too big or too small or too “far away” to be pictured directly. Thus, it is significant that the examples he invokes to reproach Euclid involve mathematical things that happen at infinity (as did his original example against Descartes, the “fastest velocity”). His own mathematical innovations, like the algorithms for the differential and integral calculus, and his nascent sense that mathematics might be full of algebras, were splendid examples of the exploitation of the blindness of symbols. But in the context of this dispute, we must remember that the yoking of the finitary and infinitary by symbols often involves icons (which then take on new functions and picture indirectly what cannot be pictured directly) and depends on certain spatial and iconic features of the symbols themselves. Icons are no more or less tied to sense perception than symbols. We might take a longer backwards look at the mathematical pathway that led from Euclid to non-Euclidean geometry, which proceeds by the consideration of particular instances essential to both fruitful generalization and the justification and correction of algorithms.2 Though on the one hand it is the record of logical investigations, it is also the investigation of novel curves and surfaces, as well as novel meanings for algebraic forms. Poincar´e observed that “analysis” opens up too many possibilities and also tends to decompose things, so that the mathematician who deploys it must also reinstate the unity of mathematical things and choose

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one possibility among many: these goals are also achieved by representation, the representation of particular instances (Poincar´e 1970: 36–37). This is, I believe, what Locke means when he appeals to the use of intuition in mathematics; and although Leibniz downplays its importance as he challenges Locke, his own work in mathematics does not dispense with intuition.

3 Locke and Leibniz on Practical Deliberation Locke distrusts “deduction from maxims” because he sees it as analogous to enthusiasm: The enthusiast has infallible truths and infers what to do in every case on the basis of them. Leibniz recommends “deduction from maxims” because he sees it as analogous to what opposes enthusiasm: the disinterested analysis of concepts, undertaken by people willing to sit down and reason together. I would argue that both of them took the legal system as a paradigm for moral reasoning, but that Locke had in mind English case law, while Leibniz had in mind the principle-dominated system of law he had learned at university in Germany. English case law begins with judgments concerning particulars, and becomes a moving system of rules that is revised as the stock of instances, and the perceived analogies within that stock, shift through time. Case law, however, works best when it is complemented by constitutionally based principles that are fixed but abstract. Conversely, a legal system that begins with principles must be supplemented by further arguments – offering canonical instances and a taxonomy governing them that is based on recognized analogies – every time it is brought to bear on particular cases that relate abstract principles to historical events. Locke writes at the beginning of Chapter 14: Of Judgment: He that will not eat till he has demonstration that it will nourish him, he that will not stir till he infallibly knows the business he goes about will succeed, will have little else to do but sit still and perish (Locke 1959: 360–362).

We exercise judgment in cases where the perceived agreement or disagreement of ideas cannot be demonstrated, and we find ourselves in the realm of probabilities. The grounds of probable knowledge are not only the conformity of our knowledge with our own experience but also the testimony of others; so it is irreducibly social. Locke’s articulation of what should be considered in the testimony of others sounds very much like Aristotle’s Rhetoric: 1. The number. 2. The integrity. 3. The skill of the witnesses. 4. The design of the author, where it is testimony out of a book cited. 5. The consistency of the parts, and circumstances of the relation. 6. Contrary testimonies (Locke 1959: 365–366).

Correct judgment emerges from the reasonable hearing-out of all sides of contrary testimonies. In matters where a probable judgment must be arrived at, the opinions of others must be duly weighed, and no empirical evidence that might bear on the decision

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should be left out, because we can never be sure what may turn up next. In Chapter 16: Of the Degrees of Assent, Locke writes that in matters of probability, it is not in every case we can be sure that we have all the particulars before us, that any way concern the question, and that there is no evidence behind, and yet unseen, which may cast the probability on either side, and outweigh all that at present seems to preponderate with us.

New cases may change the configuration of the field of cases, and so the analogies it exhibits, and so the rules that organize it, in significant ways. We will always find ourselves caught up in the clash of conflicting opinions; we have no absolute grounds to impose our opinions on others; and so we should always be ready to examine our own opinions critically and to treat the opinions of others with forbearance. For where is the man that has incontestable evidence of the truth of all that he holds, or of the falsehood of all he condemns, or can say that he has examined to the bottom all his own, or other men’s, opinions?

These tenets are embodied in the legal system: when one takes conflicts to court, one must be prepared to listen to the counter-arguments of the opposition and to treat the opposition with the formal civility imposed by the rules of litigation (Locke 1959: 369–384). Moreover, the legal system carefully controls what is allowed to enter disputes as evidence. Traditional testimonies, the further removed the less their Proof. This what concerns assent in matters wherein testimony is made use of; concerning which, I think, it may not be amiss to take notice of a rule observed in the law of England; which is, that though the attested copy of a record be good proof, yet the copy of a copy, never so well attested, and by never so credible witnesses, will not be admitted as a proof in judicature [. . .] This practice, if it be allowable in the decisions of right and wrong, carries this observation along with it, viz. that any testimony, the further off it is from the original truth, the less force and proof it has (Locke 1959: 377–378).

Locke ends this section with a dig at religion, since religion tends to view very old, very second-hand opinions as most certain; it appears to use, he observes, an inverted rule of probability. Judgment may, finally, be regulated by the apprehension of analogy. Reasoning in cosmology, biology and mathematics often proceeds by analogy to bring the more inaccessible into rational alignment with the more accessible. The use of analogy helps us to classify and to generalize, and so its use in moral reasoning apropos human action can be expected to support good judgment. Locke here approves a mode of moral reasoning that looks very much like the empirical reasoning by analogy characteristic of English case law. Leibniz whole-heartedly supports Locke’s appeal to tolerance: “Really, what we are most justified in censuring is not other men’s opinions, but their immoderate condemnation of the opinions of others [. . .] Impartiality counsels mercy [. . .]” (R&B 461). But he identifies the source of judicial impartiality, which moral judgment ought to imitate, not with its respect for empirical fact but for its allegiance to formal procedure.

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When jurists discuss proofs, presumptions, conjectures, and evidence, they have a great many good things to say on the subject and go into considerable detail. The entire form of judicial procedures is, in fact, nothing but a kind of logic, applied to legal questions (R&B 465).

By “a kind of logic”, Leibniz means a calculus of probabilities, whose development he foresaw with his usual prescience. “Physicians, too, can be observed to recognize many differences of degree among their signs and symptoms. Mathematicians have begun, in our own day, to calculate the chances in games”. He cites the work of Pascal, Huygens, and De Witt, who in fact initiated the mathematical study of chance, along with Leibniz’s own disciples, the Bernoullis, and continues, “I have said more than once that we need a new kind of logic, concerned with degrees of probability, providing us with balances which are needed to weigh likelihoods and to arrive at sound judgments regarding them” (R&B 466). The formal study of probabilities has been immensely fertile, and today bears directly on practical decisions in many ways, in the fields of economics, sociology, medicine, and computer science, inter alia. Yet once again, Leibniz overstates the virtues of formalization and its role in practical deliberation. In the American political system, the decisions of Supreme Court justices and the decisions of Congress to alter or institute legislation may make use of specific calculations of probability (concerning molecules, or animal populations, or the quantifiable aspects of human populations), but the deliberation itself is not formalized. Leibniz writes optimistically that we rise above the beasts when we leave aside “mere empirics” and are able to see the connections between truths – connections which themselves constitute necessary and universal truths. These connections may be necessary even when all they lead to is an opinion: this happens when after precise inquiries one can demonstrate on which side the greatest probability lies, in so far as that can be judged from the given facts; these being cases where there is a demonstration not of the truth of the matter but of which side prudence would have one take (R&B 476).

But in an era where the art of probability has turned into a powerful and widespread technique of analysis, that is, our own, no one has ever suggested that it can replace judicial or parliamentary deliberation. At this point, we might leave the Essay and the New Essay behind, and look instead to the written evidences of Realpolitik that Locke and Leibniz left behind them. Locke, as we all know, wrote his Two Treatises of Government anonymously. I believe he had a sense of the potency of his book, and would not have been surprised to learn that it inspired, as a necessary though not sufficient condition, two revolutions and ultimately the demise of European monarchy. Leibniz’s appeal to Europeans to pay attention to China and his bitter denunciation of Louis XIV, his various attempts to reconcile Protestants and Catholics, were less successful, perhaps because he never imagined an alternative to monarchy; but they exhibit a precise sense of power relations in the diplomatic world Leibniz inhabited, and conduct their political rhetoric at a high level. Both Locke and Leibniz reason upwards from facts and downwards from principles, as they search out and try to create shifts in the power structure that will lead to a better life for most people.

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Social conflict, organized in a parliamentary and legal system, is the engine of social reform, consolidation, and self-creation. It is a wonderful thing to watch in action, except when it devolves into the destruction of war and genocide; but these events take place precisely because the conflict has moved outside the theater of words, the dramatic platform of courtroom and congress. Both Locke and Leibniz knew the bitter cost of war and the value of diplomacy. But diplomatic debate, formal as it must be, cannot be reduced to the definition of terms and principles, deduction from principles, and the calculation of probabilities. Nor can it be resolved by the presentation of “facts”, however essential the collection of certain facts by public methods may be. Human conflicts, expressed in terms of conflicting narratives about human actions, are too ambiguous to be resolved this way, and resolutions are too embedded in existing power relations. Aristotle exhibits the ineluctable presence of narrative in deliberation about human affairs; Machiavelli exhibits the unavoidable presence of contests over power. In practical deliberation, we cannot avoid the question, what shall we do on the basis of what we have done? We must use the first person plural, and that means we shall never get to the end of reconciling stories about what, in fact, we have done and what it means. And yet we must come to some decision, because we must act.

4 Hume on Formal Experience In order to negotiate the dispute between Locke and Leibniz, I bring in David Hume’s account of experience as realized in the “formal experience” that lawyers and judges have of the law, and mathematicians have of mathematics. A successful legal system requires not only tough-minded empiricism in its management of evidence, and rigorous formalism in its appeal to principles and rules of inference for the sake of impartiality, but the specialized expertise of legal practitioners. Successful mathematics also requires not only the articulation of rules, principles and structures in well-considered inferential order, and common knowledge of more concrete procedures, counting and measuring, found in schoolbooks, but also the ongoing experience of mathematicians who test and revise rules by applying them to particular objects and problems. Leibniz overstates the virtue of formality, or does so at least in the New Essays; a Humean account of experience, and formal experience in particular, as key to the stability and improvement of knowledge can moderate Leibniz’s formalism in a way that Leibniz himself might approve, and that indeed finds confirmation in other, later writings of Leibniz. The late twentieth century reception of Hume’s doctrine was strongly colored by an association with A. J. Ayer’s foundational phenomenalism, and unduly focused on his critique of causal knowledge as a skeptical argument. Recently, however, various philosophers have tried to locate a more supple and historically accurate account of empiricism; Bas van Fraassen offers such an account in his recent book The Empirical Stance (Van Fraassen 2000). For the purposes of this argument, however, I make use of Catherine Kemp’s account of Humean experience in relation to the philosophy of law. Here and in other essays, she offers a reading of Hume

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detached from the invocation of sense data as the starting point of all knowledge (which doesn’t get one very far in either legal or mathematical epistemology) and the overstatement of his skepticism (Kemp 2002). Kemp writes that for Hume, knowledge is “an artifact of human belief. He makes belief a product of human experience, rather than a representation of the world”. This means that belief emerges out of what is reliable in our experience and persists as long as it remains reliable. Its effect on us is to limit the set of things that affect us greatly: the mind runs in the channels established by the custom emerging out of our experience.

Moreover, “the conditions that give rise to custom [. . .] are also conditions under which custom or belief is subsequently altered in our experience” (Kemp 2002: 137). For Hume, the emergence of custom out of our experience, construed as a series or succession of perceptions – and for Hume perception has a much broader connotation than sense perception – not only explains the stability and validity of our knowledge, but also the possibility we always have to revise and correct our knowledge. All knowledge, based on no more but also no less than custom, leaves open the imagining of alternatives to received truth. This possibility is the cardinal virtue of human knowing for Locke, Leibniz, and Hume, as I pointed out at the beginning of this paper. Kemp argues in particular that given Hume’s broad construal of “series or succession of perceptions”, the experience that lawyers and judges gain in the courtroom, and in the discursive review of cases and earlier judgments, is a good illustration of how custom establishes stable but revisable knowledge. She proposes that we consider the formal or conceptual aspect of law and in particular of the common law, [. . .] as that artifactual matter first produced by law’s experience, which in turn facilitates subsequent experience and the development of even more artifactual material, in the form of custom. In this picture the notion of the formal or conceptual makes sense only as part of law’s simultaneous resistance and susceptibility to change, an integrated quality I will call here law’s inertia.

This inertia, she observes, raises very interesting questions: “What are its conditions? How are stasis and change possible simultaneously in this context? Why is law both susceptible and resistant to argument?” (Kemp 2002: 136–137). Following an analogy established by both Locke and Leibniz between the law and mathematics, we may also think of mathematics as an artifact of human belief. Then, instead of talking about mathematical truth, we should talk about mathematical belief as a product of a “formal experience”, which emerges out of what is reliable in the experience of mathematicians, and persists as long as it remains reliable. Since we have set aside Ayers’ foundational phenomenalism, this empiricist strategy will not mire us in the incompatibility between mathematics and the physical causation central to naturalized epistemology. We can simply note that the effect of mathematical experience (a succession of procedures, problems, methods, canonical items and systems) is to establish customs that organize and limit the work of mathematicians. The customs that stabilize mathematical practice, recorded

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in textbooks and scholarly journals, are also the conditions under which custom or belief is subsequently altered in mathematical experience.3 Having made his famous distinction between ideas and impressions, Hume observes that some ideas (which are in themselves mere conceptions) can be transformed into lively ideas, as lively and efficacious as impressions, able to move us to action: these lively ideas he calls beliefs (Hume 1978: 1–10). Hume must then answer two questions: How it is that initially faint ideas can become lively? And, why it is that some ideas and not others are enlivened in this way? Kemp notes that his answer to both questions is experience and custom, for regularities establish relations among certain ideas and not among others. Hume calls these regularities the “constant and regular conjunction” of objects in our experience. This means that the mind can think of alternatives to what is established by custom; when an idea starts out as “mere conception”, it may or may not be the condition for the possibility of a shift in the reliability and therefore in the degree of liveliness attaching to a particular conception. Subsequent ‘experiments’ in the succession or series of impressions in our experience can begin to pile up instances on the side of a hitherto merely conceived alternative to a customary relation [. . .] As a lively conception, belief for Hume is simultaneously settled and unsettled in relation to the experience in which it emerges and to which it remains continuously subject (Kemp 2002: 138–140).

The two questions, how initially faint ideas become lively, and, why some ideas and not others are enlivened in this way at a certain point in history, are rewarding questions to ask in reference to mathematics. It often happens that in one era certain objects are described as oddities, and then set aside: they only really become part of mathematics when they enter into problems and families of problems where they stand in well understood relation with other, similar objects, and are handled by well understood procedures. Thus, the Greeks knew about the transcendental number pi, and two or three transcendental curves, but for them these entities were mathematically inert, “very faint”, as Hume would say. Only in the seventeenth century did they become enlivened – why did this enlivening take place then? Otherwise put, why do instances begin to pile up on the side of a hitherto merely conceived alternative to a customary relation? These are philosophical questions that cannot be answered without historical study, that is, without paying attention to the pragmatic dimensions of mathematical rationality. On a related issue, Hume may be corrected by Leibniz. At his most skeptical, Hume presupposes that regularities establishing relations among certain ideas are externally imposed, so that the ideas play the role of mere placeholders. By contrast, Leibniz claims that relations express internal features of things that are intelligible unities: knowledge of relations arises from the analysis of things we are aware of. The relations a thing can enter into as well as its internal features are controlled and constrained by the intelligible, unified existence of the thing. Thus for Leibniz, what we can think of as possible for a thing is constrained by the nature of the thing; this means that imagination for Leibniz is more constrained than it is for Hume, who seems to assert that we can imagine anything in any relation to anything. Leibniz would say that we might believe we are thinking something when we imagine aRb for arbitrary a and b and arbitrary R, but we are deceived, and further analysis would

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reveal the hidden contradiction. Moreover, there is no such totality as “the set of all relations of a thing” or “the set of all internal features of a thing”, so that the work of analysis is never finished. In the end I would say, with Leibniz, that Hume’s two good questions about how and why faint ideas become lively can’t be answered without referring to the content of things, to the constraints that their “internal constitution” and characteristic unity impose upon the relations into which they can enter. In the case of the law and mathematics, the things in question are strikingly formal, so that what must be addressed is the content of form as well as the form of content (Grosholz and Yakira 1998: Chapter 1). Kemp also urges that we should distinguish between the experience of ordinary citizens encountering social conflicts to be resolved and injustices to be regulated, and the experience of lawyers and judges as they work through the law as it is formulated, applied, and reformulated. But the distinction is not a disjunction: ordinary citizens know something about the law (they usually try to avoid doing things that are illegal) and understand social reality in terms of it: there is no such thing as “lawfree” experience of conflict or injustice, even though from culture to culture what causes conflict and what amounts to injustice may vary. And lawyers and judges, as they do their work, keep in mind their local experience as citizens; there is no such thing as a “pure legal mind”. Nonetheless, the experience stored in law books and legislation is activated and made effective only when human beings take it up, and effective activation requires a recognized distinction between citizens and lawyers / judges. Likewise, we can distinguish between two kinds of mathematical experience: the experience of ordinary citizens, who intermittently use mathematics to count and measure, resolve problems or explain events; and the experience of mathematicians as they make their way through a discipline where problems are formulated and solved, objects are encountered and constructed, and then investigated or set aside or transformed, and networks are formulated, extended, connected, and revised. The record of this formal experience is archived in Collected Works, journals, and textbooks. As in the case of law, the distinction is not a disjunction: ordinary citizens know something about mathematics, and understand aspects of physical reality in terms of it: there is no such thing as “mathematics-free” experience. Human beings always reckon and recognize shapes, et cetera, though from culture to culture the formulations of these activities vary. And mathematicians, as they do their work, keep in mind their local experience as citizens and agents at a certain point in history; there is no such thing as a “pure mathematician”. As with the law, mathematical experience won by wrestling with unsolved problems or stored in textbooks and journals is activated and made effective only when human beings take it up, and effective activation requires a recognized distinction between citizens and mathematicians. The great United States Supreme Court justice Oliver Wendell Holmes wrote “[t]he life of the law has not been logic: it has been experience”, characterizing what is formal in the law as the artifact of law’s experience, rather than as timeless truth (Holmes 1991: 1).4 If we acknowledge, as in the case of the lawyer and mathematician, that some kinds of experience are inherently formal, we can answer Locke’s

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objection to the arbitrariness and impertinence of form which Leibniz strives to counter in the New Essays, and Leibniz’s objection to the subjectivity of perceptual experience. The same train of thought leads to the acknowledgment that the formal experience central to the law and mathematics is also inherently social. Here is Holmes’ account of how rules emerge, develop, settle and evolve again from a series of cases: It is only after a series of determinations on the same subject matter, that it becomes necessary to ‘reconcile the cases,’ as it is called, that is, by a true induction to state the principle which has until then been obscurely felt. And this statement is often modified more than once by new decisions before the abstracted general rule takes its final shape. A well settled legal doctrine embodies the work of many minds, and has been tested in form as well as substance by trained critics whose practical interest it is to resist it at every step (Kellogg 1984: 119).

On this point, I believe that Leibniz and Hume would be in accord. Acknowledgments I would like to thank the National Endowment for the Humanities and the Pennsylvania State University for supporting my sabbatical year research in Paris during 2004– 2005, and the research group REHSEIS (Equipe Recherches Epist´emologiques et Historiques sur les Sciences Exactes et les Institutions Scientifiques), University of Paris 7 et Centre National de la Recherche Scientifique, and its Director Karine Chemla, who welcomed me as a visiting scholar.

Notes 1. A similar argument is made with respect to functions in Hintikka (2000). 2. For important discussions of processes of generalization in mathematics see Chemla (1998, 2003) and Robadey (2004). 3. See especially Lecture 4 in Van Fraassen (2000). 4. An excellent discussion of the formal experience of the law can be found in Levi (1978); and an illuminating discussion of practical deliberation is given in Garver (2004).

References Chemla, K. 1998. Lazare Carnot et la g´en´eralit´e en g´eom´etrie. Variations sur le th´eor`eme dit de Menelaus. Revue d’histoire des math´ematiques 10: 257–318. Chemla, K. 2003. Generality above abstraction. The general expressed in terms of the paradigmatic in mathematics in ancient China. Science in Context 16: 413–458. Garver, E. 2004. For the Sake of Argument: Practical Reasoning, Character, and the Ethics of Belief. Chicago: The University of Chicago Press. Grosholz, E.R. 1991. Cartesian Method and the Problem of Reduction. Oxford: Oxford University Press. Grosholz, E.R. 2005. Constructive ambiguity in mathematical reasoning. In C. Cellucci and D. Gillies (eds.), Mathematical Reasoning and Heuristics. London: King’s College Publications, pp. 1–23. Grosholz, E.R. 2007. Representation and Productive Ambiguity in Mathematics and the Sciences. Oxford: Oxford University Press.

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Grosholz, E.R. and Yakira, E. 1998. Leibniz’s Science of the Rational (Studia Leibnitiana Sonderheft 26). Stuttgart: Steiner Verlag. Hintikka, J. 2000. Knowledge of functions in the growth of mathematical knowledge. In E.R. Grosholz and H. Breger (eds.), The Growth of Mathematical Knowledge. Dordrecht: Kluwer, pp. 1–15. Holmes, O.W. 1984. Codes and the arrangement of the law. In F.R. Kellogg (ed.), The Formative Essays of Justice Holmes: The Making of an American Legal Philosophy. Westport, CT: Greenwood Press, pp. 77–89. Holmes, O.W. 1991. The Common Law. New York: Dover. Hume, D. 1978. A Treatise of Human Nature. Oxford: Oxford University Press. Kemp, C. 2002. Law’s inertia: custom in logic and experience. In A. Sarat and P. Ewick (eds.), Studies in Law, Politics and Society. Amsterdam: Elsevier Science, pp. 135–149. Levi, E. 1978. An Introduction to Legal Reasoning. Chicago: The University of Chicago Press. Locke, J. 1959. An Essay Concerning Human Understanding. New York: Dover. Poincar´e, H. 1970. La valeur de la science. Paris: Flammarion. Robadey, A. 2004. Exploration d’un mode d’´ecriture de la g´en´eralit´e: l’article de Poincar´e sur les lignes g´eod´esiques des surfaces convexes (1905). Revue d’histoire des math´ematiques 10: 257–318. Van Fraassen, B.C. 2000. The Empirical Stance. New Haven, CT: Yale University Press.

Chapter 11

Leibniz’s Conception of Natural Explanation Marta de Mendonc¸a

1 Introduction In his preface to the New Essays, Leibniz refers to the “distinction between what is natural and explicable and what is inexplicable and miraculous”, considering this distinction to be a necessary requisite of the exercise of philosophy and reason: To reject it would be equivalent to opening “the refuges of ignorance and laziness” to the incomprehensible qualities for created spirits, no matter how great they be (GP 5 59). In this way, the concept of the natural is presented as one of the fields – probably the largest – of the exercising of human reason and, in general, as the specific field of created intelligibility.1 We can say that anything that does not respond to the criteria of the concept of the natural is, therefore, unintelligible or inexplicable and miraculous.2 On the other hand, if we bear in mind the Leibnizian distinction so many times reiterated in Theodicy,3 between what is above reason and what is against reason (and is thus impossible), the opposition between natural and miraculous characterizes the concept of natural as the precise domain of reason: All that is natural is rational, and what is not natural is not rational, for it would be, should it be possible, supra rational or miraculous. This coextension of the concepts of natural and explicable transforms the Leibnizian approach to the concept of natural into a privileged access to the way in which he understands human rationality and the intelligibility of nature. But the introduction of the miraculous (or of its possibility) forces Leibniz to define more precisely the concepts of nature and natural: What kind of natural explanation can contemplate its exception, the unnatural, while still explaining it? The specific rationality of nature and natural places it, however, in such a domain that permits explaining what happens (and there is, therefore, a certain possibility of prevision) and, at the same time, leaves room for the exceptional which, if it occurs, cannot be explained by reasons of the same order. In this way, Leibniz discusses the difficulty of explaining what does not always happen but frequently happens, a

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problem that, in modal terms, could be expressed in the folowing way: What kind of necessity is there in contingency? How can one assert any form of necessity (without which there is no explanation), without eliminating contingency (without which there is no natural world for Leibniz)?

2 Definition of Natural 2.1 Ambiguity of the Term Leibniz uses the concepts of “natural” and “nature” with variable accuracy. Examples of this freedom of use are expressions such as “natural miracles” (GP 2 93) or “mysteries of nature” (GP 4 363). Considering the text of the New Essays, referred to above, the first expression should be considered internally contradictory; the same could be said about the expression “mysteries of nature”, given the supra-rationality of mystery, which Leibniz presents in the Theodicy (GP 6 73–74). In this context, however, the terms improperly used are “miracle” and “mystery”, the former, to signify the wonders of nature, the latter to refer to its secrets. In other contexts, it is the very concept of the “natural” that is subject to a certain ambiguity; Leibniz refers to this ambiguity explicitly in the Addition a` l’explication du systeme nouveau when he warns: what can be called natural in a common sense of the word must not be confused with what should be called natural in a more metaphysical sense. For example, in a common sense of the word, it is natural that we die, but it is not natural that we die of a cannon shot; that is called accidental and violent, and reasonably so; [. . .] So, when I say that everything that happens to a substance can be considered, in a certain sense, natural to it, or a consequence of its individual nature, I understand complete nature [. . .] I understand it in a certain transcendent sense, according to which each individual’s complete nature involves everything that happens to him and all the other individuals (GP 4 582).

“Nature” is another possibly ambiguous noun; it can be used to refer to a certain body’s particular nature or to the universal and supreme cause, that which pursues and always reaches its end. So, when we say, for example, that nature does nothing in vain, that nature abhors emptiness, that nature does not err, that it tends towards perfection, and other things of the kind, we should be aware that statements like that apply to “nature” in the latter, but not in the former, sense (C 7).

2.2 Characterization of Natural The concept of the natural acquires more precise outlines when Leibniz proceeds to its definition and characterization. He does this by distinguishing what is natural from what isn’t, such as what is artificial, what is preternatural or supernatural, what is essential or necessary, what is accidental, arbitrary, violent, etc. In such a context, what is natural is often part of a system of other concepts; it is distinguished from them and forms with them a complete disjunction.

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In a text written in the beginning of the seventies, Leibniz presents us with a definition of the natural, distinguishing natural, preternatural, supernatural and artificial and, in a similar way, distinguishes nature, miracle and art. In this text, natural is “what follows from movement and respite, for nature is a source of movement and respite. Or what is in accordance with experience or reason”, for “as much as habit is a second nature, so also nature is a first habit”. In this way, nature can be seen as “consuetudo mundi”. Praeternatural, on the other hand, is defined as “what happens besides the world’s habit”, or “what is unheard of, that which reason does not show, either in bodies, or in us”. Supernatural is also unheard of, but is essentially different from preternatural, because it not only happens besides nature’s habits, but is beyond nature’s capacity; that’s why its reason for being is not found in any creature. Finally, “artificial is that whose reason is not found in the bodies, but in us” (A VI 2 494). The more pronounced distinction is that between natural and supernatural; there is a true opposition between them, such that the supernatural act, the miracle, is defined as “actus non naturalis”. The classification hereby presented is based on a genetic criterion; something is called either natural or non-natural in virtue of its origin. Furthermore, what is natural is also common, and what is not natural happens “praeter consuetudinem mundi”; but this is a consequence of their different sources, which is the touchstone that allows us to recognize them, and not the definitional characteristic of the aforementioned concepts. According to this genetic criterion, the only radical opposition is the opposition between what is natural and what is supernatural, because what is preternatural and what is artificial can be seen as kinds of what is natural, being as they are ascribable to nature’s potency, in this case to man’s or to some other non corporeal creature’s potency. From another point of view, taking a normative criterion into account, what is natural is not, and cannot be mixed up with what is artificial, as they are distinguished by a difference not of degree, but of genus (GP 4 482). According to Leibniz, there is an enormous distance between the smallest production and mechanism of divine wisdom and the greater masterpieces of the limited spirit – the distance between infinite and finite. “Natural machines” have an infinite number of organs; by creating them, God reiterates infinitely the mechanism which they are. But man acts in nature over a previously given matter, and the contrivance he makes is dependent on man only in its exterior disposition. The mechanical character of each piece escapes his control and his transforming power. God creates; man transforms. Furthermore, the natural machine is different from the artificial machine because it is indestructible and accident-proof, neither of which is applicable to man-made machines. The reason for this difference is also the totality of divine causality, and the restricted nature of human causality, which prevents man from taking everything into account (GP 4 536). What is natural is therefore opposed to what is supernatural and to what is miraculous. This is the opposition more frequently referred to by Leibniz: Supernatural is what cannot be attributed to nature’s forces and miraculous is what cannot be explained through them. They are thus intimately related concepts; what is

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supernatural is, by definition, miraculous, both being different from the natural level, and above it. The explanation for the miraculous is not found in creatures, but the condition for its possibility lies in the contingency of the natural order; what is natural is such that it leaves a space open to the non natural; what is miraculous is, then, an event that must be integrated in the created order, but that cannot be explained through the laws of nature. The distinction between natural and miraculous forces us to distinguish between ordering levels: what is miraculous belongs to the general order of the universe, contributing to its realization, but does not belong to the natural order. It is a real order, but is not accessible to man. Admitting the existence of miracles is the equivalent of admitting the existence of several possible levels of considering the intelligibility of creation. These levels do not contradict, but complement each other: They are autonomous, non global domains of explanation of the cosmos. That is exactly why Leibniz refers to the laws of nature as “subordinate precepts” (Discours de m´etaphysique, paragraph 7). What is miraculous lies beside the natural order, but is not defined by its opposition to order. This is the reason for saying that God might, on certain occasions, act through continuous miracle: As an explanation of nature, occasionalism would be the unnecessary introduction of a miraculous order. That is also why what is specific of the miracle is not the fact that it is exceptional, against the predictable regularity of natural phenomena; in that case, monsters would be miraculous (GP 7 377). Arguing against Clarke, who thought that the concept of a miracle made no sense to God and that such a concept is a specifically human hermeneutical principle, pointing to what is extraordinary and seen as infrequent or exceptional, Leibniz thinks that miracles are a way of acting intrinsically, and not accidentally, different from the natural action (GP 7 413). The external accident, the exceptionality, is an expression of an internal reason. The distinction between natural and miraculous is correlative to the distinction between the “realm of nature” and the “realm of grace”. Leibniz makes this distinction by asserting that what comes originally from God does not have to come immediately from him (GP 4 573). It is not necessary for God to act immediately, supernaturally or miraculously, he says (GP 4 574). What is miraculous, what the realm of grace introduces, is what exists in the order of created becoming and cannot but be attributed to a direct action of God. God can act in such a way because the realm of nature allows it. It is possible to break the laws of nature and interfere with its predictable course. Therefore, “strictly speaking, God does not need the body to give the soul the feelings it has, but He needs the body to act in the order of nature He established” (GP 4 574). Such an opposition leads to the distinction between the mediate and immediate modes of divine acting, the former being mechanical and natural, the latter supernatural; we have here a specification of the genetic criterion of naturalness, distinguishing the natural and supernatural ways of producing something. Leibniz explains on various occasions the distinction between natural and arbitrary. Applied to natural becoming, to modifications, the opposition between natural and arbitrary presents as natural those modifications understandable through

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the subject’s own nature, as actualizations of its potency. The laws of nature are thus natural and not “as arbitrary as they may seem” (GP 4 520), precisely because of their inscription in the subject’s own nature, by their being traceable to dynamic principles inserted in the changeable nature. Natural laws do not hover above phenomena and natures, describing the regularities of their becoming; they are inscribed in nature, as dynamic structures, producing what they regulate. These laws leave a subsistent effect in things, an effect that persists and operates presently, and this is how we can understand the link between nature and action; only then can we aspire to a different explanation of phenomena, Leibniz argues, “because everything is equally derivable from everything, when what is absent, either from the temporal or spatial point of view, can without an intervening medium operate here and now” (GP 4 507). That is why an explanation of nature such as occasionalism, which denies causal efficacy to created substances, is arbitrary, that is, non natural. Modification can most properly be called natural; the natural is foremost a certain – non arbitrary – way of a thing coming to be, so that a property is natural if it is possible to explain how, in what way, it was produced by nature. We now come to the more common characterization of the natural in Leibniz’s texts: What is natural is that which is produced in nature according to mechanical principles. When he says this, Leibniz is thinking of material nature (there is also what is natural to the soul and explained by its own principles – namely, the principle of perfection): thus, we can think that matter [. . .] will not proceed by itself in a curve, because we cannot conceive how that would be done, that is, we cannot explain it mechanically, but what is natural should become distinctly conceivable were we admitted to the secrets of nature (GP 5 59).

“Natural”, “explainable” and “mechanical” are coextensive concepts in the material world, inasmuch as the expressions “laws of nature”, “mechanical laws” and “laws of movement” are coextensive. In the material world, to explain is to expose the possible generation of what one wants to explain; to understand is to infer from requirements, according to the mechanical laws; that is why the demonstration of the possibility of a concept or a phenomenon is the same as the description of the way it is produced, and the real or causal definition is the definition describing the way the definiendum is produced. In the material world, such an explanation is found by describing the structure, viz. the spatial disposition of the parts subject to movement, and by specifying the laws of movement that this structure is subject to. From the point of view of the inclination or the faculty, what is natural is opposed to what is violent, its proper character is spontaneity, and violent is what is opposed to an inclination, counteracting its spontaneous way of realization. Violent is then, by definition, something external to the inclination, counteracting its actualization: It presents itself as an obstacle. Leibniz refers to this opposition at various times (for example, when he opposes natural to violent death or natural to violent movements), but it functions only when what is natural is taken in its common, not metaphysical sense because, strictly speaking, nothing can be called violent. In that sense, the

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natural level, being all-embracing, is not specified by this opposition, and so the opposition can be considered trivial. Taken dynamically, what is natural appeals to the concept of “disposition” or “ability”; from this angle, the concepts of “natural” and “easy” come close to each other; natural is the spontaneous exercising of the faculty, which is always easier to that faculty, because it is in accordance with its nature. That is also why acting naturally always presupposes something more than the mere faculties, which, as such, are indifferent in their determination, and more than the mere passive potencies to which, as is very well known, Leibniz is always opposed. The faculty is ability, disposition, active potency of determination, power. From it derives, as an explanation of the processes of nature, the concept of “inclining reason”, or non-necessitating reason. A disposition is not a univocal principle of operations, but a determined principle of operations. Proper of the natural is thus to bend without necessitating; in this sense, what is natural is always what is easier, what follows from the disposition when no obstacle counteracts it; being non-necessitating, it may not happen; on the other hand, being easier, it is predictable and likely to happen. A positive delimitation of the concept of natural leads us to connect it intimately with the notion of order. What is natural is ordered and can be combined in an order because it acquires its naturalness through the existence of a law of transformation that makes explicit its mode of becoming: “whenever we find some quality in a subject, we ought to believe that if we understood the nature of both the subject and the quality we would conceive how that quality could arise from it” (GP 5 59). Such a demand of “conceivability” – which is definitional of what is natural – inevitably includes it in an order. The natural order is precisely the realm of intelligibility where what is natural is understood as such. Or, as Leibniz says on the same page: within the order of nature (miracles apart) it is not up to God’s arbitrary discretion to attach this or that quality haphazardly to substances. He will never give them any which are not natural to them, that is, which cannot arise from their nature as explicable modifications (GP 5 59).

3 Natural Explanation: Influence, Occasionalism and Harmony The question of the natural is, on the one hand, raised by Leibniz from the perspective of the multiplicity of principles that determine the existence of a natural order. On the other hand, the question of the natural leads him to consider the internal intelligibility of nature. In fact, by admitting a plurality of levels of order in creation, one can raise the question of the specificity of the natural order. Leibniz frequently states that, considered in the absolute sense, substances could have qualities different from the ones they have, but these qualities could not be different and simultaneously natural. What, then, makes certain principles, when articulated, constitute the order of nature? What gives the natural character to natural order? This question leads to the Leibnizian concept of natural explanation, and the answer lies precisely in the

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equivalence which he establishes between “natural” and “explicable”. The scope of the natural is characterized by what can be conceived – ideally but not actually – by any created being, because “although what creatures conceive is not the measure of God’s powers, their “conceivability” or power of conceiving is the measure of nature’s power: Everything which is in accord with the natural order can be conceived or understood by some creature” (GP 5 58). Therefore, the natural order, which is accessible to a created spirit that conceives it, does not include, in principle or by definition, anything inexplicable. One, thus, can consider unnatural, and therefore false, all explanations of the natural order that only mention or determine that something takes place without indicating how this happens. Therefore, natural explanation, for Leibniz, reveals the very concept of natural, and nature as the specific exercising of human intelligibility. On many occasions, Leibniz considers what must be understood by “natural explanation”, such as, for example: – by criticizing, as being unnatural, the explanation of nature proposed by occasionalism; – by criticizing the scholastic theory of interaction among substances or by considering to be illusory the explanation of the natural world which is based on faculties or forms; – by presenting his system of harmony as the only natural and intelligible explanation. There is not a single concept of natural explanation subjacent to all these criticisms and Leibniz works with this idea by attributing it either to some of the following aspects or to all of them:4 – to the relationship of created substances with each other, not only concerning their ontological aspect but also, and mainly, their dynamic aspect; – to the relationship of phenomena with each other; – to the relationship between substances and phenomena.

3.1 The Systematic Character of the Leibnizian Approach Before analysing the reasons upon which Leibniz’s argumentation is founded, in order to substantiate the positive character and superiority of his explanation, it is worth underlining that the Leibnizian approach is a systematic one. Even if his hypothesis were not based on positive grounds, it would be asserted a priori by the demonstration of the unnatural character of the hypotheses of influence and occasionalism; for this very reason, since it is the only natural explanation possible, it is more than a hypothesis. In fact, Leibniz considers that there are only three possible explanations of the natural order:

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– the theory of the reciprocal influence among natural beings; – the theory of occasionalism; – his theory of agreement, concomitancy, or pre-established harmony. Considering that nature is an ordered and dynamic plurality, a cosmos, Leibniz establishes the exhaustivity of these three possibilities from two different points of view. (1) In searching for an explanation of nature, one can look for the causal agent of the regular dynamism of nature, trying to find the reasons for its regular changes.5 Here there are the following theoretical possibilities:6 (a) Substances are incapable of action; activity is a prerrogative of divinity; and therefore the real changes that we perceive in nature have God as their immediate agent, and thus there does not exist a natural order of secondary causes, except illusorily. (b) Created substances are active and God does not act on them in an immediate way through the natural created order, but in a mediate way through nature itself, which was given that possibility by God. In this case, natural order, which is typical of secondary causes, can be theoretically conceived as autonomous from the first cause. It is through its consideration that the questioning of natural explanation takes place. Admitting the active characteristic of created substances, the generic possibility of action is subdivided according to its scope in created substances: – through its activity, a substance transmits to another something real, which provokes a change in it and in this way is the efficient cause of the effects observed in it; a created substance is capable of transitive activity, and the accordance and the regularity observed in nature result from the physical interaction of all substances; – a created substance, being active, is only capable of immanent activity; substances are active, but they don’t interact; in this case, the regularity and the accordance of nature do not result from a transitive action, but from an architectonic presupposition which is proved a posteriori in the natural world itself. Leibniz proposes this classification of the possible explanations of natural order in the Addition to the Explanation of the New System, where he analyses the question of the accord between the processes of the body and the feelings of the soul. In every explanation of created order, it is always God – as the first cause – who gives the soul its feelings. He does thus immediately in the system of occasional causes; He does it mediately by the nature which he has established in the two other systems; for in the system of influence, which is the ordinary one, it is by the nature of the bodies that anything is communicated to the soul, and has any influence; in my system it is by the constitution of the soul, insofar as it is the expression of the body (GP 4 579).

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The exhaustive character of the three hypotheses is due to the fact that this classification is based on a double dichotomy: First, either the substances are active, or they are not. Admitting the first possibility, the action of the substance can be only immanent or immanent and transitive. In the first case, we have the theory of pre-established harmony; in the second, the theory of the influence. If the activity of the substance is denied, we have occasionalism. In this classification of possible explanations of the natural world, the Leibnizian explanation is close to the hypothesis of influence, both of which oppose the theory of occasionalism by accepting the active character of created substances. (2) Another way of approaching the exhaustive character of the three aforementioned explanations can be found when we question the natural reason of the dynamic order that is observed in nature. This is what Leibniz does in a later text, a letter to Lady Masham (30th June 1704): supposing that ordinary things must occur naturally and not miraculously, it seems that we can say that, according to this, my hypothesis is demonstrated. For the other two hypotheses refer necessarily to miracles [. . .] And we can only find these three hypotheses. Thus either the laws of bodies and souls are disrupted, or else they are conserved. If the laws are disrupted (which must come from something on the outside), it must be either that one of the two things disrupts the other, which is the hypothesis of influence that is common in the Schools, or that it is a third party that disrupts them, which is to say God, an this is the hypothesis of Occasionalism. But finally, if the laws of souls and of bodies are conserved without disruption, this is the Hypothesis of pre-established harmony, which is consequently the only natural one (GP 3 355).

The operating criterion in this classification of the possible explanations of the natural order is diverse. In this case, the Leibnizian theory of pre-established harmony is confronted with the other two explanations, as it is the only one based on the preservation of natural laws, not admitting that in the natural order the laws of souls and bodies may be disturbed from the exterior. The exhaustive character of these three explanations also arises from two dichotomies: Either there exists disturbance in the laws of nature or there is no such disturbance in the natural order. If the possibility of such disturbance is admitted, since it must come necessarily from the exterior, it can only be due either to the other beings of nature or to God, the author of nature.7

3.2 The Unnatural Character of the Hypothesis of Influence Of the two unnatural explanations, the hypothesis of influence is undoubtedly the one which Leibniz holds in less esteem, and he loses no opportunity to criticise it. He seems to deem it unnecessary to develop the arguments demonstrating its impossibility, limiting himself on many occasions to simply stating that such influence cannot take place. In this respect, Leibniz seems to rely on the agreement and understanding of his interlocutors, even of those who oppose his explanation. In Leibniz’s opinion, the hypothesis of influence is a metaphysical impossibility, and

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he therefore sees no need to analyse on a physical basis the viability of an hypothesis already declared impossible. On this matter Leibniz agrees with Malebranche. There are many reasons why the hypothesis of influence is unacceptable; Leibniz could have said of this theory what he said of atomism: “All my system is opposed to it”. The reasons why the hypothesis is unacceptable are supported by a large part of Leibnizian metaphysics and specifically by his concept of substance (GP 2 46–47). We shall limit ourselves to referring briefly to Lebniz’s argumentation concerning natural explanation. From this perspective, the most recurrent criticisms of the hypothesis of influence are the following: (1) This is a hypothesis that violates the principle of sufficient reason. In fact, the theory of the influence is unable to account for what occurs in the body and to trace it back to the intelligible qualities of bodies (magnitude, figure and movement), and it is equally unable to account for what happens in the soul and to trace it back to the intelligible qualities of souls (perceptions and appetites) and therefore it can be said that it does not respect the principle of reason. In this respect, to accept the hypothesis of influence would be to give up on finding a natural sufficient reason for what happens both in bodies and in souls. Besides, “there is no sufficient reason to act when there is no sufficient reason to act this way” (GP 7 392–393); in other words, by failing to explain natural processes by the intelligible qualities of nature, the explanation of influence also fails to respect this exigency of the principle of sufficient reason. (2) The hypothesis of influence is a miraculous explanation and is thus unnatural. In reality, if a distant action can be considered to be miraculous, the same occurs in the case of the system of union between body and soul, for it is no more explicable to say that a body operated at a distance without means and instruments, than it is to say that substances as entirely different as body from soul operate immediately, one upon one another. That which separates their nature is much greater than that which unites them, and thus the communication between these two heterogeneous substances can only occur by miracle (GP 3 354).

(3) The hypothesis of influence is, ultimately, a pseudo-explanation, in the sense that it appeals to hidden qualities or faculties, which are nothing more than names given to what is inexplicable to us, ways of “hiding the miracle behind meaningless words” (ibid.). Leibniz defines this criticism in an indirect way, by stating that the principle of sufficient reason “puts an end to all hidden inexplicable qualities and other similar fictions” (C 11).8 Those who defend the theory of influence, appealing to these types of qualities and faculties in their explanation, are therefore obliged to admit that they do not have any explanation for natural phenomena (C 12). (4) Furthermore, the hypothesis of influence is an abusive explanation, in the sense that it includes in the explanation of natural phenomena elements which, though they might be explanatory, do not belong to, nor can operate in that order. It is abusive as it leads to the denial of the autonomy of physics,9 since the defenders of the hypothesis include substantial forms – which belong to metaphysics – in their explanation of natural phenomena. Appealing to these forms, when what is being debated is substance’s means of action and its way of operating, is a methodological

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error because it is the same as answering the question “how” by indicating “why” or proving “what” (GP 4 391). Thus, the autonomy of physics, correctly interpreted, leads us to simultaneously affirm the necessity of substantial forms and to refuse to use them in the explanation of the particular processes of nature, where they introduce no changes (GP 4 345). Physics should encounter in the properties of matter all the elements needed to explain natural phenomena; and it is physics itself, not the processes explained, that still needs a further justification. Thus, the nature of scholastic error lies in its abusive character; it does not consist in its dealing with substantial forms, but in transferring its explicative capacity from metaphysics to physics, where, due to its nature, such forms have no explicative capacity whatsoever. Metaphysics does not explain physics; it founds it, which is a completely different matter.

3.3 The Unnatural Character of Occasionalism Whereas the hypothesis of reciprocal influence is summarily put aside, criticism of occasionalism appears in many of Leibniz’s writings. Consensus on this subject is not general, and in some cases the impact of Leibnizian criticism was not even detected by his contemporaries who confounded occasionalism with the hypothesis of pre-established harmony. Jaquelot discussed this subject with Leibniz between 1703 and 1706, and the philosopher of Hanover answered him on two different moments: (1) There does not exist, in fact, an authentic discontinuity between occasionalism and pre-established harmony: The logical development of the first leads to the second; (2) But there is a real difference between the explanations of nature in occasionalism and in pre-established harmony. With regard to the first case, Leibniz affirms the possibility and even the necessity of passing from occasionalism to pre-established harmony “as long as one admits that God does not always act miraculously, as occasionalists thought, but in a way in accordance with the nature of things” (GP 3 462). Therefore, he accuses Malebranche of having gone only half of the way (GP 3 455) in detecting the impossibility of the real influence of a created substance over another, and in being unable to give a natural explanation for their union, thus making God simultaneously the interpreter and executor of the will of substances10 and making them instruments of God (C 7). Regarding the second case, in answer to an observation by Jaquelot in which he confesses to finding only a very slight difference between Leibniz’s view and occasionalism, Leibniz explains the difference between the two systems: The difference is that, for them, things are miraculous insofar as God always adapts the soul to the body and the body to the soul. Whereas with mine, all that happens ordinarily in the universe is natural and happens following the nature of things, in such a way that each of the substances accomodates itself to the other by its own nature (GP 3 467–468).

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But it is mainly from the point of view of its explicative capacity that the theory of occasionalism was criticised by Leibniz. In reality: (1) It is an explanation of nature in which everything is forced and refers ultimately to an arbitrary power of God, a power not founded on nature itself which is directly moved by God and forced to adapt itself to his plans.11 (2) Besides, to justify natural phenomena, both in occasionalism and in the hypothesis of influence, miracles are resorted to; and the difference there is only that a perpetual miracle is introduced by the authors of that view, not in stealth, as in the view of influence, but overtly, whether one agrees or not. Thus even though this action of God, of occasionally pushing the soul upon the body and the body at the soul will be continuous and common, it will not be any less miraculous, for it will always be something inexplicable to all created spirits (GP 3 354).

(3) It is furthermore an explanation that has too high a price (Spinozism12 ) and it is unnecessary to pay so high a price to explain natural phenomena (GP 4 476). (4) Occasionalism violates, as does the theory of influence, the principle of reason, because in the occasionalist explanations, substance does not justify what happens and the simple divine will, which in occasionalism justifies the dynamic processes of created nature, is not a sufficient reason (GP 3 532–533). (5) Occasionalism, besides being an unnatural explanation, appealing to a general cause in a particular matter, is also an explanation that destroys natural order itself, by denying all the efficiency of secondary causes: All is equally natural or supernatural when there is no intrinsic difference between them (GP 7 417).

3.4 The Natural Character of the Hypothesis of Pre-established Harmony Having rejected as unacceptable and miraculous the explanations of influence and occasionalism, Leibniz considers his hypothesis of harmony to be proved. Of course, there remain a large number of questions which have to be answered. But these are questions that confront any explanation, and that are certainly no more present in Leibniz’s hypothesis of harmony than in other explanations. In fact, the case is the contrary. Leibniz is also willing to accept that we cannot exactly understand the thesis of harmony (we will never understand how everything is brought into harmony in nature) and that physics itself will never become truly rigorous; but we can conceive that it is the only hypothesis that is adequate to the wisdom, goodness and power of God. Finally, Leibniz is even willing to admit that the hypothesis of harmony contains something miraculous (GP 3 143). But what is miraculous in this case is not the explanation of the processes of nature – this, to be sure, can only be natural; what is miraculous is the very instauration of the natural sphere, the original establishment of two dynamic domains completely autonomous but perfectly articulated:

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The domain of ends and of forces; the sphere of forms and of particles of matter; vitalism and mechanicism. This original agreement is the work of an immediate action of God, and could not avoid being so,13 but, once implemented, temporal changes in this double domain are – by the will of God – immediate works of nature and not immediate actions of divinity. The hypothesis of harmony appears as the only “intelligible and natural” one (GP 3 144). (1) In the first place, this means that it is the only true explanation (C 591) of natural processes, the only one that does not resort to anything external to nature in order to justify changes that occur within it. Thus, appealing to something external to nature to justify nature itself is not the same as giving a natural explanation; it is, rather, as has already been mentioned, the denial of natural order itself, maintaining the urge to explain it. (2) The hypothesis of harmony is also the only intelligible one because it is not limited to indicating that something happens, but also explains how it happens; it fulfils the demand of intelligibility, which consists in the presentation of the requisites. At this point, the operative power of the concept of force is revealed in all its importance. The presence of a certain activity in bodies forces one to deny the substantiality of movement and of the body and to consider that “movement is the phenomenon of change according to space and time; the body is the phenomenon that changes” (GP 3 623). It is force that permits the passage from metaphysics, the world of substances, to physics, the world of bodies, because, although it belongs to the domain of metaphysics, it expresses itself, nonetheless, at the imaginative or phenomenological level, as movement. In the opposite sense, the passage is equally legitimate: The metaphysical insufficiency of movement compels one to appeal to substantial forms. This intermediary character of force – its metaphysical root and its phenomenological expression – makes it the operative concept which is, at the same time, the necessary and sufficient condition of natural physical explanation. (3) Natural explanation also appears as the only non-violent explanation,14 the only one that fully respects the spontaneous nature of substance, which it in fact is. Natural processes react against violent processes, and natural explanation is precisely that which is not based on a state of violence. (4) Furthermore, natural explanation is not arbitrary. To explain in the natural sphere is to root in nature the very changing that springs from itself and to describe how nature produces it. The reason for natural changing cannot be found in a law imposed arbitrarily on things, as if they did not have their own nature with their own specific demands. This non-arbitrary character of natural explanation simultaneously demands and justifies a perfect articulation between the world of ends and the world of forces. Thus, natural explanation affirms the existence of final causes but does not use them in physics, for two different reasons:

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– in the first place, because the author of nature should not be called upon when what is being discussed is the particularity of phenomena; – and subsequently, because the secondary cause acts by its presence and not by its intelligence.

Notes 1. Cf. “[. . .] everything which is in accord with the natural order can be conceived or understood by some creature” (“tout ce qui est conforme a` l’ordre naturel, pouvant estre conc¸u ou entendu par quelque creature”; GP 5 58). 2. Cf., for example: “God is able to act beyond our understanding [. . .] but I would not want us to be forced to resort to miracles in the ordinary course of nature, and to admit utterly inexplicable powers or operations” (“Dieu peut faire au del`a de ce que nous pouvons entendre [. . .] mais je ne voudrois pas qu’on fut oblig´e de recourir au miracle dans le cours ordinaire de la nature et d’admettre des puissances ou operations absolument inexplicables”; GP 5 54). 3. Cf., for example, Th´eodic´ee, Discours Preliminaire, §§ 23 and 60; GP 6 64 and 83. 4. Part of the ambiguity found in Leibniz’s language is due to the oscillations of his ideas when he refers to bodies, considering them as substances, as well established phenomena or as compounds. 5. Accepting the fact that natural order was created, and admitting that the ultimate efficient cause of natural order is God, natural explanation does not look for a first cause of the metaphysical type – which guarantees by its conservative influence the very existence of nature – but queries the specificity of secondary causes and tries to explain the particularity of the natural passing from one state to another. 6. These possibilities are based on the very notion of created substance. Leibniz explicitly refers to this dependence when he asserts: “My Essays on Dynamics have to do with this – in them I felt the need to deepen the notion of corporeal substance, which in my judgement consists in the acting and resisting force rather than in extension” (“Mes Essays dynamiques ont de la liaison avec cecy, o`u il a fallu approfondir la notion de la substance corporelle, que je mets plutot dans la force d’agir et de resister que dans l’´etendue”; GP 4 499). 7. One can further consider a third perspective for approaching these three possibilities of explanation, which Leibniz mentions without elaborating, and in which the occasionalist theory and that of harmony coincide, denying the possibility of reciprocal action and together differentiating passivity from the theory of influence which admits this interaction. In this case, the subsequent distinction is based on the notion of substance and considers its naturally active character – in the hypothesis of harmony – or its passivity – in occasionalism. The same three possibilities of explanation, and their exhaustive character, are presented in the example of the two clocks, the perfect agreement of which Leibniz compares to the agreement between soul and body. Whereas in the previous statements, in a first dichotomy, two hypotheses were brought together distinguishing themselves from a third hypothesis, distinguishing themselves from each other afterwards, in the natural explanation of the agreement between the two clocks, all the alternatives oppose each other because the two criteria of classification previously considered are operative. In these examples each of the three hypotheses appears as the raison d’etre of a dynamic agreement. See GP 4 498–499, 500–501. 8. “Hoc principium omnes qualitates occultas inexplicabiles aliaque similia figmenta profligat. Quotiescunque enim autores introducunt qualitatem aliquam occultam primitivam, toties in hoc principium impingunt”. 9. And it also led to the discredit of substantial forms. 10. Cf., for example, R´eponse aux reflexions (GP 4 560). 11. See R´eponse aux objections contre le Systeme de l’harmonie pr´ee´ tablie . . .: “Nowhere does God’s wisdom manifest itself better than in the system of harmony, where everything is

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connected according to reasons which are rooted in the very nature of things, and nowhere is it less apparent than in the system of occasional causes, where everything is forcibly imposed by an arbitrary power” (“La sagesse de Dieu ne paroit jamais mieux que dans le systeme de l’harmonie, o`u tout est li´e par des raisons prises des natures des choses, et jamais moins que dans celuy des occasionnelles o`u tout est forc´e par un pouvoir arbitraire” (GP 4 594). 12. See Notata quaedam GGL circa vitam et doctrinam Cartesii (GP 4 314). 13. Therefore in the harmony system there is one proof of the existence of God. 14. Cf., for example, Letter to Foucher (GP 1 391) and Systeme nouveau . . .(GP 4 483–484).

Chapter 12

The Role of Metaphor in Leibniz’s Epistemology Cristina Marras

1 Introduction In the 17th century, cabinets of rarities fulfilled the role of encyclopedias, for they collected and organized knowledge in such a way that they performed a didactic function. The advent of public museums sponsored by the patrons of scientific research helped to overcome the idea that research is a private endeavor, inaccessible to most people. The criteria for the classification of knowledge used in such institutions responded to a new demand: To insert things in nature, rather than just displaying them, thereby highlighting the interconnections between the different fields of knowledge. Leibniz contributed significantly to the elaboration of these new ideas, and he worked hard to promote the diffusion and the availability of knowledge. On the one hand, with his idea of an encyclopedia, he contributes not only to a classification of the mare magnum of knowledge, but he also highlights the interconnections between the different fields of knowledge. He follows the predominant tendency of his time, which views precise definitions of all terms as a sine qua non for rigorous scientific and philosophical discourse. He was one of the most tireless promoters of a universal language as an instrument of research and as a shared medium of communication between scholars. On the other hand, however, the writings of Leibniz show an innovative use of language, flexible, open, and complementing his work on formal languages and notations. In particular, metaphor is used by Leibniz as a powerful and efficient argumentative strategy, side by side with strictly logical argumentation. In this paper, I will analyze the field of “aquatic metaphors” with particular attention to the ocean. In fact, the ocean metaphor plays a significant role in Leibniz’s conceptualization of the problems, goals and reforms he proposes in the domain of knowledge, and, beyond epistemology, it is also involved in Leibniz’s conceptualization of some central concepts of his metaphysics.1 I choose to analyze these metaphors mainly for two reasons. First, because the ocean metaphor allows Leibniz to overcome the tension between two different

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positions toward knowledge, which are expressed in the tradition through the use of other metaphors like the metaphors of the tree, the forest or the labyrinth. The first stresses the concept of unity, the latter two, the concept of multiplicity. All these metaphors suggest a hierarchical and rigid classification of knowledge. Second, because Leibniz’s choice and use of the ocean metaphor for defining knowledge confirms, in my opinion, the fact that his approach to knowledge is also reflected in his use of language. I have divided my paper into three parts. In the first part, I will summarize the properties belonging to the source – ocean – and to the target – knowledge. In the second part, I will use these properties in order to reconstruct first the Leibnizian concept, map, organization, and management of knowledge; and, second, I will reconstruct the cooperative and communicative connections between those involved in producing and using knowledge by connecting and blending the properties belonging to the metaphor-domain that has as source “ocean” and as target “knowledge”. In particular, I will focus on the Encyclopedia, Leibniz’s main project of knowledge organization. In the last part, focusing on the blend, I will highlight the pluri-multidimensional aspect evoked by the aquatic metaphors in the domain of knowledge, which shows the role of metaphor as a structuring principle of Leibniz’s epistemology. In my analysis, I use the familiar notions of target and source in terms of space/domain, following Fauconnier and Turner’s (1998) Conceptual integration network (CI).2 This model stresses the emergent character of metaphorical concepts, which emerge through a “blending” process comprising the entire process of their interactive generation. This process consists of the dynamic integration (Grady 2000) into a “generic space”, a “cross space”, and a “blend space” of elements of the different “input spaces” (source and target). In accordance with this model, I will analyze – albeit informally – the dynamic integration of the properties of the “target domain” (knowledge) and the “source domains” (ocean and other aquatic metaphors). The metaphorical process is in fact a multi-directional, rather than a uni-directional one, and it involves cognitive as well as cultural aspects. The process leads to the “blend”, i.e., the “conceptual space”, the domain which finally emerges after the combination of the properties belonging to the source and target domains.

2 The Ocean Leibniz explicitly compares the domain of knowledge to that of the ocean. In his writings dedicated to the topic of knowledge and science, the metaphor of the ocean (including beaches and rivers, ships, routes, meteorology, waves, geography, as well as navigation tools and aids, such as maps, sextants, compasses, etc.) refers to, explicitly and implicitly, all this conceptual domain. The metaphor is very often used in relation to other metaphors like that of the way, the field, the war, the army, the warehouse.

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For my analysis, I selected from a large corpus of texts a short list of quotations that exemplify the use of the ocean metaphor; in these quotations, this metaphor plays a central role in structuring the argument: 1. The whole body of science can be viewed as an ocean, which is everywhere continuous, and without any interruption or partition, even though men distinguish in it parts, to which they give names for their own use. Furthermore, just as there are unknown seas, or seas which have only been navigated by a few vessels thrown there by mere chance, so too there are sciences of which we have known something only by chance and without any planning (De l’usage de l’art des combinaisons, 1690–1716; C 530–533; my italics).3 2. But without the already known Axioms and Theorems, the Mathematicians would have troubles in advancing; in fact it is good in long procedures to stop and rest from time to time and to make for oneself as if milestones in the middle of the way, which are useful also to mark the way for others. Without them [. . .] it is like traveling on the sea without compass in a dark night, seeing neither the seabed, nor the shore, nor the stars (NE 4.7.19; A VI 6 424; my italics).4 3. [. . .] and some others compare the whole body of our knowledge to an Ocean, which is only of one piece, and it is divided in Caledonic, Atlantic, Ethiopic, Indian by arbitrary lines (NE 4.21.1; A VI 6 523; my italics).5 4. [.. . .] Mons. D’Avranches left his library to the Jesuits? It is an Ocean, where I see several rivers flowing into (Letter to Nicaise, 9 January 1693; GP 2 539; my italics).6 From the large corpus where “ocean” is used metaphorically and literally,7 and in particular from the quotations listed above, I have selected a list of definitions and properties leading to the different domains and to different aspects to which the term refers.

r r r r r r

r

The ocean is fluid, is a surface of water in movement; the ocean spreads and reduces itself, continuously (see infra §6.1). The ocean is a surface of salted water surrounded by land (GP 6 262–263). The ocean is moved by the wind, by the waves8 and by the rivers (quotation 4).9 You can use the ocean in different ways, navigate it, or just see it from the coast (quotation 1). We can be in water either in a vertical (diving) or a horizontal (floating) position (quotation 2). The ocean, the sea, is a source of knowledge, journeys, and research. Part of the ocean is certainly well known, but there are always unknown parts, seas to be discovered (il y a des mers inconnues). Someone who navigates goes from port to port, from coast to coast. The immensity of the ocean represents a positive aspect because it stimulates new researches and adventures, although sometimes the immensity and the power of the ocean can stop even the most talented swimmer, or the most expert navigator (quotations 1, 5). People can navigate alone but, especially in Leibniz’s time, the ocean was usually crossed by big ships, with very large crews.

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Oceans have arbitrary, different names; sometimes these names are given for finding an orientation, a place, a land, and a specific point in the map (quotation 3). But when the term “ocean’ is used, people refer to a totality. In fact, the ocean is considered to be a continuum, an immense surface.

3 Knowledge, Science, and the Project of the Encyclopedia The properties of the ocean can be related to the list of properties belonging to an encyclopedia as a complete exposition of all knowledge. The characteristics belonging to the project of an encyclopedia can be summarized as follows:10

r r r r r r r r

An encyclopedia is not a dictionary; in fact, it is the organization of knowledge, not of words. In an encyclopedia, there is continuity between texts, either alphabetical, conceptual, or disciplinary. The contents of an encyclopedia are unlimited. The interrelations between the elements of its pages are multiple. A reader can browse freely throughout its pages. An encyclopedia includes non-linear materials: pictures, drawings, diagrams, maps, etc. We can have a synchronic and diachronic relation with knowledge. An encyclopedia has an educational and a cultural role. An encyclopedia is the result of collective work. An encyclopedia is not a miscellanea but an ordered presentation of contents. An encyclopedia is an organon (instrument), giving a perspective on the development of knowledge.

Leibniz’s Encyclopedia organizes practical and theoretical knowledge together (A VI 4 432). It presents an external criterion of organization of knowledge, as well as an internal one: the Scientia Generalis.11 With the Scientia Generalis, Leibniz stresses the importance not only of the organization of knowledge but also of the importance of how we “know”. [. . .] [T]wo things would be necessary for men to be able to benefit from their advantages and to do all they can in order to contribute to their own happiness, at least as far as knowledge is concerned [. . .] [F]irst, a precise inventory of all the available but dispersed and ill-ordered pieces of knowledge [. . .]; secondly, the general science that must provide not only the means for making use of the available knowledge, but also the Method of judging and discovering, in order to go farther [. . .] (Nouvelles Ouvertures, 1686; A VI 4 691).12

Generally speaking, the idea of an encyclopedia is also related to the rationality underlying the transmission of knowledge, and it is connected to the historical and contextual ways and modalities of sharing and organizing knowledge at a given e´ poque. Somehow, an encyclopedia seems to be self-contradictory (Salsano 1978): It is a summa, a compendium of parts of knowledge and, at the same time, it is a homogenous framework; a synthesis of a heterogeneous world. However, it seems to me that, with his idea of an encyclopedia, Leibniz provides the solution of this apparent contradiction. The Leibnizian encyclopedia unifies what is divided (it overcomes

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the traditional divisions and separations of disciplines, as well as their organization in a hierarchical order). His project is based on an idea of “knowledge-building” as the result of an interactive relation between different disciplines and not as a cumulative and linear progression of data. The Encyclopedia represents the possibility of containing the “totality” of a continuum (the ocean of knowledge); a continuum that can always be divided in different forms (classifications, orders, indexes; i.e., as in the ocean, maps, the different names of ports, coasts, islands, etc.). Leibniz wants to preserve a concept of knowledge built upon the idea of an ordered system and, at the same time, he aims to save the intrinsic “nature” of knowledge: that of “discovery”, of improvement (A VI 4 440). A conceptualization of knowledge in terms of “ocean” allows the preservation of the specificity, the “grammar” of each field and discipline, and is able to insert them into a flexible and well structured framework, capable also of redefining itself and of accommodating its structure accordingly to the various and possible “designs” of knowledge (see infra 5.2).

4 Ocean and Knowledge: Shared Properties The properties of the ocean that cross with the properties of knowledge focus on three principal coordinates: flexibility, inter-connection, and organization. The vehicles are the ocean, the sea, and the water. Water includes mobility (navigation), and plurality (from coast to coast); water is an essential part of the net of knowledge in which each entity, element, and field is related to the other.

Ocean

Knwoledge

Movement-open space

Complete exposition of knowledge. Organization. Unity and multiplicity. Open space for re-organization. Continuity/infinity/open. Exposed to unexpected influences. Unlimited entries Different ways of organizing knowledge (each reader can build his own path). Diachronic and synchronic research Research. Discoveries, improvement of knowledge. Organon. Educational and cultural aims. Knowledge is neither eternal nor fixed. Research, cooperation, dialectic knowledge, collective work.

Borders/unlimited Fluid/moved by external agents Can be used and navigated in many ways Horizontal-Vertical movements

Travel-explorer Unknown parts

Arbitrary attribution of names To travel alone or with a crew The importance and the complex organization of a ship

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In the following table, I propose some examples of shared properties between the domain of the ocean and the domain of knowledge: The cross-space built upon these properties shows that the use of the ocean metaphor and its related properties is connected to the necessity of organizing data and knowledge, to the fact that knowledge is a cooperative enterprise, to the necessity of finding a method that combines theory and practice. In using the metaphor of the ocean and other aquatic metaphors, Leibniz wants to stress not only the methods of organizing knowledge or the ability to deal with what is unknown, but also how to find the “right route” in the difficult “journey” of research. The metaphor of the ocean stresses that the ways to travel are different, as are the different instruments contributing to a safe journey. The routes can be verified and new routes can be discovered (chemin de travers). There are very well known routes, as well as other routes in which the navigation is influenced by chance (quotation 1). Sometimes people are afraid to deal with the unknown, but, at the same time, a new and unknown situation can be a great stimulation for new knowledge, and new horizons.13 Leibniz works in order to find a via media (between theory and practice, analysis and synthesis, artificial and natural languages); he wants to find a place of convergences but at the same time he wants to maintain and preserve the differences. Somehow he was looking for finding the “North-West passage” (Serres 1980).

5 The Journey 5.1 The Map of Knowledge Before we start navigating, it is important to prepare the ship with the correct rigging: all the spars, wires and ropes bending on sails, to check the anchor, all the mechanical systems, instruments, etc.; this includes choosing the crew, collecting the maps and identifying ports, rocks and islands, and checking the weather forecast. Everything has to be proofed and checked to avoid risks and dangerous situations; but enemies, other ships and unexpected obstacles can be actually seen only during the journey. Once all the information and tools are collected, the ship can start the journey. Even if the route has been traced, during the journey it is necessary to correct it. In fact, the route has a “provisional” character, the navigation has to be adapted to the sea condition, the time, the power of the ship, the crew. Instruments, maps, and routes contribute to a safe navigation; obviously there are always unexpected factors and obstacles that can prevent a ship from a safe and “normal” navigation. As in the ocean, the immensity and the influence of external factors during navigation can interfere and modify the routes. The monitoring of the conditions is one of the basic things that have to be done before and after you set sail. So is it also in the mare magnum of knowledge; in fact, it is very important to make a careful evaluation of the sources, to monitor the knowledge available, and to analyze texts properly.

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Leibniz, in his tireless activity in different domains of knowledge, was also aware of the situation of publishing in Germany. He criticized the editors of his time; in his opinion, they were more interested in the economic aspects than in the value of the dissemination of culture (GP 2 369). In the case of knowledge, Leibniz insists on the necessity of understanding what is useful and what is good, for example, in the huge number of available books and thoughts (GP 7 159 and A VI 4 697). He recommended a rigid system of censure involving not only the “dangerous” books but also, and especially, the “useless” books (A I 1 50).14

5.2 The Organization of Knowledge Explorations, experiences, imagination, and researches give names to the coasts, islands, clouds, wind, and waves. Leibniz was familiar with the denomination of places too. He works on the classification of the names of places, he uses all the tables of definition available at his time, he suggests changes, corrections, and additions.15 To attribute a name to a place is partly an arbitrary action; it is an answer to practical needs. So knowledge does not have a fixed place, and the divisions are made by convenience. The variety of knowledge is so immense that it is necessary to use several indexes, taxonomies, and systems of classification. Leibniz knows very well, as a librarian, how to store and to catalogue knowledge (A VI 4 987). Inventories are important in order to know what is available (A VI 4 956). But an encyclopedia is not a dictionary, and Leibniz tries to establish different types of order, e.g., an inventaire g´en´eral (GP 7 158) – not an inventory of words – of the poorly organized and dispersed knowledge (C 228), and a terminological order (suivant les termes) (GP 5 506). Leibniz did not suggest traditional indexes based on titles, chapters or sections as in an essay, but he created real maps of knowledge. The index is systematic, ordered, with many entries, so that it can be changed and rebuilt differently.16 The Scientia Generalis is a science capable of establishing a demonstrative order of all the specific sciences: an encyclopedia demonstrativa (GP 7 168). But, for Leibniz, order is discovered in the development of science itself (this is related to the metaphorical concept of journey and of the navigation). The perfect scientific order is that in which propositions are arranged according to their simplest demonstrations, in the manner in which they arise from each other; but this order is not known initially, and it is discovered more and more as science is perfected (Discours touchant la M´ethode de la Certitude et l’Art d’Inventer 1688–1690; A VI 4 959).17

5.3 The Management of Knowledge Knowledge, for Leibniz, needs a reform. The need is not only to classify, to keep, or to save knowledge but also to disseminate it, to exchange it and to develop practical and theoretical knowledge (theoricis empiricis felici connubio conjungit; A IV 1

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536). All these aims are well represented by the ship, the travel, the relation between maps and routes. In fact, a ship is a central concept in the domain of the ocean metaphor and each single part of a ship contributes to the “work” of the whole.18 It is not always a question of creating great works; if each would provide only a single discovery, we would gain much in a short period of time. A single important observation or demonstration is enough to be immortalized and honored by future generations (Recommandation pour Instituer la Science Generale, 1686; A VI 4 699).19

In his many Prefaces to the Scientia Generalis, (e.g., Initia et specimina scientiae generalis de nova ratione instauratione et augmento scientiarum (A VI 4 352–356, 357–361), Introductio ad scientiam generalem modum inveniendi demonstrandique docentem (A VI 4 370–374), Nouvelles ouvertures (A VI 4 686–691)), Leibniz stresses the necessity of creating instruments to use knowledge, to render knowledge available, and the necessity of finding a method for judgment and for invention. Thus, the more a science is perfected, the less need it has of great volumes, for insofar as its elements are sufficiently established, we can discover the whole of it with the help of the general science or the art of invention (Discours touchant La M´ethode de la Certitude et l’Art d’Inventer 1688–1690, A VI 4 959).20

Leibniz entrusts the management of knowledge to the Academies. His project for the Academy of Science in Berlin (1700) was the concrete realization of his plans, which included the creation of a society for that specific purpose. He considers science as a base for human development and for the development of society (FC 7 599–618). Theory and practice, study and research, museums and libraries were the main issues of the Society. He criticizes most of the contemporary institutions, considering them devoted only to “sterile” curiosities, or being too selective (FC 7 290).

6 Blending: From Modularity to Plurality In the conceptual domain of the aquatic metaphor, the central property is that of “fluidity”; from this property we can extrapolate some central concepts of Leibniz’s, epistemology, namely movement and limits.

6.1 Fluidity In a letter to Princess Sophie of February 6, 1706, Leibniz considers the entire universe as a fluid (GP 2 370). The material of the earth is fluid and not solid, and full of movement. In his cosmology, water is considered a fundamental element; once the earth cools, atmospheric humidity washes down the surface and fills “this large cavity of our globe’s surface in order to make the ocean” (Th´eodic´ee, GP 6 262–263).21 The universe, Leibniz writes to Sophie, “is a sort of fluid made of one piece where, like in a boundless ocean, all movements are conserved and propagate up to infinity” (GP 7 567).22

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Through the metaphorical blend, the ocean becomes infinite, and the boundless propagation of its waves through the fluid medium of water serves to conceptualize the physical continuity of the universe, where everything is in contact, albeit imperceptibly, with everything else. That this is an instantiation of the metaphysical principle of continuity is apparent from the extension of the analogy to all possible worlds, each of which is “like an ocean, where the smallest movement extends its effect to whatever distance” (Th´eodic´ee, GP 6 107). This fluidity is also related to the role and function of the rivers. Rivers, water and drops are related to each other. The river “flows” and the water is the constitutive element, the conditio sine qua non, for making the river a river. Water is not a part of the river but is one of its requisites; it is based on power and not on a mechanical principle. If we look at a map and we focus on land, sea, rivers, and islands, we see continuity, individuality and interconnections. This aspect can also be found in Leibniz’s attitude toward language. Language and knowledge are interrelated. If we consider the concept of a map, for example, we see that it is the result of a combination of two kinds of “languages”: one geometric, analytic and abstract, and the other pictographic and intuitive. Formal languages, for example, are not in opposition to natural ones but they are interconnected, and related to each other. It is obvious that an artificial language is related to the necessity of clarity which is fundamental, for instance, for philosophical discourse (Praefatio Nizolii, A VI 2 409), but it does not replace natural language. Although Leibniz does not accept the “opacity” of language, he nevertheless appreciates and considers valuable the “potentiality” intrinsic to natural languages, their flexibility and “omniformative” nature (Prefatio Nizolii, A VI 2 141).

6.2 Movement In his writings, Leibniz often stresses the importance of empirical experiences. At the same time, he wants to guarantee the possibility of knowledge avoiding the necessity to start always from a clear and distinct basis. For Leibniz, experience is never “static and fixed” (can a still ocean exist?). Moreover, as Leibniz says in the preface to the NE, he does not accept the idea of a tabula rasa or the notion that knowledge derives only from our senses (in this case Leibniz uses the vivid metaphor of the marble statue23 ). The metaphors related to the ocean and to the sea contribute to the development of this concept. A trip is, for example, a combination between experiences, knowledge already available, and the imagination of the future (GR 30). There are different ways to know the sea, as there are different ways to go into the sea. Floating, for example, is the result of a balance of forces pulling up and down. Moreover, although the experiences and the knowledge are to be verified, we do not have to repeat the procedures every time. A navigator does not have to re-verify the coordinates on the map every time, but just carefully verify the route. The rules for sailing open the possibility of discoveries, and sometimes all the collected information can be used to make a new hypothesis for exploring new routes (A VI 4 704).

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6.3 Limits The concepts of “limit” and “unlimited” are interesting once we preserve the differences and a dynamic rather than static conception of “unity” as it is stressed by Leibniz on different occasions. He, in fact, considers different levels of unity (GP 2 100) but a complete vision and a complete perspective are achieved only by considering all parts (and the whole). One of the most important points highlighted by this concept of the “unlimited” is that the same “truth” (mˆeme verit´e) can be placed in different places, according to what is convenient. This stresses the “open” and “flexible” character of knowledge and of knowledge organization. The ocean is unlimited (sans bornes); it is the result of the co-existence of different parts. Where one ends the other begins; the mutual influence across the “borders” is very important in shaping the entire profile of the coast (see, for example, the relation between rivers and sea, or the fjords, the coasts, etc.). The method, the characteristica, the ships are instruments to overcome the limits of knowledge and lands, and they are useful instruments in understanding the context. Of course, the way is full of obstacles to overcome; a collective investment of efforts contributes to successfully reaching scientific results.

7 Conclusions My conclusions are twofold: one is related to the metaphor as a structuring principle of Leibniz’s epistemology; the other, to the pluri-multidimensional aspect evoked by this metaphor in the domain of knowledge.24 Leibniz displays a use of language that preserves the nature of metaphor as a creative trope rather than as conveying a conventionalized, “frozen” meaning. The properties that are involved and blended are not only “atomic” properties, but the blend is the result of “cultural-knots” (Eco 2005: 261). The blend, as I refer to it in this paper, is thus a new and unexpected rich conceptual domain created by the “activity” of the language. The view of knowledge that this metaphor helps to articulate leads to a systematic and encompassing conception of what would today be called a “scientific policy”, namely, the organization of scientific research. Leibniz contributes to a modern conception of the encyclopedia, in which the classification of knowledge goes together with a system of relations and interconnections of knowledge, which is highlighted by the metaphorical domain of the ocean. In my opinion, the metaphor of the ocean and the other aquatic metaphors help us in resolving the tension between “inventory” (that is, the storage and classification of ‘old’ knowledge) of knowledge and “invention” (that is, the continuous renovation and innovation producing ‘new’ of knowledge). Like in related metaphysical problems, in his epistemology Leibniz seeks to combine plurality with unity, dynamism with completeness, and autonomy with interdependence through the aquatic metaphors: As in, for example, the problem of the preservation of a thing’s identity in spite of the radical modification (even complete “replacement”) of its parts. In this respect, a body’s relationship with the

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matter that composes it is compared by Leibniz to that between a river and its water. Water is a part of the river, but no particular drop of water is a part of it; likewise, matter is a part of the human body, but no particular “molecule” is a part of it. This comparison serves to give form to the key Leibnizian idea of “formal” or “abstract” identity. The point of view engendered by this metaphor – the vision of an endless, continuous, flat, and fluid aquatic mass – allows for a new vision of the structure of knowledge whose image is no longer, as I said at the beginning of this paper, that of the usual “tree of knowledge” (used, for example, by Descartes in the wake of Porphyry, Boethius, and Bacon). Leibniz breaks the barriers between the different branches of knowledge or between distant fields, domains and disciplines. Rather than a fixed hierarchical classification of the sciences implied by the tree metaphor, the ocean-induced vision evokes the ancient idea of the “circle of learning” (ankhyklios paideia), where the emphasis is on the “circulation” of knowledge, the transmission of knowledge, the availability of knowledge and the interconnection of knowledge. The metaphor of the ocean and the aquatic metaphors in general allow us also to “welcome” the ideas of a non-hierarchic order (Fern´andez 2001) and a multidimensional “system” of knowledge (Serres 1968). Leibniz suggests an organization of knowledge in which different disciplines are in mutual dialogue, which takes place not only in the inter-disciplinarity of the concepts, but also in the exchange between scholars. In this respect, it is natural to think of the ships that travel around the world as carrying not only merchandise but also ideas and cooperative research projects, thus connecting disciplines and cultures. This implies, on the one hand, the continuity and cross-fertilization between the disciplines and, on the other, the “fluidization” of their boundaries. The latter are depicted through the metaphor as more or less arbitrary, like the division of the ocean in seas. They are useful as signposts, as ways of mapping the ocean of knowledge and providing means of “navigation” within it, to which, however, no ontological significance should be assigned. Furthermore, like the ocean into which all rivers flow, the contributions to human knowledge come from a variety of sources, ancient and modern, big and small, none of which should be neglected. In some of the many prefaces where he expounds his project of a new encyclopedia, Leibniz claims that it should follow a “demonstrative” order, an order resulting from different procedures. In the Nouvelles Overtures (1686), Leibniz also makes an interesting distinction between drilling (creuser) the bottom of the sea and sounding (sonder) the bottom of the sea (A VI 4 689). With this distinction he stresses two different attitudes (i.e., an ars iudicandi and an ars inveniendi), two different tools (i.e., a demonstrative logic and a creative logic), two different methods of research and investigation (for example an axiomatic method and a combinatorial method), and the theoretical and the empirical approaches to scientific knowledge. The interplay between these different approaches and instruments contributes to the discovery of a “new order”. Yet, the order in question varies from preface to preface. Furthermore, in all of them Leibniz emphasizes the need for a variety of indices, which provide a plurality

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of “ports” through which one may access the wealth of information contained in the encyclopedic ocean and crisscross it through different routes. This is one of the respects in which the Leibnizian encyclopedia is an essential tool for the “art of discovery”. The other, also conceptualized by him in terms of the ocean metaphor, lies in the encyclopedia’s capacity to reveal – by its synoptic and comprehensive character – those lacunae, those “unknown seas” yet to be explored. An encyclopedia fulfilling all these functions exemplifies a form of “organized multiple-access plural-unity”, a notion that emerges at the level of the “blend-space” engendered by the metaphorical use of “ocean” and its cognates in the conceptualization of the organization and advancement of knowledge. The aquatic metaphors and the metaphor of the ocean (as well as other central metaphors) reveal a pattern in Leibniz’s argumentative praxis, which goes beyond a strictly deductive, calculative model of reasoning. Through the analysis of the use of these metaphors, metaphor in Leibniz’s philosophy can be conceived as something more than a “rhetorical ornament”. Metaphor, in spite and in virtue of its informal character, functions as a methodical and non-conventional way of analogically structuring discourse which can contribute to a revision of the prevalent image of Leibniz’s rationalism.

Notes 1. The centrality of the metaphor of the ocean for Leibniz’s epistemology is stressed also in Fern´andez (1998), Pombo (2001) and Dascal (2001). 2. For some examples and different applications of the CI see the website: http://www.wam.umd. edu/∼mturn/WWW/blending.html. “Conceptual integration networks are equally prominent in counterfactuals, category of extension, event integration, grammatical constructions, conceptual change (as in scientific evolution), literary and rhetorical invention” (Fauconnier and Turner 1998: 54); “Blending theory, as a general theory of meaning construction, has become a useful way of securing closer connections between the way we understand language with a broader understanding of human thought and activity” (Coulson and Oakley 2000: 184). 3. Le corps entier des sciences peut estre consider´e comme l’ocean, qui est continu´e partout, et sans interruption ou partage, bien que les hommes y conc¸oivent des parties, et leur donnent des noms selon leur commodit´e. Et comme il y a des mers inconnues, ou qui n’ont est´e navigu´ees que par quelques vaisseaux que le hazard y avoit jett´es: on peut dire de mˆeme qu’il y a des sciences, dont on a connu quelque chose par rencontre seulement, et sans dessein. 4. Mais sans les Axiomes et les Theoremes d´ej`a connus, les Mathematiciens auroient bien de la peine a` avancer; car dans les longues consequences, il est bon de s’arrester de tems en tems et de se faire comme des colonnes millaires au mileu du chemin, qui serviront encore aux autres a` les marquer. Sans cela [. . .] c’est aller sur mer sans compas dans une nuit obscure sans voir fonds, ny rive, ny e´ toiles. 5. [. . .] et d’autres comparent le corps entier de nos connoissances a` un Ocean qui est tout d’une piece, et qui n’est divis´e en Caledonien, Atlantique, Aethiopique, Indien, que par des lignes arbitraires. 6. Comment! Mons. d’Avranches a encore l´egu´e sa biblioth`eque aux j´esuites? C’est un oc´ean, o`u je vois que bien des rivi`eres se rendent. 7. An extensive analysis of the quotations in which the term “ocean” is used literally and metaphorically by Leibniz is provided in Marras (2003: 41–79).

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8. In order better to recognize these tiny perceptions that cannot be distinguished in a crowd, I usually make use of the example of the roar or noise of the sea that strikes us when we are at the shore. In order to hear this noise as we do, we must hear the parts that make up this whole, that is, we must hear the noise of each wave, even though each of these small noises is known only in the confused assemblage of all the others. / Et pour juger encor mieux des petites perceptions que nous ne saurions distinguer dans la foule j’ay coutume de me servir de l’exemple du mugissement ou du bruit de la mer dont on est frapp´e quand on est au rivage. Pour entendre ce bruit comme l’on fait, il faut bien qu’on entende les parties qui composent ce tout, c’est a` dire les bruits de chaque vague, quoyque chacun de ces petits bruits ne se fasse connoistre que dans l’assemblage confus de tous les autres [. . .] (NE, Preface; A VI 6 54; my italics). 9. [. . .] the rivers flow into the sea. / [. . .] les ruisseaux se perdent dans la mer (Th´eodic´ee, GP 6 54). 10. In this section I am referring to the properties of an encyclopedia listed by Olga Pombo (2001: 267–271). 11. By “general science” I mean the science that teaches all the other sciences the method of invention and demonstration. / Scientia generalem intelligo quae modum docet omnes alias scietias ex datis sufficientibus inveniendi et demonstrandi (Introductio ad scientiam generalem modum inveniendi demonstrandique docentem 1679, A VI 4 370). See also Definitio brevis scientiae generalis, 1683–1685, A VI 4 532. There is a large literature concerning the projects of an Encyclopedia between 1500 and 1700; among others, see Rossi (2000) and Cremante and Tega (1984) which illustrates the project of an Encyclopaedia pratica et teorica at the “Istituto delle Scienze di Bologna” founded in 1714. See also Vasoli (1978). 12. Deux choses seroient necessaires aux hommes, pour profiter de leur avantages, et pour faire tout ce qu’ils pourroient contribuer a` leur propre felicit´e, au moins en matiere de connoissance, [. . .] un inventaire exact de toutes le connoissances acquises mais disperses et mal rang´ees, [. . .] et la science generale qui doit donner non seulement le moyen de se servir des connoissances acquises, mais encore la Methode de juger et d’inventer, a` fin d’aller plus loin [. . .] ce n’est pas l’enterprise d’un seul homme, ny meme de peu de personnes. 13. Leibniz to Malebranche, 2 July 1679; A II 1 479. 14. On this point see Varani (2005). 15. De rerum classibus, 1677–1680; A VI 4 1006, 1009, 1011. 16. See Tognon 1987: 38–43; see also Dascal 2001, for a detailed analysis and discussion of Leibniz’s knowledge organization and cognitive technology. 17. L’ordre scientifique parfait est celuy o`u les propositions sont rang´ees suivant leurs demonstrations les plus simples, et de la maniere qu’elles naissent les unes des autres, mais cet ordre n’est pas connu d’abord, et il se decouvre de plus en plus a` mesure que la science se perfectionne. 18. [. . .] the smallest rope has its own irreplaceable role in a big ship [. . .] / [. . .] le plus petit nerf a son usage dans le corps, aussi bien que la moindre corde dans un grand vaisseau [. . .] (Conversation du Marquis de Pianese et du P`ere Emery, 1679–1681, A VI 4 2270). 19. Il ne s’agit pas tousjours de faire des grands ouvrages; si chacun ne donnoit qu’une seule d´ecouverte, nous gagnerions beaucoup en peu de temps. 20. Aussi plus une science est perfectionn´ee, et moins a-t-elle besoin de gros volumes; car selon que ses Elemens sont suffisamment establis, on y peut trouver par le secours de la science generale, ou de l’art d’inventer. 21. Car lorsque la surface de la terre s’´etoit refroidie apr`es le grand incendie, l’humidit´e que le feu avoit pouss´ee dans l’air, est retomb´ee sur la terre, en a lav´e la surface, et a dissout et imbib´e le sel fixe rest´e dans les cendres, et a rempli enfin cette grande cavit´e de la surface de nostre globe pour faire l’Ocean plein d’une eau sal´ee (Th´eodic´ee, GP 6 262–3). 22. L’Univers estant une maniere de fluide, de tout d’une piece, et comme un ocean sans bornes, tous les mouvemens s’y conservent et se propagent a` l’infini [. . .] (To Sophie, 6 February 1706; GP 7 567; see also GP 2 370). 23. [. . .] les verit´es seroient en nous comme la figure d’Hercule est dans un marbre, quand le marbre est tout a` fait indifferent a` recevoir ou cette figure ou quelque autre. Mais s’il y

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avoit des veines dans la pierre, qui marquassent la figure d’Hercule pr´eferablement a` d’autres figures, cette pierre y seroit plus determin´ee, et Hercule y seroit comme inn´e en quelque fac¸on, quoyqu’il fallˆut du travail pour d´ecouvrir ces veines, et pour les nettoyer par la politure, en retranchant ce qui les empeche de paroitre (NE, Preface; A VI 6 52). 24. For a “multi-perspectival epistemology” see Dascal (2005).

References Andreu, A., Echeverr´ıa, J., and Rold´an, C. 2001. Ciencia, Tecnolog´ıa y Bien Com´un:La Actualidad de Leibniz. Valencia: Universidad Polit´ecnica. Cremante, R. and Tega, W. (eds.). 1984. Scienza e Letteratura nella Cultura italiana del Settecento. Bologna: Il Mulino. Coulson, S. and Oakley, T. 2000. Blending Basic. In Coulson and Oakley (eds.), pp. 175–195. Coulson, S. and Oakley, T. (eds.). 2000. Conceptual Blending [Special Issue 11(3/3) of Cognitive Linguistics]. Dascal, M. 2001. Leibniz y las tecnolog´ıas cognitivas. In Andreu et al. (eds.), pp. 159–189. Dascal, M. 2005. The balance of reason. In D. Vanderveken (ed.), Logic, Thought and Action. Dordrecht: Springer, pp. 27–47. Eco, U. 2005. Metafora e semiotica interpretativa. In A. M. Lorusso (ed.), Metafora e Conoscenza. Milano: Bompiani, pp. 257–290. Fauconnier, G. and Turner, M. 1998. Conceptual Integration Network. Cognitive Science 22(2): 133–187. [web version 10 February 2001, http://www.wam.umd.edu/∼mturn/ WWW/blending.html]. Fern´andez, J.F. 1998. El fil´osofo del Oc´eano. Irun: Iralka. Fern´andez, J.F. 2001. Organizaci´on sin jerarquias. In Andreu et al. (eds.), pp. 239–250. Grady, J. 2000. Cognitive mechanism of conceptual integration. In Coulson and Oakley (eds.), pp. 335–345. Marras, C. 2003. On the Metaphorical Network of Leibniz’s Philosophy. Ph.D. Dissertation, Tel Aviv University. Rossi, P. 2000. I Filosofi e le Macchine, 1400–1700. Milano: Feltrinelli. Salsano, A. 1978. Enciclopedia. In Enciclopedia Einaudi, vol. 1. Torino: Einaudi , pp. 3–64 Serres, M. 1968. Le Syst`eme de Leibniz et ses Mod`eles Math´ematiques. Paris: Presses Universiatires de France. Serres, M. 1980. Herm`es V. Le Passage au Nord-Ouest. Paris: Les Edition de Minuit. Pombo, O. 2001. Leibniz and the Encyclopedic project. In Andreu et al. (eds.), pp. 267–278. Tognon, G. 1987. Leibniz e la costruzione degli Essais de Th´eodic´ee. Edizione e commento dell’indice autografo. In A. Lamarra and L. Processi (eds.), Lexicon Philosophicum. Quaderni di Terminologia Filosofica e Storia delle Idee. Roma: Edizione dell’Ateneo, pp. 31–71. Varani, G. 2005. Impegno “editoriale” e temi retorici nella prefazione a Nizolio. In S. Gensini (ed.) Linguaggio, Mente, Conoscenza. Intorno a Leibniz. Roma: Carocci, pp. 39–58. Vasoli, C. 1978. L’Enciclopedismo del Seicento. Memorie per l’Istituto Italiano per gli Studi Filosofici, vol. 1. Napoli: Bibliopolis.

Chapter 13

What Is the Foundation of Knowledge? Leibniz and the Amphibology of Intuition Marine Picon

In a now classic article, first published in 1994, M. Fichant offered an assessment of Leibniz’s doctrine of the foundation of arithmetic with reference to the modern alternative of logicism and formalism. Against the temptation of seeing in Leibniz a precursor of the latter theory, he emphasized that his epistemology rested upon the “acknowledgement of the original part [played by] the intuition of some content, which every formalizing process always implies” (Fichant 1998: 296).1 He was thereby advocating an interpretative tradition initiated in the 1920s by E. Husserl and D. Mahnke (1924: 60). According to the former, Leibniz had been “the first, in modern times, to understand the most profound and precious meaning of Platonic idealism, and had therefore acknowledged that ideas were unities given ‘in themselves’ in a proper intuition of ideas [in einer eigent¨umlichen Ideenschau]” (Husserl 1956: 198).2 Fichant documented his position with a passage from Book IV of the New Essays on Human Understanding, where Leibniz does develop a theory of intuitive knowledge as the ultimate foundation for any scientific elaboration (NE 4.2.1; A VI 6 361–67), and traced this theory back to the canonical typology of cognitions set down twenty years before in the Meditations on Cognition, Truth and Ideas. However, this reading of Leibniz’s epistemology raises two questions. First, do the terms cognitio intuitiva and intuition have the same meaning in the Hanover period and in the New Essays? If not, does either of those meanings allow for the Husserlian view that Leibniz ascribed the foundation of knowledge to an original, pre-symbolical apprehension of ideas in a realistic sense?

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1 Hanover: The Hypothesis of a Cogitatio Intuitiva as an Anti-Cartesian Device 1.1 The Meditations on Cognition, Truth and Ideas: The Blind Spots of an all too Familiar Text The 1684 Meditations are generally known as the text where Leibniz first laid down the essential elements of his theory of knowledge. This theory takes there the form of a hierarchical classification of the degrees of cognition. A summary of it is given in the introductory paragraph: I should like briefly to explain what I think may be established about the different kinds and the criteria of Ideas and of cognitions. Cognition is either obscure or clear; clear cognition is either confused or distinct; distinct cognition is either inadequate or adequate; and also either symbolic or intuitive. And if it is both adequate and intuitive, it is the most perfect possible one (A VI 4 585–586).3

Here is, at the top of this hierarchy, what is usually considered as the first mention of the “intuitive cognition” later developed in the New Essays. That classification was to become all the more famous as Leibniz includes it in article 24 of the Discourse on Metaphysics, and also in various drafts presenting his project of a “general science” (A VI 4 528; 539–543; 912; 973). But the Meditations are also well known as Leibniz’s contribution to the Parisian quarrel on true and false ideas. As one will recall, this quarrel opposed Malebranche’s followers, defending a realistic conception of ideas, according to which we “see” ideas “in God”, to Arnauld, for whom an idea is nothing but the very intentional act in which we grasp this or that object. When Leibniz wrote the Meditations in November of 1684, he had not read the latest publications of the two parties, but their opposite conceptions were known to him, since he was familiar with both the Logic of Port-Royal and Malebranche’s Search after Truth (A VI 2 395; A VI 3 312–26). The question arising at this point is: how do these two commonplace descriptions of the Meditations relate to one another? More precisely: Why did Leibniz choose to lay down a hierarchy of the types of cognition in order to settle a controversy on the ontological status of ideas, and on the way we know them? The dichotomous classification, sketched in the first paragraph, is developed at length in the second one, a development in which, we should note, the word idea is virtually missing.4 It only reappears at the beginning of the third paragraph, in one of the most obscure articulations of Leibniz’s exoteric writings.

1.2 The Remote Origin of Leibniz’s Public Prohibition of the “Appeal to Ideas” Let us quickly skip the well known presentation of the various types of cognition. One will recall that the progression in that hierarchy corresponds to the growing distinction of concepts: Just as distinct cognition is the condition for discursive knowledge, which can give a description, or the “enumeration of sufficient marks” of its object,

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adequate cognition is the one in which “analysis is carried through to the end”. Let us also make clear that the last dichotomy mentioned in the introduction, opposing symbolic to intuitive cognition, is not a subdivision of adequate cognition: symbolic cognition, being the one in which characters intervene as abbreviation, is to be found in every type of knowledge. But intuitive cognition, in which “we think simultaneously of all the concepts which compose” a given concept, is necessarily adequate. So how does that classification relate to the debate on true and false ideas? This is what we are supposed to find out at the beginning of the following paragraph, when Leibniz writes: “This shows that we do not perceive the ideas even of those things which we know distinctly, except in so far as we use intuitive thought” (A VI 4 588).5 The inferential coherence between the two paragraphs is far from being clear. It could only be so if we knew what Leibniz means by the word “idea”. The beginning of this third paragraph could follow logically from the preceding one if and only if Leibniz had defined an “idea” as “that which is perceived when we grasp simultaneously all the elements which compose it”. There is no such definition in the second or in the third paragraph. However, this argumentative element is to be found somewhere in Leibniz’s writings, although not in any of his published, or exoteric texts, but in a Parisian draft written almost ten years before. It was in that draft that he laid down the unusual axiom that “We have the ideas of the simples, we have only the characters of the composites” (A VI 3 462).6 His point there was that the combination of elementary concepts, through which all complex concepts are formed, is actually only a combination of the symbolic substitutes of these elementary concepts. Our thinking faculty can grasp them individually, but cannot operate their combination as a combination of concepts, or “ideas”. If it could, this operation would, by itself, be a criterion for the possibility of the resulting complex concept. That fundamental limitation of our thinking faculty is the reason why we have to rely on the discursive procedure of analysis, that is, on definitions, by means of characters. And it is precisely this necessity that Leibniz is going to defend in the following paragraphs of the Meditations. This published text can therefore be considered as the public exposition of a conviction which had already found its private expression ten years before (see Mugnai 1976: 34). What is remarkable is the absence of any intermediary elaboration on that theme (except of course for the numerous drafts on the scientia generalis in which Leibniz defines what is a clear, and what is a distinct concept). For instance, it was not on those grounds that Leibniz chose to set the problem of assessing the possibility of a concept in his 1677 debate with Eckhard over the Cartesian demonstration of the existence of God (A II 1 311–314, now 485–489). Yet this correspondence is the true background to the question of the idea as Leibniz answers it in 1684. When writing the Meditations, he brings together that original persuasion of his, regarding the limit of our thinking faculty, and a digest version of the typology of concepts that he has been elaborating in the past years, the latter providing, in his view, the appropriate exoteric support for the former. The opposition between the two sides in the Parisian controversy matters little to him. What does matter is what they have in common: The Cartesian claim to an immediate access to ideas, whether we are

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supposed to “see them” in God, as in Malebranche’s version, or to consider the simple fact that we refer to them in our speech as showing that we do have those ideas.7 The hierarchic classification of cognitions has therefore a double function: It defines the criteria of the clear and the distinct for which Leibniz had been asking the Cartesians in vain for the past ten years,8 and it is ipso facto the list of conditions which must be met in order to make a legitimate claim to such an immediate access to the intelligible. Thinking should be free from the confusion resulting from the simultaneous perception of a multiplicity of attributes that we cannot distinguish, as well as from the abbreviating mediation of characters, so that all the elements that constitute that intelligible entity be simultaneously present to the mind which thinks of them.9 This would amount to what Leibniz called in 1675 “judging about possibility by thinking” (A VI 3 463). In accordance with the position defined at that time about the relation between language and thought, the 1684 classification of cognitions culminates in a prohibitive definition of the intuitive cognition of composed notions.

1.3 An Exception to that Prohibition? There remains the case of the “distinct primitive notions”, about which Leibniz writes, at the end of his classification, that their cognition can only be intuitive.10 Since the beginning of his stay in Hanover, he had become more and more circumspect as to the possibility for us to identify any such notion.11 But, as he wrote in 1679 to J. Vagetius, “we can nevertheless reason about them, as if we had indeed enunciated them” (A II 1 497, now 772).12 In this way, Leibniz will keep mentioning those primitive or “absolutely simple” concepts throughout his writings.13 However, when it comes to enumerating the types of cognition that men actually have, he is all the more negative about these notions and the intuitive cognition proper to them, as he writes for himself and not in the prospect of public controversy. Such is the case of the notes he made on Malebranche’s Search after Truth, when he studied that book again, sometime between 1686 and 1699. Malebranche’s developments on “pure intellection”, which support his version of the Cartesian claim to an immediate access to ideas, cause Leibniz to retort with a reminder of his 1684 dichotomous classification of cognitions: I do not think that there is any pure intellection, to which nothing would correspond in the body. It seems to me that every perception is either confused or distinct; and that a distinct perception is either composed of distinct perceptions, or that it is not irreducible. Confer what I said on true and false ideas (A VI 4 1815).14

This passage brings together conclusions of various origins. The statement that “every perception is either confused or distinct” can indeed be found in the Meditations, if we understand “perception” as equivalent to “clear cognition”. But the ensuing subdivision implies an important doctrinal change. In the Meditations, a “distinct concept” could be two things: Either a concept which can be the object of a nominal definition, or a concept of which no definition can be given, but which is immediately

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distinct, without any enumeration of its marks. The latter was the privilege of simple concepts, which are “the marks of [them]selves”, that is, of concepts that are “irreducible, and to be understood only through themselves and which therefore lack requisite marks” (A VI 4 587; my emphasis).15 The doctrinal alteration which appears here consists in merging both the distinct concepts composed of confused ones, and the concepts then considered as simple, under the same, doubly negative qualification “non irreducible”. This amounts to eliminating the latter category, by putting in the place that these concepts occupied in the hierarchy of cognitions a category of concepts simply described as still analysable. The former opposition between composed and simple concepts is replaced by a distinction between two types of composites. We have, therefore, no “distinct primitive notions”. It was a specific feature of the Meditations to have first mentioned that type of concepts at their place in the hierarchic classification of cognitions, and delayed to the fourth paragraph the question whether “men will ever be able to carry out a perfect analysis of concepts, that is, to reduce their thoughts to the first possibles or to irreducible concepts, or (what is the same thing) to the absolute attributes of God themselves” (A VI 4 590).16 In the notes to Malebranche’s Search after Truth, Leibniz simply assumes the negative answer to that question. This amounts, for him, to giving up any intuitive element in finite knowledge, or, in Cartesian terms, any “pure intellection”.

1.4 Intuition as Redundant And yet, we are not done with the occurrences of “intuition” in the Hanover period. But before we come to the last two, let us point out that no mention of that type of cognition is to be found where we should have expected it, had it actually been an original mode of apprehension of the possibility of notions: In the fourth paragraph of the Meditations, where Leibniz proceeds to expose the proper ways of assessing that possibility. Among them, the most perfect is defined in these terms: “Whenever our cognition is adequate, we also have an a priori cognition of possibility” (A VI 4 590; my emphasis).17 If adequate cognition is granted that prerogative, the hypothesis of an “intuitive” cognition appears redundant. As a matter of fact, if the ideal of adequate cognition were realized (so far our knowledge of numbers provides the only available specimen of it), that is, if we thought and wrote with characters which would make the composition of notions immediately evident, there would hardly remain any difference between adequate and intuitive knowledge. For, just as “the characters of arithmetic [. . .] express the genesis of numbers”, it would be enough to consider attentively the character expressing some concept for the simpler concepts into which it is resolvable to come to our minds immediately. Hence, the resolution of the concept corresponding exactly to the resolution of the character, at the simple sight of the characters adequate notions would present themselves to our minds without effort on our part (A III 2 451).18

That the notion of cognitio intuitiva plays no part of its own in Leibniz’s theory of the foundation of knowledge is finally made clear by the only other passage where

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it appears next to a mention of cognitio adaequata, in the contemporary De Synthesi et analysi universali: Those real definitions are most perfect [. . .] from which the possibility of the thing is immediately apparent without presupposing any experiment or the demonstration of any further possibilities – that is, when the thing is resolved into mere primitive notions understood in themselves. This cognition I usually call adequate or intuitive (A VI 4 542-43; my emphasis).19

This explicit equivalence confirms that the hierarchy of cognitions in the Meditations leads to splitting in two what was presented, in a different context, as one and the same mode of cognition, reached when the analytical process is carried out to its end. Isolating intuitive cognition had then, in 1684, one specific, polemical purpose: Its hypothetical definition as the simultaneous and pre-symbolical grasp of notions amounted, for Leibniz, to exposing to his adversaries the reasons why such cognition was beyond our finite understandings. Finally, it is in the light of the equivalence set between adequate and intuitive cognition that we should read the last occurrence of intuitive cognition in the Hanover period, in the 1688 Specimen inventorum de admirandis naturae generalis arcanis. This text contains a close paraphrase of the enigmatic beginning of the Meditations’ third paragraph (cf. above 1.2): “As to the ideas of things, we do not think them except in so far as we apprehend their possibility intuitively” (A VI 4 1617).20 Just as in the De Synthesi, this mention of intuitive cognition comes here at the end of a development on the different types of real definitions, a priori or empirical. It must therefore be granted that Leibniz does tend (if only in those two occurrences) to call “intuitive” the type of apprehension of possibility which we obtain by the establishment of the most perfect real definitions, corresponding to the adequate cognition of a notion.21 Yet it cannot be granted that “in arithmetic, definitions express an intuition of the content of the ideas” (Fichant 1998: 304; my emphasis): No occurrence of that term allows us to consider intuition as a specific type of cognition, independent from symbolical mediations and preceding them. Leibniz’s tendency to call “intuitive” the type of cognition produced by a priori real definitions will reappear in Book IV of the New Essays. It will interfere there with the description of the way in which axioms are known to us. For, determined as he is there to defend the certainty and usefulness of these propositions, Leibniz remains anxious to bar the “way of ideas”.

2 The New Essays on Human Understanding (4.2.1): A New Concept of Intuition 2.1 Twenty Years Later: Changes in Vocabulary and Permanence in the Doctrine of Ideas How is it, then, possible that intuitive cognition should reappear in the New Essays? In order to set the problem properly, it must be emphasized that, surprising as it

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may seem (considering, for instance, the important differences between the 1684 text and the 1702 letter “on what is independent of sense and matter”), Leibniz receives and confronts Locke’s doctrine of the understanding on the basis of just the same epistemological positions as defined in the Meditations. This is made clear by his first reactions to that work, set down in the “Remarks” written between 1695 and 1697 (A VI 6 3–9). Leibniz himself claims this continuity, referring his reader to the Meditations, particularly for his theses on the knowledge of possibility.22 Unsurprisingly, no mention is made there of an intuitive apprehension of notions or ideas.23 It is therefore no wonder that it should also be absent from the 1702 letter mentioned above, which associates a new version of the classification of cognitions with a typology of faculties (GP 6 491–499), as well as from Book II of the New Essays, where that classification takes the form of a typology of “ideas” (chapters 29 to 32). There, again, the definition of the various types of ideas begins with an explicit reference to its 1684 precedent (A VI 6 254).24 The absence of the theme of intuitive thought is even more conspicuous in Book III, chapter 4. Nowhere before has Leibniz been so clear in claiming the permanent validity of his 1684 positions.25 Still, this reference follows a reminder of the distinction between the notions or ideas that are “simple from our point of view” and those hypothetically characterised as “simple in themselves” (apart from the question whether we do have such ideas or not). Whilst the apprehension of these ideas could only be intuitive in the Meditations, it is now simply called “clear and distinct”.

2.2 A New Lockean Name for the Immediate Certainty of Primary Propositions The reappearance of the terms “intuition” and “intuitive knowledge” in Book IV, chapter 3, must therefore be accounted for by Locke’s own use of these expressions in the corresponding chapter of his Essay, in order to designate knowledge in its most fundamental sense: Philalethe. § 1. Knowledge is intuitive when the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other. In this, the mind is at no pains of proving or examining the truth. [As the eye sees light, so] the mind perceives, that white is not black, that the circle is not a triangle, that three [is] one and two (A VI 6 361).26

Leibniz does not contest here Locke’s conception of knowledge as bearing on the relation between two ideas, nor does he dispute the use of the term “intuitive” to denote the immediacy and utmost certainty proper to the apprehension of such propositions as the one cited. His purpose, throughout the long development which occupies the next five and a half pages in the Akademie edition, is inspired by the one “remark” that he had made, in 1695–1697, on Locke’s Book IV: “It seems to me that the Axioms are not given there quite as much consideration as they deserve” (A VI 6 8).27 We are, therefore, in a context completely different from

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the Meditations. For Leibniz now proceeds to a dichotomous classification, not of notions or ideas, but of those “truths” or propositions which exemplify what he takes to be the only true “primitive principle” of rational knowledge: “the axiom of identity, or (what is the same thing) the principle of contradiction”(A VI 6 4).28 Those propositions, in which a term is predicated of itself (or negated of its opposite), are for him, together with the “primary truths of fact”, the objects of such an immediate and indubitable knowledge. It must be noted that Leibniz inserted, in the passage from the Essay quoted in Philalethe’s opening speech, an analogy between the way in which we know such propositions and sense perception (see the quotation above). So, it appears that Leibniz is adopting here a Lockean expression to designate what, for him, has always been the type of cognition proper to axioms: sense. Rather than with the 1684 Meditations, this chapter of the New Essays is then to be related to this text of the Parisian period: The only proposition whose negation implies a contradiction, without it being demonstrable, is one that is formally identical. This is expressly said therein, so it cannot be demonstrated; to demonstrate is to show by reason and consequences. This can be shown therein to the eye, so it cannot be demonstrated. The senses show that ‘A is A’ is a proposition whose negation, ‘A is not A’ implies a contradiction formally. Now, what the senses show is indemonstrable (A VI 3 435).29

A later reflection on the foundation of truth, common to human and divine knowledge, accounts for the cognition of identical propositions in which the terms are interpreted: As long as we have eyes and a memory, we can judge about contradiction. For it is enough that the subject and the predicate of the contradictory proposition be identical, that is: that the words and the meaning of the words be the same in both places. Whether the words are the same, the eyes will judge; whether the same thing is understood in both occurrences, our memory or conscience will tell us (A VI 4 2216).30

It is, therefore, the combined operations of those two faculties which receive here the name “intuition”.31 Leibniz is now going to show that this type of knowledge takes place whenever we apprehend certain truths, which belong to the infinite class of the possible variations on the principles of identity and contradiction.

2.3 Possibility and identity The passage on which Fichant based his interpretation is the concluding paragraph of this development of “identities”. We can now examine it more closely: As for the proposition that three is equal to two and one, which you also adduce, sir, as an example of intuitive knowledge, I will tell you that this is nothing but the definition of the term three. The simplest definitions of numbers are constructed like this: Two is one and one; Three is two and one; Four is three and one; and so on (A VI 6 366).32

This argument will reappear at the beginning of chapter VII, § 10, and this time Leibniz will make his point more explicitly: The proposition in question does nothing but predicate the definiens of its definiendum, and is, therefore, simply an

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instantiation of the identical maxim “a thing is equal to itself”. Yet an incidental consideration diverts him, in our passage, from reaching that conclusion immediately: If that proposition (as all those predicating a definiens of the definiendum) can be considered as an identical proposition, subject to intuitive knowledge, it is because the definition involved is a real definition of the kind which shows, immediately and a priori, that the concept defined is possible. This is what Leibniz will mean, a few lines later, with the expression “adequate definition”. That condition for the validity of his argument will become clear if we consider a different example: The same would not be true of the proposition: “God is the being of which a greater cannot be thought”. And yet it is the traditional definition on which Anselm had based his demonstration of the existence of God (for an explicit reference to it, see A VI 4 541). But, as Leibniz has on many occasions pointed out, the compatibility of the ingredients of the definiens does not appear here ex terminis. This definition is therefore only a nominal definition, one among the many that can be given of the same object (A VI 6 267). On the contrary, an a priori real definition, which in the Discourse on Metaphysics Leibniz also calls “essential” (AVI 4 1569), entails definitional identity in its strongest sense. And such is the meaning of the restriction introduced at this point: “It is true that a hidden assertion is involved, as I have already noted, namely that these ideas are possible [. . .]”. Locke’s last example of a proposition known intuitively can only be considered as an instantiation of the principle of identity because the predicate is the real definition of the subject. Now the criterion or mark of such a definition is, as Leibniz has noted on a number of occasions, that “every real definition must contain at least the affirmation of some possibility” (A VI 4 542).33 But there comes the point in which lies all the difficulty of this passage. To his examples of “the simplest definitions of numbers”, Leibniz now adds another parenthetical consideration, and, instead of justifying it, generalizes it in the next sentence: It is true that a hidden assertion is involved, as I have already noted, namely that these ideas are possible and this is known here intuitively. Thus definitions can be said to include intuitive knowledge in cases where their possibility is straight away apparent (A VI 6 366–367).34

This double mention of intuitive knowledge can hardly be accounted for by anything that was said about it since the beginning of this chapter. Knowing that “these ideas (namely two, three, four . . .) are possible” amounts to grasping the elements whose combinations constitute their definitions (one and one, two and one, three and one) as compatible. In order for some “intuitive knowledge” to take place here (in keeping with the acceptation of this knowledge defined in this chapter, that is, as the apprehension of an identity or a contradiction within a proposition), there would need to be some predicative structure involved in those definiens expressions. Leibniz is well aware of it, since he first wrote that those definitions include “intuitive or identical knowledge”. He then erased the second adjective. For, obviously, the definiens expressions contain no such structure; they are conjunctions of terms, not propositions.35 At that point, and in the next sentence, the state of the manuscript shows the tensions with which Leibniz is struggling: The signification of “intuitive”

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knowledge which has, so to say, surfaced here, is the one once assumed in the De Synthesi, where intuitiva had appeared as a synonym of adaequata, to qualify the type of knowledge produced by the most perfect real definitions (see above § 1.4). Possibly prompted by the same sequence of thoughts as in that text, where the presence of an affirmation of possibility in real definitions had first been stated, Leibniz revives here the equivalence between the two terms, and writes, in a first version: “In this fashion all adequate definitions give [and then, in a second version, “contain”] intuitive knowledge”.36 But that is clearly inconsistent with the doctrine of intuition exposed so far. So he strikes it out, and finally writes: “all adequate definitions contain primary truths of reasons, and hence intuitive knowledge”. Can that “hence” be accounted for? It would imply that, at the foundation of knowledge, lies an apprehension of the possibility of notions or ideas (incomplex terms) based on the intuitive perception of the identity in propositions (complex terms). This is not something that Leibniz’s statements on the relations between terms and propositions seem to allow. Of course, he has noted a number of times, since the Meditations period, that “our ideas contain judgements” (GP 1 384, my emphasis), but what he had in mind then was precisely the “tacit assertion of possibility” entailed by real definitions, whether a priori or empirical (A VI 6 356).37 So, the primary truths of reason which he now claims to be contained in adequate definitions must not be mistaken for those second-order “judgements”, which obviously are not identical propositions, and are therefore not the object of an intuitive apprehension, but only result from the perception of possibility, as its effect. We are not done yet with the difficulties of this paragraph. Its last sentence contains one more puzzle, as Leibniz returns to a more general level of exposition: “Finally we can say in general that all the primary truths of reason are immediate with the immediacy of ideas”38 . The immediacy of these truths now seems to be accounted for in turn by the “immediacy of ideas”, as if there was, at the most fundamental degree of knowledge, some circularity between the evidence of the complex and of the incomplex, of propositions and ideas, or between the apprehension of a form and that of a notional content. This final invocation of an “immediacy of ideas” is all the more surprising as we have seen that an identical (or a contradictory) proposition can relate very complex ideas, as well as uninterpreted signs. So what can Leibniz mean by “immediacy of ideas”? No other occurrence of that expression is to be found in the New Essays. But chapter 9 of Book IV does provide some additional explanation on the opposition between immediacy of ideas and of feeling: [T]he immediate awareness of our existence and of our thoughts provides us with the first a posteriori truths or truths of fact, i.e. the first experiences; while identical propositions embody the first a priori truths or truths of reason, i.e. the first illuminations. Neither kind admits of proof, and each can be called “immediate” – the former because nothing comes between the understanding and its object, the latter because nothing comes between the subject and the predicate (A VI 6 434).39

A remarkable asymmetry appears here. Whilst in the case of the “first experiences”, the immediate relation lies between the cognitive subject and that which he knows, in the case of the first a priori truths, the immediate relation lies within

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the proposition itself, between the subject as one of its terms and the predicate as another. That “immediacy” is a logical relation, not a cognitive one.

3 Conclusion There is therefore no ground to invoke Book IV of the New Essays on Human Understanding as revealing a Leibnizian belief in some foundation of knowledge more original than the use of signs. The most fundamental elements of knowledge remain in the New Essays, just as they were at the time of the Meditations, real definitions – which Leibniz always considered to be “procedures by means of characters” (A VI 3 462) – and identical propositions. However, comparing his theory of signs with the tenets of modern formalism is likely to result in more difficulties than clarification. Except in some few specific occurrences, Leibniz’s references to cogitatio caeca or “suppositive thought” do not exclude that signs be interpreted. Even if there is, for him, a fictio verborum comparable to the fictio mentis pointed out by medieval nominalists, some representational content always comes along with the words.40 The question is, then, precisely whether this content has some correlate among the objective “possibilities” determined in God’s understanding. To ascertain this point, no other resort is available to us but the discursive procedure of analysis.

Notes 1. See also the conclusive paragraphs of a study first published in 1992: “Epistemologically speaking, the General Science was inseparable from the question of the idea” (now in Fichant 1998: 371). 2. Quoted by G´erard (2006: 125), who offers an illuminating presentation of the significance given to the Leibnizian themes of symbolic and intuitive cognitions by post-Kantian authors. 3. “Quoniam hodie inter Viros egregios de veris et falsis ideis controversiae agitantur, eaque res magni ad veritatem cognoscendam momenti est, in qua nec ipse Cartesius usquequaque satisfecit, placet quid mihi de discriminibus atque criteriis Idearum et cognitionum statuendum videatur, explicare paucis. Est ergo cognitio vel obscura vel clara; et clara rursus vel confusa vel distincta; et distincta vel inadaequata vel adaequata, item vel symbolica vel intuitiva: et quidem si simul adaequata et intuitiva sit, perfectissima est”. 4. The one exception is p. 587, where Leibniz writes: “I use words instead of the ideas that I have of these things [. . .vocabulis istis (. . .) in animo utor loco idearum quas de iis habeo]”. Idea is here taken as a synonym of notion, as Leibniz has done in the past (A VI 4 288). As we shall see, this is not the sense in which the Meditations are about “ideas”, in their following paragraphs (see Picon 2003). 5. “Ex his jam patet, nos eorum quoque quae distincte cognoscimus, ideas non percipere, nisi quatenus cogitatione intuitiva utimur”. 6. “Habemus ideas simplicium, habemus tantum characteres compositorum”. On the importance, and the difficulties of this text, see Dascal (1978: 180–84; 1987: 47–60), Mugnai (1976: 32–35; 2001: 38–40), and Picon (2005).

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7. The latter conception was defended by Arnauld and Nicole, following Descartes, who wrote: “By the name of ‘idea’, I understand that form of a thought, the immediate perception of which makes me conscious of that thought; so that I cannot express anything through words, as long as I understand what I say, without being thereby certain that the idea of what is signified by those words is in me [Ideae nomine intelligo cujuslibet cogitationis forman illam per cujus immediatam perceptionem ipsius ejusdem cogitationis conscius sum; adeo ut nihil possim verbis exprimere, intelligendo id quod dico, quin ex hoc ipso certum sit, in me esse ideam ejus quod verbis illis significatur]” (AT VII 160). This claim is Leibniz’s target just as much as Malebranche’s doctrine. This is confirmed by a passage of the Paraenesis de scientia generali . . .which in 1688 still promises to solve the “difficultati [. . .] cartesianae de ideis eorum de quibus loquimur” (A VI 4 973). 8. See, for instance, his correspondence with Eckard, and A VI 4 n◦ 142, De Analysi veritatis et judiciorum humanorum. 9. This makes clear that the historical model for intuitive thought, as it is defined here, is Thomas Aquinas’s doctrine of God’s knowledge as a scientia visionis (Summa theologiae, Ia p., q. 14). 10. “Of a distinct primitive notion, there is no other cognition than intuitive, while in most cases, the thought of composed notions is but symbolic [Notionis distinctae primitivae non alia datur cognitio, quam intuitiva, ut compositarum plerumque cogitatio non nisi symbolica est]” (A VI 4 588). 11. On this point, see the aporetic text De iis quae per se concipiuntur from 1677 (AVI 4 25–26), and the three successive versions of the 1679 letter to J. Vagetius (now in A II 1 768–774). 12. “De protonoematis simpliciter sive de his quae per se concipiuntur saepe cogitavi, quanquam enim putem difficile esse, ut tale quiddam ab hominibus distincte satis enuntietur, possumus tamen de illis ratiocinari, supponendo quasi ea enuntiassemus”. 13. See for instance, in the period of the composition of the Meditations, the Divisio terminorum ac enumeratio attributorum (A VI 4 n◦ 132): “[Attributes] that are simple according to the nature of things are those which are understood through themselves. ‘Being’ itself seems to be such an attribute, though it certainly is difficult for us to produce them. Now they are the first possibles, or positive Terms. Their possibility is immediately evident, from their mere intuition of them [Simplicia secundum rerum naturam sunt quae per se intelliguntur, tale attributum videtur esse ipsum Ens, et haec quidem a nobis distincte exhiberi difficile est. Sunt autem prima possibilia, seu Termini positivi, quos possibiles esse patet a priori, ex nuda eorum intuitione]” ( A VI 4 560). For the period of the New Essays, see below note 22. 14. “Non puto ullam esse intellectionem puram, sine aliquo responsu in corpore. Videtur omnis perceptio esse confusa vel distincta; et distincta vel composita ex distinctis, vel non irresolubilis. Videantur quae dixi de veris et falsis ideis”. 15. “Datur tamen et cognitio distincta notionis indefinibilis, quando ea est primitiva sive nota sui ipsius, hoc est cum est irresolubilis ac non nisi per se intelligitur, atque adeo caret requisitis”. 16. “An vero unquam ab hominibus perfecta institui possit analysis notionum, sive an ad prima possibilia ac notiones irresolubiles, sive (quod eodem redit) ipsa absoluta Attributa Dei, nempe causas primas atque ultimam rerum rationem, cogitationes suas reducere possint, nunc quidem definire non ausim”. 17. “Et quidem quandocunque habetur cognitio adaequata, habetur et cognitio possibilitatis a priori; perducta enim analysi ad finem, si nulla apparet contradictio, utique notio possibilis est”. 18. “Charactere alicujus conceptus attente considerato statim conceptus simpliciores in quos resolvitur menti occurrent: unde quoniam resolutio conceptus resolutioni characteris ad amussim respondet, characteres tantum aspecti nobis, adaequatas notitias, sponte et sine labore ingerent in mentem”. 19. “Porro ex definitionibus realibus illae sunt perfectissimae, quae omnibus hypothesibus seu generandi modis communes sunt, causamque proximam involvunt, denique ex quibus possibilitas rei immediate patet, nullo scilicet praesupposito experimento, vel etiam nulla supposita demonstratione possibilitatis alterius rei, hoc est, cum res resolvitur in meras notiones primitivas per se intellectas; qualem cognitionem soleo appellare adaequatam seu intuitivam”.

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20. “[I]deas quoque rerum non cogitamus nisi quatenus earum possibilitatem intuemur”. 21. An alternative reading of this passage is possible. In article 25 of the Discourse on Metaphysics, the act of “perceiving ideas” is reformulated in Malebranche’s vocabulary: Leibniz now defines the conditions for our “seeing [a] whole idea”. These can be, as in the Meditations, that our cognition should be intuitive, or, alternately, that it should merely be “clear”, that is, simply empirical, provided that it is not confused. This opening to empirical cognition can only be accounted for by the fact that what this polemical passage really is about is the assessment of possibility: the two cases in which we can claim to “see the whole idea” correspond to the two main types of real definitions distinguished in the precedent article (see Picon 2003: 126–127). Similarly, the “nisi quatenus earum possibilitatem intuemur” of the Specimen inventorum, concluding a passage which reminds that empirical causal definitions must also be considered as “real”, can be understood as referring to both types of real definitions, not just essential ones. 22. “As to ideas, I gave some account of them in a short essay printed in the Leipzig Acta Eruditorum, in the month of November 1684 p. 537, under the title: Meditationes de Cognitione, Veritate, et Ideis. And I wish that Mr. Locke had seen it [. . .]. Now, the possibility of ideas is shown either a priori through demonstrations, by means of the possibility of other, simpler, ideas; or a posteriori through the experiences. For what is can only be possible. But primitive ideas are those whose possibility cannot be demonstrated, and which are in fact the very attributes of God [Quant aux id´ees, j’en ay donn´e quelque e´ claircissement dans un petit e´ crit imprim´e dans les Actes des savants de Leipzig au mois de Novembre 1684 p. 537, qui est intitul´e: Meditationes de Cognitione, Veritate, et Ideis: et j’aurais souhait´e que M. Locke l’eˆut vu et examin´e [. . .]. Or la possibilit´e des id´ees se prouve tant a priori par des d´emonstrations, en se servant de la possibilit´e d’autres id´ees plus simples qu’a posteriori par les exp´eriences; car ce qui est, ne saurait manquer d’ˆetre possible. Mais les id´ees primitives sont celles dont la possibilit´e est ind´emontrable, et qui en effet ne sont autre chose que les attributs de Dieu]” (A VI 6 5). 23. A considerable change between the two periods obviously affects Leibniz’s vocabulary: In his debates with Locke, he adopts his acceptation of the term “idea” (which is compatible with his own vaguer use of it, as indicated above, note 4). However, this means that it is no longer possible for him to maintain the very clear distinction, set from the third paragraph of the Meditations onwards, between notions and ideas, a distinction corresponding to the one between “thinking” – as in “not all the things about which we think are possible [non omnia de quibus cogitamus esse possibilia]” – and “conceiving” – as in “the Cartesians need to show that [the most perfect Being] can be conceived [a Cartesianis tamen demonstrari debere, quod tale Ens concipi possit]” (both instances are from the same letter to Eckhard in A II 1 312, now 487). 24. The rest of chapter 29 will establish, against Locke, the distinction between a clear and a distinct idea, in accordance with their definitions in the Meditations. Last, the adequate idea will be dealt with in Chapter 31, there again after an opening reference to the Meditations: “I once defined ‘adequate idea’ (or ‘perfect idea’) as one which is so distinct that all its components are distinct; the idea of a number is pretty much like that [J’ay d´efini autrefois ideam adaequatam (une id´ee accomplie) celle qui est si distincte que tous les ingr´edients sont distincts, et telle est a` peu pr`es l’id´ee d’un nombre]” (A VI 6 266). The translations of my quotations from the New Essays are taken from R&B. 25. “In my little essay in the Acta of Leipzig you will find the groundwork of a good part of an account of the understanding, set out in summary fashion [Vous trouverez dans ce petit Essai, mis dans les Actes de Leipzig, les fondements d’une bonne partie de la doctrine qui regarde l’entendement expliqu´ee en abr´eg´e]” (A VI 6 296). 26. “La connaissance est donc intuitive lorsque ‘l’esprit aperc¸oit la convenance de deux id´ees imm´ediatement par elles mˆemes sans l’intervention d’aucune autre. En ce cas l’esprit ne prend aucune peine pour prouver ou examiner la v´erit´e. [C’est comme l’oeuil voit la lumi`ere, que] l’esprit voit que le blanc n’est pas le noir, qu’un cercle n’est pas un triangle, que trois [est] deux et un”. I am maintaining here (and adding in the French original) the quotation

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29.

30.

31.

32.

33. 34.

35. 36. 37.

38. 39.

M. Picon marks and brackets used by R&B to indicate the quotations from Locke’s Essay and Leibniz’s interpolations. “Il me semble que les Axiomes y sont un peu moins consid´er´es qu’ils ne m´eritent de l’ˆetre”. “In my opinion, therefore, nothing is to be considered as a primitive principle, except the experiences and the Axiom of identity, or (what is the same thing) of contradiction, which is primitive, since otherwise there would be no difference between true and false [Mon opinion est donc qu’on ne doit rien prendre pour principe primitif, si non les exp´eriences et l’Axiome de l’identicit´e ou (qui est la mˆeme chose) de la contradiction, qui est primitif, puisque autrement il n’y aurait point de diff´erence entre la v´erit´e et la fausset´e]”. “[L]a seule proposition dont le contraire implique contradiction, sans qu’on le puisse d´emontrer, est l’identique formelle. Cela se dit express´ement l`a-dedans, donc cela ne s’y peut pas d´emontrer; d´emontrer: c’est-`a-dire faire voir par la raison et par cons´equences. Cela s’y peut montrer, a` l’œuil, donc cela ne s’y peut pas d´emontrer. Les sens font voir que A est A est une proposition dont l’oppos´ee, A n’est pas A, implique contradiction formellement. Or ce que les sens font voir est ind´emontrable”. “Si habemus oculos et memoriam possumus etiam judicare de contradictione. Nam saltem requiritur ut idem sit subjectum et praedicatum propositionis contradictoriae, id est, ut eadem sint utrobique verba et idem verborum saltem sensus. An eadem sint utrobique verba judicabunt oculi, an idem utrobique per verba intelligamus, memoria sive conscientia nostra nobis dicet”. That “intuition” is, in the New Essays, the new name for cognitive functions that used to be attributed to “sensus” in Leibniz’s previous writings is confirmed by one other occurrence of that term (among the very few contained in his entire works) in the Remarks: “It is very true that we know our own existence by an immediate intuition [Il est tres vray, que nous connaissons notre existence par une intuition imm´ediate]” (A VI 6 8). Now, existence had always been, since Leibniz’s early writings, the proper object of sense apprehension: “Existence is the sensibility of a thing [Existentia est alicujus sensibilitas]” (A VI 1 457). Even if we need to be cautious about Leibniz’s varying uses of this term, there never is any overlapping between them and the acceptation of intuitive cognition defined in the Meditations. “Pour ce qui est de cette proposition, que trois est autant que deux et un, que vous all´eguez encore, Monsieur, comme un exemple des connaissances intuitives, je vous dirai que ce n’est que la d´efinition du terme trois, car les d´efinitions les plus simples des nombres se forment de cette fac¸on: Deux est un et un, Trois est deux et un, Quatre est trois et un, et ainsi de suite”. “[P]atet omnem realem definitionem continere affirmationem aliquam saltem possibilitatis”. See also GP 1 384, C 538, A VI 6 356. “Il est vrai qu’il y a l`a-dedans une e´ nonciation cach´ee, que j’ai d´ej`a remarqu´ee, savoir que ces id´ees sont possibles: et cela se connaˆıt ici intuitivement, de sorte qu’on peut dire, qu’une connaissance intuitive est comprise dans les d´efinitions lorsque leur possibilit´e paraˆıt d’abord”. As Leibniz puts it: “[D]efinitions are not truths, but explanations of terms [. . .exclusis definitionibus, quae non sunt veritates sed explicationes Terminorum]” (C 538). “Et de cette mani`ere, toutes les d´efinitions ad´equates (1) donnent (2) contiennent des connaissances intuitives”. The permanence of Leibniz’s interest for this point is confirmed by a definitional study composed in connexion with his correspondence with Des Bosses: “[E]very incomplex term can be considered as involving something complex, in as much as it affirms [its] possibility [Hinc patet etiam quomodo omnis Terminus incomplexus concipi possit ut involvens aliquid complexi, quatenus affirmat possibilitatem ]” (GP 2 472). “Enfin on peut dire en g´en´eral que toutes les v´erit´es primitives de raison sont imm´ediates d’une imm´ediation d’id´ees”. “[L]’apperception imm´ediate de notre Existence et de nos pens´ees nous fournit les premi`eres v´erit´es a posteriori ou de fait, c’est a` dire les premi`eres Exp´eriences, comme les propositions identiques contiennent les premi`eres v´erit´es a priori, ou de Raison, c’est a` dire les premi`eres

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lumi`eres. Les unes et les autres sont incapables d’ˆetre prouv´ees et peuvent estre appell´ees immediates; celles-l`a, parce qu’il y a immediation entre l’entendement et son objet, celles-cy, parce qu’il y a immediation entre le sujet et le predicatum”. 40. See for instance A VI 1 551 and A II 1 435–436 (now A II 1 664).

References Dascal, M. 1978. La S´emiologie de Leibniz. Paris: Aubier. Dascal, M. 1987. Leibniz. Language, Signs and Thought. Amsterdam: John Benjamins. Fichant, M. 1992 Leibniz et l’exigence de d´emonstration des axiomes: “La partie est plus petite que le tout”. Revista Latinoamericana de Filosof´ıa 17(1): 43–82. Fichant, M. 1994. Les axiomes de l’identit´e et la d´emonstration des formules arithm´etiques: “2 + 2 = 4”. Revue Internationale de Philosophie 48(2): 175–211. Fichant, M. 1998. Science et m´etaphysique dans Descartes et Leibniz. Paris: Presses Universitaires de France. G´erard, V. 2006. “Le bruit des id´ees”: Connaissance intuitive et connaissance symbolique chez Leibniz et Husserl. In K. S. Ong-Van-Cung (ed), La Voie des id´ees ? Le statut de la repr´esentation (XVIIe` me -XXe` me si`ecles). Paris: CNRS-´editions, pp. 125–139. Husserl, E. 1956. Erste Philosophie (1923–1924). In Husserliana, vol. VII. The Hague: Nijhoff. Mahnke, D. 1924. Leibniz und Goethe. Die Harmonie ihrer Weltansichten. Erfurt: Kurt Stenger. Mugnai, M. 1976. Astrazione e realt`a. Saggio su Leibniz. Milano: Feltrinelli. Mugnai, M. 2001. Introduzione alla filosofia di Leibniz. Torino: Einaudi. Picon, M. 2003. Vers la doctrine de l’entendement en abr´eg´e: e´ l´ements pour une g´en´ealogie des Meditationes de cognitione, veritate et ideis. Studia Leibnitiana 35(1): 102–132. Picon, M. 2005. L’exp´erience de la pens´ee. D´efinitions, id´ees et caract`eres en 1675. In D. Berlioz and F. Nef (eds), Leibniz et les puissances du langage. Paris: Vrin, pp. 179–199.

Part IV

Law

Chapter 14

Leibniz: What Kind of Legal Rationalism? Pol Boucher

In the notes of the De Conditionibus, the Doctrina Conditionum and the De Casibus Perplexis, Leibniz quoted the works of a great number of his predecessors,1 in keeping with the custom of the Leipzig Faculty of Law. By so doing, he followed a tradition of rational analysis of law combining casuistry and classification. However, he did this in an original way since his intention was not to base his own positions on both the authorities of mos italicus and romano-saxonic trends, but, on the contrary, only to retain within these the unquestionable conclusions that we can draw from the standpoint of a theory of law. He therefore immediately brought to light the difficulty we experience when we try to define the specificity and the contents of a rational process aiming to supplement or to rectify a tradition which is already intrinsically rational.

1 The “Axiomatisation” of Law We know that the tradition Leibniz follows is the late scholastic one, where the influence of Bartole was not forsaken in favor of those of the authors of legal humanism and the contractualists, because most of the scholastics and post-glossators process (i.e., studying of difficulties by the method of pro and contra,2 searching for the ratio legis and extending the solutions acquired by means of classification and deductive, inductive and analogical topics), remained topical in the romano-saxonic world. Consequently, defining the originality of Leibniz’s “method” would lead us to trying to locate the inflections or the ruptures for which he would be responsible, by comparing his academic works with all those who made, like him, an effort to study Justinian law in an “axiomatic” way or to analyze the problems of ordering creditors in saxon law. In other words, we must try to establish firstly an accurate relation between the De Conditionibus or the Doctrina Conditionum and some Dissertationes3 of the second half of the 16th century, and secondly, a connection between the De Casibus Perplexis and the works4 of the first half of the 17th century devoted to the safeties theory. P. Boucher Institut de I’Ouest, Droit et Europe, Rennes, France M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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This way of proceeding has the immediate advantage of highlighting the overlap of influences of which the Leibnizian work is the outcome. Indeed, the chronological examination of the Dissertationes of his predecessors shows that we imperceptibly go from a presentation inspired by glossators, where the main argumentation is framed by a set of marginal notes, to a more categorial and hierarchical presentation, similar to the one found in Leibnizian texts, and where a system of titles and subtitles written in capital letters allows the phases of the argumentation to be punctuated.5 Likewise, we pass here from an analysis of law stemming from post-glossators and focused on topics as instruments of judicial office, to a presentation of the legal system focused on the construction of more abstract categories. Lastly and more importantly, in both cases we have to deal with a search for certainty in judgement and determination of legal concepts, which takes the form of a systematic research of legal “axioms”. A first way of defining the originality of the Leibnizian undertaking would consequently be to consider it as a particuliar success in a wider endeavour of axiomatisation and rationalisation of law. However, two facts oppose such a solution: (1) the use of the word axiom by the lawyers of this time is often very vague; (2) the Leibnizian theory of legal conditions is not a true axiomatic. The first of these facts is evident when we study the legal works of the second half of the 16th century which tried to set out the principles of the law as axioms. These technical texts, often devoted to civil law, employ the word “axiom” in a very vague way. Thus, the anonymous treatise of 1547 entitled Axiomata legum ex receptis juris utriusque libris uses the word “axiom” to designate the following proposals relating to conditions: (1) “an absolute ablative forms a condition”, D.35.1.109; (2) “the acceptilatio cannot be done under condition”, D.46.4.4; (3) “a condition must be related to the future and not to the past or the present”, D.28.7.10; (4) “a condition is regarded as fulfiled when it ceases to exist for whoever seeks to fill it”, D.12.4.3 §.9; (5) “a condition must be fulfiled according to the specified form”, D.35.1.55; (6) “a condition is regarded as a cause”, D.12.1.37; (7) “when it is not dependent on the person who stands to benefit from it, that the condition is not fulfiled, it must be regarded as being fulfilled”, Sext, Rule 66; (8) “a provision made under a condition which will not exist, is considered as pure and simple, D.46.2.9”; (9) “this which will exist in any way is regarded as not left under condition”, D.28.5.50 §1; (10) “in the conditions of wills, one should consider the will more than the words”, D.35.1.101.

However, these statements, which are identical6 to those we can read in the De Conditionibus and the Doctrina Conditionum because they simply express the fundamental properties of conditions in Roman law, are not of the same nature. On the contrary, they differ since some of them (3, 8 and 9) simply give the definition of the condition and exclude it de facto from some legal mechanisms (2), while others state syntactic (1 and 5) or semantic rules of interpretation, which result in this last case, either from the incitative function of the condition (6), or from the nature of the suspensive event, or from the person of the conditionarius (4), or from that of the conditionator (7, 10). It would be the same with the work of P. Lambert, H. Albert and A. of Reyger, where the word “axiom” does not point to an

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undemonstrable proposition to be placed at the beginning of a deductive system, but to a proposal stating a legal property considered as fundamental and integrable in a rational system of explanation. But the best evidence of this fundamental inaccuracy is undoubtedly found in the 76 Dissertationes of the Axiomata sive enunciata Digestorum Juris Civilis Romani, because, in spite of their identity of title, style, intentions and references, 16 of them employ the word theses, 15 the word thema, 11 say propositiones, 7 say axioma, 3 use quaestiones, 2 employ conclusiones, 2 enuntiationes, 2 consectuaria, 1 assertiones, 1 parerga, and 16 do not employ a precise word when indicating formally identical statements, like the inference: if such a fact occurs, then such a sanction will or will not be applied, or, such a standard will or will not have worth. However, this inaccuracy is all the more remarkable as it appears in works of lawyers faithful to the principles of the mos italicus and who, above all, seem eager to ensure the solidity of their arguments by calling upon the two sources of rational need and doctrinal authority. As for the second, it can be regarded as paradoxical, since the hypothesis of a Leibnizian axiomatisation of substantive law seems to be based on three properties of his works on substantive law, in accordance with the requirements of an axiomatic system: (1) the reduction of the number of statements in the reorganisation of the contents of the De Conditionibus and the shift to the Doctrina Conditionum; (2) the construction of a theory of legal conditions by means of definitions and theorems; (3) the writing up of definition tables containing inclusions of concepts, i.e., potential series of arguments. However, two major reasons prevent us from interpreting the Leibnizian rationalism as an expression of an axiomatic thought which would form the system of positive laws by building the complex from the elementary, or the theorems from the definitions, by means of precise rules: (1) Although Leibniz expresses the theses of conditional law by combining definitions and theorems and although he uses the concept of rule in the De Casibus Perplexis, the concept of axiom is seldom used in his legal work and takes on different meanings. Indeed, it only appears on three occasions: (a) in question 13 of the Specimen quaestionum ex jure collectarum (axiom of Alphenus), to refer to the primarily logical principle according to which personal identity is to be defined by the permanence of the criteria for the species and not by the invariance of all the characteristics of an individual (i.e., the problem of partial description); (b) in chapter 22 of the De Casibus Perplexis where it refers to an application of transitivity to the questions of the order of powers; c) at the beginning of problem III of the De Arte Combinatoria devoted to the mathematical rule for calculating degrees of relationship (cf. Boucher 2005) for the determination of the authorized and prohibited marriages, where it is used to indicate theses whose obviousness is of a physical type (even if it presupposes metaphysical ideas). (2) The mere use of the word “axiom” is not sufficient in itself to constitute a deductive system (just as its absence does not imply the inexistence of such a system), because what matters above all is the order in which the statements are produced from theses and clearly worded rules. Relatively speaking, it is of minor interest that the “definitions” by which Leibniz constructs the system of conditional law in

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the De Conditionibus and the Doctrina Conditionum contain both authentic nominal definitions and true normative proposals taken as a base of the system, since the fundamental requirement is that any theorem is obtained only with the “definitions” and theorems that are prior to it. It is also of minor interest that the passage from the De Conditionibus to the Doctrina Conditionum comes with a reduction of the number of definitions and theorems (80 definitions instead of 160 and 70 theorems instead of 375), because this reduction only proves limited means and not the disuse of a deductive process. What is, however, of interest is that he uses incomplete statements and circular demonstrations, since he thus brings into question the very idea of an axiomatic construction. Indeed, let us consider the case of the fragmentary statements which appear from theorem 1 of the Doctrina Conditionum when it is a question of proving that “the condition implies the conditioned”, using the definitions 4, 5 and 6 of the words condition, conditioned and implication. The demonstration is as follows: “should the condition be true, the conditioned is true by def.3. Consequently, it implies this by def.6”. However, definitions 3 and 6 are the following incomplete statements: [3] “conditionality which says this at least: if the first partial proposal, or”; [6] “the implication. However the negative connexion is called”. In themselves, these “definitions” are devoid of meaning and do not allow their aims to be achieved, namely, the ratio condition/conditioned for [3] and the implication for [6]. Conversely, they have a meaning if we apply to them the definitions which supplement them; in other words, if we connect them to those which precede and follow them. But we then obtain a statement equivalent to theorem 1 since we have the sequence: [def.3] “[. . .] if the first partial statement, or”, [def.4] “condition [. . .] is true [. . .]”, [def.5] “the second, or conditioned [. . .] is also true and we say that this connexion is affirmative, in only one word we call it”, [def.6] “the implication [. . .]”. Thus, the difficulty which the existence of incomplete statements in the Leibnizian presentation entails does not result here from a departure from the deductive order (since theorem 1 uses only words previously defined), but from the legal complexity of the concept of condition which makes it impossible to give it a definition which does not include at the same time the concepts of conditioned, implication and suspension. Indeed, as a (suspensive) condition is “a future and uncertain event which suspends the transmission of a right”, dividing the indissociable components of this legal modality in order to state them firstly in necessarily incomplete definitions and to bring them together afterwards in a synthetic statement (called a theorem) that says nothing but what was already necessary to know to state the definitions, is completely opposed to the linear character of the axiomatic method. Of course, the importance attached to the principle of substitution definiens/definiendum in the demonstration of a great number of theorems is in the spirit of this method, but all the difficulty is precisely due to the fact that it can only be a large number and not their entirety, because the very contents of the concept of legal condition in its ratios with the conditioned and the suspensive event cannot be stated in a strictly linear succession of propositions. Besides, the best evidence is in the two following facts: (1) the expression of the functional relations of opposition and co-variation which link condition, conditioned, date, implication and suspension,

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only becomes really systematic by dropping the series of theorems in favour of a matrix representation, similar to that used for the combinatorials of ontic and deontic modalities (Elementa juris naturalis; A VI 1 125); (2) the De Conditionibus, i.e., the Leibnizian text which appears the most in line with the requirements of an axiomatic, contains 60 circular demonstrations. But this anomaly, which cannot be interpreted as an improbable negligence of the minimal requirements of a deductive system, is clearly explained as soon as we examine the architecture of the circular demonstrations,7 since we see there that theorems 1 and 9, i.e., precisely those which define the relations of implication and suspension between the condition and the conditioned (in other words, the system of complementary statements), occupy the central place in the argumentation and are at the origin of the branching out of theorems leading to argumentative loops. Obviously, these characteristics do not imply that there is any error in reasoning (since we can prove a theorem in a latter part of the argumentation, and assume it in a former part when this part and the latter one indicate the rhetorical order and not the logical order of argumentation), but, on the other hand, there is well and truly a natural impossibility of linear exposure.

2 The Reasons of the Substantive Law If the originality of Leibnizian rationalism does not lie in the implementation of a true axiomatic, can we still seek it in the will to reduce the substantive law to a set of founding reasons? The answer to this question is inevitably complex, because the characteristic of Leibniz is to belong to the secular tradition of rational analysis which endeavoured to widen and to gradually bring up to date the standpoints of Roman law by combining casuistry and classification. For this reason, the great majority of authors whose authority he uses in his works of substantive law feature, like him, the two following characteristics: (1) they follow the methods of the jurisconsults, such as Paul or Papinian, who closely associated logical distinctions and legal considerations and they apply it to the organisation of jurisprudential decisions; (2) they generalise the way of reasoning that Roman law used when handling cases, the order of laws and their logical exposure. Thus, their work has as a common property, that of systematizing the particularities of positive laws and to present this unification in the form of Synopsis, Methodus or Axioma (Boucher, forthcoming). But what is less noticeable, because a comparison of the works has not been tried yet, is how Leibniz went beyond their limits in legal rationalisation and systematisation; contrary to what his uncle (the lawyer Johann Strauch) thought, Leibniz accomplished this feat not by the undeniable progress which he made in the use and the coordination of definitions and theorems, but by his way of justifying and of extending the reasons of law by connecting them to the specific reasons of other disciplines. To put it more precisely, it is not the use of a demonstrative procedure applied to law or the will for theorization which constitutes the originality of the Leibnizian rationalism, since they are features common to all his predecessors. It is the fact of wanting to put

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together in just one doctrine these two opposite processes – basing the reasons of law on a more general way of rationality, and integrating individual particularisms in the resolution of cases.

2.1 The Rationalisation of the Reasons of Law We can easily highlight this originality by comparing the works he devoted to the question of the concourse of creditors with those that his predecessors composed in the first half of the 17th century to achieve university aims similar to his. We find in doctorates such as those of Dasen, C¨oppelius, Gleissemberg or von Anderten, the same formal, methodological and doctrinal components as in the De Casibus Perplexis. And this similarity is so strong that it rules out considering the will to treat law by means of a collection of definitions as specifically Leibnizian. Indeed, two obvious facts run against this: (1) the method of all these authors involves firstly defining words such as concourse, creditor, priority, etc, then to connect them in the fundamental theses of contract law, prefiguring in this way what Leibniz himself would achieve in his essays; (2) the idea of reducing the demonstration to the substitution definiens/definiendum does not have after all anything original in the context of Roman law since the word demonstratio is understood with the meaning of a ‘designation’, and because this law uses the mechanism of the legal substitution whose function is to ensure the passing on of a heritage in the event of death of the main heir, by the appointment of a substitute who would replace him in the whole of his rights and duties.8 But what we do not discover in them is the will of logical generalisation which characterises Leibnizian thought and whose systematization of perplexed cases provides us with a good illustration. Indeed, his method is not merely to make a compilation of cases. On the contrary, he proceeds to their ordering using considerations which are not doctrinal (what his predecessors would have done), but firstly logical, since he classifies them by taking the number of parties in concourse as criterion. Thus, he obtains three fundamental types of legal circularities true to the number of involved parties: the self-emancipation of a slave, the priority between two parties, the classification of safeties between three competitors, and nothing would have forbade to him to seek cases of concourse between a higher number of parties, if their resolution were not finally obtained from the general pattern applicable to the cases involving three parties. Thus, the originality of Leibniz comes from the fact that concrete cases become, in his written work, the illustration of more fundamental logical patterns and that his theses are those of a logician whose objective is to express the generality of the structures implied in the diversity of substantive law mechanisms, whereas those of his predecessors are equivalent to statements worded by pure lawyers, wishing only to report on the data of positive legislation. Of course, he remains faithful in a way to the rationalist principles of the supporters of the ratio scripta, as well as to the classifying and defining activity of the post-glossators, but at the same time he goes further than their limits when he clarifies the properties of a more general law where the concrete provisions are only one particular case of what is possible.

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This point, which could easily be demonstrated using Leibnizian works devoted to conditional law and the concourse of safeties, can be better illustrated by paragraph 12 of the chapter “use of problems 1 and 2” of the De Arte Combinatoria, which associates combinatory and logical possibility in the generalisation of a positive law stated in the Digests (D.17.1.2; repeated in Inst.3.26). Indeed, the text of D.17.1.2 shows the importance given by the Roman legislator to the systematization of concrete cases, since Gaius enumerates five types of possible mandates and associates a concrete example to each one. There is a contract of agency (mandatum) contracted between us, either when I appoint you solely in my favour, or when it is in favour of others, or when it is in my favour and that of others, or when it is in my favour and yours, or when it is in your favour and that of others. Because if it is solely in your favour that I appoint you, the contract of agency is superfluous because no obligation results from it.

This classification obviously results from an incomplete combinatorial operation since the whole set of the contract of agency possibilities includes at the same time those which are stated here, and two others whose existence Gaius does not mention: The contract of agency in favour of the trustee and the contract of agency in favour of the three parties (the principal, the trustee and the third party). But it is precisely this that Leibniz underlines in his comment when he declares: In D.17.1.2 and Inst.3.26, the following division is proposed by the jurisconsult: we contract a contract of agency in 5 ways: in favour of the principal, [in favour of] the principal and the trustee, [in favour of] a third party, [in favour of] the principal and a third party, [in favour of] the trustee and a third party. From this division, we will arrive at another which is sufficient, in the following way: its justification is the aim, in other words, the person in favour of whom the contract of agency is done and there are three: the principal, the trustee and the third party. But the combinations of three things are 7 in number, [i.e.], three unary combinations which occur when the contract of agency is done in favour of only (1) the principal, (2) the trustee, (3) the third party. The binary combinations are equal in number: [in favour] of the principal and the trustee, [in favour of] the principal and the third party, [in favour of] the trustee and the third party. And there is only one ternary combination, namely: [in favour] at the same time of the principal, the trustee and the third party. Here, the jurisconsult rejects as being of no purpose the unary combination in which the contract of agency is done in favour of the only trustee, because it is more a piece of advice than a contract of agency. There remain consequently 6 types, but I do not know why they left 5 of them, neglecting the ternary combination (De Arte Combinatoria; A VI 1 177).

It can immediately be seen that this result is obtained, not in a semi-empirical way as in Gaius’ argumentation, but by a reasoning which simultaneously takes account of the legal reality represented by the practical uselessness of a contract of agency in favour of the trustee alone (because to appoint somebody to do something in favour of himself, without any obligation constraining him, amounts to request him to do it and not to appoint him), and of the logical necessity which leads to completing the cases of substantive law by those which are possible, although not considered by the Code. Moreover, it is obtained by way of table ℵ (De Arte Combinatoria; A VI 1 174) formulated in §.3 of Problem I, which is used to calculate the types of combinations between an indefinite number of elements. Thus, it is for two reasons that the contract of agency of substantive law can be regarded as a particular translation of a more general property, and it is for this reason that its empirical definition

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must be completed by the data of pure reason. Indeed, the reasoning that Leibniz uses leads to the following conclusions: When three elements must be combined among or with themselves, the logical possibilities of combinations are 7; i.e., (in addition to the 8th case where none combine with any) 3 combinations of each one with itself ; 3 combinations of two statements ; and 1 combination of three statements . The number of “combinations” for the “exponent” 3 of table ℵ will be thus given by the formula in which the first factor, representing the number of combinations between no terms, is without practical interest, but where the last one is equivalent to one empirically possible case. Its legal non-existence is consequently the sign of a legislator’s oversight and not that of a logical impossibility (except if we estimate that a contract of agency should never be in favour of all parties because the law ratifies relations of egoistic interests, which are mutually exclusive). Nevertheless, in underlining in such a way the rational structure of concepts in order to better show their analogy, Leibniz might lead to a kind of reductionism, because to define the contract of agency as a combinatorics of relations between three parties can lead one to confuse all the legal devices which have this property in common in the same category, and to dilute the concept of contract of agency in a vague idea according to substantive law. The only manner of avoiding this indeterminacy, generated by such an abstract extension, was obviously to consider that the general formal criteria being used to define the contract of agency were to be completed by all the “circumstances” allowing one to differentiate it from formally identical, but empirically different elements. The integration of circumstances, i.e., individual particularisms, in the most abstract and the most general expression of the substantive legal provisions, became thus a need, which represents the second original feature of Leibnizian legal rationalism. But even here, he could make use of the secular juridico-logic tradition to find his own solutions.

2.2 The Insertion of Individual Particularisms in the Solution of Cases 2.2.1 The Contribution of Tradition While endeavouring to propose definitions of legal concepts, combining generality and distinctness, Leibniz was inevitably led to use in his own account the written works of the logician-lawyers of the 16th century who tackled this problem by means of various topics theories, and who were led to specify the complementary connections between description and definition. This issue, which will later find expression in Leibnizian works through the definition of the individual as a sum of predicates, is extremely complicated from a legal point of view since it requires the bringing together of theses concerning the joint use of definition, description and analogy, in a coherent doctrine. Indeed, if we consider the example of contracts, we see that the intent to depart from the strictness of the archaic formalism, historically expressed through a progressive acceptance

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of more flexible modes of agreements. The implied and innominate contracts thus gradually appeared alongside formal contracts, by way of an analogical extension of the latter properties. The aim was obviously to adapt legal institutions to the informal diversity of exchanges and at the same time to preserve the main characteristics of the first contracts. But from this point of view, the joint use of description, analogy and definition seemed perfectly justified since the first two allowed legal mechanisms to continually adapt with new empirical data, while the last guaranteed their stability. However, the difficulty was to reach this agreement between antinomic approaches and to harmonize the principles by which the transformation of law was favoured and those by which it was kept unchanged. Going from the Justinian principle that any definition is dangerous in law, but even so that some must be proposed in order to prevent its dilution in the multiplication of particularisms, logician-lawyers like Cantiuncula (died 1560), Everhardus (1482–1552), and Gammarus (died 1528), tried to harmonise description, definition and analogy by working out a theory of demonstration through the substitution of equivalents, which we find in Leibniz’s work, and through this by specifying the usual rules of logical laws within the framework of a topic. These ideas are clearly set out in the De modo disputandi ac rationandi in Jure of Gammarus (1522)9 by way of an argumentation distinguishing the essential reference of definitions and the accidental reference of descriptions, to better show how the generality of the former must be completed by the precision of the latter10 when it is a matter of distinguishing similar legal concepts such as contract and implied contract,11 which have a function of controlling exchanges in continuous transformation. For, it is not enough that the effects of these two devices are identical in a number of concrete situations in order to consider them as having the same general essence,12 just as it is not enough that the assignment of credit and the assignment of debt belong to the general category of transfer, in order to attribute them a shared essence. This conclusion is justified by the fact that the cause of a provision or an institution, i.e., its legal reason, must be distinguished from its empirical translation at a given time, because this depends on a limited number of people and circumstances which do not exhaust the whole of possibles. In short, as Cantiuncula said it in his Methodica dialectices ratio ad jurisprudentiam adcommodata: These circumstances have a function of introducing differences into the property, the obligation and all that is stated in laws. [Thus] the cause [(i.e., the legal intention corresponding to ‘why’)] changes the property. He who transfers his good to another according to a sale or a donation, makes the receiver an owner. But he who does it according to a ‘commodatus’ or an escrow, does not do the same thing, because the causes of these two transfers are not the same ones and because the first requires a complete transfer while the second does not, cf. the argument of C.4.6.6. The cause varies the obligation. Thus, he who promised because of an honest cause, is obliged; that which did it because of a dishonest cause, is not, law 26 of D.45.1 (Book 1, chap. 7, p. 160).

So, the evaluation of a legal reasoning implying definitions and descriptions meant distinguishing their respective extensions and measuring the possibility of their mutual substitution. These two requirements demanded in turn that the two following conditions be fulfilled: (1) to distinguish descriptions from definitions by

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underlining at the same time the fact that the principle of substitution definiens/ definiendum can be simultaneously applied to them, i.e., to highlight the fact that a reasoning can as well be applicable to essences as to accidents; (2) to list the cases in which we can conduct an analogical extension of legal concepts by gradually turning the definition into a description, i.e., to constitute a topic. The first condition was achieved by Gammarus when he enumerated the properties of the correspondence definiens/definiendum: (1) the defined thing is appropriate for all the elements for which the terms of the definition are appropriate; (2) the definition is appropriate for that for which the terms of the definition are appropriate; (3) the definite is not appropriate for that for which the definition is not appropriate; all that is said of the definition is also said of the definite (De loco a definitione, p. 13).

and then, when he indicated, as did Cantiuncula with the concept of “concrete accidents”,13 that a definition cannot replace a description when a decisive circumstance is not covered due to the generality of its contents: From where it follows that we are not wrong to say that a modern canonist is mistaken when he declares that a definition is good when it includes what occurs very frequently, even if it is not appropriate for certain cases included in it. However, the reasoning stated in D.4.3.1 objects to that. Because Servius had defined fraud as an operation intended to harm others and which consists in doing something and to simulate another. And Labeon protested against this definition because we find sometimes a fraud without simulation, even if a simulation generally takes place (De loco a definitione, pp. 12–13).

and finally, when he showed that the principle of definiens/definiendum substitution also applied to description, since it is a lexical equivalence in both cases: “We formulate here the rules which we stated above about definition, with this difference that we put ‘description’ where there was ‘definition’, and ‘described’, where there was ‘defined’ ” (De loco a descriptione, p. 15). As for the second, it ultimately represented one of the main aims of all the books similar to that of Everhardus (1613), which were devoted to the analysis and classification of “loci legales”. Indeed, a definition of the framework in which a legitimate analogical extension of legal concepts can apply presupposes a classification of jurisprudential arguments, when the sources of law are numerous and when the examination of the aims as well as the structure of the legal system become determining factors in the application or the prohibition of this extension. But, in this classification whose main themes are often equivalent to a tripartition of arguments according to whether they are deductive, inductive or analogical, the argument entitled “from the first to the last” takes an important place because it precisely allows a wider scope of a legal property by gradually extending it to contents increasingly foreign to its initial definition area. At the same time, it is true that this mechanism of concept extension is difficult to handle and that its advantages comes with some disadvantages. Indeed, it leads one to the standardisation of the kinds of concrete cases and to the rationalisation of their classification, while allowing to simplify the reasons of law by means of reasoning similar to that which Everhardus pointed out when he said:

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This argument is also used by Jason de Mayno in his comment of §.1 of the Institutes 4.6, in order to prove that the ‘dominium directum’ is acquired after an immemorial prescription, although, according to common opinion, one cannot acquire in a regular way by prescription, as a result of §.4 of D.43.20. In this way, an immemorial prescription is equivalent to a legal title, chapter 1 of the De praescriptionibus of the Sext, and has the value of a convention, as it is said in §.4. But a convention has the value of an agreement, beginning of D.13.5, and the ‘dominium directum’ is acquired from an agreement, as Balde put forward in his comment of the Authentic Nisi tricennale [of C.6.60] (Everhardus 1613: 728).

But it also gives rise to misleading legal generalisations when the legal reasons of the analogy are artificial or when the material differences between the situation firstly defined and that which is the subject of a description are such that their degree of resemblance finally disappears. Moreover, its handling is tricky because it contains an internal ambiguity. Indeed, the reasoning proceeding “from the first to the last” is of a transitive type and its effect is either to communicate a property through a succession of terms or to establish an order between them. But, in the first case, the argument makes it possible to lead to their equivalence and to the widening of the comprehension of the legal concept they express, while in the second, the aim is very different since the question is not any more to establish their equivalence, but indeed their inequality by way of a relation of order. But because this relation can take hold either on the differences in the comprehension of the terms connected by a system of inclusions (and then the argument is of syllogistic type), or on the positions they occupy in a more or less conventional hierarchy (the problem of norms and safeties hierarchy), or finally on a simple relation of partial similarity, it follows that the argument has a degree of certainty proportional to the material and/or legal nature of the connected terms. It raises therefore the question of the degree of similarity required in a series of material terms (since a relation of partial resemblance between n terms taken two to two does not imply that the first looks like the last if the series is important or if each time the similarity is fragmentary), and also the question of the degree of similarity required in a series of legal terms, since the very role of a fiction is to maintain the identity of form, in spite of the disparity of contents.14 Mastering the theoretical use of this argument therefore requires highlighting the relationship between the relation of order and the ratio legis. But it is precisely this that Everhardus did not manage to achieve. Indeed, he clearly underlines, as all the lawyers of this time, the diversity of the cases where the argument “from the first to the last” applies and the part that transitivity plays in them. He does the same for the traditional examples of liens hierarchy that Leibniz will take up again15 in the De Casibus Perplexis and completes them with the specific cases of romano-saxonic law. And finally, he does the same about the validity of the conclusion obtained by transitivity, concerning which he recalls that it depends on the existence of a mutual reason16 between terms. But in spite of the subtlety of his reasoning, he does not manage to present these various meanings of the argument as many various expressions of the same relation of order, because he examines them separately with a semi-descriptive topic which covers up the perception of common reasons and prevents him from expressing the logic of law and institutions in their theoretical

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forms. On the contrary, Leibniz would be able to overcome this limitation, and it is this that confers to his legal rationalism the very particular character of a partly extra-legal theorization. 2.2.2 The Originality of the Leibnizian Contribution The different works on substantive law written by Leibniz during the years 1664– 1669 (from the Specimen quaestionum until the Doctrina Conditionum) are characteristic in that they concern not only the properties of conditional law and the expression of a conclusive linearity by means of the principle of substitution of equivalents, but also by the generalisation of legal-logical concepts,17 the analogical extension of their properties18 and the jusnaturalist ordering of norms.19 Indeed, the joint intent of all these treatises seems to be the construction of models capable of ensuring the the solution of traditional legal difficulties, which include: (1) the application of logical rules to law;20 (2) the adaptation of institutional systems and temporal logic in the mechanism of precedent and subsequent conditions;21 (3) the settlement of shares in the matters of concourse22 and of possession in solidum;23 (4) the identity and personality of physical or moral entities liable to be transformed;24 (5) the hierarchy of statements or authorities in the solution of paradoxes;25 (6) the legal use of analogy.26 The first three points, which are at the centre of the De Conditionibus and the Doctrina Conditionum, and which are now known in their main lines, can be omitted in this paper. The same is the case for the fourth, which raises the philosophical question of the kind of existence of abstract entities, since it is comparatively of minor interest in the Leibnizian works devoted to positive legislation. The last two, however, have the advantages of not having been studied much until now and of combining the logical analysis and the consideration of legal circumstances in solving cases similar to the conflict opposing Evathlus and Protagoras (or Tisias and Coras) which the De Casibus Perplexis studies. Thus they highlight the original way in which Leibniz connects the traditional analyses of the argument “from the first to the last” and of the ratios definition/description in the expression of the ratio legis, in order to rationally deal with this type of case through a complete writing up. Ultimately, they allow us to understand in concrete terms how the idea of a complete writing up and the principle of the correspondence of reasons could be combined in a composite conception of legal order where realistic theses and nominalist arguments coexist, according to the very complexity of a legislation joining together individual and procedural rules. The data of this “hard case”, which Doctors considered impossible to solve without additional introduction of jusnaturalist norms, are summarised as follows in chapter16 of the De Casibus Perplexis:

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From this chapter, we usually develop the perplex controversy of the Rhetor stipulating with a disciple that a certain sum will have to be given when the disciple wins the first cause. As the disciple is late in the plea of the causes, the rhetor brings consequently an action against the other in the following way: in this case, he says, either you will overcome and you will be held according to the contract, or you will be overcome [and you will be obliged] in virtue of the res judicata: and the disciple answers: on the contrary: in this case, either I will overcome and I will not owe anything to you according to the res judicata, or I will be overcome [and I will not owe] in virtue of the contract (A VI 1 241).

The perplexity of the case obviously comes from the fact that the victory of one over the other, i.e., the relation of order, is circular. And its solution implies the finding of one indisputable criterion based on which it would be possible to restore the linearity. But, although it is true that we can delete this perplexity by introducing a norm external to substantive law, such an ad hoc solution has the defect of not respecting the principle of economy which must prevail within a legal system. So, Leibniz estimates that we must reject it in favour of a solution internal to law which is obtained when the precision of the circumstances’ description is greater. Thus, he declares: Our opinion is that this case is unjustifiably classified as a perplexed case. Because the State in which this question is discussed punishes the plus petitio tempore, either by the loss of the trial [. . .] or by the loss on appeal according to the Jus Gentium as it is customary today; in the first case Protagoras is defeated, in the second, he wins. Because, since Protagoras lays claim to the pay the disciple before the dies cedit and the dies venit occurs and before the condition is satisfied (indeed the condition of the pay is: the success in the first cause), he will be considered without any doubt as having committed a plus petitio tempore. Therefore, the cause is initially lost in this appeal and by that very fact, the condition of the pay will be satisfied because Evathlus gained the first cause in this way. And consequently, Protagoras can then rightly use an action against Evathlus, which cannot be any more invalidated by any exception, not even [the exception] of re judicata, because Evathlus is exempted by a dilatory and not a peremptory plea, on [first] hearing and not for [the totality] of the trial (A VI 1 242).

This solution obviously depends both on particularisms of Roman substantive law27 and on more general properties linked to the mechanism of appeal.28 But what is crucial is the fact that, by mentioning the legal bodies in the writing of a relation of order, it leads to a complete and rational expression of the relationship between parties, and does so without overriding from the rules of logic. This point is also underlined in the passages of the De Casibus Perplexis where Leibniz shows that we do not need to introduce a legal exemption to the traditional rule “if I overcome he who overcomes you, I also overcome you” to deal with cases in which transitivity does not apply to a succession of superiority relations, and that it is enough to complete the expression of relationships between parties by the introduction of the circumstances which modify them, in order to eliminate the conflicting conclusions. Indeed, when we express in a vague way the fact that Ulysses overcomes Ajax through eloquence and that he overcomes Hector through strength29 by writing aRb and bRc (where R represents the relation of superiority, and a, b, c, the individuals whom it connects), a questionable conclusion is drawn from it by transitivity. But this transitivity disappears when we write a R1 b and b R2 c to mention the various

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reasons for victory, because it becomes then obvious that they are effectively two different relations of superiority which do not imply any transitive conclusion. In the same way, if we express the relations of order between Evathlus and Protagoras by the expression aRb and bRa, a circular perplexed case appears, and this case disappears as soon as we add the legal bodies by writing a R1 b and b R2 a. But it is obvious that such a treatment amounts to considering circumstances as properties of relations and not as properties of individuals; in other words, it amounts to conferring quite an independent existence to these relations. Therefore, we could raise the question of the legitimacy of such an attribution. Should we consider the circumstances as properties of the parties in concourse (case of the Hector/Ajax/Ulysses conflict), or as properties of the legal system in which these parts belong (case of the hierarchy of authorities in the Coras/Tisias conflict)? In other words, should we write a R1 b and b R2 c while agreeing to impart in such a way quite an existence to the relations whose circumstances are only properties, or do we have to write on the contrary a1 Rb1 and b2 Rc2 to mean that they are only characteristics of connected individuals? More generally, is it necessary to interpret the legal rationalism of Leibniz in a sense favourable to nominalist theses, on the pretext that the principle of the inherency of the predicate in the subject is clearly expressed in such an early text as the Specimen quaestionum ex jure collectarum?30 Three main reasons are opposed to such an interpretation: (1) unlike perplexed cases of the Hector/Ajax/Ulysses type which favour a nominalist interpretation because they result from a contradictory ordering of individual properties, the perplexed cases of the Protagoras/Evathlus type naturally require a realist interpretation, because their existence and their solution depend on institutional data (i.e., the ordinary court system and the number of authorities), which are imposed on individuals and outlive them; (2) many passages of Leibnizian texts on substantive law contain explicitly realistic expressions which assume the effective existence of relations31 and hypothetical entities like conditional law;32 (3) within the framework of a theorization of some substantive law, a realistic conception of the existence of abstract entities coexists with a nominalist one, because, on the one hand, the logic of law is the expression of the more general reason described in the De Casibus, and, on the other, the matter of law comes from this “nature of things”, which is recognizable in the laws ruling the formation of parts in the case of concourse33 presented in the Doctrina, as well as in the justification of the exclusive character of the property right on tangible assets,34 reiterated in the De Casibus and the Specimen. Indeed, on the one hand, such an essential rule for the ordering of safeties, lien, status and powers, as that which is stated in the §.3 of D.44.3 and summarised by scholastics in the form “if I overcome that which overcomes you, I overcome you still more”, cannot be reduced to the expression of a mere subjective agreement between individuals, because it can be still abstract on a higher level, because the cause of the cause is the cause of what is caused and the genus of the genus is the genus of the species, and what is required of what is required is what is required of whatever is requiring, and the condition of the condition is the condition of the conditioned, and what is similar of what is similar is what is similar of what it is similar to, and the subject of the subject is the subject of the predicate, and the part

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of the part is the part of the whole. These rules can all be reversed, thus for example: the whole of the whole is the whole of the part, the predicate of the predicate is the predicate of the subject. And these rules can all be called with Everardus in the Loci argumentorum legales, the argument “from the first to the last” (De Casibus, Chap. 21).

And on the other hand, as the Specimen reiterates, based on the authority of the jurisconsult Paul, the same thing cannot be owned in Roman law by several people and according to the same title, because the property right of each one must be expressed in physical acts of possession which exclude any sharing with others. And as the classification of properties and persons into divided and undivided, material and intangible, individual and legal can be defined from the juridical ontology elaborated by Roman lawyers and Doctors by underlining the materiality of relations,35 the nominalist standpoint becomes the inevitable complementary of realist theses when we approach the field of personal rights theorised by some positive tradition. Leibnizian legal rationalism of this period can therefore be defined as the extension, partly extra-legal, of an initiative of unification and rationalisation of law, stemming from the scholastic ideal of recta ratio. It has as a fundamental characteristic the constant search for the immanent order of institutional rights and mechanisms. It is thus led either to deny the power of arbitrariness, or to circumscribe its possibilities of expression by seeking the reasons of the exception by means of a calculation able to adapt the general information of laws to the detail of individual situations. And if it recognises that we can override in some cases the normal use of logical rules, as when we do not apply transitivity as regards partnership,36 it is not in order to ratify any lapse in the rational order of institutions and things, but rather to underline that the understanding of laws assumes the complete writing up (or thinking) of the relationships that the subjects and their predicates have within specific institutional mechanisms. Therefore, the originality of Leibnizian legal rationalism is that it is particularistic, exhaustive and theorising.

Notes 1. Quoting authors as temporally distant as Guillaume Durant (1230/31–1296), Leandro Galganetto (16th–17th century) Jacob Ziegler (1480–1549), Phillibert of Brussels (1518–1570) or Oswald Hilliger (1573–1619), is not a leibnizian specificity, but a rule of legal works, justified by the fact that their opinions constituted the communis opinio doctorum. 2. Cf. the classification of traditional solutions according to the pro and contra in Chap. 33 of De Casibus Perplexis. 3. These Dissertationes, where very often the lawyer-logicians of the 16th century approach the question of legal rationality in a casuistic and ‘Euclidean’ way, include an Anonymous work of 1547, Pierre Lambert (1586), Henri Albert (1586), Arnold de Reyger (1586), and an anonymous compilation of 77 Disputationes published between 1585 and 1587. 4. These works are those of Georg Dasen (1614), Johann Ludovic C¨oppel (1625), Matthias Gleissemberg (1630), Heinrich Eberhard von Anderten (1657). They are partly distinguished from the Dissertationes of the previous period in that they deal with legal rationality from the standpoint of classification, 5. Idem for the dedication formulas, the abbreviations and the references of authors.

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6. Indeed, the following equivalences are noted: Axiomata: thesis 1; De Conditionibus: definition 62, theorem 77; Doctrina: definitions 14 and 19. Axiomata: thesis 2; De Conditionibus: theorems 180 and 184; Doctrina: theorems 51 and 52. Axiomata: thesis 3; De Conditionibus: definition 19; Doctrina: definition 48. Axiomata: thesis 4; De Conditionibus: theorem 51; theorem 49. Axiomata: thesis 5; De Conditionibus: definition 108; theorems 77 and 210; Doctrina: theorem 48. Axiomata: thesis 6; De Conditionibus: theorem 194; Doctrina : theorems 6 and 14. Axiomata: thesis 7; De Conditionibus: theorem 45; Doctrina : theorem 16. Axiomata: thesis 8; De Conditionibus: theorem 111; Doctrina : theorem 17. Axiomata: thesis 9: De Conditionibus: theorem 11; Doctrina : theorem 17. Axiomata: thesis 10: De Conditionibus: theorems 45 and 58 ; Doctrina : theorem 60. 7. Leibniz, De Conditionibus, pp. 70–74. 8. Cf. the notes of defs. 160 and 161 of De conditionibus (cases of mutual substitution and self-substitution), and Th. 117 of De Conditionibus. Idem, th.19 of Doctrina (“If it appears that something is purposefully inserted for some end, it receives an extensive interpretation; in other words, all that is equivalent in effectiveness for this purpose, can be substituted to take its place”) as well as Ths. 23 and 31. 9. This book is presented in a unpaginated edition, with the general title: Dialectica legalis in qua de modo argumentandi et locis argumentorum. De quinque universalibus et decem praedicamentis. De vitiis argumentorum legaliter disputatur. The paginated edition of Basel (1535), which was used here, further contains the De veritate ac excellentia legalis scientiae liber in which Gammarus expresses the very principles of legal rationalism (cf. p. 160: “The true law is congruent by nature with the right reason”). 10. See also: “The jurisconsult enumerates seven circumstances in the law Aut facta of D.48.19 [law 16], namely: the cause, the person, the place, time, quality, quantity, the event. Others are summarised by the following expression: who, what, where, how, why, by which, when” (Cantiuncula 1545: book 1, chap. 7, De circumstantiis, p. 159). 11. “The definition must only apply to what is such and not to what is almost such” [. . .] “And it is not always true that what we provide in such case, applies in such quasi-case, see [in the commentary of Bartole on D.48.5] the example 33, question 5, where the woman is known as the maidservant of her husband, although the law differently provides in the case of the maidservant and the woman” (Op cit., p. 172). 12. “Some of our Moderns say that a thing can be defined by its effects if they indissolubly adhere to the cause, and they do it according to D.37.4.3 §.2, where the jurisconsult affirms that we very precisely define the bonorum possessio as being a right of lien, because this right of lien is an effect of the bonorum possessio. But we can respond to this reasoning of the Moderns, that in this case, the jurisconsult gave the signification of a description to the definition” (Op. cit., p. 172). 13. “The predicament and the circumstance differ in the fact that the predicament is an accident separated from a substance by an abstraction, which occurs when we try to know the essence and the very nature of a substance by defining or dividing, which gives three, the quarter, [. . .] As for the circumstance, it is a concrete accident and which consequently adheres to the substance, like three guardianships, the quarter of the inheritance [. . .]” (Op. cit., p. 159). 14. Cf. the questions 6, 7 and 13 of the Specimen quaestionum ex jure collectarum and the problem of the juridical identity of a thing of which all original parts have gradually disappeared. 15. I.e., the conflict between the lien of the lender of mutuum and the super-lien of the dowry (Authentic Quo jure, Codex 8.17.7) and the problem of the “gratia expectativa” successively granted by two Popes (Sexte, book 3, title 3, Chap. 7, Auctoritate Martini). Cf. De Casibus Perplexis, Chaps. 26 and 29. 16. Indeed Everhardus declares: “However, to have a clear and lucid opinion on the sentence ‘if I overcome he who overcomes you etc.’, it is necessary to introduce a distinction after Petrus [of Ancharano], Cino de Pistoie in the Authentic licet patri of C.5.27, Johannes Andreae in

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18. 19. 20.

21. 22. 23. 24. 25.

26. 27. 28.

29. 30. 31.

32.

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chapter 7 [Auctoritate Martini], of the Sexte, book 3, title 3, Petrus de Ancharano in the same passage, Lambertus de Ramponibus in connexion with law 16 [Claudius Felix] of D.20.4.16, and Ludovicus Romanus at the beginning of his Council 436, and to say that that is allowed considering the end, in the following way. Either we ask the question in connexion with different cases, or we ask it in the same case. In the first case, the rule ‘if I then overcome he who overcomes you, I overcome you’, does not apply; and it is in this sense that the Authentic licet patri, law 2, §.15 and law 5, §.2 of D.38.17, and the §. his consequens of the Authentic 97 speak. In the second case, when we ask the question concerning the same case, it is necessary to subdivide: either the reason by which I overcome you is the same one as that by which I overcome that which overcomes you, and in this case, the aforesaid rule is true because I must overcome you still more, in accordance with the aforesaid law D.44.3.14, or the reason by which I overcome you is not the same one as that by which I overcome that which overcomes you and then the rule in question does not apply, and it is in this sense that the law Claudius aforesaid and the chapter Auctoritate Martini speak” (Op cit., p. 730). Leibniz’s (De Casibus Perplexis, chap. 23) will be practically the same because the argumentation is basically logical and because there is only one solution. I.e., the juridical application of transitivity in the questions of hierarchy of norms and powers, and the distributivity of disjunction and conjunction in the problems of concourse and stipulation. Cf. the questions of accrual, quasi-contract and legal personality in the Specimen. Cf. the ordering of privileges in the De Casibus. Specimen: Questions 1, 2, 12 (contradiction); De Conditionibus: Ths. 1 to 24, 79, 95 to 105 (transitivity), 199 to 201, 262 to 265, 337, 340 (disjunction, conjunction, distributivity [. . .]) ; De Casibus: Chaps. 21, 23, 32 (transitivity); Th. 3 (transitivity), Ths. 5, 7, Defs. 33 to 35. Ths. 22 to 30 (disjunction, conjunction, distributivity [. . .]). See for example: De Conditionibus: Ths. 298, 319, 323; Doctrina: Def. 22, Th. 26. Specimen: Question 4; De Conditionibus: Ths. 106 to 110; De Casibus: Chaps. 28, 31 to 40; Doctrina: Def. 38, Ths. 23, 271 . Specimen: Questions 4, 12, 15; De Conditionibus: Ths. 95 to 134. Ths. 201, 264 sq.; De Casibus: Chaps. 25, 28; Doctrina: Ths. 3, 272 , 33. Specimen: Questions 13, 14; De Conditionibus: Th. 43, Th. 225; De Casibus: Chap. 15; Doctrina: Def. 70. Paradox of the Liar: Specimen: Question 12; De Casibus: Chaps. 7, 16; Doctrina: Th. 69. Paradox of the legacy opposed to the Falcidian law: Specimen: Question 12; De Conditionibus: Def. 55; De Casibus: Chap. 13; Doctrina: Ths. 38, 63. Paradox Protagoras/Evathlus: Specimen: Question 12; De Casibus: Chap. 16; Doctrina: Th. 69. Specimen: Question 17; De Conditionibus: Ths. 255 to 280, 338, 339; De Casibus: Chaps. 21, 27; Doctrina: Def. 76. The possibility of being nonsuited for plus petitio tempore and the introduction of the dies cedit and the dies venit into the mechanism of payability of a debt. The Leibnizian solution depends on the number of legal proceedings and the concept of cause since it is sufficient to have three successive authorities so that Evathlus can appeal against the victory of Protagoras, and be exempted from paying because of his defeat on appeal. De Casibus, Chap. 23. “The foundation of a relation is given by what is included in the subject” (Specimen, Question 17). “More, since a species implies a conformity of individuals, if we have two species and that two conformities are expressed there, a genus common to these species is made up from them and a conformity of conformities is abstract. (3.) A discussion of this kind grows among jurisconsults concerning the fact of knowing if there are property and possession of incorporeal things” (Specimen, Question 17). “The conditional law establishes something in the Being. It is usually said that the condition does not establish anything in the Being, but we showed in many way the opposite of this thesis” (Doctrina, Th. 66).

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33. Cf. Doctrina, Th. 271 : “All this theorem is of great importance and it was subtly deduced from Natural Law itself, by Ancient Jurisconsults [. . .] Indeed, this question contains a kind of physical principle drawn from the nature of movement [. . .] However, just as in movement the inclination is distributed between several competitors and that the movement of the part which is pushed receives from the movement of the parts which push an equal inclination and angle on both sides when the impetus is uniform, in the same way in Law, the thing is divided so that an equal portion is assigned on each side when several are linked by an equal reason for the same thing”. 34. See Question 4 of Specimen. 35. Idem: “In connexion with the aforesaid law 3, Godefroy perfectly exposed for which reason one denies that bodies can mutually penetrate and occupy [the place of another]. (5.) Because that would first remove the reaction of bodies since there would be no resistance, then their separation, since all would be in all. And all bodies would be joined together at only one point, in the centre, because if two can be joined together in the same point, why not several, why not all?”. 36. D.17.2.19: “Whoever is accepted as associate, is only associated with whoever admitted him, and justifiably. Indeed, as the company is founded by consensus, an associate who I did not want as an associate cannot be my associate”; D.17.2.20: “Because my associate is not the associate of my associate”.

References Leibniz De Casibus Perplexis (A VI 1 231–256). De conditionibus. Ed. and transl. P. Boucher. Paris: Vrin, 2002 (A VI 1 97–150). Doctrina Conditionum. Ed. and transl. P. Boucher. Paris: Duchemin, 1998 (A VI 3 369–430). Specimen quaestionum philosophicarum ex jure collectarum (A VI 1 69–95).

Other Authors Albert, H. 1586. Axiomata juris collecta ex Digestis, de exercitoria actione, lege Rhodia, Institoria, tributoria actione [. . .] cum concordantibus C. et Inst. Helmstadt. Anonymous. 1547. Axiomata legum ex receptis juris utriusque libris et interpretum commentariis ordine certo et in litteras alphabeticas distincto, recens collecta ac edita. Lyon. Anonymous. 1585–1587. Axiomata sive enunciata Digestorum Juris Civilis Romani dispositionum exercitio in Inclyta Academia Julia quae est Helmstadii proposita. Boucher P. 2005. Calcul, r`egles et normes dans les arbres de consanguinit´e et d’alliance chez Leibniz et ses pr´ed´ecesseurs. Cahiers Philosophiques de Strasbourg. Paris: Vrin, pp. 85–115. Boucher P. Forthcoming. H´eritage et apport de Leibniz dans les probl`emes de rationalisation du droit positif. In M. Kulstad (ed.), The Young Leibniz. Stuttgart: Franz Steiner. Cantiuncula, C. 1545. Methodica dialectice ratio ad jurisprudentiam adcommodata. Basel. C¨oppel, J.L. 1625. Disputatio inauguralis de concursu creditorum eorumque praelatione. Dasen, G. 1614. Disputatio juridica utilissimam et cottidianam de prioritate et concursu creditorum, materiam tam secundum Jus Civile quam Saxonicum succincte exhibens. . . . Iena. De Reyger, A. 1586. Axiomata ex Digestis et concordantibus titulis Codicis de aedilitiis actionibus, de evictionibus et duplae stipulationibus. Helmstadt. Everhardus, N. 1613. Loci argumentorum legales authore D. Nicolao Everardo a Middelburgo jurisconsulto clarissimo et magnifico Senatus Belgici apud Mechliniam olim praeside. Praefatio consultissimi viri Dyonysii Gothofredi Jurisconsulti. Darmstadt.

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Gammarus, P.A. 1522. De modo disputandi ac rationandi in Jure. Leipzig. Gleissemberg, M. 1630. Disputatio juridica de concursu et ordine creditorum. Helmstadt. Lambert, P. 1586. Axiomata de inofficiosi testamenti. Helmstadt. Von Anderten, H.E. 1657. Dissertatio juridica de praeferentia creditorum in concursu eorumque privilegiis. Helmstadt.

Chapter 15

On Two Argumentative Uses of the Notion of Uncertainty in Law in Leibniz’s Juridical Dissertations about Conditions Alexandre Thiercelin

1 Introduction: Framework and Significance of Leibniz’s Problematic Leibniz’s main purpose in his Juridical Dissertations about Conditions (1665)1 is to enumerate and to formulate, in a rigorous way, most of the argumentative patterns the Roman jurisconsults use when they have to interpret the meaning of a statement in which a person claims to create a new right by transferring one of his rights to another person. One of the most important issues is to determine whether such a statement is juridically pure, conditional or null. If it is inferred to be juridically pure, the new right exists as soon as the statement is uttered. If it is inferred to be juridically conditional, the new right exists if and only if the condition is verified.2 If it is inferred to be juridically null, no new right is created. Leibniz wants to make these argumentative patterns explicit in order to exhibit the necessity of inferences drawn by the Roman jurisconsults:3 Even if they are not as certain as “mathematical demonstrations”, such inferences can be considered, in a sense, as demonstrations.4 Thus, analyzing the ways the Roman jurisconsults infer that a statement is juridically pure, conditional or null enables Leibniz to give an example (“specimen”) of the inferential necessity that is specific to law.5 But Leibniz’s interest in juridical conditions is based on another reason. Interpreting the meaning of a statement as juridically pure, conditional or null requires an exact and well-formed definition of juridical conditions.6 From Leibniz’s point of view, such a definition is still missing. Indeed, he considers that most definitions given by doctors in law are wrong insofar as they do not follow a propositional approach. They strive to give a definition of juridical conditions without taking into account the fact that they are conditions, and as such only partial propositions. A rigorous definition of juridical conditions requires that one start by giving a definition of what is a conditional proposition considered as a whole in law.7 Thus, the first methodological choice the young student in law makes is to consider all the statements submitted to the Roman jurisconsults as propositions. From A. Thiercelin University of Lille 3, Lille, France

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this point of view, a juridically conditional proposition is a “hypothetical” proposition. Leibniz’s decisive claim is that what is called in law a conditional proposition is what is called in logic a hypothetical proposition.8 Two consequences result from such an identification. First, the use of notions borrowed from the logical analysis of hypothetical propositions (such as “proposition”, “conditionality”, “implication”, “suspension”, “necessary”, “impossible”, “negation”, etc.) is justified in order to capture the necessity of the argumentative patterns that the Roman jurisconsults use to interpret the meaning of the statements that are submitted to them. Second, the expression “juridical logic” is meaningful. Indeed, Leibniz’s claim does not mean that there are no argumentative patterns specific to law. It does not mean that there is only one way of reasoning, one logic, which would be applied to the context of law. The notion of juridical condition has common features with the notion of logical condition, as well as with other notions that are specific to law. “Juridical logic” means that there are specific uses of logical notions in the context of law that must be described and analysed in order to show that, even if the argumentative patterns the Roman jurisconsults use are not formal, their conclusions express a real inferential necessity. Law is not only a question of rhetorical effects. Against the background of this general framework, in this paper I present two argumentative uses of the notion of uncertainty that are considered to be significant by the Roman jurisconsults when they have to deal with propositions that are claimed to be juridically conditional. Indeed, I uphold that one of Leibniz’s most important results in his Disputations is to establish that the notion of conditionality used by the Roman jurisconsults is proper to law because its definition includes a specific notion of uncertainty. Such a juridical conditionality justifies him in speaking of “juridical logic”.

2 An Epistemic Property of Juridical Conditions The first argumentative use of the notion of uncertainty that Leibniz presents is directly connected with what he considers as one of the most specific properties of juridical conditions. According to this property, a proposition connected to another, in which a right is claimed to be transferred from one person to another, is a juridical condition if its truth value is not known with certainty to be the true or the false by the person who utters the proposition when he utters it: “T11: A juridical condition is uncertain. For if it is certain that it is true, the disposition is pure, T332 and DF30, if [it is certain that it is] untrue, [it is] null, T144 and DF31” (A VI 1 111).9 Such a proposition (meaning a juridical condition) exerts a suspensive effect on the proposition it is connected with (preventing the right from being really transferred) until its truth value is known with certainty to be the true or the false, i.e., in Leibniz’s words, until “Certa Conditio est”: DF33: Is certain the condition of which the event (in the actuality) is certain. DF34: The event is [certain] when DF35: It exists, i.e., is present at the moment in time when it is said to be existing, or DF36: It lacks, i.e., is not present at the only moment in time when it can be. DF37: It is in suspense before the event.10

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If the event described in the proposition means that a juridical condition occurs, the condition is said to be existing: Its suspensive effect is stopped and the proposition it is connected with is purified. The right (which is a part of the “conditioned”) is transferred from the person Leibniz calls the “conditioner” to the person he calls the “conditionee”.11 If the event does not occur and cannot occur anymore, the condition is said to be defeated: The proposition it is connected with has its juridical effect cancelled. It is as if no proposition had been uttered. Thus, in order to infer whether a proposition means a juridical condition or not, it is necessary to determine the epistemic state of the person who utters the proposition when he utters it. A proposition means a juridical condition only in an epistemic context specified by what a juridical agent knows at a certain moment in time. For instance, let us consider the following testamentary proposition uttered by a father: “I want my daughter to receive 100 x when she marries”. The father dies, and once his last will is known, it turns out that his daughter was already married when he wrote his testament. The problem is the following: Are we justified in considering the juridical condition as already satisfied and therefore the testamentary proposition as pure, or should we consider it as still conditional so that the daughter must divorce and marry again in order to receive the legacy? One of the first determinations the Roman jurisconsults consider in order to solve this problem is the epistemic state of the father when he wrote his testament. If it is proved that he knew his daughter was already married, then this first wedding does not satisfy the juridical condition on which the legacy depends: The Roman jurisconsults infer that the father wanted to give his daughter a legacy if and only if she got divorced and married a second time. On the contrary, if it is proved that her father did not know she was already married, the juridical condition is satisfied with the first wedding: When they read it, the Roman jurisconsults infer that the testamentary proposition is pure so that the daughter immediately receives the legacy.12 Once again, such an argumentative pattern, which uses the epistemic state of the person who utters a proposition in order to determine its juridical meaning, is based on the very definition of “juridical condition”. As such, uncertainty is not a secondary property of juridical conditions but one of those that Leibniz presents as justifying a distinction between logical and juridical conditions.13 Such an epistemic property of juridical conditions is important for two reasons. First, it compels Leibniz to give an epistemic definition of modalities. Second, it compels him to present the way in which the Roman jurisconsults distinguish several kinds of uncertainty.

2.1 An Epistemic Definition of Modalities Leibniz gives the following epistemic definitions of the modalities: DF30: A condition is said to be necessary either owing to the conditioned, DF10, or owing to the disposition, T49, or in itself and once again from the point of view of things; as such every condition is from the beginning either necessary or impossible; or from our point of

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view; as such is necessary [the condition of which] it is certain that it is true, DF31: Impossible [the condition of which it is certain] that it is untrue, and it is presently impossible either absolutely or for a given time. DF32: Is certain what we know to be necessarily as it appears (A VI 1 103–104).14

Leibniz makes a distinction between two points of view: “the point of view of things” and “our point of view”. As soon as (“ab initio”) a proposition is uttered as a condition, it has a truth value that is the true or the false, even if it is not known yet. From that objective point of view a condition is said to be necessary or impossible. Uncertainty is not a third truth value. Nevertheless, when a proposition is uttered as a condition, we are not always able to know immediately (“ab initio”) with certainty whether its truth value is the true or the false. From the restricted point of view of our information (“a parte nostri”), we must wait until we have enough information (appearances) to be justified in inferring that the condition is necessary or impossible. Leibniz calls an “event” the moment in time when the truth value of a proposition uttered as a condition is known with certainty to be the true or the false, because what is described in it occurs or is very likely to occur. The point is that it is only “a parte nostri” that a proposition can mean a juridical condition. From an objective point of view (“a parte rei”), it makes no sense to consider a proposition as a juridical condition insofar as the suspensive effect that a juridical condition exerts depends on the fact that its truth value is not known yet with certainty to be the true or the false. Therefore, it is only in a specific epistemic context that a proposition means a juridical condition. In DF30 Leibniz presents another distinction between logical and juridical conditions. A proposition uttered as a condition means a juridical condition if the person who utters the proposition (when he utters it) does not know with certainty whether its truth value is the true or the false. Furthermore, a proposition uttered as a condition means a juridical condition if the connection between it and the other proposition with which it is connected (what Leibniz calls the “conditioned”) is entirely based on the wish of the person who utters it: He is the one who decides to make the truth value (and so the juridical efficiency) of the proposition uttered as the “conditioned” depend on the truth value of the proposition he utters as a condition.15 As such, Leibniz calls a juridically conditional proposition a “disposition” (“dispositio”).16 Therefore, a proposition uttered as a condition in a juridical context or including juridical notions in its content is only a seeming-juridical condition if its connection with the “conditioned” is not entirely based on the wish of the person who utters it, but is necessitated either by the content of the “conditioned” (“owing to the conditioned”), or by the meaning of the juridical conditional proposition of which it is part (“owing to the disposition”), or “in itself”. As far as the juridical conditionality is concerned, the words “necessary” and “impossible” signify that the truth value of the proposition meaning a juridical condition (exerting a suspensive effect) is known with certainty (“from our point of view”) to be the true/the false. On the other hand, as far as those three kinds of conditionality are concerned, the words “necessary” and “impossible” mean that it

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is true/false that the proposition uttered as a condition is, from the point of view of things, a condition for the proposition with which it is said to be connected. Nevertheless, those three kinds of non-juridical conditionality are different from each other and must be specified.

2.1.1 The Conditions Necessitated “Owing to the Conditioned” Leibniz calls such conditions “extrinsic” conditions insofar as their connection with the “conditioned” is not based on the wish of the person who utters them but on the content of the “conditioned”.17 Leibniz makes a distinction between two kinds of extrinsic conditions: DF10: Is extrinsic the condition of which conditionality is based on the nature of things. Its species are: the condition which is necessary to the conditioned, i.e., such as it suspends the conditioned because of the nature of things; and the condition to which the conditioned is necessary, i.e., such as it implicates the conditioned (A VI 1 102).18

Pol Boucher (in Leibniz 2002: 199) gives two examples in order to illustrate each of those two kinds. An example of the first kind would be: “I want Titius to inherit 100x if 100x exists”. Insofar as the proposition “if 100x exist” is necessitated because of the nature of things by the proposition “I want Titius to inherit 100x” (whether the testator likes it or not, Titius cannot inherit 100x if 100x does not exist). But because what is necessitated here is the condition and not the “conditioned”, the proposition “I want Titius to inherit 100x if 100x exist” is juridically pure. In order to make such a proposition a juridically conditional one, the testator must add a proposition of the following kind: “I want Titius to inherit 100x if a boat comes from Asia”. Of course, it is required that the testator does not know yet with certainty whether a boat will come or not from Asia. An example of the second kind would be: “I want Titius to inherit if he frees my slave”. In order to have the right to free the testator’s slave, Titius should have inherited the slave first. Therefore the “conditioned” is necessitated by the condition: As such, it is not a juridical proposition and the proposition “I want Titius to inherit if he frees my slave” is juridically null. Such seeming-juridically conditional propositions, propositions in which the proposition connected as condition is identical (“conditio identica”) with the other proposition,19 are one kind of what Leibniz calls “perplexed propositions” (“propositiones perplexae”)20 and such propositions are impossible: They have no juridical meaning and must be said to be juridically null.21

2.1.2 The Conditions Necessitated “Owing to the Disposition” When they have to interpret the juridical meaning of a proposition, the Roman jurisconsults make a distinction between what the utterer wants (his wish) and what he introduces indirectly as a means to obtain what he wants. This distinction is very important insofar as it enables one to carry out substitutions without prejudice to the juridical meaning of the proposition: What is introduced only indirectly in the

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proposition can be substituted for another expression that is equivalent to it because it is similar to it, whatever this similarity may be.22 Thus, the meaning of a proposition that has the value of a juridical condition is not reduced to its expressed words. This point is important because, as we shall see, the possibility to carry out such substitutions increases the probability that the truth value of the proposition uttered as a juridical condition is the true. For the time being, we must keep in mind that a condition necessitated “owing to the disposition” is an expression that is introduced only indirectly in a proposition meaning a juridical condition: It is a means for the person who utters it to obtain certain juridical effects he directly wants. For instance, let us consider the following testamentary proposition in which a mother writes: “I want my sons to inherit if they are emancipated from the tutelary control of their father by his wish”. In case their father dies before having emancipated them, the problem is the following: Are we justified in considering that the proposition that until then meant a juridical condition, “if they are emancipated from the tutelary control of their father”, is now defeated because it can no longer be satisfied? From that point of view, the proposition “I want my sons to inherit” would be null and the sons would not have the right to inherit. The Roman jurisconsults reject such an interpretation. They believe that the conditional proposition “if they are emancipated from the tutelary control of their father” is necessitated only “owing to the disposition”, insofar as the mother did not care about the way her sons would be emancipated. She just wanted her sons to inherit from her through their father (“fideicommis”). From that last point of view, the meaning of the proposition “if they are emancipated from the tutelary control of their father” is juridically equivalent to the meaning of the proposition “if their father dies”. Thus, the Roman jurisconsults infer that the proposition “I want my sons to inherit” is purified by the fact their father died.23 If someone wanted to defeat this equivalence and to infer that the juridical efficiency of the proposition is cancelled by the fact the father died, he should have to prove that the mother wanted her sons to be emancipated by their father’s wish for a very specific reason. Then the expression “by his wish” could not be said to be necessary “owing to the disposition” anymore. It would have been directly wanted by the mother. 2.1.3 The Conditions Necessitated “in Itself” Once again, insofar as it is not based upon the utterer’s wish, such conditions do not mean juridical conditions but only logical conditions and, as such, they have no juridical meaning: from a juridical point of view, it is as if they were not added.24 Leibniz’s epistemic definition of modalities enables him to specify the distinction between logical and juridical conditions: A proposition means a juridical condition if, when a person utters the proposition, she does not know whether it is true or false; two propositions are connected in a juridically conditional way and, as such, mean a juridical conditional proposition, if their connection is only based upon the will of the person who utters it.

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2.2 Two Juridical Kinds of Uncertainty The first argumentative use of the notion of uncertainty by the Roman jurisconsults to decide whether the juridical meaning of a proposition is pure, conditional or null is not only based upon an epistemic definition of modalities. It also requires a distinction between two main kinds of uncertainty: “it is uncertain whether” and “it is uncertain when”.25 The first kind of uncertainty concerns the very truth value of a proposition. The person who utters the proposition when he utters it does not know yet with certainty whether or not the event he describes will occur. For this reason, such a proposition means a juridical condition: It exerts a suspensive effect on the proposition it is connected with and so the right provided by it does not exist yet. But it is possible that the person who utters a proposition when he utters it knows with certainty that its truth value is the true even if he does not know yet with certainty the moment in time when the event he describes will occur. This second kind of uncertainty does not carry a suspensive effect but only a dilatory effect: The proposition to which it is attributed does not mean a juridical condition but a date in time. The difference between a condition and a date in time is very important in Roman law, insofar as a right provided by a date in time already exists even if it is delayed.26 Nevertheless, such a distinction between “it is uncertain whether” and “it is uncertain when”, suspensive effect and dilatory effect, juridical condition and date in time, does not depend only on the epistemic state of the person who utters a proposition when he utters it. In order to specify the kind of uncertainty that must be attributed to a proposition, it is necessary to consider some other parameters, for instance, the juridical nature of the proposition that it is connected with: “T197: A date in time which is uncertain when [it occurs] means a condition in testaments” (A VI 1 134).27 Even if it is proved that the person who uttered a proposition when he uttered it knew with certainty that its truth value was the true, even if it is proved that the only thing he did not know yet was the moment in time when the event described was to occur, insofar as he uttered a testamentary proposition and not a contractual proposition the Roman jurisconsults would infer that such a proposition is not a pure proposition, provided with a date in time, but a conditional proposition. From the point of view of the law, the argumentative potency attributed to the utterer’s epistemic state (“it is uncertain when”) is less important than the potency attributed to the fact that what he uttered is a testamentary proposition. For example, let us consider the proposition in which it is said: “I want Titius to receive 100x when my heir dies”. The problem is to say whether the partial proposition “when my heir dies” means a juridical condition or a date in time. Several arguments may be used. The first one is that the utterer used the word “when” and not the word “if” to connect the two propositions so that it would seem that the partial proposition “when my heir dies” does not mean a juridical condition but a date in time. But such an argument does not have much potency insofar as Leibniz says that the word “when”

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may be used to mean a juridical condition: It is one of the “signs”, i.e., one of the “formal words”, for the juridical conditionality (DF62 note t; A VI 1 105). A second argument would consist in considering whether the utterer knew with certainty the truth value of the partial proposition “when my heir dies” when he uttered it. Of course, he knew it was the true, since every man is mortal. But he could not know yet when his heir would die. So the proposition “I want Titius to receive 100x when my heir dies” should seem to be juridically pure: The partial proposition “when my heir dies” would mean a date in time and exert only a dilatory effect on the legacy. Nevertheless, this argument is defeated by a third one according to which the complete proposition is juridically conditional because the proposition “I want Titius to receive 100x” is testamentary.28 T197 is one of the rare theorems for which Leibniz does not give a demonstration. He is content with noting that the Roman jurisconsults consider that “a date in time which is uncertain when” means “a date in time which is uncertain whether” in testamentary propositions. Does that mean Leibniz fails to understand the reason justifying the use of such an argumentative pattern?

3 Uncertainty and Use of Probabilities in Law Next to this prominent argumentative use of the notion of uncertainty in law, based upon the very definition of juridical conditions he strives to formulate, Leibniz presents another argumentative use of this notion. Uncertainty is juridically relevant when considering whether a proposition means a juridical condition or not. But it is also juridically relevant when estimating the value of a right provided by a juridical condition.29 Indeed, the value of a conditioned right depends in part on the degree of uncertainty according to which the truth value of the proposition exerting a suspensive effect could be the true.30 Such a partial dependence is important since Leibniz justifies the possibility of a conditioned right to be estimated with the possibility of estimating the certainty that the truth value of the proposition meaning the juridical condition is the true: “T258: Nevertheless a conditional right can be estimated, for certainty can be estimated by hope as a common measure” (A VI 1 139).31 Thus, other things being equal, the value of a right provided by a juridical condition is all the more important when the probability, according to which the truth value of the proposition exerting the suspensive effect is the true, is higher. The notion of probability is explicitly used twice by Leibniz in his Dissertations.32 It must be understood as a hope-fear ratio33 that enables Leibniz to present an analogical system according to which a right provided by a juridical condition is similar to a fraction between 0 and 1, the right that is null being similar to 0 (such a right is cancelled insofar as it is known with certainty that the truth value of the proposition meaning its juridical condition is the false) and the right that is pure being similar to 1 (such a right is purified insofar as it is known with certainty that the truth value of the proposition meaning its juridical condition is the true):

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T256: There is the same ratio between: null right

conditional right

pure right

impossible condition zero

uncertain condition fraction

necessary condition whole umber

Indeed an impossible condition makes a null right, T144, a necessary condition makes pure right, T332, an uncertain condition makes a conditional right, T11. But a conditional right is the medium between a pure right and a null right; it is more than the former and less than the latter: as a fraction between zero and the whole number (A VI 1 139).34

In such a perspective, the most uncertain juridical condition is similar to the fraction 1/2: The reasons to believe that the truth value of the proposition could be the true are equal to the reasons to believe that the truth value of the proposition could be the false.35

3.1 The Latitude of a Juridical Condition In spite of such an analogical system, it is important to notice that the estimation of uncertainty the Roman jurisconsults deal with and Leibniz presents in his Dissertations is not a quantifiable one.36 In order to understand correctly this use of the notion of probability in law, we must consider the notion of “latitude”. The latitude of a juridical condition is the totality of all the different ways for it to be satisfied. Of course, the wider this latitude is, the higher the probability that the truth value of the proposition that means the juridical condition is the true: “T276: The wider the latitude of a condition is, i.e. the more numerous the possible ways for it to be fulfilled are, the higher the hope is. Indeed the hope separately exists in each way” (A VI 1 141).37 Therefore, all other things being equal, a right provided by a juridical condition that has a wide latitude is more advantageous than another right provided by a juridical condition that has a less wide latitude. Leibniz stresses some seemingly insignificant determinations that must be taken into account when it comes to estimating the latitude of a juridical condition and so the value of the right provided by it. For instance, all other things being equal, an affirmative condition is more advantageous than a negative condition because the latter can be satisfied only in one way, i.e., we must wait for the moment in time when we will know that the contrary is not possible anymore, whereas the former can be satisfied in numerous ways as long as we do not know it is impossible. Therefore, the latitude of an affirmative condition is far wider than the latitude of a negative condition and the value of a right transferred under an affirmative condition is higher than the value of a right transferred under a negative condition.38 Another significant determination: All other things being equal, because the more numerous the ways of satisfying a condition are, the higher the probability that its truth value is the true, so too the latitude of a disjunctive condition is wider than

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the latitude of a simple condition and far wider than the latitude of a conjunctive condition.39 Conversely, the more detailed the only way of satisfying a condition is, i.e., the more numerous the conjoined conditions it includes are, the lower the probability is that its truth value is the true.40 Therefore, the use of the notion of probability in law should not be overinterpreted. There is nothing in Leibniz’s Dissertations such as statistical methods that would enable an estimation of the probability according to which an event may occur. By introducing the notion of latitude, Leibniz shows that the problem with which the Roman jurisconsults deal, when they strive to estimate the probability of a juridical condition, is a problem of meaning. It amounts to giving, first, an interpretation of what a proposition means juridically, i.e., to deciding whether it means a juridical condition or not and then, if it does, to indicating the precise extent of its latitude, i.e., the different ways for this juridical condition to be satisfied, whether those ways are the ways expressed by the utterer or other ways considered as juridically equivalent by the Roman jurisconsults. In other words, estimating the probability of a juridical condition does not mean calculating the probability that the event it refers to will occur. It means estimating its latitude, i.e., enumerating the juridically equivalent ways of satisfying it.

3.2 A Juridical System of Equivalences Leibniz strives to present the argumentative system of juridical equivalences the Roman jurisconsults use in order to proceed with substitutions in a partial proposition meaning a juridical condition without changing anything in what its utterer is likely to have meant. Of course, the more numerous the substitutions for such a proposition are, the more probable it is that its truth value is the true. From that point of view, Leibniz makes a distinction between two general ways of interpreting a juridically conditional proposition: An “intensive” way and An “extensive” way. The latitude of a juridical condition depends, first, on the nature of the proposition it is connected with: If it is a contractual proposition, the meaning of its juridical condition will be interpreted in an intensive way so that no substitution will be allowed. Its latitude is limited to what is explicitly written. On the contrary, if the proposition is a testamentary one, the meaning of its juridical condition will be interpreted in an extensive way so that substitutions will be allowed.41 Thus, whereas a proposition is normally said not to mean a juridical proposition at all if it is connected with a proposition that means an impossible juridical condition (because it requires something that is forbidden by the law), a testamentary proposition connected to such a proposition will be interpreted in an extensive way, not as a juridically null proposition, but as a juridically pure one.42 Interpreting in an extensive way means not to be bound by what is explicitly written. We have already seen the case of conditions which are necessary “owing to the disposition”. Leibniz labels, in this way, every expression explicitly included in a proposition meaning a juridical condition, but which the Roman jurisconsults

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considered to be only indirectly wanted by the person who uttered the proposition. Thus, it can be substituted by another expression considered as juridically equivalent. Such a case is very near another one according to which an expression explicitly included in a proposition meaning a juridical condition, but considered by the Roman jurisconsults as indirectly wanted by the person who uttered it, i.e. only as a means to an end, can be substituted by another expression considered as juridically equivalent to that end.43 But there is one special case of substitution Leibniz seems very interested in: The case of “conditions of wishing” (“conditiones voluntatis”). Indeed, the latitude of such juridical conditions includes, besides the exact satisfaction of what is explicitly wanted by the utterer, what I will call its “approximation”. One way of inferring that such an inclusion is actually the case, i.e., that a proposition means juridically a condition of wishing, is to show that the proposition means an order.44 By “approximation” I mean the obedience that appears in the greatest effort tending to the fact ordered without carrying it out fully. A condition of wishing is satisfied by such an obedience, and an order has the meaning of being a condition of wishing.45 The point is that an order can be satisfied even if the ordered fact has not been carried out. The order is obeyed insofar as the “conditionee” who was ordered does his best to do what is ordered. Therefore, having the meaning of expressing an order is a relevant determination in case the Roman jurisconsults want to estimate the probability of a juridical condition: Such a meaning enables them to include in the latitude of this juridical condition the approximation of the fact explicitly expressed by the “conditioner”.46 Leibniz strives to account for some of the arguments used by the Roman jurisconsults to infer that a proposition means an order and, as such, a juridical condition of wishing. For instance, because the form of address is said to be “the form of ordering”, if the “conditionee” who must satisfy the fact explicitly introduced in the proposition meaning a juridical condition is addressed by the “conditioner”, i.e., is denoted by the use of the second person, the Roman jurisconsults are justified in inferring, in a presumptive way, that such a juridical condition means an order, i.e., a condition of wishing.47 Such an argument means that the “conditionee” is to be identified with certainty in the proposition meaning the juridical condition. If the “conditionee” is only “designated” with what Leibniz calls a “property” (for instance, “I want the person who marries my daughter to receive 100x”),48 the juridical condition cannot mean an order. Otherwise, an aporia would result insofar as it may happen that several persons satisfy the condition without it being possible to say who is to be considered as the “conditionee”.49 Another argument (which we have already met) in favour of interpreting a juridical condition as a condition of wishing is the argument that a proposition that means a juridical condition is a testamentary proposition.50

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Nevertheless, according to T48 and T49, if there is a proof that the fact introduced in the proposition meaning a juridical condition is chosen by the “conditioner” for a particular purpose so that it cannot be substituted by any equivalent, such a juridical condition cannot mean a condition of wishing: it is only satisfied by the fact that it is explicitly described by the “conditioner”.51 For instance, let us consider the following testamentary proposition: “I want my daughter to receive 100x if she marries Aelius and I want her to give him those 100x if she does not marry him”. The testator’s daughter dies before being of marriageable age. Are we justified in saying, in an extensive way, that the condition is satisfied by her death and that the 100x have to be transferred to Aelius for the reason that she did not marry him? The Roman jurisconsults consider that such a condition, as it was expressed by the father, had a special meaning for him since it was a means for him to obtain the result that his daughter marry Aelius. Because she did not refuse to marry Aelius (she was just too young to marry when she died), Aelius is not justified in receiving the 100x. The juridical condition “if she does not marry him” can be satisfied only by her explicit refusal to marry Aelius.52 There is no place for substitutions and juridical equivalences here.

4 Conclusion: Hypothetical Propositions in Law We are now justified in following Leibniz when he partly grounds the meaningfulness of the expression “juridical logic” on the fact that the conditional propositions, with which the Roman jurisconsults deal, are hypothetical in a sense that is proper to the law. By striving to give a rigorous definition of juridically conditional propositions, Leibniz isolates two important properties. First, such propositions are not hypothetical in themselves, for instance with respect to their grammatical aspect. They are inferred to be hypothetical propositions on account of the epistemic context in which they are uttered. Second, they can be compared to each other on the basis of their respective probability, i.e., on the basis of the totality of equivalent substitutions it is possible to apply to each of their parts that constitute a juridical condition. Such an epistemic contextualization of the logical notion of conditionality and such an approach to meaning in terms of explicit / tacit meaning compel the Roman jurisconsults to use numerous argumentative patterns, partly grounded upon presumptive ways of reasoning, in order to determine the juridical meaning of a statement, and they enable Leibniz to provide an account for a properly juridical theory of what is a proposition.

Notes 1. Disputatio juridica (prior) de Conditionibus and Disputatio juridica (posterior) de Conditionibus (A VI 1 97–150). 2. In the De Conditionibus, Leibniz makes no distinction between the adjectives “juridical” and “moral” and speaks of “moral conditions” to refer to what today’s lawyers call “juridical

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4.

5. 6.

7.

8. 9.

10.

11. 12.

13.

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conditions”. In this paper we will follow the latter in order to avoid using an adjective fraught with ambiguities. Leibniz ends the first part of his Disputationes with the following very clear words: “Atque hic ipsos Terminos simplices C[onditio]nem ingredientes spectavimus. Prohibuit me inopinatum quiddam nunc totum exequi. Quare de ipsa Dispositione, quando nulla, C[onditiona]lis, pura intelligatur, restabit altera Disputatione, si Deus aspiraverit, speculari” (A VI 1 124). The second part is presented as follows: “Q.D.B.V. pars altera qua ipsa dispositio, quando nulla, c[onditiona]lis, pura sit, explicatur” (A VI 1 130). “Hic illud saltem praeterire non possum, tanto ingenio tantaque profunditate in reddendo jure versatos esse J[uris] C[onsu]tos veteres, ut in certissimas ac pene mathematicas demonstrationes eorum responsa redigendi laboris potius sit in digerendo, quam in supplendo ingenii” (A VI 1 101). Leibniz titles the new version he gives of his Disputationes in 1667–1669: “Specimen certitudinis seu demonstrationum in jure exhibitum in doctrina conditionum” (A VI 1 369). Leibniz makes this need explicit by adding a section headed “Praeliminaria” in the Specimen. In this new section, between the “Proemium” and the first chapter of the Specimen Leibniz stresses the necessity to give a rigorous definition of juridical conditions. Against some doctors in law who are satisfied with giving “Synonymias” and making distinctions between “Homonymias”, the young student in law grounds his claim upon the authority of Thomas Hobbes. By introducing the model of philosophical rigour in law, Leibniz rejects as ill-formed some so-called definitions of juridical conditions by doctors in law such as “modus”, “causa”, “privatio puritatis” (A VI 1 370–371). Only a propositional approach enables a rigorous definition of juridical conditions and exhibits the necessity of the Roman jurisconsults’ reasonings when they have to say whether a juridical proposition is “pura”, “conditionalis” or “nulla”. The originality of this approach is stressed by Schepers (1975: 3). “Nos procedemus, ut arbitror, paulo solidius, et rem sua natura incompletam (qualis est Conditio, quae extra Propositionem Conditionalem esse non potest) in ordine ad Complementum, seu conditionatum, aut potius totum quod h.l. est Propositio Conditionalis, definiemus” (A VI 1 371). “Doctrina de Conditionibus pars quaedam est Logicae Juridicae, agens de Propositionibus Hypotheticis in jure . . .” (A VI 1 370). “T11: C[onditi]O M[oralis] est incerta. Nam si certum est veram esse, dispositio pura est, T332 et DF30, si falsam, nulla, T144 et DF31” (A VI 1 111). In this paper, we will refer to definitions and theorems Leibniz gives in his Disputationes with the letters “DF” and “T”, respectively. “DF33: Certa Conditio est, cujus eventus est (idque in Actualibus) certus”/“DF34: Eventus est, cum”/“DF35: Existit, id est illo tempore, quo existere dicitur, praesens est, vel”/“DF36: Deficit seu illo tempore, quo solo esse potest, praesens non est.”/“DF37: Pendet ante Eventum” (A VI 1 104). DF68: “Conditionarius est subjectum deducti in Conditionatum, seu persona, cui jus, quod Conditionatoris fuit, Dispositione tribuitur” (A VI 1 105). T335a, note p, law D.35.1.68. Leibniz presents another way of solving this problem in his note. Even if it is established that the father knew his daughter was already married when he wrote his testament, the Roman jurisconsults are justified in interpreting his statement as if the proposition “when she marries” was not added and thus in considering his statement as juridically pure. Indeed, if such a proposition meant a juridical condition it would compel the daughter to divorce. But divorces are against the interest of the state. So the argument “In fraudem Legum adjecta” (DF114; A VI 1 107) can be used in order to neutralize the juridical effect of the proposition “when she marries”. And because the main proposition concerns a marital engagement it is juridically pure and not null: “[Si conditio est impossibilis] in sponsalibus [dispositio est pura]. Ita enim receptum est” (T335; A VI 1 146) This epistemic property enables Leibniz to consider that, from a juridical point of view, a proposition can be said to mean a conditional proposition even if no “formal word” (usually indicating the conditional “aspect” of a proposition (for instance the sign “if”) is used in it,

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15.

16. 17.

18.

19.

20.

21. 22.

23. 24.

25. 26.

27. 28.

A. Thiercelin but provided it is not known with certainty when it is uttered whether one of the circumstances described in it will occur or not. In such cases, the juridical condition is said to be added in a “tacit” way: “Si Circumstantia aliqua incertum est an sit, Dispositio est C[onditiona]lis. Id enim tacite continet: si illa circumstantia sit” (T192; A VI 1 133). That is the reason why it is so difficult to decide whether a proposition is juridically conditional or not: it may be juridically conditional whereas it has no conditional “aspect”, it may not be juridically conditional whereas it has a conditional “aspect”. DF62: “Propositio est Conditionalis (Pura) figura, id est sola dispositione verborum, vel expresse et figura et sensu, vel tacite solo sensu” and note t: “Figura C[ondition]num absolvitur verbis formalibus, ea sunt Copula, in U[ltima] V[oluntate] ut plurimum: esto, testator enim pro imperio loquitur, et Signa: si, cum, quis, etc . . .” (A VI 1 105). “DF30: Conditio necessaria dicitur vel Conditionati, DF10, aut dispositionis, T49, ratione, vel in se et sic iterum a parte rei, sic omnis conditio ab initio est necessaria vel impossibilis; aut a parte nostri, ita necessaria est, quam veram esse certum est,”/“DF31: Impossibilis, quam falsam, et vel omnino, vel dato tempore, ea est impossibilis impraesentiarum”./“DF32: Certum est, quod scimus necessario tale esse, quale apparet” (A VI 1 103–104). DF11: “Dispositio est propositio, cujus veritas a voluntate pendet ejus, qui est Arbiter Dispositi, qui si Dispositum aliquo dato verum esse vult, nec aliter declarat suam voluntatem, Dispositio est Conditionalis. ” and DF12: “Arbiter est Persona, qua efficaciter volente res est, et alias non est” (A VI 1 102). DF67: “Disponens Persona est Conditionator, cujus ultimo actu voluntatis declarativo valida est dispositio” (A VI 1 105). DF66: “Propositio Conditionalis Moralis, cujus nempe Conditio et Conditionatum sunt Moralia, dicetur a nobis inposterum Dispositio in specie” (A VI 1 105). In note l of T332 Leibniz writes that the “Conditio Extrinseca” is the one that “per se inest C[onditionato]”. As such, it is extrinsic to the utterer’s wish whereas a juridical condition is intrinsic (“Conditio Intrinseca”) to his wish (A VI 1 146). “Conditio Extrinseca est, cujus Conditionalitas ex re ipsa est. Ejus species sunt: Conditio necessaria Conditionato, quae per rei naturam id suspendit; et Conditio, cui Conditionatum necessarium est, quae infert” (A VI 1 102). DF53: “Conditio Identica, quae prorsus eadem est cum Conditionato”. In note o Leibniz gives an example of such a condition: “si servum haereditarium manumiseris [. . .] haeres esto” (A VI 1 104). DF55: “Si Conditio Conditionato opposita est, dicitur Propositio Perplexa, cujus Conditio et Conditionatum non possunt simul existere vel non existere”. In note q Leibniz considers explicitly the propositions in which the conditions are identical to the propositions they are connected with as a kind of perplexed propositions (A VI 1 104). T146: “Perplexa dispositio non est moralis, nam est impossibilis, DF.55. Impossibile autem morale non est. Fictio enim ad impossibiles non extenditur” (A VI 1 130). T49: “In C[onditio]nem actui necessarium deductum est aut expressum, aut quod ei utcumque simile. Nam quod necessario facimus, inviti facimus ut plurimum. Si igitur C[onditiona]tor totam C[onditio]nem libentius omisisset, quanto magis partem?” (A VI 1 115). T49, note p, law C.6.25.3 (A VI 1 115). T331: “Si in se extra dispositionem necessaria est Co [PURA EST DISPOSITIO]. Omne enim quod necessario et ipsa vi adest frustra adjicitur seu est pro non adjecto” (A VI 1 146). Leibniz does not give clear examples for that kind of necessitated conditions. Respectively: “incertum est an” and “incertum est quando”. DF45: “Dies certus aut incertus est, an vel quando, vel an et quando” (A VI 1 104). T286: “Legatum dilatum in diem incertam quando non transmittitur. Nam dies certus differt actionem, dies incertus quando differt jus (non igitur transmittitur quia nondum quaesitum est, T246), dies incertus an, seu Co per T192, suspendit utrumque, T9” (A VI 1 141). T192: “Si Circumstantia aliqua incertum est an sit, Dispositio est Clis. Id enim tacite continet: si illa circumstantia sit” (A VI 1 133). “Dies incertus quando in U.V. facit C[onditio]nem” (A VI 1 134). T197: “Dies incertus quando in U[ltimate] V[oluntate] facit C[onditionem]” and note o, law D.35.1.75 (A VI 1 134).

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29. Such an estimation is necessaray when a “conditionarius” wants to transform a right that is transferred to him under a suspensive condition (“sub conditione”) into a right that would be transferred under a resolutive condition (“ad conditionem” or “sub modo”). This transformation means the right is considered as his own as long as it is not known with certainty that the truth value of the proposition meaning the initial suspensive condition is the false. Nevertheless, such a transformation requires that he gives the “conditionator” an assurance according to which he will give him back the right if the condition is defeated. In order to fix the amount of the guarantee, the value of the conditioned right must be estimated. T318: “Qui ad C[onditio]nem (seu sub modo) accipit, ei cavendum est, existente C[onditio]ne (modo deficiente), rem in integrum restitutum iri. Quod tutior sit qui dat” (A VI 1 145). 30. It depends also on the value of the thing that is the content of the right. T265: “Quo pluris est C[onditiona]tum, hoc jus C[onditiona]le est majus. Puta si A erit, 100 habeto; si B, 200. Supposito A et B esse aeque incerta, pluris est C[onditi]o B quam A” (A VI 1 140). 31. “Potest [JUS C[ONDITIONA]LE] tamen aestimari, certitudo enim potest aestimari spe tanquam communi mensura” (A VI 1 139). 32. T274: “C[onditi]o aestimantibus penitus ignota, incertissima est, v.g. si Titius liberos habebit, neque vero quisquam sciat quis sit ille Titius. Tum enim circumstantiae non apparent, ex quibus probabilitas in alterutram partem esse possit” (A VI 1 140). T275: “Quo C[onditi]o est operosior, hoc est minoris. Probabilius enim est minus quam majus extiturum esse” (A VI 1 141). 33. T271: “[. . .] Incertitudo enim spe aestimatur, et timore, seu opinione futuri boni et mali” (A VI 1 140). 34. “Parem inter se rationem habent:

35.

36.

37. 38.

39. 40.

Jus nullum

Jus C[onditiona]le

Jus purum

C[onditi]o impossibilis cyphra

incerta fractio

necessaria integrum

Nam C[onditi]o impossibilis jus nullum, T144, necessaria purum, T332, incerta C[onditiona]le efficit, T11. Jus C[onditiona]le autem est medium inter purum et nullum; hoc majus, illo minus: uti fractio inter nullum et integrum” (A VI 1 139). DF38: “Incertissima [conditio] est, cujus contraria aeque certa est” (A VI 1 104). T273: “Si C[onditi]o incertissima est, tantum distat a puro, quantum a nullo, id est puri dimidia est. Aequalis enim est spes, id est distantia a nullo; et timor, id est distantia a puro” (A VI 1 140). Whereas he stresses a proposition of which it is impossible to know the truth value cannot mean a juridical condition (DF39: “Ignoranda [Conditio est], cujus veritas aut falsitas sciri non potest” (A VI 1 104)), it is worth noticing that Leibniz considers as the most uncertain the juridical condition in which nobody knows what a proper name refers to. Cf. T274 already quoted in note 26. But could we not say that on account of this ignorance it is impossible to know the truth value of the proposition? Dascal (2005: 43) stresses the ambiguity of Leibniz’s use of the word “probability” insofar as it may belong to what Dascal calls Leibniz’s “algorithmic model of rationality” or to the “non-algorithmic model” he developed in part thanks to the study of argumentative patterns used by the Roman jurisconsults. “Quo major est latitudo C[onditio]nis, seu quo pluribus modis contingere potest, hoc major spes est. A quolibet enim modo separatim spes est” (A VI 1 141). “Co affirmativa pluris est quam negativa, pluribus enim modis negativae contraria existere potest, v.g. si Titius non riserit, toto enim tempore omnibus pene momentis contingere potest ut rideat. Ergo contraria est pluris, T.276 et T.262, sed illa ipsa negativae contraria est affirmativa” (T277; A VI 1 141). “C[onditi]o disjunctiva tanti est, quanti sunt C[onditio]nes disjunctae computatae (id est additae ad 0)” (T263; A VI 1 140). “Conjunctiva, quanti sunt conjunctae (detractae a puro). C[onditi]o enim disjunctiva major est simplici, per T.276. Conjunctiva minor, per T.275, minor autem est detrahendo a puro, major addendo ad nullum” (T264; A VI 1 140).

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41. T46: “C[onditi]o in U[ltima]V[oluntate] interpretationem extensivam recipit, non intensivam, in Contractibus contra. Contractus enim est cum debituro, T34, in quo non praesumitur consensus nisi ad expressum, qua quo plus obligatus est eo magis damnosa ei dispositio est. Verba autem ultimae Voluntatis a Testatore sunt, T33, cui existentia C[onditio]nis damnosa non est, nam post mortem demum debetur” (A VI 1 114–115). T46, note l: “extensiva est, per quam pluribus modis impleri potest C[onditi]o; intensiva, per quam plura ad eam implendam requiruntur” (A VI 1 114). 42. T334: “Si C[onditi]o est impossibilis, in U[ltima] V[oluntate] dispositio est pura” (A VI 1 146). 43. T48: “Si apparet expressum ob certum finem a C[onditiona]tore ascriptum esse, deductum in Conditionem intelligitur aut ipsum, aut quod efficaciam ad illum finem aequipollet. Aeque enim volumus, quod aeque utile est” (A VI 1 115). 44. “In Jussum deductum est aut factum, aut in subsidium obedientia. Nam summus conatus ad factum tendit, et si assequi non potest, in voluntate subsistit, DF134” (T51; A VI 1 115). 45. DF133: “Conditio Voluntatis est, quae requirit obedientiam.” DF134: “Obedientia est voluntas efficax, seu summus conatus faciendi quod jussum est, quia jussum est, seu Parendi.” DF135: “Jussum est conditio voluntatis, quae obendientia contenta est” (A VI 1 109). T52: “Jussum est C[onditi]o voluntatis, DF135” (A VI 1 115). From this point of view a special issue is to determine whether an order is obeyed or not. It is obeyed if the “conditionarius” can certify that he did his best to do what was ordered. DF136: “Summus Conatus in jure nostro sic effertur, si per aliquem non stet quo minus fiat. Stat autem non solum per eum, qui impedit, sed et qui non facit, quantum se posse intelligit” (A VI 1 109). 46. Thus, according to T263 and T264, we could say that, other things being equal, the juridical condition of which the latitude includes the satisfaction of the fact or its approximation is a disjunctive condition and for this reason its probability is higher than the probability of a juridical condition of which the latitude excludes such an approximation and proves to be simple. 47. T63: “Compellatus Jussus praesumitur. Ea enim est forma jubendi, DF141” (A VI 1 116). DF141: “Compellatus est, quem alloquitur Conditionator in Conditione, seu ad quem deductum in conditionem in secunda persona accomodatum est” (A VI 1 109). 48. “DF52: Demonstratio est proprium loco subjecti positum” (A VI 1 104). 49. T60: “[Conditio in FACTUM COLLATA est] si C[onditiona]rius est omnino incertus. Puta: qui filiam meam ducet, haeres esto; si ea nullum vellet, et C[onditi]o non in factum sed obedientiam deducta esset, omnes essent haeredes, qui ipsam vellent, T51” (A VI 1 116). 50. T62: “Omnis C[onditi]o potestativa in U[ltima] V[oluntate] voluntatis esse intelligitur, potestativa faciendi etiam jussum. Potestativa enim in C[onditiona]rium Collata est, DF122, ei juberi potest, qui obstrictus est, acquirit enim ex testamento, DF68. Jussum igitur praesumitur, per T46. C[onditi]o autem dandi obedientia contenta non est, T58” (A VI 1 116). 51. T58: “Si apparet factum ob peculiarem utilitatem electum esse [Conditio in FACTUM COLLATA est]; quisque enim quod utile est prae inutili velle praesumitur” (A VI 1 115). 52. T58, note s, law D.35.1.101.

References Dascal M. 2005. The balance of reason. In D. Vanderveken (ed.), Logic, Thought and Action. Dordrecht: Springer, pp. 26–47. Leibniz, G.W. 2002. Des conditions. Translation P. Boucher. Paris: Vrin. Schepers H. 1975. Leibniz’ Disputationen “De Conditionibus”: Ans¨atze zu einer juristischen Aussagenlogik. In K. M¨uller, H. Schepers, and W. Totok (eds.), Akten des II. Internationalen Leibniz-Kongresses, vol. 4 (= Studia Leibnitiana Supplementa 15). Wiesbaden: Franz Steiner, pp. 1–17.

Chapter 16

Contingent Propositions and Leibniz’s Analysis of Juridical Dispositions Evelyn Vargas

In our search for certainty, contingent propositions may be regarded as attesting the limits of human reason. It is a generally accepted view that Leibniz’s attempt to account for our knowledge of contingent propositions is a philosophical failure. Early in his philosophical career, Leibniz was engaged with the project of reforming traditional logic. His attempts to develop a juridical logic, that is, a logic of normative inference, may be seen as part of this ambitious project.1 As Leibniz himself pointed out later, he regarded the reasoning of jurists in contingent matters as representative of logic or the art of reasoning, akin to mathematical reasoning in necessary matters.2 In his dissertation on difficult cases in law, he also compared the decision of juridical cases to the resolution of geometrical problems.3 In addition, he claimed that both geometers and jurists apply analytical procedures.4 These miscellaneous references might suggest that Leibniz proposed the mathematical method for jurisprudence; but if this were the case juridical reasoning could stand side by side with mathematical reasoning only because it is a particular instance of the latter. My purpose in this paper is to examine to what extent the geometrical analogy can be applied to the understanding of the juridical procedure of deciding on conditional rights. This exposition has three main objectives: First, to outline Leibniz’s claim that jurists apply the analytical method (section 1.1), second, to clarify the relation between particular cases and laws (1.2), and finally, to compare juridical reasoning ‘in contingent matters’ and apodictic infallible reasoning (2). The early texts on moral conditionals and hard cases in law will show that the process of reasoning by which a conditioned right is inferred involves the resolution of the case into the elements of law but is grounded in a conditional obligation resulting from a free will.

E. Vargas University of La Plata, La Plata, Argentina

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1 Resolving Problematic Cases in Law: The Concept of case and Analytical Method 1.1 The Analytical Method Before introducing Leibniz’s account of the analytical method in jurisprudence, it is necessary to distinguish between the use of demonstrative inference for the proof of juridical rules and the process of decision making in legal practice. The purpose of the mathematical or Euclidean method is to obtain a system of propositions on the model of Euclid’s Elements, which consists in introducing definitions, axioms and postulates, and then theorems which are deduced from them. It has traditionally been seen as a way of presenting propositions which are already known. Heinrich Schepers, in an article on Leibniz’s doctrine of juridical conditionals, has remarked that Leibniz applied the mathematical model for his demonstrations of the theorems of this doctrine, not merely in terms of the external structure we described above but in its deductive core (Schepers 1975: 3). This is not to say, however, that Leibniz conceived the practice of logical reasoning by jurists as if they proceed by deduction when they try to interpret and apply law to particular cases.5 In his dissertation on difficult cases in law,6 he defines a case as the antecedent of a hypothetical proposition; in juridical cases, the antecedent is a fact and the consequent is a right or juridical effect.7 This meaning, according to Leibniz, has a geometrical origin, so it might be argued that the implication between ‘fact’ and ‘right’ in a juridical case could be compared to the relationship between ␲␶␻␴␫␵ ˜ (case) and ␨␩␶␩␮␣ ´ (what is sought) in geometry. Moreover, Leibniz indicates that jurists can demonstrate a juridical effect from facts in ordinary cases, or the impossibility of perplexing cases. He writes: Abstracting from all these uses, the case in general is the antecedent of a hypothetical proposition, but applying it to jurisprudence, such antecedent is called fact and the consequent jus and a case is defined as fact in accordance to law (A VI 1 235).8

In his commentary on the first Book of Euclid’s Elements, Proclus had characterized ␲␶␻␴␫␵ ˜ as the construction and alteration of the position of a geometrical object by transposing lines, points or figures.9 In ancient geometry, the construction of new geometrical objects concerned the procedure called regressive analysis. In Pappus’ words: Now analysis is the path from what one is seeking, as if it were established, by way of its consequences, to something that is established by synthesis. That is to say, in analysis we assumed what is sought as if it has been achieved, and look for the thing from which it follows, and again what comes before that, until by regressing in this way we come upon some one of the things that are already known, or that occupy the rank of first principle. We call this kind of method ‘analysis’, as if to say anapalin lyses (reduction backward). In synthesis, by reversal, we assume what was obtained last in the analysis to have been achieved already, and, setting now in natural order, as precedents, what before were following, and fitting them to each other, we attain the end of the construction of what was sought. This is what we call ‘synthesis’ (Pappus 1986: 82).

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Also, Pappus had distinguished two kinds of analysis. It can be employed in evaluating a hypothesis (theorematical analysis) or in the search of existential proofs for geometrical constructions (problematic analysis).10 In general, ancient regressive analysis is a method of searching the necessary conditions to resolve a geometrical problem or to demonstrate a theorem. It involves the finding of appropriate principles, previously proved theorems and constructions by which the problem can be solved or the theorem demonstrated. It is a method of invention but it is not the solution or proof itself. Pappus also claimed that the proof is the reverse of analysis.11 Leibniz himself had an inferential conception of the method of geometrical analysis.12 We can compare this account, for example, with Leibniz’s description of the method in the New Essays: The analysis of the Ancients, according to Pappus, consisted in taking what is demanded and drawing from it the consequences until one reaches something given or known. I have observed that, for this purpose, the propositions must be reciprocal, in order to ensure that the synthetic demonstration be able to go over the traces of the analysis backwards, but it is always to draw consequences.13

Although the many issues concerning the nature of geometrical analysis cannot be traced here, for our present purposes it is necessary to take into account that, according to the inferential interpretation of analysis, what is sought is the theorem or solution; so if the antecedent or case is ‘the thing from which it follows’, it implies the theorem or solution as its consequence (reversibility or reciprocity). But in juridical cases, the antecedent or particular event would imply some right or juridical effect. The similarity between practical deliberation and geometrical analysis had been remarked by Aristotle in the Nicomachean Ethics (III 3, 1112b15–29); he compared reasoning by means to a given end in practical matters and reasoning from what is sought to something we already know how to construct or prove. In the following years, Leibniz would emphasize the teleological aspect of the method of analysis, for example in medicine;14 but, as we shall see, it is also relevant for our present purposes. Another feature of the method analysis that Leibniz usually pointed out concerns the resolution of a complex problem into simpler problems whose solution we know.15 Now if the analogy between juridical procedures and geometrical methods captures Leibniz’s view, the process of decision of a juridical case can be compared to the resolution of a geometrical problem, but it is quite problematic to see the inferential link between the juridical effect and its factual antecedent in terms of the features we described above, namely, reversibility. In the following sections, I will examine to what extent this analogy between problematic analysis and the legal practice of deciding juridical cases could be valid for Leibniz.

1.2 Dispositions as Juridical Cases According to its general definition, a case is the antecedent of a conditional proposition. But in his dissertation, Leibniz, as Euclid would have suggested, studied only

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the problematic cases since the non-controversial ones were left to the apprentice or reader.16 The controversial cases that Leibniz examined consist of dispositions or moral conditionals, which express particular legal institutions such as contracts and testaments. A conditional proposition, more generally, consists of two partial propositions, the condition and the conditioned.17 After defining conditional propositions in general he writes: A disposition is a proposition whose truth depends on someone’s will, who is the arbiter of the disposition and who, if he wants what is disposed to a given end to be true, does not declare his will otherwise and the disposition is conditional. The arbiter is the person by whose will the matter in question and not another is carried out (A VI 1102).18

A disposition is a conditional proposition, and, as such, it is valid if the condition or antecedent implies the consequent. If these two propositions are affirmative, the implication is called illatio (ibid.). But if a conditional has a juridical effect, it is a moral conditional, that is, if the condition is fulfilled, some right is to be conceded.19 Thus, once the condition is fulfilled, it is legitimate to infer or demand the consequent. Now the legal obligation results from the decision of the arbiter, that is, someone who cedes something to which he has a right by means of a juridical act, for example, when imposing conditions in testaments and dowries. In other words, an obligation is introduced in a situation in which no previous obligations exist. Leibniz’s definition of legal disposition is not only descriptive, but also explanatory and can be used in legal reasoning. According to it, resolving a disposition or conditional right will consist in deciding whether the consequent (jus) is implied by the antecedent. In order to show that a particular disposition is valid, and that it is legitimate to demand what is stated in the consequent, the case has to be related to the appropriate norm, that is, it is necessary to find the rule for the conditional statement.20 Consider, for example, the disposition called ‘demonstratio’, in which the condition is implicit because it is the subject of a universal categorical proposition.21 Then the original proposition can be resolved into a hypothetical proposition in which the subject of the former proposition becomes the antecedent of the conditional (for example, ‘any person who marries my daughter will receive 100 pieces of gold’ becomes ‘if someone marries my daughter, he will receive 100 pieces of gold’). So, if both the antecedent and the consequent of the conditional are true, the disposition is valid. Interestingly, in juridical logic the most ‘elemental’ statement is not the categorical universal proposition but the conditional; thus, by transforming the original categorical statement, the complex case is reduced to the simplest case of disposition, and in order to do so the jurist applies the relevant rule and definitions. Leibniz disagreed with those who objected that a judicial decision could be exclusively based on law because it would require knowing the most accepted interpretation. For Leibniz, when the act of judicial interpretation of a particular legal document depends on the judge’s decision, his decision can be free or regulated; if regulated, he can take into account juridical norms alone, or additional rules which are foreign to it. This division by dichotomies exhausts all the possible criteria and

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establishes a taxonomy in terms of their certainty.22 For the young jurist, legal decision making cannot lie in the unfettered discretion of the judge; since positive law is founded in reason, if it is not evident which interpretation would be the most accepted, Leibniz proposed to appeal to the interpretive rules of natural reason.23 In problematic cases or, in Leibniz’s terminology, ‘perplexing cases’, the fact stated in the antecedent seems to imply mutually incompatible juridical effects.24 Consequently, a variety of different interpretations would seem to be possible as to which right or rights should be conceded but, most importantly, it is necessary to elucidate whether the juridical effect is actually produced.25 As we have seen, the procedure to decide which legal interpretation must be chosen will involve the resolution of the complex case into its elements, that is, as a conditional statement consisting of a condition and its juridical effects, and show which implication is valid, if any. A problematic case results from a perplexing juridical act or disposition.26 Now if a disposition is expressed or reduced to a perplexing proposition, it will consist of two incompatible propositions,27 and therefore it cannot be valid since their conjunction is impossible and when the antecedent and the consequent are opposed to each other no juridical effect can be inferred.28 In other words, the interpreter can resolve the problematic case in the same way he decides unproblematic cases, that is, by considering the statement which expresses the juridical act and applying the pertinent rules to its general form, particularly those which hold for a conditional proposition consisting of incompatible partial propositions. But dispositions are not only conditionals, but also moral conditionals; in the next section, I will analyze their special features more specifically.

2 Juridical Reasoning: The Doctrine of Conditions as its Foundation Ordinarily, interpreting a case will consist in the legal practice of considering it to be an instance of a general norm.29 Appropriate legal rules could be employed in the process of searching for reasons so as to offer an argument to support the legal claim. In conditional rights, the aim of interpreting the particular case is to establish whether the juridical effect is produced. For this purpose, the interpreter has to find the pertinent rules. Since these rules are definitions or theorems based on definitions, the rules of jurisprudence are the rules by which the interpreter can pass from the case to its definition, and given that legal documents which express conditional rights are based on dispositions, which are in turn expressed in conditional statements, the process of interpretation of a moral conditional proceeds from the case to its formal structure. In addition, Leibniz had explicitly included the method of analysis as a valid procedure to interpret legal texts.30 In consequence, it might seem plausible to attribute a formalist view about legal discourse to Leibniz. The theorems of the doctrine of conditions represent the interpretive rules by which the particular case can be seen as implying the juridical effect. But although

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the singular case represents some universal rule, the case represents a general rule only as regards its truth value and formal structure as a conditional proposition. In general, the rules permit reducing each case to the basic form of implication, and then to its truth conditions. But despite the similarities between this procedure and the method of analysis we presented in section 1.1, this not to say that the normativity involved in dispositions (i.e., conditional obligation) is reducible to logic’s normativity (i.e., logical necessity). Compare, for example, the following conditionals: 1. If someone marries my daughter, he will get my property in Cornelia. 2. If a magnet attracts iron, then corporeal emanations pass from one to the other. Example 1 represents a disposition or moral conditional, but example 2 is a proposition that we assume to be true in Leibniz’s natural philosophy. The antecedents of both conditionals are contingent propositions; in dispositions, the fact stated in the condition has to be contingent (i.e., uncertain) because it implies a conditional right;31 in the case of our second proposition, the antecedent, namely ‘a magnet attracts iron’, is based on a contingent fact.32 But it is plausible to sustain that once they are joined to their requisites or necessary consequences, the resulting conditional is a necessary truth. Since an observation is a contingent universal proposition such as ‘Magnets attract iron’,33 if in conditional 2 we can consider attraction as a case of motion, and take into account the principle that ‘whatever moves is moved by another body’, then attraction may be regarded as an instance of the principle, and the proposition ‘If a magnet attracts iron, then corporeal emanations pass from one to the other’ could be inferred from the principle and the observation since the iron is put into motion by the particles the magnet emits but those particles are not observable.34 The conditional statement is then a universal necessary truth. In valid dispositions, on the other hand, once the fact or facts stated in the antecedent occur, the condition is not uncertain anymore and the consequent is true, that is, the juridical effect or conditionality is necessary.35 The observational statement and the disposition may seem to be similar, but in the case of the latter, the singular case represents an irreducible kind of conditional, that is, an elementary form of proposition and no inclusion between the concepts of the partial propositions (e.g., things in motion and magnets) is involved. The inclusion between concepts can be expressed in terms of the relation between a whole and its parts, in which the ‘parts’ of a concept constitute its definition. In moral conditionals, on the other hand, the antecedent is some contingent particular fact and, more importantly, the relation of conditional obligation is irreducibly dyadic. Firstly, a conditional proposition only asserts the connection between the antecedent and the consequent.36 The truth of the condition cannot be deduced since the antecedent is a contingent particular fact and the conditional right is valid in virtue of the truth of the antecedent.37 Also, for moral conditionals, some specific rules apply in order to determine the juridical effect. For them, we can show not only that if the consequent is false the antecedent is false, but also that if the condition is not true, the consequent is not true, from which it follows that the partial propositions

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are convertibles (A VI 1 375): for example, it is not the case that someone gets my property in Cornelia unless he gets married to my daughter. But Leibniz makes clear that truth conditions are not the only things at stake: From a disposition like conditional 1 and the truth of its antecedent we do not simply infer the truth of the consequent, but a legal obligation.38 Also, it is reasonable to claim that Leibniz proposed that in juridical deliberation the doctrine of conditionals can be applied to justify a decision. Since a contract or a testament is a particular legal arrangement deliberately instituted for the sake of its legal effect, it might seem that the legal interpreter should find the commitments originally made by the arbiter. More specifically, in order to decide on a problematic case, the interpreter attempts to infer the arbiter’s intention of accepting the rule that the particular disposition represents.39 The rule expresses the arbiter’s purpose as it is made explicit by the interpreter, but this purpose may be real or only supposed by the interpreter.40 Since the legal decision or juridical effect depends on the validity of the particular conditional, the interpreter must consider the connection or conditionality the arbiter creates between the antecedent and the consequent,41 and in doing so the jurist assumes he is acting as a vir bonus, which constitutes the ground of validity of the disposition. The link between the case or fact that constitutes the antecedent and the conditioned right is established on the base of the arbiter’s purpose, that is, by a final cause which can be real or assumed by the interpreter. For this reason, the impossibility that the antecedent is fulfilled but the consequent is not given is only a ‘moral impossibility’;42 it is assumed that the arbiter’s purpose is that the truth of the antecedent implied the fulfillment of the consequent or conditioned right. Consequently, the interpreter’s inference is only probable. He can only conjecture about the sense of a contract or testament.43 For these reasons, it is important to emphasize that even if a problematic case can be resolved by showing that the juridical effect is null because the conditional statement is impossible, the conditional link in a disposition is based on a free will. Let me conclude this section with some additional remarks on the distinction between the legal practice of forming a case and the practice of deciding on it, which can be introduced in support of my view. In his Dissertatio de arte combinatoria, Leibniz characterized a case as a combination of the elements, the ‘simples’ or loci communes. Jurisprudence is similar to geometry in that both have elements and cases, the latter being a combination of the former.44 A juridical case is a combination of the elements of law, that is, act, thing, person and right.45 Since the combinatorial art can be employed in the process of forming a juridical case, analysis can be seen as the complementary process of finding the elements that constitute the case in order to determine its legitimacy. Now a disposition is necessary by virtue of the arbiter’s will; his free decision cannot be arbitrary not only in the sense of being logically impossible, but also because the interpreter assumes the good will of the arbiter in a valid disposition. For these reasons, the particular dispositions that instantiate the rule can only be similar in form, since they have in common their conditional structure and the conditional obligation on which it is grounded. In its most elemental structure, a conditional right is a kind of relation, thus the rule typifies a certain relationship or ‘respectus’.46

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3 Conclusions In sum, the young Leibniz conceived the process of interpreting law as an inferential procedure. But as we have seen, according to Leibniz, juridical reasoning cannot be seen as a particular kind of mathematical reasoning. Nevertheless, it does not elude reason. Juridical hermeneutics makes evident the distinction between two different conceptions of the propositional link; while juridical illatio represents the connection between the general rule and the case in valid dispositions, conceptual in-esse expresses the relation between a conceptual whole and its parts in definitions. Although the juridical decision of a problematic case will involve resolving a complex whole into its elements as geometers do, the validity of a moral conditional cannot be determined with absolute certainty by considering its terms in the way formal logic does, since the ‘elements’ are not concepts but the relation of obligation which moral conditionals typify. What needs emphasis is that it constitutes a specific domain of rational knowledge which has to be distinguished from geometrical certainty. Moral conditionals represent an irreducible type of propositional link grounded on a final cause; insofar as they constitute a valid juridical act, the grounds of conditional obligation have to be explained by reference to logic and will. Later on, in the years following the reform of dynamics, final causes and God’s free will as the arbiter of contingency in nature will play a role in Leibniz’s natural philosophy; whether his earlier conceptions of juridical contingent propositions had some influence on these views have yet to be examined.

Notes 1. See, for example, his preface to De Conditionibus (A VI 1 101) but also his Dissertation on the Art of Combinations where the art of forming cases in jurisprudence is regarded as an application of this art (see A VI 1 168; 177; 189 and Section 2 below). 2. Nimirum pro comperto est, ut Mathematicos in necesariis, sic Juriconsultos in contingentibus Logicam, hoc est rationis artis, prae caeteris mortalibus optime exercuisse. (C 211). 3. A VI 1 235, quoted below. 4. Geometrae et Iurisconsulti Analytici magis, medici vero et politici Combinatorii sunt (A VI 3 431). 5. Leibniz was well aware of the difference between producing law by demonstrating a general juridical norm and applying law to a particular case. For the distinction between ‘proof’ and ‘consequence’ in juridical logic see Kalinowski (1977: 186–188). 6. De casibus perplexis in jure (A VI 1 235–256) was written by Leibniz in 1666 to obtain his doctorate at the University of Altdorf, which he obtained in February 1667 at the age of 21. 7. See the passage quoted below (A VI 1 235). 8. Casus vocem apud Mechanicos natam vicini Geometrae primi adhibuerunt in rem suam, quibus ␲␶␻␴␫␵ ˜ est ipsa figura (seu linearum, superficierum, corporum ad se invicem positus), de qua deinde ␨␩␶␩␮␣, ´ nimirum quantitas, ratio, analogia, uti apud JCtos jus de facto demonstratur. Unde problemata eorum ␲o␭´␷␲␶␻␶␣ similia sunt controversiis JCtorum distinctione expediendis, add. Dn. Erhard. Weigel. Analys. Euclid. sect. 2. C.12. n. 4., et impossibilia casibus perplexis, in quibus pro solutione est advertere et demonstrare impossibilitatem, quod Algebra praestat. Manavit inde vox ad Medicos, et Theologos Moralistas quoque, qui

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10.

11. 12.

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14. 15.

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propterea et Casuistarum titulum ascivere, Speidel. Spec. lit. C. n. 27. A quibus omnibus abstrahendo, casus in genere est antecedens propositionis hypotheticae, applicando vero ad Jurisprudentiam, tale antecedens dicitur factum, consequens jus; et casus definietur factum in ordine ad jus. ‘The case (␲␶␻␴␫␵)’, ˜ Proclus proceeds, ‘announces different ways of construction and alteration of positions due to the transposition of points or lines or planes or solids. And, in general, all its varieties are seen in the figure, and this is why it is called case, being a transposition in the construction’ (Heath, Introduction; in Euclid 1956, vol. 1: 134). Heath (ibid., 134n3) also suggests that: ‘Tannery rightly remarks (1887: 152) that the subdivision of a theorem or problem into several cases is foreign to the really classic form; the ancients preferred, where necessary, to multiply enunciations. As, however, some omissions necessarily occurred, the writers of lemmas naturally added separate cases, which in some instances found their way into the text. A good example is Euclid I.7, the second case of which, as it appears in our text-books, was interpolated. On the commentary of Proclus on this proposition, Taylor rightly remarks that ‘Euclid everywhere avoids a multitude of cases”. ‘Now analysis is of two kinds. One seeks the truth, being called theoretical. The other serves to carry out what was desired to do, and this is called problematical. In the theoretical kind we suppose the thing sought as being true, and then we pass through its concomitants [consequences] in order, as though they were true, and existent by hypothesis, to something admitted; then, if that which is admitted be true, the thing sought is true, too, and the proof will be the reverse of analysis. But if we come upon something false to admit, the thing thought will be false, too. In the problematic kind we suppose the desired thing to be known, and then we pass through its concomitants [consequences] in order, as though they were true, up to something admitted. If the thing admitted is possible or can be done, that is, if it is what the mathematicians call given, the desired thing will also be possible. The proof will again be the reverse of analysis. But if we come upon something impossible to admit, the problem will also be impossible’ (Hintikka and Remes 1974: 9–10). See note 10. I use this expression in a similar way to what Hintikka and Remes (1974: 31ff) call ‘the propositional view’ where the authors distinguish between the propositional interpretation of analysis (analysis of proofs) and their instantial interpretation (analysis of figures), according to the latter the method does not proceed from one proposition to another but from some geometrical object to another, which involves a complex network of connections rather than a linear deductive structure. L’Analyse des Anciens estoit, suivant Pappus, de prendre ce qu’on demande, et d’en tirer des consequences, jusqu’`a ce qu’on vienne a` quelque chose de donn´e ou de connu. J‘ay remarqu´e que pour cet effect il faut que les propositions soyent reciproque, a fin que la demonstration synthetique puisse repasser a rebours par les traces de Analyse, mais c‘est toujours tirer des consequences (NE 4.17.5; A VI 6 484, my emphasis). See also A VI 4 476. For an account of this use of the method of analysis in medicine and physiology, see for example Vargas (2001) He writes to Conring in March 1678: Definitio autem ideae alicuius compositae in partes suas resolutio est; quemadmodum demonstratio nihil aliud quam veritatis in alias veritates jam notas resolutio est. Et solutio alicuius problematis quod in efficiendo consistit est resolutio in alia problemata faciliora, sive quae jam constat esse in potestate. Haec est analysi mea, in Mathematicis aeque quoque aliis scientiis probata et succesura. Si quis aliam habet, mirabor si non ad hanc denique redubit, ejusve pars aut corollarium erit (A II 2 398). See note 9. 1. Propositio Conditionalis est, quae hoc continet: Si illa Propositio vera est, haec vera est. 2. Illa Conditio dicitur, haec Conditionatum (A VI 1 102). (= A conditional proposition is that which contains: If that proposition is true, this proposition is true). In his version for the Specimina Juris he writes: 1. PROPOSITIO autem CONDITIONALIS (cui opponitur PURA), v.g. si homo est animal, Petrus sentit; si navis venerit, Titius 100 habeto, est qua: constat ex

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19.

20. 21.

22.

23. 24.

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E. Vargas duabus 2. PROPOSITIONIBUS PARTIALIBUS tanquam materia et junctura earum tanquam forma quae junctura seu 3. CONDITIONALITAS ad minimum hoc dicit: si propositio partialis prior, seu Is 4. CONDITIO (quam imposterum scribemus Co, et Conditionatum Ctum, et Conditionale Cle, et Conditionatorem Ctorem, et Conditionarium Crium) vera est (v.g. si homo est animal, si navis venerit) qua: ipsa effertur in modo non indicativo, sed conjunctivo; vera etiam est posterior seu 5. CONDITIONATUM, qua; jam effertur in modo directo, seu indicativo (Petrus sentit, Titius 100 habebit), et hanc juncturam dicimus affirmativam, uno verbo 6. ILLATIONEM (A VI 1 371). (= (1) But a conditional proposition (which is opposed to a pure proposition), e.g., ‘if man is an animal, Peter has sensations’, ‘´ıf the ship arrives, Titus will get 100 pieces of gold’, consists of two partial propositions (2) as matter and their connection or form whose connection or conditionality (3) says at least this: if the first partial proposition or condition (4) is true (hereafter Co for condition, Ctum for conditioned, Cle for conditional, Ctorem for conditioner, Crium for conditionee), for example, ‘if man is an animal’, ‘if the ship arrives’, which is expressed in indicative or direct mode, the latter partial proposition or conditioned (5) is also true, which is not expressed in indicative but in conjunctive mode (‘Peter has sensations’, ‘Titus will get 100 pieces of gold’) and we say this connection is affirmative; in one word, (6) illatio.) Dispositio est propositio, cujus veritas a voluntate pendet ejus, qui est arbiter Dispositi, qui si Dispositum aliquo dato verum esse vult, nec aliter declarat suam voluntate, Dispositio est Conditionalis. Arbiter est persona, qua efficaciter volente res est, et alias non est. Propositio igitur Clis vel spectatur in se, et ita ratione forma et materiae, vel in effectu, quod ad Scopum nostrum juridicum attinet, et ita vel non habet effectum, juris Clem, seu medium inter purum et nullum, et dicitur a nobis [8.] LOGICA, vel habet, et dicitur [9.] MORALIS [. . . ] (A VI 1 371). (= Therefore a conditional proposition is considered in itself, in virtue of its form and matter, or in its effect, which pertains to our juridical scope; and so it has no juridical conditional effect, i.e., between pure and null, and we call it logical conditional or it has a juridical effect and it is called moral conditional . . . ). Note the definition of ‘rule’ as theorem: Theoremata seu regulas ex definitionibus demonstrabiles adjiciamus (A VI 1 372). Leibniz demonstrates the rule that every demonstration is a condition in Theorem 14 as follows: Omnis demonstratio est Co. Quia demonstratio est subjectum propositionis categoricae universalis necessariae, per d. 17., talis autem resolvi potest in hyotheticam, v. g. omnis homo est animal, seu: si quis est homo, ille est animal, quod eleganter observavit Th. Hobbes lib. De corpore, in tali autem resolutionem subjectum fit antecedens, antecedens est Co, per d. 4. Quare omnis demonstratio per resolutionem Co est ( A VI 1 380). He had previously defined demonstrations as a kind of implicit condition as follows: (Definition 17) Subjectum propositionem Categoricae universalis necessaria (A VI 1 379). Note that he remarks that demonstrations in this sense are dispositions: Haec propositio est universalis, et necessaria, non quidem ex natura rei, voluntate tamen testatoris (ibid.). JUDICIS ARBITRIUM vel (3) liberum, 9, vel regulatum, 10, quanquam regulae illae non tam juris sunt, quam commoditatis, humanitatis, aequitatis, etc. EX JURE mero (5) nos 11. 12. seqq. Rem decidendam arbitramur, cribratis opinionibus extremam quasi graviorem et in fundo residentem eligentes. Nam sententias de industria sic disposuimus, ut gradibus speratae certitudinis crescant (A VI 1 236–237). Nos speramus ex mero jure decidi omnes casus posse [. . . ] quod si jam interpretatio incerta est, adhibendae regulae interpretandi rationis naturalis ( A VI I 239–240). Casum igitur (proprie) PERPLEXUM definio (eum, qui realiter in jure dubius est ob) copulationem contingentem plurium in ipso eum effectum juris habentium, qui nunc mutuo concursu impeditur (A VI 1 236). DISPOSITIO PERPLEXA est, quando intelligi potest, quis actor, quis reus; et quaestio est utrum actori jus competat (A VI 1 240). For my present purposes, I do not consider those cases in which the difficulty to resolve them lays in how to determine the order or priority of rights to be conceded, for example in

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dividing a certain property when no testament is available (see for example case XXIX and the definition of concursus perplexus (A VI 1 243)). In conditional propositions more generally, we have the following definition: Si conditio conditionato opposita est, dicitur Propositio Perplexa, cujus Conditio et Conditionatum non possunt simul existere vel non existere (A VI 1 104). And for moral conditionals the following rule applies: perplexa dispositio non est moralis, nam est impossibile (A VI 1 129). The first rule for perplexing cases states the following: dispositio perplexa invalida est, et qui se super ea fundat, nil obtinet (A VI 1 240). According to the instantial interpretation of geometrical analysis, we are concerned with particular cases or instantiations (for example ‘a circle passing through points A, B and C’) of the general theorem to be proved referring to a certain kind of geometrical object, for example ‘any circle’ (see note 12). He distinguishes between rhetorical, grammatical and logical analysis: Interpretatio per linguam quamlibet sive eadem, sive diversam, vel sensum explicat et dicitur paraphrasis, vel artis dicendi ad verba applicat, et dicitur analysis (A VI 1 338) . . . Analysis Logica est occurrentium Definitionum, Dividionum, Propositionum, Syllogismorum, Ordinis; et singulorum non solum ratione inventionis seu locorum ex quibus sumta sunt, sed et ratione judicii seu maximarum ad quas exigenda sunt consideratio (A VI 1 339). For conditional rights the condition is contingent (A VI 1 375) or uncertain (A VI 1 111). In the first version of the Doctrine on Conditions, the term ‘Observation’ included not only universal propositions but also historical or singular observational propositions in so far as their truth depends on experience or induction: Divisio haec in determinatas et determinatas est quasi in Theoremata, id est propositiones ex terminis veras, et Observationes, id est propositiones ex sensu vel inductione veras: illae sunt rationis, v.g. totum esse majus sua parte, hae facti, v.g. dari mundi, ut omnes historicae propositiones (A VI 1 398). Propositio omnis est vel singularis, hinc Historia, v.g. Magnes in Mecha Arabiae sursum trahit loculum ferreum Mahumedis, fingamus enim exempli gratia, hoc ita esse, vel Universalis contingens ex inductione singularium pendens, hinc Observatio, v.g. Magnes trahit ferrum; vel Universalis necessaria ex ipsis terminis demonstrabilis, hinc Scientia, v.g. Quicquid movetur, ab alio movetur, vel si magnes trahit ferrum, necesse est corporea effluvia ex magnete in ferrum ire (A VI 1 284). The following passage from the Dissertation on the Art of Combinations might suggest that observations can be demonstrated by other observations: Omnes propositiones singulares quasi historicae, v.g. Augustus fuit Romanorum imperator, aut observationes, id est propositiones universales, sed quarum veritas non in essentis, sed existentia fundata est; quaeque verae sunt quasi casu, id est DEI arbitrio. [. . . ] Talium non datur demonstratio sed inductio. Nisi quod interdum observatio per observationem interventu Theorematis demonstrari potest (A VI 1 199). (= All singular propositions, such as the historical ones, e.g., ‘Augustus was the emperor of Rome’, and observations, i.e., universal propositions whose truth is not grounded in the essence but in existence, are true as if by chance, that is by God’s decision. [. . . ] There is no demonstration of them but induction, unless the observation can be sometimes demonstrated by means of a theorem in virtue of the observation.) See especially A VI 1 284 quoted above. Note also that in the mathematical tradition observations are universal propositions which describe ordinary experience and can be employed as principles or first premises of a demonstration. See Dear (1987) Si Co existit, dispositio purificatur (A VI 1 429). Also: Si Co extitit, Ctum, seu Jus et verum et praesens est (A VI 1 148). Nam propositio Conditionalis abstracta est, nihil aliud dicens quam terminorum, seu propositionum partialium connexionem (A VI 1 373) . . . Jus est vel nullum, vel Cle, vel purum [. . . ] Et variant pro causis quae sunt: Co impossibilis, contingens, necessaria (A VI 1 420). From ‘Si navis venerit, Titius 100 habebit’ and ‘navis venit’ we infer ‘Titius habeto 100’. Porro Tractatio Specialis de Propositionibus Conditionalibus dividitur in Natura et Effectum. Natura est Facti, ut sciamus quando aliquid Co etc. sit; Effectus Juris, ut sciamus posito quod

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41.

42. 43. 44. 45.

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E. Vargas sit Co, quid hoc in jure importet. Natura igitur Cnum partim necessariis consequentiis, partim praesumta Voluntate ejus cujus voluntas pro regula esse debet, seu Interpretatione absolvitur (A VI 1 375). Interpretationis scopus est mentem alicujus ex signis probabiliter colligere. Signa autem sunt verba, vel aliud quiddam, ut facta, circumstantia, etc., concurrentibus autem pluribus signis unum alterum explicat (A VI 1 375). (= The scope of the interpretation is to infer with probability someone’s purpose from signs. But signs are words or other things such as facts, circumstances, etc.; concurrent circumstances or several signs, however, explain each other.) Note for example in testaments: Arbitrium in U.V. est aut expressi aut boni viri (A VI 1 118). Note that we can speak of the juridical effect of the complete conditional proposition: [. . . ] restat ipse effectus totius dispositionis, seu propositionis conditionalis qui est: Jus (A VI 1 375). Then although for conditional rights the condition is contingent (ibid.) a perplex case has no juridical effect: Ad Cnes impossibiles pertinent perplexae, id est, quando Co per se possibilis est, sed non cum Cto, ubi Co et Ctum sibi obstant (A VI 1 376). This expression does not appear in the texts quoted, but see, for example, Leibniz’s early use of the phrase ‘to prove morally’ (A VI 1 111). In the passage to which we referred above (see note 2), Leibniz included as a sample of logical reasoning in law ‘conjectures about the sense of laws, contracts and testaments’ (C 211). Porro Ars casuum formandorum fundator in doctrina nostra de Complexionibus (A VI 1 189) Jurisprudentia enim cum aliis Geometriae similis est, tum in hoc quod utraque habet Elementa, utraque casus. Elementa sunt simplicia [. . . ] Casus complexiones horum [. . .] Termini quorum complicatione oritur in Jure diversitas casuum sunt: Personae, Res, Actus, Jura (ibid.). Inter Terminos primos ponantur non solum res, sed et modi, sive respectus (A VI 1 195). For rights as respects see A VI 1 94–95.

References Aristotle. 1980. Nicomachean Ethics. Tr. W.D. Ross, rev. J.L. Ackrill and J.O. Urmson, Oxford: Clarendon Press. Dear, P. 1987. Jesuit mathematical science and the reconstruction of experience in the early seventeenth century. Studies in History and Philosophy of Science 18: 121–164. Euclid. 1956. The Thirteen Books of the Elements. Transl. T.L.Heath. New York: Dover. Hintikka, J. and Remes, U. 1974. The Method of Analysis. Its Geometrical Origin and Its General Significance. Dordrecht: Reidel. Kalinowski, G. 1977. La logique juridique de Leibniz. Conception et contenu. Studia Leibnitiana 9(2): 168–189. Pappus of Alexandria. 1986. Book 7 of the Collection, vol. 1. Ed. A. Jones. (Sources in the History of Mathematics and Physical Sciences, 8). Springer: New York. Proclus. 1792. The philosophical and mathematical Commentaries of Proclus on the first book of Euclid’s Elements. Tr. Thomas Taylor, with as Translator’s preface his dissertation on the Platonic theory of ideas, and further material. London: Published for the author. Schepers, H. 1975. Leibniz’ Disputationen ‘De Conditionibus’: Ans¨atze zu einer juristischen Aussagenlogik. Akten des II. Internationaler Leibniz-Kongress, vol. 4., Wiesbaden: Steiner: 1–18. Tannery, P. 1887. La g´eom´etrie grecque. Paris: Gauthier-Villars. Vargas, E. 2001. Analysis and final causes in Leibniz. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress), vol. 3. Berlin: Leibniz Gesellschaft, pp. 1306–1312.

Chapter 17

Leibniz on Natural Law in the Nouveaux essais Patrick Riley

Il y a des maximes fondamentales qui consitutent le droit mˆeme . . . qui, lorsqu’elles sont enseign´ees par la raison pure et ne viennent pas du pouvoir arbitraire de l’Estat, consituent le droit naturel. (NE 4.7.19; A VI 6 425).

Why should Leibniz’s strongest and most characteristic claim about “natural law” or natural justice appear in NE 4.7.19, “On propositions called maxims or axioms” – a chapter which opens with the claim that “the geometers” have often undertaken to “demonstrate” evident propositions? Why does “natural law” soon follow geometrical demonstration? Why should Leibniz not have taken up natural law/justice (at least sustainedly) in its “natural” place – in NE 2.28 (“Of other relations”), in which he discusses, albeit cursorily and disappointingly, Locke’s tripartite theory of law: “natural/divine”, “civil”, and “of reputation”? After all, in the very next chapter of NE, 2.29, – which “anticipates” 4.7.19 – Leibniz says something more consequential and characteristic than anything in 2.28: If anyone would want to write as a mathematician in metaphysics or in ethics, nothing would prevent him from doing so with rigor; there are some who have made it their profession and have purported to provide mathematical demonstrations outside of mathematics, although success in this has been rather rare.1

He repeats this claim, with a Roman-jurisprudential variation, early in book 4: There are considerable examples of demonstrations outside of mathematics [. . .] one can say that the jurisconsults – particularly the ancient Roman jurisconsults – have many good demonstrations [. . .].2

And then in the conclusive part of book 4 – i.e., 7.19, which finally gives the definition of droit naturel as a dictate of la raison pure, not of pouvoir arbitraire – Leibniz adds: But in order not to let you think, Sir, that the good use of these maxims is confined to the limits of the mathematical sciences alone, you will find out that it is not lesser in jurisprudence,3

where jurisprudence is the science of universal justice.

P. Riley Harvard University, Cambridge, Massachusetts, USA

M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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It is no accident that Leibniz on “natural law” appears most consequentially in 4.7.19. But why? Because that whole chapter is on “axioms” and on “demonstration”, starting with geometry – but not stopping there. But why should Leibniz, in 4.7.19, discuss (“so to speak”, pour ainsi dire) first “geometrical demonstration” and then “moral demonstration”, hors des math´ematiques? Why should moral demonstration, “outside of mathematics”, be the very last, concluding part 19 of the extremely long 4.7, so that “natural law” is defined only after the other “demonstrative” sciences? It has something, surely, to do with Leibniz’s (mainly) admiring, approving view of Plato’s Meno in NE 1.1: [. . .] [T]he whole of arithmetic and the whole of geometry are innate; they are in us in a virtual manner [. . .] as Plato has shown in a dialogue where he has Socrates leading a young man into abstruse truths only by means of questions and without teaching him anything.4

But in Meno itself (as Leibniz well knew) the “v´erit´es abstruses” include both geometry and ethics. For the structure of the Meno is, first “virtue”, then geometry, then virtue again. When in Meno an impasse is reached over the moral question, “What is virtue?”, Socrates pulls Meno’s slave (“anyone you like”) out of the crowd of Meno’s retainers, elicits astonishing geometrical knowledge from this unlettered (and un-numbered) boy, and then says, in effect, that just as geometry is “wisdom”, so after all is virtue (which is knowing the “eternal verities”, such as the “absolute moral ideas” of the Phaedo 75d). Plato’s hope, in Meno 82a ff., is plainly that the contestability of morality (e.g., virtue) may be redeemed by the necessity of geometry (so that moral necessity and geometrical necessity will be logically alike: reason-given, universal, not subject to Heraclitean flux). And Leibniz in NE 4.7.11 (the “geometry” chapter) shares that Platonizing hope when he asks, “And what could we do better than reducing the controversy, i.e., contested truths, to evident and incontestable truths; wouldn’t this amount to establishing them in a demonstrative manner?”5 Like Meno (also praised by Leibniz in Discours de m´etaphysique 26, with reservations about “reminiscence” (A VI 4 1571), Leibniz’s NE says that geometers are indeed privileged, but adds that the Roman juriscounsults – the experts on “natural” law and justice – “have many good demonstrations”, and that the Roman lawyers (such as Cicero of De Legibus and De Finibus) “speak, all of them, in such a precise and clear way that they in fact reason in a form quite approaching demonstration – indeed, it is often actually demonstrative”.6 And the Pr´eface to the NE – written last, after the mathematizing of droit naturel of 4.7.19 was fully in place – includes la morale (natural theology and natural jurisprudence) among the “demonstrative sciences”, together with logic, mathematics/geometry, and metaphysics (A VI 6 50), as will be seen later in this article. That is why Leibniz says in NE 4.4.6 that “the idea” of justice is “not of our invention, any more than those of the circle and of the square” (A VI 6 393): Once again the morality/geometry parallel of the Meno is paramount, since justice is not any more our invention than are the definitions of circularity and of squareness, i.e., not at all. And that is also why he says, in the M´editation sur la notion commune de

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la justice, written concurrently (1703–1704) with the NE, that “invention” has no more place in God than in “us”: It is agreed that whatever God wills is good and just. But there remains the question whether it is good and just because God wills it or whether God wills it because it is good and just: in other words, whether justice and goodness are arbitrary or whether they belong to the necessary and eternal truths about the nature of things, as do numbers and proportions (R 45).

The voluntarist view of Epicurus, Calvin, Descartes, and Hobbes, that everything is invented/created, Leibniz laments, would “destroy the justice of God” (R 46).7 It is almost as if Leibniz postponed his treatment of “natural” law/justice from its natural place in 2.28 (contra Lockean law) to the very late chapter (4.7) in which axioms, maxims, geometry, and “demonstration” are dominant – partly in admiring reminiscence of the Meno (soon to be praised yet again in Leibniz’s Platonizing letter to Hansch of 1707 (D 2 222–225), but also so that “natural law/justice” can be together with God and the natural immortality of the soul (NE 4.10–11) which are needed if natural justice is finally to have place beyond the “human forum” – so that natural theology and natural immortality are the guarantors of droit naturel. After all, for Leibniz that droit naturel, as an “eternal verity” – no more our “invention” than the circle – needs an eternal and necessary mind in which all verities are grounded. That is to say, for jurisprudentia universalis one needs not just “natural” law/justice but a divinity (demonstrable through natural theology) who both (a) “grounds” natural justice and (b) upholds natural justice eternally; and that in turn requires human “natural” immortality, a` la Phaedo, as against Locke’s mere probability of immortality in the Essay (“Locke too much weakened the generous philosophy of the Platonists” which had demonstrated immortality (Letter to Jaquelot, 1704; GP 3 261). After all, Leibniz says in his Monit`a on the Locke-admired Samuel Pufendorf – from 1706, just after the 1705 revision of the NE – that “universal jurisprudence” entails that “the ruler of the universe [. . .] has allotted rewards for the good and punishments for the wicked”. And that “his plan will be put into effect in a future life, since in present life many crimes remain without punishment [. . .] [and since] it is possible to demonstrate the immortality of the soul by natural reason” (D IV 3 280). [. . .] I find it very bad that celebrated people, such as Samuel Pufendorf and Christian Thomasius, teach that one knows the immortality of the soul, as well as the pains and rewards which await us beyond this life, only through revelation. The Pythagoreans and the Platonists understood this rightly. [. . .] All doctrines of morals, of justice, of duties which are based only on the goods of this life, can be only very imperfect. Take away the [natural] immortality of the soul, [and] the doctrine of providence is useless, and has no more power to oblige men than the gods of Epicurus, which are without providence (Letter to Bierling, 1716; D V 390).

For Leibnizian “natural law/justice” to “work”, then, one needs (equally natural) “natural” theology (monotheism) and “natural immortality” – and the three come together, as a natural trinity, in book 4 of the NE, where one first gets moral “demonstration” hors des math´ematiques (4.7.19) (droit naturel as la raison pure), and then

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gets not just God as defender of natural justice (in an immortal eternity) but God as the ground (though never the cause) of the “eternal verity” of both mathematics and la morale (4.10–11) (A VI 6 446–447). Fusing the Anselmian proof of God (the ens perfectissimum, since logically possible, exists ex necessitate) with the Augustinian proof through the “eternal verities”, Leibniz finally says that one can always ask “where would these ideas be, if no spirit existed, and what would happen in this case to the real foundation of the certainty of the eternal verities”.8 To which the right answer is that “this leads us finally to the last foundation of the truths, namely, to this supreme and universal spirit which cannot fail to exist, whose understanding – to speak correctly – is the region of the eternal truths, as St. Augustine has recognized”,9 and that these necessary truths must be “grounded in the existence of a necessary substance”.10 As against the Lockean version of “natural/divine law” – as something willed by God to protect his own “workmanship”, to which he has a natural right through creative labor (a view repudiated by Leibniz in Observationes de principio iuris of 1700 (D IV 3 270–275) – Leibniz begins with “eternal” geometry and with practical demonstration hors des mathematiques, then finds all eternal truth (theoretical and practical) in an eternal “mind” which also realizes (in a double sense) natural justice in eternity (the “region” of naturally immortal substances). And that is why Leibniz says, in an early version of the Pr´eface to NE, that “the author’s [Locke’s] philosophy destroys what seems to me to be the most important – that the soul is imperishable”11 – adding that Locke’s notion of the mere probability of immortality, perhaps through a miracle, “is directly opposed to Platonic philosophy”.12 For Leibniz, Locke subverts the “natural” immortality which “natural” law/justice requires, and then wrecks “natural law” itself by hinging it on divine “creationthrough-labor” – since for Leibniz natural law/justice is geometrizingly eternal, while Creation is both temporal and a “mystery”. For Leibniz, Genesis/genesis does not “cause” the eternal and the necessary. All of this argumentation, from the NE and from related pieces, is then reflected a decade later (1714) in Leibniz’ Principes de la nature et de la grace – with the Monadologie being the summa of his final thought: All minds [esprits] entering in virtue of reason and of eternal truths into a kind of fellowship with God, are members of the City of God [. . .] this perfect state in which there is no crime without punishment, and no good action without a proportionate reward.13

Here “fellowship with God” is precisely “in virtue of” reason-given “eternal truths”, such as mathematical “proportion”, which all minds share; in the “perfect state”, droit naturel is actual. And this is why NE 4.7 is as it is: first geometry/mathematics (as in Meno), then God as “ground” (never cause) of all v´erit´e, then natural immortality (of God’s truth-loving “fellows”) for the realization of (practical) v´erit´e (as in Phaedo, and even in Apology insofar as Socrates will get natural justice only insofar as he is immortal). If in NE 2.28 Leibniz just shows that Locke (with his “will” of a “lawgiver”) is incomplete and inadequate as a natural lawyer, in Book 4 he finally, Platonizingly gives his own positive views fully – echoing what he had said earlier in 1.2.12:

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There is no precept which one is indispensably obliged if there is no God who does not leave any crime without punishment nor any good action without compensation.14

In short: Leibniz really did postpone his full treatment of (extra-Lockean) “natural law” until he first demonstrated geometry, God, and immortality – literally “first things first.” Here Leibniz is most nearly like the Timaeus (41b-d), where Plato draws together God, justice, immortality, and eternity, saying that “children of gods” will be worthy of immortality if they are willing to follow “justice” – whose “divine part” will be “sown by God himself”. (For Plato, immortality is the reward of justice; for Leibniz it is the condition of justice.) And Plato has for Leibniz the further advantage of being lumbered with neither “creation” nor “will”: for mere “genesis” is unworthy of eternity (Republic 526b) and mere “willing” is a popular fiction (Protagoras 249a–252b). Thus Leibniz’s chapter 4.7.19 in the NE is no mere “commentary” on the corresponding part of Locke’s Essay (“Of Maxims”): It is, rather, a Platonizing, geometrizing rejection. For in Essay 4.7.9, Locke, far from “privileging” geometry, in effect deflates it: “general ideas [in geometry] are fictions and contrivances of the mind, which carry difficulty with them”. For example, does it not require some pains and skill to form the general idea of a triangle (which is yet none of the most abstract, comprehensive, and difficult), for it must be neither oblique, nor rectangle, neither equilateral, equicrural, nor scalenon: but all and none of these at once. In effect, it is something imperfect, that cannot exist: an idea wherein some parts of several different and inconsistent ideas are put together. It is true, the mind, in this imperfect state, has need of such ideas, and makes all the haste to them it can, for the conveniency of communication and enlargement of knowledge; to both which it is naturally very much inclined. But yet one has reason to suspect such ideas are marks of our imperfection [. . .].

Not only, for Locke, do geometrical “maxims” lack any privileged priority; they cannot throw necessitating light on so-called “other” eternal verities, and above all not on practical ones: When these principles [. . .] are made use of in the probation of propositions, wherein are words standing for complex ideas; viz. man, horse, gold, virtue: then they are of infinite danger, and most commonly make men receive and retain falsehood for manifest truth and uncertainty for demonstration (Essay 4.7.15).

For Locke geometry is not (as in Meno) a kind of key or clue to “virtue”; there is no bridge between them, via eternity. Thus, for Locke virtue must be revealed by Scripture, which is “so prefect a body of ethics, that reason may be excused from that enquiry”.15 The so-called aeternae veritates, Locke adds, are not “eternal propositions” – e.g., “virtue is wisdom” – which are “actually formed, and antecedent to the [human] understanding that at any time makes them” (Essay 4.11.14). But if they are “made” they are not “there”: Meno and Phaedo are wrong, and so too must be Leibniz’s admiration for those works. What Locke is actually saying is that moral ideas such as “virtue” do not come (as it were) “after geometry”; and insofar as Leibniz places droit naturel in the “geometry/demonstration” chapter, he is deliberately arguing for the very thing that Locke thought “infinitely” dangerous and false.

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With all of these just-discussed “preliminaries” in place and in mind, one can turn to a full consideration of droit naturel in Leibniz’s Book 4. “There are fundamental maxims constituting the law itself”, Leibniz writes in NE 4.7.19, “which, when they are taught by pure reason, and do not arise from the arbitrary power of the state, constitute natural law”. That privileging of “pure reason” over “the arbitrary power of the state” – that privileging of Plato over Hobbes – leads to what Leibniz calls jurisprudentia universalis or jurisprudence universelle. And the central idea of this universal jurisprudence, which aims to find quasi-geometrical eternal moral verities equally valid for all rational beings, human or divine, is that natural justice is “the charity of the wise” (caritas sapientis) – that it is not mere conformity to sovereign-ordained “positive” law (in the manner of Hobbes’s De Cive and Leviathan), nor mere negative refraining from harm (Codex Iuris Gentium; A IV 5 57 ff.). The equal stress on “charity” and on “wisdom” suggests that Leibnizian natural law is a kind of fusing of Platonism – in which the wise know the eternal truths such as “absolute” goodness (Phaedo 75d), which the gods themselves also know and love (Euthyphro 9e–10e), and therefore deserve in natural justice to rule (Republic 443d–e) – and of Pauline Christianity, whose key moral ideal is that charity or love is the first of the virtues (“though I speak with the tongues of men and of angels, and have not charity, I am become as sounding brass or a tinkling cymbal”; 1 Corinthians 13). There is, historically, nothing remarkable in trying to fuse Platonism and Christianity: For Augustine’s early De Doctrina Christiana 1, 27, with its notion that justice is “ordered” or “measured” love, is just such a fusion. But Leibniz, the last of the great Christian Platonists – who also tried to fuse “wise charity” with the highest degree of Roman law, honeste vivere (to live honorably) – left the world just as Hume, Rousseau and Kant were about to transform and “secularize” it definitively. It is not surprising, then, that in his greatest writing on “natural” justice, the M´editation sur la notion commune de la justice, Leibniz should begin with a verbatim paraphrase of Plato’s Euthyphro – in which the gods themselves do not make or change eternal moral verities, but eternally love them because they are true – and then equate the legal-positivist Hobbes with the Thrasymachus who insists (in Republic 338c) that justice is merely the interest of the most powerful, and with the Epicurus who says that there is no “natural” justice, merely artifice and fear (as against Plato’s Theaetetus 172b, which holds that “in the sphere of right and wrong” there is “something natural”, not just “arbitrary public decision” – such as the judicial murder of Socrates.)16 Leibniz’ most bold and striking equation of “natural law” with Christian-Platonic “wise charity” is to be found in his remarkable Elementa Iuris Perpetui,17 which begins by insisting that natural justice is not simply the “first” of the virtues, a` la Aristotle or Aquinas, but that such justice “contains” all of the moral virtues, and that it relates to “the public good” or “the perfection of the universe” or “the glory of God” – where these three distinct things are morally equivalent in Leibniz’s usual sense (the sense that in working with wise charity for the common good of humanity one is following the “presumptive will” of God as just monarch of the best of all possible worlds – Elementa Iuris Perpetui (M 1ff.).

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But the really bold and striking thing in this 1695 writing is that Leibniz goes on to say that the precepts of the eternal law, which are called ‘natural’, are nothing other than the laws of the perfect state. The principles in question are three: neminem laedere, suum cuique tribuere, pie vivere. The first [to injure no one] is the precept of peace, the second [to render each his due] is that of commodious living, the third [to live piously or charitably] is that of salvation (M 1).

In this remarkable paragraph, the “eternal”, the “natural”, and the Roman are made equivalent (as “perfect laws”), and that jurisprudential Trinity then governs not just the “human forum” but the perfect state of the best kosmos – at least once one transforms honeste vivere into pie vivere. No longer are Roman legal maxims just historical residues of a concrete legal and jurisprudential system; they have become the principles of “natural” (indeed of “eternal”) justice. But this is not surprising in Leibniz, who could rank himself among those for whom “the Roman laws are not considered as laws, but simply as written reason [la raison e´ crite]” (GR 648). And when Leibniz goes on to say, slightly later, that since “the love of God” or of the summum bonum “prevails over every other desire”, the “supreme and most perfect criterion of natural justice consists in this third precept of true piety”, and that “human society itself must be ordered in such a way that it conforms as much as possible to the divine” (to that “universal society which can be called the City of God”), he has finally equated the eternal, the “natural”, the Roman “written reason”, and the divine. And since universal justice is caritas sapientis, he has equated the eternal, the natural, the Roman, the reasonable, the divine, and the charitable. (Even for so very synthetic a mind as Leibniz’s, this is an amazing synthesis!) If in the Preface to the Theodicy one had learned that the duty of wise charity is given by “supreme reason” (not just revelation), in the Elementa Iuris Perpetui charity is the heart of living piously, and that pious living is a “sublimated” form of Roman-law honeste vivere. In the end, then, Leibniz the “natural lawyer” wants to say something like this: Roman justice = Christian caritas sapientis = reason = nature = eternity = divinity. For after the writings of the geometers there is nothing that one can compare, for force and solidity, to the writings of the Roman jurisconsults [. . .] never has natural law been so frequently interrogated, so faithfully understood, so punctually followed, as in the works of these great men (Letter to Kestner, 1716; D IV 3 267).

But with the near-geometry (pour ainsi dire) of the Roman jurisconsults, “these great men”, one returns to Leibniz’s already-cited claim in the NE that Roman jurisprudentia usually “approaches” demonstration (in a rigorous sense) and sometimes achieves it (A VI 6 370). And with that one turns to the remarkable paragraph in the Pr´eface to the NE in which Leibniz ranks la morale with the “other” demonstrative sciences, then divides la morale into the natural theology which proves God and immortality, and the natural jurisprudence which illuminates droit naturel. The soul originally contains the principles of several notions and doctrines, which are merely roused on certain occasions by external objects, as I hold along with Plato [. . .] The Stoics called these principles prolepses, that is, fundamental assumptions or what we

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take for granted beforehand. Mathematicians call them common notions (koina`ı e´ nnoiai). Modern philosophers give them other excellent names; and, in particular, Julius Scaliger named them semina aeternitatis item zopyra, as much as to say, living fires, flashes of light [traits lumineux], hidden within us but appearing at the instance of the senses, like the sparks which come from the steel when it strikes the flint. And not without reason it is thought that these flashes [´eclats] indicate something divine and eternal, which appears above all in necessary truths [. . .] such as we find in pure mathematics and especially in arithmetic and geometry, [and which] must have principles whose proof does not depend upon instances nor, consequently, upon the witness of the senses, although without the senses it would never have come into our head to think of them. This is a point which should be carefully noted, and it is one which Euclid so well understood that he often proves by reason that which is evident enough through experience and through sense-images. Logic also, along with metaphysics and ethics [!a morale], of which the one forms natural theology and the other natural jurisprudence, are full of such truths; and consequently their demonstration can come only from the inner principles which are called innate (A VI 6 49–50).

Here Leibniz’s strategy is to appeal first to acknowledged “common notions” in mathematics and geometry – even Hobbes, after all, revered Euclid – then to transfer that demonstrable necessity to “natural jurisprudence” (or what the M´editation calls “the science of right”). And to move from mathematical to moral “demonstration” is Platonic, in the manner of Meno and Phaedo. This is why Leibniz can say, in a letter to Bossuet, that “there is harmony, geometry, metaphysics, and, so to speak ethics [la morale] everywhere” – for all of these are related quasi-Platonic notiones communes (D I 531). But why does “demonstration” matter so much – as when Leibniz insists that such demonstration is possible not just in logic and metaphysics but also in la morale, of which natural jurisprudence or right is a branch? Here one should turn above all to Leibniz’s letter to the Landgrave Ernst of Hessen-Rheinfels from September 1690: One cannot escape by saying with M. Arnauld that we must not judge God by the ideas we have of justice, for it must be the case that one has an idea or a notion of justice when one says that God is just; otherwise this would only be to attribute a word to him. As for me I believe that just as the arithmetic and the geometry of God is the same as that of men, except that God’s is infinitely more extensive, in just the same way natural jurisprudence, in so far as it is demonstrative, and every other truth is the same in heaven and on earth. Failing this, God would act as a tyrant, would do what would be called tyranny in a man, by using an absolute power. One must not imagine that God is capable of doing that which would be called tyranny in men (GR 238–239).

“Natural jurisprudence, in so far as it is demonstrative”: That is the key phrase in this letter. But how far can one “demonstrate” full Leibnizian justice from Platonic mathematical-geometrical “eternity” alone? One can’t, in a word – unless one “mathematizes” justice very radically, as Leibniz himself sometimes does (“now consist justice, goodness, beauty, no less than mathematical things, in equality and proportion, and are therefore no less aeternae et necessariae veritatis” – Unvorgreiffliches Bedencken; GR 434–435). And that is why Leibniz’s “perfectionism” must be folded in at this point (to account for caritas/love as a sentiment de perfection, whether the object of that charity is God or man). For, as John Rawls (2000: 110) has rightly urged, Leibniz “maintains that the principles of perfection [. . .] are [also]

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eternal truths: They rest on and lie in the divine reason. These truths are superior to and prior to the divine will”. Indeed “also” would scarcely be the right word – for the necessary existence of “the perfect being”, God, is (pour ainsi dire) the privileged Anselmian “eternal verity” which is primus inter pares: without the eternal “mind” of God to know (but never cause) the eternal truths, there would be no “other” verities (NE 4.11.13; A VI 6 447). For Leibniz always insists that while God does not ( pace Descartes) cause eternal, necessary truths by mere genesis, he nonetheless “finds” those verities “imbedded” [inditis] in his understanding. First God must exist, owing to “perfection”; “then” (as it were) he finds eternal verity in his sapientia, not in his voluntas (ibid.). In this sense “Platonic” eternal verity needs a “necessary” ens perfectissimum as its “ground” – and therefore the Plato-Anselm connection is stronger than it might have seemed. “Perfection” yields a necessary God; he then finds all other truth in himself; and the perfection which necessitates him is the basis of love, the “feeling of perfection” in others which underlies justice as wise caritas (“to love is to find pleasure in the perfection of another”). And that is why Leibniz can say that “the apex of metaphysics and that of ethics are united in one by the perfection of God”. One cannot love God without knowing his perfections or his beauty. And since we cannot know him except in his emanations, there are two ways of seeing his beauty, namely in the knowledge of eternal truths (which consist in reasons, numbers, figures, orders, changes) [. . .] and in the knowledge of the harmony of the universe (La f´elicit´e; GR 580–581).

There, indeed, Plato and Anselm blend into each other; Athens and Canterbury timelessly occupy the same space. Leibniz’s practical perfectionism emerges most plainly in his NE anticipating Observationes de Principio Iuris from 1700 (D IV 2 270–275), in which the claim that “God is the supremely perfect Being, and the supremely perfect distributor of goods” glides into the moral-political assertion that “the intrinsic perfection or badness of acts, rather than the will of God, is the cause of justice”, and that “the basis on which a certain action is by its nature better than another comes simply from the fact that a certain other action is by its nature worse, such that it destroys perfection, or produces imperfection” (D IV 2 273). Here Leibniz’s perfectionism and his quasi-Platonic anti-voluntarism all but fuse. And perfectionism and antivoluntarist wise charity also fuse in Leibniz’s great essay, The radical origination of things (1697): [. . .] The very law of justice declares that each should participate in the perfection of the universe and in a happiness of his own in proportion to his own virtue and to the degree in which his will has regard to the common good; and by this is fulfilled that which we call charity and the love of God, in which alone, in the opinion of wise theologians, consists the force and power even of he Christian religion.18

ForLeibniz,twin-founded“demonstrative”naturaljurisprudence(justiceuniverselle), grounded doubly in Platonizing mathematical “eternity” and in (moral) “perfection”, is in a position to refute a bad voluntarist trinity: hyper-Calvinism, hyper-Cartesianism, and hyper-Hobbesianism.19

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In the end it is quite clear what Leibniz opposes and what he favors in the NE (especially Book 4): He is against tyranny, despotism, and willfulness, and he is for charity, benevolence, and reasonability. That is why he constantly argues against the “dangerous opinion” that “all justice, all morality comes not from the nature of things but from the despotic will of God”20 – a sentence from a 1711 letter to the Platonist Hansch, who after Leibniz’s death brought out Leibnitii Principia Philosophiae more geometrico demonstrata. If one personalizes these dislikes and likes, he is hostile to Calvin, Descartes, and Hobbes (as radical voluntarists who deny or destroy Platonic eternal verities), and he is favorable to Plato, St. Paul, and Augustine (as caritas-lovers). Indeed unless one recalls Leibniz’s prominent place in modern mathematics and science (especially dynamics) he will look briefly (in the moral sphere) like an ancient chastising modernity. Robert Mulvaney (1975: 215) captures Leibniz’s philosophical likes and dislikes, hopes and fears, perfectly when he says that “Leibniz’s life-long opposition to Cartesian voluntarism and to the Hobbesian-Thrasymachan identification of justice and power” led him to insist that there is “a standard of goodness [which is] objective, so to speak, even for God”. As Leibniz, echoing the NE, said with final lapidary precision a few months before his death: “Will without reason would be the “chance” of the Epicureans. A God who acted by such a will would be a God only in name”.21 Leibniz’s mentioning of Epicurus is no accident: for it was Epicurus who famously said that there is “no natural Justice” – in explicit opposition to Plato’s argument that in the field of “right and wrong” there is something natural, “with a reality of its own” (Theaetetus 172b). Is it (so to speak) Epicurean chance that Leibniz translated the Theaetetus only a few months after first insisting that natural justice is (eternally, necessarily, demonstratively) “the charity of the wise”? Or do not all of these “Platonisms” hang coherently together, making Leibniz the greatest “Christian-Platonist” after Augustine – not least in the Nouveaux essais sur l’entendement humain?

Notes 1. “Si quelqu’un vouloit e´ crire en mathematicien dans la m´etaphysique ou dans la morale, rien ne l’empecheroit de le faire avec rigueur; quelques uns en ont fait profession, et nous ont promis des demonstrations math´ematiques hors des math´ematiques, mais il est fort rare qu’on y ait r´eussi” (A VI 6 260–261). 2. “Il y a des exemples assez considerables de demonstrations hors des math´ematiques [. . .] on peut dire que les jurisconsultes ont plusiers bonnes demonstrations, surtout les anciens jurisconsultes romains” (NE 4.2.9; A VI 6 370). In the case of the jurisconsults, these demonstrations are actually successful – Leibniz implies. 3. “Mais afin que vous ne pensiez pas, Monsieur, que le bon usage de ces maximes est resserr´e dans les bornes des seules sciences math´ematiques, vous trouverez qu’il n’est pas moindre dans la jurisprudence” (A VI 6 425; my emphasis). 4. “[. . .] toute l’arithmetique et toute la geometrie sont inn´ees, et sont en nous d’une maniere virtuelle [. . .] comme Platon l’a montr´e dans un dialogue o`u il introduit Socrate menant un enfant a` des verit´es abstruses, par les seules interrogations sans luy rien apprendre” [NE 1.1.5; A VI 6 77]. On this passage see Beeley (2006).

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5. “Et que pourroit on faire de meilleur, que de reduire la controverse, c’est a` dire, les verit´es contest´ees, a` des verit´es evidentes et incontestables; ne seroit-ce pas les etablir d’une mani`ere demonstrative?” (A VI 6 419). 6. “[. . .] parlent tous d’une maniere si juste et si nette qu’ils raisonnent en effˆet d’une fac¸on qui approche fort de la demonstration, et souvent est demonstrative tout a` fait” (4.2.9; A VI 6 370–371). 7. For a full treatment of Leibniz’s Platonizing anti-voluntarism, see Riley (2003). 8. “[. . .] o`u seroient ces id´ees, si aucun esprit n’existoit, et que diviendroit alors le fondement de cette certitude des v´eritez e´ ternelles” (NE 4.11.13; A VI 6 447). 9. “[. . .] cela nous mene enfin au dernier fondement des veritez, savoir, a` cet esprit supreme et universel qui ne peut manquer d’exister, dont l’entendement, a` dire vrai, est la region des v´eritez e´ ternelles, comme St Augustin l’a reconnu” (ibid.). 10. “[. . .]il faut bien que ces v´eritez necessaires soyent fond´ees dans l’existence d’une substance necessaire” (ibid.). 11. “[. . .]la philosophie de l’auteur detruit ce qui me paroist le plus important. C’est que l’ame est imperissable” (A VI 6 48). 12. “[. . .] est directement oppos´e a` la philosophie Platonicienne” (ibid.). For Leibniz’s full view of Plato’s defense of “natural immortality”, see Riley (forthcoming). 13. Monadology and other Writings, ed. Latta. Oxford, 1898, p. 421. 14. “[. . .] il n’y a gueres de pr´ecepte a` qui on seroit oblig´e indispensablement s’il n’y avoit pas un Dieu qui ne laisse aucun crime sans chastiment n’y aucune bonne action sans recompense” (A VI 6 96). To this ‘Philalethe’ replies: “The ideas of God and of a future life must then be also innate” (Il faut donc que les id´ees d’un Dieu et d’une vie a` venire soyent aussi inn´ees), to which ‘Theophile’ answers: “I agree with this, in the sense I have explained” (J’en demeure d’accord dans le sens que j’ay expliqu´e). 15. Letter to Molyneux; Locke’s Correspondence, ed. De Beer, vol. 6, p. 283. 16. It is worth remembering that Leibniz made (in 1679) Latin versions of Theaetetus and of Phaedo – the two Platonic dialogues which turned out, a quarter-century later in the 1704 NE, to be crucial for “natural” justice and for “natural” immortality, i.e., for droit naturel as conceived by Leibniz. And that is certainly “foresight”, if not actual omniscience. 17. From 1695, the year of Leibniz’ first known reference to Locke’s Essay (see Letter to Burnett, June 1695; GP 3 162). 18. In Monadology and other Writings, ed. Latta. Oxford,1898, p. 349. 19. To see this entirely one needs not just the droit naturel of the NE, but caritas as a sentiment de perfection from other works which surround (and are consistent with) the NE themselves. 20. “. . .non rerum natura sed despotico quodam Dei arbitrio constet” (D V 167). 21. “La volont´e sans raison seroit le hazard des Epicuriens. Un Dieu qui agiroit par une telle volont´e, seroit un Dieu de nom” (Fourth letter to Clarke, 1716; GP 7 374).

References Beeley, P. 2006. Leibniz et la tradition platonicienne: Les math´ematiques comme paradigme de la connaissance inn´ee. In F. Duchesneau and J. Griard (eds.), Leibniz selon les Nouveaux essais sur l’entendement humain. Paris and Montr´eal: Vrin and Bellarmin, pp. 35–47. Mulvaney, R. 1975. Divine justice in Leibniz’s ’Discourse on Metaphysics’. Studia Leibnitiana 15: 61–82. Rawls, J. 2000. Lectures on the History of Moral Phi1osophy, ed. B. Herman. Cambridge, MA: Harvard University Press. Riley, P. 2003. Leibniz’s M´editation sur la notion commune de la justice, 1703–2003. The Leibniz Review 13: 67–81. Riley, P. Forthcoming. Leibniz on the Greeks as founders of a sacred philosophy [the 1714 Vienna lecture]. In H. Rudolph (ed.). Leibniz’s Stellung zum Judentum. Stuttgart: Steiner Verlag.

Part V

Ethics

Chapter 18

Authenticity or Autonomy? Leibniz and Kant on Practical Rationality Carl J. Posy

1 Introduction I must start this paper with a double disclaimer: First, really I am a guest in this volume on Leibniz, a guest from the Kant world. Most of my attention these past few years has been on Kant and on the origins of his critical philosophy; I’ve viewed Leibniz mainly as an influential predecessor. Secondly, though my title speaks of the type of rationality and notion of self that figure into moral deliberation, I shall be equally concerned with the metaphysics of objects in Kant and monads in Leibniz. But I’ll try to turn these disclaimers into assets. Regarding my “visitor’s status”: I will try to reverse my habitual emphasis, and leverage some of Kant’s divergences from Leibniz better to understand Leibniz himself. Thus in the first part of the paper I will argue that Kant’s systematic metaphysics is an attempt to resolve a tension that he (Kant) found between Leibniz’s pure monadology on the one hand and its empirical application on the other. Setting out that tension will, I believe, illuminate major themes in Kant’s mature thought but also some of Leibniz’s own philosophical strategies. As for metaphysics and ethics: here too I hope to turn my Kantian perspective to Leibnizian advantage. Kant, perhaps most of all philosophers, connects metaphysics and ethics; so in Part 2 I will highlight the metaphysics underlying his theory of moral autonomy and show how that illuminates nascent themes about action and self in Leibniz. All of this will come with rather sweeping strokes that do some damage to the richness of Leibniz’s and Kant’s philosophical thought. But these parts aim to convey more structure than detail. In Part 3 though, I will try to show you how Kant’s theory of imagination puts phenomenological meat on these structural bones, both metaphysical and practical. It fleshes out the distinction between what Marcelo Dascal (2001, 2003, 2004) has called “hard Reason” and “soft rationality” in Leibniz’s thought, and it gives content to the places where Kant deviates from Leibniz. But at the end, I will suggest that Kant’s shifts from Leibniz come at a cost to the notion of self and to the role of reason in ordinary moral thought. And this will be a cost that Leibniz doesn’t incur. Au contraire, in Leibniz we will find a confluence of reason and rationality. C.J. Posy The Hebrew University of Jerusalem, Jerusalem, Israel

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2 From Leibniz to Kant in Theoretical Philosophy So let’s first depict that tension that Kant found in Leibniz’s thought between pure monadology and its empirical applications. I’ll start by laying down the tension and then sketch the Leibnizian and Kantian strategies for dealing with it.

2.1 Leibniz, the Pristine Picture We all know that, for Leibniz, the fact that Caesar crossed the Rubicon and indeed all Caesar’s past and future are encoded in Caesar’s complete concept.1 Indeed we know that, however obscurely, the whole world and its history are encapsulated in that concept as well.2 To make this work, Leibniz assumed a two dimensional hierarchy (actually a lattice-structure) of concepts. First of all, ordinary predicates are arranged according to their degree of generality, with the most general concepts at the top and such that lower concepts result from conjoining some higher ones or by explicitly denying some others.3 Figure 18.1 gives a rough picture, assuming that there are only three highest concepts. In the jargon of the times, the lower concepts are said to be determined positively or negatively regarding the higher ones from which they are defined. Leibniz says that the higher concepts are “contained” in the lower ones. Those on the bottom row are “completely determined” (predicatively complete) with respect to this hierarchy. But this is just a momentary snapshot; Caesar’s individual concept also tracks the stages of his life.4 I like to capture this via Figure 18.2. There will be blocks of descriptions in this infinite chain that cover his crossing the Rubicon, his victories, his Senate career and his assassination. Only a full complete concept – the series of predicatively complete slices – describes a true individual; only such concepts are singular concepts. This rather combinatorial notion of unpacking is the heart of Leibniz’s conceptual containment

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theory of predication. For ultimately our sentence (“Caesar crossed the Rubicon”) is true in virtue of these combinatorial facts and God’s instantaneous grasp of them. I want to emphasize just three aspects of this cognitive hierarchy: (i) First its metaphysical side: For one thing, there is nothing more to Caesar than what is encoded in his concept, no undescribed residue, no personal essence. That’s why – borrowing a scholastic term – Leibniz speaks of the complete concept as the haecceity of the individual.5 It also follows from this that Caesar is an individual substance – his concept is an infima species and thus can, as Aristotle says, never serve as a predicate – that any substance different from Caesar must have a different complete concept,6 and that he is an indivisible (simple) thing, a monad. Indeed, any two distinct components of a composite individual would have to differ at some corresponding place in their respective individual concepts. The resultant description of that composite would be “undetermined” at that place, and could not be complete, and thus would be a general concept. Composite individuals can have only general concepts. Figure 18.3 shows this.

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Let me add that I also see in the sequential aspect of these complete concepts a framework producing the notions of (internal) causality and (primitive active) force: Causality (or at least local causality) because a complete concept is, after all, a concept, and the stages it describes – Caesar’s present position on a barge, for instance, and his immediately past position – are thus conceptually and hence necessarily interconnected. Similarly, the force propelling Caesar on this barge (the fact that he will in a moment necessarily be at his next position) is also encoded in the stages of his individual concept. Indeed, global causality follows as well: Brutus’ and Cassius’s and Caesar’s individual concepts must be coordinated,7 and in the end everything must ultimately reflect everything else. In effect, the unity of the world-whole rests upon the unity of any individual in the world. (ii) Second, the epistemological element: To grasp Caesar’s complete concept is to know all there is to know about Caesar. Indeed, the ultimate justification of the claim that Caesar crossed the Rubicon is that unpacking his concept will yield the description of a river crossing. Moreover, this is the very model of “clear and distinct” knowledge (See MK; L 292). For such a grasp gives complete knowledge and allows one to distinguish Julius Caesar from anything else real or imagined (e.g., some other person who is just like Caesar except for one detail). To be sure, only God can fully grasp an infinite complete concept. But when He does have such a grasp, He in fact grasps the whole world as well. And His knowledge is immediate (in Leibniz’s terms “intuitive”): God doesn’t need deducing and unpacking; He just looks at the complete concept. That’s the advantage of an infinite intellect: this quick jump to the bare-basic string. (iii) Finally the “semantic” component to this picture: And there is indeed a preternaturally modern semantic aspect. For, if we combine this epistemology with the containment theory of predication we find the base for a rarified version of the modern “assertability theory of truth” favored by Michael Dummett and others.8 Assertabilism is known for its definition of truth – knowledge (or proof or “warranted assertability”) in “an epistemic situation” replaces the more standard notion of referential “truth in a model” – and for its special conditions for negations and quantifiers. Thus, under assertabilism an assertion A is false in a situation (i.e., ∼A, is true) if and only if the situation contains sufficient evidence that A will never be assertable. And assertabilist semantics imposes an asymmetry between existential and universal assertions: A universal (∀x)A requires only a general method converting any demonstration that x is in the domain (for any x) to a demonstration of A(x); but an existential (∃x)A is assertable in a situation only if we already have some a in the domain such that A(a) is already assertable. Now, if you look at Leibniz’s views on these matters you will see that he endorses these definitions of truth and negation, and adopts the assertabilist asymmetry between universal and existential quantification. He defines “truth” by saying: “That is true, therefore which can be proved, i.e., of which a reason can be given by analysis” (GI §130). And here is his definition of negation: I define as ‘false in general’ that which is not true. For it to be established that something is false, therefore, it is necessary either that it should be the opposite of a truth, or that it should contain the opposite of a truth, or that it should contain a contradiction (i.e., B and

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not-B), or that it should be proved that, however long an analysis is continued, it cannot be proved that it is true (GI §57).

As for the quantifiers: Universal quantification is of the form, “All A’s are B’s”; and Leibniz will view this as true only when there is a conceptual rule linking “being an A” to “being a B”.9 And the existential conditions are appropriately different. Indeed in two related ways: First, in establishing the existence of an individual (Leibniz’s example is Peter), God considers the entire concept as a global infinite whole rather than looking at conceptual containments among its parts. And correlatively, the ultimate determiner of existence is the way this global character fits into the overall “goodness” of its world (see GI §§71–74). So, as I said, Leibniz is formally a semantic assertabilist. To be sure, he differs from modern assertabilism on a couple of prominent details: Unlike Dummett and co. Leibniz doesn’t invalidate the principle of bivalence,10 and unlike them he combines his assertabilism with the standard referential (correspondence) theory of truth. “Truth”, he says, “i[s] the correspondence of the proposition in the mind with the things in question” (NE 4.5.11; see also NE 4.5.2). But these are differences that prove the analogy: Leibniz’s assertabilism is bivalent because God is the knower. God has no open questions, so there will be no situation in which neither A nor its negation is known. And Leibniz accepts the correspondence theory simply in virtue of his ontological principle of haecceity: what is known of Caesar is what is true of Caesar himself, and vice versa. Indeed, this special assertabilism simply highlights Leibniz’s systematic philosophy: The semantics of predication, truth and falsity; the metaphysics of substance, simplicity and force; the frictionless clockwork of God’s grasp; all seamlessly united; each philosophically flowing from the others. And this systematicity was for Leibniz the pride of his philosophy.11

2.2 The Tension Kant idolized this systematicity as well; it was for him the goal of all thought. But the fact is that many have found – as did Leibniz himself – famous problems about contingency and about human freedom in this complex of ideas: Since all truths are ultimately analytic and thus necessary, there seems to be no place for the contingency so obvious in our human grasp of the world. And if all our actions are foreknown by God, what place is there then for freedom of action and moral worth? Leibniz wrote explicitly about these issues, and Kant addressed them in his Critical Philosophy. But Kant’s pre-critical work – most prominently his “Physical Monadology” of 1756 and his “Inaugural Dissertation” of 1770 – highlights a broader tension in the Leibnizian philosophy: How in general to integrate this pristine picture with the possibility of human knowledge and the metaphysics of empirical objects. Both of these works (as well as several in between) explore the discontinuity and connection between what Kant calls the “sensible” and the “intellectual”. For it is not Caesar the monad who crossed the Rubicon. Nor was it Rubicon the monad (were there such a thing) that was crossed. It is Caesar’s body that intersected a different

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spatially extended body. And this is a problem on all three fronts: Metaphysically, spatio-temporal bodies fare poorly under the Leibnizian picture; as does human knowledge about these things; as does empirical truth. Bodies fare poorly because, as divisible, they cannot be true objects. They lack complete concepts. Their parts, such as they are, cohere in virtue of the artificial unity imposed by the viewer, and not because of metaphysical reality itself. They have, in Leibniz’s terms, subjective, “phenomenal” unity.12 Human knowledge – based as it is on sensory perceptions – goes down too: For we are not frictionless conceptual-analysis machines. We learn what we can from perceptual experience. Indeed, that is a sort of friction – gumming up, and ultimately bounding our conceptual grasp. Stare as I might at Caesar’s barge, I will never know its full past, and can only imagine its potential future. This perceptual grasp will never distinguish the barge perceived from possible other barges which may have different pasts or futures. It is “confused” in that sense. And certainly I cannot conceptually unpack the causal laws governing Caesar and the barge. As for truth: Just keep in mind that we form our empirical concepts from this confused inaccurate experience, and we form our empirical judgments from these concepts. There is no chance that these judgments could possibly accurately depict the way things are. Leibniz as a scientist could not denigrate human knowledge or empirical objects, and, as a theologian, he would not impugn the substantiality of matter.13 So this should be a philosophical challenge and project for Leibniz: Allow for human knowledge, but preserve the pristine and abstract calculus of conceptual containment and its metaphysics of monads. Certainly, as I said, this challenge helped shape Kant’s philosophical program, but if – using these Kantian spectacles – we see this tension as central to Leibniz’s thought as well, then we can read much of his work throughout his own career as stages of his attempts to reconcile the abstract pristine and empirical poles. I won’t elaborate upon that here. For now, I will simply outline his metaphysical and epistemological strategies in very general terms.

2.3 Leibnizian Strategies I should say that from an epistemological point of view one can – and Leibniz does – view this tension as a source more of friction than of conflict. There is one object of knowledge (reality, the world) which is grasped with varying degrees of clarity. And so we find in his work a trio of degree-theoretic epistemological strategies. (a) He distinguishes necessary from contingent truths simply on the basis of how much unpacking is needed to establish them: “Caesar is human”, for instance, is necessary because we know it by unpacking a finite piece of Caesar’s individual concept. “Caesar crossed the Rubicon” is contingent, because it would take an infinite analysis to establish this fact simply on the basis of conceptual containment. (For God, of course, the distinction remains otiose.) (b) When – as we saw for existence claims – the issue is one of total grasp rather than comparison and containment, then

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Leibniz sometimes speaks of approximation and “continuous analysis”, processes whose model comes from the calculus.14 And (c) other times – especially when he is concerned to preserve our human freedom – Leibniz will speak of a partial grasp which “inclines but does not necessitate”.15 Speaking ontologically – where the differences in degree engender differences in type – we find two prominent strategies: Reduction and infusion. Sometimes he writes as if phenomenal entities are composed of basic monadic, simple components. (And so the properties of the former are reduced to the properties of the latter.16 ) But sometimes he tried to infuse the 2nd class phenomena with extra being (extra life) from the pristine realm. This, for instance, is his correction of Descartes’ notion of force in the famous vis viva controversy.17 Once again, each of these strategies posits a single framework housing and relating the two opposing pulls. That is Leibniz’s guiding premise: One truth, one all encompassing reality.

2.4 Kant’s Solution I won’t detail Kant’s own “pre-Critical” attempts to reconcile these pulls other than to say that, like Leibniz, he too attempted to coordinate them in a single metaphysical system that contained and connected Caesar the non-extended monad together with Caesar the physical body. Instead, I will turn directly to the Critique of Pure Reason and show you how it sharpens the tension (Leibniz’s opposing pulls become irreconcilable poles) but ultimately remains thoroughly Leibnizian. First the sharpened tension: Instead of the single Leibnizian spectrum from God’s abstract clear conceiving to Caesar’s confused perceiving, Kant now posits two distinct human faculties: Understanding (the faculty of empirical cognition, based upon passively received and finitely limited sensory experience) on the one hand, and Reason (the faculty of pure thought, abstracted from the conditions of empirical experience) on the other, both belonging to a single human knower. And, having recognized the understanding as a separate faculty in its own right, Kant goes on to blaspheme against each of the fronts in Leibniz’s pristine philosophy. Cognitively, Kant takes human perceptions rather than God’s infinite grasp as singular representations; indeed in the Understanding no conceptual grasp is ever singular. There are no infima species and no infinite conceptual analyses.18 And it is perceptual grasp that now counts as immediate; not in virtue of being a short conceptual deduction, but because it is not conceptual at all. In epistemology, Caesar, according to Kant, now knows that his barge is crossing the river, because he sees it do so, perceptual friction notwithstanding. Ontologically, Kant’s “empirical realism” now counts the barge, the river, and indeed the “river crossing event” as legitimate individual objects, their merely phenomenal unity notwithstanding. Space and time – the media within which these objects are extended – are also real. And semantically, Caesar’s judgment that the barge crossed the river, this, in Kant’s eyes, is now true simply in virtue of that perceptual knowledge, as are judgments that each of these things actually exist.

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Moreover, in the Second Antinomy, Kant explicitly rejects any attempt to connect this empirical standpoint back to the metaphysics of monads, either via a strategy of reduction or one of infusion: The Understanding’s empirical domain must stand on its own, Kant insists. It will not countenance the infinite division of matter that a reduction to monads would require, nor will it admit an infusion of unexperienceable metaphysical simples to complete our empirical experience (see A434/B462 and A435/B463). Try to do these things – as Leibniz does – and the result is internal contradiction. It is easy, however, to let this blasphemy hide how thoroughly Leibnizian remained Kant’s agenda and his execution of it. Yes he replaces the cognitive hierarchy of concepts with the phenomenology of perception; but from this cognitive base he then recreates within the Understanding a humanized version of the full pristine picture, a unity of epistemology, semantics and ontology. In epistemology, Kant’s theory of empirical synthesis and his doctrine of categories now play the role of justification heretofore played by Leibniz’s notion of “conceptual unpacking”. Synthesis tells us that Caesar’s perception becomes a barge perception, because he organizes (synthesizes) his perceptual manifold according to the concept barge. Without that conceptual organization, Caesar would have no more than a subjective jumble of impressions. And the categories come to guarantee that such syntheses can indeed justify objective judgments. For instance, Caesar’s organization of the barge positions – first on the near side, then the far side of the river – this ordering will be objective and not merely phenomenological only if it can be causally explained; that is, only if he can find a causal rule dictating similar motion in similar situations.19 You might wonder how a perception can be conceptually organized and yet remain immediate (= non-conceptual), and I’ll address this in Part 3, but my point now is to show you that this new epistemology is part of a unified Leibniz-inspired program. Thus, in ontology, Kant parallels Leibniz’s distinction between object and aggregate by his own distinction between legitimate empirical objects – the barge, the river, the river crossing – on the one hand and mere conceptually defined aggregates on the other – the sum of all spatial objects, the history of all events. And, like Leibniz, Kant sets predicative completeness as the test between them (A57-2/B599600). Caesar’s perception of the barge suffices to guarantee that he (or us or our heirs) can eventually answer any question about it. No grasp of the world-whole can ever make such a guarantee. There will always be unanswered questions, uncertainty and endless conjecture about this world whole (A477/B505 ff.). Kant even maintains Leibniz’s parallel between the unity of a self and the unity of the world. Famously, his Transcendental Deduction argues that the causal unity of nature presupposes the unity of the knowing self (the “transcendental unity of apperception”). Indeed, the unity of apperception underlies the mundane unity imposed by each of the categories (see, in particular, A125). As for semantics, Kant in fact now adapts the Leibnizian semantics to create a full empirical assertability account of truth, one which humanizes each of the assertability conditions: Existence, for instance, depends upon actual current sensory

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perception, together with a conscious sortal organizer (see A225/B272). And a negation will be now established by proving unexperienceability. That is the heart of Kant’s arguments against reduction and infusion in the Antinomy.20 He even maintains the Leibnizian union between assertabilist and referential truth: Kant too quite blithely defines truth as “agreement with the object” (A58/B83). This is just the Leibnizian haecceity doctrine made human: There is no more to an empirical object than what we can eventually know of it. So, as I said, Kant’s theory of the Understanding humanizes the entire Leibnizian framework of semantics, epistemology and ontology. But this is only half the story. For having done so for the Understanding, Kant effectively does the same for Reason. Reason, to be sure, is a human faculty – its concepts are derived by abstracting from the Understanding’s day to day experience. Nevertheless, unlike Leibniz, Kant will not say that perception is merely Reason with friction. Perception, he says, is receptive; Reason is spontaneous. And this is a difference that makes an epistemological difference: The epistemic pessimism that characterizes the Understanding – those unanswered questions which make the world-whole into a mere aggregate – all this is the outcome of receptivity. The “key” to answering those questions, says Kant, is not in us, and that is why there are “endless conjectures” without certainty (A480/B508). Reason, however, abstracts from receptivity. It is a faculty of pure ratiocination, and when we deal with pure reasoning, says Kant, we can “demand and expect none but assured answers to all the questions” we might ask (ibid.). A sort of epistemic optimism characterizes pure reasoning. (A nice goal, that empirical knowledge never reaches.) However, given that epistemic difference, as I said, Kant once again relativizes the entire Leibnizian framework: He provides Reason with its own metaphysics (the notorious Things-In-Themselves) and its own semantics (mind-independent truth). To be sure, when the abstraction that yields Reason is legitimate – in mathematics and in “transcendental philosophy” – then Reason will have some influence upon the empirical realm of the Understanding: Mathematics shapes the form of perception (space and time), transcendental philosophy regulates the structure of scientific research. But this formation and that regulation are always external to the Understanding. Mathematical objects do not exist empirically (A719/B747), and the regulative force of reason gives no objects at all. Ontologically, the two faculties are and must remain firmly separate. No strategy of reduction or infusion can bring them together. To do so – to connect the pure and the empirical in this way – will lead only to antinomy. With respect to empirical thought, Understanding is the home; and within Understanding, Reason is alien and destructive. So Kant’s theoretical philosophy proposes two full-service cognitive schemes: The one based on receptivity (Understanding) the other purely intellectual (Reason). And instead of what I have called “a sliding cognitive friction” which leads (according to Leibniz) to confused cognition, Kant proposes a sharp inter-system distinction: Reason’s epistemic optimism, Understanding’s eternal open questions. Leibniz’s systematicity is, as I said, recreated twice over in Kant’s critical philosophy. Indeed, he will say that Leibniz’s (and his own pre-critical) mistake is to try to make do with one single overriding framework, a single semantics, a single ontology.

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3 Moral Theory and the Acting Self 3.1 Kant’s Moral Theory Turning to Kant’s moral theory, we are now concerned with ethical justification, and Kant now invites us to eavesdrop upon the individual human practical deliberations (say) of Brutus and Cassius contemplating Caesar’s assassination. It is fruitful to observe how this new focus plays out in Kant’s systematic terms. Ontologically we focus on acts (with moral weight) rather than physical actions or activities (which are merely events). It is now the agent’s motives (expressed by their maxims) rather than empirical concepts which serve to sort out our acts. Thus, famously, the same physical action carried out by Brutus and Cassius counts as different moral acts. Each will have its own maxim – Cassius acts to serve a “lean and hungry” ambition, Brutus to serve democracy and the republic – and each deserves its own moral evaluation. And our justifications are now moral rather than simply epistemic: Cassius commits an evil deed; Brutus can, in the end, be “the most-noble Roman of them all”. This is because, according to Kant, Cassius and Brutus must apply Kant’s “universalization test”. Each must calculate and see whether construing his individual motive as a universal maxim will lead to one or another form of contradiction. Cassius’ motive fails this test, Brutus’ presumably passes. We can even see a parallel to semantic assertabilism here, or at least an analogy: Moral justification replaces epistemological justification, and passing the universalization test will act like semantic success. Now, when universalizing, Brutus and Cassius must abstract from their personal histories – that is, from the social and genetic forces that formed their natures and motives – and must similarly ignore the emotions and feelings which accompany their maxims. That’s how they assume their choices to be real, free choices. To be sure, one must be careful here: Brutus, even as moral agent, still wields a knife, thrusts it into a physical body, and (causally) expects Caesar to die. Really it is psychological causality from which they actively abstract. But that is enough to put themselves into the second scheme – the one of Reason and its things in themselves. Here, indeed, is the origin of Kant’s notion of autonomy: Reason performs the universalization test, and maxims that pass the test are thus products of reason itself. In choosing such a maxim, Reason is choosing its own product. Maxims which are not universalizable (maxims which ultimately express no more than an individual nature) these are intruders from the other (the empirical) scheme. Choosing such a maxim – mixing the schemes – is not logically flawed, as such mixing was in the theoretical philosophy. It is simply morally flawed. In saying all this, our orientation towards the two schemes has shifted: Reason and its scheme are the home base. It is the empirical scheme which is now alien, or as Kant puts it “heteronomous”. This impacts both the epistemology and the metaphysics of morality: Epistemologically, Kant should, and indeed does, accord to ethical deliberation the same epistemic optimism of which I spoke a moment ago.21 Metaphysically, both the actions and the notion of self to which they belong – the

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ethical self, the actor, the agent – is reason’s self.22 It contains those (and only those) things about us which are universal or universalizable. And so, it is no surprise, that Kant, preserving still the self-world parallel, fits this moral self so naturally into his clockwork, noumenal “kingdom of ends”. Kant’s cognitive split now gives us two perspectives on our acting selves, Reason’s and the Understanding’s. The former assumes freedom of action, the latter, as we saw, must presuppose a universal causality. No strategy of epistemic approximation will work here. The dichotomy itself – the jump between moral and epistemic justification – this is Kant’s solution to Leibniz’s problem of freedom. But once again the two projects are not equal. Within morality, reason’s perspective is the home. Haecceity, as it were, belongs to Reason’s self. So if there is a unified acting self, and if it is not an empty abstraction, then it must, at best, be a sum of two unequal partners.

3.2 Action and Self in Leibniz Let’s now turn back to Leibniz and use our Kantian spectacles to highlight his version of the ontology, epistemology and semantics of action and the acting self. Ontologically, certainly the Leibnizian monad is no composite self. Brutus’ self is not, no self is, a sum of disparate parts in the way it was for Kant. For one thing, there are no two camps or schemes from which to draw disparate selves. Brutus’ self, or any self, is just the ordered union of its states, as reflected in its single, attenuated, complete concept. Now you may think that this has not done us that much good: One might (or God might) slap together a few (ok, a lot) of those vertical complete slices to get a fully saturated individual concept as in Figure 18.2. A vast slap-dash conjunction is scarcely different from Kant’s heterogeneous union. But that is not going to happen in Leibniz’s scheme. Or, to be precise, it is no more likely that God would do that than it is that He would choose a world of random connections. In fact, of course, it is for Leibniz one and the same Divine choice. Monad and world reflect one another. The world itself has pattern, and style and final causes;23 and once we have an ordered universe – with scientific laws at work – then each individual concept will reflect that natural order. But there’s more here: For, each mature individual concept will have themes that run through the sequence of stages, a sort of leitmotif (or several) within the overall symphony that is a life. Hamlet’s brooding nature, Macbeth’s ambition, these are names we give to drifts and flows in their lives, tendencies in the sum of their deeds. So the Leibnizian self’s unity – and indeed the world’s unity – is far from being artificial. It is endemic. Here is the place for inclinations, desires and appetites that serve to individuate acts in Kant’s practical philosophy. The leitmotif gives an internal rhythm and order to these appetites and inclinations, a subjective version of primitive force in physics. And a desire projects these forward (“dimly” Leibniz will insist). These together

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yield the notion of inclination that does not necessitate; for, of course, projection might not be consummated. All of this is built into the very structure of monads. Speaking epistemologically, these trends and patterns, these inclinations, these aspects of an individual concept will not be revealed by any ordinary conceptual containment. There is no “unpacking” here. To grasp these things it is not enough to work through the concept sequentially, however quickly. Rather one must – God must – grasp the whole, stand back, and then attend to the patterns that emerge from such a distant perspective. The unity here is endemic rather than merely sequential, and these endemic aspects – that bear true goodness (or lack of goodness) – are the aspects of individual concepts that God will consider in determining value and thus existence. And that, if you will, is Leibniz’s assertabilist semantics of existence. Here, in fact, we don’t have semantics by analogy, as we did in Kant. In Leibniz’s system goodness and truth (of an existential claim) actually do coincide. What of our human grasp? Well, recall that God is doing two things here: Grasping the endemic unity of an individual and grasping how that individual fits into the goodness of the world. And a finite human agent must approximate these with two separate skills. The latter of these translates into the agent’s ability to “size up” his practical situation: To know what he needs or wants and to assess which of the available choices is “right”. The former activity translates into one’s ability to grasp one’s own endemic unity. This is more than simple “apperception”, grasping oneself as a perceiver. We are talking here of self-grasp as an agent, not just a perceiver. Caesar must be aware of his motives and goals, and many of these are subtle and subtly grasped: Cassius’ jealousy is not Iago’s. Macbeth’s ambition is not Caesar’s. In the end, in a rich life and a complex world, the pattern will be peculiar to the individual. So an agent must be aware of the flow and pattern that characterized his prior decisions and their effects. Practically he must be able to project this flow forward; to sense, in particular, what are and what are not the appropriate continuations; and to sense this in any given situation. Now Kant teaches us that morally the agent must be able to give this grasp a name and express it as maxims. And Leibniz says as much in DM §34: But the intelligent soul, knowing what it is and being able to say this little word ‘I’ which means so much, not merely remains and subsists metaphysically (which it does in a fuller sense than the others) but also remains the same morally and makes it capable of punishment and reward.

Once again, these skills are not a matter of conceptual analysis – finite or infinite – and for us humans, they can’t come from assuming some infinite total perspective. They come from grasping our own endemic qualities. Thus, as Leibniz insists, I think that one is more worthy of praise when one owes the action to one’s good qualities, and the more culpable in proportion as one has been impelled to it by one’s evil qualities. To attempt to assess the action without weighing the qualities whence they spring is to talk at random and to put an imaginary indefinable something in the place of causes (T, Appendix IV, §19; GP 6 421).

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To be sure, such knowledge may be hard won. Cassius knows what he wants (as for that matter does Iago). Hamlet must work hard to uncover his own desires. Macbeth almost gets it wrong. (He thought he was ambitious; really he wanted to be manly before his wife.) The complexity and layers of what I called “a rich life” add some “friction” here, and indeed Leibniz is aware of the difficulty.24 But the knowledge is available. Indeed, for Leibniz, self awareness is the one human perception that is truly “intuitive” (NE 4.2.1; A VI 6 367). And, for better or for worse, his model of the self and his refined conception of self knowledge fit this awareness squarely into his integrated philosophical system.

4 Imagination I turn now to my promised look at Kant’s theory of imagination. I don’t mean here what he calls “reproductive imagination” – the automatic association of impressions that figures in the empiricist – and Leibniz’s own – philosophy of mind. This is a subjective business – images, after all, present spatial-temporal things – and often a source of error, even of a certain beastlike, lower cognition (MON §28). I mean rather what Kant calls “productive imagination”, a faculty that figures prominently in the epistemology of his theory of judgment, and something he regards as his own special insight (A120 n.).

4.1 Four Uses of Productive Imagination Kant distinguishes two general types of judgments: “determining” judgments – the familiar subsuming of an individual under a given general predicate – and “reflective” judgments, which proceed in the opposite direction. That is, in a reflective judgment you start with some particular data and pass to a general principle that “unifies” the data.25 Each of these can rest on the productive imagination in one of two ways – I call them anchored and unanchored uses of the imagination – and so there will be four Kantian uses of the productive imagination. I’ll briefly sketch each. 4.1.1 Determining Judgments A. Anchored Imagination: Caesar’s judgment that his barge is moving is a paradigm here. He will subsume his perceptual manifold under the barge concept in justifying this claim. He will, in particular, connect his keel and deck perceptions on the one hand, and separate them from, e.g., his perception of the adjacent driftwood. In practice, this means that Caesar will project (imagine) future views of the barge. In some the driftwood will remain; in some the barge is driftwood-free. But the keel and deck will persist in all of these imagined continued glances, and indeed in the same geometrical relation. The concept “barge” dictates that rule for the projections,

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and that, indeed, is what it means to organize the perceptual manifold according to this concept. To be sure, Caesar won’t have a full conscious array of these possibilities. He will have rather a “horizonal” awareness of possible continuations of his current glance. The phrase is Husserl’s (1913: §27), but it captures quite well Kant’s point that future directed projections are part of any objective perceptual experience. This projection to future views, tied as it is to a given actual perceptual glance this is anchored productive imagination. B. Unanchored imagination: Mathematical thought is the paradigm here (see A713/ B741). Caesar as a geometer might use one of the barge’s triangular sails as a sample case for studying triangles. He will ignore (in technical terms “abstract from”) its color and texture, its actual size and location, leaving only those features the sail has in common with all triangles. Because of this abstracting, Caesar’s constructions and proofs will be valid a priori for all triangular objects. (Caesar the analyst would do the same for the boat’s trajectory.) These mathematical abstractions need not anchor Caesar’s mental work on an actually perceived triangle or observed motion. He could just as well use a drawn figure, and even an entirely imaginary one. Hence my title: “unanchored” imagination. 4.1.2 Reflective Judgments A. Anchored imagination: This is the heart, according to Kant, of perceiving a beautiful object as beautiful (see CJ; Ak. V 203 ff.). Sometimes, says Kant, we experience objects having an aspect of style or unity that is not exhausted by any articulated general concept. There is something else in such experiences, guiding the imaginative horizon more than what is given by any discursive concept. Kant’s examples include seeing certain flowers and freely drawn patterns, also appreciating music and poetry without invoking the underlying technical concepts. In these cases, one feels that some parts of the manifold fit together in a horizon-forming, rule-like way; here too we implicitly consider alternative ways the manifold might be ordered, perhaps a shift in brush stroke, or a slight change in the meter of a poem. As in ordinary perception, some will be accepted, some will not. But unlike ordinary perception, the order and guidance are not given by a well formulated general concept that would apply equally well to other things. To be sure, a thing of beauty will usually fit within a well defined medium, and we can give the thing a name to help recognize it again: I can well know that I am listening to Beethoven’s Ninth Symphony while I appreciate its beauty. But we must keep in mind that in beautiful music and a beautiful poem the artist has made choices that are right in a way more specific than anything the medium or any rules of craft could predict, and that naming it designates it without limiting it to any such rules or description. Our sense of beauty communicates these facts to us. B. Unanchored imagination: Kant’s paradigm case here is concept formation: That is, moving from the primitive individual perceptions – of particular trees for instance – to the unifying empirical concept (“tree” in this case) under which they all fall (see for instance Lectures on Logic (Jasche) I.§5). Now, before actually

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articulating the concept, one will have a palpable sense that there is in fact some common regularity that unifies these perceptions (perhaps the root-trunk-branch structure). There is (perhaps implicitly) a sense of common order that could guide one’s imaginative projections. And this sense, once it becomes strong enough, allows us to imagine a paradigm instance – ultimately what Kant might call a “schematic tree” – guides us in shaping subsequence anchored horizons. He speaks of the “free play” of imagination in testing and determining permissible variations on the schema. In practice, once such a schematic tree is fixed, it will tell us which features belong and, in each case, which do not. The articulated concept, “tree”, comes later to give a name to this sense of guided unity. Scientific discovery – finding an overarching general law to unify particular observed laws – is a second case of this same reflective judgment. We have in both of these activities – discovery and concept formation – just as we did in perceiving beauty, a grasp of form without a formula, a point at which the horizon is ordered in a way that is not (or not yet) given by an explicit rule. But in scientific discovery and concept formation, the cases in which a formula eventually emerges, we use the unanchored imagination: For here the discovered unity – once it has been articulated – applies in principle to many other cases. Clearly we have here phenomenological meat for Kant’s theory of the Understanding and Reason. Anchored determinate imagination fills out the notion of organization under an empirical concept that is so important to the Understanding. And unanchored reflective imagination shows how such empirical concepts are derived from concrete perceptual experience. Even the anchored reflective imagination – the cognitive grasp of beauty – even that has a systematic place; it shows, as I promised, how a perception can be ordered in a rule-like way, yet remain non-conceptual, and thus immediate. And the unanchored determinate imagination is Kant’s cognitive theory of abstraction. It provides the phenomenological side of the faculty of Reason. Weighing anchor from particular perceptions is precisely what moves us from Understanding’s receptivity and pessimism to Reason’s spontaneity and epistemic optimism.

4.2 Leibnizian Infrastructure But let me point out, again as I promised, five ways in which this Kantian faculty can provide infrastructure for latent Leibnizian themes as well. (1) Certainly the anchored determining imagination fleshes out Leibniz’s claim that a monad’s present is pregnant with its future. For we now see that insofar as Caesar’s present perception of his barge is a barge-perception, it must implicitly project to future perceptions of the same barge. This is the anchored determining imagination. (2) And this same anchored imagination gives meat to the Leibnizian notions of appetite and desire. To say that Macbeth’s murder of Duncan was motivated by his appetite for the monarchy is really now to say that he (Macbeth) imagines

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the horizon of possible outcomes of the deed, and in all of them he sees himself crowned king. Brutus similarly imagines a renaissance of Roman democracy following his own act of imagination. To be sure, these imaginings precede the acts themselves; there’s no current perception here; and this is part of why Leibniz calls such projection faint and dim. Nevertheless, this is equivalent to anchored imagination, since it is a single act that is subsumed under a single motive. (3) But it is the unanchored reflective imagination that is at work, I believe, when Macbeth “sizes up” his practical situation and comes to recognize – perhaps slowly – what it means for him and what choices he faces. He’s really very close here to the phenomenology of concept formation: Inarticulate feelings of opportunity coalesce into defined options – murder or duty – falling under defined maxims, and lead ultimately to recognizing the moral worth of each. (4) And the self knowledge that stands behind these assessments – Macbeth’s recognition (such as it is) of his own ambition, or of his need to seem manly – here it’s anchored reflection, the aesthetic grasp, that gives this. The grasp of drifts and patterns in one’s own life is the horizon-forming grasp of what Leibniz called one’s own special qualities. This is the heart of what has come to be called “authentic” choice and action, fulfilling the possibilities born of one’s own history and nature (see Heidegger 1927: §9). There is even an emotional parallel here to perceiving beauty: The feeling of rightness in discovering a calling or career is akin to the joy of uncovering a heretofore hidden (but familiar) unity in a perceived object. And there is a practical component: The familiarity of the “right” option serves as sensory goad to pursue that option. True appetite and desire and so, too, authentic choice all stem naturally from the sequential features of one’s individual concept. Global features, to be sure, but sequential features nonetheless. So, authentic action is a natural kin to physical causality. It is, as Kant says of freedom, a sort of causality in its own right (see A444/B472). And indeed we learn about ourselves, as we do about the causal world in the same way: Extrapolating from our past experience. God’s (existential) value judgments about a world and the individuals in it may well come from a global glance and a sense of balance. So God needs no boost from imagination, anchored or not. We humans are beset by partial information, doubt and even self illusion. These are frictions – humanly inevitable frictions – that require reflective judgment and imagination. Here, I believe, is the phenomenology of “soft rationality” Dascal (2001) speaks of – a “non-conclusive form of rationality”; in fact, however, it is simply engaging with friction to make our daily and our deepest choices. (5) Finally there’s a lesson here about “hard reason” – the “conclusive alternative to soft rationality” – as well. You might think that conceptual containment and its clockwork combinatorics are all there is to hard reason. And indeed this is a paradigm of frictionless ratiocination. But Kant teaches us a more

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subtle definition of friction: It is whatever impedes ultimate complete determination, whatever forces unsolvable problems upon us. And so we have a correspondingly more subtle definition of hard reason. A discipline that is legitimately optimistic – mathematics for instance – is a discipline governed by hard reason. So hard reason too, for us humans, like soft reason, and like ordinary perception, has its own element of imagination, the unanchored imagination of determining a priori judgments.

4.3 Ethics and Imagination in Kant Now this same machinery of imagination should play prominently in Kant’s ethical theory too. Macbeth imagines future kingship; that’s the anchored determining imagination behind subsuming the murder under his maxim of monarchical ambition. And the universalization test – the test for subsuming his maxim under the moral law – this seems straightforwardly parallel to the unanchored imagination of mathematics and its hard reason. He will imagine a paradigm situation in which everyone accepts the same maxim – “do what you can to become king” – and will search to see if it contains contradictions in will or in concept. Famously, he does find a contradiction in will: we but teach/Bloody instructions, which being taught return/ To plague th’ inventor. This even handed justice/ Commends the ingredients of our poisoned chalice/ To our own lips (Macbeth, Act I, scene 7, lines 7–12).

Brutus, doing the same exercise, presumably will not find such a contradiction in his own maxim. And just as Caesar the mathematician will abstract irrelevant details from his paradigm case, so too Macbeth and Brutus the moral reasoners will have to ignore features of their imagined paradigm cases. But, in fact, Kant does not depict the universalization test in this way. On the contrary, in the “Typic” of the Critique of Practical Reason he explicitly denies that imagination is at work in subsuming an act or maxim under the moral law. “The moral law”, he says, “has no other cognitive faculty to mediate its application to objects of nature than the understanding (not the imagination)” (CPrR; AK.5: 69; my emphasis). Why does he say this? He could not be denying the phenomenology of hard reason here. Well, moral abstracting is different from mathematical abstracting, and that difference is the culprit here. For, Cassius and Macbeth and Brutus must in practice ignore the causal forces acting upon themselves, and upon each of the players in their respective paradigm scenarios. If they didn’t, they would be assuming their players to be causally determined, and thus immune from any moral evaluation. So while mathematical abstraction ignores a certain particularity from its model instances, this ethical abstraction suspends the very possibility of the actor’s being an empirical being.26 Imagination in ethical deliberation is not only unanchored; it is empirically unanchorable!

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There is a terminological point here: Kant will not use the term “imagination” for projections with empirically unrealizable abstractions. But the point is deeper. This abstraction is crucial to Kant’s solution to the problem of freedom: It defines the abstract ethical realm, and guarantees that it will not intersect with the empirical world, structured by causality. So Kant is not denying the phenomenology. If we ever do universalize, then this is what it must feel like. Rather, he is denying the relevance of phenomenology to the philosophical theory of universalization.

4.4 Kant’s Costs What goes for determining judgment goes for reflective judgment too. Once again, Kant’s moral theory should incorporate the special, aesthetic feel of authentic self knowledge. Moral deliberation after all begins with a sense and then an articulation of one’s goals and wants and needs. The clearer these are grasped, the more decisive the action. The clearer these are articulated, the more precise the moral evaluation. Yet, once again, the very same gap between the purely ethical and the empirical will kick in here, and for the very same reasons. Reflective self knowledge is knowledge of the empirical causal roots of desire (this, as we saw, is a Leibnizian lesson), and as such, for Kant, it must remain morally outside. Here lie the philosophical costs I mentioned at the start. One cost is epistemological, the place of self knowledge in this scheme of Reason: Those hard-won skills of self discovery, of uncovering one’s own nature, and of this projecting of one’s goals; these skills are now set on the sidelines. Cassius and Hamlet and Macbeth are not idle literary artifices. They embody the stuff and friction of real decision making. The skills that they display or lack or strive to acquire – these skills are at the very center of our moral psychology. Yet in Kant’s second scheme, the one of ethics, these skills take no part in the ultimate moral evaluation. Yes, Kant knows all about the craft of skillful judgment (about seeing and interpreting patterns in one’s own life). We saw that he in fact gave us the machinery to describe this craft. But the causal force of these patterns and their emotional effect make them external – non-systematic – factors. It is not merely that, for Kant, this knowledge is fallible because it is empirical. Kant is no Cartesian. That would make it no worse than any empirical knowledge. What’s bad is simply that this empirical self knowledge, together with the skills designed to acquire that knowledge, these are the aliens in the home of pure practical reason. The other cost is metaphysical: Personal goals and natures – Cassius’ crass ambition, his brooding “lean and hungry look”; Brutus’ elegance, his patriotism – these things and everything else that makes up their empirical personalities, these things are, in the moral scheme, brute facts about them. To be sure, they are not ignored in moral deliberation. But – just like the physics and biology of stabbing – in this ethical project they belong to the now second class empirical scheme. They never serve as ethical justifications. So the “empirical selves” – the authentic selves – are here alien elements of the ethical world. And there is no – there can be no – strategy

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of “reverse infusion” that will allow them somehow to structure ethical discourse and thus give them ethical status. To allow such a strategy would close the door to freedom, and, in Kant’s eyes, doom the award of any moral value. Famous critics see this as a deep flaw in Kant’s system: Think of Kierkegaard’s insistence on the aesthetic basis of personality (Either/Or, volume two) and of twentieth century existentialists who claim that Kant has sacrificed authenticity on the altar of Reason’s autonomy.27 We can now see their point. Kant found tension between Leibniz’s pristine picture and its empirical application. He resolved this tension by positing two realms, at best tangent to one another, each a full Leibnizian system in its own right. In so doing, he reshaped Leibnizian strategies and gave human flesh to Leibnizian notions of reason and rationality. And by removing any bridge between the Understanding’s objects and those of Reason, he believed he solved Leibniz’s problem of human freedom. But in so doing he alienated our daily soft rationality and our human moral experience from the hard reason of moral thought. And that is a price that Leibniz will not pay. His philosophical strategies rest exactly on denying any such gap. For him, the self of motivation and desire is the true metaphysical self. And the reason of moral thought exists together with the rationality of daily action. Acknowledgments The research for this paper was supported by the Israel Science Foundation (Grant #914-02). The final version of the paper was written while the author was a Senior Fellow at the Dibner Institute for the History of Science and Technology, Cambridge, MA. I am grateful to the ISF for its support, to the Dibner Institute for its invaluable resources and to its staff for their hospitality and assistance.

Notes 1. “[I]f some man were able to carry out the complete demonstration by virtue of which he could prove this connection between the subject, who is Caesar, and the predicate, which is his successful undertaking, he would actually show that [. . .] there is a reason in that concept why he has resolved to cross the Rubicon rather than stop there, and why he has won rather than lost the day at Pharsalsus, and why it was reasonable and consequently assured that this should happen” (DM §13). 2. “[Every substance] expresses, albeit confusedly, everything that happens in the universe, past, present and future” (DM §9). 3. Kauppi (1960) develops the idea that this hierarchy of concepts has a lattice structure. 4. “But in my opinion it is in the nature of created substance to change continually following a certain order which leads it spontaneously (if I may be allowed to use this word) through all the states which it encounters, in such a way that he who sees all things sees all its past and future states in its present” (DB; L 493). 5. “God [. . .] in seeing the individual notion or haecceity of Alexander, sees in it at the same time the basis and the reason for all the predicates which can truly be affirmed of him[. . .]” (DM §9). See also DB; L 493. 6. Here we find a source of the Principle of the Identity of Indiscernibles: There could be no elements of distinguishable objects that are not reflected as differences in their individual complete concepts.

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7. Their perceptions of the stabbing must coincide. This is a local version of the principle of “pre-established harmony”. 8. Dewey (1938) is the origin of the term “warranted assertability”. The formal recursion conditions were first set out in Heyting (1930). Dummett (1978) gives a comprehensive modern account of this semantics. 9. This is his famous “intentional” approach to truth. 10. “ ‘Not true’ and ‘false’ coincide. So‘not false’ and ‘true’ will coincide also. [. . .] From these it is also proved that every proposition is either true or false [. . .]” (GI §3). 11. “Consideration of this system also shows that, when we penetrate to the foundations of things, we observe more reason than most of the philosophical sects believed in” (DB; L 496). 12. “[T]his unity that collections have is merely a respect or relation, whose foundation lies in what is the case within each of the individual substances taken alone. So the only perfect unity that these entities by aggregation have is a mental one, and consequently their very being is also in a way mental, or phenomenal” (NE 2.12.7; A VI 6 146). 13. See, for instance, Leibniz’s remarks on transubstantiation in his letter to Des Bosses of January 24, 1713 (GP 2 473–475; L 607–609). 14. “But the concept of Peter is complete, and so involves infinite things; so one can never arrive at a perfect proof, but always approaches it more and more, so that the difference is less than any given difference” (GI §74). 15. Thus, for instance: “And therefore I say that motives incline without necessitating and that there is a certainty and infallibility but not an absolute necessity in contingent things” (Leibniz’s 5th paper, par. 9; LC 697). 16. “There must be simple substances, since there are compounds, for the compounded is but a collection or an aggregate of simples. But where there are no parts it is impossible it is impossible to have extension or figure or divisibility. The monads are the true atoms of nature; in a word they are the elements of things” (MON §§2, 3). 17. “And although all the particular phenomena of nature can be explained mathematically or mechanically by those who understand them, it becomes more and more apparent that the general principles of corporeal nature and of mechanics themselves are nevertheless metaphysical rather than geometrical and pertain to certain forms of indivisible natures as the causes of what appears rather than to the corporeal or extended mass” (DM §17). 18. See Lectures on Logic (I.1, §11 n.) for the elimination of infima species. See B39–40 for the rejection of infinite conceptual analyses. 19. Posy (1984) develops this point in detail. 20. Thus, for instance, “[. . .] the existence of the absolutely simple cannot be established by any experience or perception, either outer or inner” (A437/B465). 21. “We must be able, in every possible case, in accordance with a rule, to know what is right and what is wrong, since this concerns our obligation, and we have no obligation to that which we cannot know” (A476/B504). 22. See, for instance, A539/B567. 23. Indeed, one lesson of the Theodicy is that there is even more order than that required simply to balance good and evil in the world. 24. Thus, in a letter to Arnauld of July 14, 1686, he notes that “[. . .] the concept of myself in particular, and of every other individual substance is infinitely more inclusive and more difficult to grasp than is a specific concept such as that of a sphere [. . .]” (GP 2 47–59; L 331–338). 25. In reflective judgment, says Kant, “only the particular is given, and the universal has to be found for it” (CJ Ak. V, 179). 26. Indeed, this suspension of causality leads us to think of the act as occurring outside of time itself. See A539–40/B567–568. 27. “In Kant, this universality goes so far that the wild man of the woods, man in the state of nature, and the bourgeois are all contained in the same definition and have the same fundamental qualities. Here again, the essence of man precedes that historic existence which we confront in experience” (Sartre 1946: 27).

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References Leibniz Correspondence with Clarke (GP 7 345–440; L 675–717) [= LC]. Clarification of the Difficulties which Mr. Bayle has found in the New System of the Union of Soul and Body (GP 4 517–524; L 492–497) [= DB]. Discourse on Metaphysics (GP 4 427–463; L 303–328) [= DM]. General Inquiries About the Analysis of Concepts and Truths (C 356–399; P 47–88) [= GI]. Meditations on Knowledge,Truth and Ideas (GP IV 422–426; L 291–294) [= MK]. Monadology (GP VI 607–623; L 641–652) [= MON]. Theodicy (GP 6 21–247; Translation E.M. Huggard, Yale University Press, 1952) [= T].

Kant Kant’s gesammelte Schriften, edited by der Deutschen (formerly K¨oniglichen Preussischen) Akademie der Wissenschaften, 29 vols. Berlin, Walter de Gruyter, 1902 –. [= Ak]. Concerning the Form and Principles of the Sensible and Intelligible World [Cited as “Inaugural Disseratation”] (Ak, vol. II). Critique of Pure Reason; A = 1st ed. (Ak, vol. IV); B = 2nd ed. (Ak, vol. III) [= C Pu R]. Critique of Practical Reason (Ak, vol. V) [= C Pr R]. Critique of Judgment (Ak, vol. V) [= C J ]. The Employment in Natural Philosophy of Metaphysics Combined with Geometry, of which Sample I Contains the Physical Monadology (Ak, vol. I) [Cited as “Physical Monadology”]. Lectures on Logic [Jasche Edition] (Ak, vol. IX).

Other Authors Dascal, M. 2001. Nihil sine ratione → Blandior ratio. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress), volume 1. Berlin: Leibniz Gesellschaft, pp. 276–280. Dascal, M. 2003. Ex pluribus unum? Patterns in 522+ Texts of Leibniz’s S¨amtliche Schriften und Briefe VI, 4. The Leibniz Review 13: 105–154. Dascal, M. 2004. Alter et etiam: Rejoinder to Schepers. The Leibniz Review 14: 137–151 Dewey, J. 1938. Logic: The Theory of Inquiry. New York: Holt. Dummett, M. 1978. Elements of Intuitionism. Oxford: Oxford University Press. Heidegger, M. 1927. Sein und Zeit (= Jahrbuch f¨ur Ph¨anomenologie und ph¨anomenologische Forschung 8). T¨ubingen: Neomarius Verlag, 8th Edition, 1957 (translated as Being and Time by J. Macquarrie and E. Robinson, New York, Harper and Row, 1962). Heyting, A. 1930. Sur la logique intuitionniste. Bulletin de l’Academie Royale de Belgique 16. Husserl., E. 1913. Ideen zu einer reinen Ph¨anomenologie und ph¨anomenologischen Philosophi (= Jahrbuch f¨ur Ph¨anomenologie und ph¨anomenologische Forschung 1 (translated as Ideas: General Introduction to Pure Phenomenology by W.R. Boyce Gibson, New York, Collier, 1962). ¨ Kauppi, R. 1960. Uber die Leibnizsche Logik (= Acta Philosophica Fennica. 12). Kierkegaard, S. 1944, Either/Or (Volume 1, translated by D. Swenson, and L. Swenson; Volume 2, translated by W. Lowry). Princeton, NJ: Princeton University Press (Revised by H. Johnson, Garden City, NY, Doubleday – Anchor, 1959). Posy, C. 1984. Transcendental idealism and causality. In W. Harper and R. Meerbote (eds.), Kant on Causality, Freedom and Objectivity. Minneapolis, MN: Minnesota University Press, pp. 20–41. Sartre, J-P. 1946. L’Existentialisme est un humanisme. Paris: Les Editions Nagle (translated as Existentialism and Humanism by P. Mairet, London, Methuen, 1948). Shakespeare, W. 1954. Macbeth. In E.M. Waith (ed.), The Yale Shakespeare, revised edition.

Chapter 19

The Place of the Other in Leibniz’s Rationalism Noa Naaman Zauderer

The question of how “otherness” may be related to the “self” has dominated philosophy in the 20th century. Various approaches have been taken to “otherness”, that is, to the relation between “I” and “Other”, by continental philosophers such as Edmund Husserl, Martin Buber, Martin Heidegger, Jean-Paul Sartre, Emmanuel L´evinas, and Jacques Derrida. Unsurprisingly, Leibniz held a rather definite position concerning this issue, as well as with regard to many other current philosophical themes. In a short essay, apparently written in 1679, Leibniz states: The other’s place is the true point of view both in politics and in morals. Jesus Christ’s precept of putting oneself in the other’s place is not only good for the end our Lord speaks of, i.e., morals, in order to know our duty with respect to our neighbor, but also for politics, in order to know what designs our neighbor may harbor against us. One’s best access to these designs is obtained by putting oneself in his place [. . .] This fiction stimulates our thoughts, and has served me more than once to guess with utmost precision what was concocted elsewhere (DA 164).

The recommendation to put oneself in the place of another, originating in the moral scriptural precept “What you don’t wish to have done to you, don’t do to others”, is elaborated upon and used by Leibniz as a wide-ranging heuristic principle. Leibniz applies this principle to a variety of theoretical and practical domains, including epistemology, politics, ethics, jurisprudence, argumentation, negotiation and legislation.1 As shown by Marcelo Dascal, the presence of this principle is especially prominent in Leibniz’s discussions of issues that cannot be algorithmically or conclusively resolved (Dascal 1993: 402–403; 1994: 108–109, 112ff). A “right” decision in these domains would be one that maximizes the total amount of perfection one can achieve. Acknowledging the unavoidable confusion of human perceptions, Leibniz proposes the “other’s place principle” as an efficient heuristic tool, guiding us to make our choices in conformity with the principle of perfection. This principle, Leibniz maintains, cannot serve as a sure sign of truth. It inclines our choices without necessitating them, thus serving “only to detain us, to arouse our N. Naaman Zauderer Tel Aviv University, Tel Aviv, Israel M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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attention and to help us in learning about the consequences and the magnitude of the evils which our actions can cause to the other” (DA 165). This principle, in other words, provides us with a better understanding of the meaning and consequences of our choices. Leibniz insists that it is not the volitions of the other that one should anticipate, but rather his expected choices, his judgments, what he intends to do under the circumstances: It is possible to distinguish, further, between the will one would have if one were in the other’s place – which can be unjust, such as, for example, not wanting to pay – and the judgment one would make in that case, for one will always be forced to acknowledge that one must pay. Will is a lesser sign than judgment. Yet, neither the one nor the other is a sure sign of truth (ibid.).

However, the use Leibniz makes of the principle implies that in some cases one may need to envisage the other’s appropriate choices, what he ought to do under the circumstances. In the New Essays (1.2.4; A VI 6 91) Leibniz discusses the ethical rule calling on us to “do to others only what we are willing that they do to us”. Acknowledging the difficulties in applying this rule, Leibniz states: “we would wish for more than our share if we had our own way; so do we also owe to others more than their share?”. “I will be told”, he goes on to observe, “that the rule applies only to a just will. But then the rule, far from serving as a standard, will need a standard” (NE 1.2.4; A VI 6 91–92). Note that Leibniz uses this same language to criticize Descartes’ criterion of truth, clarity and distinctness. Yet, the content of these two criticisms is not the same. With regard to the ethical rule, Leibniz seems to point to the problem of circularity: To be able to apply this rule one needs to know, in advance, the meaning of “just will” under the circumstances. It is precisely at this point that Leibniz calls upon his heuristic principle. “The true meaning of the rule,” he concludes, “is that the right way to judge more fairly is to adopt the point of view of other people” (ibid.). In this passage, Leibniz seems to suggest that any attempt one makes to measure the wishes and expectations of others, while viewing them from his own first person perspective, is prone to bias and prejudice, no matter how sharp and incisive his thinking may be. Such an assessment should not be made in a purely intellectual manner, based on a consideration of pros and cons. To be carried out properly, it must involve both the intellect and the imagination.2 Only if one actually imagines himself in the concrete place of the other, under the conditions that shape his choices, will he be able to transcend his own self-interested perspective and discover insights that would otherwise not occur to him. This concrete imaginative feature seems to enable us not only to think about but also to feel the multifaceted situation of the other, to experience a feeling of identification, indeed of empathy, with the other, and thus to approach the situation with the “correct” point of view. The place of the other is thus tangible and concrete, even when the questions to be decided upon are themselves universal and abstract. When applied in ethical contexts, the OP principle is meant to help one know his duty with respect to the other and act on his behalf. “Put yourself in the place of another,” Leibniz states, “and you will have the true point of view for judging

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what is just or not” (Meditation on the Common Concept of Justice; R 56).3 In other contexts, however, the OP principle may be applied to one’s own benefit. Such is the case in politics, in negotiation, in disputation and also in contemplation, that is, in one’s own internal reasoning. The principle may help me foresee the moves taken by my opponent that are likely to work against me, and to plan my responses accordingly.4 The recommendation to put oneself in the place of the other may be applied either in “real” inter-subjective encounters, where the other is really present, or in cases where one is engaged in an inner dialogue, when the other’s presence is only imaginary. Both cases seem to involve a concrete imaginative feature, followed by an affective element of emotional identification or empathy. Such an attitude may also be applied when the presence of the other is not personal but rather textual, in which case the principle may serve as an interpretive device.

1 The Place of the Other – Some Ethical Roots The “other’s place principle” is deeply anchored in Leibniz’s understanding of justice as “the charity of the wise” (caritas sapientis),5 defined by him as “goodness towards others which is conformed to wisdom”.6 Leibniz takes the essence of justice to be no less founded in the immutable nature of things than are the principles of mathematics. In his Opinion on the Principles of Pufendorf he states: Justice, indeed, would not be an essential attribute of God, if he himself established justice and law by his free will. And, indeed, justice follows certain rules of equity and of proportion [which are] no less founded in the immutable nature of things, and in the divine ideas, than are the principles of arithmetic and geometry (R 71).

However, as shown by Patrick Riley, Leibniz understands “justice” not merely in terms of “wisdom” and “eternal truthfulness” but also in terms of charity and benevolence (Riley 1996: 141ff; R 4–7). “Charity”, according to Leibniz, is a “universal benevolence”, that is, “a universal habit of loving or of willing the good”.7 Note that Leibniz defines charity in terms of love. “Justice”, he states, “is charity or a habit of loving conformed to wisdom” (Felicity, R 83). To love, in his view, is “to convert the happiness of another into one’s own” (L 137), that is, “to find pleasure in the perfection of another” (Felicity, R 83).8 Pleasure, in Leibniz view, is “a knowledge or feeling of perfection, not only in ourselves, but also in others, for in this way some further perfection is aroused in us” (ibid.). The emotive element of charity in Leibniz’s definition of justice is rooted in his notion of “disinterested love”. Those who possess this kind of love, in Leibniz’s thinking, seek the good and happiness of another not only as a means but for its own sake. What Leibniz calls “disinterested love”, in other words, is “independent of hope, of fear, and of regard for any question of utility” (R 171). Leibniz seems to be indicating that it is precisely because we are pleased by things desired for their own sake that the happiness of those we love turns into our own (ibid.).9

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It is by means of this notion of disinterested love, as suggested by Brown, that Leibniz is able to reconcile the apparently egoistic psychology of Hobbes with the possibility of altruism implied in Grotius’s assumption of a natural sociability in human beings (Brown 1995: 426).10 That is, by insisting that we should love our neighbor without any self-interest in mind, Leibniz does not deny the presence and importance of self-interest (Hostler 1975: 51). Rather, he merely releases himself from the binary or duality of means and ends, claiming that “there is in justice a certain respect of the good of others, and also for our own, but not in the sense that one is the end of the other” (Elements of Natural Law, L 136).11 Leibnizian love, defined as “converting the happiness of another into one’s own” (L137), thus makes it possible to satisfy both egoism and altruism.12 The reconciliation of egoism and altruism in Leibniz’s notion of justice may have its roots in the principle of continuity. More specifically, I suggest that the continuum between the different degrees of justice explains the coexistence of egoism and altruism in the Leibnizian conception of justice. As Riley observes (1996: 185–186), commentators agree that what is most distinctive and valuable in Leibnizian justice is its insistence on a continuum between the negative and the positive notions of justice (“ius strictum” and “universal benevolence”, respectively).13 Leibniz attacks Hobbes’s narrow conception of justice, as being confined to the demand not to injure others. At this lowest degree of justice, Leibniz explains, one is motivated by selfinterest, e.g., by the fear that someone else will do the same to him (Meditation on the Common Concept of Justice, R 54). On the higher level, however, which Leibniz calls “equity” or “distributive justice,” one is obliged “to give to each his due” (R 172). On this level, one is required not only to avoid injuring others but also “to do good to everybody – but only so far as befits each one or as much as he deserves” (ibid.).14 In accordance with the principle of continuity, each and every level on the scale contains all the lower levels, but has an extra component endowing it with its own distinctive nature and raising it above those that precede it. Therefore, at the middle degree of justice, while one may be benefiting others as much as he can, he may also be satisfying his own self-centered interests that are rooted in the lowest degree of justice. It is thus due to the principle of continuity that one may promote both his own self interest and the happiness of another, satisfying both his egoistic and altruistic interests. Now, as is well known, one of the most prominent expressions of the Leibnizian principle of continuity lies in his view that divine and human justice are defined by the same principles and rules, differing from one another only in degree.15 This notion of “universal justice” yields another Leibnizian theme, according to which the love of God may be seen as a sort of model for earthly love of another.16 Accordingly, Leibniz seems to take one’s love of his neighbor as a concrete embodiment of one’s true love of God. This view is clearly implied by Leibniz’s claim that “one cannot know God without loving one’s brother” (Felicity, R 84).17 In the same spirit, he states that “charity towards one’s neighbor is only a consequence of the love of God”.18 He goes on to say: [. . .] St. John was right to say that there are man liars among those who say that they love God. He has also given the true sign for recognizing them. I recognize the love of God only in those who show ardor for producing the good in general (ibid.).

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Thus, one’s love of his neighbor, in Leibniz’s thinking, appears to be a tangible manifestation of one’s love of the infinite. This conception may provide us with another way of explaining the reconciliation of self-oriented and other-oriented interests. I propose that in Leibniz’s notion of charity and love, the pleasure one gains by promoting his own self-interests and the pleasure he gains by contributing to his neighbor’s happiness are not in conflict precisely because they constitute parallel expressions or manifestations of the true love of God. As we turn to wisdom, the second element of Leibnizian justice, we find that this notion is formed and modeled by the infinite wisdom of God. Leibniz defines wisdom as “the science of happiness” (R 54, 171). In Meditation on the Common Concept of Justice he insists that “justice conforms to the will of a sage whose wisdom is infinite and whose power is proportioned to it” (R 59). Leibniz states that those who act according to justice “find that they would not be wise at all (that is, prudent) if they did not conform themselves to the will of such a sage” (ibid.). Sometimes, however, Leibniz presents a more moderate view, claiming that “the just man himself will be accustomed to act with the highest reason, or at least he will be ready to obey the wise man, which suffices here” (M 35). As shown by Dascal, the Leibnizian notion of universal wisdom suggests that the just man endeavors to act in the most rational way, that is, in a way that comes closer to God’s, the supremely wise being (1993: 395–396). That is, in order to act justly one should adopt a universal, global point of view, aiming to promote the common good as much as possible. In doing so, one must strive to imitate the wisdom of God. Due to our limited perspective as mere creatures, however, we cannot obtain the global point of view which is the privilege of the infinite wisdom of God, and thus cannot fully comply with the definition of justice as “the charity of the wise” (Dascal 1993: 401). To this end, Leibniz provides us with some practical heuristic aids, among them the OP principle. This tool, as I shall show, serves to implement both elements of justice, that is, not only of charity (universal benevolence) but also of wisdom. As stated by Riley, the equal emphasis that Leibniz puts on “wisdom” and “charity” in his definition of justice suggests that his practical thought is a kind of fusion of Platonic and Christian themes (1999; 1996: 156–159). Riley goes on to indicate that for Leibniz, what is essential is that Christian “charity” and Platonic “wisdom” are in equilibrium. The two elements of justice, the affective and the intellectual, shape and form one another. Charity is subject to wisdom and moderated by it, while wisdom is enriched and enhanced by the element of charity. The contribution of charity to wisdom in Leibniz’s definition of justice is summarized in his claim that “one cannot be just without being benevolent” (GR 500). This insight divorces Leibniz from the long-standing intellectualistic tradition, exemplified not only by ancient thinkers but also by Descartes, a tradition that reduces both morality and rationality to the rule of reason over the passions (Naaman Zauderer 2001). The subordination of wisdom to charity is explicitly affirmed by Leibniz’s claim that “one cannot have wisdom without having charity (which is the real touchstone of virtue)” (Felicity, R 84). The subordination of charity to wisdom, on the other hand, that is, the assertion that charity must be regulated and confined by wisdom, implies that sensitivity to the

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preferences of the other should not be understood as boundless altruism, nor should it mean ignoring the self. Leibniz insists that the claim “that justice commands us to consider the interests of others while we neglect our own, is born of ignorance of the definition of justice” (R 171). Wise charity or love, according to Leibniz, must be “proportional” to the degree of perfection one recognizes in others (Riley 1996: 156). Leibniz further states that “the zeal of charity must be directed by knowledge so that we do not err in the estimation of what is best” (De Justitia et Novo Codice, GR 621–622). The interdependence between charity and wisdom in Leibniz’s notion of justice seems to be parallel to the interdependence between the love and knowledge of God. “One cannot love God”, Leibniz states, “without knowing his perfections, or his beauty” (R 84). This statement is anchored in Leibniz’s notion of love as finding pleasure in the perfections of another. In the case of inter-subjective relations, this means that the love of another requires one to know the peculiar qualities of his beloved. As applied to God, Leibniz believes that we come to know God as we discover the divine sciences, that is, the eternal truths of reason and the marvels of nature: Since we can know him [God] only in his emanations, these are two means of seeing his beauty, namely in the knowledge of eternal truths [. . .] and in the knowledge of the Harmony of the Universe [. . .] That is to say, one must know the marvels of reason and the marvels of nature (R 84).

But in what sense should one love God in order to know Him properly? Because God’s perfections “are infinite and cannot end”, Leibniz further explains, “one cannot know God as one ought without loving him above all things, and one cannot love him thus without willing what he wills” (R 59). This claim, I propose, uncovers the most fundamental assumptions underlying the Leibnizian conception of otherness. For it is not only when the “other” is the divinity, the most perfect being, but also when he is human, in inter-subjective relationships, that one cannot know what occurs in the other’s mind by pure “intellectual” means. To approach such an understanding of another one must not only think about but also feel the wishes and expectations of the other, emotionally, not only intellectually, imagine himself in his place. It is only if one experiences a feeling of empathy with the other, that is, if he strives to will what he wills, to whish what he wishes, to choose what he chooses, that he will he be able to transcend his own self-centered viewpoint and “as if” intrude into the peculiar perspective of another. It is here again that the love and knowledge of the transcendent appears to be a kind of model or ideal of one’s love and knowledge of his neighbor. “To will what he wills” – the phrase Leibniz uses referring to one’s true love of God – is, in my view, the most accurate expression of the empathy one is required to feel towards his neighbor, at least in ethical contexts. Ironically, however, the recommendation to put oneself in the place of another, in the other’s peculiar point of view, has no meaning with regard to God, who does not possess any limited, peculiar “point of view” but rather dominates all possible perspectives at once.

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2 The Place of the Other in Polemics The mutual balance between charity and wisdom, underlying Leibniz’s notion of justice, seems to form his attitude toward the other not only in the ethical implementations of the OP principle but in other contexts as well. For even when the “other” is my adversary or my most hostile enemy, in order to anticipate his moves or even to manipulate them, it is preferable for me to try to figure out his role, to imagine myself in his place and thus to manifest a certain degree of identification with him. This use of the principle, which may be called “methodic”, “instrumental” or “strategic”, as Dascal terms it (1994), is in no way cut off from its “original” ethical roots. Leibniz, as we have just seen, seeks to avoid the egocentric perspective, not only in ethics but also in other fields, practical and theoretical. Yet, to the same extent, he seeks to stay away from the opposite pole, to avoid being assimilated into the perspective of the other, for such assimilation involves abolition of the self. At this point, he seems to depart from Descartes’ attitude towards the “other”, be its presence personal, textual, real or only imaginary. In what follows, I wish to reconsider the Leibnizian attitude towards the other in polemic contexts through a comparison with Descartes. The vast differences between the two attitudes towards the “other” – the Cartesian and the Leibnizian – are used here to illuminate some significant points regarding each of them separately. In order to assess what role, if any, Descartes attributes to the presence of the “other”, we must consider not only his declared positions but also his practice and philosophical temperament. This issue is particularly intriguing in the case of Descartes, whose intellectual biography and philosophical style testify to the coexistence of two opposing tendencies. In many respects, Descartes may be viewed as a typical monological thinker. The search for truth constitutes, for him, an inner, private experience that requires one to withdraw into his own thoughts, to remain completely attentive to the ideas in his soul. The monological nature of Descartes’ thinking consists, first and foremost, in the non-formal and non-public dimension of his method for searching after the truth. As I have shown elsewhere (Naaman Zauderer 2004), Descartes assigns an infallible status to the “natural” functioning of pure mind when it follows its own nature and operates without “external” disruptions. The “natural” mode of functioning of the pure mind serves, for him, as a sort of model for the “appropriate” way of thinking, one that may lead us, ultimately, to the knowledge of truth. On the basis of these assumptions, he develops a non-formal conception of justification, whose standards are internal to the human mind. These standards are shaped and formed by the “natural” operations of the pure intellect, rather than by the notion of truth, in the way we might find in some formalistic methods of proof.19 In setting out to justify a proposition, according to Descartes, one should show that the cognitive procedure by means of which this proposition has been actually discovered conforms and displays the “natural” functioning of the pure mind. Reconstruction of the process of discovery thus constitutes, for Descartes, a fundamental component of justification.

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The Cartesian conception of justification has an essentially non-public character. Being subject to internal, non-formal and subjective standards of evidence, the justification of propositions seems to be accessible only from a first-person perspective, to a subject considered on its own, and not from the point of view of another. It is by no means surprising, therefore, to find that Descartes praises the monological form of thinking, while disapproving of philosophical dialogues and debates.20 In a disputation, he believes, each side strives for victory rather than genuinely searching for the truth (AT VI 68: CSM I 146). This attitude is expressed by Descartes not only theoretically but also practically, as he often tends to be rather antagonistic towards his interlocutors and critics. He is frequently unwilling to take the content of their objections into consideration, exempting himself by means of various “ad hominem” arguments that focus on the personal competence of his critics.21 At the same time, however, one cannot but wonder at the many debates and dialogues which Descartes undertakes with his contemporaries. Indeed, Jean-Luc Marion has indicated that much of Descartes’ philosophical work is the product of debates with his contemporaries which he himself initiated (Marion 1995). Setting aside the issue of Descartes’ motives in initiating the objections to his writings, it should be asked which notion of dialogue he had in mind while seeking a public debate regarding his views. Replying to this question requires examining Descartes’ expectations from readers of the Meditations with regard to what he describes as the analytic method of analysis. In the Second Replies, Descartes insists that only the analytic method, in accordance with which his arguments in the Meditations are organized, is appropriate for dealing with metaphysical issues (AT VII 155–157; CSM II 110–111). For this method alone, Descartes maintains, “shows the true way by means of which the thing in question was discovered methodically” (AT VII 155; CSM II 110). The analytic method, in other words, begins with what is epistemologically prior, that is, prior in the order of discovery, and not with what is logically prior, as is usual in synthetic methods of proof (AT VII 156; CSM II 111). Descartes argues that the analytic method requires of the reader a high degree of attention and concentration (AT VII 155–156; CSM II 110). This is so mainly because he is required to follow the complete chain of arguments and consider each of the conclusions according to its place in the overall order of reasons, rather than in isolation. This method, Descartes states, “contains nothing to compel belief in an argumentative or inattentive reader” (ibid.). Yet, “if the reader is willing to follow it and give sufficient attention to all points, he will make the thing his own and understand it just as perfectly as if he had discovered it for himself” (AT VII 155; CSM II 110). The argumentative, inattentive reader appears to be anyone who is not willing to make the effort involved in considering the complete chain of arguments. Such an impatient reader judges each of the conclusions separately, before having acquainted himself with the complete sequence. This type of reader observes Descartes’ arguments from the “outside”, intermixing Descartes’ ideas with his own counterarguments (AT VII 157: CSM II 112; AT III 283–284: CSMK 168–169). Therefore, he fails to notice the actual order of discovery associated with the issue at hand

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and thus cannot but fail to comprehend the justifications given by Descartes to his arguments. It is not surprising, therefore, to find that Descartes considers such a reader to be incapable of clearly and distinctly apprehending the truth (AT VII 157; CSM II 112). Descartes and Leibniz, it would seem, suggest two fundamentally opposed conceptions of dialogue, that is, two different views of the nature, preconditions and ends of intellectual encounters with others. Nevertheless, before setting these two philosophers against each other, I shall refer to some elements shared by them. Both thinkers seem to suggest that to understand the other’s opinions and stances, one should transcend one’s own point of view, if only temporarily, rather than listening “from the outside”. Both also agree that the other’s opinions or moves should not be viewed and evaluated in isolation, cut off from their concrete context. Yet, there are vast differences between the two. Descartes offers the Meditations to be examined and criticized by his readers; but the kind of dialogue he seeks is as close as possible to the model of a monologue. Dialogue of any sort seems to be alien to him, as if it were forcibly or artificially imposed on him. To cope with this discrepancy, he offers a model of dialogue which seeks to become a monologue to the greatest extent possible. In this model, the opponent must step into the shoes of the proponent, as far as possible, attempting to fully adopt his perspective and evaluate things by reference to his standards. Thus, there appears to be no real encounter with the other, with whatever is distinctive about him and his peculiar point of view. Rather, there is only an apparent or pseudo-encounter, for the opponent is required to abandon, even if only temporarily, everything that is peculiar to his way of thinking, and fully adopt that of Descartes. While this may enable Descartes to impart his ideas to readers, it cannot allow him to learn anything new through the encounter with his critics (Naaman Zauderer 2004). For Leibniz, by contrast, inter-subjective encounters are integrated into the process of discovery. In his view, the presence of the other – either real or imaginary – plays a formative role in establishing the individual’s perspective. Hence, by calling on us to occupy the place of the other, Leibniz does not mean that we should renounce our own perspective in favor of another. In order to extend our own point of view rather than replace it, we must take over the concrete place of the other without abandoning our own. Only by occupying both places at the same time can we ensure a real encounter between differing points of view that mutually enrich and enhance one another. This means that the consideration of the other’s needs, objectives and preferences should not be followed by an alienation of the self. Rather, these factors must be weighed and evaluated against other considerations, including those deriving from one’s own original stance. A crucial difference between the two approaches lies in the one-sided dimension of Descartes’ view. He makes particularly high demands of his readers and of whoever might engage in a critical dialogue with him. Yet it is doubtful whether he makes the same demands of himself as he faces his critics. This one-sidedness emerges not only in practice, in the way he actually debates with his interlocutors, but also in the kind of reasons he provides to support his own notion of a dialogue. Descartes might have answered that he would be willing to enter into a mutual

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debate only with someone who accepts in advance the constraints imposed by his methodology. Such a response, if given, would not only limit the scope of those taking part in such a dialogue with him, but would further intensify the monological nature of his thinking. For even with regard to such an ideal opponent, who fully meets his requirements, Descartes’ “narrow” model of critical dialogue seems to dictate at the outset both its ends and its results. It does not allow for the possibility of a real encounter between conflicting points of view, nor does it acknowledge the value of such an encounter as a means to enrich and elaborate each of the original views. It is precisely at this point that the essence of Leibniz’s notion of dialogue differs. As repeatedly shown by Dascal, Leibniz truly believed that the more we expose ourselves to conflicting conceptions and views, the more we obtain clear knowledge of the truth. As opposed to the one-sidedness characterizing Descartes’ attitude towards the other, Leibniz’s principle is indifferent to the personal identity of those who fulfill it. In the New Essays, the encounter with alien, unfamiliar positions is viewed as a means to avoid errors. Leibniz calls on us to fight against our natural tendency to attach ourselves to people who think like we do, to read texts that reflect our own positions, and to expose ourselves to lines of thought that resemble our own. All these are taken to be a source of self-deceptions and erroneous judgments: Although we cannot will what we want to, just as we cannot judge what we want to, we can nevertheless act ahead of time in such a way that we shall eventually judge or will what we would like to be able to judge or will today. We attach ourselves to people, reading material and ways of thinking which are favourable to a certain faction, and we ignore whatever comes from the opposite faction; and by means of these and countless other devices, which we usually employ unwittingly and without set purpose, we succeed in deceiving ourselves or at least changing our minds, and so we achieve our own conversion or perversion depending on what our experience has been (NE 2.21 23; A VI 6 182).

However, we may also put these natural tendencies to a positive use, and take advantage of them by exposing ourselves to various challenging circumstances. In so doing, we are advised by Leibniz to put ourselves in the place of our neighbor, to use the principle of the other’s place.

3 Concluding Remarks Leibniz seems to propose an intriguing conception of otherness. What is most significant in his view, I believe, is not only his challenging non-intellectualistic understanding of justice underlying his notion of otherness, but also the parallelism he seems to find between the human “other” and the divine. In Leibniz’s thinking, to be sure, one’s attitude towards the infinite dwells, to some extent, in his attitude towards his neighbor. Consequently, the love and knowledge of God, of the transcendent being, have a formative role for the analysis and evaluation of ethical inter-subjective relations. It is against this background that Leibniz considers wisdom and charity, the two elements necessary for justice, as mutually dependent. Only by truly loving another, Leibniz suggests, can you know him properly, and vice versa; it is only as you come

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closer to know the other, to an understanding of his peculiar, idiosyncratic traits, that you can be sensitive and empathic towards his wishes and needs. This line of thought is applicable not only in ethical contexts but in other contexts as well. For even when the other is my adversary or debater I’m advised by Leibniz to strive, not only intellectually but emotionally as well, to put myself in his place, to see his skin “from the inside”, as the feeling of empathy is described by Sherman (1998: 110). Only in this way can one correctly envisage his adversary’s subsequent moves. However, in my opinion we may still consider both conceptions introduced in this paper, the Leibnizian and the Cartesian, as two plausible alternative outlooks regarding the way understanding and criticism relate to each other. According to the Cartesian outlook, a temporal suspension of the critical point of view appears to be a prerequisite for understanding the other, while the Leibnizian outlook sees criticism and comprehension as mutually dependent and intertwined. It is in the space between these two alternatives that we may wish to locate ourselves. Having gained a proper understanding of the positions of the other, having listened to his views, we may then ask ourselves whether we should temporarily suspend our critical point of view, or whether we should adopt criticism as formative to our understanding both of the other and of ourselves. Acknowledgments I wish to express my gratitude to Marcelo Dascal for making me acquainted with the fundamental role of controversies in Leibniz’s thought. I would also like to thank Dr. Ariel Merav for his helpful remarks.

Notes 1. I shall refer to this principle, from now on, as “the other’s place principle”, or, in brief, the OP principle. 2. The imaginative feature of the OP principle is discussed in depth by Emily Grosholz (1993: 67–70). 3. As I shall immediately show, Leibniz believes that operating on behalf of one’s neighbor, that is, for the latter’s own happiness and welfare, contributes to one’s own benefit and happiness as well. 4. For a profound discussion of the “strategic” implementations of the OP principle and of how these implementations relate to its ethical use, see Dascal (1994: 111–115). 5. Meditation on the Common Concept of Justice, R 45ff; preface to the Codex Iuris Gentium, R 171; Felicity, R 83. 6. Meditation on the Common Concept of Justice; R 54. See also preface to the Codex Iuris Gentium; R 171. 7. As Leibniz explains to Arnauld, charity is “a universal benevolence, which the wise man carries into execution in conformity with the measures of reason, to the end of obtaining the greatest good” (March 23, 1690; L 360). 8. Alternatively, in a letter to Arnauld, Leibniz defines love as “pleasure derived from the happiness of others, and pain from the unhappiness of others” (November 1671; L 150). In the same vein, Leibniz states in the preface to the Codex Iuris Gentium that love is “rejoicing in the happiness of another” (R 171). However, as suggested by Hostler (1975: 49), this latter definition is misleading, since it obscures the fact that for Leibniz, “loving another is not being pleased by his happiness so much as by his personal qualities and attributes”, that is, by his distinctive perfections that make him happy.

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9. “In truth, the happiness of those whose happiness pleases us turns into our own happiness, since things which please us are desired for their own sake” (R 171). 10. This claim is reasserted by Leibniz on many occasions. In a letter written in 1696 he explicitly states that “the positions of Grotius and Hobbes are easily reconciled” (GR 655; cited in Brown 1995: 417). In his preface to the Codex Iuris Gentium, he states: “While each benefits others as much as he can, he may increase his own happiness in that of the other” (R 173). Likewise, in Felicity he states that “one even advances one’s own good in working for that of others” (R 84). See also R 72, 171. 11. “Otherwise”, Leibniz goes on to explain, “it may follow that it will be just to abandon some wretched person in his agony, though it is in our power to deliver him from it without much difficulty, merely because we are sure there is no reward for helping him. Yet everyone abominates this as criminal, even those who find no reason for a future life; not to mention the sound sense of all good people which spurns so mercenary a reason for justice” (ibid.). 12. Hostler (1975: 48). A similar idea was anticipated by Spinoza regarding virtue. Spinoza, Ethics, V, 42. 13. This issue is extensively discussed by Grosholz (1993). Leibniz discusses the different degrees of justice in his preface to the Codex Iuris Gentium (R 171–172) and also in Meditation on the Common Concept of Justice (R 53ff.). Note that in Meditation Leibniz’s analysis of the different degrees of justice (R 54–56) aptly exemplifies the concrete and imaginary features of his OP principle. 14. Leibniz refers to the third degree of right as “piety (or probity) in universal justice” (R 172). At this highest degree of justice one is required to live honestly (or rather piously) and to tend toward the common, universal good. 15. See, for example, R 48–49, 69, 71, 174; NE 2.30.55. On these grounds Leibniz claims that “he who acts well, not out of hope or fear, but by an inclination of his soul [. . .] acts more justly than all others, imitating, in a certain way, as a man, divine justice” (R 72). Moreover, in the Principles of Nature and Grace he states: “The spirit not only has a perception of the works of God but is even capable of producing something which resemble them, though in miniature” (sec. 14; L 640). 16. In The Principles of Nature and Grace Leibniz argues: “God being also the most perfect, the happiest, and therefore the most lovable of substance, and true pure love consisting in the state which cause pleasure to be taken in the perfections and the felicity of the beloved, this love must give us the greatest pleasure of which one is capable, since God is its object” (sec. 16; L 641). 17. As suggested by Brown (1995: 426), this indicates that one cannot love God without loving one’s brother, or, as Leibniz phrases it, “he who loves God loves all men” (G VII 75), but to the degree that reason permits (ibid.). 18. To Andreas Morell, 1697 A I 14 254–255 (cited by Riley 1996: 142). 19. Leibniz’s method seems to exemplify such a formalistic conception of proof. See Naaman Zauderer 2004: 48; Naaman Zauderer 2001: 1417–1418. 20. See, for example, AT VI 68–69: CSM I 146; AT VI 16: CSM I 119; AT VI 31: CSM I 126. 21. Some examples are found in the Seventh Replies (AT VII 461: CSM II 309; AT VII 466: CSM II 313; AT VII 492: CSM II 333; AT VII 526–527: CSM II 358; AT VII 546: CSM II 373), as well as in Descartes’ replies to Gassendi (AT VII 347–350: CSM II 241–242; AT VII 351–353: CSM II 243–244; AT VII 357–359: CSM II 247–249). This issue is extensively discussed in Mullin (2000).

References Brown, G. 1995. Leibniz’s moral philosophy. In N. Jolley (ed), The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press, pp. 411–441. Dascal, M. 1993. One Adam and many cultures: The role of political pluralism in the best of possible worlds. In M. Dascal and E. Yakira (eds.), Leibniz and Adam. Tel Aviv: University Publishing Projects, pp. 387–409.

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Dascal, M. 1994. Strategies of dispute and ethics: Du tort and La place d’autruy. In Leibniz und Europa (VI. Internationaler Leibniz Kongreß). Hanover: Leibniz Gesellschaft, pp. 108–116. Descartes, R. 1964–1976. Œuvres de Descartes. Edited by C. Adam and P. Tannery. Paris: Vrin [=AT]. Descartes, R. 1985. The Philosophical Writings of Descartes, vols. 1 and 2. Translation J.G. Cottingham, R. Stoothoff, and D. Murdoch. Cambridge: Cambridge University Press [=CSM]. Descartes, R. 1991. The Philosophical Writings of Descartes, vol. 3. Translation J.G. Cottingham, R. Stoothoff, D. Murdoch, and A. Kenny. Cambridge: Cambridge University Press. [=CSMK]. Grosholz, E. 1993. Leibniz and the two labyrinths. In Dascal and Yakira (eds), pp. 65–77. Hostler, J. 1975. Leibniz’s Moral Philosophy. London: Dickworth. Marion, J-L. 1995. The place of the Objections in the development of Cartesian metaphysics. In R. Ariew and M. Grene (eds), Descartes and his Contemporaries: Meditations, Objections and Replies. Chicago: The University of Chicago Press. Mullin, A. 2000. Descartes and the community of inquirers. History of Philosophy Quarterly 17(1): 1–27. Naaman Zauderer, N. 2001. Leibniz and Descartes: Two conceptions of error and rationality. In H. Poser (ed.), Nihil Sine Ratione (VII. Internationaler Leibniz Kongreß). Berlin: Leibniz Gesellschaft, pp. 1412–1420. Naaman Zauderer, N. 2004. The loneliness of the Cartesian thinker. History of Philosophy Quarterly 21(1): 43–62. Riley, P. 1996. Leibniz’ Universal Jurisprudence. Cambridge, MA: Harvard University Press. Riley, P. 1999. Leibniz’s political and moral philosophy in the Novissima Sinica. Journal of the History of Ideas 60(2): 217–239. Sherman, N., 1998. Empathy and imagination. Midwest Studies in Philosophy 22: 82–119.

Chapter 20

Morality and Feeling: Genesis and Determination of the Will in Leibniz Adelino Dias Cardoso

“Nothing is less servile and more appropriate to the greatest degree of freedom than to be always lead to the Good, and always by one’s own inclination, without any constraint and without any displeasure”. (To Clarke; GP 7 385).

1 Introduction On the Leibnizian view, determination is the fundamental feature of action, including free action and, above all, divine action as full freedom. Determination means, at this level, the intrinsic motivation of the agent, its inclination to such and such act rather than another. The act of Creation itself has a reason, and this reason is a subjective motive, the natural inclination of God to the best.1 Unlike a typically rationalist morality, for Leibniz the autonomy of the moral subject consists in acting through intrinsic motives (GP 7 392), thus originating a “happy and desirable” (GP 6 390) necessity, in not putting itself in a chimerical position of total indifference to any possible decision. The determination introduces a middle intelligibility, between strict necessitarianism and purely fortuitous chance: It is the typical intelligibility both of physics2 and of morality.3 Its scope comprises those events that come spontaneously into being due to its nature and whose modal status is that of something possible that comes into existence or not depending on the circumstances that can affect such existence. The determination characterises the type of order and causality inherent in the nature and actions of any human subject. Nature and freedom, recalling here a relevant Kantian dichotomy, are intimately connected by a common intelligibility. Indeed, the elucidating principle of the operation of a natural being is the same that clarifies the action of an intelligent being: In both of them, the present state is the result of its precedent states and moves into the future, inflecting its movement towards one or another direction, according to a natural, but not necessary, chain. Therefore, determination is not a state but a process linked to a dynamic understanding of being. As to morality, more specifically, Leibniz focuses on the devices immanent to the will that incline, though not necessarily. A.D. Cardoso Lisbon University, Lisbon, Portugal

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2 Morality and Natural Intelligibility Morality is one of Leibniz’s basic interests, and it reveals a most distinctive feature of his philosophical personality, as he says in the New Essays (NE 1.1; GP 5 63). Unlike the Cartesian tendency to subordinate morality to physics (Descartes 1644: 14), Leibniz subordinates physics to a moral intelligibility: “Therefore, one can say that physical necessity is founded on moral necessity, i.e., on the choice of the wise man; and the former as well as the latter must be distinguished from geometric necessity” (Theodicy, Preliminary Discourse, 2; GP 6 50). This is one of the major achievements of Leibnizianism: To introduce a gap between mathematics and physics, and to establish a very close bond between physics and morality.4 In fact, Leibniz draws a very strong distinction between geometrico-metaphysical necessity and physico-moral necessity.5 The former is strict necessity, in the strongest sense of the word, logical necessity that is regulated by the principle of identity; the latter is necessity in a weak sense, being exercised at the level of a contingent order, regulated by the principle of the best, which founds the primacy of finality in physics (To Clarke; GP 7 389). This primacy is clearly expressed by Leibniz: “Far from excluding final causes and the consideration of a being that acts with wisdom, it is hence from there that everything must be deduced in physics” (To Bayle, 1698; GP 3 54). Hence, it is from there that everything must be deduced, i.e., first of all the existence of the world, whose sufficient reason is the principle of the best: “For what is necessary, is so by its essence, since its opposite implies contradiction; but the existing contingent owes its existence to the principle of the best, which is the sufficient reason of things” (To Clarke; GP 7 390). The actual world is intrinsically contingent in its own genesis: Its existence does not include any metaphysical necessity, only a moral one. The actual world is, in absolute terms, the most perfect of all possible worlds6 and from this derives the adequate point of view concerning the consideration of nature. Therefore, moral perspective is not extrinsic to science, namely to physics: “The search for final causes within physics is precisely the practice of what I believe one must do, and they who wanted to banish final causes from their philosophy did not consider enough their relevant utility” (Tentamen Anagogicum; GP 7 271). Mechanism entirely elucidates nature’s efficiency but does not exhaust nature’s significance. One loses very much in science by not considering finality. Thus, Leibniz does not follow the modern tendency to open a gap between science and religion. Accordingly, physics and mathematics should testify to God’s presence in nature by exhibiting its marvels. Likewise, symmetrically, the books of religiosity should use the extraordinary achievements of science to glorify God. The intimacy of physics and morality is expressed through the perfect reciprocal correspondence between the order of efficient causes and that of final causes: Eyes are organs, their finality is vision and their internal mechanism is disposed to perform spontaneously their function in an extremely appropriate way. Leibnizianism’s beauty, the poetic and religious side of its science and also its actuality, are strictly connected to the homology of nature and morality. Actually, in morality just as in any other field, continuity is the touchstone of a good philosophy. Morality concerns minds, concerns the community they establish

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with God, a community that is “a moral world in a natural one” (Monadology, §86; GP 6 622). Grace has a specific economy and an intrinsic intelligibility. However, it does not work independently of nature or against it: “[. . .] things lead to grace through the very means of nature” (ibid.). Grace continues and perfects nature, gives it a more elevated sense, as expressed in Principles of Nature and Grace: “[. . .] so that nature itself leads to grace and grace perfects nature making use of it” (sec. 15; GP 6 605). The relationship between nature and grace is one of interpenetration: Not only does grace improve nature, but it also gives nature a new, more complete sense.

3 The Leibnizian Project of a Philosophical Morality Despite the general tendency of his time, Leibniz stresses final causality and, which is more, he views nature through the prism of morality: Geometrical and metaphysical consequences necessitate, but physical and moral ones incline without necessitating. There is even a moral and voluntary element in what is physical, through its relation to God, since the laws of motion are necessitated only by the best (NE 2.21.13; GP 5 164).

Parallel to this diffuse morality, Leibniz intends to set the bases of a philosophical morality, embracing a program of research in which he is led to face some difficulties concerning philosophical morality’s legitimacy, its mode of elaboration and its place in a philosophical system. In its broadest sense, morality is natural reason exercising itself in the actions that aim at the fulfilment of the human being: “Morality is what right reason (prudence or the true care for one’s own good) makes equivalent to natural reason” (Definitionum juris Specimen; A VI 3 592). The legitimacy of a philosophical morality is the object of a severe criticism in a book that had a remarkable impact in mid-17th century Europe: De l’usage des passions (1641) by F. Senault. In the preface to his work, the author asserts imperatively the thesis that Christian morality is the only true morality, the alleged virtues of pagans being nothing but sinful and criminal acts: “All the actions that man has done without the assistance of grace were criminal and, if we believe Saint Augustine, all his actions were sins” (Senault 1641: Preface). The target of Senault’s criticism is Stoicism,7 which inspired much moral reflection in the transition from the 16th to the 17th century and which is a crucial concern of moral discourse during the 17th century. In his offensive against Stoicism, the author aims at harmonizing reason and faith, nature and freedom, through an argumentative strategy similar to the one we find in the Tableau des passions humaines (1620) by Co¨effeteau, according to which a morality based on reason does not imply any nullification of feeling.8 Arnauld introduces a surplus of vigour and passion in his opposition to the tendency to rehabilitate a morality at a merely human scale, be it called natural or rational. The religiosity of Port-Royal, where Arnauld pontificates, is one of the most troubling phenomena and also the most typical of the European religious

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consciousness in the 17th century. Moral righteousness and virtue may be very dignified at the human level, but they have nothing worthy from the standpoint of salvation, which is the only issue that matters. Salvation requires formal invocation of Christ, the only true mediator between man and God. Arnauld’s De la n´ecessit´e de la foi en Jesus Christ pour eˆ tre sauv´e, written in 1641 and very opportunely published in 1701 by Dupin, who adds an enlightening preface, is an invaluable document. As usual, Arnauld reacts on the spot against a recently published book, De la vertu des payens (1641) by La Mothe le Vayer, who refines the Jesuit’s doctrinal perversity. According to Arnauld, Jesuitism, and especially the Jesuit missions, is the very focus of the doctrinal epidemics that affects Christendom with inevitable effects on morality (Cardoso 2000). In order to tackle directly the root of the problem, the great theologian shows the uselessness of all our acts performed outside the institutional reality of Christendom, the only route to salvation. Outside the Church and its sacraments, all routes lead to damnation. Arnauld maintains a radical heterogeneity between faith and reason, between the knowledge of God through natural light of reason and faith.9 Reason is sufficient to show the necessity of the one and only God and of its Providence in the government of nature and human matters, but it is not sufficient to understand man’s nature and value as well as his radical incapacity to reach perfection by himself alone. After Adam’s sin, humanity fell into such a state of incapacity that no philosophy can elucidate through mere reason. Original sin is the crucial event of Arnaldian anthropology, which is emphatically pessimistic. Unable to cure himself, the human being needs Christian medicine: Christ is the only doctor who cures man from the disease caught by Adam and of which the most obvious affection is pride: “For the deepest and the most dangerous of all injuries we received through the original sin is pride, and other injuries are nothing but consequences of it” (Arnauld 1641: 90). Original sin and incarnation are the basilar stones of the Christian building: incarnation has its reason of being in the original sin; Christ is the mediator as a man, not as God’s son. Christ participates in divine and in human nature, even in its most vile and abject aspects, which also constitute his deepest features. Only faith in Christ can save: This is the leitmotiv of Arnauld’s formal charge against a morality inspired by the mere light of reason. Faith must be necessarily based on authority; thus, it cannot do without supernatural revelation,10 which is the only way to the fundamental mystery of the Incarnation, from which the spirit of Christianity flows: a spirit of humility, entirely distinct from that of all pagan philosophies and moral doctrines which idolize human faculties11 and give man a power and initiative he absolutely does not have.12 Therefore, the function of faith consists in bringing man back to his true place by acknowledging the decayed state of his nature and the vanity inherent in the vain project of changing the self into the source of light, that is to say, the only agent and author of his own fulfilment. That is the point of conflict vis-`a-vis Christian Stoicism of the early seventeenth century, e.g., Charron’s, according to which man can, through self-examination, know himself and cure his original pride and presumptuousness.13 In fact, Arnauld’s diagnosis on the human condition is the same as Charron’s, although they differ deeply on the kind of medicine and on the good doctor: “[. . .] to study oneself

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and to learn to know oneself: This is the foundation of wisdom and the way to every good” (Charron 1986: 44). Arnaud opposes the thesis of Christ as the only doctor to the statement cure yourself, implicit in Charron’s procedure – “examine, spy and know yourself” (Charron 1986: 45). For the apologist of the purest Catholic orthodoxy, Socratic humility is nothing but a secret self-sympathetic pride. There is a radical gap between natural law and the experience of Christian faith, even if natural law is inspired in a careful meditation and rational weighting. The value of philosophy, namely Cartesian philosophy, which Arnauld assumes in his doctrinal combats, is merely instrumental, for it serves truths that surpass it. Leibniz, on his part, understands that the relationship with God belongs to man as a natural being: “[. . .] religion concerns everyone equally” (Parall`ele; GR 56). Morality, as we have seen, is natural reason exercising itself in actions leading to human fulfilment (“prudence or true care of one’s good”; Definitionum juris Specimen; A VI 3 592). Under the terms of Leibniz’s Parall`ele, reason is the agent of human community, but also of the community of God and men, which constitutes a “truly universal Monarchy or a general Republic” (Monadology § 86) to which all spirits are called, irrespective of historico-cultural contingencies and whose law is the law of nature: “God [. . .] is doubtlessly the author of the law of nature, and also the common Lord and ruler of the whole universe” (Parall`ele; GR 54). The foundation of Christianity re-establishes and culminates the religion of the wise and of the fair men of all times, the only antidote against the human tendency to pervert true religion. Here lies the principle of a universal religion, consonant with the law of nature, the basis of Catholicity: “the law of nature is the Catholic religion” (GR 49). According to Leibniz, natural theology is the basic level, the deepest stratum of all knowledge, including the principles of good conduct. Human morality is based on natural theology or, more precisely, it is its practical component: “So it can be said that natural theology – with its two divisions, theoretical and practical – contains both real metaphysics and the most perfect moral philosophy” (NE 4.8.9; GP 5 413). Morality consists mainly in practice: “but morality demands more practice than precepts” (To Thomas Burnett, 1705; GP 3 302). It is a matter of learning, which every human being performs during his existence: Moral principles exist inside man as natural dispositions. Natural and divine law are one and the same thing: The voice of consciousness that talks to man, within his own heart, being a modality of the divine voice – in Leibnizian terms, “Reason is God’s natural voice” (To Morell, 1698; GR 138). Christ has come to confirm rather than to dismiss the morality of reason; to confirm by correcting its deviations, by rectifying it: The little right these persons have in calling themselves Christian while supporting those same things Jesus Christ came to destroy, is surely evident to all those who do not consider Christianity as a political faction or as a simple name, and acknowledge that Christianity is an institution devoted to rectify morality, and therefore to destroy superstitious opinions and practices” (Parall`ele; GR 61).

Through this corrective confirmation, the universal church embraces all human beings, not only those who have been purified by the baptismal water.

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The New Essays gives very precise indications about the way of elaborating morality: Leibniz’s point of view does not adjust to meet a morality that is built more geometrico. On the contrary, moral principles are not based on reason’s ideas, similar to geometric axioms, but on intrinsic devices of the moral subject himself: It is absolutely impossible that there should be truths of reason which are as evident as identical or immediate truths. Although it is correct to say that morality has indemonstrable principles, of which one of the first and most practical is that we should pursue joy and avoid sorrow; it must be added that that is not a truth which is known solely from reason, since it is based on inner experience, or on confused knowledge; for one only senses what joy and sorrow are (NE 1.2.1; GP 5 81).

Leibniz gives the example of the maxim that commands to follow joy and to avoid sorrow. It is an indemonstrable principle, and its status is that of a habit or internal disposition. As to this, the author uses the word instinct to stress the primordial level to which it belongs: “However, the maxim which I have just advanced [to pursue joy and to avoid sorrow] seems to be of a different nature; it is not known by reason but by an instinct, so to speak” (ibid.). The use of reason and demonstration are based on practical axioms, which work at a pre-linguistic level. Leibnizian morality is inseparable from an interpretation of Christianity as a religion of interiority and feeling, in which the formal side of Christian praxis is secondary.14 The typical Leibnizian definition of morality derives precisely from the experience of Christianity as a religion of charity: “Morality is the science of affections” (C 556).

4 Determination of the Will. The Subjective Character of moral Judgement It is not surprising, therefore, that the first delineation of philosophical morality takes place precisely in De affectibus (1679), where the author tries to elucidate the genesis and constitution of the will, which is not self-generated: “No one is the voluntary cause of his own will” (Confessio Philosophi; A VI 3 137). The birth of the will occurs as a result of the confluence of intellection and affect. Resuming a path open in the Confessio Philosophi (1673–1674) and which will culminate in the thesis that we do not want to want, Leibniz asserts that the will is born from the “sentence” (sententia) or, in the terms of his letter to Morell (September 1698), “[. . .] the will is born when force is determined by enlightenment” (GR 138). The Leibnizian view of the will is that of a disposition to act according to the representation of some good. Will is conatus intelligentis (C 498) or, according to the first formulation of the author, conatus rei cogitantis (A VI 1 463). Determination, in the moral sense as a disposition of the will to act, originates in the ultimate judgement of our practical understanding: “Determination is the ultimate judgement of our practical understanding or the conclusion to the issue on which we deliberate” (C 198). The will does not, however, infallibly follow this judgement of our practical understanding, proceeding often through a tacit judgement that goes together with

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the perception of a state of things, as Leibniz expresses wonderfully in paragraph 51 of his Theodicy: When determining ourselves to want, we do not always follow the ultimate judgement of our practical understanding, but when we want we always follow the result of all inclinations that come from the side of reasons as much as from the side of emotions, and this often takes place without an express judgement of our understanding (Theodicy, 51; GP 6 130).

Will is a power we find only in rational beings, but it does not emerge from nothing: It responds to the natural appetite of living beings, which is analogical to will and anticipates it: “Sensitive appetite corresponds to will or intellectual appetite” (A VI 3 600). The will deepens and intensifies natural spontaneity and raises it to the level of freedom, defined as the spontaneity of the intelligent being. Freedom properly is not founded on the absolute indetermination of the will, but on primitive dispositions: “The root of freedom lies in primitive dispositions” (De dispositionibus internis; GR 327). Anticipating a Kantian formula, we might say that in Leibniz, will is practical reason. However, unlike Kant (for whom moral motivation of the agent consists in a special kind of feeling – the feeling of respect – that includes no elements of pathos, that is to say, no inclination), Leibniz conceives rational action as the result of a subjective judgement, which incorporates the appetitive level of the subject. Inclination is not an extrinsic element disturbing the exercise of free will. Instead, it constitutes its life, the internal motive that moves and leads will to act. In its most general sense, will is inclination: However, it is necessary to explain first the nature of will, which has its degrees; and in this general sense, one can say that the will consists in the inclination to do something according to the proportion of good it comprises (Theodicy, 22; GP 6 115).

Even in God, will proceeds by inclination; its motive to act is the achievement of the best. Inclination is the expression mediating fortuitous chance and fatalistic necessity. It implies a moral causality, which denies the thesis of freedom as stable equilibrium or complete indifference that would launch the boat of will in the most uncertain storm, by excluding any intrinsic motivation of our action. Proceeding by inclination means being determined through motives – “the will always operates through motives” (GP 6 413) – i.e., by a contingent mode of determination, since the field of inclination is always composite, for the will is submitted to the influence of an infinity of mutually opposite inclinations. There is not, therefore, only one inclination, for such inclination would be a necessitating one. No matter how strong an inclination might be, its efficacy is always contingent; it determines infallibly the will but, de jure, does not abolish other possibilities: When one proposes to oneself to make a choice, e. g., to go or not to go out, the question is whether, considering all internal and external circumstances, motives, perceptions, dispositions, impressions, emotions, inclinations, I am still in a state of contingency or I am constrained to make a given choice, e.g., to go out. The question is whether this proposition, which is eventually true and determined – considering all circumstances taken together I would choose to go out – is contingent or necessary. To this I answer that it is contingent, for neither I nor any other mind more enlightened than me could demonstrate that the opposite of this truth implies contradiction (To Coste, 19.12.1707; GP 3 401).

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Will is a rational power that determines itself according to the representation of some goods; it is not a naked faculty without disposition to act. In searching for the archaeology of will, we shall always find in its foundation the representation of some good or a core of inner dispositions through which minds become singular: “In fact, there are in the mind certain primitive dispositions, which do not derive from external things. And then one must say that, contrarily to what one usually supposes that nature is, minds distinguish themselves by their own nature” (De dispositionibus internis; GR 327). It follows that the notion of neutral freedom is incomplete, chimerical. Leibniz goes still further in his refusal of neutral freedom.15 It is an absurd fiction, and, what is more, it is harmful: “The motives of the good and of the evil are not opposite to freedom, and, far from converging to our happiness, the power to choose without reason is useless and even very harmful” (GP 6 432). Far from being an ideal, freedom, when considered as power, means a drastic imperfection, since it would imply an impassive agent unable to praise the real goods that would become worthless: [W]e have shown that, in order to be free, it is enough that our representations of good and evil, and other internal and external dispositions incline us without necessitating. We also do not see how pure indifference can contribute to happiness; on the contrary, the more one is indifferent, the more one will be impassive and unable to praise real true goods (GP 6 420).

Will is a power aimed at the good, that acts always by means of the prevailing inclination, since “the prevailing inclination always wins” (GP 6 132). The interesting question concerns the manner in which this inclination (or the most advantageous representation) is formed. Indeed, such a representation is not merely intellectual since many confused perceptions take place, which escape the subject’s control.16 Thus, the scope of free will surpasses the sphere of pure rationality. To be free is to determine oneself by reasons, emotions, and inclinations. The moral subject acts by the awareness he has of the situation; the mode of entanglement in the situation is an intrinsic part of the situation. Consciousness, namely moral consciousness, is all but transparent to itself; it is unable to perceive the complete game through which the mind determines itself internally.17 Here lies the labyrinthine character of freedom: Consciousness, through which the moral subject directs his action, is formed insensibly and unconsciously within the subject himself, incorporating an obscure zone connected with the body and the psychic automatisms, namely “habits”.18 Consciousness is not conscious of itself, of the way in which it is progressively formed. The ground where consciousness evolves is that of belief, which incorporates the experienced memory of the subject and not simply rational arguments: However, it can be seen from this that since all belief consists in the memory of one’s past grasp, of proofs and reasons, it is not within our power or our free will to believe or not to believe, since memory is not something which depends on our will (NE 4.1.8; GP 5 340).

Just as it happens with memory, so too consciousness does not depend on the subject: It is in our power to do what we want, but not to want what we want, because

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belief escapes the control of rational will: “Since then, one’s opinion is not in the power of the will, the will itself is not in the power of the will too” (A VI 3 132). In the expressive Leibnizian words, “consciousness is not in our power” (A VI 4 1394). Asymmetry between reason and consciousness is the focal point of Leibnizian morality. In fact, to say that choice is always determined by perception – “their choice is always determined by their perception” (NE 2.21.25; GP 5 168) – is not enough; it is still necessary to assert the composite and therefore subjective nature of perception. So, in contrast to intellectualistic procedures, the moral judgement, according to Leibniz, focuses on the fact that the human being, seen as a whole, acts through a complete will. Now the question is: What is a complete will? Excluding the possibility of pure balance (something like a zero degree of the will), Leibniz, in accordance with an usual procedure of his own, distinguishes several degrees in the scale of will, ranging from an antecedent will, without any sufficiently marked inclination, to a consequent or final will, infallibly inclined to this or that good.19 Leibniz assigns three qualifying adjectives to effective will when it is about to act: Full, total, and complete. Whatever the word, what is aimed at is always the same: To establish the continuity of power and act, to assert the causality of the will. The will is aimed at the act – in Leibnizian terms, it tends to determine itself (Theodicy, 48; GP 6 129) – the act is born from the power of the will through a process of inner determination. This means that volition is not an immediate operation, but the result of an elective process that implies the consideration of a plurality of goods, among which we have to choose through a procedure similar to the one that occurs in material nature. Leibniz explicitly points out this similarity.20 The Leibnizian explanation of the inner process of determination of the will evinces the continuity between nature and freedom. Both cases exhibit the same kind of intelligibility. Ultimately, determination is the general intelligibility of the actual world, not only from the viewpoint of its mechanism, but also from the viewpoint of its conception. Indeed, as it is said in the Summary of Metaphysics, among all series of compossible beings, there is one series alone which is determined – “Moreover, this series is the only one which is determined” (GP 7 290) – i.e., ruled by the principle of extremality: de maximis et minimis. This single series is that which gathers the maximum of variety within unity, the one whose order is so complete and rich that it is effective in all of its elements, without gaps or fragmentations. Now, this is the reason why this series is the only one that can exist spontaneously by itself. The contemplation of such a world is a source of pleasure, and divine election roots in this the consideration of being. Creation is not merely a logical exercise of a computational understanding, but an absolutely free act, i.e., an act resulting from an inner motivation, an infallible tendency to harmony: “There is moral necessity in the election of the whole series of contingent things, as the most convenient series” (To Des Bosses; GP 2 423). God acts and creates by inclination, when representing the best as apt to exist. The immediate motive of creation is the world’s beauty, the pleasure caused by its contemplation. The Fiat through which God acquiesces in the existence of the actual world responds to this finality. In more precise terms, the world is a source of pleasure for minds.

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5 Conclusion From an adequate viewpoint, it is not the will that must adjust itself to the world and to be ruled by it, it is rather the world that adjusts itself to the will and is ruled by it: Not the finite will of the creature, but an infinite will, which can only be satisfied by the acme of perfection. Natural reason itself, then, can guarantee “that things are made in a way that surpasses our wishes” (Principes de la Nature et de la Grace, 16; GP 6 605). God creates the world through an act of love: continuous creation and love towards creatures are one and the same thing, since to create is to make effective the object of the will. Leibniz’s God is an excellent mathematician whose understanding is exercised in the finest combinatorial games; but that is not his true face. He is the God of love, who, by the exercise of the will, makes effective all the perfection that the world of creatures can entail. In Leibnizian terms, perfection is not a state but an exercise of improvement. For Leibniz, the world order obeys a universal plan, in the same way as for Stoic philosophers. However, this order is not prescribed once and for all, so as to abolish the contingency of the phenomenal flux: It is inventively and permanently written and rewritten. Furthermore, individual cooperation and achievement is an intrinsic part of the achievement of the whole (GP 6 134). Leibnizian anthropology is defined by perfectibility, since especially in it does the demand for endless progress reveal itself “because minds are the most perfectible substances” (Discourse on Metaphysics, 36). According to Leibniz, perfectibility is attained through two inseparable paths, science and morality. Science contributes to unveil the beauty of things. Far from opening a gap between the subject and the object, the acme of knowledge, expressed in the knowledge of exuberant detail, is a source of astonishment and wonder (GP 7 545). Science transfigures the common view; it reveals the prodigious and marvellous side of things. The accurate exercise of science by itself bridges the gap between faith and reason, tied together by the affinity of a common way of thinking.

Notes 1. “Therefore, although we have a freedom of indifference, that saves us from necessity, we never have an indifference of balance, which relieves us from determinant reasons. There is always something that inclines us and leads us to choose, but it cannot force us. And, just as God is infallibly driven to the best, although he is not driven to the best necessarily (by a different way than through a moral necessity), we are always infallibly driven to that which touches us the most, but not necessarily. [. . .] And, although we are not always able to perceive all little impressions that contribute to determine us, there is always something that determines us between two contradictories, the case never being equal from one and another part” (To Coste, 19. 12. 1707; GP 3 402–403). 2. “Going back to the matter of your first letter, the chain of things is always contingent, and a state does not follow necessarily from another precedent state; either there is a beginning

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or not. The connexion between two states is a natural, not necessary, consecution, thus it is natural for a tree to carry some fruits, even though it can arrive, through certain reasons, that it does not carry them” (To Bourguet, February-March 1716; GP 3 588). See the letter to Coste of 19 December 1707, quoted above. The Confessio Philosophi (1673) starts this Leibnizian main way of thought through the distinction between arithmetic and geometry, as sciences about quantity (scientiae de quantitate), and physics and morality, as sciences about quality (scientiae de qualitate) (A VI III 118). This distinction will be pursued, e.g., in NE 4.17.23; GP 5 478. “But when one goes deeper into the search of reasons, one finds that the laws of motion could not be explained by purely geometrical principles or from mere imagination principles. It was also that which led very skilful philosophers to believe that the laws of motion are purely arbitrary. Here they are right if they take arbitrary as what comes from choice and what is not by geometrical necessity, but one must not extend this notion to believing that such laws are completely indifferent, for one can show that the laws of motion derive from the wisdom of their author or from the principle of the greatest perfection, which has made him choose them” (Tentamen Anagogicum; GP 7 271–272). “Now, this supreme wisdom, linked together with a no less infinite goodness, could not possibly go without choosing the best. For, just as a smaller evil is a kind of good, so a smaller good is a kind of evil if it obstructs a greater one; and there would be something that might be corrected in the actions of God, if one could find how to make it better. And just like in mathematics, when there is not any maximum or minimum, finally nothing well distinguished, everything happens equally. Or, if that is not possible, absolutely nothing happens. One can say the same with regard to perfect wisdom, which is not less ordered than mathematics, and that, if there were not the best (optimum) among all possible worlds, God would not have produced any” (Theodicy, 8; GP 6 107). Cf. Discourse on Metaphysics, 3; GP IV 428–429. “Let us use our emotions, let us teach to the Stoics that nature does not make anything useless; once nature has given us some fears and hopes, nature understands that we will employ them to acquire the virtues and to fight against the vices” (Senault 1641: 122–123). “For, first of all, virtue, however eminent it might be, does not destroy what is fully according to reason. But what is more reasonable than seeing a human being touched by piety and compassion towards the miseries of his fellow creature? Towards his friend? Towards his relative? [. . .] Being all these motions so fair, wouldn’t it be an excessive cruelty to want to banish them, in spite of nature? However who does not know that such emotions are exercises of the virtue?” (Co¨effeteau 1620: 40–41). “Once the definition of faith, that Saint Augustine gave us, teaches us that all knowledge we can have through the light of natural reason has nothing in common with it” (Arnauld 1641: 85). “It is about something of which one will be convinced, if one pays attention that faith must be founded on the authority. Now, the knowledge that pagans had about the Providence of God was not founded but on reason, as it is necessary to agree. Thus, such knowledge might be nothing but a mere science, not a true faith, for it lacked three essential conditions to the true faith. 1) First, because it derives from the light of reason, not from divine revelation; 2) for it was clear, not obscure; 3) for it was natural and human in its substance, resulting from the mere human mind, and not from any supernatural divine principle. And it is certain that the two first conditions without the third are not enough to establish a true faith” (Arnauld 1641: 87). “For one sees that the most constant maxim of their morality is nothing but lections of pride, in order to teach the human beings to rely only on themselves and to venerate only their reason; in order to establish their happiness only on the enjoyment of their own goods; to acknowledge only themselves as the authors of their virtue and happiness” (Arnauld 1641: 114–115). “However little we reflect on the conduct of all wise pagans, we will not see there anything (in all who most testified their love to virtue and their hatred to the vice), except that they all idolize their wisdom, virtue and reason; that they regarded themselves with a perfect

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A.D. Cardoso inner satisfaction; that they praised themselves and totally pleased with themselves, with their alleged advantageous qualities, either these qualities pleased or not pleased the others. And that they lived in this secret glory and praised themselves silently, in the vanity of their thoughts, without testimony and words; and after having disdained the most excellent thing there are on Earth, they opened their mouth to speak against Heaven and measured themselves with Divinity. For one sees that these blasphemies were continuously the conversation of the most virtuous pagan philosophers” (Arnauld 1641: 125–126). “There are other defects that are more natural and inner to the human being, for they rise from and in himself. The greatest defect and root of all others is pride and presumptuousness (the first and original failure of the world, a plague of the spirit and the cause of all evils) through which one is content with oneself, one can not give up to someone else, one disdains its enchantments, one keeps one’s own views and intends to judge and condemn the other opinions and those which one does not understand [. . .] Now, this illness derives from unknowing oneself, for we never truly feel the weakness of our mind. Thus, the greatest illness of the spirit is ignorance, not that of arts and sciences and of what is on the books, but that of oneself, which is the motive of this first book” (Charron 1986: 144). “It has always been evident that ordinary people put devotion in the formalities: solid piety, i.e., the light of virtue, has never been the share of the great number. One must not be astonished by it, because nothing is so in line with human weakness; we are touched by the exterior and the interior requires discussion, which few people are able to do. For true piety consists in feelings and in practices, the formalities of devotion imitate it” (Theodicy, Preface; GP 6 25). “The followers of Molina became very confused by this false idea of indifference of balance. One asked them not only how it was possible to know to what an absolutely undetermined cause would determine itself, but also how it was possible that from there could result a determination without any source. For to say with Molina that it [the indifference of balance] is a privilege of the free cause is to say nothing, it is to give to such cause the privilege of being chimerical. It is pleasant to see that they torment themselves in order to exit from a labyrinth, where there is no way out” (Theodicy, 48; GP 6 129). “For my part, I do not oblige the will to always follow the judgement of the understanding, since I distinguish this judgement from imperceptible perceptions and inclinations. I argue, however, that the will always follows the most advantageous representation, distinct or confused, of good or evil, which results from reasons, emotions and inclinations, although the will can also find motives to suspend its judgement” (GP 6 413). “And if we do not always notice the reason which determines us, or rather by which we determine ourselves, it is because we are as little able to be aware of all the workings of our mind and of its usually confused and imperceptible thoughts as we are to sort out all the mechanisms which nature puts to work in the bodies” (NE 2.21.13; GP 5 164). “However, although our choice ex datis in all inner circumstances taken together is always determined and, regarding the present, it does not depend from us to change our will, it is true that we have a great power over our future volitions, choosing certain objects of our attention and getting accustomed to certain ways of thinking” (To Coste, 19.12.1707; GP 3 403). “The will in general is called antecedent, when it is distinguished and views every good separately as a good. [. . .] One can say that such will is effective by itself ( per se), i.e., in such a way that the effect would follow, if there was no stronger reason that hinders it. For, this will does not go to the last effort (ad summum conatum), otherwise it would never fail to make its effect, God being the Lord of the things. The entire and infallible success pertains only to the consequent will, as I call it. It is the full will, and concerning it this rule is in vigour that one would never fail to do what one wants, when one can do it” (Theodicy, 22; GP 6 115–116). “Now, this consequent, final and decisive will, results from the conflict between all antecedent wills, both those which tend to the good and those which reject the evil: and total will results precisely from the concurrence of these particular volitions: as in mechanics the compound motion results from all the tendencies which concur to the same movable and satisfies equally each tendency as much as it is possible to do it at the same time” (Theodicy, 22; GP 6 116).

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References Arnauld, A. 1641. De la n´ecessit´e de la foi en Jesus Christ pour eˆ tre sauv´e. Œuvres Compl`etes de messire Antoine Arnauld. Paris-Lausanne, 1775–1783, vol. X. Cardoso, A.D. 2000. Uma nova heresia a` medida de um novo mundo: a ofensiva de Arnauld contra a doutrina do pecado filos´ofico. Philosophica 15: 117–133. Charron, P. 1986. De la sagesse. Paris: Fayard. Co¨effeteau. 1620. Tableau des passions humaines, de leurs causes et de leurs effects. Lyon: Chez Claude Prost. Descartes, R. 1644. Principes de la philosophie. AT IX-2. Senault, F. 1641. De l’usage des passions. Paris: Compagnie des Marchands Libraires du Palais.

Chapter 21

Leibniz and Moral Rationality Martine de Gaudemar

1 Introduction In order to ask the question of moral rationality in Leibniz, I have taken into account two related senses: The one concerning the natural foundations of a moral rationality, and the other, a possible future improvement for rational beings, especially human beings. The two senses are connected in Leibniz if the natural abilities of rational beings are themselves perfectible. My purpose is to argue that rationality, in so far as it purports to produce instruments of thought and to improve the activity of thinking, can contribute to moral improvement. The symbolic mediations, especially the ones involving calculation and the use of signs, as well as narrative procedures and other kinds of language use, cannot – in Leibniz’s case – be opposed, as in Nussbaum’s (1990) reading of Aristotle, to a moral rationality that would be different in nature, i.e., qualitative rather than quantitative. There is no reason in Leibniz to oppose a moral rationality coming from an Aristotelian influence to a calculating or utilitarian rationality, for the notional distinction between them is not a conflictive opposition. Leibniz links the qualitative and the quantitative, i.e., a consequentialist and a perfectionist approach. Leibniz’s rationalism improves the moral approaches offered in the history of philosophy – be they Aristotelian, Stoic, Christian, or even Spinozistic – by putting them at the service of a moral end of rationality itself. The first part of this chapter presents the Leibnizian elements of the naturalistic or realist thesis: There is a moral rationality that is natural, or even instinctive. The second part claims that natural rationality can, and consequently must be perfected; that is to say, it must be led to an upper degree of perfection, and then improved (“the perfectionist thesis”). Through this latter approach, the calculating of cases, the use of schemas, procedures of evaluation, symbols, internal strategies for selfmotivation, and so on, appear as different tools in order to perfect natural morality for the benefit of the City of God.

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2 There is a Natural Moral Rationality This thesis is expressed in terms of three modalities.

2.1 There is An Intelligibility of Human Behavior Insofar as the will results from the feeling of the goodness of an object or an action, it is naturally directed according to the inclination, every voluptas or delectatio being the perception of a perfection: “The will is an effort that we make in order to do something, because one thinks it is good”.1 Leibniz adopts the Aristotelian thesis according to which every human being naturally turns towards a good (Nichomachean Ethics I, 1095a–1097b), but he improves it in accuracy with a concept of the will that integrates the past of the agent and the context of the object at the same time, the prevalent inclination resulting from that integration through unconscious calculation: Besides our past inclinations and dispositions, there are new structures of objects which contribute to form our inclination, and all these inclinations put together, and working against contrary inclinations, never fail to form a total prevalent inclination.2

The spontaneous integration of the data of the situation that are internal and external, temporal and spatial, assures an appropriateness of the will to the context, which the reflexive thought will be able to moralize or to improve. It is an unconscious calculation, which has to be improved by reflection.

2.2 Moral Laws are Coordinated with the Laws of the Universe This is the thesis of the two reigns, the one of the efficient causes and the other of the final causes. The explanation of the material phenomena must be restricted to the efficient causes, to the laws of the movements of the body, but the rational subjects follow the laws of the mind, where “all is made by effort or desire, according to the laws of the good”,3 so that the explanation of the behaviors has to appeal to the teleological schema of the “moral cause”. As Leibniz writes in the Monadology: 78. The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances, since they are all representations of one and the same universe. 79. Souls act according to the laws of final causes through appetitions, ends, and means. Bodies act according to the laws of efficient causes or motions. And the two realms, that of efficient causes and that of final causes, are in harmony with one another.4

Therefore, human behaviors governed by the laws of action do not take rational beings away from the general intelligibility of the universe, but place them in a special register of rationality, which we will describe as more complex, rather than a different kind of rationality. Indeed, that level of rationality combines in an identical situation the objects of the universe or beings without either memory or future, which are subordinated to the laws of movement, and the subjects, persons or spirits

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that follow also moral laws, which encompass the past and the future of the universe in the form of an infinity of insensible perceptions. It is a more global level of rationality: the strictly logical conception is, in my opinion, a particular level within it, which has to be developed. At the same time, the position of the laws of determination of the will according to the nature of the objects of the universe founds a natural convergence of the feelings of appreciation, and therefore generates what we can call a natural normativity, which goes against any relativistic subjectivism. We can think that the regularities of those feelings are what naturally lead us to think that there are moral laws of behavior, followed the more often by the human societies (even by bandit societies). That is what Leibniz puts forward against Locke’s subjectivism in the Nouveaux essais. Rules are considered through different social practices and contexts, but must be ordered according to a non-arbitrary criterion.

2.3 The Natural Abilities of Men Prompt them to Rationality and to the Moralization of Rationality A stronger formulation of the naturalistic thesis that leads to the perfectionist thesis. Leibniz asserts it in the third paragraph of the Preface to the Nouveaux essais (A VI 6 48f.). Referring to Plato, the School, Saint-Paul, and the Stoics, he says that the eternal laws of reason remain etched/imprinted in the minds or spirits, and that, combined with a logic which is also natural to us, they found a natural jurisprudence, that is improved when we can insert the exceptions into the rule, without having to escape it in order to get used to the various situations: “Exceptions are rules which limit the extension of other rules”.5 As a start, men meet each other, agree about the rules that come from natural normativity, and find some ways, some formulas that, in the manner of schemata, are capable to coordinate them in that situation. Therefore, Leibniz produces a very flexible method appropriate to the diversity of concrete situations while keeping, through conceptual analysis, a firm leading thread. In Chapter 2 of NE’s book I, Leibniz specifies that the principles of morality are less well-known by reason than by instinct, so to speak: There are thus in us instinctive truths that are innate principles which we feel and approve even though we have no proof of them; nevertheless, we obtain this proof when we can account for such an instinct.6

That implies that the rules of behavior to which we naturally refer to are not inert; they are active like abilities, virtualities or tendencies. We understand that they drive us to this action rather than to another, and even drive us to clarify their mode of activity, since we are led to look for their reasons and to prove them. This implies a natural tendency to rationality, whose mark is the pleasure we feel in understanding the reasons for our behavior. In Leibnizian perfectionism, to prove the rules is to improve them.

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There is, therefore, no acceptable opposition between reason and an agency rooted in affections. We are always guided by reason, either without knowing it – reason acts like a natural method, that is to say, in the manner of an instinct – or methodically – when we intentionally use our rational resources. Judgments are rooted on feelings and emotions. Reason, as an organ, has several registers. There are two types of truths: there are truths of feeling and truths of intelligence. Truths of feeling are for those who feel them, and for those whose senses are configured as ours. For example, when we find ‘bittersweet’ to be a pleasant taste. And it is for this reason that one is justified in saying that tastes should not be disputed. But I believe that truths of intelligence are universal, and that that which is true in them regarding ourselves is also true regarding angels and even God. These eternal truths are the fixed and immutable point upon which everything turns.7

When we use reason without being aware of it, we are limited to the truths of feeling. But when we realize that the moral appreciations are convergent, that they are different expressions of the same functions and produce agreements between minds, we are led to justify that harmony and to discover the truths of intelligence that it shows. Leibniz mentions the agreement of the spirits as showing or demonstrating a kind of “instinct of conscience” (NE 1.2.9; A VI 6 93), with the double meaning, cognitive and moral, that he gives to the notion of conscience, and that will remain linked to it until nowadays (see de Gaudemar 2004; A VI 4 1586).8 The instincts of conscience naturally and without any reasoning lead to something that reason orders; they produce a natural disgust for the contradictions in behavior or in discourse. Therefore, they are equivalent to a rough form of morality that rationality can improve by producing formulations that are accessible to analysis and discussion, and even sometimes, in a few areas, to demonstration. Moralization cannot therefore be separated from rationalization, since it is associated with its progress. So far, we could think that the Leibnizian theorization, in harmony with an Aristotelian influence from which it borrows naturalism and teleology, does not go further than the Nicomachean Ethics. Yet, those concepts already carry the germ of a surpassing; they are likely to exceed the opposition between an instrumental and a calculating rationality on the one hand, and an axiological rationality (the two types of rationality Nussbaum views as opposed) on the other. Indeed, Leibniz emphasizes an indissolubly moral and rational spontaneity, but he stresses the necessity felt by the rational human being who wants to highlight spontaneity and to disentangle it from the customs it could be mistaken for, which produces some darkness: “it is difficult to disentangle instincts and various other natural habits from customs”.9 The work of reason, methodical or spontaneous, is at the service of moral rationality because there is fundamentally only one Reason (and not a theoretical reason as opposed to a practical reason), made of abilities that are likely to be directed towards a good and, thus, to be improved. I shall argue that Leibniz avoids both a dogmatic normativism (Plato, Kant) and a relativistic utilitarianism. The Leibnizian conception (“perspectivism”) is not a relativistic point of view, but it allows a pluralistic expression of universality, which is well-ordered by the scheme of “the place of the other”.

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The dispositional view of the mind, then, develops into a perfectionist concept, according to a continuous line drawn from the cognitive to the moral. I shall examine that continuity through the maxim of “the place of the other”, a maxim that formulates a natural tendency of minds. In the Nouveaux essais, Leibniz formulates it (NE 1.2.4) as a truth of instinct, similar to what we do in walking or jumping without thinking about it – that is to say, according to movements that are naturally efficient. Immanent to behavior, this formulation of the rule is declared to be insufficient: Concerning the rule that stipulates that we should do unto the others only that which we would like them to do unto us, it does not only need proof but also declaration.10

That is to say, the formulation of the rule, and in some cases the demonstration of the rule, is the first step of a rational morality that would not be a mere blind spontaneity at the manner of instinct. Why does the formulation make the rule better? Because, as a natural rule, it cannot be used as a norm, i.e., as a reference or an instrument of measure: “that rule, far from being used as a measure, would need it” (NE 1.2.4; A VI 6 92). In that paragraph, Leibniz only confers a moral meaning to a rule that is still morally indeterminate, that is moral only virtually, and so, that depends on use in context in order to become a moral rule: “The true meaning of the rule is that the place of the other is the true point of view for judging more equitably once we position ourselves in it”.11 This formulation is not only equivalent to the first one; it is superior to it as it introduces a hierarchy that was missing in the pure principle of formal reciprocity which the first formulation stipulated. That hierarchy appears at the same time as the values of truth and equity, whose meaning is universal. Therefore, values are what is universally considered as good, or better for everyone, whatever the circumstances. The declaration and the formulation of the rule therefore allow for the emergence, in the context of the rule, of particular habits or arbitrary regularities, while showing its capacity to fit different situations, a capacity that shows its universality, which is at least a virtual one. Thus, the work of reason becomes a demonstrative work. I think that case may be generalized: A lot of rules and schemata are morally indeterminate, and are fit for bandit societies as well as for the City of God. According to the use of them, behaviours are more or less good. They need, in order to be appreciated, a criterion, a scheme or a middle term.

3 A Rationality Perfected by Morality I want now to show that there is in Leibniz a moral perfectionism that lifts rationality to higher perfection, by leading it to its end or destination (the City of God) and making explicit its meaning, i.e., the meaning of Leibnizian perfectionism. The process of moralization that makes rationality become moral comprises three points.

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3.1 The Moralization of the Reciprocity Schema I start from the Leibnizian use of calculation in order to make clear what is at stake. The possible and desirable moralization of the reciprocity schema that constitutes the rule of taking the place of the other is a good example of such a process. It is a schema that Leibniz at the same time states, describes, and extends to the status of “better”, and even of “the best”. The “golden rule”, as the injunction to take the place of the other is widely known, is a fundamental principle of ethics. I claim, however, that it is not an actual moral principle in Leibniz, but a consistency principle which has to be “moralized”. The use of the golden rule is a simple test, similar to the universalization of maxims in Kant. So the rule shows its procedural nature, analogous to an evaluation tool. The golden rule is a tool for reflection. The golden rule refers to both a mental ability and an everyday use which is transformed into a test of consistency for a decision that takes place in a relational context, a test designed to prevent undesirable consequences of the decision for us. Leibniz orders many heterogeneous practices, individual, social or political, on a scale, thus engendering a symbolic form – a tool capable to improve the work of thinking when deliberately used. We can situate ourselves on this scale, acknowledging our point of view, which varies according to what we are dealing with or who we put in the place of the other. Such a variation is possible because the place of the other is empty: It is a formal reciprocal structure. Moral decision consists in choosing what is likely to fill the place: oneself, another person, or a community. As a tool for reflection, positioning oneself in the place of the other helps to elucidate one’s own “thinking place”. The maxim, thus, does not replace moral decisions, but leads to them as reasonable conclusions of reflection. Acting in accordance with the conclusion drawn by using this tool is an issue of motivation, i.e., of “appetitions”, desires and love of the good. There is no strict necessity to follow the conclusion. The moral act may be in accordance with the conclusion, it may express the conclusion, but it is not the very conclusion. For example, there is no right to lie, but there are several possible derogations of the prohibition of lying, depending on circumstances and partners (cf. “Saying a falsity is not condemnable”, DA: Chapter 16G). It is necessary to have an explicit criterion or a rule of interpretation. The improvement of morality depends on our motivation for using tools of thinking that are likely to clarify the situation and help the choice.

3.2 Calculus: its Virtues and its Limits Analogously, the use of calculation for deciding one’s behavior needs to be moralized, since calculus is, as such, morally indeterminate. Calculation is a tool for the rationality of choice, and it improves its value or perfection. But only within certain limits, for, insofar as it concerns only understanding, the calculation points to an incalculable point of decision, which is the point of choie, of making up one’s mind, i.e., the very mental act the reasons prepare and organize, inclining towards it, but not constituting it.

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This is not only a matter of free will or determination. Even a similar decision in the result of the calculation and in the effective act of decision shows a difference between the level of thinking of the value and the consequences of an action and the level of the energetic resources of desiring to achieve a better state of affairs. The intelligibility model of choice is, obviously, God’s choice of the best of possible worlds, which implies love as a sine qua non (a requisitum). Such a love may be clarified, directed, but not constituted, if it is rooted in natural appetitions towards goods. Human symbolic means of calculation can be applied to infinitesimal perceptions and appetitions. But this only pushes back the limits of calculation, without actually suppressing them. Only God, who has a perfect view of the law of any series and of the entire world, overcomes these limits through his “intuitive knowledge”, not through symbolic, “blind” calculation, which he, unlike us humans, does not need. Calculation has to be put at the service of the better, but the good nature of the tendencies combined with the resources of calculation promotes a moral orientation without assuring it. What is natural is not necessary, because it may meet some contingent obstacles or difficulties. Perfectionism itself is an option which implies a complex organization of appetitions. In order to lead to a perfectionist thesis, we can formulate an argumentation, and maybe a reasoning conclusion, but the conclusion cannot be cut off from the premises: What remains is always a conditional sentence (as the paradox of Achilles and the tortoise has made clear). Three conclusions can be drawn from this second point. 3.2.1. In Leibniz, the resources of calculation are likely to improve the decision by highlighting consequences of action, and giving criteria for a hierarchy of behaviors. They constitute the power of calculation. For example, there is no absolute right to personal private ownership: Ownership is only something that has to be preferred to the lack of ownership in most cases. Knowing whether a particular case justifies an exception to this rule depends on the circumstances, including who claims to be the owner (as in the famous case of Cyrus). Formal and calculating procedures are tools to clarify the choice between different solutions, to estimate probabilities and minimize risks. These tools are complements and improvements to an art of judging which remains, as such, an art, because there are similarities and never identities between different concrete situations, which envelop individuals and infinity. Judgment may be exercised and strengthened, but not replaced by calculation. Nevertheless, I think the Leibnizian contribution to the issue at stake lies first in striving to give a larger role to formal and calculating procedures within a process which necessarily remains an art. This is the reason why many other new procedures are to be invented, which will fit the variety of situations in everyday life. For example, the use of narrative texts in order to compare different historical situations is a productive tool, and Leibniz uses it without clearly conceptualizing it. 3.2.2. A second feature of the Leibnizian contribution consists in pushing back the limits of calculation.

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Even in the ideal case of God, that is, a perfect intelligence who can completely elucidate and clarify the motivations and consequences of every decision according to different aims, there is some point of incalculability, namely, between the different proposals that are considered and the best solution adopted. It is that point that makes the proposition that God chooses our universe as the best of possible worlds contingent. God’s choice is infallible but not necessary, because the possible decree that God considers in calculating is not the same decree by which he determines himself to actualize the possible decree of creation. So no demonstration of their identity is possible, and a demonstration would leave a remainder, as in all other contingent propositions. A calculus of possibilities prepares God’s decisions by giving its conditions, but does not produce that inference which goes from possibility to existence and that Leibniz names illatio inexplicabilis (De illatione; A VI 4 861 ff.), insofar as the development of such an inference would be infinite. The point of incalculability is related to something incommensurable between the calculus of goods and God’s will of the best. What has to be preferred cannot be determined by a deduction, but is chosen by a “conatus” named desire or love, which says “Yes” to the conclusion and approves it. Why something exists rather than nothing depends on the reasons for God to choose existence. Incalculability is not generated by a lack in rationality. An imaginary change of places between us and God when explaining human behavior will show it. God knows that Caesar intends to cross the Rubicon, but no demonstration corresponds to such knowledge, for there is no general method to infer the behaviors of free minds capable of saying “Yes” or “No” to a decision proposed by the intellect. Not all the persons called “Caesar” will make the same choice under analogous circumstances. Another Caesar could have inhibitions or scruples that might be greater than those of the historical Caesar, yielding a “No” rather than his historical counterpart’s “Yes”. Yet, moral rationality can benefit from calculative rationality, precisely by calling attention to the danger of a hasty use of the latter in the former. 3.2.3. From the above, I draw some consequences for finite minds. We, finite minds, have to use different and suitable tools to clarify our choices, and weigh their value as exactly as the matter allows it. These tools are the substitutes for the infallible vision we lack. Furthermore, we have to motivate ourselves (which is not needed in God’s case) to get and to adopt the best decision. The internal strategies and tools we use are analogous regardless of whether they serve a purely pragmatic or a moral aim: There is no essential discontinuity between these aims, but a progression from self-serving actions to moral ones. Leibniz leans on natural or regular habits and actions in order to improve their direction towards a better aim. It is morally certain (i.e., highly probable) that God wants the best and acts in accordance with it, Leibniz claims. But for us, it requires much work to want and love the good. In the cases where love of God and of the good are lacking, calculation may only improve the efficiency of action.

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3.3 Conversation between Minds Hence the need for theology. Faith, or at least strong beliefs, are required to complete the calculation and evaluation of our aims. We need beliefs in the good nature of God, and in the certainty (if the proposition which expresses it is not demonstrable) of his choice of the best of all possible worlds. These beliefs are decisive for a moral improvement that requires the love of God. They give us an affective help, a motivation for the actualization of the virtual City of God, a reason to approve the very existence of this universe. Rationality appears as a step towards morality. As the optimum is relative to a will and to an aim, we need to be confident of the will and the aim of God, which belong to the realm of eternal truths. The confidence in God’s promises, that is, in the power of God’s speech acts, is required for hope and the approval of existence. Is existing better than not existing? Is the suffering enveloped in individual existence better than being a non-suffering and non-existing being, like a stone? Preferability is grounded on God himself. Therefore, morality requires confidence in a person, whose name is usually “God”. It gives a meaning to the name “God” as “an existencifying entity, a cause for existence to prevail over non-existence”.12 Such a confidence is an individual belief in what a person promises.

4 Language and Rationality My third starting point is the status of language, because where calculation shows its own limits there remain the resources of speech and “conversation”. I assume now three theses, namely, (1) logical structures of minds are, in Leibniz, the same as linguistic innate forms; (2) universality is a linguistic ability – we virtually share a universal conversation; (3) natural light (or reason) is expressed in language as well as in calculation. So there is, in language, a natural transition and a natural bridge from inclinations, impulsions and insensible perceptions to a formal and conscious calculation, because many levels or linguistic areas are likely to be formalized. On the one hand, language is imprinted in a natural inclination to “conversation” or a tendency to mutual agreement, when we share our thoughts with other minds. Furthermore, the different languages are, for a great part, analyzable and formalizable tools. There is continuity in the linguistic phenomenon, from the dynamical view of infinite appetitions where language is rooted, through a strictly deductive view in a formal semiotic system, up to the pragmatic theory of language use. Contemporary research in cognitive science or philosophy of mind may be related to the Leibnizian views of language. Between the unconscious calculation of insensible perceptions and an effective formalization of linguistic levels are the bridges of pragmatics, which deal with speech acts, and of narrative theories dealing with stories and myths which give some sense to existence. These bridges provide the continuity of rational abilities,

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which may be placed together and work for moral improvement. There is no reason to opt for the one or the other exclusively, but there are on the contrary good reasons to make them concur in morality. I shall take a single example to emphasize the moral use of language through its natural rationality: The structural role of predicative sentences in the feeling of responsibility. Any feeling envelops a truth, and a truth is virtually a true proposition. The feeling of responsibility virtually implies a predicative structure of propositions by which we can attribute a predicate to a subject. The predicative structure of propositions makes language a tool and a condition for moral imputation, whose corresponding feeling is a confused perception. There is a correspondence between a confused feeling of responsibility, the predicative structure of propositions, and the declaration of responsibility or imputation, through which the grammatical and logical subject becomes a moral one. Morality is thus a complex form of rationality, active at different levels of thinking. Rationality consists in using all of our resources and abilities in order to be citizens of the universe and participate in a universal conversation, a conversation that amounts to rational interaction, that shows its effectiveness through agreements that are real because we actually live together thanks to them. To be sure, a perfectionist thesis, grounded on our natural abilities, is a thesis that relies upon its metaphysical and conditional premises. It cannot be categorically asserted, no more than moral norms. But their being highly desirable grants the whole Leibnizian way of doing philosophy a genuine style and a conditional character.

5 Conclusion In conclusion, I claim that the Leibnizian conception of morality cannot be used in a battle for or against a calculating model of rationality, such as the one conducted by Martha Nussbaum. The reason is that calculative rationality is, in Leibniz, a natural tool for morality, which is in fact a more complex form of rationality. Utilitarian uses of a calculating form of rationality show only that its intrinsic morality is not yet actualized, remains virtual and is still hidden in rough versions of form. Leibnizian perfectionism calls for making rationality more complex, soft and flexible in order to contribute to the advent of the City of God. Calculation has to draw its models in the infinitesimal calculus and living machines, rather than in geometry or artificial simple machines, because the infinite is the very mark of the fundamental order of things. A teleological approach and a perfectionist method are fit to it. Leibniz is not a mere Aristotelian philosopher: He leads Aristotelianism and its “practical syllogism” to a better degree of perfection by demonstrating that there is no contradiction between instrumental rationality, formal rationality, maxims of prudence, and loving the good. His continuist and infinitist approach directs different forms of rationality towards the aim of a better state of affairs. His constant stress

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on the necessity of logical or formal procedures, which test the value of actions, prevents his views on moral rationality from any too weak interpretation. There is only one reason, according to different registers and levels, and a soft level of rationality is never a weak one, but a complex one which envelops all the other levels as particular cases. Leibniz conciliates the promise of an actualization of the City of God with rules and procedures, such as the use of “the place of the other”, through which individuals become ever freer from their narrow context, in order to be citizens of the universe, and share a universal conversation. This is the Leibnizian claim for universality.

Notes 1. “La volont´e est un effort qu’on fait pour agir, parce qu’on l’a trouv´e bon” (A VI 4 1405; Du franc-arbitre, 1678–1682). 2. “Outre nos inclinations ou dispositions ant´erieures, encore les dispositions nouvelles des objets contribuent a` nous incliner, et toutes ces inclinations jointes ensemble, et balanc´ees contre les inclinations contraires ne manquent jamais de former une inclination totale pr´evalente” (GR 480; Conversation sur la libert´e et le destin). 3. “[. . .] tout se fait par l’effort ou le d´esir, selon les lois du bien” (R´efutation in´edite de Spinoza, ed. M. de Gaudemar, 1999, Actes du Sud, pp. 34–35). 4. “78. L’ˆame suit ses propres lois, et le corps aussi les siennes, et ils se rencontrent en vertu de l’harmonie pr´ee´ tablie entre toutes les substances, puisqu’elles sont toutes des representations d’un mˆeme univers. 79. Les aˆ mes agissent selon les lois des causes finales par app´etitions, fins et moyens. Les corps agissent selon les lois des causes efficientes ou des mouvements. Et les deux r`egnes, celui des causes efficientes et celui des causes finales, sont harmoniques entre eux” (GP 6 620). 5. “Les exceptions sont des r`egles, qui bornent l’´etendue des autres”. 6. “Il y a donc en nous des v´erit´es d’instinct qui sont des principes inn´es, qu’on sent et qu’on approuve, quand mˆeme on n’en a pas la preuve, qu’on obtient pourtant lorsqu’on rend raison de cet instinct” (NE 1.2.4; A VI 6 91). 7. “Car les v´erit´es sont de deux sortes : il y a des v´erit´es de sentiment et des v´erit´es d’intelligence. Les v´erit´es de sentiment sont pour celui qui les sent et pour ceux dont les organes sont dispos´es comme les siens, par exemple lorsque nous trouvons que l’aigre doux est agr´eable. Et c’est pour cela qu’on a raison de dire qu’il ne faut point disputer des goˆuts. Mais je crois que les v´erit´es d’intelligence sont universelles, et que ce qui est vrai l`a-dessus l’est aussi pour les anges et pour Dieu mˆeme. Ces v´erit´es e´ ternelles sont le point fixe et immuable, sur lequel tout roule” (Letter to Sophie, 1696; GR 379). 8. “[. . .] voluerat quia bonum putarat” (Confessio Philosophi; A VI 3 115–149; Belaval (ed), Paris, Vrin, 1961, p. 67). 9. “Il est difficile de d´emˆeler les instincts et quelques autres habitudes naturelles d’avec les coutumes” (NE 1.2.20; A VI 6 98). 10. “Quant a` la r`egle qui porte qu’on ne doit faire aux autres que ce qu’on voudrait qu’ils nous fissent, elle a besoin non seulement de preuve, mais encore de declaration” (NE 1.2.4; A VI 6 91). 11. “Le veritable sens de la r`egle est que la place d’autrui est le vrai point de vue pour juger plus e´ quitablement lorsqu’on s’y met” (NE 1.2.4; A VI 6 92). 12. “Ens existentificans, causa cur Existentia praevaleat non-existentia” (C 534).

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References de Gaudemar, M. 2004. La notion de conscience. In G. Pigeard de Gurbert (ed.), L’exp´erience et la conscience. Paris: Actes du Sud, pp. 187–241. Nussbaum, M. 1990. The discernment of perception: An Aristotelian conception of private and public rationality. In M. Nussbaum, Love’s Knowledge. Oxford: Oxford University Press, pp. 54–105.

Part VI

Decision Making

Chapter 22

Leibniz’s Models of Rational Decision Markku Roinila

In his article “The balance of reason” Marcelo Dascal has shown that the metaphor of weighing reasons on the scales of the balance of reason is prominent in Leibniz’s writings (Dascal 2005). In this paper, I shall discuss this metaphor and argue that in his practical rationality Leibniz also applied another relatively unknown heuristic model of decision-making, which is related to his work in the philosophy of nature and the philosophy of mind, and which is applied in situations where the values in question compete with each other. These models are based on estimation rather than calculation. I shall concentrate on these two models, which are common in human practical rationality, and leave out the third and most demanding model, the famous calculemus, where the reasons are analysed thoroughly and the analysis itself acts as a kind of method of decision making. With this method, the opponents can in cases of controversy simply calculate the right answer or the highest probability of success of some proposed course of action.1 It is clear, however, that in all human affairs a complete analysis of all relevant reasons is not possible or is extremely difficult and time consuming. This is why Leibniz developed other, less demanding models of rational decision-making.

1 Deliberation in the Soul In order to describe the differences between the two models, I shall first briefly sketch the deliberation in the soul, as presented by Leibniz in his Nouveaux Essais and Essais de Th´eodic´ee. In deliberation, there are different inclinations towards the good present in the soul whose conflict forms the complete volition. Usually there are both conscious volitions, based on clear and distinct perceptions and unconscious appetitions, based on confused knowledge. These inclinations, be they conscious or not, may be united if they lead in the same direction. If they are of equal strength, but lead in opposite directions, they are mutually exclusive. If they lead in different directions, the strongest are victorious. The deliberator can affect

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the directions of these inclinations only indirectly by developing his or her understanding and adopting good habits – in this way the moral agent can, as it were, manipulate his or her future deliberations.2 The behaviour of these impulses is comparable to the beginnings of motion, or conatuses, as Leibniz describes them in his early work Theoria motus abstracti. There Leibniz states that every body in collision transfers to the other a conatus equal to its own without thereby losing any of its original conatus (§10; GP 4 229). The multiple conatuses last only for a moment before they are resolved into one resultant conatus (§17; GP 4 230). If the conatuses are unequal, the resultant conatus will retain the direction of the greatest conatus, and have for its magnitude the difference between the original conatuses (§18–20; GP 4 230–231).3 Since the final result of the balance is determined by how things weigh against one another, I should think it could happen that the most pressing disquiet did not prevail; for even if it prevailed over each of the contrary endeavours taken singly, it may be outweighed by all of them taken together [. . .] everything which then impinges on us weighs in the balance and contributes to determining a resultant direction, almost as in mechanics (NE 2.21.40; A VI 6 193).

The idea is presented in different terms in Essais de Th´eodic´ee, §22, where Leibniz makes a distinction between antecedent and consequent wills in the divine decision concerning the moral goodness of the best of all possible worlds. The consequent will is what Leibniz understands as the will which executes the action and thus as the last stage of deliberation. The antecedent will is a particular will, which is directed to a single good, whereas the consequent will takes into account all the antecedent goods. Consequent will, final and decisive, results from the conflict of all the antecedent wills, of those which tend towards good as well as of those which repel evil; and from the concurrence of all these particular wills comes the total will (GP 6 116).

Although Leibniz himself does not employ this distinction in human practical rationality (as far as I know), I think it can be done with some qualifications. In human deliberation the will concerns the apparent good and the antecedent goods are to be understood as conscious volitions which concern some apparent good. While the divine judgement concerns only volitions, in human deliberation there are also appetitions, which consist of confused knowledge. Often these appetitions consist of a mass of minute perceptions, which when combined have a sensual vivacity and can be understood as passions of the mind. These passions often capture our attention and, in this way, they affect deliberation. Minute perceptions can also affect deliberations even though they are not noticed in themselves, since they add that certain something (which cannot be expressed) to all cognition. The consequent will concerns all these different elements present in the judgement. Both divine and human decision can be understood as an outcome of different strivings for the good, although in human deliberation are also present elements which we are not aware of, and which can lead us astray from the real good. In a straightforward practical decision the strivings for the good clearly favour some course of action. In this case the deliberation is easy. Often, however, there

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are so many antecedent wills and appetitions towards different courses of action that some conflict between them is inevitable. The “collision” of these original strivings produces new strivings, which are outcomes of both conscious volitions and appetitions. The eventual result of all these different elements is the prevailing effort, which makes a full volition or the consequent will (NE 2.21.39; A VI 6 192).

2 The Models of Rational Decision As we have seen, in Leibniz deliberation takes two forms. Sometimes the goods are mutually exclusive and one has to decide between them or make a compromise where both are included in the sense that goods are distributed among parties. This first kind of deliberation can be applied in simple situations, where the values are independent of each other. The second kind of deliberation is a more complicated one, since the goods are not exclusive and one has to consider all of them. In this case, the deliberator should pick the ones that contribute most to the desired goal and try to form an optimum between them. These two kinds of deliberation require two different kinds of models of decision. Before going into the details of the models, however, I shall present a further distinction between two kinds of considerations, which is related to both models. These two considerations are related to different stages of deliberation: (1) Choosing the good or goods in each situation (2) Estimating the likelihood of the occurrence of the good or goods in question The first consideration is related to the assessment of the good and the second is related to the consequences of the proposed act or settlement. Leibniz makes the distinction in NE 2.21.66: The question of how inevitable a result is, is heterogeneous from – i.e., cannot be compared with – the question of how good or bad it is. So in trying to compare them, moralists have become muddled, as can be seen from writings on probability (A VI 6 205–206).

It is easy to see that this kind of estimation in the Leibnizian framework concerns all moral deliberations. In addition to considering what the good is in each situation, we also have to consider whether the proposed act or settlement has any hopes of promoting that good. Since Leibniz is a consequentialist in ethics and regards the consequences of virtuous action as contributing, besides to general perfection, also to one’s own happiness, he thinks a moral agent should consider both the goodness of the act itself to himself or herself, and its consequences to the general good. As I continue to present the two models of deliberation, my hypothesis is that these two considerations are inherent in both of them.

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2.1 The Pair of Scales Model In simple cases, where the values are independent of each other, there may be two kinds of situations. There may be an either-or situation, when one has to deliberate between two independent alternatives. An example of this would be: should I stay or should I go? The options exclude each other and one cannot help but decide between them. A more complicated variant of this kind of situation is a case where two parties have a claim to some good and a compromise is sought. In this case, the judge or the middleman strives to distribute some of the goods to one side and some of the goods to the other side and both parties are persuaded to make some concessions so that a rational compromise or agreement can be found. This rational balancing, typical of political or economical controversies, can also be performed in several stages (in cases, for example, where there are different types of goods or several parties). If one can calculate the exact number of goods received by each party, it is possible to use the calculemus-method. In this case, the situation might be compared to an interrupted game of chance, where the stakes are evenly distributed among the players and where one can apply methods of calculating probabilities, which Leibniz developed in his various writings.4 Usually, however, the reasons can only be estimated. These kinds of deliberations can be illustrated by the traditional metaphor of a pair of scales, where in the former case the amount of weight in the left or right cup decides the case for the one or the other.5 If the weight in the left cup is heavier than in the right cup, the option represented by the left cup is chosen. The deliberator collects reasons or evidence on both sides and the weightier alternative wins. In the latter case, a compromise can be established by making an agreement on where the goods are distributed. In this kind of situation, a balance between the cups is sought. The first kind of balancing is common in proceedings of criminal law, where the decision settles whether the accused is guilty or not guilty. The judge accepts or rejects different degrees of proofs for or against the guilt of the accused and evaluates them. By combining proofs, the judge may come to a conclusion for or against the alleged guilt of the accused. When discussing this simple balancing of reasons, Leibniz often uses the method of presumption, which is a supposition, which stands unless contrary proof appears.6 In moral deliberations, the agent forms different estimations of the proposed actions and balances them with each other (in several stages, if necessary). These estimations also include the consideration of the consequences of the proposed actions as one aspect, or as a weight in the left or right cup of the pair of scales. Thus, among the reasons to be added to either side are included both the goodness of the proposed act and its estimated probability of causing favourable consequences. It might happen that an action which is better than another is ignored, because the lesser good is estimated to have a higher degree of probability of succeeding. Thus, the balancing concerns the overall goodness of the proposed actions. If the reasons or evidence clearly favour one side, a presumption is formed which holds unless significant proofs to the contrary view are encountered. The

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presumption works as a sufficient reason, which is enough to determine the balance between reasons. The determination happens pseudo-mechanically in the sense that while the balancing happens “automatically”, one can affect the “weights” or reasons indirectly by developing one’s understanding and preparing oneself in advance against temptations posed by sensual images of confused perceptions. The second kind of balancing strives at compromise by distributing the goods in a way that is agreeable to all parties. Some good is given to some party, which makes a concession to the other parties, and the same goes for the other parties. By negotiating, a rational balance can be achieved, where each party makes some concessions but gains some other goods. This kind of rational compromise is typical of peace negotiations and economic or political agreements. As in the more simple balance, the probability of the desired consequences of the agreement should be considered among the reasons. The overall result of the compromise should promote general perfection as much as possible. Thus, the compromise in itself can be seen as a moral act. For this reason, it might become necessary to persuade the parties to settle for less of the good than is possible, since a compromise which is less profitable to different parties might have better consequences for the long-term good, such as peace. Thus, it might be rational, for example, to leave some controversial issue unsolved or to leave some disputed area to a neutral sovereign. In both kinds of balancing (for-against and compromise) the selection of reasons should be performed carefully and one should take every noteworthy reason into account, as Leibniz explains when he uses the economic metaphor of accounting: For a right decision to be made in a case where reasons have to be weighed against one another, many things are needed. That is almost the way it is with merchants’ account books. For in those one must not ignore any amount, each separate amount must be carefully ascertained, and they must be put in good order and then listed accurately. But some items are omitted, either because they escape one’s mind or because one passes too quickly over them. And some are not given their correct values – as in the case of the book-keeper who carefully adds up the columns on each page but incorrectly computes the individual amounts of each line or entry before extending them into the column (NE 2.21.67; A VI 6 206–207).

One should carefully select the appropriate components in question and add them up to either the one or the other side without forgetting the estimated consequences the proposed actions cause. The reasons act as weights and the side that includes the more significant reasons wins. When it is not necessary to decide the case for or against some party, one might also strive at a compromise and distribute the goods or reasons to both sides.

2.2 The Vectorial Model Simple balancing in a pair of scales between two alternatives is often too limited a model for difficult decisions. In the Leibnizian balance of reasons, there are in many cases multiple goods present when forming a decision. In these cases, the

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simple weighing between different alternatives is not the adequate method. One has to strive for an optimum, where all the goods are observed in the final decision. The idea of optimization is prominent in various areas of Leibniz’s thought: Metaphysics, philosophy of mind, aesthetics, practical rationality and justice. The optimization model of deliberation is an instance of a larger doctrine of mathematical physics, which has its roots in the differential calculus. Today the doctrine is known as the calculus of variations.7 Finding an optimal solution in practical rationality is very difficult. Due to their limited abilities of cognition and reasoning, it is rare for men to succeed in this, but they can strive for a solution which approaches the unique optimum (which always exists) as closely as possible. God’s choosing the best among all possible worlds has been seen as a special instance of this model, since his infinite understanding makes it possible to find an objective optimum among the alternatives.8 The optimization model of practical rationality has been briefly mentioned by Louis Couturat (1985: 562–565) and discussed by Jon Elster (1975: 123–124). Jaakko Hintikka has paid more attention to this model, arguing that it was developed by Leibniz in order to help in difficulties over rational decisions and thus contains systematic value (Hintikka 1987: 98–100). Simo Knuuttila has argued that this model, which he calls the vectorial theory of rational decision, can be considered Leibniz’s most original contribution to practical rationality (Knuuttila 1998: 333). The details of the model, however, have remained obscure, since Leibniz seldom discusses it explicitly. In what follows, I shall try to provide a preliminary reconstruction of the model and present some examples where Leibniz seems to apply it. The complicated balance of the vectorial model is significantly different from the simpler one of weighing between options on a pair of scales, as can be seen in Th´eodic´ee, §324. First, Leibniz introduces the traditional pair of scales model as Bayle’s view of the soul in the following way: He demonstrates amply enough [. . .] that the soul may be compared to a balance, where reasons and inclinations take the place of weights. According to him, one can explain what passes in our resolutions by the hypothesis that the will of a man is like a balance which is at rest when the weights of its two pans are equal, and which always inclines either to one side or the other according to which of the pans is the more heavily laden. A new reason makes a heavier weight, a new idea shines more brightly than the old; the fear of a heavy penalty prevails over some pleasure; when two passions dispute the ground, it is always the stronger which gains the mastery, unless the other be assisted by reason or by some other contributing passion (GP 6 308).

Then Leibniz goes on to introduce his new model: Nevertheless, as very often there are diverse courses to choose from, one might, instead of the balance, compare the soul with a force which puts forth effort on various sides simultaneously, but which acts only at the spot where action is easiest or there is least resistance (GP 6 309).

The reference to the easiest action seems to be related to the optimization method discussed in Leibniz’s memoir Tentamen anagogium, where he discusses the shortest route a ray of light takes between two points. There are various possible paths

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which the ray of light can take, but it always takes the optimal path, which is the shortest route between the source and the goal.9 In deliberation, different inclinations form different paths or variations going in different directions. The best choice is a unique optimal solution between them, which always exists. Thus, the best decision in an ideal case is the optimum between different goods (“effort on various sides simultaneously”) and it is reached when all of these inclinations are apperceived and the unique optimal solution is found (“action is easiest or there is least resistance”). While God chooses the best of all possible worlds with his infinite understanding, men act on the basis of appearances they perceive. The more developed one’s understanding is, the more informed one is of the real goods involved in each case and the more adequately one can contribute to the general perfection, which is ruled according to final causes, as Leibniz argues in Principes de la Nature et de la grace, fond´es en raison, §14: As for the rational soul, or mind, there is something more in it than in monads, or even in the simple souls. It is not only a mirror of the universe of created things, but also an image of the divinity. The mind not only has a perception of God’s works, but it is even capable of producing something that resembles them, although on a small scale [. . .] Our soul is also architectonic in its voluntary actions; and in discovering the sciences according to which God has regulated things (by weight, measure, number, etc.) it imitates in its realm and in the small world in which it is allowed to work, what God does in the large work (GP 6 604–605).

God can see perfectly that the basis for his choice of the best world is some criterion or a combination of several criteria (depending on how certain Leibniz’s writings are interpreted). For men, it is much more difficult to know about the motives of our actions and we can also easily err in the choice of the appropriate ways of evaluating the good and of the consequences the proposed acts produce. In human deliberations, minute perceptions blur our judgements and we may be affected by sensual pleasures, which we mistakenly regard as real goods. However, by manipulating our action, by adapting good habits and our understanding, we can approach the optimal decision in complicated deliberations and sometimes perhaps even reach it. In itself, the vectorial model can be only a heuristic device, which cannot give any certain results. However, by applying the model the moral agent can map the situation, make discoveries and, in an ideal case, find an optimum between carefully selected different inclinations, which all lead to the good. Whether or not we can reach the optimum, the deliberation is a pseudo-mechanical arithmetic of reasons, where reasons incline but do not necessitate. In the pair of scales model, the deliberator adds up reasons to either the left or the right cup and weighs between them. In the vectorial model, one multiplies the separate values in order to find a balanced optimum between them. In a letter to Burnett (1/11. 2. 1697), Leibniz notes: “I came to see that there is a species of mathematics in estimating reasons, where they sometimes have to be added, sometimes multiplied together in order to get the sum. This has not yet been noted by the logicians” (GP 3 190).

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An important feature of the vectorial model is that it can be expressed in a geometrical manner. The deliberator can use figures in order to sketch or map the situation better. In this, Leibniz was influenced by Arnauld and Nicole’s L’art de penser, the so-called Port Royal Logic. In the last chapter of the work, when discussing lotteries, the authors argue that one should not only think about the good, but also take into account the probability that the good will take place: In order to decide what we ought to do to obtain some good or avoid some harm, it is necessary to consider not only the good or harm in itself, but also the probability that it will or will not occur, and to view geometrically the proportion all these things have when taken together (Arnauld and Nicole 1965: 353).

This description clearly refers to the two considerations of the assessment of both the good and the probability that the good takes place. In the Nouveaux essais, however, Leibniz generalizes the idea to apply to all assessments in complicated situations: In this as in other assessments which are disparate, heterogeneous, having more than one dimension (so to speak), the magnitude of the thing in question is made up proportionately out of two estimates; as with a rectangle, where two things have to be considered, namely its length and its breadth (NE 2.21.66; A VI 6 206).

The vectorial model can be understood as a functional analysis between different goods. When we think about Leibniz’s account of deliberation in practical matters, it is clear that the values in question are only estimations and consequently the resulting function is also uncertain.10 Often the values to be estimated are impossible to evaluate by quantitative methods. However, the vectorial model can have great heuristic value, since by employing it we can compare different proposed options and map them with respect to different criteria.11 Although Leibniz usually applies the model without explicating details, there are a few cases where it is elaborated more clearly. Perhaps the best example is Leibniz’s discussion of happiness in a draft related to scientia generalis. There Leibniz considers the good, in this case happiness ex ductu bonitatis in durationem. If we are to discuss that properly, must we use mathematical operations and say that the whole of the good consists in how long the good can be sustained [ex ductu bonitatis in durationem] as in land-measurement a field [are] is measured by breadth and length [ex ductu latitudinum in longitudinem]? (GP 7 115).

There are two separate values, the duration of good and the intensity of good. If the agent is inclined to choose the maximum possible intensity of good, the result is great happiness, which will only last for a short time. If the agent chooses the maximum duration of good, one’s happiness is not very intense (GP 7 115). Leibniz argues that eternal, however small evil, can outweigh a temporal, however great good. By turning the issue upside down, he can argue that in the long run strong sensual feelings (passions) are harmful and if the oil-lamp is burning with too great a flame, it will soon go out (GP 7 116). Thus we must strive at reasonable intensity of good, which lasts for a long time. In this way, the different inclinations (duration of good and intensity of good) “combine and the volition is the result of the conflict

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amongst them” (NE 2.21.39). One encounters both values to a degree, but the overall result is better than either of the extremes. When we choose rationally in this case, we try to find a course of action which brings about the optimal good. At least we can estimate whether it is more reasonable to choose an act which is better, or to choose another act which is slightly worse but the prospect of success is greater. It might happen, however, that sensual temptations lead us to believe that a great intensity of good is the best we can choose. Following this wrong idea of the good, the proposed actions produce something else than the best effect. Even if we choose the act that is the most probable concerning the eventuation of the good, it is a wrong act, because our idea of the good is misguided. If we were to present the idea in a geometrical manner, one could take as coordinates the duration of the good and the intensity of the good. Thus we end up with Leibniz’s figure below, where longitude represents the duration of the good and latitude the intensity of the good (GP 7 115). The whole of the good is represented by the ring of the semicircle below. The ring also shows the corresponding combinations of different values. When the breadth of the area (latitude) varies, the length (longitudo) of it rises or falls, and vice versa (GP 7 115–116). One might suppose that the largest area can be found by drawing rectangles inside the semicircle, although Leibniz does not say so. Be that as it may, the largest rectangle is found by the multiplication of the middle points of both longitudo and latitudo.

Perhaps Leibniz thought that with the geometrical analysis of a function one could compare different suggested combinations of the values by non-quantitative methods and find the best one, although there is no mention of it in the text in question. One could also speculate that his analysis situs, a mathematical method of comparing properties of figures, developed at about the same time, had something to do with this comparison. Since there is no textual evidence I am aware of, I shall not dwell on these possibilities. Instead, let us look at another text where Leibniz tries to apply exact values to a similar example. In a letter to Arnauld in 1671, he describes the estimation of a good man (beauty) in respect to canon law. Leibniz writes: “Presuming that a man has wisdom of the degree of three and power in the degree of four, his total estimation would be twelve and not seven, since wisdom is of assistance to power” (A 2 1 174).

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The beauty of a person is not his or her wisdom and power added up, but a balanced optimum (product or multiplication) between these properties. It is not enough to balance wisdom and power against each other as in the pair of scales model or to strive to form a compromise where wisdom and power are equally great. This would work if the properties of wisdom and power were independent of each other. As Leibniz argues, this is not the case, since on a higher level wisdom can contribute to power (“wisdom can be of assistance to power”) and probably also vice versa, although Leibniz does not say so explicitly. Because the properties compete with each other, to estimate the overall value of the good man, both values have to be taken into account and the final estimation is a balanced optimum between them. This passage is something of an exception in Leibniz’s writings, since this is the only instance, so far as I know, where he gives definite quantities to such values as wisdom and power. The idea, however, is essentially the same as in the draft of evaluating happiness in general science discussed above, and can be illustrated by a similar geometrical figure. A more metaphorical way of arguing is adopted in another memoir from 1671, called Grundriss eines Bedenckens von Aufrichtung einer Societ¨at in Deutschland, which concerns scientific academies. Leibniz describes the properties of a good prince as follows: “If power is greater than reason, he who possesses it is either a lamb who cannot use it at all, or a wolf and a tyrant who cannot use it well” (A IV 1 531).12 If the person in question has too much wisdom compared to power, he is overpowered, and if he has much more power than wisdom, he is a tyrant. The former kind of “overpowered” persons are suitable for councillors of princes and the latter kind of persons are bad rulers or tyrants. The ideal prince is of course an optimum between these criteria. He has a beautiful soul, and here Leibniz argues in a similar fashion he argued above to Arnauld. As has been noted, the vectorial model is essentially a heuristic device. The values in question are continuous and have an infinite number of degrees. Thus, one can discuss whether a little greater amount of good compared to the same duration of good would be better than a little less amount of good with longer duration of good, or whether a different combination of wisdom and power would be more optimal for general perfection than another combination. Because of these continuous degrees of values, there is an infinite number of possible combinations (variations), of which there can be only one single best one, the optimum. By applying the model, it is easier to find these possible variations in each case and compare them to each other. To sum up, human rational decision in complicated and uncertain situations is, in an ideal case, an optimum between separate inclinations leading to the good, not a simple choice between good or bad. When deliberating in complex situations involving several cooperative goods, one reflects on the situation and chooses the most important relevant criteria which constitute the good in question. After determining the good in question, the deliberator considers which of the proposed actions best bring about the desired good. In the last phase of deliberation, the agent can compare the overall value of different proposed courses of action, “map” them by employing

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the vectorial model, and choose among them. If the optimal course of action can be found, it is chosen. If one cannot grasp the optimum, one should at least choose the option which is best considering the alternatives, or which seems to cause the least evil or imperfection in the world.

3 The Rationality of the Models In general, human practical rationality functions under uncertainty due to the limited cognition of spirits. Under this condition, which can be eased but not abolished, men should try to act as rationally as possible not only for their own benefit, but also for the benefit of general well-being or happiness. In the final analysis, these two come to the same thing: One must hold as certain that the more a mind desires to know order, reason, the beauty of things which God has produced, and the more it is moved to imitate this order in the things which God has left to his direction, the happier it will be (GR 581).

For this reason, it is of utmost importance that men act as rationally as possible. I shall proceed to examine how rationality is realized in the two models of deliberation we have discussed above. In the pair of scales model, the reasons considered may be estimations or demonstrated proofs. Depending on the nature of these reasons, the weighing of reasons may be “soft” or “hard” reasoning. In practical cases, the estimation of reasons (especially the estimation of consequences) usually employs “soft” rationality. As soon as the probability-calculus Leibniz envisioned is completed, these estimations would be replaced by calculations, thus enabling rigorous reasoning. As we saw, this is possible in cases where exact goods can be calculated. Thus, sometimes (in economic treaties, for example) one can simply calculate the share of each party, but there are often other factors involved which cannot be calculated, such as the consequences of treaties (moral, political, economic), personal questions, etc. These additional reasons complicate the deliberation and significantly affect the balancing. For these reasons, one should avoid rash decisions in order to deliberate properly, as Leibniz argues in a fragment called Zur allgemeinen Characteristik (1677): After long pro and con discussions, most of the time it is emotion rather than reason that claims the victory, and the struggle ends there with the Gordian knot cut rather than untied. This is especially pertinent to the deliberations of practical life in which some decision must be finally made. Here it is only rarely the case that advantages and disadvantages which are so often distributed in many different ways on both sides, are weights as on a balance (GP 7 188).

If we apply the vectorial model, we should strive at the best possible combination of different inclinations to the good within the limits of our cognitive abilities, or at least choose the combination which is least harmful regarding both our own good and the general well-being. The more developed our understanding of the world and God’s nature is, the better rational decisions we make.

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A practical example of the use of the vectorial model would perhaps be the buying of a new washing machine. If we have an unlimited amount of cash at our disposal and complete knowledge of the quality of washing machines available, we simply go to the nearest shop and buy the best machine there is. If we are less fortunate, we settle for a less good alternative, but try to buy a good machine despite this limitation. Within our budget, we try to buy as good a washing machine as possible. We might take a few simple criteria as a basis for our choice. A good combination of values in this case would be quality and price. I might compare different washing machines by taking into consideration their alleged efficiency (for example, amount of water and electricity needed in the washing process, the speed of the process etc., as outlined by a consumer magazine or the manufacturer) and their relative cheapness. In order to find good value for money, my best choice would be a moderately cheap machine, which is not the best on the market, but of good enough quality. Put otherwise, I have sufficient reason to choose precisely this washing machine. Although it is uncertain if the buying of a washing machine can be regarded as an ethical action, we can here extend the example to include moral values. We can assume that a virtuous man buys the machine that is least harmful to the ecosystem of the world and in this way promotes general well-being. After having determined the machines that have a good combination of quality and price, he can compare them and choose the one that produces the least harm to the global ecosystem. To be sure, if a certain machine is an optimal choice, it is reasonable to think that it also has the feature of being the most ecological one. After these two independent considerations, the moral agent can be said to have deliberated rationally, and while the choice is perhaps not the best possible in an objective sense, it is the best possible within the limits of his or her abilities. While an expert in washing machines can tell the quality of the machine by looking at technical details and examining the machine thoroughly, an ordinary consumer has only vague ideas of these properties. He or she can only estimate the machines roughly according to some principles by employing the vectorial model. Although deliberation in this manner is rational, it is not certain. Following Dascal’s description of the weighing of reasons in the pair of scales model, I would like to say that the vectorial model also “acknowledges the limitations of the hard rationality and considers the balance of reason to be valuable even when it is only able to provide less than conclusive and therefore questionable decisions” (Dascal 2005: 29). Acknowledgments I would like to thank Professors Olli Koistinen and Donald Rutherford for their comments on an earlier version of this paper, the Finnish Academy of Science and Letters, ¨ and the Emil Ohmann Foundation for a grant which made this contribution possible.

Notes 1. “Modum ergo tradere aggredior, quo semper homines ratiocinationes suas in omni argumento ad calculi formam exhibere controversiasque omnes finire possunt, ut non jam clamoribus

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3. 4. 5. 6.

7. 8. 9.

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rem agere necesse sit, sed alter alteri dicere possit: calculemus.” (Guilielmi Pacidii initia et specimina Scientiae generalis) (GP 7 125). For an example of Leibniz’s drafts on this kind of calculating, see Calculus consequentiarum (C 84–89). In NE 2.21.35 Leibniz argues that men should make themselves laws and rules for the future and carry them out strictly, avoiding situations which are capable of corrupting him. They should render their conceptions of real goods more vivid by useful activities which the philosopher recommends. These include farming, gardening, collecting curiosities, making experiments and inquiries, conversation or reading. Idleness is to be avoided. Good company can help in developing virtue, since perfection is intensified from reflecting on others perfections. See also Garber 1982: 169. See Leibniz 1995. This metaphor is already present in Homer’s Iliad, Book VII. My presentation of the pair of scales model is largely based on Dascal (2005). A representative example can be found in NE 4.16.9, where Leibniz discusses the degrees of assent: “When jurists discuss proofs, presumptions, conjectures, and evidence, they have a great many good things to say on the subject and go into considerable detail. They begin with common knowledge, where there is no need for proof. They next deal with complete proofs, or what pass for them: judgements are delivered on the strength of these, at least in civil actions [. . .] then there are presumptions, which are accepted provisionally as complete proofs – that is, for as long as the contrary is not proved [. . .] Apart from these, there are many degrees of conjecture and of evidences” (A VI 6 464). For the history of the calculus of variations, see Goldstine 1980. For this interpretation of God’s choosing of the best of all possible worlds, see Rescher 2003 and Gale 2002. In Tentamen anagogium Leibniz argues as follows: “I shall propose as a general principle of optics that a ray of light moves from one point to another by the path which is found to be easiest in relation to the plane surfaces which must serve as the rule for other surfaces” (GP 7 273). His view is related to the famous solution of the brachistochrone problem, where the problem is to determine the path down which a particle will slide from one given point to another not directly below in the shortest time. While the initial velocity is given, friction and air resistance (gravity) is neglected. The solution is a cycloid. For details, see Goldstine 1980: 30–66. In mathematics the idea of a function was made popular by Galileo in his Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze (1638) and developed further by Torricelli, Descartes, Roberval, Wallis, and Gregory (Kline 1972 I: 338). Leibniz used the term in its modern sense, that is, to mean any quantity varying from point to point on a curve. The curve can be illustrated by a co-ordinate system. Jon Elster (1975: 124) has argued that Leibniz seems to have used the vectorial model before he had the mathematical tools to apply it to practical problems. This view seems plausible, since most of the examples we have of its use are from the end of the 1660’s and the beginning of the 1670’s, that is, from the time before Paris, where Leibniz concentrated on mathematical research. However, there are also examples of the use of the vectorial method after the Paris period. Marc Parmentier (1993: 473–474) sees here a preliminary stage of differential and integral analysis. He also notes that Leibniz’s model always needs a qualitative component – that is, choosing the variables in question. In the same memoir, Leibniz also repeats the concept of the beauty of a man as an optimum between power and l’esprit as presented to Arnauld. See FC 7 30.

References Arnauld, A. and Nicole, P. 1965. La logique ou l’art de penser, contenant, outre les regles communes, plusieurs observations nouvelles, propres a` former le jugement. Ed. P. Clair and F. Girbal. Paris: Presses Universitaires de France.

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Couturat, L. 1985 (1901). La logique de Leibniz.. Hildesheim: Olms. Dascal, M. 2005. The balance of reason. In D. Vanderveken (ed.), Logic, Thought and Action. Dordrecht: Springer, pp. 27–47. Elster, J. 1975. Leibniz et la formation de l’esprit capitaliste. Paris: Aubier-Montaigne. Garber, D. 1982. Motion and metaphysics in the young Leibniz. In M. Hooker (ed.), Leibniz: Critical and Interpretive Essays. Manchester: Manchester University Press, pp. 160–184. Goldstine, H.H. 1980. A History of the Calculus of Variations from the 17th Through the 19th Century. New York: Springer. Hintikka, J. 1987. Was Leibniz’s deity an akrates? In S.Knuuttila (ed.), Modern Modalities. Studies of the History of Modal Theories from Medieval Nominalism to Logical Positivism. Dordrecht: Kluwer, pp. 85–108. Kline, M. 1972. Mathematical Thought from Ancient to Modern Times I–III. Oxford: Oxford University Press. Knuuttila, S. 1998. Old and new in Lebniz’s view of rational decision. In S. F. Brown (ed.), Meeting of the Minds. The Relations Between Medieval and Classical Modern European Philosophy. Turnhout: Brepols, pp. 333–346. Leibniz, G.W. 1995. L’estime des apparences. Ed. M. Parmentier. Paris: Vrin. Parmentier, M. 1993. Concepts juridiques et probabilistes chez Leibniz. Revue d’histoire des sciences 44: 439–485.

Chapter 23

The Specimen Demonstrationum Politicarum Pro Eligendo Rege Polonorum: From the Concatenation of Demonstrations to a Decision Appraisal Procedure J´er´emie Griard

1 The Aim of the Text After the abdication of John II Casimir, Europe occupied itself with the election of his successor by the Polish nobles. Even La Fontaine composed a poem on this subject addressed to the Princess of Bavaria: Interest and ambition/ Working for the election/ Of the Monarch of Poland. /We believe here that the task/ Is advanced: and the spirits/ Will soon give the prize/ To the Lorrainer, then to the Moscovite/ Cond´e, Neuburg; since merit/ On all sides creates the problem [. . .].1

The four candidates, all foreigners, were the Duke of Lorraine, Charles IV; the Grand-Duke Alexis, son of the Tsar Alexis I; the Great Cond´e, first prince of royal blood, supported by Louis XIV; and finally Philip William, Duke of Neuburg, supported by the Archbishop and Elector of Mainz, John Philip von Sch¨onborn. The minister of Sch¨onborn, John Christian von Boineburg, had just introduced the young Leibniz to the court of Mainz. Before returning as Ambassador to the Diet of Warsaw where the election would be held, Boineburg asked his prot´eg´e to write a text defending Neuburg’s candidature. Leibniz fulfilled that request, but instead of writing a simple apology for Neuburg and three pamphlets against each of the other candidates, he provided an implacably reasoned text presented in an objective form: the Specimen demonstrationum politicarum pro eligendo rege Polonorum (An Essay of Political Demonstrations for the Election of the King of Poland ). This essay leaves no doubt concerning the best candidate and for this reason might be discredited. We might even forget about it, as Russell would have counseled, since, according to him, Leibniz’s choice of a courtier rather than an academic led “to an undue deference for princes and a lamentable waste of time in the endeavor to please them” (Russell 1937: 2). But instead of following Russell in such a dead-end, we should instead consider what Leibniz himself suggests in his February 11, 1697 letter to Burnett:

J. Griard Alexander von Humboldt Foundation, Germany

M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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I’ve strongly supported the thoughts of Mr. Petty, who illustrated the application of mathematics to economic-political matters. I myself, in a small book anonymously printed in 1669 on the election of the King of Poland at the request of an Ambassador who had to go to Warsaw, showed that there is a type of mathematics with respect to the evaluation of reasons and that sometimes it is necessary to add them, sometimes multiply them together, in order to determine the sum. This has not been remarked enough by logicians (A I I3 551).2

Since the Specimen is not a work on politics but a political work, we should begin by examining its structure, revealing how it operates and affords an example of applied mathematics with respect to the evaluation of reasons.

2 The General System To clarify the elements of this system, we need to first look beyond the surface and consider the pseudonym Leibniz uses. This tactic, which the Specimen inaugurates, will reoccur in Leibniz’s later political texts. In 1677, for example, Leibniz signs his De jure suprematus ac legationis Principum Germaniae (On the Right of Sovereignty and Legation of the Princes of Germany) with a pseudonym which takes the form of a pun: Caesarinus F¨urstenerius or, in English: Caesarin Prince (i.e., the prince is a little Caesar). Beyond the explicit reference to a little princely Caesar, we also find an implicit reference to Leibniz’s sponsor. By substituting the letters D, O, E, C for T, U, U, S and adding a 23rd, E, we obtain the following anagram: Ioannes Fredericus Caesar. Leibniz composed this work at the request of John Frederick of Hanover who wanted the same sovereignty as Caesar (the Emperor). In this work, Leibniz attempts to demonstrate that a prince just like the Prince of Hanover enjoys sovereignty in his states, while still being a member of the empire: This prince is indeed a “little Caesar”. If the pseudonym for the 1677 treaty disguises the identity of its author, the one used for the Specimen falsifies it. “Georgius Ulicovius Lithuanus”, though the sound is similar to “Gottfriedus Guillelmus Leibnitius”, attempts to appear, above all, Polish. “Georgius” requires few comments. However, “Ulicovius”, for those who know a bit about the toponymy of the region, evokes the region of Ulikowo in the extreme West of Poland. The suffix “covius” is a likely Latin transcription of the Slavic “kowo” which in the composition of toponyms designates a field. Leibniz clearly attempts to evoke a Slavic origin. And to achieve the Polish identification, he unambiguously presents Ulicovius as “Lithuanus”, originating from Lithuania, a grand-dukedom at the Eastern extremity of Poland, incorporated exactly 100 years earlier by the Union of Lublin which later created the elective Polish monarchy. Leibniz attempts to pass for a Pole rooted all over the country, from one end to the other. This implies assuming another person’s standpoint as a “true point of perspective in politics as well as in morals” (A IV 3 903).3 Next, since Leibniz does not address all Polish people, but rather particular voters (the nobles), in the first proposition he treats them tactfully by identifying the good of the State with the good of the nobles. We will later return to this point. Finally, in proposition 22, Leibniz states that it is necessary to elect a Catholic, because “for one who is not catholic, exterior security is either impossible or

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difficult, impossible for an heretic, difficult for a schismatic” (A IV 1 20).4 We almost forget that it is someone who belongs to the Confession of Augsburg who writes these lines. Leibniz’s duplicity can be explained not only by the religion of his employer, but also and especially by his audience: Poland is Catholic, so it therefore requires a Catholic king. This is characteristic of Leibniz’s whole approach. He starts from the facts and a given situation in order to trace, in concreto, the portrait of the best candidate. At the same time, he manages to abstract from the declared candidates, so that his text might not be seen as a conspiracy against any of them. It is therefore from Poland and its institutions that Leibniz will progressively infer, by linking propositions, which king will afford the most appropriate match to these.

3 The Chain of Propositions 3.1 The Justification of the Polish Institutions and the Method Unlike Rousseau, who advocates reforming the Polish constitution in his Considerations on the Government of Poland, Leibniz only aims to take advantage of the existing Polish institutions for a better future. This procedure is characteristic of what I have elsewhere called his institutional conservatism (Griard 2004). In the political domain, as in the metaphysical, it is never a question of the best state of affairs in an absolute sense, but always in the relative sense of the best possible one in given circumstances. Thus, regarding political regimes, Leibniz always prefers to look for the means of amending institutions already in place rather than substituting new ones, i.e., he refuses to consider any institution as the absolute best. Though he rejects democracy for Poland, Leibniz does allow it in other cases, particularly for small cities: . . .[The] exercise of democracy can not take place in Poland. Historically, the exercise of a democratic regime is seldom to be found in the past, except for a people of a limited number, ordinarily enclosed in the walls of a single city, for example in Athens, Rome, Carthage, Syracuse, etc. (prop. 16, A IV 1 16).5

After dismissing the possibility of a democratic regime for Poland, Leibniz briefly reflects on the relationship between sovereign and subjects that he will develop in On the Right of Sovereignty and Legation of the Princes of Germany of 1677. This he will then characterize with the expression of “quasi contractus”, that is a “quasi-contract” (see Griard, forthcoming). As Leibniz writes in the Specimen: The use of sovereign power belongs to the Usufructuary, the Dictator, the Regent, and also the King who is at the foundation of the various orders; it for sure involves a temporal right that has been imposed upon others, either through the course of time itself, or by the fulfillment of a condition or the will of others. Thus in Poland the king holds sovereign power, since in the interval that separates elections, he has no superior. But instead, during the Elections, the exercise of sovereign power is consolidated with the ownership on hold and can be made null and not forthcoming. This however creates an obstacle, as Grotius

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justly noted, not for the overarching character of power itself, but only for its mode of possession (prop. 16, A IV 1 16–17).6

It is interesting to remark Leibniz’s comparison between the sovereign and the usufructuary, a comparison supported by the use of the term “consolidatum” that refers to “consolidatio” defined in the Digest 7.2.3, as usufruct united with ownership. Thus, the sovereign is the usufructuary of sovereign power whose ownership belongs, in the case of Poland, to the nobles who elect him. In effect, by correcting Aristotle’s definition of a sovereign to accord with all forms of government,7 Leibniz holds that: The citizen is one who either takes part in government or would take part in it if this role had not been transferred to another (for example to a College of betters or the person of a Prince). [. . .] In the Republic of Poland, this role is only that of the nobles and of those the nobles admit (prop. 20, A IV 1 16).8

By correlating this quote with the previous one, we can see that Leibniz thought that the Polish nobles, in the capacity of citizens of the Kingdom of Poland, possessed this sovereign power. According to definitions in proposition 16, it seems that Poland could not be a democracy, because democracy demands that the power be exercised in a continual manner by the assembled citizens, this being the case with “the Athenian people or the Romans [who] assembled every day in the public place for deliberation”9 (prop. 20, A IV 1 16). But since this is not the case with the whole group of Polish nobles, Poland is therefore an elective monarchy. Poland could be considered a kind of democracy only in the electoral period, during which the citizens (i.e., the nobles) exercise the supreme power in its most reduced form, consisting simply in choosing the one upon whom to bestow its ordinary exercise. This division of the supreme power between a usufructuary who acts as the sovereign and an owner who possesses it as a mere citizen evokes the situation in civil law where the management of affairs is administered for the sake of someone else. In such a situation, someone, in the absence or incapacity of the good’s owner, takes it upon himself to manage this good. This is a typical example of a quasi-contractual situation where, even though no convention has been established between the parties, the de facto manager manages the good in the owner’s interest. Reciprocally, the owner, upon his return or recovering of capacity, honors the engagements undertaken by the manager (while the owner defaulted). In the case of Poland, there is a conventional designation since the sovereign is elected. Still, since this election implies a translation and not an alienation, we are not faced with a social contract, but rather a quasi social contract. This convention is not based on the function of the sovereign. This is always distinct. It is instead the reason why during the electoral periods the exercise of sovereign power remains “in suspense”. It is also why, as mentioned, the power exercised by the nobles is only exercised in its most reduced form. This convention, rather than grounding the function of the sovereign, is content to name him, to incarnate a sovereign who, for want of being incarnated in a king, takes the form of an assembly of citizens. Otherwise, there would be no reason for proceeding to an election, but Poland would be led to

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become a democracy in which the people (i.e., the whole group of citizens, i.e., the whole group of nobles) governs. The election of a king involves choosing a name-holder to be this king and does not consist in justifying the government’s monarchical character. Instead, the preexistence of this monarchical character makes it possible to hold the election. Even if there were no election, Poland would not be less in need of a king. And thus, if the relationship between, for example, the nobles and Sire John Casimir is conventional, the relationship between the king and the nobles is not. No will can further intervene after the election. The nobles cannot legally depose the king. Similarly, the king cannot unilaterally renounce his function as he could if his role were purely contractual. When the Prince of Valois-Angoulˆeme, who had been elected King of Poland, renounced his crown to collect the crown of France left by the death of his brother Charles IX and become Henry III of France, the Polish nobles, rather than accepting this act of abdication, vainly set off in pursuit to keep him within the limits of the Polish kingdom. This somewhat burlesque epic of nobles chasing their fleeing king to return him by force to his throne testifies less to the Slavic disposition for tragicomedy than to the non-contractual character of the royal function, notwithstanding the conventional character of the king’s designation as a substitute for hereditary succession. While setting limits to the role of the noble voters, Leibniz tries to justify the electoral process. This is what he endeavors in the first 19 propositions. In order to give the reader a notion of these fastidious justifications, I will simply list the most striking points, which more directly determine the qualities the elected king ought to have. As has already been mentioned, the good of the state is identified with the good of the nobles and requires the liberty and security of Poland. This end serves the interest of the whole of Christendom due to Poland’s geographic situation. Having shown that neither democracy nor aristocracy suits Poland, Leibniz concludes that Poland needs a king. After discussing the institutions, he rapidly justifies his reasoning, claiming that “the election cannot be left to chance, but must be rational”,10 and remarking that: “For the rest, we could deliberate to see if destiny is like an oracle and a sign of the divine will. But these things have nothing to do with politics. It is the theologians who will debate about them”11 (prop. 20, A IV 1 18). Leibniz here tries to preempt any objection based on the lazy argument that what ought to happen will necessarily happen, whatever we do. It is as a politician that he considers a question that cannot be resolved except with reason. We will try to follow Leibniz in his resolutely rational approach.

3.2 The absolute talents of the candidate A comparison seems to be the most appropriate means of determining the terms of the problem. Of course, we have not reached this point in the Specimen, but the ensuing developments tend to make us evoke the divine computations presiding over creation. Propositions 20 and 21 suggest that the king ought to be a

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well-known figure and that the king should reign himself and not through a viceroy. The comparison is simple: Just as it is necessary that God should know the essence of the monads before creating them in order to assure that they are all compatible with each other, it is necessary that the electors, having to choose a candidate over others, should know this candidate in advance in order to ensure that he suits the requirements of Poland. In other words, just as the simple substance needs to insert itself in a web of relations constituting universal harmony, the King of Poland must also insert himself in a web of relations: Relations with the nobility, with Poland’s institutions, between Poland and the whole of Christendom, between Poland and each of the Christian world powers, and, finally, between Poland and what is called the “barbarian” world. Each of these relations itself results from a manifold of factors. We intentionally use the terms “relation” and “factor”, since Leibniz has promised a type of mathematics with respect to the evaluation of reasons. But before discussing the relative talents of the best candidate, it is necessary to first discuss their absolute talents, following the plan of the Specimen. Keeping in mind the comparison with God and creation as a guideline, we can note that if the best candidate’s relative qualities should fit a condition of compatibility, the absolute qualities would need to fit the requirement that the candidature itself is possible and does not present any internal contradiction. The king must therefore be just, prudent and experienced, since “. . .it is evident that all the virtues are potentially contained, to put it this way, even if not formally, in this one who is just and prudent” (A IV 1 22).12 To these absolute moral qualities we can add physical qualities that amount to the absence of flaws: We must not elect a child or an invalid. Propositions 28 and 29, which state these conditions, refer directly to proposition 21 and the idea that the king alone must govern (a child, because of lack of experience could be manipulated, while a valetudinarian would be obliged to leave governing to ministers who overrule him).13 Leibniz emphasizes the age of the candidate, specifying that, discarding both children and invalids, since prudence is preferable to force, it is best to “choose closer to old age than to childhood” (corr. prop. 30, A IV 1 26).14 According to Leibniz, who was only 23 at the time, temperance comes with age. The best candidate should also be patient, modest, and peaceful enough, should not belong to an unruly family, should be tolerant towards dissidents, and should finally not have adopted the customs of despotic governance. All these qualities are valuable for every king, whatever his kingdom. Then, beginning with proposition 37, Leibniz proceeds with the consideration of what he called the relative talents.

3.3 The Candidate’s Relative Talents These relative talents are those which apply specifically to Poland and the alliances which are or should be its own. Leibniz digresses here, discussing the nature of true friendship, kindness and gratitude. Propositions 37–46, being on this topic, contain

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reflections on natural law which will also be found 24 years later in the preface to the Codex juris gentium diplomaticus (Diplomatic Code of the Law of Nations). These propositions state that true friendship is the delight in the happiness of another, that the true friend prefers a greater good for the other to a smaller good for himself. True friendship also supposes the perpetuity of such a relationship. This is difficult for princes to maintain in so far as reasons of state prevail over their personal sentiments. It is impossible between states since these are civil persons in which natural persons are in perpetual flux. Therefore, the recognition of a kindness obtained from another will depend on the cause from which it results, whether it is voluntary or not. If it is voluntary, and only in this case, it is necessary to return it in kind. However, if the cause is voluntary, but aims to recompense a third person, then no recognition is required. This reflection allows Leibniz to encourage the Polish nobles, whom the maneuvers of Louis XIV and Cond´e tried to corrupt, not to feel obliged to them. Having finished his digression, Leibniz returns with proposition 47 to considering the criteria for the selection of the best candidate. Since this candidate should be agreeable to the Christian world, Leibniz dedicates a section to Christianity. Next, conforming to the first degree of the natural law, that of strict law or equality, prescribing to wrong no one (to which the first precept of Ulpian corresponds), the candidate should not be harmful to Poland. Thus one must not elect an enemy, but rather a sincere friend. Friendships declared at the last moment should be rejected, as in the case of a candidate who would convert to Catholicism in the hope of obtaining the crown. Finally, the last propositions, which are deduced from the whole arsenal of preceding propositions, concentrate mostly on the earlier propositions, having as leitmotif the claim that the elected king should not be too powerful, whether by himself or with the support of a foreigner. The end of the Specimen returns to its beginning. At the beginning, Leibniz defends the idea that Poland is sufficiently powerful by itself for its own peace and that in Poland, all the power rests in the hands of the nobility. This monopolistic possession of state power is the reason for the equality required between the nobles: If the power rested in the whole, the inequality of parties would at the same time weaken this total power by weakening one of these parties. It would also be a source of division and internal conflicts. Furthermore, if the King of Poland were too powerful, this power could constitute a menace to the nobles and therefore to Poland itself. Yet, if, as Leibniz would say two years later in a November 1671 letter to Arnauld, “to aid is to multiply and to harm is to divide” (GP 1 74),15 and if this power of the king competes with the power of the nobles, the power of Poland will not result from a subtraction, but from a division. We add and subtract what is identical, but multiply and divide what is different. The power of Poland is that of the nobles. But the power of the nobles is not that of the king. Exercising a power that makes multiplicity a unity, the king has only what could be called a federative power. This is the reason why, if the king had an absolute power, his power turned against the nobles would risk annihilating their power and, consequently, Poland’s. Against a considerable royal power that would

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be either more profitable or harmful as it were more considerable, Leibniz prefers the prudence of a lesser power. Even if it presents a lesser advantage, it also presents less risk. In order to better understand this point, it is necessary to further consult the letter to Arnauld which has just been cited, where Leibniz claimed that the king must be just, prudent and experienced (i.e., wise): If someone is wise with the value of three and powerful with the value of four, the total value of this person will be twelve and not seven, since wisdom can use any degree of power. Similarly with homogenous quantities, a person with a hundred thousand gold coins is richer than one hundred people each possessing a thousand. Since the union determines the usage, the first will become richer even at rest; the others will lose even by working (GP 1 74).16

We can apply these reflections to Poland. The power of Poland is that of the nobles, so it is not found in the king. On the other hand, Poland’s wisdom is not in the nobility since the nobility is not capable of forming a democracy, but only a monarchy. Wisdom, therefore, belongs to the king. The value of a regime functioning according to this model, with power in the nobility and wisdom in the king, will therefore be equal to the power of the one times the wisdom the other. To paraphrase Leibniz, we can say that the wisdom of the king can use any of the nobles’ degrees of power. Thus, the wisdom of the king is more important than his personal power and the safeguarding of the nobles’ power is more important than its growth through an exterior factor. The value of the Polish regime is therefore the product of two factors or the combination of two elements: The wisdom of the king and the power of the nobility. But, more generally, it is the Specimen as a whole that is the fruit of a twofold combination. The first aspect of the combination appears, as we have just discussed, in the linking of propositions. These are not deduced from each other in a linear manner. It is not from a proposition n −1 that we deduce a proposition n from which we could then deduce a proposition n + 1. If the deduction is obliged to resort to an earlier stated proposition, Leibniz’s deductions rest on many propositions at a time. In mathematical terms, we could say that deduction in the Specimen is not an injective application, but rather a surjective one. Thus, just as in mathematics where a surjective application makes it the case that all elements of the whole at the end are the image of at least one element at the point of departure and not of one and only one, a proposition n will be deduced from the conjunction of a proposition n − x and a proposition n − y. Beyond this first aspect of the combination by linking propositions, allowing that new propositions can be deduced from the combination of many others, we can also see a second aspect. This time it takes place at the level of the entire text. The evaluation of the candidates does not involve an algorithm for calculating the probabilities. Leibniz does not intend to make a political prediction (i.e., to evaluate the chances for each candidate to be elected). Instead, he wants to make a political prescription, to suggest who is to be elected, which candidate the nobles should elect. It is therefore not the chances of each candidate that are evaluated, but the reasons for electing them. It is for this reason that while combinatorial analysis is traditionally used in the calculation of probabilities, Leibniz uses it here

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as a decision appraisal procedure, i.e., to deduce the reasons and not the chances. It is what he calls “a type of mathematics with respect to the evaluation of reasons”, a type of mathematics that “has not been remarked enough by the logicians” (A I 13 551).

4 Combinatorial Analysis as a Decision Appraisal Procedure In the Specimen, Leibniz applies to politics the method that he expounded in 1666 in his De Arte Combinatoria. Each proposition plays what can be called the role of a simple element, and the combination offers the picture of the best possible king for Poland. It serves, in each of its successive conclusions, to compare each of the candidates with this picture in order to determine to whom it best corresponds. Belaval wrote in his Inititiation a` la philosophie de Leibniz that Leibniz’s rationalism is at the same time more modest and more ambitious than Descartes’. More modest since sensations, images, concepts can only express a reality which escapes direct intuition; there is no means for our knowledge to get to the foundation of things; our thought always remains in part blind; we lack adequate ideas; we cannot [. . .] reach up to first terms; the absolute is beyond our reach. But on the other hand, Leibniz’s rationalism is more ambitious and much more radical than Descartes’: what he loses in content, he gains, and much more, in form. We do not reach up to first terms: nevertheless, if we can be sure of the inclusion of a predicate in a subject, even though this predicate and this subject are the expressions of a superior and inaccessible reality, our knowledge will be absolutely certain. [. . .] The form of reasoning affords an absolute value: if God could abandon his intuition and successively think through the chain of consequences, this process would be identical, and not just analogous, to our deduction, though his ideas would not become identical to our own (Belaval 1993: 135).

Belaval’s remarks apply well to Leibniz’s political thought. In the case of the King of Poland’s election, Leibniz addresses the subject “King of Poland” in simple terms that are like its predicates. It is hence sufficient to analyze each of the subjectcandidates in order to compare their predicates with those of the subject King of Poland. The more predicates of “Kind of Poland” a candidate has, the higher the chance he has of being the best candidate, and therefore the electors should choose him over the others. Leibniz does not bother to do this, but it would have been possible to attribute a score to different candidates on the basis of the propositions considered and weighted. The propositions do not all have the same importance. Some are implied by others. We can take here for example the propositions related to age. The king should not be a child (prop. 28) or he would not be a person of well-known character (contrary to prop. 20), he would not reign himself (violating proposition 21), he would not be prudent or experienced (conflicting with proposition 20). Furthermore, if he is not a person of well-known character, all the other personal qualities, independent of age, cannot be evaluated. Proposition 28, that the king should not be a child, is therefore an insurmountable obstacle for the candidature of the Tsarevich, since it alone causes the other propositions to be either incompatible or undetermined. If it is not respected, proposition 28 is like a null factor.

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When dealing with propositions that do not reciprocally imply or contradict each other, for example propositions 24 and 25 (that the king must be just and prudent), the value of reasons is determined by their multiplication. Suppose candidate A has scores of 3 for prudence and justice while candidate B’s prudence is 4 and justice 2. In these two cases addition gives us 6 (3 + 3 and 4 + 2) and we cannot decide which is better. But that would be a methodological error since great prudence used for injustice, as is notably the case with Cond´e, is worth less than lesser prudence serving justice (4x2 is only 8, while 3x3 is 9). It is also the case that a large desire for justice is worth less than a small desire if the first is pursued imprudently and the latter prudently. Thus, each quality can present different degrees: We are in the order of more or less, i.e., of addition and subtraction; one is more or less prudent, more or less just, etc. But considered together, these qualities are multiplied. It is therefore necessary to be everything at the same time to be the best candidate, without having too much of one characteristic and not enough of another. Permitting a pun, we can say that Leibniz promotes the product “Neuburg”. It is a product of as many factors as there are decisive propositions in the Specimen, and these factors themselves are so many simples corresponding to predicates included in the subject “King of Poland”. But where does Leibniz find these simple terms? It cannot be through analyzing the concept “King of Poland”. If Leibniz analyzes the subjects corresponding to the different candidates into their different predicates, he cannot proceed in this way for the King of Poland. We could then accuse him of defining the King of Poland as one who should have the qualities of Neuburg. Then, by comparing the four candidates with the thus defined subject, he could conclude that Neuburg most resembles the King since Neuburg is the one who most resembles Neuburg. Leibniz must therefore explicitly give the origin of the predicates included in the King of Poland. This origin cannot be found elsewhere than in Poland itself: Leibniz thus prefers a relative but objective origin to an absolute but subjective one (relative because the best King of Poland is only conceived in connection with Poland and would likely not be the best for another kingdom, but objective because he only considers the facts that concern Poland, avoiding any interpretation). Leibniz adds at the end of the Specimen the obligations that are required for all candidates. The nobles of the kingdom had agreed on these obligations, as authorized by the King and the Queen and confirmed by Lubomirski, the King’s Grand-Marshal, ten years earlier, in 1659. To each of these conditions, Leibniz adds in parentheses the correspondent propositions in the Specimen’s demonstration. This addition testifies well to his concern to have these propositions recognized as objective and not subjective regarding Poland. Five steps are therefore necessary for Leibniz to solve the question of the King of Poland’s election: first, the analysis of Poland itself in order to find simple terms; second, from these simple terms about Poland, the inference of simple terms that through synthesis form the abstract portrait of the King of Poland; third, the analysis of the candidates in simple terms; fourth, the comparison between the simple terms found by the analysis of the candidates and the simple terms found by inference

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through the analysis of Poland; and last, the decision procedure permitting the estimation of the degree of conformity between each candidate and the model King of Poland.

5 Epilogue Even if it is difficult to generate some surprising effect in this way, we can nonetheless conclude our reflections with a historical narrative. We started with four candidates. Which one was finally elected? It wasn’t the Tsarevich nor Cond´e nor the Lorrainer, as we might have expected. But, despite his brilliant evaluation in Leibnizian terms, it was not Neuburg either. It was a fifth man: Michael Wisnowiecki, a Pole, who was elected, despite himself, by the Polish nobles who violated Leibniz’s 60th proposition according to which it is necessary to elect a foreigner in order not to stir up internal dissension. The Polish nobles would have four years to regret their choice of a king who did not know how to deal with the high nobility’s agitation and lost Podole and Ukraine to the Turks and Cossacks, respectively. But in their defense, and not to discredit the Specimen’s persuasive force, we can simply note that the voters had not read it. It could only be printed in the first half of June, which did not leave enough time for it to reach Warsaw, where on the 19th, the Diet elected Michael as King. Though, historically, a complete waste of time, the Specimen is of interest because it offers a new approach to the rationality of political decisions. It gives an example of reason trying to estimate the best possible decision in a given situation.

Notes 1. “L’interest et l’ambition/Travaillent a` l’´election/Du Monarque de Pologne./On croit icy que la besogne/Est avanc´ee; et les esprits/Font tantost accorder le prix/Au Lorrain, puis au Moscovite,/Cond´e, Nieubourg; car le merite/De tous costez fait embarras [. . .]” (Marty-Laveaux 1877, vol. V, pp. 66–67). 2. “J’ay fort approuv´e autres fois les pens´ees de feu Mons. Petty, qui faisoit voir l’application des Mathematiques aux matieres oeconomico-politiques. Moy mˆeme, dans un petit livre imprim´e l’an 1669 sans mon nom sur l’election d’un Roy de Pologne a` la priere d’un Ambassadeur qui devoit aller a` Warsovie, je fis voir, qu’il y a une espece de mathematique dans l’estime des raisons, et tantost il faut les adjouter, tantost les multiplier ensemble, pour en avoir la somme. Ce qui n’a pas est´e remarqu´e des Logiciens”. 3. “La place d’autruy est le vray point de perspective en politique aussi bien qu’en morale”. 4. “. . .qui Catholicus non est, ejus salus externa aut nulla aut difficilis. Nulla, si est Haereticus; difficilis, si Schismaticus”. 5. “. . .nec Democratiae exercitium in Polonia locum habere potest. Democratici Regiminis exercitium vix alibi quam in populo exiguo, unius fer`e civitatis muris incluso, ab omni retr`o memoria repertum, v. g. Athenis, Romae, Carthagine, Syracusis, etc.”. 6. “In Usufructuario, in Dictatore, in Inter-Regnantibus, in Rege quoque, qui ordinibus subset, summae potestatis exercitium est; jus scilicet temporale, quod in alterum, aut ipso temporis lapsu, aut implemento conditionis, aut voluntate alterius, recasurum est. Ita in Polonia

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7. 8.

9. 10. 11. 12. 13. 14. 15. 16.

J. Griard quoque Rex Summae Potestatis exercitium habet; nam tempore intercomitiali superiore caret. At durantibus Comitiis exercitium summae potestatis ejus, velut proprietati consolidatum, in pendenti est, et irritum reddi potest. Quod tamen ut Grotius rect`e distinguit, non ipsi Summitati Potestatis, sed modo habendi officit”. “Ita emmendanda Aristotelis definitio, ut omnibus formis quadret” (A IV 1 16). “Civis est, qui Regiminis particeps aut est, aut esset, nisi id ali`o (v. g. in Collegium optimatum aut Principis personam) translatum esset. [. . .] Tales in Republica Polonica sunt soli Nobiles, et quos Nobiles admittunt”. “. . .Athenarum aut Romae populus ad deliberationes in foro quotidie convˆenit”. “Electio non per sortem, sed rationalis esto”. “Caeter`um an Sortes rect`e Oraculi instar, et velut Signa voluntatis divinae, consuli possint, nihil ad Politicum; Theologi ea disceptabunt”. “Hinc patet, in eo qui Justus et Prudens sit, Virtutes omnes virtualiter, ut sic dicam, licet non formaliter, contineri”. We know Leibniz’s critique of super-ministers (“ministrissimes”), which he shares with Thomasius (Robinet 1994: 214–216). “. . .Rex poti`us senio qu`am pueritiae vicinior eligendus”. “Juvare autem esse multiplicare, et nocere dividere [. . .]”. “Fac aliquem esse sapientem ut 3, potentem ut 4, erit tota ejus aestimatio ut 12, non ut 7; nam quovis potentiae gradu sapienta uti potest. Imo in homogeneis, qui centena aureorum nummum millia habet, ditior est, quam sunt centum, quorum quisque habet mille. Nam unio usum facit; ipse lucrabitur etiam quiescendo; illi perdent etiam laborando”.

References Belaval, Y. 1993. Leibniz: Initiation a` sa philosophie, 7th ed. Paris: Vrin. Griard, J. 2004. Le meilleur r´egime selon Leibniz. Philosophiques 31: 349–372. Griard, J. Forthcoming. Leibniz’s social quasi-contract. British Journal for the History of Philosophy. Marty-Laveaux, Ch. 1877. Œuvres compl`etes de La Fontaine. Paris: Daffis. Robinet, A. 1994. G. W. Leibniz. Le meilleur des mondes par la balance de l’Europe. Paris: Presses Universitaires de France. Russell, B. 1937. A Critical Exposition of the Philosophy of Leibniz. London: Allen and Unwin.

Chapter 24

Declarative vs. Procedural Rules for Religious Controversy: Leibniz’s Rational Approach to Heresy Fr´ed´eric Nef

I propose to employ the conceptual contrast between procedural knowledge and declarative knowledge instead of the contrast stressed by Marcelo Dascal (2001, 2005) between soft and hard rationality in Leibniz’s thought. I propose to examine the interplay between declarative and procedural knowledge in Leibniz’s religious thought, and in particular Leibniz’s approach to heresy. If there is a domain where soft rationality is dominant, it seems that it would be such a field, governed by theological disputes apparently deprived of hard rationality. I will show that the opposite is true: Even in that sort of sub-domain, the two types of rationality are present. I shall define the Leibnizian concept of heresy and give some criteria and examples of its use in Leibniz’s writings. I shall consider in some detail his response to the classical question “Is heresy a crime?”,1 and analyze the strong connection between religious controversy in general and the philosophical treatment of heresies, showing that the contrast between declarative and procedural approaches to heresy illuminates some underestimated aspects of Leibniz’s religious thinking.

1 Reason, Rationality, Rationalism: A Reminder Reason is neither a faculty, nor an ideal, as a Kantian interpretation would falsely suggest. Reason is a concatenation of truths of two types: eternal truths (either dogmatic or mathematical ones) and positive truths (laws of nature). The mind can be helped by natural light in arts and sciences and by the light of faith (lumi`ere de la foi) in religion. Hence “natural light of reason” and “God’s divine revelation” are complementary: Almost every thing we have said is manifest through the natural light of reason, but what is the secret economy of divine council in order to restore man to his first condition can be known only through God’s divine revelation?2 It is thus necessary that sane reason, as a natural interpreter of God, be capable of judging the authority of those who claim to interpret the divine will before admitting them [to controversy], but once these [new] interpreters have demonstrated the legitimacy of their faith, reason must submit itself to the deference of faith.3 F. Nef Ecole des Hautes Etudes en Science Sociales, Paris, France M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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Is this a form of relativism, of double truth? Leibniz’s answer is the following: There is only one reason and not several ones – there is no “fragmentation of reason” in the various domains of rationality; reason does not change according to the field to which it is applied. Reason is naked and pure (la raison pure et nue, T, Discours Pr´eliminaire, § 1) and is distinguished from experience, unable by itself to unify the multiplicity of prismatic subfields. Faith in that respect is comparable to experience and miracles are similar to natural events in physical experience. But this experience specific to faith is transmitted by tradition, which has authority regarding controversies. Accordingly, there is then one reason and several fields of experience and so, regarding metaphysical principles and pure mathematics, pure reason is eventually independent from experience. Miracles are hard facts, even if they constitute an exception to the laws of nature, and faith is hard reason, when it is justified by reasoning. Therefore there is a hard theological rationality based partly on hard facts, even when they violate natural laws.

1.1 Faith Leibniz distinguished first fides and assensus and, second, simple faith without reflection (assensus rationibus destitutus; ST 52)4 and faith with reflection, justified by reasoning. He admits the existence of practical faith (Fides sive assensus practicus; ST 54). Christian faith has a public character: “I do not accept Christian faith on the basis of a private reason, but on the basis of the testimony of catholic church about miracles and martyrs, and of the perpetual tradition and scriptures kept inside the church” (A VI 4 2323; GR 27–30).5 Faith is both free and non-voluntary, since Leibniz refuses to admit an obligation to believe.6 Faith is a type of belief, but moreover, it is a combination of theories and practices: Religious beliefs supervene on rites. There is no real independence of religious beliefs, even if opinions determine the correctness or incorrectness of rites. Dogmas considered as beliefs can be either rational or irrational. Rational dogmas are either natural, like the belief in a divine providence, or revealed, like belief (or faith) in Jesus-Christ’s resurrection. Irrational dogmas can be either voluntary, like several heresies, or involuntary, like the errors of the pagans. True religion, revealed religion grounded on natural religion, is a set of practices or rites, completely distinct from false devotion (think about Moli`ere’s Tartuffe ou l’Imposteur, 1664). Faith supervenes on sincere dedication and we are right to maintain that Leibniz would have endorsed the contemporary anthropological thesis, according to which belief is supervenient on action.

1.2 Why Think that There is Soft Rationality? As elsewhere, Leibniz makes use of the presumptive argument (anybody is presumed innocent, until proven guilty) in theology. Presumption governs practice,

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and that makes possible the confusion between the pragmatic use of argument and the pragmatic nature of reason. Theology is a species of “universal jurisprudence” (Grua 1953; see also Riley 1996). Practical theology is almost equivalent to universal jurisprudence (Adams 1994: 195). The domain of practical theology is large, but not identical with the whole of theology. Jurisprudence is based on the logic of probability, but this latter is not soft rationality. For all these reasons, we may doubt that theology, as a whole, should be identified with a sort of soft rationality. Moreover, jurisprudence and law are precisely defined and distinguished concerning man and relative to God. We have to distinguish right (jus) and quasi-right (quasi jus), i.e., our right to expect something from God. Quasi-right is twofold: ex congruo and ex condigno. Ex congruo is distributive justice and through quasi-right ex condigno our merits are rewarded. Ex condigno is commutative; through quasiright ex condigno, the commutation between sins and redemption is realized and achieved. There is, therefore, one single rationality, one single reason, but several kinds of rationalism. If we draw a distinction between the connection of truths grounded on essences (reason), the universal and unique disposition of the human mind to use reason (rationality), and the application of rationality to a domain (types of rationalism), we can conclude that Leibniz’s rationalism is both logical (Couturat-Russell), jurisprudential (Grua), and theological (Baruzi). Each domain is an entrance into the system.

1.3 Je Viens a` la M´etaphysique It could be objected that there is at least a fourth entrance into the system, perhaps the main one: Metaphysics. But from the point of view of discussing Leibniz’s rationalism, metaphysics is identical to logic. True metaphysics, in so far as it is distinct from verbal metaphysics, is not different from logic (ars inveniendi); moreover, metaphysics is identical to natural theology, in virtue of the convertibility between truth and goodness.

2 Declarative vs. Procedural: Definition Let us define in an informal way (by an enumerative definition, not a stipulative one) what is declarative and what is procedural. To give the internal structure of a database, to axiomatize a body of knowledge, is declarative. “To know that p”, “to infer q from p”, “to expand if p, then q to: if p, r . . . then q” are typical expressions or moves of declarative thinking. On the contrary, to know how to do something is relative to procedural strategies in various domains (war, cooking, cycling, etc.). To refute p, to give an argument in favor of p, to decide who is right and who is wrong, are highly representative of procedural thinking. Declarative knowledge is mainly logical, metaphysical and geometrical; usually based on deduction, it

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corresponds to a dogmatic style. Procedural thinking is mainly juridical, theological. The disputational structure of argumentation is symptomatic of procedural thinking.7 Leibniz applies his formalist and anti-intuitionist theoretical principles in all fields of his philosophy: “I hold that in order to reason with evidence everywhere, one must keep some constant formality. There will be less eloquence and more certainty”.8

3 The Problem of Heresy Heresy is a dogmatic error inside Christian theology defined by the Church in Leibniz’s sense. Leibniz does not list new heresies; he accepts the list established by the Councils’ records and decrees and considers, for example, Marcionism as a heresy (A VI 4 2533). Leibniz endorsed Johachim of Fiora’s condemnation by Petrus Lombardus who declared him a heretic (A VI 4 2578). The history of heresies (haeresi historia) is a part of theology (GP 1 72) and Leibniz accepted the distinction between haeretica, schismatica, fanatica (Letter to Thomasius; GP 1 23). These few examples show that Leibniz took the heuristic power of this apologetic concept very seriously. Heresy is relative to vraie religion (Moses, Jesus-Christ, Mohammed), whereas in false religion there are no heresies (Zoroaster, Brahma) (D I 678ff.). Thus, some religious doctrines are false but nonetheless not heretic. For example, the Stoic doctrine of the world’s soul is a bad doctrine9 – but not a heresy. More generally, naturalism, of which Stoicism is a kind, is not a heresy (GP 7 333–334). It is a philosophical error but not a heretical doctrine. Leibniz’s use of the concept of heresy exhibits the same duality of conservative and innovative strategies as elsewhere in his system. Thus, heresy is defined as a will to reform radically the Church10 and, at the same time, a traditional heresy can be mentioned in order to show that a philosophical doctrine is mistaken.11 Leibniz adds a new category: half-heretics. A half-heretic is something more than a schismatic (potentially heretic). We face, therefore, a sort of continuum: schismatic, half-heretic, material heretic (i.e., involuntary heretic), formal heretic (i.e., voluntary heretic). In this way, Leibniz considers the French clergy as half-heretic and sees a connection between this fact and some epistemological doctrines of the Cartesians considering antiquity as a source of certitude, but not Scholastic and casuistic: These are the nice principles of some Sorbonnists or other figures of France’s clergy, which are considered half-heretic among us. For, in this way the door is open for anyone who dares to oppose what is done in the Church and who despises its judgments [. . .]. This is why he will accuse [. . .] the Scholastics of sophistry [cf. Descartes, Arnauld] and the Casuists of license [cf. Pascal]. So that it is not he that holds these people to be heretics – they do all that is needed for that. And if the Pope dared to excommunicate them at our time, and if they got some secular support, they would remain within the schism, as Luther and Zwingli: unless they would abandon the bad principle that reduces infallibility to antiquity [cf. Pascal, Pr´eface au Trait´e du Vide], and separates it from the modern practice.12

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Leibniz usually takes for granted the distinction between material and formal heresy. Concerning material heresy, he was accused of being too indulgent when he did not refuse salvation to material heretics. Leibniz’s solution to the classical problem of the legal nature of heresy derives from this distinction between material and formal heretics (see GR 210–212).

3.1 Heresies are Also Philosophical Errors: Five Examples Mohammedanism (or “destin a` la turque”) is an involuntary irrational dogma of absolute divine omnipotence negating human freedom (opposed to the belief in divine providence), supervening on laziness and arrogance. Manichaeism or Gnosticism is a voluntary irrational dogma supervening either on libertinage or the free spirit adepts or ingratitude (the goodness of creation is ignored). We can note that intellectual vices (heresies) supervene on moral vices: non-observance, effrontery, dissoluteness, oblivion. Three other heresies exhibit deeper conceptual confusions. Arians believe the son of God is only the first creature (Ariani vero Filium Dei volunt esse primam creaturam; ST 34; A VI 4 2367). In that case, the cult of Jesus-Christ is unreasonable, as there is confusion between creature and creator. Photinians believe Jesus-Christ is only a man (Photiniani autem ex simplici homine faciunt Filium Dei; ibid). In that case, the cult of Jesus-Christ is pagan. Socinians believe no cult of Jesus-Christ is necessary. Socinianism is very close to Mohammedanism. The last one is the more consistent (rectiusque ex ipsorum hypothesibus; ibid.), but unreasonable: Logical consistency is only a condition for reasonability. Heresy is both contrary to reason and to virtue.

3.2 Are Heresies Crimes? Leibniz uses the distinction between material and formal heresy. The first is caused by accidental ignorance, the second by malicious disobedience. Only the second has to be punished. But the punishment must be used only for curing the depraved will and not as a commutative retaliation. Leibniz insists that if nobody can be a saint and formally a heretic at the same time, we cannot completely exclude the possibility of a partial material heresy in a saint if, for example, an opinion became unorthodox after his death. As “the intellect corrects the will, and the will corrects the intellect”,13 it is not enough to inflict a punishment on the heretic; it is also necessary to demonstrate to him the falsity of his heresy. But we know that true demonstrations are not frequent and that the risk of propagation of formal heresies through passive infection, as in an epidemy, is enormous.14 Leibniz thinks that, in such a case, the punishment of the charismatic leaders must be more severe, because unreflectively joining formal heresy is, in a certain way, close to material heresy (a point on which Leibniz was vehemently criticized by institutional theologians). In the controversy with Pellisson,

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Leibniz remarked in 1690 that the Catholic theologians affirm that the criteria of salvation for material heretics are “the internal marks of a movement of the Holy Ghost”.15 Leibniz answers that these motives cannot be explained, that we can only have probability (vraisemblance) with such “marks”, and that a man cannot be excommunicated if there is only a probability that his will is wrong. On this point, too, Leibniz was judged too liberal. The main point is that Leibniz affirms that the real criterion is obedience and that opinions are not voluntary: If the material heretic is disposed to change his opinion, when his superiors say he is wrong, it is enough.16

3.3 Procedural Aspects of the Fight Against Heresies Leibniz condemns heretics because they attempt to destroy charity in the Church and among men. But if we use force (Inquisition) or treachery (like some Jesuits used or use to do), we will cause a rebellion of heretics and the situation will be worse, because the loss of charity among men will be greater (religious wars, revolts of fanatics and enthusiasts); heretics will look for supreme sacrifice, which they will falsely and outrageously call “martyrdom” (martyrium) and in that case, they will be close to winning (think of terrorists’ strategies). What is, then, the winning strategy for the wise men? Leibniz thinks that a balance between toleration and force must be firmly kept, and that the rules of weighing pros and cons are not known in that case, even if we know, for example, that in general anathemas, intimidation and excommunication are useless (Cf. Pichler 1870). If there is no unique winning strategy against heresies, philosophy could be used in order to prevent the formation of such heresies (a prophylactic use of reason, opposed to a curative one, which is in the power of the Church). In that respect, the fight against philosophical misconceptions cannot be separated from the general fight against heresy: “[. . . I would have the courage to assure that no solid objection against the atheists, the Socinians, the naturalists and the Skeptics will ever be raised without the constitution of this philosophy”,17 i.e., a philosophy opposed to the Cartesian conception of matter. We have insisted on the fact that Leibniz wanted to keep a balance between opinions, and that heresies can be considered as exaggerations of opinions. Does Leibniz consider heresy as simplification? The use of the expression “exaggeratedly wrong dogma” (dogme outr´e) in Leibniz’s writings seems to imply the opposite.18 Leibniz characterized heresy as “un dogme outr´e” several times in the Th´eodic´ee. But Leibniz in fact does not adopt this view and his characterization has to do with the procedural approach to religious controversies. “Outr´e” does not mean “false”, but denotes a bad move in a discussion. According to Leibniz, Descartes’ doctrine of the essence of body is potentially schismatic. The Systema Theologicum is almost silent on heresies, as it is an irenic writing, but Leibniz denounces the metaphysical origin of a potential theological schism concerning the rationalization of the Eucharist dogma. The Cartesian metaphysical error is to consider that the essence of bodies is only extension. This

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erroneous philosophical opinion has theological consequences. To begin with, there would not be, in that case, substantial change in the Eucharist, and this is potentially unorthodox.19 Next, as Cartesians cannot believe something metaphysically impossible (i.e., implying a logical contradiction), they cannot believe in transubstantiation.

3.4 The Cannibal Case Concerning resurrection, Leibniz examines a casus: When a cannibal is resurrected, what will remain of his body, as parts of it will have joined the owners of their original wholes? Solution: We must know that not everything which has belonged to a body is necessary to the essence of this body.20 The justification of this solution is the following: There is in each body a “flower of substance” (alchemical vocabulary?) and the cannibal will return the flowers of substance belonging to eaten persons, while keeping his own substantial flower. The cannibal can return flowers of substance without losing his own.

4 Law and Theology: Universal Law is the Same for God and Man Law, according Leibniz, is a set of presumptions (v´erit´e par provision and not conjecture), probabilities and prejudices, founded on particular reasons. Theology is a set of demonstrations, revelations and testimonies of tradition, grounded on general reasons. Therefore, we could say that theology is harder than law (if we maintain this way of speaking). We prefer to affirm that there is a declarative element in theology, exactly as there is a procedural element in law. When Leibniz gives a theory of legal conditions, he is working on the declarative side of law, its conditional structure. In the context of the criticism of Antitrinitarianism, Leibniz makes use of a general strategy: To demonstrate the non-repugnancy of mysteries and dogma (the Trinity, the Eucharist) with metaphysical and logical necessity (Letter to Loeffler; D I 17–21). This method is presumptive and therefore close to jurisprudence. But there is a difference between explaining the mysteries of religion and explaining civil laws: the first is not necessary, whereas the second is. In order to terminate a social conflict, it is necessary to explain the laws, but when we arbitrate a religious controversy on dogmatic matters, the explanation of the mysteries is not necessary.21 The more universal is religion, the closer it is to natural law; a universal religion is therefore identical to natural law: And although divine Reason surpasses infinitely our [reason], one can say without impiety that we share reason with God, and that it constitutes the links not only of all society and of friendship among men, but also of God with man. [. . .] Reason is the principle of a universal and perfect religion, which one can justly call the Law of nature. [. . .] the Law of nature is the Catholic religion (Leibniz’s underlining).22

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Among the main heresies and schisms fought by Leibniz, we find as particularly representative of Leibniz’s natural theology: (i) Socinian heresy, (ii) Calvinist predestinationism, and (iii) Antitrinitarian heresies. Leibniz defends the dogma of incarnation, the harmony between human freedom and divine omnipotence and also, as do Whitehead and Peirce, the relational nature of God. In those cases, heresy or schism look simpler than the true doctrine of the universal Church, but Leibniz shows that these deviations are more complex from the point of view of Reason, in so far as they lead to very intricate antinomies.

5 Procedural vs. Declarative Method in Theological Controversies: Leibniz vs. Bayle in the Th´eodic´ee, Discours Pr´eliminaire Leibniz characterizes Bayle as a partisan of the declarative or mathematical method in philosophical and religious controversies. He translates Bayle’s assertions in procedural guise. We could put the two ways of rational discussion in front of each other and give a procedural translation of declarative language (T, Discours pr´eliminaire, §§75–82). Leibniz insists that he had commented extensively to Bayle in §75–76 of the Preliminary discourse: I was especially at pains to analyze this long passage where M. Bayle has put down his strongest and most skillfully reasoned statements in support of his opinion: and I hope that I have shown clearly how this excellent man has been misled (§77).

Unfortunately, the meaning of the text is a bit masked, because Leibniz put his comments in brackets and it is necessary to reconstruct the dispute by pulling apart Bayle’s bold assertions and Leibniz’s incidental objections. According to Bayle, religious controversies have to conform themselves to the rules of deductive method: Every philosophical dispute assumes that the disputing parties agree on certain definitions [. . .] and that they admit the rules of Syllogisms, and the signs for the recognition of bad arguments. After that, everything lies in the investigation as to whether a thesis conforms mediately or immediately to the principles one is agreed upon (§75).

Definitions and syllogisms characterize the Aristotelian demonstrative method in the Second Analytics. It is well known that Leibniz himself prized very much the deductive method he defended against the Cartesians, but he refused to apply it mechanically to disputes or controversies. However, it is not a decisive reason for contrasting soft (disputational) and hard (deductive) rationality. I think that the procedural vs. declarative contrast is more relevant here, because there is no value judgment in this distinction, whereas the opposition between soft and hard could turn curiously negative towards what is called “soft”. Leibniz thus objects: “This would be desirable, but usually it is only in the dispute itself that one reaches such a point, if the necessity arises which is done by means of the syllogisms of him who makes objections” (ibid.).

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Bayle firmly relies on some rules of the deductive Aristotelian-Euclidean method, whereas Leibniz considers the dispute game as a succession of moves, in which some of these rules could be applied. For example, he puts “advanced by the opponent” in brackets after Bayle’s rule. Whereas Bayle thinks in an absolute way, Leibniz thinks in a contextualist one. He refused, as always, to separate methodology and real controversy. Bayle gives some precisions: “whether the premises of a proof are true [. . .] whether the conclusion is properly drawn; whether a four-term Syllogism has been employed; whether some aphorism of the chapter de oppositis or de sophisticis elenchis, etc., has not been violated” (ibid.). But Leibniz judges these precisions pedantic and useless: “It is enough, putting it briefly, to deny some premise or some conclusion, or finally to explain or get explained some ambiguous term” (ibid.). Bayle considers that a player won the game when he fulfilled these conditions: “One comes off victorious either by showing that the subject of dispute has no connection with the principles which had been agreed upon [. . .]” (ibid.). Here Bayle judges that to win is to be consistent with principles agreed upon explicitly before the dispute. He sees no real difference between a demonstration and a dispute, which both consist in deriving consequences from postulates. Leibniz translates this declarative description into a procedural description: “that is to say, by showing that the objection proves nothing, and then the defendant wins the case” (ibid.). However, the translation aforementioned goes both ways. When Bayle completes the sentence with a procedural equivalent: “or by reducing the defender to absurdity” (ibid.), Leibniz translates it in demonstrative mode: “when all the premises and all the conclusions are well proved” (ibid.). Concerning “the aim of the dispute”, Bayle and Leibniz deeply disagree. Bayle believes that there is one single aim of the dispute the victory of one of the participants: “The aim in disputes of this kind is to throw light upon obscurities and to arrive at self-evidence” (T 116). Leibniz, however, sees very well that the aims of opponent and defendant are not the same: “It is the aim of the opponent, for he wishes to demonstrate that the Mystery is false; but this cannot here be the aim of the defendant, for in admitting Mystery he agrees that one cannot demonstrate it” (ibid.). Bayle and Leibniz, accordingly, do not evaluate “victory” in the same manner. Bayle affirms that victory belongs to the one who has clear ideas: This leads to the opinion that during the course of the proceedings victory sides more or less with the defender or with the opponent, as to whether there is more or less clarity in the propositions of the one than in the propositions of the other (T 117; GP 6 94).

Very impressively, Leibniz opposes to this Cartesian internalist epistemology a social-externalist conception of the dispute: That is speaking as if the defender and the opponent were equally unprotected; but the defender is like a besieged commander, covered by his defense works, and it is for the attacker to destroy them. The defender has no need here of self-evidence, and he seeks it not; but it is for the opponent to find it against him, and to break through with his batteries in order that the defender may be no longer protected (T 117; GP 6 94).

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Bayle attributes the victory in the dispute to the one who proves that his opponent has fallen into obscurity: “Finally, it is judged that victory goes against him whose answers are such that one comprehends nothing in them, [. . .] and who confesses that they are incomprehensible” (§76). However, this criterion of victory seems subjective to Leibniz: “It is a very equivocal sign of victory, for then one must needs ask the audience if they comprehend anything in what has been said, and often their opinions would be divided” (ibid.). Even when he recognizes the importance of rules concerning conceptual distinctions, “[t]he order of formal disputes is to proceed by arguments in due form and to answer them by denying or making a distinction” (ibid.), Leibniz thus reveals a contradiction in Bayle’s thought between criteria of clarity and the very nature of theological disputes: It is permitted to him who maintains the truth of a Mystery to confess that this mystery is incomprehensible; and if this confession were sufficient for declaring him vanquished there would be no need of objection. It will be possible for a truth to be incomprehensible, but never so far as to justify the statement that one comprehends nothing at all therein. It would be in that case what the ancient Schools called Scindapsus or Blityri (Clem. Alex., Stromateis, 8), that is, words devoid of meaning (ibid.).

In the passage above, Leibniz is, therefore, making a very useful distinction between two types of incomprehensibility.23 The first is simply identified as void of content (blitiri); the second is the mark of mystery. As theological disputes are concerned with mysteries, criteria of comprehensibility cannot be applied without qualification. A little later (§78) Leibniz contrasts between Bayle’s method of evidence and the lack of evidence proper to mysteries: M. Bayle continues thus in the same passage: ‘For this result we need an answer as clearly evident as the objection’ [. . .] I have already shown that it is obtained when one denies the premises, but that for the rest it is not necessary for him who maintains the truth of the Mystery always to advance evident propositions, since the principal thesis concerning the Mystery itself is not evident.

There is a last difference between the two religious thinkers: Bayle has an offensive vision of dispute, Leibniz a defensive one. Bayle says: He [the defeated, i.e., the defendant] is condemned thenceforth by the rules for awarding victory; and even when he cannot be pursued in the mist wherewith he has covered himself, and which forms a kind of abyss between him and his antagonists, he is believed to be utterly defeated, and is compared to an army which, having lost the battle, steals away from the pursuit of the victor only under cover of night (ibid.).

Whereas Leibniz explains: Matching allegory with allegory, I will say that the defender is not vanquished so long as he remains protected by his entrenchments; and if he risks some sortie beyond his need, it is permitted to him to withdraw within his fort, without being open to blame for that (ibid.).

We must conclude that Leibniz was aware of the distinction between procedural and declarative uses of rationality; the terms of this opposition cannot be identified with a distinction between different fields of rationality, and neither are some parts of Leibniz’s thought harder or softer than others – a distinction Dascal stresses when he correctly says that soft rationality is pervasive in most parts of Leibniz’s writings.

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In nearly every field and subfield, Leibniz was familiar with the interplay between those two varieties of reason. In that sense, Leibniz’s rationalism is both procedural and declarative and his model of the judge of controversies as a wise man, inspired by charity and prudence, could still be a model for our times. Acknowledgments I would like to thank Marcelo Dascal for his very careful and precious help.

Notes 1. The key text is: “Sur Thomasius. Utrum haeresis sit crimen?” (GR 210–212). 2. “Et quidem quae hactenus diximus [God does not want the death of the sinner, because he is perfectly good] fere omni ipso ex rationis lumine manifesta sunt; et quae fuerit in restitudendis hominibuis divini consilii arcana oeconomia a solo DEO relevante dicsi potuit” (ST 16; A VI 4 2361). 3. “Proinde necesse est rectam rationem tanquam interpretem DEI naturalem judicare posse de auctoritate aliorum DEI interpretum, antequam admittantur, ubi vero illi semel personae suae legitimae fidem, ut ita dicam fecerunt, jam ratio ipsa obsequium fidi subire debet” (ST 20–22; A VI 4 2362). 4. “[. . .] consistat in eo mentis statu quo fit ut qui eum habent perinde affecti ataque ad agendum patiendumque compositi sunt ac illi qui rationum sibi sunt conscii , imo ad aliquando efficacius”. 5. “Tametsi fides Christiana non ratione privata, sed testimonio Ecclesiae Catholicae scriptisque in ecclesia conservatis [. . .]”; “holicae a miraculis et martyriis accepto, et traditione perpetua Specimen demonstrationum catholicarum seu apologia fidei ex ratione”. 6. “D EFINITIONES 1) Obligatio: necessitas imposita sub poenae justae metu; 2) credere est conscium esse rationum nobis persuadentium; 3) in potestate sunt, quae fiunt si velis; 4) metus est voluntas evitandi; 5) conscientia est nostrarum actionum memoria. E XPERIMENTUM : Non est in potestate nostra, nunc meminisse alicujus rei praeteritae aut non meminisse. P ROPOSI TIONES : I. Conscientia non est in potestate; [. . .] II. Credere aliquid aut non credere non est in potestate; [. . .] III. Eorum quae non sunt in potestate nulla obligatio est; [. . .] IV. Nulla est obligatio credendi [. . .]” (De obligatione credendi; GR 181–182; DA 44–46). 7. Some examples in the field of religious controversy may be given. Declarative: Averro¨es (Decisive Discourse, first level), Bayle (in Th´eodic´ee), Luther (The Bondage of the Will). Procedural: Averro¨es (Decisive Discourse, second level), Leibniz (in Th´eodic´ee), Erasmus (De Libero Arbitrio). 8. “Je soutiens qu’`a fin de raisonner avec e´ vidence par tout [my emphasis], il faut garder quelque formalit´e constante. Il y aura moins d’´eloquence et plus de certitude” (GP 4 292–293). 9. “Cette mauvaise doctrine est fort ancienne et fort capable d’´eblouir le vulgaire” (T 55; GP 6 54). 10. “[. . .] ce sont des visionnaires . . .ils ne sont gu`ere meilleurs que les h´er´etiques, puisqu’ils ont la pr´esomption de r´eformer la Ste Eglise” (A VI 4 2223). 11. “M. de Soissons remarque que de faire consister la nature de l’homme en ce qu’il pense est une des h´er´esies des trois premiers si`ecles” (A VI 4 2117). This passage is excerpted by Leibiz from a review of Huet’s Censura Philosophiae Cartesianae (Paris in 1689; French translation in C. Poulouin (ed.), Nouveaux m´emoires pour server a` l’histoire du cart´esianisme, 1996). 12. “Ce sont l`a les beaux principes de quelques Sorbonistes ou autres supposts du clerg´e de France, qui passe pour demi-h´er´etique parmi nous. Car ainsi la porte est ouverte au premier venu qui ose s’opposer a` ce qui se fait dans l’Eglise et qui m´eprise ses jugements [. . .]. C’est pourquoi il accusera [. . .] les Scholastiques de sophistique [cf. Descartes, Arnauld] et les casuistes de licence [cf. Pascal]. De sorte qu’il ne tient pas a` ces gens-l`a d’ˆetre h´er´etiques, ils font tout ce

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13. 14. 15. 16. 17.

18. 19. 20. 21. 22.

23.

F. Nef qu’il faut pour cela. Et si le pape les osoit excommunier dans le temps o`u nous sommes et s’ils trouvoient quelque appuy seculier, ils demeureroient dans le schisme comme Luther et Zwingle: a` moins que de renoncer a` ce mauvais principe qui r´eduit l’infaillibilit´e a` l’antiquit´e [cf. Pascal, Pr´eface au trait´e du Vide] et qui les s´epare de la pratique moderne” (Dialogue entre Poliandre et Theophile; A VI 4 2225; my additions and italics). “Intellectus emendat voluntatem, et voluntas emendat intellectum” (ST 211). “Schisma inter maxima est orbis et Ecclesia mala, et qui ejus autor est summo se scelere obligat; qui vero in schismate haeret culpa sua gravissime peccat” (Positiones; A VI 4 2353). “[. . .] les marques int´erieures d’un mouvement du St Esprit”. Lettres de Leibniz et Pellisson, IV, Second m´emoire (D I 702–707; DA 315–321). “[. . .] illud confirmare ausim, Atheis, Socinianis, Naturalistis, Scepticis nunquam nisi constitutam hac philosophia solide occursum iri” (Letter to Thomasius, 30 April 1669; GP 1 26; BO 115). See Newman’s (1846) notion of the historical development of dogmas. “Aversio a Catholicae Ecclesiae dogmatibus nascitur” (ST 200). “[. . .] verum sciendum est non illud ad essentiam unius cujusque corporis pertinere quod ei unquam unitum fuit” (ST 300). Remarques sur le livre d’un antitrinitaire anglais (D I 24–26). “Et quoique la Raison divine surpasse infiniment la nˆotre, on peut dire sans impi´et´e que nous avons la raison commune avec Dieu et qu’elle fait non seulement les liens de toute la soci´et´e et amiti´e des hommes [philanthropia], mais encore de Dieu et de l’homme [theophilia]. La Raison est le principe d’une religion universelle et parfaite qu’on peut appeler avec justesse la loi de la nature. La loi de la nature est la religion catholique” (Parall`ele entre la Raison originale ou de la Nature, le Paganisme ou la corruption de la Loi de la Nature, la Loi de Mo¨ıse ou le Paganisme r´eform´e et le Christianisme ou la Loi de la Nature r´etablie; BA 352, 354, 355). For a detailed analysis of Leibniz’s handling the problem of the incomprehensibility of the mysteries of faith, with special attention to the passages here discussed, see Dascal (1987: 93–124).

References Leibniz Baruzi, J. 1909. Leibniz. Avec de nombreux textes in´edits. Paris: Librairie Bloud. Correspondance avec Thomasius. French translation by R. Bod´eu¨ s. Paris: Vrin, 1990 [= BO]. Systema Theologicum (= Examen religionis christianae; A VI 4 2355–2455). French translation by M. Emery, Exposition de la doctrine de Leibniz sur la religion. Paris, 1819 [= ST]. Essais de Th´eodic´ee (GP 6 1–487). Edited by A. Farrar, translated by E.M. Huggard; La Salle, IL: Open Court, 1985 [= T].

Other Authors Adams, R.M. 1994. Leibniz. Determinist, Idealist, Theist. New York: Oxford University Press. Baruzi, J. 1907. Leibniz et l’organisation religieuse de la terre. Paris: Felix Alcan. Dascal, M. 1987. Leibniz. Language, Signs and Thought. Amsterdam: John Benjamins. Dascal, M. 2001. Nihil sine ratione → blandor ratio. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler. Leibniz Kongress), vol. 1. Berlin: Leibniz Gesellschaft, pp. 276–280. Dascal, M. 2005. The balance of reason. In D. Vandervecken (ed.), Logic, Thought and Action. Dordrecht: Springer, pp. 27–47.

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Grua, G. 1953. Jurisprudence universelle et th´eodic´ee chez Leibniz. Paris: Presses Universitaires de France. Pichler, A. 1870. Die Theologie des Leibnizs, aus gedruckten und ungedruckten Quellen mit besonderer R¨ucksicht auf die kirchlichen Zust¨ande der Gegenwart. M¨unchen: J. C. Cotta. Newman, J.-H. 1846. An Essay in the Development of Christian Doctrine. London: J. Toovey. Riley, P. 1996. Leibniz’s Universal Jurisprudence. Justice as the Charity of the Wise. Cambridge, MA: Harvard University Press.

Chapter 25

Apology for a Credo Maximum: On Three Basic Rules in Leibniz’s Method of Religious Controversy Mogens Laerke

1 Introduction Throughout his life, Leibniz was involved in religious controversy. As an adolescent in Lutheran Leipzig he reads Laurentius Valla and Martin Luther (GP 3 143, 481; Baruzi 1907: 192, 238). Arriving at the Court in Mainz under the protection of the Catholic Baron von Boinebourg, he has the opportunity to discuss the positions of for example the Socinians or to speak in person with leading Roman Catholic controversialists like the Wallenburch brothers. The sketches for the Demonstrationes catholicae testify to these controversialist occupations in the late 1660s and early 1670s (A VI 2 518–535). Later, the ecumenical project of reuniting the Christian Church is at the center of his involvement in the religious debates of his time. These activities are accompanied by extensive reflections on the nature of religious controversy as such and on the method of conducting them. This is not surprising, as, according to Leibniz, the lack of an adequate method for discussing religious matters is one of the primary reasons for schism and religious dispute: “[. . .] the way of disputation or discussion is ineffective, as long as there is no judge or regulated form that the disputing parties are obliged to follow exactly” (A I 2 11). Leibniz also writes that we could very well establish the truth of religion and end many of the controversies that divide people and cause so much evil for the human race, if we would meditate with order and proceed in the way we ought to (GP 3 192).

One of the first developed texts on this method is the extraordinary Commentatiuncula de judice controversiarum from around 1670 (A VI 1 548–559). His letters to Thomas Burnett from the late 1690s bear witness to similar preoccupations in the mature years. In this chapter I give an account of three basic normative rules in Leibniz’s theory of ordered religious controversy.

M. Laerke University of Chicago, Chicago, USA

M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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2 The Need for a Method of Controversy In a Promemoria zur Frage der Reunion der Kirchen sent to Ernst Von HessenRheinfels in November 1687, Leibniz points to the regrettable experience that religious controversies constantly degenerate into disordered disputes that often lead to war, persecution and mutual excommunication. Everybody follow their own rules; they do not listen to the others; they enter interminable arguments constantly straying from the primary object of discussion. This is the “vice of confused disputes” (A VI 2 387–389).1 As Leibniz puts it: “One gets lost in a labyrinth of disputes” (A VI 4 2249). For this reason, controversies are “often only good to turn spirits sour and to give rise to new controversies” (A I 5 11). Leibniz speaks of a “method of the ignorant”, sometimes of “a certain spirit of contradiction” (FC 3 86; A VI 4 2250). In other words, when it is not simply a question of outright abuse of religion, internal schism and religious dispute are often a problem of methodology. Consequently, the first condition for overcoming religious dispute is “a method, which will surely always terminate them, following the principles of an incontestable prudence” (A VI 4 2260). In order to overcome sectarian dispute and transform it into an ordered controversy one must first of all proceed with moderation: “There must be limits and moderation in everything” (D V 355); “nothing renders a dispute more recommendable than the moderation of those who dispute”. An ordered controversy must function in such a way, he writes, that “the nature of the dispute obliges people to speak moderately in spite of themselves” (K IV 430). According to this extraordinary formula, moderation does not simply concern the behaviour of the individual participants, but must also work in spite of the participants. Thus, moderation must be inscribed in the form of controversy itself: Those who fight would have their arms tied up so much that they would not be able to move except in an ordered and measured way, and they would be drawn forward by machines that would carry everything out, like in naval combat where the movement of the vessel and the force of the canon give the law to those who fight (FC 1 83).

In this respect, the methodus disputandi for religious controversy proposed by Leibniz is similar to the method for scientific controversy he tried to elaborate under the name of a characteristica universalis, which would allow solving all disputes on natural things through simple calculation: Calculemus! (GP 7 188–200; GP 3 605). Both scientific and religious controversy must be governed by constraining rules. It is, however, not the same type of rules in the two cases. In religious controversy, in order to find an appropriate model, we must turn to the procedural rules governing a court of law. Leibniz compares it to a tribunal where “the judges and rulings oblige those who dispute to observe a certain order” (FC 2 32; A VI 4 575, 577, 2162). The establishment of this softer logic (blandior ratio) of jurisprudence implies the use of a calculus of probabilities and an elaborate logic of presumptions (Dascal 2001; Adams 1994: 192–213). Leibniz gathers all this under the heading of a “balance of reason”, an intellectual instrument for pondering or weighing reasons (GP 7 521). The metaphor is carefully elaborated in the Commentatiuncula de judice

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controversiarum from 1669–1671, but is present in numerous texts throughout his work (A VI 1 548–559; A VI 4 2250, 2259; C 210–214, 337–339; GP 3 191–194; GP 5 192, 446–448; GP 7 187–188, 521; FC 2 32, etc.; Dascal 2005). But how does this juridical balance of reason present itself specifically in relation to religious controversy, and what original principles does it give rise to? It goes without saying that I have no pretension of giving an exhaustive answer to this question, but I can point to some of the fundamental elements implied by the method. I will point out how Leibniz’s method for religious controversy is governed by three basic conceptions or rules of conduct: First, a practical or procedural rule, which is defined as a juridical version of the golden rule, namely a rule of charity moderated by prudence (caritas prudentis). One could here speak of a Pauline rule of love adjusted to fit the requirements of law and justice. Secondly, an Augustinian conception of dogma that we can call “permissive” – but without the pejorative connotations that this term often has among moralists. I would define it as Leibniz’s credo maximum, because it is strictly opposed to the minimal dogmatics proposed by the partisans of a credo minimum in the 17th century. Finally, I believe that this conception of a credo maximum acquires a particularly strong and obligatory meaning through the special notion of piety as Amor Dei super omnia, which is expressed in Leibniz’s adoption of the Jesuit slogan Ad majorem Dei gloriam. These three conceptions, Pauline, Augustinian and Jesuit, are basic “moderators” in Leibniz’s normative theory of “moderate” religious controversy.

3 The Golden Rule The rule of rules that must govern all controversy, and not only religious controversy, is the rule of reciprocal charity often termed “the golden rule”: “Quod tibi non vis fieri, alteri ne feceris” – “Do not do unto others, what you do not wish others do unto you” (Matthew 7:12; Tobias 4:15; Luke 6:31). As it has been noticed many times by a number of commentators, Leibniz very often appeals to this rule, and in a variety of senses, from the Nova methodus discendae docendaeque jurisprudentia of 1667 to his discussions of Christian Thomasius’s theory of natural right in the correspondence with Bierling around 1712 (A VI 1 260–354; D V 384–389). According to Leibniz, this rule is fundamental to both jurisprudence and politics, but also to true theology, simply because jurisprudence and theology “conspire,” as Leibniz explains as early as the Nova methodus (A VI 1 294). Appealing to the golden rule in relation to religious controversy is far from original at the time. Leibniz shares this appeal with dogmatic minimalists like Sebastian Castellio and Hugo Grotius, who assimilate the golden rule to St. Paul’s idea of a “law written in the hearts of men” (Romans 2:15; Castellio 1981: 54; Grotius 1991: 318). It is also akin to the sunkatabasis, “capacity of taking in” or “wise tolerance” to which Erasmus appeals in his De amabili concordia ecclesiae from 1533 (Erasmus 1992: 836–837). Similarly, charity is the most important precept in Spinoza’s notion of true religion as presented in the Tractatus theologico-politicus from 1670

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(Spinoza 1999: 464–481). If we follow this principle, says Spinoza, “no room is left for controversies in the Church” (Spinoza 1999: 474–475). In other words: appealing to this rule in order to formulate a method for resolving religious controversies is perfectly commonplace in the philosophical and theological discourse of the 17th Century. In the Christian tradition, however, the golden rule is first of all a rule of love, of caritas. This is not Leibniz’s full position on the question. In a passage in the Conversation du Marquis de Pianese et du P`ere Emery that has been highlighted by Marcelo Dascal, the use of the golden rule is conceptualized as an obligation to “go all the way round the thing” or to “examine the pros and cons with equal application and with the spirit of a disinterested judge” (A VI 4 2250; Dascal 1993). This appeal to a disinterested judge indicates that the golden rule is not only a rule of reciprocal love: It is not simply “the will to procure the felicity of the other,” as we can paraphrase Leibniz’s definition of true love (A VI 1, 34, 464; A VI 2 485; A VI 4 1357, 2793; A II 1 173–175; GP 3 207; GP 7 73; etc.). It is rather to procure justice, something that requires that the love of the other must be moderated or measured. And moderating love in a just way requires prudence, for according to the Elementa juris naturalis, “Justice [is] the habit of loving others [. . .] as long as this can be done prudently” (A VI 1 465). In order to become just, the love of the other “must be curved by prudence”, as Leibniz puts it in the same text. The originality of Leibniz’s appeal to the golden rule resides in this reflexive development of it: not simply as a rule of caritas, but as a rule of caritas prudentis, which turns it into a full law of justice.2

4 The Permissive Credo Maximum An answer to the problem of religious schism and dispute often proposed in Protestant milieus consists in distinguishing between two types of dogma. On the one hand, there is a set of primary dogmas, which constitutes a credo minimum containing only a few articles of faith. These articles are necessary to believe. On the other hand, there is a multitude of secondary and essentially unimportant dogmas. These are called adiaphora, and can to a certain extent be neglected. It is a way of dealing with the problem of sectarianism by neglecting small differences and by holding on to the general agreement on the common foundations of religion. The credo minimum is often closely connected to the Pauline virtue of charity. Jacqueline Lagr´ee has done a very useful survey of the dogmatic minimalists in the 16th and 17th centuries, from an early irenic thinker like Sebastian Castellio to a Saumur theologian like Isaac d’Huisseau, or again a deist like Edward Herbert of Cherbury, an Aristotelian like Grotius, or a naturalist like Spinoza. Most of these positions, otherwise very different, have theoretical foundations that can be traced back to the Stoic theory of common notions (Lagr´ee 1991). I believe that we can formulate Leibniz’s position on dogmatics as being strictly the opposite of that of the minimalists. Leibniz does not promote a credo minimum, but a sort of credo maximum, if the reader will kindly allow for such a neologism.

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The first reason for proposing such an interpretation of Leibniz’s dogmatics is a negative one, and arises from a consideration of the primordial status of the golden rule: Breaking the golden rule under the pretext of some other dogmatic disagreement amounts to reversing the relation between the first and the subaltern principle of religion. No dogmatic disagreement can be of such importance that it could justify breaking the rules by which disagreement is solved. In these cases, he who is wrong is not he who holds an erroneous belief, but he who blames and excludes the other for holding what he believes to be an erroneous belief. As Leibniz writes: It is these temerarious condemnations in which the spirit of sects and the source of a large part of the ills of Christianity truly exist. One cannot truly love God when one does not love one’s fellow man; and to love is not to precipitate judgement that he will soon be on his way to Hell and the Devil to stay there eternally as an enemy and blasphemer of God (FC 2 92).

The basic anti-sectarianism that governs Leibniz’s irenic project demands that we do not condemn others. But this does not mean that we should reduce religion to a common dogmatic denominator, or believe that the golden rule itself exhausts the dogmas of religion. The minimalists moving in that direction are not exactly on the wrong track, but they confuse theory and practice; they make the method for determining the meaning of dogma the sole dogma; the method of controversy and the object of controversy are conflated. This confusion is not Leibniz’s. What he is searching for is a conformity between theory and practice, not a reduction of theory to practice (A VI 4 2200). The heuristic and practical rule of caritas prudentis is not conceived as the foundation of a reduced dogmatic theory. On the contrary, the practice of caritas prudentis involves a very pluralistic conception of dogmatic theory, negatively defined by the effort of depreciating almost nothing: “Je ne m´eprise rien!” is an exclamation often found in Leibniz (GP 3 384, 562; GR 114, 115, 127). Even the most hysterical mystics benefit from his good-willed appreciations – Antoinette Bourignon is an “admirable girl” (GR 110)! The imaginations of the cabbalists hold their part of the truth (A I 5 109; GP 6 625). One must simply “take them from the good side,” separate the grain from the straw, or the gold from the dirt (GP 3 624, 384). Sometimes a lack of cognitive clarity is counterbalanced by beauty of expression (GP 3 552; GP 7 497). In any case, if “it doesn’t harm anybody”, what purpose does reprobation serve except for deepening conflict and schism? “As for me, I think that everything is good [. . .] all the bad things among us are due to the fact that we always have something to reproach others for” (GR 111). We should therefore try not to exclude any theoretical possibility as long as it does not conflict with the practice of caritas prudentis. What Leibniz proposes as the dogmatic foundation of religion is indeed very far from the “common notion” of religion proposed by the dogmatic minimalists. The background for such a profoundly pluralistic position is not Stoical, but rather Augustinian. I will cite a passage from the Confessions, Book XII, chapter 31, that I think is strikingly close to what I believe is also Leibniz’s position. St. Augustine writes: So, when one man has said: ‘He [i.e., Moses] meant the same as I’, and another: ‘Not that, but what I mean’, I think I can say in a more religious way: ‘Why not both, instead, if both

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are true? And, if there is a third, and a fourth, and any other truths that anyone sees in these words, why may it not be believed that he saw all these, and that, through him, the one God has tempered the sacred writings to the perceptions of many people, in which they will see things which are true and also different?’ // As for me (and I am saying this from my heart, without any fear), were I writing something aimed at the highest authority, I should prefer to write in such a way that each man could take whatever truth about these things my words suggested, rather than to put down one true opinion so plainly as to exclude other opinions, if there were no falsity in them to offend me (Augustine 1953: III, 405; translation slightly corrected).

The passage speaks very much for itself. It should be noted that when Leibniz annotates the Confessions, probably around 1689–1690, he lists this text among passages that he considered “memorable” in the part of St. Augustine’s work concerning “moderation” (moderatio) in the explication of the Scriptures (A VI 4 1687). Seeing some link between Leibniz’s method of moderation and St. Augustine’s position in chapter XII of the Confessions is therefore not without some textual support. Finally, one can highlight a passage from a letter to the Jesuit Bartholomew des Bosses written in 1707, where Leibniz discusses the violent disputes surrounding the condemnation of Jansenius’s Augustinus. Here, he quite clearly adopts a position similar to that of St. Augustine in the Confessions: I am also far from approving the persecution of those who hold opinions that teach nothing criminal. Not only should honest people abstain from such persecutions, but they should also abhor them. As for those over whom we have some authority, we should labor to deter them from [persecuting] [. . .]. For what is this other than a sort of violence against which one can only protect oneself through a crime (by abjuring that which one believes to be true)? In this way, the more merit somebody has, the more he suffers under such tyranny [. . .] [I]t is with equal arms, and not by force and fear, that one must overturn their errors; or even, leave the errors in place: it is a lesser evil in these matters than to behave in such a way (GP 2 337; my italics).

5 The Obligatory Credo Maximum But the argument can be taken further. It is one thing to charitably affirm the possibility (and acceptability) of a plurality of interpretations of religion like St. Augustine. This is a “permissive” position founded on the precept of charity, and it corresponds to a “weak sense” of a credo maximum. It would be quite another thing to affirm that this plurality of interpretations is an essential part of religion and that we must try to advance the development of them all. This latter position is what I would call a “strong sense” of a credo maximum. I believe that Leibniz does in fact defend such a strong sense of the credo maximum, and that this position results from his conception of yet another precept, different from that of caritas prudentis, namely, the obligation to love God, Amor Dei super omnia. More precisely, it is founded upon the subaltern principle that follows from this, namely to do everything for the glory of God – Ad majorem Dei gloriam or “For the advancement of the glory of God”, as Leibniz adopts the well known slogan of the Jesuits (Leibniz cit. in Baruzi 1907: 88).

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In the Commentatiuncula de judice controversiarum from 1669–1671, Leibniz affirms that it is not necessary to know exactly what is the adequate meaning of the expressions of the dogmas of faith, but that it is sufficient to affirm that whatever is signified by these expressions is true. This eminently open position, not on the truth of dogma but on the meaning of truth of dogma, is what Leibniz calls a “disjunctive faith”. He compares it to the confused idea which an ignorant peasant may have of the dogmas of faith (A VI 1 551). Rather than proposing a sufficient minimal set of dogmas, disjunctive faith implies a conception of the sufficient minimal intelligibility of dogma. We can find similar affirmations in Leibniz’s remarks from 1690 on Paul Pellisson-Fontanier’s R´eflexions sur les diff´erends de la religion and again in the Annotatiunculae written on John Toland’s Christianity not mysterious in 1701 (A VI 1 78; D V 145). But disjunctive faith is only the first moment in Leibnizian dogmatics. A note written by Leibniz in the margin of a letter from Pellisson from December 1690 refers straight back to the position of the Commentatiuncula twenty years earlier: “One must be equitable in everything, and nobody can be so more than God. It would be an absurd injustice to wish that these peasants leave their wagon to study controversies” (A I 6 144). It suffices for the peasant to have a confused idea of the dogmas of religion. But this is not the case for everybody: It is true that religion and piety do not depend upon profound sciences, because they have to be within reach of the simplest people. But those to whom God has given the time and the means to know him better, and consequently to love him with a more enlightened love [un amour plus e´ clair´e], should not neglect any occasion to do so [. . .] (GR 91).

A love that includes an effort to understand and know the nature and will of God is what Leibniz terms an “enlightened love” (amour e´ clair´e) of God, where “zeal is accompanied by illumination” (GP 6 27). It is greater because it is more perfect in its expression. The love of God, Leibniz writes, “is greater to the extent that one is more enlightened. Those who have it through demonstrations have it with greater firmness and perfection; on condition that the practice conforms to the theory” (A VI 4 2200; A I 4 79–80). In other words, there is a gnoseological component inscribed in the practice of piety, a will and an obligation to know: “True love is founded upon the knowledge of the beauty of the loved object” (GR 91). The reason for this must be sought in Leibniz’s general conception of true love, which implies the will to do everything in our power to understand the other: To love a thing is to take pleasure in the knowledge of it. Therefore the more profound the knowledge one acquires of this thing, the more pleasure it will procure us. Apply this to the love of God. He who wishes to love God over all things must therefore, before anything else, apply himself to know the beauty of God (D I 20).

This “dynamic concept of light-love”, according to an expression invented by Andr´e Robinet, is primarily construed in opposition to the enthusiasm of the mystics and their ideas of mystical revelation: “Why call light that which makes us see nothing?” (NE 4.19.1; GP 5 487; Robinet 1994: 158–160). Loving implies in its very concept the effort to know the nature and will of the loved object. This is indeed also the case with the amor Dei super omnia, which constitutes the second fundamental rule

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of faith for Leibniz, apart from that of caritas. Therefore, love and enlightenment or knowledge are closely connected in the notion of faith. Not knowing what one believes in is “faith without light”. It is not a “living faith” because it “awakens no love” (A I 2 354; Robinet 1994: 158). For this reason, Leibniz writes to Edme Piron on the doctrines of religion: “I hold that every man is obliged to an examination according to his capacity and his position in order not to be guilty of negligence” (A I 7 330). Leibniz sums up quite neatly his position in a letter to Pellisson in October 1690: I come to the last point, whether a true love of God over all things is sufficient for salvation. I dare not decide it, and I would avoid saying it in the terms put down by Mister Pellisson, as if he who loves God could be saved without taking the pains of disputes and controversies. I would rather say the contrary, and I admit that the safest is not to neglect anything, and that true love even commands it. One must search for the true Church [. . . .] and carefully use all means of knowing the revealed will of God (A I 6 119).

But how does this obligation not to neglect anything present itself in relation to the pluralistic dogmatics of the permissive credo maximum? I would argue that it does nothing but make it obligatory – it adds obligation to permission: not only can we allow a plurality of possible meanings, but we must also affirm a plurality of meanings. What we finally discover in our search to understand God is not a clear and distinct idea of the one true meaning of revealed dogma. Quite on the contrary, it is a clarification, which implies a non-reducible proliferation of meaning. I have tried to show exactly this on another occasion: in Leibniz, revealed truths are by definition susceptible to receive several interpretations – this is even what distinguishes them from natural truths (Laerke 2004). In other words, the truth of each revealed dogma is defined as a set of possible meanings. Clarifying or “enlightening” faith makes explicit a multiplicity of possible meanings enveloped implicitly in disjunctive faith: it is the exposition of all the possible meanings of revealed dogma. The enlightened love of God does not here consist in choosing one of these possible meanings, but in affirming the possibility of all of them at the same time. As Leibniz puts it in the letter to Pellisson quoted above: For the love and glory of God, we must not neglect anything, for true love commands it. An enlightened faith is the faith that affirms all possibilities at the same time, and that understands a dogma from all the possible points of view at a time (this is where the golden rule comes in again). The dogmatic solution is essentially pluralistic. It is in this sense that we must understand Leibniz’s remarks on the cabbalistic anthology Kabbala Denudata in a letter to Ernst von Hessen-Rheinfels in January 1688: I value what is good everywhere, and I am quite happy about this difference between ways of thinking [fr. genies] and designs, which makes that nothing is neglected, and that God’s honour is advanced in several manners (A I 5 43).

This passage explains very clearly what I mean by a credo maximum in the strong sense. It is the rule of enlightened love, which prescribes that we neglect nothing that might advance the glory of God – Ad majorem Dei gloriam.

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6 Response to a Possible Objection There is, however, a passage written in 1694 that could threaten my interpretation, at least in relation to Leibniz’s mature position. Here, he makes the following statement about the Roman Catholic conception of transubstantiation: It does not seem to follow that since Transubstantiation [. . .] can be affirmed without overturning any principles of the Protestants, it ought to be affirmed. For it does not follow that whatever we are not able to refute is true (A I 10 112).3

It could seem that Leibniz here flatly denies that we should consider true the possible meaning of the Eucharist that is the Roman Catholic transubstantiation, and that he affirms the Protestant principles. This is, however, far from being the only possible interpretation of this passage. In fact, all that Leibniz denies is that the possible meaning proposed as the true meaning of the Eucharist proposed by the Catholic Church, i.e., transubstantiation, should necessarily be adopted if it cannot be refuted. He denies that any possible meaning, for example transubstantiation, should be privileged in relation to other possible meanings, for example pure representation, consubstantiation or impanation, or indeed the possibility towards which Leibniz himself inclines, that of comperception.4 In this text, Leibniz argues against the Roman Catholic contention that their position is privileged, or that the possible meaning proposed by the Roman Catholic Church should be considered to be superior to other possible meanings. This was in fact often argued by Catholic controversialists on the grounds that a long and venerable tradition supports the Roman Catholic interpretation. It is commonly called the argument of prescription. It was first proposed in Tertullian’s De praescriptione haereticorum. At Leibniz’s time, Pieter and Adriaan Van Wallenburch reused it in their Tractatus generales de controversiis fidei (1670). Leibniz knew these two brothers well from his days in Mainz (A VI 4 2471–2472; A VI 1 294, 547, 548–559; GP 3 481; GR 199; A I 6 77; NE 4.15.6; GP 5 440–441). I take the passage from 1694 to be an objection to the argument of prescription and nothing else, and certainly not a full denial of the truth of transubstantiation. In the passage, Leibniz simply objects to the idea that if there is indeed a presumption of truth of revealed dogma (GR, 216; GP 6 68–69, 83–84), there is not a presumption of truth of this or that interpretation of truth, i.e., of this or that possible meaning of the dogma presumed true. The text from 1694 does not in any way contradict the strong interpretation of the credo maximum, but rather the contrary, because it does not confirm that some possibly true meaning should be neglected, but that all possibly true meanings should be taken in to equal consideration.5

7 Conclusion The three principles of the “method of moderation” that I have tried to point out – respectively Pauline, Augustinian and Jesuit in inspiration – are in reality quite simple. They can be summarized as follows: (a) always consider a dogma from the

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point of view of the other, but only adopt it as your own with prudence (St. Paul); (b) do not exclude any possible meaning of dogma (St. Augustine); (c) do not neglect any possible meaning of dogma (The Company of Jesus). The simplicity of these rules does not diminish their explanatory power in relation to Leibniz’s often somewhat puzzling behaviour in his treatment of other Christian positions than his own, which remains the one expressed in the Augsburg Confession. These rules may help to understand the rationale behind texts like the Systema theologicum, where Leibniz poses as a Catholic. They may also help to understand why his efforts to explain a Roman Catholic dogma like transubstantiation have nothing to do with the near conversion that his mentor the Baron Von Boinebourg hoped for, or why these efforts cannot be reduced to a mere will to please a Catholic correspondent, like Bertrand Russell argued concerning the Des Bosses correspondence. These rules may finally, and most importantly, help to understand the odd position of Leibniz in the landscape between natural and orthodox Christian theologies in the 17th century, in a sense affirming them all, and neglecting none.6 Acknowledgments Research for this paper was funded by the Carlsberg Foundation. I thank Anna Lærke for correcting the English language. Any remaining blunders are entirely my own.

Notes 1. This text, now translated under the title “Vices of Mingled Disputes” (DA: Chapter 1), is discussed by Marcelo Dascal in Chapter 2 of the present volume. 2. For a more detailed account of this question, see M. Laerke (Forthcoming). 3. The passage has been highlighted by Robert M. Adams in a somewhat different context (Adams 1994: 354). I have followed Adams’ translation. As Adams correctly notes, there is sufficient textual evidence for maintaining that the young Leibniz was ready to accept both Lutheran consubstantiation and Catholic transubstantiation. Our question is therefore whether the position Leibniz defends in this text from 1694 represents a substantially different stand, or whether it expresses another aspect of a same theory. I believe the latter assumption to be the correct one. 4. Leibniz does not on this occasion specify towards which Protestant interpretation he would himself incline at this point of his life. He often claims to adhere to the Augsburg Confession, which admits real presence in the Eucharist. The radical Calvinist solution by pure representation or symbolism is here excluded, and there is an effort to accomodate Roman Catholicism. But he also has doubts concerning consubstantiation and impanation, which he does not find in conformity with his Lutheran (or rather Evangelical) confession. Leibniz seems to incline towards the possibility of comperception according to which the body of Christ and the bread are perceived simultaneously, a position that he draws in an ubiquitist direction in order to accomodate certain less radical Calvinists (GP 2 390; GP 6 60–61). 5. This does not mean, however, that Leibniz completely denies the validity of the prescriptive argument (FC 1 147, 175, 276; GR 198; A II 1 537). But it is only valid on the condition clave non errante, that is, the Church must first prove that it is the “true Church” (FC 1 205; GR 191–192, 215–216). Furthermore, as a part of a full answer to the question that I can only suggest here, it should be noted that for Leibniz the prescriptive argument is never conclusive but only one “weight” among others on the balance of reason that should finally allow each

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person to decide for himself towards which possible meaning enveloped in disjunctive faith he will incline. 6. With the strange exception, I must add in order to conclude, of the scandalous theology of Spinoza, which constitutes the somewhat anomalous limit of the Leibnizian credo maximum.

References Adams, R. M. 1994. Leibniz. Determinist, Idealist, Theist. New Haven, CT: Yale University Press. Augustine. 1953. Confessions. Transl. V.J. Bourke. In The Fathers of the Church, Vol. 21. New York: Fathers of the Church, Inc. Baruzi, J. 1907. Leibniz et l’organisation religieuse de la terre. Paris: F´elix Alcan. Castellio, S. 1981. De arte dubitendi et confitendi, ignorandi et sciendi. Leiden: Brill. Dascal, M. 1993. One Adam and many cultures: The role of political pluralism in the best of possible worlds. In M. Dascal and E. Yakira (eds.), Lebniz and Adam. Tel Aviv: University Publishing Projects, pp. 387–409. Dascal, M. 2001. Nihil sine ratione → Blandior ratio. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress. Vortr¨age), vol. 1. Berlin: Leibniz Gesellschaft, pp. 276–280. Dascal, M. 2005. The balance of reason. In D. Vanderveken (ed.), Logic, Thought and Action. Dordrecht: Springer, pp. 27–47. Erasmus. 1992. De amabili concordia ecclesiae. In C. Blum, A. Godin, J.-C. Margolin, and D. M´enager (eds.), Erasme. Paris: Robert Laffont. Grotius, H. 1991. Meletius. In J. Lagr´ee, La raison ardente. Paris: Vrin. Laerke, M. 2004. Entre l’enthousiasme et le naturalisme: strat´egies argumentatives dans la conceptualisation leibnizienne des myst`eres. Paper presented at the International Conference Les enjeux du rationalisme moderne: Descartes, Locke, Leibniz, Carthage. Laerke, M. Forthcoming. The Golden Rule: Charitas / Prudentia. Aspects of Leibniz’s method for religious controversy. In M. Dascal (ed.), The Practice of Reason: Leibniz and his Controversies. Amsterdam: John Benjamins. Lagr´ee, J. 1991. La raison ardente. Paris: Vrin. Robinet, A. 1994. G. W. Leibniz. Le meilleur des mondes par la balance de l’Europe. Paris: Presses Universitaires de France. Spinoza, B. 1999. Trait´e th´eologico-politique. Ed. F. Akkerman, J. Lagr´ee, and P.-F. Moreau. Paris: Presses Universitaires de France.

Part VII

Religion and Theology

Chapter 26

Convergence or Genealogy? Leibniz and the Spectre of Pagan Rationality Justin E.H. Smith

For Leibniz, knowledge of geometry is innate. It is not obtained from the world of experience, but rather applied to that world. Yet in the Novissima Sinica, a Jesuit compendium of news from China to which Leibniz contributed a preface in 1697, we find Leibniz arguing that the Chinese are indeed good scientists, even if their science is based upon a “mere empirical geometry”. This is all they are capable of, Leibniz argues, since they lack knowledge of “things incorporeal” (Leibniz 1957, § 2). It is worth asking why Leibniz would deviate from his ordinary account of geometry when it comes to the Chinese, even if he would acknowledge that in all other respects Chinese geometry is just as well equipped to deal with the world as Western geometry. One intriguing suggestion is that Leibniz, like Descartes, believes that knowledge of God – which is to say knowledge of the true God – functions as a precondition of geometrical knowledge and of anything else to which a rationalist would ascribe an a priori status. I would like to argue that Leibniz’s account of the limits of Chinese knowledge of geometry provides perhaps the clearest illustration of a more general understanding, to which Leibniz was sympathetic and which has its roots in early Christian theology, of the relationship between knowledge of God on the one hand and possession of wisdom, including knowledge of a priori truths, on the other. This chapter, which is part of a larger project on the roots of ethnography in the early modern philosophical concern with human origins, is motivated by the conviction that what early modern philosophers have to say about human cultures beyond Europe’s borders tells us quite a bit about their conception of humanity itself. This much has been well noted by scholars of political philosophy, who have paid due attention to the importance, e.g., of Native Americans and the idea of the savage in the social-contract theories of Hobbes and Locke. But here the philosophers are primarily interested in drawing lessons from cultures outside of Christendom. What interests me here is early modern philosophical speculation as to how those cultures got there. Not, What can they teach us? but, Who are they? I shall focus on the example of Leibniz, showing in particular that, as in so many other aspects of his thought, the philosopher is of at least two minds with respect to J.E.H. Smith Concordia University, Montreal, Canada M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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the question of the possibility of attaining philosophical wisdom in the absence of knowledge of the divine truth of Christianity. At times – and for the most part earlier in his career – Leibniz wishes to hold on to the view that scientific or philosophical knowledge has knowledge of the true God as a precondition. At other times, he wants to say that some non-Christians are perfectly well equipped to arrive at all the truths to which any human has access, simply by the use of their own reason and senses. In this respect, Leibniz’s own thought presents in nuce an illustration of the tension between two very different ways of thinking about the relationship between revelation and knowledge: The tradition of ancient theology or prisca theologia, on the one hand, and natural theology on the other. According to the former view, the attainment of wisdom by any person is possible only in virtue of a line of descent from ancestors who received divine truth directly by way of prophecy. According to the latter view, human beings are capable of coming to wisdom simply by using their natural faculties, without any genealogical connection to the scriptural tradition of the Christian world. The tension between these two views – genealogy and convergence – was at the heart of early modern thinking about the nature of cultural difference.

1 The Problem of Chinese Wisdom As Franklin Perkins notes (2004: 11f.),1 the extent to which the various early modern philosophers draw on cross-cultural empirical data can be matched up to no small extent with their respective theories of human nature (or the absence of it in individual humans). Descartes, for example, does not dwell on the Persians or the Chinese (though he does mention them more often than the index to the English edition of his writings would lead us to believe). The world outside Europe, Descartes may have thought, could only provide complicating and messy evidence against the universality of his claims, and, more damagingly, against the a priori method of producing claims about what sort of entity a human being is. This, as Perkins notes, is why far-away cannibals were, if a potential embarrassment to Descartes, celebrated by skeptics such as Montaigne. Cannibals and other so-called savages threatened to disconfirm universalizing claims made by Europeans about humanity. But the Chinese presented a very different sort of problem: Their advanced civilization (advanced, that is, according to all the indices that interested Europeans) threatened European claims to particularity. Some thinkers, such as Leibniz, were happy to move beyond European particularism. As Perkins shows, attention to Leibniz’s engagement with China reveals the philosopher at his best, employing the method and principles familiar to us from other, better known aspects of his work in a creative way. Leibniz was intensely interested in Chinese civilization, though certainly not in the same way in which Montaigne was interested in Native Americans. Here we may attribute the difference not so much to deeper differences between the two thinkers as to a more general difference between the way Native Americans and

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Africans, on the one hand, and the Chinese, on the other, were conceptualized in Early Modern Europe. Robert Fage, in A Description of The whole World, with Some General Rules touching the use of the Globe, gives us an insight into early modern ethnography that is in its general outline representative of its time: [T]he inhabitants of Libya are a base and vile people, thieves, murderers, treacherous, and ignorant of all things, feeding most on dates, barley, and carrion, counting bread a diet for holidayes . . .[Negroes] are of little wit, and destitute of all arts and sciences, prone to luxury, and for the most part Mahometans (Fage 1658: 58f.).

The Chinese, in contrast, are lively, witty, wondrous artists, they make wagons that sayl over the land as the ships go over the Sea: the art of Printing and making of guns is more ancient with them then with us: they have good laws according to which they do live; but they want the knowledge of God, for they are heathens, and worship the sun, moon, and stars, yea and the Devil himself that he may not hurt them (ibid.).

The first two groups pose very different conceptual problems than those posed by the last one. Fage’s account is repeated by numerous thinkers, and in some form we find his central points being echoed by Leibniz. The Chinese, for these thinkers, are not inferior when it comes to their technology or their codes of conduct. But how then, the question arose, could they arrive at such good laws and come up with such sophisticated wagons if they want knowledge of God? Pagan savages are, in a sense, quite easy to explain: They confirm the conviction that without the true religion, one will end up living like a debased animal. But the prospect that a civilization with no knowledge of the true religion could nonetheless do so well for itself was a question that demanded explanation. For throughout much of history, divine truth was the only guarantor of the certainty of the various lesser truths, such as those of geometry, which in turn underlie the sort of technology the Chinese had demonstrably produced. As Descartes explains towards the end of this long tradition: [W]hen I consider the nature of the [rectilinear] triangle, it most clearly appears to me, who have been instructed in the principles of geometry, that its three angles are equal to two right angles [. . .] yet I may readily come to doubt of the truth demonstrated, if I do not know that there is a God: for I may persuade myself that I have been so constituted by nature as to be sometimes deceived, even in matters which I think I apprehend with the greatest evidence and certitude (Descartes 1996: Fifth Meditation; AT VII 69–70).

For Leibniz as well, geometry is innate, and while there is no such explicit claim for the God-dependence of such innate knowledge, it seems there is good reason to inscribe Leibniz into the same tradition as the one we have just seen Descartes avowing. The belief in the God-dependence of certain knowledge goes back a long way. An earlier ancestor of this idea is the view that to be a philosopher at all is simply to know God. For early Christian philosophers, such as Origen and Clement of Alexandria, Christ is Logos; the incarnation is not the beginning of Christ, but only a change of mode. Moses is the ultimate philosopher because, as a prophet, he grasps the Logos intuitively and immediately. Other people have to work their way

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up through the pedagogy of grammar, arithmetic, music, logic, etc. before getting to the divine truths that alone are constitutive of wisdom. In the early modern period, Adam too is often invoked as the supreme philosopher. Thus for example in the 1660s Robert South claims that Adam came into the world a philosopher, which sufficiently appeared by his writing the nature of things upon their names; he could view essences in themselves, and read forms without the comment of their respective properties: he could see consequents yet dormant in their principles, and effects yet unborn, and in the womb of their causes (Aarsleff 1993: 169f.).

One common task then was to include the prophets of the Hebrew bible in the family of Christian philosophers by emphasizing their capacity to foreknow the truth that would only be accessible to non-prophets after the birth of Christ. Another related and perhaps harder problem was to find a way for pagan philosophers, thought to lack the direct line to the divine enjoyed by the prophets, to be included within the same family. As early as Dante, who consigned all the pagan philosophers to the relatively comfortable first circle of hell, there emerged a problem of how to include the pagan Greeks among the wise if they had no access to genuine philosophical wisdom either in the way Moses did, by prophecy, or in the way, say, Augustine did, by access to revealed scripture. Some accounted for this problem by appealing to a hidden esoteric tradition that would link the wisest Greeks – those in the Orphic-Pythagorean-Platonic tradition – to the Hebrew prophets, with some even suggesting that Plato disappeared into the desert for a while to study directly under Moses. By the time of the China mission, a similar strategy was being employed to account for Chinese wisdom in the manner that had long been employed for the pagan Greeks. This is the movement often described as Jesuit Figurism, a leading member of which was Leibniz’s correspondent Jacques Bouvet.2 Many were emboldened by the discovery, familiar already to Marco Polo, of Christian churches in China, which were only much later determined to be founded by Nestorian Christians from Syria in the 7th century. Members of the Figurist movement had an interesting take on the nature of Chinese technology and law that I think may shed some light on Leibniz’s comment on “empirical geometry”. For the Figurists, while the Chinese have a great legal system and great machines, they have no understanding of the principles underlying either of these. Confucianism was often portrayed as a system of laudable rules, the reasons for which had been forgotten in the flow of centuries. This contrasted sharply with the assessment of, e.g., Buddhism and Taoism, which were taken as garden-variety idolatry. The Chinese wandered so far, and stayed there for so long, that they forgot the ultimate reasons for their wisdom, which were, namely, exactly the same sequence of revelations that made the acknowledged forebears of Christian Europe wise. The Chinese became, as it were, wise automata, and missionary activity was in fact nothing more than the task of reminding them who they really were. This basic conviction led to some rather extreme cases of what we would today think of as theory-ladenness in observation. Take for example the collectively

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written Jesuit text Confucius sinarum philosophus, written between 1660 and 1670 and published in 1687: Three characters, zhou, ship, shu a weapon and min, a household utensil, when put together make up the character pan. This is the name of the man the Chinese call Pan Gu, ‘Pan of ancient times’. They believe that he was the first man on earth. Hence a European has surmised that the man we call Noah is called Pan by the Chinese (Intorcetta et al. 1687: 187f.).

This European was Bouvet, who read the upper part of the character for pan as “Great Boat with eight persons on board,” i.e., Noah and his family in the Ark (Intorcetta et al. 1687: 187f.). Such an interpretation, as with the Sumatran rhinoceros taken for a unicorn in the flesh at long last, involves the subsumption into a familiar universe of references of what would otherwise remain completely uninterpretable. Much effort was expended to interpret Chinese writing in already familiar terms (see Kircher 1667). While some saw Chinese characters as a deformation of Hebrew, the more common Near Eastern ancestor of the Chinese writing system were the Egyptian hieroglyphs.3 In this connection, early on, Leibniz does explicitly entertain the idea that there may be one origin. He writes in the mid-1670s that Egypt has been most highly valued above all others. Whether the Chinese are from the Egyptians or the latter from the former, I dare not say; certainly the similarity of their institutions and hieroglyphics along with their shared kind of writing and philosophizing suggests that they are consanguineous peoples. Both are parents of the arts and sciences (A IV 1 270–271).

But this is as close as Leibniz gets to an explicit statement of a prisca theologia account of Chinese civilization. Leibniz wrote with evidently only some irony that the Christians should bring Chinese missionaries to Europe to teach ethics, while of course continuing to send European missionaries to teach about philosophical truth. Leibniz’s view of the Chinese is conflicted, nonetheless. His view shifts dramatically from the preface to the Jesuit Novissima Sinica of 1697, through the scattered comments in the Nouveaux Essais of 1704, and up to the Discourse on the Natural Theology of the Chinese, left uncompleted at the time of his death in 1716 at the age of 70. Broadly speaking, Leibniz moves gradually from a prisca-theological to a natural-theological understanding of the Chinese. Let us outline some of the notable moments in the course of Leibniz’s engagement with sinology. In the 1670s, as we have seen, he speculates on the possibility of direct descent from the Egyptians. In 1697, Bouvet sends him a diagram of hexagrams from the I Ching. Leibniz interprets the sequences of solid and broken lines as proof of the Chinese independent discovery of the binary calculus. In the same year, Leibniz sends a letter to Duke Rudolph of Brunswick including diagrams from the I Ching, and suggests that these are the expression of knowledge of a fundamental Christian truth of which most philosophers remain unaware. After all, he writes, one of the high points of the Christian faith, which is not easy to impart to pagans, is the creation ex nihilo through God’s almighty power. Now one can say that nothing in the world can better present and demonstrate this power than the origin of numbers, as it is represented here through the simple and unadorned presentation of One and Zero or Nothing.4

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In the Novissima Sinica of 1697, the Chinese appear to go down in his estimation again; he remains mute about origins but insists that, in virtue of the evident distinctness of Chinese civilization, their geometry and laws must be in a way simulacra. But it is over the course of the early years of the 18th century that Leibniz enters into his major correspondences with Europe’s best sinologists. In the Nouveaux essais of 1704, Leibniz’s position is somewhat more moderate than it had been in the Novissima Sinica. Now, even if Leibniz believes, as he writes in the Nouveaux Essais, that “[w]ith regard to ancient writings [. . .] we need to understand Holy Scriptures above all things”, he anticipates that the day will come when “the Romans, Greeks, Hebrews and Arabs have been used up”, and, at this point “the Chinese will come to the fore with their ancient texts” (NE 3.9.5; A VI 6 336). Scripture, then, is a valuable, but not exclusive, source of ancient wisdom. Over a decade later, Leibniz seems thoroughly convinced of the innate capacity of the Chinese to arrive at the same basic truths that prisca theologia would have us believe could only come from genealogical connection to Christ as Logos. In the Discourse on the Natural Theology of the Chinese, still unfinished in 1716, Leibniz defends the Chinese view that Li [spirit] can govern in the world without interposing itself in mundane affairs. As Albert Ribas has convincingly argued, it is significant that at the same time as Leibniz was composing this work, he was in a heated controversy with Samuel Clarke over Newton’s natural philosophy, and was convinced that in England natural philosophy was in a state of decay. Most problematic for him was what he perceived as Newton’s view – which also has echoes in Cudworth and More’s doctrines of plastic nature or archaeus – that the world is God’s sensorium. For Leibniz, it is much more pious to suppose, along what he thought were traditionally mechanistic lines, that God need not insert himself into the mundane and drudging affairs of nature in order for this nature to work smoothly. All that is needed are a few perfect laws that God would set down at the Creation (Ribas 2003: 69f.). Leibniz proclaims in the Discourse that the Chinese, unlike the English, who are inadvertently lapsing into paganism by reintroducing a meddling God, or a world soul, or a supernatural “Deus ex machina”, are right to “reduce the governance of Heaven and others things to natural causes and distance themselves from the ignorance of the masses, who seek out supernatural miracles” (Discours, § 2).5 Here, it seems almost that Leibniz believes that it is precisely the isolation of the Chinese from the scriptural tradition, and their consequent need to rely on nature alone for their understanding of the divine, that is itself the fortunate cause of their theological superiority to the English.

2 Prisca Theologia, Natural Theology, Pre-Adamism and Degenerationism Both natural theology and prisca theologia insist that all truth is one, but they comprehend this truth from opposite directions. Prisca theologia says that all truth is one in virtue of genealogy; natural theology says it is one in virtue of natural

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convergence. A useful analogy recommends itself from modern evolutionary theory. Dolphins and quadrupeds look nothing alike until you dig under the surface, but if you do so, as the anatomist Edward Tyson (1680: 16f.) did as early as 1680, you can distinctly make out vestigial handbones in the flippers. You can discern that, in spite of differences, they are basically the same in virtue of some distant and unobservable shared starting point. Puffins and penguins, by contrast, have many of the same adaptive traits even though entirely unrelated, because each inhabits a polar environment; they come to the same conclusion because they inhabit the same world. There was one other strain of thought on human origins that is worth mentioning briefly, as it fits neither the prisca theologia nor the natural theology view of human nature and origins, and indeed threatens them both. This approach emphasizes both separate points of origination and separate destinies for distinct human groups. The French Protestant thinker and radical religious reformer Isaac La Peyr`ere (1596– 1676) made much of the fact that in St. Paul’s letter to the Romans (5: 12–14), there is an allusion to the sin that prevailed before law came into the world with Adam.6 This strongly suggested that there must have been people before Adam, the “pre-Adamites”, and that, quite possibly, the descendants of this separate creation are the inhabitants of the distant corners of the world. Separate creations seemed to some in the early modern period to be particularly useful to account for phenotypic and cultural variation, and for vast geographical dispersion from the area around Baghdad where the Garden of Eden was presumed to be located. In the 17th century, the doctrine was, for the most part, perceived as heretical and associated mostly with radical sects. It was not, in its inception, racist – the point of it was not to deny the full membership of savages in the human family, but rather, principally, to deny that the Old Testament offered an account of the history of the world. Instead, it offered a history of the Jews, and did not concern the Chinese or the Native Americans at all. Many of La Peyr`ere’s arguments came from observed inconsistencies in scripture (he makes much of the fact that Moses is purported to be the author of Deuteronomy . . .in which the death of Moses is described), but also from accumulating evidence about the plurality of versions of the world’s ancient history – including those suggested by Chinese, Babylonian, and Mexican chronology – and about the absence of reasons to support one version over another. La Peyr`ere propounded relativistic arguments to question the literal truth of scripture, though these same arguments easily mutated, among later supporters of the pre-Adamite theory, into arguments for the inferiority of the people held to have a separate creation, on the presumption, evidently, that with respect to the creation of species, as with segregation, there could be no “separate but equal”. Popkin maintains that Leibniz did not seem to be interested in the historical, chronological, anthropological questions that provided the ammunition for the preAdamite theory. He was, Popkin (1993: 381) writes, very much concerned to discuss other theologies outside of Christianity in terms of their ideological content, but not their differing claims about the facts of human history [. . .] His efforts to unite the churches within Christendom, and then to unite them with Islam and Chinese religion, did not involve finding common historical ground, but rather common metaphysical and moral ground.

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Yet we know from scattered passages that Leibniz was a committed monogeneticist, and that he believed that human phenotypic diversity is a consequence of environmental influence over time. Thus he notes in the Otium hanoveranum, published posthumously in 1718, that all of humanity must belong to the same species, even if “they have been changed by different climates just as we see that animals and plants change their nature, in becoming better or degenerating” (Otium hannoveranum; cited in Pagden 1982: 138f.). For Leibniz, then, there is only one origin for human beings, and subsequently the boundaries of the human species remain rigidly fixed. In this respect, Leibniz may be described as a “moderate degenerationist”, who believes that human diversity can be accounted for in terms of environmental pressures over time in different habitats. Here Leibniz may be contrasted with figures such as John Locke who believe that the lines between human and animal species are easily blurred. Locke, for example, argues that [t]here are creatures in the world that have shapes like ours, but are hairy, and want language, and reason. There are naturals amongst us, that have perfectly our shape, but want reason, and some of them language too [. . .] If it be asked, whether these be all men, or no, all of humane species, ‘tis plain, the question refers only to the nominal essence (Essay 3.6.22).

For the most part, early modern thinkers stuck by the principle that, as Edward Tyson puts it in his 1699 treatise, Orang-Outang, sive Homo sylvestris: “inter hominem et non-hominem medium non datur”.7 In this respect, Leibniz is squarely in the camp of the majority of moderates on the question of human cultural and phenotypic diversity. For him, radical difference is a mere superficial layer of individuals, concealing but not diminishing their underlying commonality. Leibniz appears to agree with Tyson that there are no missing links between humans and non-humans (even if this agreement would seem to violate Leibniz’s commitment to the principle that, when it comes to the taxonomy of any natural beings other than humans, natura non movit per saltum).8 For Leibniz, to the extent that environmental adaptation happens in a population, this change is morally charged – it may occur for the worse or the better – even if degeneration can never occur to the point where a group would lapse altogether beyond the borders of humanity. The group with whom Leibniz has nothing in common are those, like the racist pre-Adamites (if not La Peyr`ere himself), who would take a theory of the separate creation of different human populations to make the case that those created independently of the descendants of Adam and Eve are not truly human. It would be tempting to seek to root Leibniz’s anthropology in his metaphysics, in which such great emphasis is put on the idea that all individual substances express the same order of co-existence, all monads in the end are endowed with the same content. What makes this content look different is that, for the most part, expression in finite monads is confused, perceptions of most sectors of the world are “petite”. Every monad is in its way omniscient, even if it’s a sort of low-level omniscience that never rises to the conscious level. This means that, for Leibniz, you really can expect inhabitants of some South Pacific island to know the Nicene creed. They know everything (if not, admittedly, in a way that is of any practical use to them).

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Of course, Leibniz is also the last of the thoroughgoing optimists in the history of philosophy. His confidence that we all agree and can all come to agreement if we just reason hard enough would give way over the course of the 18th century to an increasing perception of radical – and unbridgeable – anthropological difference. Not surprisingly, this difference is emphasized most by those who are most intent on denying that human beings qua human beings share anything in the way of essence or any set of basic a priori truths. Thus Locke, for example, after listing reported practices of various peoples that are outrageous in their cruelty towards the ill, the elderly, and children, concludes that this is proof enough of the relativity of moral principles: There is scarce that Principle of Morality to be named, or Rule of Vertue to be thought on [. . .] which is not, somewhere or other, slighted and condemned by the general Fashion of whole Societies of Men, governed by practical Opinions, and Rules of living quite opposed to others (Essay 1.3.10).

One of the great ironies of early modern ethnography is that it was the religious and creationist world-view that spoke in favor of common origins for all humanity, while the abandonment of the need to interpret human diversity in scriptural terms easily led to polygenesis. Polygenesis, and the corollary belief in the essential difference between different groups, would enjoy its most widespread success in the context of 19th century American slavery, and would present itself as the account of human origins most in keeping with the best scientific evidence. The fact that this account of human diversity remains controversial in the 17th century may be traced in part to the enduring imperative in the period to stay faithful in speaking of origins to the traditional religious conception of humanity, according to which men are created in the image of God, and are in this respect absolutely distinct among natural beings; and according to which all men, in virtue of this God-likeness, are, notwithstanding physical differences, equal. The opposition to natural theology intimated by Locke and expressed with full force by Hume is a part of the story of the emergence of modern scientific racism over the course of the 18th century – if all of humanity is not a reflection of God, then gradations of quality become possible, greater and lesser proximity to the ape. This is the foremost lesson of Popkin’s study of pre-Adamism: That the religious radicalism that motivated Isaac La Peyr`ere to deny the global applicability of the biblical account of human origins quickly mutated into an apology for slavery and exploitation of non-white races. 19th-century racist polygeneticism, of which La Peyr`ere’s theory is a precursor, was ultimately replaced by a scientifically grounded monogeneticism over the course of the 20th century, and, for better or worse, even in a secularized context the case for moral responsibility towards a particular group of creatures continues to be indexed to evidence about shared ancestry. Leibniz, whether in the natural-theological vein of the end of his life, or the more traditional theological vein of the Novissima Sinica, may effectively be serving as an apologist for the missionaries. But he believes missionary work is a worthwhile project only because he presumes the full humanity of the Jesuits’ targets, and because he is convinced of the moral urgency of conversion, which is for him

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ultimately nothing other than a return. The fact that Leibniz conceives the inhabitants of different parts of the world as descendants of Adam and Eve – even if he is noncommittal on the details as to how they got there – explains not only his moral conviction that missionary work is good, but also underlies his theoretical account of the intellectual and technological attainments of other cultures.

Notes 1. I do not pretend to approach Leibniz’s sinology with anything approaching the completeness of Perkins’s work. What interests me here is what Leibniz’s interest in the Chinese reveals about his views on the origins of rationality and wisdom. Before Perkins’s work, much other very useful literature has appeared in recent decades, by both philosophers and historians of China, on Leibniz’s sinology. See, in particular, Mungello (1977) and Poser and Li (2000). 2. On Figurism, see Mungello (1999) and Lundbæk (1991). 3. For a thorough account of the reception of Chinese writing in 17th-century Europe, see Porter (2001). 4. This relatively rare expression in German of Leibniz’s views gives us nice insight into some of his more openly mystical inclinations. The original text runs as follows: “Nun kann man wohl sagen daß nichts in der welt sie beßer vorstelle, ja gleichsam demonstrire, als der ursprung der zahlen wie er alhier vorgestellet, durch deren ausdr¨uckung bloß und allein mit Eins und Null oder Nichts, und wird wohl schwehrlich in der Natur und Philosophi ein beßeres vorbild dieses geheimnißes zu finden seyn” (Letter to Duke Rudolph of Brunswick, 2/12 January 1697; A 1 13 117). 5. Discours, § 2. References are to Li and Poser’s (2002). The best English translation is Rosemont and Cook (1977). 6. See la Peyr`ere (1655); published the following year in English as Men before Adam (London, 1655). For a thorough study of the life and work of La Peyr`ere, see Popkin (1987). For one of the most important contemporary critical responses to the pre-Adamite theory, see Hale (1677). 7. “Between man and non-man there is no intermediary [being]” (Tyson 1699: Preface). 8. Giuliano Gliozzi (1977) would describe Leibniz’s position as “diffusionism”. “Degenerationism” is associated mostly with 18th-century natural historians such as Buffon and Maupertuis, but the term “degeneration” occurs in connection with accounts of variety in plants and animals at least as early as Francis Bacon. “Plants”, he writes, “sometimes degenerate to the point of changing into other plants” (Novum Organon, 30).

References Aarsleff, H. 1993. Descartes and Augustine on Genesis, language, and the angels. In Dascal and Yakira (eds.), pp. 169–195. Dascal, M. and Yakira, E. (eds.). 1993. Leibniz and Adam Tel Aviv: University Publishing Projects. Descartes, R. 1996. Meditationes de Prima Philosophia. In Oeuvres de Descartes. Edited by Ch. Adam and P. Tannery. Paris: Vrin. Fage, R. 1658. A Description of The whole World, with Some General Rules touching the use of the Globe. London: J. Owsley. Gliozzi, G. 1977. Adamo e il nuovo mondo: La nascita dell’antropologia come ideologia coloniale: dalle genealogie bibliche alle teorie razziali (1500–1700). Florence: La Nuova Italia. Hale, M. 1677. The Primitive Origination of Mankind. London: W. Godbid for Shrowsberry.

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Intorcetta, P. et al. 1687. Confucius sinarum philosophus, sive Scientia Sinensis latine exposita. Studio & opera Prosperi Intorcetta, Christiani Herdtrich, Francisci Rougemont, Philippi Couplet, Patrum Societatis Iesu. Iussu Ludovici Magni . . .Tabula chronologica monarchiae sinicae. Paris: Daniel Horthemels. Kircher, A. 1667. China monumentis, qua sacris qua profanis, nec non variis naturæ & artis spectaculis, aliarumque rerum memorabilium argumentis illustrata. Amsterdam: A. Jansson. Leibniz G.W. 1718. Otium hanoveranum sive miscellanea, Godfr. Guilielmi Leibnitii. Edited by Joachim Frederic Fell. Leipzig. Leibniz G.W. 1957. Novissima Sinica. Transl. D.F. Lach. Honolulu: The University Press of Hawaii. Leibniz G.W. 1977. Discourse on the Natural Theology of the Chinese. Transl. H. Rosemont Jr. and D. J. Cook. Honolulu: The University Press of Hawaii. Leibniz G. W. 2002. Discours sur la th´eologie naturelle des Chinois. Ed. and German transl. W. Li and H. Poser. Frankfurt: Vittorio Klostermann. Lundbæk, K. 1991. Joseph de Pr´emare, 1666–1736, S.J.: Chinese Philology and Figurism. Aarhus: Aarhus University Press. Mungello, D. 1977. Leibniz and Confucianism: The Search for Accord. Honolulu: The University Press of Hawaii. Mungello, D. 1999. Great Encounter of China and the West, 1500–1800. Lanham, MD: Rowman & Littlefield. Pagden, A. 1982. The Fall of Natural Man: The American Indian and the Origins of Comparative Ethnology. Cambridge: Cambridge University Presss. Perkins, F. 2004. Leibniz and China: A Commerce of Light. Cambridge: Cambridge University Press. La Peyr`ere, I. 1655. Prae-adamitae, sive exercitatio super versibus 12, 13 et 14 capitis V epistulae D. Pauli ad Romanos, quibus inducuntur primi homines ante Adamum conditi. Amsterdam. Popkin, R.H. 1987. Isaac La Peyr`ere (1596–1676): His Life, Work, and Influence. Leiden: Brill. Popkin, R.H. 1993. Leibniz and Vico on the Pre-Adamite theory. In Dascal and Yakira (eds.), pp. 377–386. 381 Porter, D. 2001. Ideographia: The Chinese Cipher in Early Modern Europe. Stanford, CA: Stanford University Press. Poser, H. and Li, W. (eds). 2000. Das Neueste u¨ ber China: G. W. Leibnizens ‘Novissima Sinica’ von 1697. Internationales Symposium. Berlin 4. bis 7. Oktober 1997. Frankfurt: Steiner. Ribas, A. 2003. Leibniz’s Discourse on the Natural Theology of the Chinese and the LeibnizClarke controversy. Philosophy East & West 53(1): 64–86. Tyson, E. 1680. Phocaena, or the Anatomy of a Porpess, dissected at Greshame Colledge; with a Praeliminary Discourse concerning Anatomy, and a Natural History of animals. London: Benjamin Tooke. Tyson, E. 1699. Orang-outang, sive homo sylvestris; or, The anatomy of a pygmie compared with that of a monkey, an ape, and a man. To which is added, A philological essay concerning the pygmies, the cynocephali, the satyrs, and sphinges of the ancients. London: Thomas Bennet and Daniel Brown.

Chapter 27

“Paroles Enti`erement Destitu´ees de Sens”. Pathic Reason in the Th´eodic´ee Giovanni Scarafile

’Ntender non la pu`o chi no la prova Dante, Vita Nova Dem Ursprung, dem Gedanken entfremdet, gen¨ugt dir dann weder das Wort noch das Bild A. Sch¨onberg, Moses und Aron

Prologue My aim is to show which model of rationality Leibniz uses in the Theodicy in order to capture the incommensurable nature and the absolute and individualizing inherence of evil. The point of departure (1) is the ineluctability of some traditional criticisms of the theodicies, which, often rightly, cast doubt on the effectiveness of the answers provided by philosophy. Re-reading Leibniz’s text, in an attempt to respond to these dramatic doubts, requires first of all (2) that an adequate paradigm of understanding – an epistemological issue – be proposed. Adopting this paradigm leads (3) to a concept of theodicy with a stable symbiosis between experience and abstraction, between the presentification of evil and the delay in representation by the logos. (4) Erroneous interpretations have at different times viewed the theodicy as (4.1) consisting of the purity of the formal logical conditions in which the process of accounting for evil is undertaken or as (4.2) the removal of the difference between commensurability and incommensurability of evil. The phenomenology of incommensurable suffering (5) reveals the operation of an underlying “pathic faculty” which is decisive for the individual’s constitution. The next step (6) is to return to the linguistic paradigm which is at the basis of the mysteries of faith, as sustained by Leibniz in the Th´eodic´ee, and which underlies the examination (7) of the value of Leibniz’s hoped-for “analogic intelligence”. This path leads to the discovery of a specific form of rationality (8) at work in Leibniz’s text – here called “pathic reason” – capable of acknowledging the scandal of evil, which, according to the critics, is removed by the theodicy.

G. Scarafile University of Salento, Lecce, Italy

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1 The Ineluctable Nature of the Criticisms of the Theodicy Let me introduce the working hypothesis underlying this chapter on a purely personal note: I myself have always been particularly impressed by the criticisms of the theodicies, especially those concerning Leibniz’s theory. It is an undeniable fact that, because the questions they pose are so radical and so relevant today, these criticisms continue to fascinate us. How can one not feel called upon to answer the dramatic question posed by Dostoevskij, when he observes that even if at the end of the world at the moment of eternal harmony something so precious will come about and will be revealed that it will be enough to overcome all men’s misdeeds, all the blood they have spilt [. . .] what use is hell for the butchers, what can hell rectify, when the infants have already been massacred? And what harmony is this, if there is hell? (Dostoevskij 1974: 251ff.).

The criticisms I will look at can be linked to two main polemics: (a) Leibniz’s theodicy supposedly does not place enough importance on the individual dimension – the “concrete existence” of the single individual. The theodicy claims to have higher aims, but – even accepting the existence of these aims – evil, the irrational, does not stop being such simply because it is preordained for a good and rational purpose. It is unacceptable that what happens to men should be judged from a point of view that transcends them: After all, should not the beings and the events of this world be measured with their own yardstick? (b) the Th´eodic´ee is alleged to obtain its results by presupposing abstract reason, showing indifference towards what it seeks to know. Is it not inhuman to believe that the suffering of a human being can become the humus for future harmony? Suffering as such cannot be transcended and there is no way it can be accounted for. Therefore, Leibniz’s magnificent system supposedly fails in that which makes it unique “as the greatest attempt ever made to shift philosophical thought away from man and to conceive of him starting from the infinite Whole of which he is part” (Friedmann 1962: 256–257).1 Significantly, Sertillanges (1954: 46) has observed: Laws, general cases, are only abstractions; what exists is individuality, and if the problem of individual evil has not been solved, the Prime Mover is at fault. This truth must be proclaimed firmly for it has been misunderstood more than once in Christian apologetics. Some have dared to say that as God owes nothing to anyone, he could carry out his grand design ignoring pain and suffering, without caring about miserable humans. We are nothing before him: that he should treat us as nothing is right. Such arguments are repellent.

These initial considerations already pose some crucial questions: How important is the individual dimension in the theodicy? What type of reason must one use in the attempt to defend God from the accusation of being the creator of evil, and what path does Leibniz actually follow on this? Is it really plausible that the issue of individuality, Leibniz’s constant concern, actually disappears in the Essais de Th´eodic´ee? Briefly put: is Leibniz’s theodicy still relevant?

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2 Verstehen: Progressus ad Futurum and Regressus ad Originem The direction of the previous questions calls for renewed attention to the not-tounderestimated paradigm of understanding (Verstehen) and to its significance in the debate on Methodenstreit. This is a rather delicate area, whose in-depth study is beyond the scope of this chapter. Nevertheless, I would at least like to outline, with Heidegger, Husserl and Merleau-Ponty, the general reference points in this hoped-for re-thinking. In order to avoid the risk of philodoxy, philosophy must allow a kind of movement backwards. One needs to be able to recapture the mainspring of sense (Sinngenesis) which led to the doctrine of the philosopher under study. The condition for authenticity in carrying thought forward, progressus ad futurum, is necessarily regressus ad originem. It is necessary to move from the doctrine to the “primary possibilities” within which it may have emerged, according to a model indicated by Heidegger (1929: 195): By repetition of a fundamental problem we mean making explicit its primary possibilities which are still hidden. In putting these possibilities to work, the problem is transformed; but this is the only way to safeguard its problematic nature. Safeguarding a problem, moreover, means keeping the inner forces that enable it to be a problem alive and free, at the bottom of its essence.

This requires going beyond the boundary constituted by act intentionality, which underlies our judgements, to admit the existence of a more general orientation towards the world, antepredicative operative intentionality (fungierende Intentionalit¨at), as Husserl (1929: 291) indicates: Living intentionality leads me, commands me, determines practically my whole practice, also in the natural way I think, whether it produces being or appearance, and when, in its vital operation, it remains inexplicit and covert, and therefore beyond my knowledge.

Thinking about a doctrine will be all-embracing to the extent that one manages to achieve a re-positioning with respect to the interrelation between the essential individuality of the philosopher being studied and the world. The success of the operation will not lie in any sort of grasping, but in “repositioning the causes and the sense of the doctrine within a framework of existence” (Merleau-Ponty 1945: 29). What might incorrectly be seen as the aim of such an activity, which eludes the grasp of discussion, constitutes a destination: thinking-an-author becomes thinkingwith-an-author. The researcher is thus required not just to follow in the footsteps of the philosopher studied, something that happens every time a reasoned commentary is made of the text, but rather to identify the sense of those footsteps and to advance further along that path. As Merleau-Ponty (1945: 27–28) remarks, [w]hether it is a thing perceived, a historical event or a doctrine, “understanding” means recapturing the total intention [. . .]. The task is to recover the formula of a unique attitude towards other things [. . .] A certain way of shaping the world, which the historian must be able to recover and to adopt.

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3 Philosophical Theodicy The hermeneutics introduced with this paradigm means that even the definition of theodicy is far from being conclusive. It is not without relevance therefore to ask ourselves some fundamental questions in the attempt to bring out the unexplored “primary possibilities”. When the search for the meaning of evil is carried out with rational arguments, using the tool of logical consistency, of non-contradiction, of global systematicity, starting from unequivocal concepts such as God’s existence, omnipotence, omniscience, and goodness, and when the purpose is vindication, the theodicy becomes philosophical theodicy, an “apologetical response to the accusation that God’s justice allows evil to exist in the world” (Poma 1995: 6). Reason tries to acquit God of the indictment of being involved at some level with the problem of evil. Indicting is not something everybody finds himself capable of doing, for taking legal action presupposes a precise ability. Taking God to court implies that man has acquired a position towards the world and before God himself. Philosophical theodicy becomes possible in that the Greek conception of man has been definitively surpassed, since “it would never have entered the head of any Greek philosopher that the eternal order of the universe needs to be justified because of mortal man” (Moretto 1988: 247). In the Greek world, man is affiliated with the affairs of the universe, though not indifferent to the problem of evil, as is shown by Epicurus’s famous tetralemma handed down to us by Lactantius in De ira Dei (Lattanzio 1973: 659): God either wants to eliminate evils and cannot, or can and does not want to, or does not want to and cannot: if he wants to and cannot, he is impotent, but this cannot happen to God; if he can and does not want to, he is envious, and nor does this suit God: if he neither wants nor can, he is envious and impotent, and therefore is not even God; if he wants to and can, and this alone is what is suitable for God, where then do evils come from and why does God not eliminate them?

In order to achieve the indictability mentioned above, a totally new paradigm would have to be introduced. This step is taken with Christianity and it can be symbolically traced in the Biblical story of the Creation, in particular in Genesis 2.19f., where God grants man the power to name things. The act of naming is not merely an affirmation of identity. Nomen est omen: The destiny of things is written in the name. The man the Biblical God empowers to name things is a man placed at the top of the creation. Naming, in the Biblical sense, is ordering things in one’s own terms. The universe is therefore represented in the form of humanity. Man, at the top of creation, is endowed with new responsibility. This is at the root of the legitimacy of the legal process mounted by philosophical theodicy. Finally, in the modern age, indictability is translated into “tribunalization”: In the modern age, this is the ‘initial’ [. . .] philosophical tribunal. Three quarters of a century before Kant’s Critique and Fichte’s Doctrine of Science, philosophy had been made into a court in which man tried God for the problem of evil in the world (Marquard 1991: 95).

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Regardless of the results, the tribunalization of God implemented by the theodicy by means of philosophical reason achieved its initial objective: To tie the destiny of God to that of reason. The theodicy, allowing us to “plead the case for God, although this case is simply that of our reason which, out of arrogance, cannot see its own limits” (Kant 1991: 131), becomes logodicea, or the “justification of reason as the final unifying principle which cannot be contradicted by any presumed knowledge deriving from supernatural intervention or revelation” (Cassirer 1986: 346). Together with these two dimensions, two others make up the specificity of Leibniz’s theodicy. Firstly, the specific concept of reason, identical to God’s reason, the portion of reason we possess is a gift of God, and consists of the natural light we were left with even after the Original Sin, this portion is identical to the whole and differs from that of God only in the way a drop of water differs from the ocean, or rather, the finite differs from the infinite (GP 6 84).

It is a type of reason, continues Leibniz, that is valid in that it is a concatenation of truths. “Proper reason is a concatenation of truths; while corrupt reason is confused by prejudices and passions” (ibid). Secondly, it is for these reasons that it can judge a priori, with reference to the eternal truth into whose sight it is admitted. This has great importance in understanding the specificity of the Leibnizian theodicy. Leibniz’s theodicy, a priori, is not to be confused with other types of theodicy, like the a posteriori one, formulated in Alexander Pope’s An Essay on Man. This, however, cannot be used as a refusal to consider what comes from the domain of experience: It is true that one can imagine possible worlds free from sin and misery; [. . .] but these very worlds would be, from another angle, greatly inferior to ours in goodness. I could not show them to you in detail, for how can I know and how can I show you infinites and compare them? But you must judge it with me ab effectu, since God has chosen this world as it is (GP 6 108).

4 Logos: Delayed and Inappropriate Statement of Account Based on what has been said so far, the inevitability of delay can be considered an unavoidable condition for the very existence of the theodicy. In the attempt to justify the mala mundi, the philosophical endeavour that deals with the theodicy must distance itself from these evils. In fact, just as in everyday life, being too close to an object leads to invisibility, so when dealing with the theodicy, by stepping back one tries to get a clearer vision of the thing one must explain. The conceptualization of the presence of evil, an aspect of “mediacy”, begins from the immediacy of evil itself, directly or indirectly experienced. The greater the immediacy of evil, the more urgent it is to start the phase of justification-rendering accounts. In the theodicy, there is a symbiotic relation between the immediacy of evil and the delay in giving a statement of account. The two terms in the relation, immediacy and mediacy, cannot be considered independently of each other.

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Unfortunately, the distance between immediacy and mediacy sometimes becomes so great that the focus of debate becomes rarefied, and while the subject may not disappear, the results are largely distorted. This is the outcome in at least two cases: (4.1) in cases where the aims of the theodicy are considered to have been achieved insofar as the formal logical conditions for giving a statement of account have been fulfilled; (4.2) in cases where the difference between commensurable and incommensurable evil has not been made a subject of discussion.

4.1 Arithmetic of Thought as Shipwreck of Reason With reference to the scandal of evil, the “arithmetic of thought” can be compared to the “shipwreck” of reason. Just when one believes that the desired purity of the required conceptual tools will give privileged access to evil, then evil withdraws. In other words, the analysis that believes it can in some way grasp evil (by only conceptual, formal logical or philological means) finds itself reasoning in the absence of evil. It is precisely here that one realizes the meaning of an erroneous approach to the question of evil, or, to use the paradigm mentioned previously, the short-circuit between operative intentionality and act intentionality, when the latter tries to repress the former.

4.2 Incommensurable and Commensurable Evil Pain, suffering, affliction, and physical malaise are terms often used as synonyms. In fact, they are specific gradations of suffering, characterized by the degree of harm inflicted homo patiens. We shall now examine this aspect and its implications for our topic more closely. There are pains that, though violent, leave no trace on those who suffer them, once they pass. “A merely physical pain is a minor thing and leaves no trace in the soul. Toothache is an example: a few hours of violent pain caused by a bad tooth, once they have passed, are no longer anything” (Weil 1988: 86). In this sense, a kindly view has been taken of pain. It has a healthy function, an alarm-bell that forces the individual to pay more attention, to avoid worse consequences. This view of pain was part of a conceptual model which is now obsolete. Ren´e Lariche (1949: 121), the pioneer of modern neurosurgery and pain therapy, remarks: I am always more convinced that pain is not a natural thing [. . .] it is not part of human physiology as a beneficial defence warning [. . .] A defensive reaction? But from what? Against cancer, which usually starts to hurt when it kills? [. . .] Pain does not protect man, it humiliates him.

Pain gives us a perspective of our limit by letting us see the shortcomings of limits. Suffering becomes an opportunity to become more aware of our own individuality.

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Precisely because the experience of suffering is tied to the knowledge of the inexorability of one’s own experience, each individual feels he has been thrown into an existential situation in which he alone can feel the urgency of pain. In pain, nobody is replaceable. What more than pain makes us feel our limit? It is for this reason, therefore, that pain contributes to the defining of individuality. “This reference point, which we see as ‘I’ [. . .] becomes a quite peculiar ‘I’ in pain” (Natoli 1986: 17). First of all, pain then breaks in like an unexpected event. Breaking in [from ˘ ˘ irrumpere: “break” (rumpere) in (in-)] clearly denotes the consequences for the person affected. The violence of pain is the incontrovertible, unyielding certainty of catastrophe. Pain, inevitable and unpredictable, feeds on pain. It is beyond any possible control, it is steadfast, irreconcilable, unjustifiable. When one is caught up directly or indirectly in an uncontrollable pain, nothing can make sense. Pain overcomes sense. The only possible sense is to reject the pain, to deny it a sense. It is precisely this distance from sense that makes vain any attempt at explanation. Words lose their value, there is only space for lamenting or for silence. The person feels part of a more powerful destiny in which he can only remain silent. Man is imprisoned in his pain. The impact of pain disempowers the very being of the person who suffers it, prevents action, reduces the person’s ability to react, and makes it impossible for him to leave the stage on which his tragedy is being played out. One cannot escape pain. It admits no other response than consternation and disorientation. Disorientation means being forced to view reality with new eyes, in a new light. It is the very radical character of pain that is responsible for a new vision of the world. The world is seen from a different perspective. If every perspective is different from all others, the vision of reality that is triggered by pain is even more starkly different. Disorientation is transformed into an orientation within existence. The immediate outcome of suffering is [a] sidetracking from our usual way of seeing life; it casts a different light on our life, it makes it necessary to change track, to question our understanding of ourselves, of others of the natural world, it punctures and reorders our beliefs, it brings us back to reality and especially to our finiteness (Zanardi, undated: 59–60; my italics).

Pain falls silent and gradually becomes the consciousness of pain. The consciousness of an impairment, of a privation, that changes the enjoyment of what used to belong to us. This privation increases our distance from the world, and weakens its hold. Under the weight of the pain suffered, one no longer feels the need to extend oneself, to act, to take the initiative. Exactly the opposite happens: one becomes passive, observing reality rather than participating. Such an individual personally experiences the lack of all prospects: [S]uffering is essentially an experience consisting of feeling an obstacle and a laceration, making us feel unsuited to the world around us. From this world we receive stimuli to re-adapt, but in suffering these stimuli surprise and upset us, creating a sort of discontinuity and failure which makes us feel weak and incapable. We feel inadequate, we perceive the fragility of our being, we feel alone, we learn of finiteness and we feel the need to get to know ourselves, others and nature again (Zanardi, undated: 60).

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The presence of physical pain above the normal threshold is such that thought is blocked, and is prevented from turning to anything outside the pain itself: pain becomes the thought of pain. Only when the impotence produced by pain has been assimilated is there an initial evolution in the pain, namely a “knowledge of suffering”. It is the immediate knowledge of suffering and, at the same time, a new perspective in the vision of things. The diminished access to one’s own faculties also triggers a “suffering of not knowing”: the direct experience of pain, in other words, exposes one to error.

5 Individuation and Pathicity Reference to the phenomenology of pain enables us to discover the role of feeling and of living experience and to demonstrate the value of these dimensions which in pain become visible due to the threshold of extraordinary intensity reached, but which obviously do not disappear when pain is absent, i.e., under normal conditions, when they are not under the scrutiny of attention. Moreover, this enables us to deduce the indissoluble connection between “inadvertent feeling” and the constitution of identity.2 What is actually so interrelated with life itself that no immediate visibility is required? Is there anything that constitutes life more than the possibility of its negation, as it emerges in pain? It is the awareness of this deprivation that constitutes a factor of individualization. This factor therefore appears, independently of the will of the person experiencing, when one finds oneself unable to carry out one’s vital functions; it springs from the sense of expropriation. Ex-proprius indicates the force of being taken away from oneself, and therefore the revelation of one’s own real nature. For this revelation, feeling is therefore decisive. Feeling and lived experience are parts of a precise faculty, namely, pathicity. It would be useful to clarify some concepts that will be used in the rest of this chapter. Two separate, interacting dimensions converge in the concept of experience: It is in fact the knowledge and the practice of things acquired in trials made by ourselves and others. The Greek term ␧´ ␮␲␧␫␳´␫␣ indicates not only experience proper, but what is obtained by passing through. In the Latin form of the term, the semantic core refers to the term ex-perientia, in which the addition of “ex” to the verb perior signals the completion of the passage through, what remains after it has been tried. Getting through and the indispensable nature of the trial: this is how we can sum up what etymology tells us about “experience”. Two separate but interacting dimensions can be identified: (a) the first phase, sensitive, antepredicative, primary; (b) the second phase, intellectual, predicative, the conceptual organizer of the material presented. These dimensions can, however, be indicated with different terms: in the first case as ␲␣␽o␵, ´ affectio, Erlebnis and therefore life lived, sense – we have entered the realm of feeling, of pathicity; in the

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second case, as ␧´ ␮␲␧␫␳´␫␣, experientia, Erfahrung and therefore experience in the sense of the constitution of an object, the ideality of a representation, signification. In lived experience there is the sense of a new gnoseological approach to psychological facts: Approaching life with life. This is possible only if the living thing is considered in a vital act which lets it re-live (Nacherleben). The other is therefore an event. If intentionality, in the sense of aiming at a target, constitutes a way of relating logically, then being taken as a target (as in the case of pain), the root of passive subjectivity, embraces all mankind. It can be rightly raised to become not merely an anthropological, but an ontological, dimension. On this, Masullo (2004: 126) acutely observed: This is actually the condition not only of emotion but of any lived experience. Not only is there no truly human pleasure or pain, reasoning or action, imagination or memory, albeit hidden away but always ready to spring out and make itself felt in the various moments of life, that does not bring with it ‘the astonishment of the manifestation of the self’ and “ ‘the anguish of being affected by events for no reason’. Every occurrence affects me, just me, without me knowing why, just as I do not know where this ‘me’ comes from and where it is going, or even why it has been just my turn to be affected. With this ‘happening to me’, the consciousness of ‘me’ yet again goes beyond its present con-sistency and precisely in this I exist.3

The individuation that can be expressed by pathicity therefore belongs to the relation between operative intentionality and act intentionality. It coordinates the passage from the former to the latter and requires the latter to refer to the former as its source and as the condition for its truthfulness. The principle of individuation constitutes the individuation of an absolute inherence, or rather, of an absolutely individualizing inherence.

6 The Linguistic Paradigm of the Mysteries of Faith At this point, let us recall for a moment the linguistic paradigm adopted for the mysteries of faith, with particular reference to what is written in §54 of Th´eodic´ee, Preliminary Discourse (GP 6 80). It is not possible, explains Leibniz, to achieve “adequate notions” of the mysteries, but merely imperfect explanations. Precisely because of this, a particular way of naming is needed: It is not the absolute word, a sort of mirror in which the thing is reproduced exactly, that can save us from uttering “paroles enti`erement destitu´ees de sens”, but an expressive reference made possible by an “analogical intelligence”. Preserving the mystery requires “an explanation that is sufficient for belief but never enough for understanding” (§56). After all, continues Leibniz, when there is no longer the critical warning laying down that the ineffability of the unfathomable must be preserved, one can repeat what the Queen of Sweden said about the crown she had given up: “Non mi bisogna e non mi basta”. In other words, concludes Leibniz, “[a] certain ‘what it is’ is enough for us [. . .], but the why [. . .] escapes us and is not at all necessary”.

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As we know, the position of the mysteries of faith refers firstly to a particular version of the relation between faith and reason, but above all to a special convention concerning the type of language that can be used to refer to them: “The mysteries can be explained just enough for us to believe them, but they cannot be understood nor can we be shown how they are produced” (§5). What happens in the gap between the explanation that suffices for belief and the impossibility of achieving a conclusive understanding? The definition of this particular convention, continues Leibniz, is common to other dimensions of reality: “similarly in physics we can, up to a certain point, explain many tangible qualities, but imperfectly, because we do not understand them”. It is in this sort of extension of the applicability of the convention of the mysteries of faith that Leibniz seems to authorize the operation that I, at least in part, would like to try to carry out, in response to the following questions: (a) what is inherent to the language convention adopted for the mysteries of faith? (b) concerning the theodicy issue, what is involved in using the “analogical intelligence” that Leibniz talks about? (c) are there other aspects of theodicy that have a “special convention”? In particular, can we use the same paradigm for physical evil? And if this is possible, what are the consequences for theodicy and for the reason operating in it?

7 Commensurability and Incommensurability of Physical Evil As we know, one of the three divisions in theodicy concerns physical evil, which can be made to serve a function: It thereby becomes a way to acquire a greater good. We know that the way Leibniz deals with physical evil in Essais de Th´eodic´ee is made possible by his adoption of the Augustinian schema which envisages the de-substantiation of evil, in Chapter VII of Confessions: “the evil whose origin I was seeking is not a substance”, writes Augustine, “because if it were a substance it would be a good” (Augustine 1997: 204). However, the mechanism of denying the substantiality of evil risks breaking down before certain forms of evil which, by their very nature, cannot be made to serve any function nor be accounted for. This is the case of incommensurable evil. As Ricoeur (1996: 90) remarks, [e]vil is the breaking point of every system of philosophical thought: if it understands evil, that is its great success; but evil understood is no longer evil, it has ceased to be absurd, scandalous, without law and without reason. If it does not understand it, then philosophy is no longer philosophy, at least if philosophy must understand all and stand as a system with no loose ends.

The very “difference” of this different scenario in which reason finds itself, made up of the incommensurability of evil, calls for a new form of response, the adoption of a new paradigm.

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According to traditional approaches, in fact, consciousness would be undeniably faced with the impossibility of finding a sense, an essential structure, and would therefore be condemned to total silence. This silence would in fact correspond to a deafening cry of defeat, due to a misjudged approach consisting of erroneously extending the objectifying conception of being to all reality, wrongly considered the only valid path to knowledge. There are, however, dimensions of reality, and incommensurable evil is one of these, whose power lies in the impossibility of attributing to the justice of the logos what does not pertain to the logos. The incommensurability of evil, Leibniz seems to be saying, requires a different mode of expression which, while not forgetting the need for the “presentification” of evil but taking into account that it is impossible to achieve an eidetic vision, still leads, perhaps more effectively, to the Theatrum Iniquitatis, where the question becomes empirical. Therefore not just Unde malum?, but also Quomodo mala? The incommensurability of evil is the stumbling block of a form of reason that believes it can approach what is to be known independently of what is to be known, in the double sense of not considering any possibility that the knower may change or that the method of knowing may vary in order to adapt to the nature of the thing to be known. The incommensurability of evil is the point of no return for a form of reason that therefore recognizes impassivity as the key to knowing. If the need to account for all forms of suffering (not so much in the sense of justifying them) is not met, theodicy risks imploding. This makes it urgent to adopt a different paradigm for the form of reason that wants to take on the difficult task of naming the unnameable, avoiding the enormity of the “idle words” of the theodicies championed by Job’s friends. In the Th´eodic´ee, the fact that the language paradigm of the mysteries of faith is extended to incommensurable evil makes explicit a different dimension of reason, which I am going to call “pathic reason”. Before briefly examining the specifics of pathic reason, I would like to recall that the dimension of incommensurable evil was not foreign to Leibniz’s thought, as has been suggested in the (perhaps rather clumsy) attempt to argue the case of Leibniz’s supposed optimism. In 1677, Leibniz and Eckhard discuss whether existence is perfect. If one accepts the tradition based on the equivalence of being and good, then pain, in that it is existent reality, would be a perfection, i.e., something very different from the traditional definition of pain as “privation of good”. I: then pain is also a perfection? He: pain is not something positive, but the privation of tranquillity, just as darkness is the privation of light. I: it does not seem to me that pain can be called the privation of pleasure any more than pleasure can be called the privation of pain. In fact both pleasure and pain are something positive. And the relation between pain and pleasure is very different from that between darkness and light. In fact darkness cannot spread and dissolve if there is no light, and there are no deeper shades of darkness where light is absent. In contrast, pain does not exist merely for the elimination of pleasure and one pain is stronger than another: it follows that the all-perfect Being must also have pain (GP 1 214).

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In the answers that followed, Eckhard was to put forward the traditional arguments again, conceding that pain was positive only as sensation, but as pain it would remain a deprivation, non-being. This was how Eckhard actually defended the goodness of the existent. As Poma (1996: 625) remarks: Pain is introduced here by Leibniz like the real stumbling block of ontology, which with its dramatic inalienable reality makes it impossible to accept that being and good are equivalent [. . .] The point Leibniz drives home is precisely the reality of pain and the moral impossibility of considering it a mere deficiency of being in the traditional ontological sense.

8 Analogy and Pathic Reason In what terms, then, can we refer to pathic reason? What is the relation between analogy and pathic reason? To answer this question we have to go back to the earliest findings of transcendental phenomenology. In Ph´enom´enologie de la Perception, when wondering about the power of a “successful expression”, in the sense of “effective” but also of “adequate to the nature of the thing”, Merleau-Ponty (1945: 212) observes that an expression is successful if it manages to make “exister la signification comme une chose au coeur mˆeme du texte” (my italics), “to make the meaning exist as a thing in the very heart of the text”. In other words, the “success”, as it were, of an expression does not refer to the improbable and perhaps impossible task of “presentifying” the thing to be named, so much as to an analogizing inclusion, “as a thing”, whose power is such that it can overturn the canonical distinction between sign and signification. It is no accident that the French philosopher uses a particular expression to indicate the miracle of the transformation of the convention: “[l]a signification d´evore les signes”, “meaning devours the signs” (ibid.). Where intended meaning can be recuperated is in perception. The representational consciousness is perspectival in nature. The condition that allows visibility is the special relationship set up between the perceived object and the ground. In Merleau-Ponty’s words: The object-horizon structure, i.e. the perspective, does not hinder me when I want to see the object: although it is the means used by objects to conceal themselves, it is also the means used to reveal themselves. Seeing means entering a universe of beings that show themselves, and they would not show themselves unless they could be hidden behind each other (Merleau-Ponty 1945: 212; my italics).

All things are understood by Abschattungen, by adumbrations, never simultaneously nor synchronically, but only of facets, each of which is what it is in that it contains a reference to the others. This first fact suggests a different view of the relation between perception and imagination. We must assume they are in constant interaction, in the sense that there exists a dialectical link between presence and absence, according to what is contained – albeit in an entirely different context – in the famous Hegelian assertion that every object “is in itself in that it is for others and it is for others in that it is in itself” (Hegel 1996: 100).

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Representation also involves a stage of the thing in the sense of stage-in-relationto, like a point of view that unfolds starting from a gaze. It must be made clear that no reference is being made to a gaze from the universe4 on the part of a supposed angelic being. In other words, one must beware of the so-called “dogma of immaculate perception” (Kaplan 1982: 2152). Talking about gaze obviously involves referring to a “situation of the gaze” or to being the embodiment of consciousness, the indispensable angle of reference for the entire reality observed. The possibility of unveiling the thing, when by this one means the minimum objective identity to be found underlying any intentional act, occurs neither in an aseptic environment nor in an anaesthetizing way. Adopting a perspective is always accompanied by a decision to look in one direction or the other, by a desire, a question, a doubt: “it is always a behaviour that evokes the thing according to a certain standpoint [. . .] The ‘intended’ object differs according to the perspective, but also according to the inherent quality of the perspective that ‘intends’ it” (Melchiorre 1977: 20). Assuming the above, several consequences follow: A language that only considered the relation between naming and determination, i.e., that wanted to name the this of the thing, das Diese, referring only to the aspect of presence, would lead towards the disintegration of the thing itself, according to what Hegel says in the opening pages of the Phenomenology of Spirit: If they really wanted to say this piece of paper on which they opine, and if they really wanted to say it, it would be impossible, because the tangible this, which is being opined, is inaccessible to the language of the consciousness, to what is in itself universal. In the actual attempt to utter the thing, the thing would disintegrate; those who started a description of it, would not be able to complete it, but would have to leave it to others who, in turn, would end up confessing that they were talking about a thing that is not. They therefore opine on this piece of paper, this one here which is quite different from that one there, but they talk about ‘real things, about external or tangible objects, about absolutely single essences’ etc.; that is, about all this they say only the universal; [. . .] when I say: a single thing, I express it as a universal whole; since every thing is a single thing; and equally, this thing is all one needs (Hegel 1996: 68–69; my italics).

Regarding naming, I will briefly consider a passage where Leibniz discusses what I would call the parrot’s syndrome: The understanding, however, cannot occupy itself barely with words, like a parrot. It must perceive some meaning, albeit general and confused, or – so to speak – disjunctive” (Short Commentaries on the Judge of Controversies; A VI 1 550–551; DA 12).

What Leibniz is discussing here, in the context of the general issue of the nature of a believer’s belief in the mysteries of faith, is the relationship between word (i.e., the believer’s words) and object (i.e., the believer’s objects of faith). This relationship may be investigated from different points of view, and one can lean towards opposite directions regarding the degree of intelligibility. As observed by Dascal, it is necessary to reach the right modulation between presence and absence, indirectness and directness:5 Whereas the solution proposed by Leibniz in the Judge of Controversies failed because it leaned too heavily towards unintelligibility, the solution which consists in attempting to prove the possibility of the mysteries leans too heavily towards intelligibility and therefore

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is also unsatisfactory. What is needed is some compromise which will ensure more than confused knowledge of the mysteries [. . .] but without requiring an a priori proof of their possibility, which would amount to requiring full intelligibility (Dascal 1987: 115).

Besides, if one reads what Leibniz writes in §23 of the Short Commentaries through the lenses of phenomenological categories, it is possible, I think, to find in this paragraph a confirmation of the hypotheses of the present chapter. Thus, if I heard Christ saying ‘this is my body’, it is necessary that under the sound ‘this’ I perceive confusedly all its antecedents in the period, which certainly includes the bread and whatever is contained in it. In order not to determine in this confused interpretation whether the bread is made of the body of Christ or whether something that is contained in it is actually the body of Christ, it would be sufficient to understand [the ‘this’] as ‘that which is the body of Christ’ (DA 12).

Don’t we find here a description of another symptom of the parrot’s syndrome? And doesn’t this new symptom consist in the conviction that the possibility of naming corresponds to the simple pointing by means of “this” to a present referent? As argued above, however, in order to define whatever is, not only presence is necessary, but also absence. Thus, it is necessary to envisage a language that is structurally capable of indicating the determination of the being, without excluding absence, i.e., the other than being. It is therefore necessary to refer to a word that can say/express the initself-ness of the being, but also the equally inclusive (for the identity of the being) non-determination. As has been pointed out, [a] language of this kind immediately addresses a reality, but while it is defining this reality it ends up above all capturing its network of relations and its link with the rest of existence: in this dual process, Being itself may appear, the logos which is shared and which binds that which is different. On this middle ground, in the belonging to each other that distinguishes beings, in this uni-diversity, the naming word may finally bloom (Melchiorre 1982: 38).

In the First of the Logische Untersuchungen, Husserl (2001: 291) distinguishes between “indicative signs”, or signals (Anzeichen) and “expressive signs” or expressions (Ausdr¨ucke). Indicative signs, like road signs, have the simple function of indicating something. Their function consists in standing for something other and in pointing us to the referent. This is different from expressive signs, such as a smile for instance. A smile is in fact a sign of the joy felt, in the sense that it indicates joy, it refers to joy, but it is itself an expression of that joy. In this case, there is a participation that constitutes the value itself of the sign. In this type of sign, there is an immediate intentional transfer between the physical appearance of the sign and its intentional meaning. The word capable of expressing evil must be of this second type: Not merely indicant and denotative but expressive, capable of suggesting the thing and the constellation of which it is part, without causing it to be hidden. It must therefore be a transparent word, an authentic word, which at every moment contains an invitation to return to it and to re-actualize the process leading to the re-materialization/ re-semantization of its content.

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In the analogical word, therefore, a structural transition is set up between the said and the unsaid. It is precisely this dynamic of constant transition that structurally excludes the possession of the thing desired. The logic of the analogical word is not exclusory, but inclusive; by convention, it cannot stake any claim, unless it is in opening towards the indeterminate. Secondly, it is reasonable to suppose that the fact that it is impossible to achieve possession of the thing constitutes a form of loss of power in the ability to name. It is not so much the knowing subject’s ability of unequivocally naming things that guarantees the event/advent of the analogical word, as the readiness to drop one’s aloofness, that is, the willingness to let every saying be preceded by a hearing. This change of perspective is, however, not without consequences, since it involves the knowing subject adapting to the thing known. It is, therefore, not the knower’s impassiveness but the opposite, his “pathicity”, the capacity to adapt to the thing to be known, that grants knowledge of the thing itself. And therefore, even merely on the basis of the analyses mentioned here, we have every right to ask ourselves whether it is not unjustified to remove the participative component of the intentional consciousness, since, as we have tried to show, every intentional relation originates from a being-with; a being of the thing for the self and of the self for the thing. When faced with things (and not only the more scandalous things like incommensurable evil), it seems that the condition for understanding the universal element is a modification of individual responsiveness. The condition for accessing the universal component, inherent to the experience of things, even the most unnameable, is the critical verification of a Zentrierung, the investment in one’s own life. It is in the space of this centering that philosophizing is defined. Here there arises a new order of the tasks of reason, not to exalt impassivity but to represent the courage and responsibility of the incarnation, as the authentic condition for a form of thinking in the sense of participation in the core of a finite human person, determined by love, in the essentiality of all possible things. In this sense, philosophy is a form of life and of experience, Erleben. It should be stressed, however, that pathic reason does not advocate in absolute terms the centrality of lived experience tout court; rather, it underlines that lived experience cannot be avoided in the attempt to gain access to the essential and the impersonal in ideas. As has been pointed out, what must be done is to envisage a type of reason and therefore a philosophy “that inherits from the “subjective thinkers” [. . .] all the radicalness of first hand experiencing-thought, [. . .] that must always speak for itself, and not by hearsay, but that cannot and should not speak of itself ” (De Monticelli 1998: 77; my italics).

9 Conclusion Our position, when faced with the incommensurability of evil, is similar to that of Dante vis-`a-vis the vision of the Ineffable. Intent as we are on searching for a word capable of naming the scandal of evil, the unnameable, we can only conclude with the same plea as the poet facing the Ineffable: “e fa la lingua mia tanto possente /

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ch’una favilla sol della tua gloria / possa lasciare a la futura gente”; “And make my tongue of so great puissance / That but a single sparkle of thy glory / It may bequeath unto the future people” (Il Paradiso, XXXIII, 70–72).

Notes 1. While the supposed incapacity of the theodicy to cope with the individual dimension due to abstract reason is a problem in philosophy tout court, its real scandal is applied to the philosophy of Leibniz, who, as we know, paid constant attention to the individual in his speculation. This is so true that it can certainly be said that the paradigm of individuality is the key to his philosophizing. 2. Notice that the relation between what I call ‘inadvertent feeling’ and individuality largely corresponds to the relation between “petites perceptions” and individuation dealt with directly by Leibniz in NE 2.9.1 (GP 5 121), Th´eodic´ee, §403 (GP 6 357), Remarques sur Le livre de l’origine du mal, §3 (GP VI 402), and Monadologie, §21 (GP 6 610). 3. I would like to point out that a decisive contribution to the definition of a paradigm of pathicity in Italy was made by Aldo Masullo. 4. ‘The gaze from nowhere’ somehow evokes the ideal formulated by Nagel, concerning the possibility of a condition of excellence for morality (and more generally for philosophy) insofar as it believes reality can be approached from a perspective of impersonal vision which is, in a sense, a-historical. 5. For the reconstruction of the debate on the Short Commentaries, I refer to Antognazza (1999: 117–141) and (2001). I wish to thank Maria Rosa Antognazza who gave me access to important information on this issue.

References Agostino. 1997. Le Confessioni. Milano: Fabbri. Antognazza, M.R. 1999. Trinit`a e Incarnazione. Il rapporto tra filosofia e teologia rivelata nel pensiero di Leibniz. Milano: Vita e Pensiero. Antognazza, M.R. 2001. The defence of the mysteries of the trinity and the incarnation: An Example of Leibniz’s “other” Reason. British Journal for the History of Philosophy 9(2): 283–309. Cassirer, E. 1986. Cartesio e Leibniz. Roma-Bari: Laterza. Dascal, M. 1987. Leibniz. Language, Signs and Thought. Amsterdam: John Benjamins. De Monticelli, R. 1998. La conoscenza personale. Introduzione alla fenomenologia. Milano: Guerini. Dostoevskij, F.M. 1974. I fratelli Karamazov. Milano: Garzanti. Friedmann, G. 1962. Leibniz et Spinoza. Paris: Gallimard. Hegel, G.W.F. 1996. Fenomenologia dello Spirito. Firenze: La Nuova Italia. Heidegger, M. 1929. Kant und das Problem der Metaphysik. Bonn: F. Cohen. Husserl, E. 1929. Formale und transzendentale Logik. Halle: Niemeyer. Husserl, E. 2001. Ricerche logiche, Milano : Il Saggiatore. Kant, I. 1991. Sul fallimento di tutti i tentativi filosofici in teodicea. In I. Kant, Scritti sul criticismo. Bari-Roma: Laterza, pp. 129–148. Kaplan, B. 1982. Lo studio del linguaggio in psichiatria. Il metodo comparativo evolutivo e le sue applicazioni alla simbolizzazione e al linguaggio in psicopatologia. In S. Arieti (ed.), Manuale di psichiatria. Torino: Boringhieri, 2150–2163. Lariche, R. 1949. La chirurgie de la douleur. Paris: Masson. Lattanzio. 1973. De Ira Dei. In Lattanzio, Divinae Institutiones. Firenze: Sansoni, pp. 627–677.

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Marquard, O. 1991. Esoneri. Motivi di teodicea nella filosofia dell’epoca moderna. In O. Marquard, Apologia del caso. Bologna: Il Mulino, 93–115. Masullo, A. 2004. Paticit`a e indifferenza. Genova: Il Melangolo. Melchiorre, V. 1977. Metacritica dell’eros. Milano: Vita e Pensiero. Melchiorre, V. 1982. Essere e parola. Milano: Vita e Pensiero. Merleau-Ponty, M. 1945. Ph´enomenologie de la perception. Paris: Gallimard. Moretto, G. 1988. Teodicea, storia e jobismo. Archivio di Filosofia 1–3: 245–271. Natoli, S. 1986. L’esperienza del dolore. Milano: Feltrinelli. Poma, A. 1995. Impossibilit`a e necessit`a della teodicea. Torino: Mursia. Poma, A. 1996. Dall’ontologia all’etica: Leibniz contro Eckhard. Archivio di Filosofia 1–3: 614–638. Ricoeur, P. 1996. Kierkegaard. La filosofia e l’ “eccezione”. Brescia: Morcelliana. Sertillanges, A.D. 1954. Il problema del male. La soluzione. Brescia: Morcelliana. Weil, S. 1988. Attesa di Dio. Milano: Rusconi. Zanardi, A. Undated. La sofferenza: senso del limite e occasione. In Filosofia del dolore. Matera: Societ`a Filosofica Italiana.

Chapter 28

The Authority of the Bible and the Authority of Reason in Leibniz’s Ecumenical Argument Hartmut Rudolph

The relationship between particular revelation in Holy Scripture and natural revelation, between faith and reason, between theology and philosophy, is a persistent, basic theme in Christian theology. The young Luther had introduced his reformatory change with a forensic soteriology, consciously and radically formulated in opposition to Aristotle (see especially his 1515–1516 Lectures on Romans).1 Philosophy and rhetoric entered into the discussion within Protestantism first, and in a fundamental way, via the sacramental controversy of 1524 and beyond. Luther’s chief argument against the Swiss theologians Ulrich Zwingli and John Oecolampadius and other so-called “enthusiasts”, found in his great polemical position paper, Vom Abendmahl Christi. Bekenntnis, 1528 (WA 26 261–509), a work repeatedly cited by Leibniz,2 may be set forth as follows: The sole basis of faith in the real presence of Christ in the sacrament of the altar consists of the clear words of Christ in Matthew 26: 26, “Hoc est corpus meum” (“This is my body”). Each and every attempt, whether by means of the metaphysics of transubstantiation (as undertaken since the Fourth Lateran Council of 1215; Denzinger and H¨unerman 1991: nr. 802) or by rhetorical means (as employed by Luther’s opponents in Switzerland and Upper Germany), that is to say, any attempt to resort to an interpretation fitting in more easily with strictly natural understanding, was for Luther an act of unbelief turning God or Christ into a liar.3 Luther wished to exclude unconditionally summoning the word of God before the judgment seat of natural reason,4 taking rather the reverse path in correspondence with I Corinthians 1:19 (“I will destroy the wisdom of the wise, and will bring to nothing the understanding of the prudent”) and 3:19 (“For the wisdom of this world is foolishness with God”). In line with this, the Augsburg Confession from 1530 – and Leibniz described his denomination as that which follows the Augsburg Confession,5 because he refused using the term “Lutheran”6 – affirms in the Pseudo-Augustinian words: “The reason proper to all men is not suitable for understanding godly things”.7 Lutheranism down to the period of Leibniz had brought about a number of controversies on account of the exclusivity of revelation vis-`a-vis all possibilities of cognition of a natural kind. Owing, among other factors, to the Lutheran philosophers H. Rudolph Berlin, Germany M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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in Helmstedt, the quarrel had led to an establishment of metaphysics within the Lutheran faculties (Wittenberg included). However, this by no means meant ranking reason above revelation, as would be the dominant position in the 18th century as a result of Biblical criticism by Deists and in German theology of the Enlightenment. On the contrary, Lutheran orthodoxy held fast to the unlimited authority of the word of God, claritas scripturae (and in particular in the debates on scripture and tradition as the fundaments of faith defined by the Council of Trent). Scripture was considered as self-interpretation (sui ipsius interpres). But this still did not rule out the validity of Aristotelian school philosophy with regard to the systematization of the contents of belief and discussion of them according to the rules of logic and dialectic. In this way, the “scientificization” of theology, in the sense of a methodical formal step-by-step rationalization of theology, was reached. With this as preparation, it came about – not yet on account of Martin Chemnitz and his Examen Concilii Tridentini (4 volumes, 1566–1573), whose ideas were to be given thorough consideration by Leibniz, but owing instead to Johann Gerhard (Loci theologici from 1610 to 1622, 2nd ed. 1625) – that theopneumatics, the verbal inspiration of Holy Scripture as the word of God,8 was taught for ensuring in a more or less scientific way its authority. Incidentally, this was done in exactly the same way as in the Swiss Reformed church, where the impulse came from the two Basel Hebraists Johann Buxtorf Senior and Junior. For them, as also for Lutheran orthodoxy later, particularly Abraham Calov,9 the vocalization10 of the Hebrew text was also “verbally inspired”. Let us go back to the question we began with, that of the relation of theology to philosophy, revelation to reason. There are certainly academic notions aimed at harmonizing both areas; to be sure, a determination of this kind – which was to become significant with regard to Leibniz and developments in the 18th century (Reventlow: 3rd part) – only has validity as far as reason or school philosophy are applied by theologians, namely, for the methodological, didactic, and rhetorical analysis of the theology of the various truths of belief and their logical connection. It is evidently from this specifically reformatory inheritance of a subordination of reason to the authority of Holy Scripture that the following sentence, with which Leibniz in 1683 introduces a basic passage on the theme of reason and revelation, derives: The foundation appropriate to our faith is not human reason but rather, the authority of God in His self-revelation. And that suits both our weakness and also divine wisdom. For the darkness of the human mind is so great that it is incapable of finding anything that is certain or reliable, even in the course of a long chain of reasonable considerations (A IV 3 269).

But then, Leibniz goes on: How few have dared [. . .] to assert that an arithmetical calculus can properly be derived from them if they have not found these considerations confirmed through various tests, [. . .] even though the entire art of calculation consists of rules that are few in number and easy to grasp. Is not a mistake going to turn up all the more easily when it is a matter of questions of the divine, questions that lie at a great distance from our imagination and our sensory experience? For this reason the truth, which in the case of salvation, really has to be comprehensible to people in general, would be accessible only to a handful of people and

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only the wisest among these had not God in His transcendent wisdom and goodness given a helping hand to us – with a new principle of cognition – and at one and the same time to the uneducated – with a manifesto, that is, a revelation which in the cognition of godly things proves to be just as excellent as experiments in the natural sciences. However just as in the natural sciences there is nobody who, if he has enough understanding, does not trust sense perception in preference to clear calculations – no clever astronomer is going to prefer his hypothesis to observations – so also, when reason and revelation are at odds, no one is going to distrust reason and substitute forcibly compelling revelation to fit the considerations of this reason of ours. I do not contest that which, along with me the most significant theologians acknowledge: When natural reason has established something with weighty arguments in such a way that, should one give no consideration to revelation, there is apparently no possible doubt about the matter and that revelation would yield the very same sense without a forced interpretation, then it is wiser to follow the sense of a proposition which accords with reason than pursue its terms on their very highest level, because with gifted men nothing goes against the grain more, and nothing leads novices to shrink back from religion more than when things of any kind are asserted by those giving instruction in piety in an absurd imperious way; by such a procedure one is only abandoning the authority and the name of Holy Scripture or of the church, and all the more certainly breeding hypocrisy and libertinism (A IV 3 270; see also Pichler 1869: 225).

It would be so nice if one could separate philosophy from theology, reason from faith, as was the case with the first Christians. But “for weighty reasons lying concealed in His wisdom God has permitted that gradually reason becomes entwined with faith when learned and world-famous Christians saw the necessity of fighting against godlessness in every possible way and every kind of weapons” (A IV 3 270). With respect to the question of the divine and primal nature of Scripture, Leibniz views, on the one hand, the witness of the church and the witness of history, that is, historical research which also demonstrates the historicity of Scripture. He recognizes as well the teaching role of the church. With Leibniz, there is a circle: we thank the church for faith in the sole authority of Holy Scripture, and we can only believe the church because Scripture teaches us this (A IV 3 276): Just as philosophers do not shy away from constructing their hypotheses with their natural reason on the basis of sufficient observations and, in turn, do not shrink from deducing other phenomena from these hypotheses, so we, too, have the beginning of the circle and its end (“principium et finem circuli”): like a witness, as it were, the church declares Holy Scripture to be correct, and, in turn, as a teacher recommends Scripture as well as the tradition of the church. Finally, as teacher the church determines the canon of Holy Scripture (A IV 3 277).

Here, in a piece on the reunion of the churches from 1683, Leibniz characterizes the relation of revelation and reason, religion and philosophy, as something that has grown historically. He analyzes it in a way that one could almost consider as belonging to the sociology of knowledge: The terms of reference are adapted to each social stratum; they differ in the case of simple workmen and slaves from in the cases where educated people and intellectuals are concerned. What he in general designates in his famous Examen Religionis Christianae (1686; later known as Systema Theologicum) as the foundation of one’s recognition of the truth of the Christian faith, namely Holy Scripture, piety in Antiquity, and ipsa recta ratio, i.e., reason itself applied in the right way, and the fides rerum gestarum, i.e., a suitable

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consideration given to the historical facts – he applies solely to an ordering of reason and revelation as the foundations of faith (A VI 4 2356f.). The course of the argumentation in the piece on the reunion of the churches from 1683 is instructive here: Seemingly, the statement in the first sentence is unequivocal in its clear exclusion of reason as the foundation of faith, that is, its clear positioning of divine revelation in Holy Scripture above reason. However, the fourth and fifth sentences reduce the unequivocal statement of the first sentence to a generality that has practically forfeited its relevance to the argumentation in relation to reason and faith; and I dare say that the latter sentences rather correspond more to Leibniz’s metaphysics than the first one. The witness of the Bible is subordinated to reason or, more exactly, suspended in favour of the criterion of exclusion of what is contrary to reason. For Leibniz, a criterion like this does not mean a lessening of the authority of Holy Scripture, because he is convinced of the harmony of reason with divine procedure and with God’s revelation. Here he stands in flat contradiction to Luther’s argumentation; for Luther, as has just been described, the word of God signifies the crisis of all human reason. In the Discours pr´eliminaire of the Th´eodic´ee, Leibniz nevertheless interprets I Corinthians 1:20 (“hath God not made foolish the wisdom of this world?”) as saying that the authority of Holy Scripture in respect to the “motifs de cr´edibilit´e” is tested once and for all before the tribunal of reason and then (“dans la suite”) all probabilities whose logic, as stated in § 28, is still incompletely developed, are sacrificed to Scripture (§ 29; GP 6 67). To a certain extent, there is a prologue in the courtroom of reason before man, the Christian, submits to the authority of Scripture. One could speak of a prepositioning of reason ahead of revelation de jure and the validity of Holy Scripture de facto. The “foolishness” and “offence” which Paul speaks of, is, for Leibniz, divine wisdom on the basis of the imperfection of man as far as the employment of reason is concerned. The “skandalon” (“stumbling block”) of the Jews and the “moria” (“foolishness”) of the heathen (I Corinthians 1:23) are the sign of a persistent imperfection of man, not – as with Luther – the inescapable judgment over all human reason. This should be demonstrated by a single example, taken from the piece on ecclesiastical reunion, the Unvorgreiffliches Bedencken of 1698 (published for the first time only recently; Vorausedition A IV 7 n. C3 142), which will enable us to examine the way in which Leibniz handles these differentiations in ecumenical practice. Here Leibniz applies the ecumenical method of his own devising. His starting point is that the intra-confessional controversies are based on a defective shifting of the switches in one’s preliminary philosophical understanding. Hence, what makes for a resolution is not appealing to earlier confessions or to relevant passages in Scripture nor by reducing the confessions to their supposed bases or the kinds of declarations that can be tolerated by both sides, but rather by an analysis of the mistakes in each philosophical presupposition, which gives rise to a seeming theological-systematic controversy. This divergence, in turn, makes it impossible for the contending parties to agree objectively because they think they have to renounce fundamental parts of their creed when faced with attempts of union of this kind. Instead of charging the other party with heresy – this is Leibniz’s expectation – the required effort must be

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centred on Christian love, on warning one’s fellow Christian and leading him on the path of truth by giving him insight into the consequences (never intended) of his utterance (Vorausedition A IV 7 nr. C3 142, e.g., fol. 176–184). The method by which this love is realized among dissenting Christians and churches is a philosophical one, since it is a question of a common truth available to all participants as reasonable beings.11 In the case of the real presence of Christ in the Lord’s Supper, this means the demonstration of the harmonization of this mystery with reason or, otherwise, the refutation of the view that to think of the real presence substantially introduces a figment counter to reason (Vorausedition A IV 7 nr. C3 142, fol. 258–314). Leibniz’s extensive argumentation concerning the decretum dei absolutum and the divine attributes (Vorausedition A IV 7 nr. C3 142, fol. 184r–257r) constitutes the attempt to introduce such an insight into the discussion of universalism and particularism of divine Election, which was being so violently disputed between Lutherans and Calvinists, and also within the Calvinist churches themselves. What resulted is an almost comprehensive exposition of the problem of theodicy, in which Leibniz, of course, regards universalism as the only possibility for grasping divine Election by Grace that is compatible with the divine attributes. Respect is given to particularism (or even a so called double predestination) as a consequence that follows logically from the idea of Election – and also in a “historical” sense cannot be doubted – that is, that God in His eudokia (in His good will) chose Peter, whereas the eudokia passed Judas by. And this must have in God, “who is wisdom and constancy itself” (Vorausedition A IV 7 nr. C3 142, fol. 252r), a causa impulsiva praedestinationis, which, say, with Luther, is ascribed to the deus absconditus, the unfathomable. However, Leibniz refuses to appeal to this on two grounds. The first is that every speculative assertion of a double predestination, of a limiting of the universalism of Election by Grace to only one part of mankind, necessarily leads to a contradiction; the second reason is that this Election by Grace could no longer be the “decretum dei absolutum” or affect the divine qualities, the divine perfection. Proceeding more geometrico, he proves that basing a double predestination on the “absolutum dei decretum” requires a thought-progression in infinitum, unless, turning things around, one were to connect a` la Pelagius the content of the divine Election by Grace with man’s free will. Since God cannot decide and do anything without a reason, the only remaining solution is a return to Holy Scripture, in which can be found the “impulsive cause of God’s will and of his decisions becomes discernible by [. . .] the succession of the good results,12 if not a priori, at least a posteriori” (Vorausedition A IV 7 nr. C3 142, fol. 252v). Leibniz draws a parallel between the refusal to base the damning of the “reprobati” speculatively on the “decretum absolutum”, and the cognitive rules of natural science: the former, theological-philosophical speculation is just as little indicated as “it is in physics allowed to seek refuge in qualitates occultae as far as the cause of a natural object can be recognized otherwise” (Vorausedition A IV 7 nr. C3 142, fol. 252v).13 Especially with this point, it becomes apparent that Leibniz hopes to bring about the ecclesiastical unity of the divided confessions through an objective settlement which expects nothing more from the disputants than the use of reason.

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In ecumenical discussion, Leibniz brings in the authority of Holy Scripture only as a supplement, i.e., only in the (practically unique) case that the use of reason leads to speculations which are no longer unmistakably reasonable – to conclusions, so to speak, leading to “occult qualities”. In the ecumenical discourse in the Unvorgreiffliches Bedenken, there is only one single situation of this sort, namely, in the question just described of double predestination. However, even Leibniz’s recommended manner for handling this situation follows in general the procedure established in the rational scientific method by analogy with the methods of the natural sciences. Herewith he is still following in 1698 the account previously explained, which he had described as early as the 1680s in his great writings on ecclesiastical union, regarding the relationship between reason and revelation, reason and the authority of Holy Scripture. Acknowledgments Translation of the German original by Joseph B. Dallett (Ithaca, NY).

Notes 1. See, e.g., WA 56 337 and 371. Leibniz himself refers to Luther’s Anti-Aristotelianism of 1516 (Th´eodic´ee, Preface; GP 6 57). 2. See De differentiis doctrinalibus, de praesentia reali et similibus (A IV 4 568); Excerpta ex disquisitionibus de gradibus unitatis (A IV 5 525). 3. See, e.g., Vom Abendmahl Christi. Bekenntnis (WA 26 283f. and 326). 4. In this connection Luther calls reason a “Wettermacherin”, that is to say, a witch or enchantress (WA 26 321). 5. “[. . .] me confirmer dans les sentimens moder´es des Eglises de la Confession d’Augsbourg” (GP 6 43). 6. “[. . .] den namen Lutherisch, kan ich [. . .] gar nicht wohl leiden, und wer die Christliche antiqvit¨at liebet und kennet, dem wird er, als nach der Secte schmeckend, nicht anstehen” (“I cannot endure the term ‘Lutheran’; everybody who likes the Old Christianity, will avoid it, because the expression tastes of sectarianism”, 1698; A I 15 833) As late as 1715, he supplies the reminder that this term taken from the name of an individual is bound to stir up quarrels among the other groups and that the Old Church rejected this (Baruzi 1907: 285). 7. Augsburg Confession, article XVIII (about the free will): “liberum arbitrium [. . .] habens quidem iudicium rationis, non per quod sit idoneum in his, quae ad Deum pertinent” (“free will [. . .] can, in a certain sense, be justified by reason; but this is not for matters which refer to [man in the face of] God”, Bekenntnisschriften: 73 4). Admittedly, what is missing in Melanchthon’s formulated statement in the Augsburg Confession (article X; Be-kenntnisschriften: 64 1f.) on the real presence of the body and blood of Christ in the Eucharist is the sharp precision of Luther’s argumentation (Neuser 1968: 450–473). Leibniz regarded Melanchthon as a model on account of his moderation in the efforts aimed at an agreement between the Roman Catholic and the Protestant positions; as early as 1677 he refers to him as “vir sine controversia et prudentissimus et moderatissimus” (A IV 2 127); see also A VI 1 323 (1667) and A I 9 197 (1693). 8. God is the actual author of Holy Scripture; this statement does not pertain simply to its factual content, but Gerhard teaches the literal inspiration of its words. This confers a quality of revelation on the text of the Bible (Hauschild 1999: 437).

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9. In his major work, Systema locorum theologicorum (12 volumes, 1655–1677), auctoritas, perfectio, perspicuitas, and efficacia are named as the four fundamental qualities of Holy Scripture (“affectiones scripturae sacrae”). Unclear passages in Scripture should be interpreted “secundum analogiam fidei” in line with its clear central statements (Hauschild 1999: 437f.). 10. Traditionally called “dotting” (Ger. “Punktierung”). This refers to the addition to the Hebrew text – which normally contains only the consonants – of signs (some, but not all of which, are indeed dots) that indicate the vowels, a practice that amounts of course to choices that have interpretive consequences. 11. Just as those theologians in the age of the Reformation who were formed by Humanism and ecumenically inclined, e.g., Martin Bucer, appealed to the Aristotelian formula “omne verum vero consonat” (Nicomachean Ethics, A 8, 1098 b 10–11), so, too, did Leibniz on occasion. The view underlying this formula is relevant both to the method of ecumenical efforts and also to the determination of the relationship between scientific cognition and Biblical exegesis. In the context of the interpretation of the Biblical story of creation in Genesis, Leibniz acknowledges that he is content with explaining those aspects of cognitive understanding gained in accordance with reason in a way that does not contradict Holy Scripture. “Car ‘verum vero non dissonat’ ”; April 8th (18th) 1698, to Thomas Burnett of Kemney (A I 15 489). See also Pichler (1869: 221), with reference to Leibniz’s Excerpt Joh. Georgij Wachteri de recondita Hebraeorum Philosophia 1706; Foucher de Careil 1854: 74). 12. “causa impulsiva voluntatis et decretorum divinorum [. . .] per bonam consequentiam”. 13. “[. . .] man in Physicis befugt ist ad qualitates occultas seine Zuflucht zu nehmen, so lang die Uhrsach des nat¨urlichen dinges sonst zu ergr¨unden ist”.

References Baruzi, Jean. 1907. Leibniz et l’organisation religieuse de la terre d’apr`es des documents in´edits. Paris: F´elix Alcan. Die Bekenntnisschriften der evangelisch-lutherischen Kirche. 1963. 5th ed. G¨ottingen: Vandenhoeck & Ruprecht. Denzinger, H. and H¨unerman, P. 1991. Enchiridion symbolorum definitionum et declarationum de rebus fidei et morum, 37th ed. Freiburg im Breisgau: Herder. Foucher de Careil, A. 1854. R´efutation in´edite de Spinoza par Leibniz. Pr´ec´ed´ee d’un M´emoire. Paris: Institut de France. Hauschild, W.-D. 1999. Lehrbuch der Kirchen- und Dogmengeschichte, Vol. 2. M¨unchen: Kaiser. Leibniz, G.W., Vorausedition (see the Internet publication in http://leibniz-potsdam.bbaw.de or http://www.leibniz-edition.de/). Luther, M. 1883 ff. Werke. Kritische Gesamtausgabe. Weimar: B¨ohlau [= WA]. Neuser, W.H. 1968. Die Abendmahlslehre Melanchthons in ihrer geschichtlichen Entwicklung (1519–1530). Neukirchen-Vluyn: Verlag des Erziehungsvereins. Pichler, A. 1869. Die Theologie des Leibniz aus s¨ammtlichen gedruckten und vielen noch ungedruckten Quellen . . . dargestellt. First part. Munich: J.G. Cotta. Reventlow, H.G. 1985. The Authority of the Bible and the Rise of the Modern World. Philadelphia, PA: Fortress Press.

Chapter 29

Leibniz on Creation: A Contribution to His Philosophical Theology Daniel J. Cook

1 Introduction Although Leibniz is arguably the last major European philosopher to undertake a rationalist defense of theistic doctrines, Robert Sleigh recently noted that the study of Leibniz’s “philosophical theology is in its infancy compared to the study of some other aspects of his philosophy” (Sleigh 2001: 165). In this paper, I hope to fill in some details in what Sleigh calls “the initial map of [. . .] the relevant terrain” of Leibniz’s philosophical theology. I wish to examine a doctrine central to his theistic apologetics that has been neglected or dismissed in recent Leibniz scholarship, especially in the English-speaking world. There is no more important doctrine in Leibniz’s philosophy than creation; it, in Robert Adams’ words, “has the largest role in Leibniz’s metaphysics” (Adams 1994: 94). Many interpreters of Leibniz have stressed the centrality of creation for his thought, yet at the same time argue that the notion of creation is ultimately “unintelligible” and any effort to describe it is “nonsense” (Broad 1975: 148). It is a “miracle” or a “Christian mystery” (Rescher 1973: 183) and thus Leibniz’s theory of creation is doctrinally, not philosophically driven. While creation may have a place in revealed theology, it “will clearly not do as a doctrine of a philosophical system” (Rescher 1973: 183). Another interpreter says, “theological orthodoxy [. . .] requires Leibniz to acknowledge that God creates the universe out of nothing” (Jolley 1998: 601). Such views would appear correct since Leibniz assumes that Creation (henceforth used as a proper noun when referring to the creation of the universe) is part of revealed theology, not natural theology. Indeed, in perhaps his most revealing comment on Creation, Leibniz says: “I admit the supernatural here only in the beginning of things” (T 66; GP 6 42). If Creation is a supernatural event for him, then by definition it cannot be part of any natural theology. Nevertheless, the above mentioned interpreters of Leibniz are wrong to claim that Creation must be dismissed as “nonsense,” spurned as “miracle” or “mystery”

D.J. Cook Brooklyn College, City University of New York, New York, USA M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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and seen only as a requirement of orthodox Christian dogma. I believe that Leibniz employs various forms of argument to defend this core doctrine of his philosophical theology. By philosophical (as opposed to natural) theology, I refer to those doctrines such as Creation that, though revealed, can be defended on rational grounds. The author of a recently published work entitled Philosophical Theology and Christian Doctrine defines philosophical theology as “revealed theology [. . .] refined and tested” by philosophical analysis (Hebblethwaite 2004: 37). Leibniz’s arguments in defense of Creation range from the purely deductive and dialectical to less logically compelling ones – from “hard” to “soft” reasoning. They take their inspiration from many sources, from history and geology to Plato – from jurisprudence to binary arithmetic. In this paper, I will touch upon some of his strategies in defense of Creation. In this way, I hope to demonstrate that while Creation is part and parcel of revealed religion for Leibniz, it occupies quite a different role for him than other mysteries or miracles that form the basis of orthodox Christian doctrine. It is important to note that the problem of the origin of the universe is not a purely theological one. In recent years several cosmologists (e.g., Hawking 1991) have argued that a theory of creation is the best possible explanation for a coherent cosmogeny. One writer has recently noted that: “A fully developed cosmological theory will tell us not just why the universe has developed as it has, but also why there exists a universe to develop in the first place” (Everitt 2005: 111).

2 Is there a Problem of Creation Out of Nothing? While it may be true that, in Jolley’s words, “theological orthodoxy [. . .] requires” the belief in creatio ex-nihilo, an examination of this doctrine is quite revealing.1 First, there is the problem of what “nothing” means here. There is only one direct reference in the Bible (in the Apocrypha) to the world being created out of nothing.2 The Bible opens: “In the beginning of creation, when God made heaven and earth, the earth was without form and void, with darkness over the face of the abyss [. . .]”. It is doubtful whether the writers of Genesis 1:1–2 possessed a literal notion of nothingness. Nevertheless, as the editors of the New English Bible say, “[t]hat creation arose out of nothing – that is, not out of materials at hand – became the usual understanding of this verse” (Sandmel et al. 1976: 1). However, not all commentators on Genesis 1: 1–2 assumed that the world was created out of absolute nothingness; such a belief would be logically absurd, since ex-nihilo, nihil fit –from nothing, nothing is created. Indeed, the latter is an “eternal truth” for Leibniz (GR 98). To understand “Creation from nothing” in the literal sense would be to deny a logical truth for Leibniz, something he cannot accept, for it would be against reason. On the other hand, the same cannot be said concerning the denial of other Christian Mysteries, for denial of them does not entail a contradiction. If one accepts the dictum “nothing cannot be created from nothing”, one possibility is that God created the world strictly from something already “in” Himself. One version of this would be neo-Platonic. Leibniz occasionally talks in such terms:

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“[. . .] it is very evident that created substances depend upon God, who preserves them and who even produces them continually by a kind of emanation” (DM §14; A&G 46). In the Monadology (§ 47; A&G 219), he talks of “continual fulgurations of the divinity” as the sole cause of all creatures. Both these figures of speech imply a necessary activity of God, occurring because of his very nature. However, Leibniz talks more often in a purely Platonic vein about Creation, where God deliberately and freely creates the world. Leibniz does believe that the “eternal truths” or Platonic forms exist, but only in God’s mind; they have no independent reality. Leibniz’s theory of Creation does substantially differ from Plato’s, whose Creation story in the Timaeus has the Demiurge creating the world out of pre-existing matter, in that Leibniz does rule out the possibility of eternal matter. The great Leibniz scholar, Paul Schrecker, has noted that whatever the actual ontological status of the Platonic forms and “Leibniz’s eternal essences”, “in regard to this point he was inspired by his Platonic studies”. “Leibniz’s eternal essences”, Schrecker reminds us, “are not merely unchanging forms but dynamic agents. Every essence or possible reality, according to Leibniz, tends towards existence, and the force of this conation is proportional to the quantity of reality or perfection involved in the essence” (Schrecker 1958: 500). In Leibniz’s own words [. . .] in possible things, or in their possibility or essence itself, there is a certain demand or (so to speak) a claim for existence: in short, that essence tends by itself towards existence [. . .] the degree of this tendency being proportionate to the quantity of essence or reality, that is, to the degree of perfection of the possible involved. Perfection, indeed, is nothing but quantity of essence (MO 86; GP 7 303).

To be sure, God determines which of these eternal essences or possibilities will be realized, since in Leibniz’s words, “possible things, having no existence at all, have no power to make themselves exist” (A VI 4 2232). We know that the creation (or destruction) of any genuine substance is a miracle for Leibniz; a fortiori, the Creation of the world. Nothing “can make itself”. However, which substances will be created is determined by their concepts or “existence-demanding” natures as Schrecker argues. As one commentator says, it might be “possible to infer existence from the essences of possible substances, [. . .] although [. . .] inferences about their existence from their essences would also require God-like knowledge of the best” (Phemister 2005: 68). Whatever its ultimate status, something existed “before” Creation that was not corporeal, but “invisible”, whether it was “part” of God, emanations/fulgurations from God or “striving possibles” in God.3 Commenting on these first verses of Genesis, Leibniz writes: (He) created. Accordingly creation ex-nihilo is not grounded in Sacred Scripture, but rather in a certain tradition [that is] not free from error. It is true indeed that Chaos or Atoms, or another material did not exist – co-eternal with God – from which the world was made. Nevertheless it is false that the earth is literally made from nothing as if it were from matter. It is an eternal truth: nothing comes from nothing. Hence, it is more correct to say, with the author of the Letter to the Hebrews, chap. 11, verse 3, that the visible is made from the invisible [. . .] (GR 98; translation modified, D.J.C.).4

Given this rather convoluted passage as an example, one can see why it is difficult to ascertain Leibniz’s canonical view on the nature of creatio ex-nihilo. Leibniz

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ultimately had an agnostic position on this issue. In a letter to Bourguet (1715), near the end of life, he concluded (after presenting three models of the universe, two eternal and one created) that “I do not yet see any way of demonstrating by pure reason which of these we should choose”(L 664; GP 3 582). The reason for Leibniz’s non-dogmatic position – whether the world was created strictly out of nothing by God and/or exactly what this “nothing” was or wasn’t – was that it was not a key issue for his central concern, namely “demonstrating by pure reason” the existence of God as Creator. Like many Christian apologists, the possibility of the eternity of the world (e.g., as assumed in Aquinas’ “third way”) did not affect the ultimate validity of the cosmological argument. Leibniz explicitly confronts this issue by claiming that “even by supposing the world to be eternal, the recourse to an ultimate cause of the universe beyond this world, that is, to God, cannot be avoided” (MO §85; GP 7 302). Given the Principle of Sufficient Reason (PSR), Leibniz says, the first question we have the right to ask will be, why is there something rather than nothing? For nothing is simpler and easier than something. Furthermore, assuming that things must exist, we must be able to give a Reason for why they must in this way, and not otherwise (A&G 210; GP 6 602).

Thus for him, the question is a legitimate one; it is a “fact” that must be explained. Indeed, as Patrick Riley (2004: 79) has recently noted, it is “the Leibnizian question”! An explanation for the nature as well as the existence of the world is logically necessary for Leibniz. Here physics, as Leibniz says, points to metaphysics: So far we have spoken as simple physicists; now we must rise to metaphysics, by making use of the great principle, little used, that nothing takes place without sufficient reason, that is, that nothing happens without it being possible for someone who knows enough things to give a reason sufficient to determine why it is so and not otherwise (A&G 209–210; GP 5 602).

Even an eternal material world would require an explanation for the nature of its existence. Thus Leibniz says: Hence there is a reason even for eternal things. If we imagine that the world has existed from eternity, and that there have been only globules in it, a reason must be given why there should be globules rather than cubes (A VI 4 1645; A&G 31–32; translation modified D.J.C.).

Though cosmologists, like theologians, may dwell on the ultimate metaphysical question: “Why is there something rather than nothing?” others dismiss this concern about the origin of the universe as unscientific, irrational and even morbid. To them, it simply disguises a concern for “existential” or religious questions like “Why are we here?” “What is the purpose of it all?” For “village atheists” like Bertrand Russell, such questions are pointless and intellectually illegitimate. The universe just is – it is a brute fact. There can be no logical answer to the question, “Why is there something rather than nothing”, so why ask the question? In this vein, asking the question, “Why is there something rather than nothing?” deserves the same flip answer given by a student to the professor’s question on this issue: “Why?” She answered “Why not?”.

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While one may argue that Leibniz’s own project to explain the sheer existence or nature of the cosmos is misguided, the idea that Creation has no place at all in a philosophical system is rejected by many as too narrow and not to be so easily dismissed. Proponents of such systems – including empirically or scientifically based ones – do believe that the question is a legitimate one. The answer goes beyond nature and the purview of science, and hence is, by definition, supernatural (as Leibniz explicitly states), but nevertheless fulfills a rational demand. Furthermore, as a rational concept, Creation – unlike other miracles and Mysteries for Leibniz – can be argued for apart from “revelation” or “theological demands”. I would argue that for Leibniz, the word “supernatural” used in characterizing the miracle of Creation does not mean that it is ultimately mysterious, in the sense of the other Christian mysteries, which elicited quite different defenses from him. Nor would he claim that belief in Creation is ultimately irrational or arbitrary; rather, it constitutes a rational explanation that necessitates going beyond the physical world.

3 Creation as the Only Genuine and Necessary Miracle for Leibniz Creation occupies a singular place in Leibniz’s metaphysics as the only supernatural event allowed. For this reason, he often calls it a miracle – indeed one that is not an exclusively Christian mystery: “such are the miracles reserved for God alone, as for instance Creation” (T 88; GP 6 64). Even Bertrand Russell (1937: 184; my italics) says, “[w]henever Leibniz is not thinking of theological objections, he regards God’s action on the world as entirely limited to creation”.5 Leibniz often talks of miracles in his philosophical writings and it is not difficult to find a simple definition of the term, usually along the lines of a divine action that exceeds the power of any created being (e.g., DM §16; A&G 48–49). His use of the concept of miracle is often ambiguous, since he distinguishes two senses of the word, a “stronger” and a “weaker” one. Most miracles, for Leibniz, do not exceed the power of some created being (including angels); they are defined as relative to some order in nature (i.e., a set of physical laws). Others, however, that violate the natural order, appear “absolute” or “real,” and are direct actions of God – “miracles of the first rank” as he calls them (Adams 1994: 94; A&G 345), such as His freely choosing to create the world. But, as Leibniz says in the Discourse on Metaphysics (§ 6), what passes for extraordinary is extraordinary only with respect to some particular order established among creatures; for everything is in conformity with respect to the universal order. This is true to such an extent that not only does nothing completely irregular occur in the world, but we would not even be able to imagine such a thing (A&G 39).

Not only could God not create a world for no reason (given PSR), but God could not create an intrinsically non-ordered world – a world of pure chance or chaos – though our world (or an event in it) might appear “irregular” or miraculous to us. Elsewhere, he says, “[n]o possible series of things and no way of creating the world

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can be conceived which is so disordered that it does not have its own fixed and determinate order and its laws of progression [. . .]” (LPW 78–79; GP 7 312). The upshot of Leibniz’s theory of Creation is that miracles other than Creation are not a necessary feature of his philosophical theology, either theoretically or practically (i.e., in his actual biblical exegesis). For Leibniz, Creation is the only miracle necessary for any systematic philosophical theology. This is why, in his debates with fellow thinkers, the term “miracle” is regularly used only in a negative or pejorative sense – often with the derisive term “deus ex-machina”. He accused his Cartesian and Newtonian contemporaries of unnecessarily multiplying miracles which “would destroy not only our philosophy which searches for reasons, but also the divine wisdom which provides for them” (R&B 66; GP 5 59). Indeed, the main purpose for Leibniz’s theory of Creation is to avoid the need for repeated recourse to miracles. Any miracles (including the creation of individual substances) were part of the Creation of the world. In effect, Leibniz posits one “big” miracle, which obviates the need for any further “little” ones. Leibniz’s views on miracles, like that of Creation, demonstrate his thoroughgoing rationalism. L.W. Beck (1969: 235) regrets that Leibniz was at “his most backward looking” in the Theodicy because of, among other things, “his defense of miracles”. Much of the confusion on this issue is based, like Beck’s, on the mistaken conflation of mysteries and miracles. The Theodicy does contain a defense for the reasonable belief in the Christian mysteries – along legal lines (the strategy of onus probandum). However, biblical miracles are treated in a standard rationalist fashion in that he attributes them to the natural powers of created beings and hence the purview of natural philosophy. Leibniz, in his earlier writings, attempted various nuanced metaphysical defenses of some of the Christian mysteries such as transubstantiation, but his treatment of biblical miracles is consistently quite different. Indeed, he distinguishes quite emphatically between “texts on which the Mysteries are founded, where the theologians of the Augsburg Confession deem that one must keep to the literal sense” and cases where “a literal translation” would be “unsuitable”. As an example, he continues [. . .] all commentators agree that when our Lord said that Herod was a fox he meant it metaphorically; and one must accept that, unless one imagine with some fanatics that for the time the words of our Lord lasted, Herod was actually changed into a fox” (T 87; GP 6 63).

Leibniz’s hermeneutical efforts usually entail interpreting the literal text to explain away “miraculous” elements rather than developing a metaphysical or esoteric theory to support the literal text. An excellent example of the latter is his detailed, purely naturalistic interpretation of the Balaam episode in the Book of Numbers, which he – following Maimonides – interprets as a dream or vision, rather than as (f)actually happening. He then explains the vision allegorically, not unlike some sort of Freudian interpretation.6 Though it is beyond the scope of this paper, a good case can be made that Leibniz gave up his earlier efforts at any metaphysical defense or explanation of the Christian mysteries, restricting his approach to “softer”, legal ones. Whether he continued to believe in a metaphysical defense of the Christian

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mysteries as well (e.g., his doctrine of substance as a basis for the doctrine of transubstantiation) has been the focus of some discussion among Leibniz scholars in recent years.7 In practice, however, he seems to rely only on weaker, pragmatic arguments in his later years. While one may accept that the Mysteries are indeed miracles of a first order – that is, genuine actions attributable only directly to God – rather than ones governed by “subordinate maxims”, such miracles, like all genuine miracles for Leibniz, were “present at Creation”. All genuine miracles (including the Mysteries) are governed by general rational principles consonant with God’s Creation of this, the “best of all possible worlds” and unfold according “the system of pre-established harmony”. Many will think that such miracles are not really miracles, since they follow a pre-set pattern. But, Leibniz answers: It will be said also that, if all is ordered, God cannot then perform miracles. But one must bear in mind that the miracles which happen in the world were also enfolded and represented as possible in this same world considered in the state of mere possibility; and God, who has since performed them, when he chose this world had even decreed to perform them (T 152; GP 6 132).

All genuine miracles (including those of the Christian Mysteries) were in effect “programmed” at Creation; Leibniz, at one point, compares the world to a music box or (anachronistically) a player piano. I [. . .] think that the physical world is so skillfully made that the body, by its own laws, responds to what the soul asks; and that the same is true of the soul, which is naturally representative of the body. The physical world is like a machine which plays tunes, just as though a skilful player were playing on it (NS 179; GP 3 468).

Thus, while a distinction between genuine miracles and Mysteries for Leibniz might be valid because of the different types of arguments he offers in defending them, the question nevertheless arises whether all genuine miracles (including those connected to the Christian Mysteries [e.g., the Resurrection et al.]), should not ultimately be treated in the same fashion by him. If God arbitrarily “inserted” miracles of any kind (including those required for the on-going occurrences of certain Christian Mysteries, such as the Eucharist) in the world after the fact, he would be “tinkering” with or changing his Creation, derogating from God’s omniscience and omnipotence. This is a recurrent theme in Leibniz’s arguments with Samuel Clarke on the nature of miracles (L 684, 690, 714). Such tinkering would also derogate from God’s goodness as well as that of his Creation, since the latter would not have been the best of all possible worlds that could have been created. If the smallest evil that comes to pass in the world were missing in it [i.e., if God were to tinker with it in order to remove it], it would no longer be this world; which, with nothing omitted and all allowances made, was found to be the best by the Creator who chose it (T 128–129; GP 6 107).

Leibniz did understand the implications of his strict doctrine of Creation and, at times, struggles with it. If we accept his doctrine that the creation and annihilation of all substances is a miracle that is within God’s power alone, it raises an issue concerning the nature of any consequent essential changes in any substances. As

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an astute commentator recently put it, “[e]ven God does not actually change the substance. God cannot alter what is in the monad’s concept. God has the power to create or destroy or to replace one monad by another, but not to change its essence” (Phemister 2005: 25 n. 21). How then, for example, does Leibniz undertake to explain the transition of a particular substance or monad from a non-rational state to a rational one? At one point in the Theodicy, he reluctantly allows for the possibility that such a development would be a natural one, but then explicitly prefers a “special operation” that would apparently entail replacing the non-rational essence with a rational one. He calls the process “a kind of transcreation”, denying that such divine act is “miraculous” like that of creation. He rationalizes this option, saying that the “latter is easier to admit, inasmuch as revelation teaches much about other forms of immediate operation of God upon our souls” (T 173; GP 6 153). Later in the same work while discussing the identical problem, he mentions his earlier solution, as one that can “dispense with miracles in the generating of man”, since “it avoids the repeated miracles of a new creation” (T 361; GP 6 352–353). He calls his solution “a certain middle way between creation and an entire pre-existence”; it “is a kind of traduction, [. . .] it does not derive the soul from a soul, but only the animate from an animate” (ibid.). Though Leibniz explicitly denies that this process is a miraculous one, his appeal to “revelation” and God’s “immediate operation” is exactly what characterizes the basis of miracles for him! The substitution of transcreation or traduction (whatever they exactly mean) for creation does not resolve the underlying problem that either option, whether miraculous or not, entails some sort of incipient presence at Creation. Perhaps one should reverse Russell’s quote at the beginning of this section to read that “[w]henever Leibniz is thinking of theological objections, he regards God’s actions on the world as entirely limited to creation”. Stuart Brown (2001: 2) has argued that “[i]n post-Cartesian philosophy new forms of rationalism emerged in which miracles and other particular acts of providence were either played down or even denied”. Leibniz’s rationalism should be recognized as one of the latter. However, unlike Spinoza and Hobbes, who understood scripture primarily in moral or moralistic terms, Leibniz saw biblical revelation as a manifestation of Divine reason and its text, the Bible, as “truth-bearing”. Scripture had to be properly interpreted in order to demonstrate its rational core. Such an interpretation had to be defended against those who interpreted the Bible in fundamentalist, millenarian, mystical, fideistic or even strictly moralistic terms.

4 Other Evidence for the Rational Belief in Creation Creation is a supernatural event in the sense that it transcends the natural order. However, for Leibniz, it is not beyond reason or intrinsically mysterious. Leibniz did believe that “Creation is an act of divine revelation” (Loemker 1972: 88), but a revelation open at least in part to all rational beings, and not an esoteric mystery open only to the converted. Creation is indeed the only “Christian” Mystery that is common to the other Abrahamic faiths: Judaism and Islam. Furthermore, for Leibniz, at least some understanding of Creation existed among advanced pagan cultures, in particular the Chinese and the Greeks.

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One example is the implicit awareness of Creation among the ancient Chinese, because of their knowledge of binary arithmetic as reflected in the various combinations of the unbroken and broken lines of the Hexagrams of the Yi-Jing, whose origins are traditionally ascribed to Fuxi, the legendary early Chinese ruler. Thus, Leibniz prefaces the summary of his “discovery” of binary arithmetic to Father des Bosses: [. . .] I think the substance of the ancient theology of the Chinese is intact and, [. . .] can be harnessed to the great truths of the Christian religion. Fohi [Fuxi], the most ancient prince and philosopher of the Chinese, had understood the origins of things from unity and nothing, i.e., his mysterious figures reveal something of an analogy to Creation, containing the binary arithmetic [. . .] that I rediscovered after so many thousands of years, where all numbers are written by only two notations, 0 and 1 (Cook and Rosemont 2000: 134; my italics).

Another is the inspiration of classical Greek philosophy, especially the “holy” doctrine of Plato (in Leibniz’s very own words),8 for his “Metaphysics of Divinity,” as Christia Mercer (2001: 173–252) has called it. Since Creation in some form is an accepted doctrine in both pagan and theistic cultures, Leibniz implicitly appeals to an ex-consensu gentium type of argument. An appeal to such mutual corroboration of so central a doctrine as Creation was, for Leibniz, an appeal to the deepest kind of rationalism – one based on the innate ability of all humankind (properly educated, of course) to arrive at an understanding of the ultimate truths governing our world. Such a common denominator among all rational beings represented, for Leibniz, the basis for his lifelong ecumenical and irenic efforts, within Christendom as well as beyond it.9

5 Conclusion For Leibniz, knowledge of Creation did not necessarily assume knowledge of revelation. The doctrine of Creation could be revealed in the religious sense, but was also open to human reason and scientific understanding. But, however it was received,10 knowledge of Creation was consistent with reason. In a letter to Christian Spener, the natural scientist and anatomist, Leibniz argued that “many things lead me to think that [. . .] [the early history of the world] is consistent with reason and Holy Scripture” (D II 2 176). Acknowledgments The author wishes to thank Dr. Lloyd Strickland for his helpful comments and his aid in locating and translating passages in the Leibnizian corpus on Creation and Creation ex-nihilo.

Notes 1. For a discussion on possible meaning(s) of creatio ex-nihilo for Leibniz, see Savage (1998: 103–131). 2. “I beg you, child, look at the sky and the earth; see all that is in them and realize that God made them out of nothing, [. . .]” II Maccabees 7:28 (Sandmel et al. 1976: 243). For a detailed

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3. 4.

5.

6. 7. 8.

9. 10.

11.

D.J. Cook discussion on the origin and meaning of creatio ex-nihilo in the early (Judaeo-) Christian tradition, see O’Neill (2005: 449–465). For an excellent discussion of these various options and the problems each entails, see Wilson (1989: 275–281). Savage (1998: 103). There is strong evidence that this reflects F.M. van Helmont’s view, though the text itself was ghostwritten by Leibniz. However, Leibniz explicitly claims that he has “mixed in many of my thoughts that do [not?] clash with some of my friends opinions” (GR 98). In general, I think Russell wrongly conflates orthodox doctrinal demands with metaphysical ones. In this regard, many 20th century English-speaking commentators on Leibniz, including some of those cited in the opening section, have been influenced – consciously or unconsciously – by Russell. In his later Preface (Russell 1937: vi), Russell concludes that Leibniz “had a good philosophy [. . .] and a bad philosophy [. . .]”. The ‘good’ Leibniz is the pure logician whose doctrines can be deduced from his basic premises – a Spinozist malgr´e lui. The ‘bad’ Leibniz is the politically and religiously correct courtier who trimmed his rationalist sails to the prevailing orthodoxy. For a more detailed discussion of Leibniz’s treatment of biblical miracles, see Cook (1990: 267–276). For a recent discussion of this issue, see Goldenbaum (1999). “The whole doctrine of Plato concerning metaphysics and morality is holy and just. [. . .] and everything he says about truth and the eternal ideas is truly admirable” (my italics) (Riley 2002: 113; GP 3 17). For a detailed example of the latter, see Perkins (2004: 45–107). In Leibniz’s time, besides the Judaeo-Christian appeal to revelation, two general types of explanation were prevalent – one intellectual, the other historical – for the receipt of such knowledge. The first claimed that superior minds could access it through the exercise of their own reason. A variation on this position was that intellects closer in time to the original Creation – when man was relatively less corrupt – were privy to such knowledge. The second approach often believed in the doctrine of ancient theology (prisca theologia) which held that key parts of the Judaeo-Christian revelation were passed down to the pagans at the time of Moses or even the Patriarchs, by various prophets who were also the fountainheads for knowledge of the true God among various pagan groups (Hermes Trismegistus, Fu-Hsi, etc). These various explanations were not mutually exclusive. For example, Leibniz’s Jesuit correspondent in China, Joachim Bouvet, used all these strategies to convince Leibniz that the ancient Chinese were privy to “knowledge of the true system of nature,” including Creation. See his letter to Leibniz, 4 November 1701 (LKC: 154ff). Leibniz doubted the historical basis for these doctrines (Cook and Rosemont 2000: 135–136), but happily accepted their intellectual congruence. Among such efforts of “reason” were Leibniz’s detailed geological observations, found in his Protogaea and elsewhere in his scientific writings. His attempts at an empirical corroboration of the general truth of the biblical account of Creation in such works are examples of another form of rationality in the service of revealed religion for Leibniz.

References Leibniz DM = Discour se on Metaphysics in A&G. LKC = Leibni z korrespondier t mit China. Translated by R. Widmaier. Frankfurt: V. Klostermann, 1990.

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LPW = Leibni z: Philosophical Writings. Translated by G.H.R. Parkinson & M. Morris. London: J. Dent & Sons, 1973. MO = On the Ultimate Origination of the Universe. In G.W. Leibniz: Monadology and Other Philosophical Essays. Translated by P. Schrecker and A.M. Schrecker. Indianapolis, IN BobbsMerrill, 1969. NS = Leibni z  s ‘N ew System  and Associated Contemporar y T exts. Translated by R.S. Woolhouse and R. Francks. Oxford: Clarendon Press, 1997. T = T heodicy: Essays on the Goodness of God, the Freedom of Man and the Origin of Evil, A. Farrer (ed); E.M. Huggard (tr). La Salle, IL: Open Court, 1985.

Other Works Adams, R.M. 1994. Leibniz: Determinist, Theist, Idealist. New York: Oxford University Press. Beck, L.W. 1969. Early German Philosophy. Cambridge, MA: Harvard University Press. Broad, C.D. 1975. Leibniz: An Introduction. London: Cambridge University Press. Brown, S. 2001. The regularization of providence in post-Cartesian philosophy. In R. Crocker (ed.), Religion, Reason and Nature in Early Modern Europe. Dordrecht: Kluwer, pp. 1–16. Cook, D.J. 1990. Leibniz: Biblical historian and exegete. In I. Marchlewitz and A. Heinekamp (eds.), Leibniz’ Auseinandersetzung mit Vorg¨angern und Zeitgenossen. Stuttgart: F. Steiner Verlag, pp. 267–276. Cook, D.J. and Rosemont, H 2000. “Leibniz, Bouvet, the doctrine of ancient theology and the ¨ Yijing. In W. Li and H. Poser (eds.), Das Neueste uber China: Leibnizens Novissima Sinica von 1697. Stuttgart: F. Steiner Verlag, pp. 125–136. Everitt, N. 2005. Review of B. Rundle, Why is There Something Rather Than Nothing (2002). Religious Studies 41: 111–116. Goldenbaum, U. 1999. Das Labyrinth der Christlichen Mysterien. In D. Berlioz and F. Nef (eds.), L’Actualit´e de Leibniz: Les Deux Labyrinthes. Stuttgart: Steiner, pp. 153–176. Hawking, S. 1991. A Brief History of Time. New York: Bantam Books. Hebblethwaite, B. 2004. Philosophical Theology and Christian Doctrine. Oxford: Blackwell’s. Jolley, N. 1998. Causality and creation in Leibniz. The Monist 53: 591–611. Loemker, L.1972. Struggle for Synthesis: The 17th Century Background of Leibniz’s Synthesis of Order and Freedom. Cambridge, MA: Harvard University Press. Mercer, C. 2001. Leibniz’s Metaphysics: Its Origin and Development. Cambridge: Cambridge University Press. O’Neill, J. C. 2005. How early is the doctrine of Creatio ex-nihilo?. Journal of Theological Studies (New Series) 53: 449–465. Perkins, F. 2004. Leibniz and China: A Commerce of Light. Cambridge: Cambridge University Press. Phemister, P. 2005. Leibniz and the Natural World: Activity, Passivity and Corporeal Substances in Leibniz’s Philosophy. Dordrecht: Springer. Rescher, N. 1973. Logical difficulties in Leibniz’s metaphysics. In I. Leclerc (ed.), The Philosophy of Leibniz and the Modern World. Nashville, TN: Vanderbilt University Press, pp. 176–188. Riley, P. 2002. Review of G.W. Leibniz, S¨amtliche Schriften und Briefe I, 17. The Leibniz Review 12: 107–121. Riley, P. 2004. Review of G.W. Leibniz, S¨amtliche Schriften und Briefe IV, 5. The Leibniz Review 14: 65–88. Russell, B. 1937. A Critical Exposition of the Philosophy of Leibniz. London: Allen & Unwin, 2nd ed. Sandmel, S., et al. (eds.). 1976. The New English Bible with the Apocrypha. New York: Oxford University Press. Savage, R. O. 1998. Real Alternatives. Leibniz’s Metaphysics of Choice. Dordrecht: Kluwer.

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Schrecker, P. 1958. Leibniz and the Timaeus. The Review of Metaphysics 4: 495–505. Sleigh, R. 2001. Remarks on Leibniz’s treatment of the problem of evil. In E.J. Kremer and M.J. Latzer (eds.), The Problem of Evil in Early Modern Philosophy. Toronto: University of Toronto Press, pp. 165–179. Wilson, C. 1989. Leibniz’s Metaphysics: A Historical and Comparative Study. Princeton: Princeton University Press.

Part VIII

The Metaphysics of Rationality

Chapter 30

For a History of Leibniz’s Principle of Sufficient Reason. First Formulations and Their Historical Background Francesco Piro

1 How Many Formulations to PSR? The claim that “Nothing is without reason” (nihil est sine ratione) is one of the oldest components of Leibniz’s philosophy. The so-called Confession of Nature against Atheists (1668; A VI 1 489–493) implicitly introduces it, the contemporary prospect of Universal Demonstrations proclaims this principle and makes it the basis of the proof of God’s existence (A VI 1 494), the Theory of Abstract Motion (1671) grounds on it some general precepts on equilibrium and its preservation, which would be common to Natural Philosophy and Political Science (A VI 2 268). It is, however, more difficult to specify the exact content of the claim known as the Principle of Sufficient Reason (= PSR). One must recall that Leibniz offers different definitions of it: (i) A first instance stems from the definition of the expression “sufficient reason” in terms of the “totality” or “aggregate” of requisites, meaning the set of necessary conditions for something’s existence. This definition appears at the beginning of the 1670s and is constantly repeated in the Paris writings as well as in the first hanoverian writings.1 Conversely, even though it reemerges sporadically, one rarely encounters it in Leibniz’s writings after 1680.2 Instead, at least one time, Leibniz mentions this definition as one of his youth’s convictions which brought him very close to the “abyss of fatalism”.3 We will call PSR1 this model of explicitation of the PSR. (ii) In his maturity, the Principle of Sufficient Reason often is defined as an immediate consequence, if not as a synonym, of the Analytic Doctrine of Truth. What the PSR establishes is that “every true proposition may be proved a priori” or that “every true proposition is based on a connection between the concept of the predicate and that of the subject”.4 We will call PSR2 this more mature model of explicitation.

F. Piro University of Salerno, Salerno, Italy

M. Dascal (ed.), Leibniz: What Kind of Rationalist?,  C Springer Science+Business Media B.V. 2008

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(iii) There are cases which do not seem to fit either model; for instance, when Leibniz defines the PSR by resorting to one of its applications, like Archimedes’s theorem of static equilibrium; or those in which he identifies the PSR with the thesis according to which what exists has a “better reason” than what doesn’t exist, or that every fact of our world has a “determining” reason or a “prevailing reason”.5 Such passages seem to associate the PSR to another of Leibniz’s principles, the Principle of the Best (PB), that many scholars consider structurally different from the PSR.6 These explicitation attempts do not share the same contents. In fact: – They do not share the same object. PSR1 has as its object “that which exists”, that is, the states of things of a world. PSR2 concerns propositions or true assertions (enonciations v´eritables) and, more precisely, all assertions that are true but not identical, including those that an analysis may demonstrate as necessary. Therefore, the thesis that contingent truths are always justifiable is only one of its applications.7 In the third case – if we may consider it as another attempt of explicitation of Leibniz’s PSR and not as a family of its exemplifications – one returns to truths of fact alone, distinguishing these from those which are logically necessary. – They do not share the same presuppositions. PSR2 depends upon the Analytical Doctrine of Truth, more exactly, upon the predicate-in-the-subject foundation of truth. PSR1 recalls the logic of conditional assertions that Leibniz studied in his youth – especially in its juridical applications – which remains an important chapter in Leibniz’s logical and meta-logical studies.8 The formulations inspired by the Principle of the Best remind one of the logic of comparative sentences studied by Leibniz since his first writings on controversial theological or juridical questions and their solutions.9 – Only PSR1 proposes a direct definition of the concept of “sufficient reason”. In general, in Leibniz’s mature writings, this concept remains undefined or is defined through other concepts such as “determining reason” or “prevailing reason”. I am not the first interpreter to point out how different these definitions are. Frankel (1994) observes that Leibniz interprets the PSR at times as a “Principle of Causality” (referring to events), at other times as a “Principle of Grounds” (referring to assertions), and at times as a “Principle of Reasons” (referring to choices). This distinction would seem to be confirmed by our classification, though the latter also suggests a kind of internal evolution. But what is the sense of this evolution? Should we simply consider it as a progressive purification of Leibniz’s “logicism”? Or, rather, are his metaphysical and theological preoccupations with the possible “fatalist” implications of PSR1 the deciding factor? Or are these two questions intertwined? Furthermore, the sense of what we called PSR1 is decidedly obscure. It resembles a “Principle of Causality” more than any later formulation of the PSR, but it

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is evident that Leibniz tries to define it accurately, looking for terms that are different from “cause” and its correlates. Without understanding Leibniz’s scope and objectives at the time of PSR1 , understanding its later evolution becomes difficult. Therefore, I will devote the following pages to outlining a brief history of PSR1 , including the sources, the logical grounds, and the metaphysical implications of it. Furthermore, I will try to highlight why it appears more committed to necessitarian views than the later explicitations of the PSR. This last point is probably the most important in comprehending the overall sense of the evolution which intervenes in Leibniz’s rationalist metaphysics and the peculiar equilibrium between “strong” and “soft” rationalism which occurs there.

2 PSR1 and Natural Necessity Although the history of PSR1 does not begin in 1671–1672, it will be convenient to begin our analysis with a brief “demonstration” of the primary proposition “Nothing is without reason, that is, everything has a sufficient reason” offered in the Demonstration of the Primary Propositions (A VI 2 483):10 Proposition that must be demonstrated: “Nothing is without reason, i.e., everything has a sufficient reason”. First Definition: “A sufficient reason of something is that for which, once posited, the thing exists”. [Df. of SR: x is SR of A, iff: x → A]

Second Definition: “A requisite of something is that in virtue of which, when it is not posited, the thing does not exist”. [Df. of r: y is r of A, iff: (∼ y →∼ A)]

Demonstration: (1) “Whatever exists has all the requisites which are needed for its existence. Per Def. 2” . [(A → r1 )& . . . .(A → rn )] (2) “All its requisites having been posited, a thing exists”. [(r1 & . . . rn ) → A] (3) “Therefore, all the requisites constitute a sufficient reason. Per Def. 1”. [(r1 & . . . rn ) → SR] (4) “Therefore, whatever exists has a sufficient reason”. [(for every A), there is a SR such that SR ←→ A]

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One should note a number of things regarding this attempt at demonstration. Firstly, Leibniz is decidedly cautious on the kind of logical implication used in his “demonstration”. Is it a material implication or a strict implication? Or something else? As we shall see, Leibniz’s ambiguity on this point is constant. Proposition 2 is the low point of the whole of Leibniz’s demonstration. Leibniz explains it by asserting that: “In fact, if the thing does not exist, it means that there is something lacking, in virtue of which it does not exist” (A VI 2 483). This assumption presupposes a hidden presence of the Principle of Plenitude, at least in the form of a symmetry between the fact of existence of x and the fact of its non-existence. One could find a “reason” for both of these facts. Probably, Leibniz mainly wishes to establish that the analysis of facts can be complete. But his justification of this possibility is quite circular. Without insisting on the limits of this early writing, however, one should comprehend what its objective is. It is evident that what Leibniz effectively wishes to establish is that the concept of “sufficient reason” is equivalent to that of the totality of requisites and is therefore definable through the latter. Yet, why was this question so important to him? As I maintain elsewhere (Piro 2001), the most direct antecedent which Leibniz considers is Hobbes’s attempt at demonstrating that a “whole cause” (causa integra) – identified with a plethora of causally necessary conditions (causa sine qua non, necessarium per hypothesin et requisitum ad effectum producendum) – is always “sufficient” in that it produces its effect.11 The two philosophers’ passages are similar in that they try to bridge the gap between necessary and sufficient conditions through a purely combinatory mechanism. However, to understand the sense of this strange operation we must go further back. As such, saying that A is sufficient for B simply means that “A → B” is true. Nevertheless, in the Scholastic tradition, the term had gained a stronger meaning beginning with the famous debate on Avicenna’s axiom: “once posed the cause, it is necessary that the effect should also be posed” (Avicenna 1977, 2: 319–320).12 In this context, the expression “sufficient cause” came to indicate exactly that cause for which Avicenna’s axiom is true. This usage can already be ascertained in the age of Thomas Aquinas.13 There was however a diffuse argument against Avicenna’s axiom, used both by Averroists and Thomists. This argument is based on the assumption that – at least in the case of the causes operating in the “sub-lunar” sphere – any operating cause could find an external impediment in the realization of a certain effect. Therefore, since it is possible that [A & ∼B], it cannot be necessary that [A → B].14 Now this argument could be avoided by formulating a causality model based on the distinction between “partial causes” and “total causes”, as it happened in the course of the 14th century and particularly since Ockham. In light of this distinction, a “total” or “whole” cause can be a conjunction of several “contributing causes”, each of which counts towards an explanation of how the event took place. At this point, one could also suggest that, considering all the contributing causes at play, one could have established beforehand which impediments would have de facto occurred and which would not.15 Therefore, the effect that is realized is, in fact,

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caused by that combination of causes which is unimpedible at the moment x. There is a sense in which it is right to assert that the event B is necessitated by its cause A: When A is given, B is no longer “impedible”. In this specific sense, one may speak of “natural necessity”. The price of this thesis is that it makes it hard to demarcate clearly between the “contributing causes” themselves and the background adjuvating conditions, the so called “sine qua non causes”. It became usual to speak indefinitely of “required causes” or “requisites”.16 This model and the consequent terminology was largely accepted, even by authors trying to define the word “cause” more precisely. For example, Francisco Suarez states that once one posed all the “requisites” for a natural cause to operate effectively (positis omnibus requisitis ad actionem), then not even God could forestall its effect: “How could one forestall a natural action which has no obstacle?” (Suarez 1599: I 507).17 Of course, Suarez also maintains that God, if He so wishes, could eliminate the requisites themselves. But what counts is the logical character acquired by the relation between the totality of requisites and the taking place of the event itself. However, these theses had in the mouth of Schoolmen a profoundly different meaning, if not an altogether opposite one, if compared with that found in Hobbes’s and the young Leibniz’s writings. The final objective was in fact to establish that an act is “free” only when it escaped from this kind of necessity. Beginning with Molina (whom Suarez follows on this count), an act is free if and only if the agent’s will, although all requisites for action are in place (positis omnibus requisitis ad agendum), is still indifferent, namely able to do otherwise. What counts in this definition is in fact that all that is necessary for action – including good reasons from the agent’s point of view – may be already given but the action remains nevertheless impedible, no longer from the outside but on the agent’s own part.18 This definition of free will is what, obviously, Leibniz means to contest in his 1672 demonstration, and this explains the points of contact with Hobbes. Both authors build their battle against freedom of indifference with the same move, that is, by assuming that the holist and determinist model of the “totality of requisites” is not only needed to explain the effects of natural causes, but also to define more generally what may happen in the world. If Hobbes – as Zarka (2004) notes – builds on the basis of his theory of causality a “general theory of events”, Leibniz seems to be doing something very similar. However, affinities end here. And this is not only because Leibniz has in mind a very different cosmology from that of Hobbes, as well as a different answer to the problem of freedom. There is an even more important factor to highlight. To assume the canons of “total causality” as the basis of a theory of what can happen implies a deep transformation of the concept of “requisite”. Since Ockham, Scholastic philosophy subdivided “total causes” into solely sufficient causes and – at the same time – sufficient and sine qua non causes. God’s will is both the sufficient and the sine qua non cause of the world, whereas the same fire could be provoked by different factors combined.19 Modern Schoolmen not only share, but also generalize, this approach: The possibility of alternative realizations of the same event proves that causal links are afforded by essentially different entities.20 Briefly, the common view on natural necessity assumed that

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N(A → B) & ∼N(B → A), where A is the cause and B the effect. In the case of free acts (including the world’s creation) an inverse logic seems to apply, as free will always maintains the “potency of opposites” (potentia ad alterutrum), [∼N(A → B) & N(B → A)], and a free action can only be born from free will. Now, in this case too, Hobbes and Leibniz seem to be moving on a different terrain, in which the requisites are logical conditions and not solely factual ones. But whereas Hobbes takes this position without further justifications – we could say, simply as a generalization of his model of motion’s geometrical analysis – Leibniz is fully aware of what he is doing, and in fact this is probably the motive which pushes him to find another word – that of “reason” and no longer that of “cause” – so as to define the totality of requisites. In a few words, PSR1 extends a logical model formerly used for natural facts (and not for free actions) to free actions. But it also extends a logical model formerly used in the domain of philosophy of action (and not in that of natural philosophy) to natural philosophy. Let’s see why.

3 The Necessary Conditions 3.1 The Rehabilitation of Sine Qua Non Causality To understand how Leibniz’s PSR is born, we must at this point go back in time and consider what the young Leibniz thinks about the concept of “cause”. In Leibniz’s time, the most diffused definition of causality was that of Francisco Suarez, according to whom “cause” is “a principle which by itself influences something else”.21 Leibniz himself ridiculed this definition by citing it as a model of “obscure” definition (A VI 1 558; A VI 2 418). However, Suarez’s definition represents an attempt to differentiate causality from the logical or epistemic relations usually identified with it.22 For Suarez, the idea of “cause” differs from the more general idea of “principle”, because causal relations always concern essentially distinct entities. Furthermore, the cause is something active; therefore, adjuvating circumstances could not be called “causes” but “conditions”. If the old School spoke of “sine qua non causes” when referring to those circumstances, Suarez rather imposes modern terminology: conditiones sine qua non.23 Now, already in his earlier writings Leibniz overturns the logic of this approach. To find out about this, look at the comment which a much younger Leibniz (maybe in 1663–1664) devotes to Suarez’s definition of cause, when he finds it in Daniel Stahl’s famous handbook Compendium Metaphysicum: (Stahl): “A cause is a principle which by itself influences something else”. (Leibniz): “Be A the cause and B the effect. A is the cause if B cannot be without it, but A can well be without B” (A VI 1 26).

Leibniz immediately finds out that this defining grid applies to the notion of “principle” like to that of “cause” (ibid.). However, he insists in trying to define the concept of cause on the basis of the relation of conditional necessity, arriving, a few pages later, to a first sketch of the idea of “requisite” elaborated on this basis

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(A VI 1 28). It seems therefore evident that he is not satisfied with considering Suarez’s definition of causality “obscure”, but he wishes to substitute its vaguely animistic idea of a cause which “acts” with that of a cause linked by a logical connection with the effect. Even though, at this moment, the logical relation analyzed by him is one which entirely moves from the effect towards the cause: An effect implies necessarily that given cause, but not vice-versa. Now, why does Leibniz choose this path to define causality? Looking at his early writings, it is quite obvious that this choice can be attributed to his eagerness to demonstrate God’s existence starting from natural phaenomena. The relationship between God and World is in fact a typical example of what Ockham would have called a “precise cause” (causa praecisa), that is, sufficient and sine qua non. Now Leibniz tries to demostrate that this is true even for the single states of things. The Confession of Nature against the Atheists – which Mercer (2001: 71–82) singles out as the moment of the PSR’s appearance in Leibniz’s writings – is fundamentally devoted to explaining how certain physical phaenomena, such as bodies’ consistency or elastic bouncing, cannot be explained without recourse to God himself. Although Leibniz quickly overcomes the propension to attribute some physical effects to God’s work directly, he retains his propension to justify phaenomena by holistic explanations. Ultimately, a thorough explanation of any natural fact implies a recapitulation of the entire story of the universe and therefore implies also acknowledging God as architect of the world. Leibniz’s choice of a sine qua non model of causality is therefore explainable as an attempt to harmonize physics and theology, and to guarantee a demonstrability of God’s existence through regression from effect to cause. There is, however, another aspect of this question, whic acquires growing relevance by the end of the 1660s. As we have seen, Leibniz is aware that not all explanatory principles are causes. Modern Schoolmen elucidated this distinction by a theological example: The Father is not the cause of the other persons of the Holy Trinity, but He is their principle. Leibniz doesn’t provide the same example, but it is known that he refuses the expression “its own cause” (causa sui) used by Spinoza, because it seems to him inappropriate to express the relation between the essence and the existence of the same entity, that is God.24 We must, therefore, admit that not every sine qua non condition is a “cause”. However, by separating the term “reason” from the common expression “to give a reason”, Leibniz introduces the idea that there is a class of explanatory principles which, while a broader system if compared with that of causes, is nonetheless specifically functional for explaining what de facto occurs. This class includes firstly what the Aristotelian tradition would have called “formal causes” and “final causes”: The inner and essential dispositions of minds and the cosmic finality of “harmony”, as well as the rules which derive from it. This idea is perhaps already contained in nuce in the Confession of Nature against the Atheists which attributes all to God, but also evokes his will to harmonize the world. But it is evident in a letter to Jakob Thomasius of December 1670, which – even if it occasionally employs the old terminology – considers mechanical causes as “material reasons” setting “rational reasons” against them (A II 1 36–37). At this time, Leibniz begins to look for an accurate definition of the word “requisite”, with the following results:

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(i) Analysing the notion of “priority” – the etymological basis of the word “principle” – Leibniz remarks that there are two different types of priority, “natural” and “temporal” (A VI 1 483). The concept of “natural priority” was already known by the Schoolmen who used it in order to clear up some passages in Aristotle.25 Leibniz’s originality lies in his giving this notion a purely epistemic character. “Preceding by nature” is what, compared with something else, is thinkable with enhanced “clarity and distinctiveness” (A VI 1 483) or is “easier to understand” (A VI 4 180). (ii) A requisite is a condition of the coming into being of something. If r is a requisite and R its “committant” (requirens), it is always true that: ∼ r →∼ R [= R → r], but the contrary relation is true only for complete sets of requisites. Differently from other conditions, however, the requisite is “preceding by nature” what it conditions, and is, therefore, a condition of intelligibility and not only of existence (A VI 2 283; A VI 4A 624). (iii) The requisites are divided into those which only precede “by nature” and those which also precede “in time”. A cause precedes the effect also in relation to time (A VI 1 483). Leibniz states that the cause is external to its effect: “In fact, a cause is a reason posed outside the thing itself, that is the reason of its production; but the reason may be contained within the thing itself” (A VI 4 1360). We must, therefore, suppose that the changes of a given individual can be explained (mainly) through “external requisites” and his actions (mainly) through “internal requisites”. However, even the external cause has a “natural priority” over the effect. This assumption vouchsafes the logical ordering of successive phaenomena through time (A VI 4 180). It is necessary to note that (iii) smacks of the “mechanicism” of the young Leibniz, that is, of his conviction that mechanic causality is the only form of causality. It is possible that his mature logical studies of requisites serve to adapt this third point to the developments of the metaphysics of individual substances, which introduces an causality immanent to the substance itself.26 But the basic ideas are stable elements within Leibniz’s thought. We can use them to propose an overall evaluation on the path leading up to the formulation of the PSR1 . First of all, Leibniz’s requisites are a new model of sine qua non causality, bridging the gap between the absolute sine qua non cause (God) and events. One could call this model “procedural” as opposed to the “circumstantial” model, which prevailed in the former Scholastic tradition.27 Leibniz often expresses this nature of his “requisite” by recourse to the juridical concept of “suspension”. The absence of the requisite “suspends” the corresponding fact: “Requisite is a naturally preceding suspension factor (vulgarly said: a sine qua non cause)”(C 12).28 This passage includes both what is old and what is new in Leibniz’s concept of requisite. Moreover, Leibniz’s new model of sine qua non causality does something more than explaining events. It establishes how to analyze them (we could say, how to logically reconstruct them) so as to attribute to them their quality of facts inhering in a given world, that is, of effective components of the logical space which Leibniz calls the “series of things”. The true object of Leibniz’s PSR1 may perhaps be

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defined with an expression Leibniz adopts in his Monadology, § 32: “the existing fact or the true fact” (GP 6 612). To speak of a metaphysics of “facts”, for the young Leibniz, means attributing to him an ontology nearer to Stoicism than to Aristotelianism, an interpretive hypothesis which seems hazardous at first glance. It is much less so, however, if we remember how important the question of divine prescience of future contingents was at the time and if we try to glean Leibniz’s position on this issue at the days of PSR1 . Now, even in cases where free acts such as Pilate’s (A II 1 117) or Judas’s (A VI 3 116–119) sins are discussed, Leibniz never speaks of complete concepts of individuals as he will do from 1677 onwards (A VI 4 1374). His entire explanation is based on the idea of the “series of things”. It is true that PSR1 builds a more liberal ontology than Hobbes’s and admits some irreducible “internal” requisites for minds and their actions. But it doesn’t privilege these requisites over the “external” ones.

3.2 Involving and Universal Expression Therefore, what PSR1 is unable to do is to preserve the difference between individuals while assuming a logical connection between their states. It doesn’t only affirm that all the facts constitute a logical chain that begins with God’s choices. Relying on the identity between logical and existential conditions, it leads to the idea that each notion concerning a created entity can arise only by the combination of those primary atomic concepts which are the “attributes” of God himself. This idea appears in Leibniz’s Paris writings De summa rerum and reappears in his more mature writings.29 But in Paris’ time it seems to lead Leibniz to the conclusion that individuals themselves are nothing but “modes” or “affections” of God’s essence or substance.30 Nevertheless, I would suggest that even the – at a first sight – Spinozist passages of Leibniz’s Paris writings can be interpreted as the first steps of a typical Leibnizian doctrine, namely that of Universal Expression. The historically paradoxical side of this doctrine is that it arises from the goal of establishing the connection between the states of different individuals and ends up by explaining why they remain different and autonomous in spite of this connection. This double face of Universal Expression already appears in one of the earlier 1676 fragments, namely the Meditation on the Principle of Individuation (A VI 3 490–491). It begins with the classical question whether a total cause (causa integra in Leibniz’s words) is always a sine qua non for the occurrence of the effect. Now, since there are entities – for instance, geometrical figures – which can be produced through different “modes of production” (modus productionis), one could affirm that the same effect can be produced by different causes (as Modern Schoolmen usually thought). But Leibniz denies that this conclusion can apply to concrete individuals. It is impossible that a process of production leaves no traces in its product, however difficult to perceive these traces may be. Prima facie, this fragment seems to affirm only that an effect always makes its cause inferable and therefore “involves” (involvit) it. But this conclusion is obtained

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by assuming a semiotic correspondence between effects and causes. If and only if the effect preserves the whole information of its cause – namely if it is an adequate expression of it – causes and effects are mutually connected and the one allows one to infer the other. Therefore, each individual must have the properties of a perfect container of information, at least a memory to connect past and present. Therefore, the whole universe must be composed only of persisting “minds”.31 This passage lets us see the first steps of the doctrine of individual substances. But there is also another element in it worth noticing. In Paris, Leibniz becomes certain that causes and effects are mutually linked and that nobody can understand one of them without understanding the other (A VI 4 1963). But this equivalence or equipollence cannot be justified without some further nomic assumptions about our universe. Universal Expression is needed, as well as laws of continuity and conservation. Therefore, we find in Leibniz’s post-Paris writings a difference between factual conditions and cosmological laws, which lacked at the time of PSR1 . Consequently, Leibniz now has a new problem to solve: Which kind of logical space allows for the joining of laws, factual conditions, and inner dispositions of substances? His decisive step was that of resolving this difficulty through the same philosophical doctrine he had begun to use since 1677–1678 in order to prove the substantiality of individuals: The doctrine of “complete concepts”. Since the individual substances mirror the whole universe, it is obvious that God can see the whole universe through their concepts. These concepts are “built purposefully” (fabriqu´es expr´es) to contain and join very different premises and to grant God the possibility of calculating their logical consequences (GP 2 46). Briefly put, I see complete concepts not only as Leibniz’s answer to the puzzles concerning individual identity, but also as his answer to the question: How can such heterogeneous grounds, as those needed for the deduction of contingent truths, be joined? For example, God’s decrees reflect God’s engagements rather than previously given factual conditions (in other words, statements about them are statements about an entire world, not about a particular fact in this world). The complete concepts are just that logical space in which these assertions can be considered as “(hypothetically) necessary truths”, which afford the inference of more particular contingent truths (A VI 4 1516–1517; A VI 4 1400). It is not accidental that this kind of logical space concerns a kind of entity that always supplies (sometimes at a very low level) an interpretation of the world itself, as Leibniz’s “expressive” individual substances are.

4 The Sufficient Reason: from Necessitation to Inclination We could at this point return to the main difficulty found in PSR1 , namely the shift from the entailment of the requisites in the (concept of their) “committant” [R → r] to the opposite relation [(r1 &. . .rn ) → R] and, therefore , to the equivalence [(r1 &. . .rn ) ←→ R]. Without this step, the assumption that the analysis of facts can be complete would become inconsistent, since there would be no moment in which

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nothing else is required. But, on the other hand, which kind of implication is this? Since the propositions of the form [R → r] are necessarily true, it would seem obvious to assume that also the ones who express the opposite relation are. But, once applied to the whole series of the things, such a conclusion would immediately lead to a necessitarian metaphysics. Everything which exists would flow necessarily from God’s eternal essence. The aversion to modal notions declared in works like The Philosopher’s Confession (1672–1673) is probably an indication that Leibniz was aware of this difficulty. In fact, there are passages in which he comes close to a necessitarian point of view: What can one possibly mean by saying that something [. . .] does not exist, all its requisites existing nonetheless, if not that a defined does not exist although there exists a definition for it, or that it is and it is not at the same time. If something doesn’t exist, it is quite necessary that some requisites for it are lacking [. . .] (A VI 3 132–133).

Here the relation between (r1 &. . .rn ) and R is seen as conceptual even if Leibniz is clearly speaking of existent entities or states of affairs. It is just the confusion later avoided by the distinction between between “complete concepts” and “full causes”, the two different heirs to the “totality of requisites” of his early writings. Leibniz, therefore, was not yet over with the “necessitation” paradigm. But to think that he is not able to distinguish between causal necessity and logical necessity would be ungenerous. He already possesses his main counter-argument against “fatalists” a` la Hobbes, namely, the argument of the non-actualized possibilia. Even the very fatalistic letter of May 1671 to Magnus Wedderkopf cursorily mentions the possibilia (A II 1 118). And The Philosopher’s Confession infers from them that the world is contingent, even though it is realized by a God who necessarily exists and who is necessarily good, like a syllogism in Darapti or in Felapton infers the particular from the universal (A VI 3 127–128). Nevertheless, it is hard to find some metaphysical justification for possibilia at the level of PSR1 and it is interesting to remark that Leibniz himself will perceive this lack of justification as a difficulty in his later writings.32 These ambiguities can be explained by looking at the main metaphysical question Leibniz faces at this age, namely free will. As we have seen, for Molinists, even when our will has all the requisites to act, it still has the power of doing otherwise (potentia ad alterutrum). Now, Leibniz contests this doctrine because it is morally obnoxious, as it identifies “free” with “arbitrary”. But he contests it also because it is illogical, since a cause cannot be already sufficient while still indeterminate. If A is sufficient for B, it is true that [A → B], which implies, by logical conversion, [∼B →∼A] (A VI 3 123). Therefore, a sufficient will to act is also a will wholly determined to enact that particular deed.33 If, therefore, the alternative possibilia subsist, they subsist only as intentional objects in the deliberating intellect. This is what Leibniz is willing to concede. But, because an accomplished will is a fact which one must be able to account for through a sufficient reason, one must then go back to the will’s motivations, and these infallibly determine the will itself. Differently from the Scholastics, at no point in his reasoning can Leibniz “pull the plug” by introducing a free “contingent cause” to

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stop the regression. Therefore, it would seem that the possibility of doing otherwise never took place. And, since this argumentative scheme is valid not only for man, but also for God himself, PSR1 seems to imply a theology nearer to emanationism than to creationism. What Leibniz needed was a new justification for possibilia in light of the difference he had established between reasons and causes. In fact, if the Leibniz of PSR1 is uncertain about the notion of “possibility”, it is not because he sees no use for it, but because he has two different ways of using it. A first model is that of counterfactual hypotheses which serves to find the causes of a given phenomenon. For example, the Hypothesis Physica Nova of 1671 employs this model by comparing an “abstract physics”, which establishes what would ensue from the sole scheme of the mechanical bump, to a “concrete physics”, which individuates causes of phenomena not explained by this scheme.34 In this instance, obviously, the examination of alternative possibilities serves only to find true causes, so that it might be called an eliminativist conception of possibility. The other conception of possibility is that which intervenes in choices. Leibniz analyzes it as referred to problems such as interpretive choices in juridical or theological texts, as well as conflicts in the law. In this case too, the decision that gets to a certain exitus is the judgment that determines which possibility is more “presumable” or more “likely”, leaving aside alternative possibilities. But Leibniz emphasizes that even eliminated possibilities are requisites of the decisional process. We could say that here the elimination is factual but not logical, but we cannot give an account of the reasons of a choice without mentionning the alternatives.35 Now, one may say that Leibniz’s entire doctrine of possible worlds is the effect of the combination of both these conceptions of possibility. It is, however, indubitable that PSR1 substantially favors the first, whereas a good portion of Leibniz’s mature metaphysics is built on the basis of the second conception. One must of course remember the powerful imagery of the “striving possibles” which establishes an analogy between the logic of creation and the plastic rationality that is typical of the deliberative processes.36 But a conclusive step is the doctrine of infinite analytical truths, insofar as it establishes that, for contingent truth, a complete elimination of the alternative possibilia – namely, their reduction to contradiction – is impossible: [. . .] when, analyzing the proposed truth, one sees it as depending on a truth whose opposite implies contradiction, one can say that this is absolutely necessary. But, if even analyzing in depth as much as possible does not lead to elements of given truth, one must say that the said truth is contingent and that it originates in a prevailing reason which inclines without necessitating (GP 6 413).

This passage permits us to identify what Leibniz calls “inclination” and how it can be distinguished from “necessitation”. Let us assume that we have the possibles [x, y] and a “prevailing reason” A which makes x preferable to y [Rp xy]. Even admitting [N ( A → Rp xy)], we cannot conclude that, once given A, y is impossible [A →∼ P (y)], since y was mentioned in the former passage and cannot be eliminated while preserving the sense of that of that passage. Therefore, it cannot be true that [N (A → x)] since y is incompossible with x, but possible. Therefore, one can

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infer only [A → x], which is not a necessary connection. I would suggest that this is the basic way through which Leibniz distinguishes “inclination” from “necessitation”. What the difference between “infinite” and “finite” analysis explains is that there is no way to reduce the relation (Rp xy) to a way of reaching x directly from A. Of course, I don’t mean that this is the only way Leibniz tries to solve the problem of contingency. Another strategy is that of affirming that even what we called “A” – namely, the set of evaluations on which deliberation is grounded – is contingently chosen by God. On this solution, however, the Principle of the Best would be quite another principle than the PSR.37 But I am not trying to analyze Leibniz’s solutions to the problem of contingency, which are many and perhaps inconsistent with each other. What I am trying to do is to give a more precise meaning to the conceptual opposition “necessitation/inclination”, quite absent at the time of PSR1 . Leibniz’s criticisms of the concept of “necessitation” don’t only concern absolutely necessitarian philosophies such as Spinoza’s. What Leibniz is criticizing is a whole tradition which identified determination and necessity, suggesting therefore that contingency could be introduced – if one wished to introduce it – only by admitting quite indetermined causal agents. In order to avoid this paradoxical consequence, Leibniz had to find a kind of determination which would never lead to necessity. Choice was a good model for him insofar as it can be seen as a determination which arises from indetermination, that is, from the – of course, only ideal – presence of incompossible possibilia. Finally, one may ask whether this evolution changes Leibniz’s views on human freedom. However paradoxical, I don’t see this as a primary goal from Leibniz’s point of view. Affirming the logical contingency of the laws that rule our actions doesn’t imply that we could change them. When turning from divine to human actions, Leibniz’s approach always becomes more “compatibilist”, although the causality to which Leibniz refers is the immanent causality of substantial forms and not mechanical causality.38 Therefore, when using the logic of choices for God’s creation, Leibniz is mainly trying to give an account of the general features of events as such, not of the particular features of our actions. The structure of Leibniz’s PSR can be better understood if one starts from the things which are “reasons of themselves”: The identical truths of logic, but also the cases of perfect symmetry or static equilibrium in natural philosophy. Therefore, to say that something needs a “reason” for something means to see this thing as a rupture of a formerly symmetrical situation and – therefore – to search for the factors which could (ideally) restore symmetry. This is the meaning of the description of the requisites as elements which pose or suspend something when they are posed or suspended. Now, this model applies because events are information and information can be decoded as referring to something else (“expression”, Leibniz would say). But events contain information also because they are not all that is possible, otherwise they would be redundant. To say it in a theological way, the existence of our world cannot be gratuitous, but it cannot also be a logical consequence of God’s eternal existence. Notice that this question doesn’t only concern the Creatio ex nihilo as such, but all events, since the doctrine of “continued creation” assumes that each moment of time is one of God’s “fulgurations” (Monadology §47;

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GP 6 614). Although events are only particular consequences of God’s “yes” to the best of the possible worlds, God didn’t so far finish pronuncing this “yes”. And, of course, the other central point of the question is that the mature Leibniz, while developing his ideal of completeness through the doctrine of complete concepts, seems at the same time to give a more relativist account of it. Complete concepts are complete insofar as we consider them as already containing such elements as rules, laws-of-succession, and so on. But it is impossible to give a deduction of these premises. This doesn’t mean that the PSR runs amok at this point, but that a complete deduction is not the only possible way of “giving reason” of something, to justify something, or to take a decision in relation to something. In the last analysis, the mature formulations of the PSR seem to open the door to a plurality of ways of “giving reason” to events, with a considerable transformation of the sense of the PSR itself with respect to its first formulations.

Notes 1. The most important occurrences are: A VI 2 483; A VI 3 118, 573, 584, 587; A VI 4 1388. 2. I can quote only a passage of 1688, “Et cum ratio rei plena sit aggregatum omnium requisitorum primitivorum [. . .]” (A VI 4 1616), and another from the fourth letter to Clarke, “La nature des choses porte que tout evenement ait prealablement ses conditions, requisits, dispositions convenables, dont l’existence fait la raison suffisante” (GP 7 393). 3. De libertate, Contingentia et Serie Causarum, Providentia (A VI 4 1653): “Ego cum considerarem [. . .] nihil existere nisi positis singulis requisitis, ex his autem omnibus simul vicissim consequi ut res existat, parum aberam ab eorum sententia, qui omnia absolute necessaria arbitrabantur [. . .]”. 4. De principiis praecipue contradictionis et rationis sufficientis (A VI 4 803–806); De Veritatibus Primis (A VI 4 1443); De libertate et necessitate (A VI 4 1445); and again A VI 4 1616, 1645, 1654–1655; C 12. 5. See NE 4.11.13; and especially GP III 402 (“[. . .] raison determinante [. . .] c’est la raison du meilleur”); further examples: GP 3 529, 594; GP 6 413. 6. The best arguments for such a distinction are Rescher’s (e.g., 1979: 34–35). 7. A fine analysis of this point is that of Sleigh (1994). 8. A VI 1 101–124, 127–150, 370–389. On this first theory of conditionals, see Schepers (1975). 9. Commentatiuncula de judice controversiarum 1669 (A VI 1 555–557; DA 17–21); De casibus perplexis (A VI 1 231–258), Elementa Juris Naturalis 5 (A VI 1 465–480). On the first one, see Marras (2001). On the metaphor of balance in Leibniz, see Hawtorne and Cover (2000) and, chiefly, Dascal (2005). 10. My translation owes much to that proposed by Sleigh (1994). Another translation for requisitum could be “requirement” (Adams 1994: 117–118). 11. De Corpore, XI, 3–5 (Hobbes 1839, I: 107–108). 12. Maier (1949) shows that this widely discussed dictum sums up ideas exposed in Avicenna’s Liber de Philosophia Prima, VI. 13. See Aquinas’s account on Avicenna’s theory of causality in Quaestiones Disputatae de Veritate 23/5 (Thoma Aquinas 1970, vol. 3: 651–652). The fundamental work on these discussions is Maier (1949). 14. Maier (1949: 219–250). 15. Quodlibeta, I/17 (William of Ockham 1980: 90–91).

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16. Maier (1949: 249) quotes an interesting passage attributed to Marsilius of Inghen: “ [. . .] positis causis necessario requisitis et sufficientibus ad productionem alicuius effectus [. . .] de necessitate producitur ille effectus”. 17. See Suarez’s Disputatio XIX/1: “[. . .] etiam Deus ipse non posse facere ut, in sensu (ut vocant) composito, causa qua natura sua necessario agit, ab agendo cesset, positis omnibus requisitis ad actionem [. . .] Quomodo enim potest naturalis actio impediri nullo posito impedimento?” 18. Molina (1588: 11) “Agens liberum dicitur, quod positis omnibus requisitis ad agendum, potest agere et non agere”. Suarez accepts this definition in his Disputatio XIX/4 (Suarez 1599: 518). 19. Quodlibeta, I/1 (William of Ockham 1980: 8–9). See on this passage Goddu (1996). 20. See Suarez’s Disputatio XXVII/5: “[. . .] hic numero effectus, si ejus individua natura et entitas absolute consideretur non determinat nec postulat necessario (necessitate scilicet connaturalis et intrinseca) ut ab hac numero causa fiat et non ab alia [. . .]” (Suarez 1599: 601). That sufficient conditions can be unnecessary (just as the necessary conditions can be insufficient) was remarked much later even by Mackie (1993). 21. Disputatio XII/2: “Causa est principium per se influens esse in aliud” (Suarez 1599: 282). 22. A broad reconstruction of Suarez’s theory of causality is proposed by Carraud (2002: 103–166). 23. Disputatio XVII/2 (Suarez 1599: 428). See Oviedo’s (1663: 190) later formulation: “Conditiones non influunt, sed requiruntur”. 24. A VI 4 1372; A VI 4 1773. See Di Bella (2005: 77–82) for a careful analysis of these passages. 25. See the discussion on “natural priority” (natura prius) in Oviedo (1663: 189–192), who refers to Aristotle’s Metaphysica, V, 1019a, 1–5. 26. See for example A VI 4 403–406; 563–564; 872ff. On this later evolution of the doctrine of requisites, see Di Bella (2005: 239–264). On substantial forms as causal agents, see Brobro and Clatterbaugh (1996). 27. No doubt that this procedural model of sine qua non causality could find forerunners in the School tradition. I refer mainly to the debates on “sacramental causality”; see Goddu (1996: 358–359). But it is hard to establish how much Leibniz knew about these debates. 28. “Requisitum is suspendens natura prius (vulgo: causa sine qua non)” (C 471). 29. “Et cum ratio rei plena sit aggregatum omnium requisitorum primitivorum (quae aliis non indigent), patet omnium causas resolvi in ipsa attributa Dei” (A VI 4 1616). 30. See mainly A VI 3 573, 514, and 518–519. 31. Formerly, Leibniz had admitted both persistent and “momentary” minds (A VI 2 266–267). 32. A VI 4 1452 and 1460. See Adams (1994: 12–15) for a fine analysis on this early doctrine of contingency established on the “things possible in their own nature”. 33. Let us remark cursorily that many Schoolmen accepted this, even when discussing about God. From an Ockhamist point of view, God’s absolute power is no more actual. See Randi (1986). On the contrary, Scotists and Molinists admitted an actual power of doing otherwise. 34. See Leibniz’s Theoria Motus Abstracti (A VI 2 264–268) and the writings on mechanics that follow suit (e.g., A VI 2 314–315). 35. Leibniz seems to see confusedly this point already in his Elements of Natural Law, when he affirms that the requisites of a presumption are also requisites of the eventually opposed conclusion (A VI 1 472). 36. The idea is introduced already at the end of the 1670s, in De Veritatibus Primis (A VI 4 1442–1443) and the Dialogue entre Theophile et Polidore (A VI 4 2227–2230). See the nice account by Wilson (2000) on its implications. 37. See De libertate a necessitate in eligendo (A VI 4 1454); Discours de m´etaphysique, § 13 (A VI 4 1548); De Libertate, Contingentia et Serie Causarum (A VI 4 1658); GR 342–343; GP 2 496. According to Adams (1994: 36–42), this strategy is not indispensable for Leibniz. 38. Even in his more libertarian accounts of God’s freedom, Leibniz points out that man cannot have such a freedom (A VI 4 1454) and that the laws explaining our choice are determined by God (Discours de m´etaphysique, § 30: A VI 4 1562).

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References Adams, R.M. 1994. Leibniz. Determinist, Theist, Idealist. New York: Oxford University Press. Avicenna. 1977. Liber de Philosophia prima sive Scientia Divina, critical ed., S. Van Riet, Vol 2. Louvain/Leiden: Peeters-Brill. Brobro M. and Clatterbaugh, K.C. 1996. Unpacking the monads. The Monist 79: 410–425. Carraud, V. 2002. Causa sive ratio. La raison de la cause de Suarez a` Leibniz. Paris: Presses Universitaires de France. Dascal, M. 2005. The balance of reason. In D. Vanderveken (ed.), Logic, Thought and Action, Dordrecht: Springer, pp. 27–47. Di Bella, S. 2005. The Science of the Individual: Leibniz’s Ontology of Individual Substance. Dordrecht: Springer. Frankel, L. 1994. From a metaphysical point of view: Leibniz and the Principle of Sufficient Reason. In R.S. Woolhouse (ed), Gottfried Wilhelm Leibniz. Critical Assessments, Vol. 1. New York: Routledge, pp. 58–73. Goddu, A. 1996. William of Ockham’s distinction between ‘real’ efficient causes and strictly sine qua non causes. The Monist 79: 357–367. Hawtorne J. and Cover J. A. 2000. Infinite analysis and the problem of the lucky proof. Studia Leibnitiana 32(2): 156–165. Hobbes, T. 1839. Opera Philosophica quae scripsit omnia. Ed. G. Molesworth, London: Bohn. Mackie. J. L. 1993. Causes and conditions. In E. Sosa and M. Tooley (eds), Causation. Oxford: Oxford University Press, pp. 35–55. Maier A. 1949. Studien zur Naturphilosophie der Sp¨atscholastik, Bd. I: Die Vorl¨aufer Galileis im 14. Jahrhundert. Roma: Edizioni di Storia e Letteratura. Marras, C. 2001. Leibniz and his metaphorical models: the ‘trutina rationis’. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress), Vol. 2. Berlin: Leibniz Gesellschaft, pp. 780–784. Mercer, C. 2001. Leibniz’s Metaphysics. Its Origin and Development, Cambridge: Cambridge University Press. Molina, L. 1588. Concordia liberi arbitrii cum gratiae donis, divina praescientia, providentia, praedestinatione et reprobatione. Lisboa : Riberi. Ockham, W. of 1980. Quodlibeta septem. (Opera Theologica, vol. 9). New York: St. Bonaventure University. Oviedo, F. de 1663. Cursus Philosophicus, 2nd edition. Louvain/Leuven: Borde. Piro, F. 2001. Hobbes, Pallavicino and Leibniz’s ‘first’ Principle of Sufficient Reason. In H. Poser (ed.), Nihil sine ratione (VII. Internationaler Leibniz-Kongress), Vol. 3. Berlin: Leibniz Gesellschaft, pp. 1006–1013. Randi, E. 1986. Il sovrano e l’orologiaio. Due immagini di Dio nel dibattito sulla “potentia absoluta” tra XIII e XIV secolo. Firenze: La Nuova Italia. Rescher, N. 1979. Leibniz. An Introduction to his Philosophy. Oxford: Blackwell. Schepers, H. 1975. Leibniz’ ‘Disputationes de Conditionibus’. Ans¨atze zu einer juristischen Aussagenlogik. Akten des II. Internationalen Leibniz-Kongresses, Vol. 4. Wiesbaden: Steiner, pp. 1–17. Sleigh Jr., R.C. 1994. Leibniz on the two great principles of all our reasonings. In R.S. Woolhouse (ed.), Gottfried Wilhelm Leibniz. Critical Assessments, Vol. 1. New York: Routledge, pp. 31–57. Suarez, F. 1599. Metaphysicae Disputationes, in quibus et universa naturalis theologia ordinate traditur. Venice: Bareti. Thoma Aquinas 1970. Quaestiones Disputatae. De Veritate. Romae: Sancta Sabina. Wilson, C. 2000. Plenitude and Compossibility in Leibniz. The Leibniz Review 10: 1–20. Zarka, Y-C. 2004. Libert´e, n´ecessit´e, hasard: la th´eorie generale de l’´ev´enement chez Hobbes. Rivista di Storia della Filosofia 49(1): 249–262.

Chapter 31

Innate Ideas as the Cornerstone of Rationalism: The Problem of Moral Principles in Leibniz’s Nouveaux Essais Hans Poser

Since Plato we have been well acquainted with the view that there are elements of the soul which do not depend on experience, such as algebraic or geometric theorems. Since Aristotle, the rejection of this view has also been well known, namely the position according to which the soul is, in the beginning, nothing but an empty sheet of paper which is able to collect impressions by means of the senses, whereas a further step of abstraction allows concept and theory formation. This contrast is picked up by Descartes, who introduced new elements to the old Ciceronian concept of innate ideas. Locke criticized this transformation, whereas Leibniz defended it in adding to the Aristotelian-Lockean Nihil est in intellectu quod non antea fuerit in sensu his well-known excipe: intellectus ipse. All this leads to Kant’s Copernican turn, which takes innate ideas to be a priori conditions of the understanding, precisely as forms of thinking or categories (Poser 2006). This historical development can be seen as a transformation of modal conditions, namely, as a problem of necessary truths. So, Leibniz introduced his concept of absolute necessity, according to which a proposition is necessarily true if its negation implies a contradiction; moreover, in his Nouveaux Essais he developed a theory of disposition which aims at a clarification of the process of gaining necessarily true principles from innate ideas. As he rejected Plato’s solution involving a kind of re-memory, he was forced to explain innate ideas as a faculty, namely as a kind of possibility of the soul to transform obscure impressions by means of reflection into distinct knowledge, independent from each sense-experience. Mark Kulstad has called this the “reflection theory of innate ideas” (Kulstad 1991: Chapter 4); but it needs a further clarification, for Leibniz distinguishes between “naked possibilities”, “faculties or dispositions” and a kind of power (“puissance”) which allows the transformation just mentioned – a power which itself belongs to the mind (“Mens agit”) (Poser: Forthcoming b). Now, a big problem concerning innateness still remains: The Leibnizian approach, developed in the Nouveaux Essais, is normally discussed against the background of absolute necessity and v´erit´es de raison, that is, against the background

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of the Principle of Contradiction; but Leibniz adopts the concept of innate ideas as well in his theory of moral necessity depending on the Principle of the Best, which cannot be reduced to the Principle of Contradiction. Therefore, this kind of necessity is not an absolute, but a contingent one! Hence it is difficult to understand how moral principles can be innate, since Leibniz, in many cases, makes it clear that human beings can never reach a demonstration of contingent truths. It is this problem which I intend to discuss here. My thesis is the following: In his solution, Leibniz uses his disposition theory as a theory of instincts, which we obey; but these instincts can be clarified and transformed into moral principles by means of the process of reflection, so that they are clearly understood by the vir bonus not as instincts, but as moral necessities. The outcome, therefore, is to take moral laws as a conditioned necessity: They hold under the condition of the vir bonus. Today, we need the reflection on a priori conditions of knowledge as well as of morality; but we have to admit that we never can reach unconditioned truths. However, this does not imply relativity in the sense of arbitrariness – it implies that we have to look up and to reflect on the conditions. This shall be done here in the case of the Leibnizian approach.

1 Leibniz on Morality Leibniz never wrote a whole essay on ethics or morality, yet questions of morals are a central theme from his early papers up to his Th´eodic´ee. He always demands a clarification of the foundation of morals and especially of justice, and discusses moral necessity as an obligation which is connected with moral principles. So, he explains at the beginning of his Nouveaux Essais that Locke has primarily dealt with theoretical philosophy – Leibniz calls it “speculative” philosophy – whereas he himself has been attracted by questions of morality.1 These questions are most certainly not neutral ones: 1. Traditionally, the Church claimed that moral rules depend on theology; and even Christian Wolff, a decade after Leibniz’ death, had been accused of being an atheist, for he had argued that moral rules would be valid “even if there were no God” (Wolff 1720: § 20), since they depend on reason alone. 2. Due to Descartes, not only logic, arithmetic and geometry depend on God’s will, but also moral rules; notwithstanding, he had offered a morale par provision, founded on rationality, and formulated as stoic-pragmatic rules. In order to get rid of the Cartesian dependency of logic, arithmetic and geometry on God’s will, Leibniz had introduced his concept of absolute (logical, geometrical, or metaphysical) necessity, belonging to the essence of God. For these absolutely necessary propositions, he had brought in the concept of v´erit´es de raison, of which the negation is a logical contradiction. They are true in each possible world, whereas this does not hold for the contingent truths, the v´erit´es de fait. This causes a new

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problem within the Leibnizian approach, for on the one hand he always explains that moral principles do not stem from logic, since their negation does not imply a logical contradiction. Yet on the other hand, Leibniz would deny that moral laws would be true only in a couple of worlds; their very specific kind of necessity demands them to be true in each possible world as well, independent from the question of whether their possible individuals might follow them or not. Even if we accept that all contingent truths depend on the Principle of the Best (which normally holds only for the best of all possible worlds), it would be wrong to take moral principles only as principles of the best world or – much worse – as the expression of an arbitrary decision of God’s will. Therefore, they must possess a unique kind of necessity and a unique connection with understanding. As is well known, Leibniz speaks of moral necessity, which he calls a hypothetical necessity as well;2 however, this is meant for all contingent propositions, since they hold for the whole created world due to the Principle of the Best, which is essential to follow, since this is God’s will. This moral necessity has “a certainty and infallibility, but not an absolute necessity”, Leibniz writes to Clarke; but what is meant here are nothing other than “les choses contingentes” (GP 7 390).3 Therefore, it does not meet what we are looking for, namely the way in which moral principles have to be understood. Even if contingency differs from mere chance, and even if it is characterized by a negation free of contradiction, this is not enough to specify moral rules adequately. This is the modal theoretical part of the problem. But there is a further difficulty, which depends on the fact that Leibniz takes moral principles in his Nouveaux Essais as innate ideas in the narrow sense of Descartes and Locke, namely as propositions which can be founded on reason, so that they have to be seen as a priori truths, if one uses a Kantian terminology.

2 The Logical Background In order to show the difficulties just mentioned, let us start from a short passage in his M´editation sur la Notion Commune de Justice, where Leibniz formulates a clear alternative: “The question is [. . .] whether the justice or the goodness is arbitrary or whether it belongs to the necessary and eternal truths, as numbers and proportions” (M 41).4 His answer in the Discours de M´etaphysique is as expected; there he speaks of “eternal truths of metaphysics and geometry and consequently the rules of the good, of justice and of perfection”, which clearly shows that morality and justice belong to “eternal truths”: They all are by no means the outcome of God’s will; for “they derive from [God’s] understanding, which depends just as little as his essence on his will” (DM §2; A VI 4 1533; GP 4 428).5 This short passage gives an important hint, for it indicates that the essence and the understanding of God (and that means rationality in a wide sense, including goodness, wisdom and justice) have to be taken as primary to the will in such a way that the (good) will is exposed to the understanding. Now, Leibniz makes no substantial distinction between God’s understanding and that of human beings, but only a gradual one (see GR 471). This

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implies that human moral insight as a rational insight differs from that of God only gradually, namely in its complexity. This is, by the way, what prevents an attack from the side of the Church, for Leibniz always would have been able to argue that his concept of morality is founded on God’s understanding and goodness. Naturally, even within the area of moral propositions, there are elements of rationality dependent on logic, for otherwise an argument and, more importantly, a rational foundation would be impossible. In fact, Leibniz has emphasized this several times, as for instance in his Elementa Juris Naturalis and again somewhat later in his Modalia Juris (A VI 1 465f. and 480; A VI 3 2758–2760). But in both cases he presupposes that the acting one is a vir bonus: “Obligation is what is necessary to do for a vir bonus” (A VI 1 465),6 he says, for: “Every prudent [person] is a vir bonus” (A VI 4 2758).7 But what Leibniz intends to elaborate at that moment is nothing but the logical structure of some elements of deontic logic, whereas he does not deal with the problem of how to develop a foundation of the content in question (Poser 2001). However, it is clear that he excludes moral principles or moral rules from absolutely necessary truths, since their negation implies no contradiction at all.

3 Moral Principles as Innate Ideas From the Syst`eme Nouveau on up to the Monadology, Leibniz always insists that each soul of each individual represents the whole universe in such a way that there is nothing which is not yet given in each soul – namely innate – from the very beginning. But in his Nouveaux Essais he only mentions this, and in rejecting Locke’s central thesis of a tabula rasa, he uses the Cartesian/Lockean terminology of innateness, due to which ideas and especially principles are called innate, which in their foundation as rational concepts or rational principles are independent of sense experience.8 Leibniz mentions at least four different kinds of innate ideas, namely – concepts as e.g. possibility, essence, existence, which – as Plato had already pointed out – cannot undergo any further conceptual analysis; these are the well known Leibnizian prima possibilia or termini primitivi which the intellect can grasp and has to grasp in an intuitive way, since otherwise we would not be able to use them; but Leibniz puts them aside in his Nouveaux Essais, since they are no true propositions – and it is those in which he is interested; – notiones communes, as ex nihilo nihil fit, from which Descartes starts; these are traditionally understood as being independent of any sense experience, but evidently true and therefore truths of reason and by this absolutely necessary ones; – principles of logic, arithmetic and geometry, which are taken as evident, so that their negation would imply a contradiction, since Leibniz (wrongly) believes that they are or depend on identities; and all theorems which can be deduced from them, so that no sense experience is needed for a demonstration: these principles and theorems are the absolutely necessary truths; and finally – moral principles, which are contingent.

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It is this last point that seems to be quite unreasonable, since against the background of Leibniz’s theory of truths of reason one would expect that moral principles as contingent truths would have to be excluded from strong rationality, whereas as eternal ones they would have to be included. This causes the problem which I want to discuss here.9 Leibniz starts in a very cautious way in saying that we cannot avoid the use of absolutely necessary truths in connection with moral, juridical and theological propositions;10 but this concerns nothing more than what we found in connection with the modalia juris. Now, Philalethe/Locke explains that ethics is a “demonstrative science” without having any innate principles;11 and he repeats this somewhat later. Leibniz answers: “I grant you, that some moral rules are not innate principles; but this does not preclude their being innate truths, since a derivative truth will be innate if we can derive it from our mind” (NE 1.2.4.; A VI 6 91; GP 5 83).12 He adds: “Moral science is innate in just the same way that arithmetic is, for it too depends upon demonstrations provided by the inner light”.13 However, maybe this holds for deductions within this science, whereas as long as the principles are not innate, one cannot conclude that each moral rule is an innate truth. In this situation, Leibniz goes on in an unexpected way: But there are two ways of discovering innate truths within us: by illumination and by instinct. Those to which I have just referred are demonstrated through our ideas, and that is what our natural light is. But there are things which follow from the natural light, and these are principles in relation to instinct. This is how we are led to act humanely: by instinct because it pleases us, and by reason because it is right. Thus there are in us instinctive truths which are innate principles that we sense and that we approve, even when we have no proof of them – though we get one when we explain the instinct in question (ibid.).14

This is unexpected in so far as one would not believe that a rationalist as Leibniz is would introduce instincts in connection with moral and absolute necessity. He notes that this holds even for logic, for without being aware of it, we connect our experiences by means of instincts; nevertheless, if we would reflect on it, we would see that they are connected in the way that correct legal or mathematical propositions are. Robert McRae comments on this as follows: “It would appear moreover that most of the principles on which the demonstrative sciences are based are known only by instinct, and it is a nice question to what extent they are doomed to remain so” (McRae 1976: 120). Thinking of logic, arithmetic and geometry, this causes no further difficulties, because Leibniz presupposes that one can reduce them to identities, and identities are evidently true. But this does not hold for moral or juridical propositions. So let us pick up McRae’s question and concentrate on moral principles. McRae correctly points out that Locke in his Essay explicitly accepts instincts of morality, which Locke himself calls innate: Nature, I confess, has put into Man a desire of Happiness, and aversion to Misery: These indeed are innate practical Principles which (as practical Principles ought) do continue constantly to operate and influence all our Actions, without ceasing [. . .], but these are Inclinations of the Appetite to good, not Impressions of truth on the Understanding (Essay 1.3.3).

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But Leibniz does not agree, as we saw. This depends on a different understanding of what instincts are. It is this which demands a further analysis.

4 Instincts The concept of instinct does not belong to the center of Leibniz’s philosophy. Besides the Nouveaux Essais he uses it in some marginalia on J.-G. Wachter’s Origines juris naturalis, written after 1704; and in his Th´eodic´ee he has listed it in the Index, where the hint to §310 reads “instinct – mel´e avec la raison”. This corresponds to a much earlier passage in De Justitia et Jure, where Leibniz says that the Jus naturale (which nature teaches all animals) consists for human beings in actions done “recta ratione”, whereas for animals by “natural instinct”.15 In other occurrences, Leibniz clearly attributes instincts to beasts, and ratio to human beings (GR I 147); but this does not exclude humans behaving as animals following instincts. Yet this does not solve our problem. It seems to be the case that outside the Nouveaux Essais, Leibniz discusses instincts primarily in connection with the jus naturae – particularly in the notes on Wachter; this is significant for our problem of moral principles, since moral science and natural law ( jus naturae) both belong to Leibniz’s Justitia universalis. As a consequence, there are only a small number of contributions which deal with the Leibnizian concept of instinct (besides McRae 1976, Ripalda 1972 and 1975, and Lamarra 1995). The Leibnizian turn to instincts and their use has two problematic aspects. Firstly, the connection under consideration concerning the difference between absolute and contingent truths is not a question of the difference between God’s will and God’s power, which, due to Leibniz, were mixed up by Clarke in confusing absolute and moral necessity,16 since only human beings and animals follow instincts, whereas this does not hold for God. Even if moral necessity holds for all contingent facts, it is important for men as well, since freedom and responsibility depend on the contingency of an act as a pre-condition of morality. What, then, about being steered by instincts? Secondly, Leibniz introduces instincts as a part of his theory of cognition, especially for a foundation of ethics. But just this last element is excluded by McRae, who writes: “Because Leibniz distinguishes instinct from natural light as confused knowledge from distinct knowledge, we pose that what is confusedly perceived in undemonstrated axioms is their logical necessity” (McRae 1976: 120). Now, moral principles are clearly not logical necessities, as McRae admits, but something different, in between absolute necessity and mere contingency. On the one hand, Leibniz explicitly writes in his Nouveaux Essais: If it be asked how one can know and investigate innate principles, I reply [. . .]: apart from the instincts the reason for which is unknown, we must try to reduce them to first principles (i.e. to identical or immediate axioms) by means of definitions, which are nothing but a distinct setting out of ideas.17

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In his Th´eodic´ee, Leibniz says that even spirits, the “blissful ones”, do not always have complete knowledge; and remembering the index of the Th´eodic´ee, this means that they have instincts as well as humans, for “we do not always grasp the reasons of our instincts” (GP 6 300).18 But on the other hand, these quotations indicate the ability to overcome instincts at least partly. Therefore, Leibniz is concerned much more with the rational part of moral necessity, saying that it is a “happy necessity”, which “forces the wise man [i.e. the vir bonus] to act morally, whereas an indifference concerning the dissimilarity between good and evil has to be understood as a lack of goodness and wisdom” (Theod. II, §175; GP 6 219).19 And somewhat later he adds that this kind of determination, this “moral necessity” has to be taken as “the obligation to choose the best” due to the Principle of the Best.20 All this demands a further clarification of what innate instincts are, which I will undertake by picking up from Lamarra (1995) as well as from Ripalda (1972) and extending their analysis to moral principles. Leibniz uses the term “instinct” in his Nouveaux Essais more than twenty times. There he explains: It seems to me that everyone understands instinct to be an inclination which an animal has – with no conception of the reason for it – towards something which is suitable to it. And even men ought to pay attention to these instincts: they occur in humans as well, though our artificial way of life has almost wiped out most of them (NE 3.11.8; A VI 6 351; GP 5 332).21

This reveals several important points: 1. Instincts are inclinations. In his notes on Wachter, Leibniz writes: “Instincts are primary and lasting impulses” (GR 673, note aq).22 This fits together with the remark that one has to distinguish between instincts and emotions.23 Thinking of Leibniz’ thesis that innateness is a disposition or faculty, this means that emotions are what in fact happens, whereas instincts are the powerful dispositions behind them. 2. Normally we have no concept of the reason of an instinct. So we love our parents “sola natura” and by a “natural instinct”, as Leibniz quotes from Wachter (GR 673, P 25 Schol.). But they have an important task, because they “guide our nature to something, which we, due to our nature, cannot understand adequately” (GR 676).24 3. Instincts are suitable in order to act in accordance with the problems we face in life. Moreover, “[i]nstincts [. . .] lead us to the Good” (GR 678, ad p. 19).25 This suitability goes back to God’s choice of the best of all possible worlds in following the Principle of the Best. 4. Instincts can be wiped out depending on artificial life conditions. Thus, Leibniz comments on Wachter’s thesis that our tendency to reach a higher perfection depends on a “natural instinct of the spirit” as follows: “All these have their fundament in the wise instinct of nature, but depending on our weakness, they rush out in an exaggerated manner” (GR 674, note at).26 This is in accordance with an interesting remark written in 1712 in an appendix to a letter to Pierre Coste (the translator of Locke’s Essay into French), a remark on Shaftesbury’s

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Characteristicks of Men. It makes clear that there are changes in human natural instincts, up to a loss of presence; but “one has kept the advantage in morals, where reason and sentiment fortunately come together” (Remarque sur Characteristicks of Men; GP 3 431).27 Moreover, and much more important than the negative influence is the possibility of the ratio to control instincts: Instincts belong to the utilities of nature, “but it is the task of the ratio to govern it [the instinct], so that it does not immediately lead to acting”, as Leibniz comments on Wachter (GR 679, Ad p. 29).28 This indicates that instincts themselves play an important role. Leibniz describes it in one of his defenses of his Syst`eme Nouveau in 1698 in the following way: The alleged conflict between mind and body is nothing but a difference in inclinations, born by distinct thoughts or by obscure thoughts, namely by reason or by instincts and passions: the instinct is so to say a constant passion and born with us, whereas the passion is like a temporary and passing instinct; one might add the custom in between these both inclinations, which is longer lasting than the passion, but not born with us as the instinct (Addition a` l’Explication du systeme nouveau; GP 4 576f.).29

To take instincts as dispositions instead of quasi-mechanic causes admits a determination of an action by ratio. This is much more than a sheer possibility; moreover, it includes an obligation: Leibniz mentions in a note belonging to the Scientia generalis that instincts “have to be governed by reason” (GP 7 113).30 All this does not exclude God having created humans in such a way that in very complex situations our behavior is guided by instincts instead of reason.31 And it fits together with an introductory remark of the Nouveaux Essais, that “some of God’s eternal laws”, which include moral ones, are “engraved in the depth of our souls [. . .] in a legible way, through a kind of instinct” (NE 1.1.4; A VI 6 76; GP 5 68):32 If these laws are legible, we have the obligation to read them, namely to make them explicit in order to be able to follow them for rational reasons. Nevertheless, this is only a hint, and not really the solution to the problem of how instincts and reason can fit together in such a way that the outcome consists in a demonstrative science of morals. According to Lamarra, it is the Leibnizian concept of expression which has to bridge the gap between instinct and understanding: Leibniz infers from the instinctive character, and therefore innate, of natural inclinations present in the soul the innateness of rational truths that correspond to them in the intellect: the passage from instinctive principles to rational precepts, from inclinations of the soul to the truths of the intellect, is possible for him by his characteristic concept of expression. A rational truth corresponds to instinctive inclination only in so far as the human soul finds complete expression in the intellect. Thus practical inclination, which acts as a behavioral principle for the substance, is expressed through the intellect, assuming the form of precept or moral truth; since, however, the principle expressed is innate, the moral truth constituting its rational expression must be considered as equally so (Lamarra 1995: 201).

On this line, one might argue in a very Leibnizian way that moral instincts as contingent ones indeed have to be understood in such a way that they, on the one hand, cause an act by their inner potentiality and power, and, on the other hand, that this acting and the instincts involved therein must have a reason going back to the Principle of the Best, independent from our knowledge of it, just as it happens in

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nature: the dominion of causes and the dominion of reason always correspond to one another. This is an interesting way of looking at the problem, and it shows the fruitfulness of Leibniz’s metaphysics; but in fact we need a much narrower connection, for expression does not explain how we are able to obtain those eternal rational principles and follow them for good reasons. Ripalda (1975: 180) uses a different approach, since he sees instincts as a part of Leibniz’s concept of small perceptions, namely as denoting the psychic continuity between small perceptions and reason. This is much closer to the key of the Leibnizian solution of our guiding problem, but he does not really meet the point even in his elucidating earlier contribution, which centers around the important dynamical problem of appetite, tendency and puissance on the way from small perceptions to reflection (Ripalda 1972: 20f.). Already at the very beginning of Chapter I.2 of his Nouveaux Essais, where instincts are introduced, Leibniz declares that “one of the first and most practical [indemonstrable principles] is that we should pursue joy and avoid sorrow” – something which “is not a truth known solely from reason, since it is based on inner experience, namely on confused knowledge; for one only senses what joy and sorrow are”, which means without being expressed by means of concepts (NE 1.2.1; A VI 6 88; GP 5 81).33 This is the key, since somewhat later Leibniz explicitly calls precisely this principle (to follow joy and to avoid sorrow) an instinct.34 The point, which has to be taken as the most important one in our context, is this: Even if instincts are inclinations leading to affections, they are, due to this understanding, not completely and totally separated from cognition, but taken as an inner experience, moreover, as a kind of knowledge, namely as confused knowledge! This is the reason why Leibniz can say: Every feeling is the perception of a truth, and that natural feeling [the natural instincts for what is upright and good] is the perception of an innate truth, though very often a confused one as are the experiences of the outer senses. Thus innate truths can be distinguished from the natural light (which contains only what is distinctly knowable) as a genus should be distinguished from its species, since innate truths comprise instincts as well as the natural light (NE 1.2.9; A VI 6 94; GP 5 86).35

The reason why, in particular, moral principles or rules are innate as instincts instead of rational insight depends on their suitability and on their importance for everyday life in order to sustain society, as we already heard: These principles are “engraved in the soul, namely as necessary for our survival and our true welfare” (NE 1.2.2; A VI 6 89; GP 5 81).36 Demonstrations need time, whereas we should be in a disposition to act immediately in an appropriate way. Therefore instincts are indispensable. But Leibniz emphasizes that this is not sufficient for a foundation, since joy is primarily orientated to the present, whereas a long lasting joy – which is nothing but happiness – is orientated to the future; and this, however, depends on reason, “which leads us to the future and to what lasts” (NE 1.2.3; A VI 6 90; GP 5 82).37 Therefore, it is reason which transforms “an inclination which is expressed by the understanding” into “a precept or practical truth; and if the inclination is innate then so also is the truth – there being nothing in the soul which is not expressed in the understanding, although not always in distinct actual thinking” (NE 1.2.3; A VI 6 90; GP 5 82).38 The connection Leibniz expresses here holds for each innate

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truth, for all of them are given at the very beginning as dispositions, potentialities or faculties, so that starting from inner impressions as confused knowledge, the understanding transforms this knowledge into a clear and even distinct one. Therefore, it is not only possible, but also necessary for the understanding to transform the outcome of an instinct into knowledge of a higher degree.

5 Moral Necessity Reconsidered The way from confused to clear or distinct knowledge consists in a mere clarification of the content of knowledge, but this does not include anything concerning the kind of necessity of the moral principles in question. As already stated, we need a further characterization of this specific modality of moral principles as well as of moral rules. As we heard, Leibniz calls this necessity a happy one, which “demands to follow the rules of the perfect wisdom” (Th´eodic´ee, § 344; GP 6 319).39 This is “an obligation of reason, which always has its effect on the wise”, since these are always “good reasons” (ibid.),40 as Leibniz says, namely depending on the Principle of the Best.41 That indicates the connection with Leibniz’s fundamental principles in taking the moral principles as special cases of the Principle of Sufficient Reason. But even this does not say very much concerning the kind of necessity; of course, Leibniz, in answering Philalethe/Locke, admits that ethics is a demonstrative science; however, his notes on deontic logic already mentioned have shown that one has to presuppose a vir bonus. Thus, the ethical necessity in question is a hypothetical necessity – a term which Leibniz normally uses in dealing with phenomena, but which fits very well into the context, here. In an attachment to his Th´eodic´ee, he says with respect to moral necessity: This kind of necessity which by no means excludes the possibility of its opposite, has this designation only in the sense of an analogy; in fact, it does not depend on the mere essence of the things, but on what lies outside and above them, namely on the will of God. That necessity is called a moral one, since necessity and obligation are equivalent for the wise (GP 6 386).42

For the will of the wise, it is “natural to choose the good”; this is an “obligation of reason, which always has its effect on the wise” (ibid.)43 – neither as a causal determination, nor as a logical compulsion, but as the choice of the strongest, namely most reasonable inclination. And the more creatures follow this necessity, the more they draw nearer the state of perfect felicity.44 Let us have a look at the hypothetical presupposition of the wise, which Patrick Riley (1996) has analyzed so carefully. On many occasions, Leibniz defines in his writings: “The vir bonus is someone who loves everyone, as far as reason admits it”, and he goes on: “To love is to delight oneself in the felicity of others” (Codex juris gentium diplomaticus, Praefatio; A IV 5 60f.; GP 3 386).45 Putting these elements together, Leibniz defines: “Justice is the charity of the wise” (A VI 4 2890) and “charity is the attitude to love everyone” (A VI 4 2891).46 All this shows that we do not start from identities, but from clear and distinct concepts as a science demands; so we really reach Leibniz’s foundational concepts of his Justitia universalis, and

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by this his idea of a moral demonstrative science. To understand the necessity in question as a hypothetical one allows Leibniz to take them as eternal truths even for those worlds where the condition of a vir bonus is not fulfilled, since “it does not depend on the mere essence of the things” of the world, as we just heard. Putting things together, the validity of moral principles has a fourfold foundation: 1. The primary source consists in an instinct, which is innate and which makes us follow a feeling of love or charity as an innate moral principle. 2. For the wise or the vir bonus, this is an obligation. 3. Within a rational foundation it is transformed into eternal and universal moral rules as a hypothetical necessity, presupposing the vir bonus. 4. These rules are part of the Justitia universalis, aiming at the highest possible felicity, which consists in loving everyone. All these elements are connected in an orientation of our actions towards the Principle of the Best and towards perfection and maximizing harmony, which all together are guiding principles of reason. This reasoning goes further than mere truths of reason, it is more than the sheer combination of concepts, but it includes an innate affection towards the good. What remains is the question of how to combine these different elements, since they belong to different areas – the first one to instincts, which are innate, the second one to wisdom, the third one to reflection in order to build up the intended theory of morality as a demonstrative science, whereas the last one embeds the whole into the frame of the Leibnizian prime principles. What Leibniz intends is to show that his kind of rationalism can solve the problem in so far as it admits perceptions as a kind of unreflected, obscure knowledge: Innate instincts belong to these perceptions as inner states, and they have to be taken as dispositions, faculties or virtualities, which will be so to say activated by outer perceptions, i.e. in a given situation. Therefore, we gain the possibility not only to react and to act in accordance with instinct, but also to reflect on our aims and to reflect on the principles behind these. In just this sense is it possible to transform the moral instinct of charity into moral rules. In taking the innate instinctive principles as the inner and innate fundament, which is elaborated by apperception depending on nothing but well-defined concepts and a priori deductions, we are able to build up the intended demonstrative science of morals without the need of outer sense impressions. In this perspective, innate ideas are the cornerstone of rationalism.

Notes 1. “Vous [Philalethe/Locke] avi´es plus de commerce avec les Philosophes speculatifs, et j’avois plus de penchant vers la morale” (NE 1.1; A VI 6 71; GP 5 63). 2. “4. Il y a des necessit´es, qu’il faut admettre. Car il faut distinguer entre une necessit´e absolue et une necessit´e hypothetique. Il faut distinguer aussi entre une necessit´e qui a lieu, parce que l’oppos´e implique contradiction, et laquelle est appell´ee logique, metaphysique ou

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3. 4. 5.

6. 7. 8. 9. 10.

11. 12.

13. 14.

15. 16.

17.

H. Poser mathematique; et entre une necessit´e qui est morale, qui fait que le sage choisit le meilleur, et que tout esprit suit l’inclination la plus grande. 5. La necessit´e Hypothetique est celle, que la supposition ou hypothese de la prevision et preordination de Dieu impose aux futurs contingens” (5th Letter to Clarke, §4f.; GP 7 389). “[la necessit´e morale] [. . .] il y a une certitude et infallibilit´e, mais non pas une necessit´e absolue dans les choses contingentes” (5th Letter to Clarke, § 9; GP 7 390). “On demande [. . .] si la justice ou la bont´e est arbitraire ou si elle consiste dans les v´erit´es n´ecessaires et e´ ternelles de la nature des choses, comme les nombres et les proportions”. “C’est pourquoy je trouve encore cette expression de quelques philosophes tout a` fait estrange, que les verit´es eternelles de la Metaphysique ou de la Geometrie (et par consequent aussi les regles de la bont´e, de la justice et de la perfection) ne sont que des effects de la volont´e de Dieu, au lieu qu’il me semble, que ce sont des suites de son entendement, qui asseurement ne depend point de sa volont´e non plus que son essence”. “Aequum, Debitum est quicquid necessarium est fieri a viro bono”. “Omnis prudens est vir bonus”. See p. 2759, where Leibniz gives a further analysis, which he has withdrawn. “Ainsi j’appelle inn´ees les verit´es, qui n’ont besoin que de cette consideration pour estre verifi´ees” (NE 1.1.21; A VI 6 84; GP 5 70). As far as I know there is only one contribution, which seems to articulate this modal problem, namely S`eve (1983); but in fact he discusses only the problem of natural law. “[. . .] il paroit que les verit´es necessaires, telles qu’on les trouve dans les Math´ematiques pures et particulierement dans l’Arithmetique et dans la Geometrie, doivent avoir des principes, dont la preuve ne depende point des exemples, ni par consequent du t´emoignage des sens [. . .]. La Logique encore avec la Metaphysique et la Morale, dont l’une forme la Th´eologie et l’autre la Jurisprudence, naturelles toutes deux, sont pleines de telles verit´es; et par consequent leur preuve ne peut venir, que des principes internes, qu’on appelle inn´es” (NE Preface; A VI 6 50; GP 5 43). “PH. La Morale est une Science demonstrative, et cependant elle n’a point de principes inn´es” (NE 1.2.1; A VI 6 88; GP 5 80). “PH. Les Regles de Morale ont besoin d’estre prouv´ees, donc elles ne sont point inn´ees, comme cette regle qui est la source des vertus qui regardent la Societ´e: ne faites a` autruy que ce que vous voudri´es qui vous fut fait a` vous mˆeme. – TH. Vous me faites tousjours l’objection, que j’ay d´eja refut´ee. Je vous accorde, Monsieur, qu’il y a des regles de morale, qui ne sont point des principes inn´es mais cela n’empeche point que ce ne soyent des verit´es inn´ees, car une verit´e derivative sera inn´ee, lors que nous la pouvons tirer de nostre esprit” (NE 1.2.4; A VI 6 91; GP 5 83). “La science Morale [. . .] n’est pas autrement inn´ee que l’Arithmetique. Car elle depend aussi des demonstrations que la lumiere interne fournit”. “Mais il y a des verit´es inn´ees, que nous trouvons en nous de deux fac¸ons, par lumiere et par instinct. Celles que je viens de marquer, se demonstrent par nos id´ees, ce qui fait la lumiere naturelle. Mais il y a des conclusions de la lumiere naturelle, qui sont des principes par rapport a` l’instinct. C’est ainsi que nous sommes port´es aux actes d’humanit´e, par instinct parce que cela nous plaist, et par raison parce que cela est juste. Il y a donc en nous des verit´es d’instinct qui sont des principes inn´es, qu’on sent et qu’on approuve, quand mˆeme on n’en a point la preuve, qu’on obtient pourtant lors qu’on rend raison de cet instinct”. “Ius naturale Jurisconsulti definiunt quod natura omnia animalia docuit, [. . .] cum scilicet homines faciunt ex recta ratione, quod animalia ex instinctu naturae” (A VI 4 2778; GR 615). Leibniz criticizes Clarke as follows: “On confond la necessit´e morale, qui vient du choix du meilleur, avec la necessit´e absolue; on confond la volont´e avec la puissance de Dieu. Il peut produire tout possible, ou ce qui n’implique point de contradiction; mais il veut produire le meilleur entre les possibles” (5th Letter to Clarke, § 76; GP 7 409). “Et lors qu’on demande le moyen de connoitre et d’examiner les principes inn´es; je r´eponds [. . .], qu’except´e les instincts dont la raison est inconn¨ue, il faut tacher de les reduire aux premiers principes, c’est a` dire, aux Axiomes identiques ou immediats par le moyen des

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18.

19.

20.

21.

22. 23. 24. 25. 26. 27.

28. 29.

30.

31.

32. 33.

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definitions qui ne sont autre chose qu’une exposition distincte des id´ees” (NE 1.2.22; A VI 6 101; GP 5 92). “Il en est d’eux [les bienheureux] comme de nous, qui n’entendons pas tousjours la raison de nos instincts. Les Anges et les bienheureux sont des Creatures aussi bien que nous, o`u il y a tousjours quelque perception confuse mel´ee avec des connoissances distinctes” (Th´eodic´ee, § 310; GP 6 300). In Leibniz’ Index to his Th´eodic´ee we read: “Instinct – encore dans les bienheureux”, § 310. “[La necessit´e morale] est une heureuse necessit´e qui oblige le Sage a` bien faire, au lieu que l’indifference par rapport au bien et au mal seroit la marque d’un defaut de bont´e ou de sagesse”. “[. . .] c’est une necessit´e morale, que le plus sage soit oblig´e de choisir le meilleur” (Th´eodic´ee, § 230; GP 6 255). Concerning Leibniz’s foundation of justice on the concept of the vir bonus see Riley 1996: 144ff. “Il semble que tout le monde entend par l’instinct, une inclination d’un animal a` ce qui luy est convenable, sans qu’il en conc¸oive pour cela la raison. Et les hommes mˆemes devroient moins negliger ces instincts, qui se decouvrent encor en eux, quoyque leur maniere de vivre artificielle les ait presque effac´es dans la pluspart; [. . .]. La Sympathie ou Antipathie signifie ce qui dans les corps destitu´es de sentiment repond a` l’instinct de s’unir ou de se separer, qui se trouve dans les animaux. Et quoiqu’on n’ait point l’intelligence de la cause de ces inclinations ou tendances qui seroit a` souhaiter, on en a pourtant une notion suffisante, pour en discourir intelligiblement”. “Impulsus originarii et durabiles sunt instinctus”. “[. . .] instinctus ab affectibus esse distinguendos” (GR 678, ad p. 19). “Natura nostra nos etiam ad ea impellit, quae ex natura nostra adaequate non intelliguntur, ut ostendunt instinctus naturales”. “[. . .] instinctus [. . .] prosunt qui[a] ad bonum ducunt”. Leibniz repeats on page 680, ad p 42/44. “Haec omnia in sapiente naturae instinctu fundamentum habent, sed nostra imbecillitate ultra modum erumpunt”. “Malheureusement les hommes, par leur maniere de vivre artificielle, ont perdu beaucoup de leur instinct naturel par rapport au Physique, o`u peutetre des Sauvages nous passent. Mais on a conserv´e d’avantage dans le moral; et heureusement la raison et le sentiment y concourent”. “[. . .] inter utiles naturae est instinctus, sed rationis est instinctum hunc regere, ut non statim in actus erumpat”. “Pour ce qui est des combats qu’on suppose entre le corps et l’ame, ce n’est autre chose que la diversit´e des penchans n´es des pens´ees distinctes ou des pens´ees confuses, c’est a` dire des raisons ou des instincts et passions: l’instinct estant pour ainsi dire une passion durable et n´ee avec nous, et la passion estant comme un instinct passager et survenu; a` quoy on pourroit joindre l’accoustumance qui tient le milieu entre ces deux sortes d’inclinations, estant plus durable que la passion, mais non pas n´ee avec nous comme l’instinct”. “[. . .] es hat auch die g¨uthige Natur oder vielmehr der grund-g¨uthige Gott in uns nicht weniger als in andre thiere eine gewiße verborgene Krafft oder instinct geleget, so uns anstatt der vernunfft in sinnlichen dingen auch vor der erfahrung einiger maßen zum leitstern dienet. Es muß aber solcher instinct von dem verstande regieret und sonderlich m¨aßigkeit dabey gehalten werden”. “C’est pourquoi l’Auteur infiniment sage de nˆotre e´ stre l’a fait pour nˆotre bien, quand il a fait en sorte que nous soyons souvent dans l’ignorance et dans des perceptions confuses, c’est afin que nous agissions plus promtement par instinct, et nous ne soyons pas incommod´es par des sensations trop distinctes de quantit´e d’objets, qui ne nous reviennent pas tout a` fait” (NE 2.20.6; A VI 6 165; GP 5 151). “Et les loix eternelles de Dieu y sont en partie grav´ees d’une mani`ere encore plus lisible, et par une espece d’instinct”. “Et quoyqu’on puisse dire veritablement, que la morale a des principes indemonstrables, et qu’un des premiers et des plus practiques est, qu’il faut suivre la joye et eviter la tristesse, il faut adjouter que ce n’est pas une verit´e, qui soit connue purement de raison, puisqu’elle est

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34. 35.

36.

37.

38.

39. 40.

41. 42.

43. 44.

45.

46.

H. Poser fond´ee sur l’experience interne, ou sur des connoissances confuses, car on ne sent pas ce que c’est que la joye et la tristesse”. “[. . .] les instincts comme celuy qui fait suivre la joye et fuir la tristesse” (NE 1.2.9; A VI 6 92; GP 5 84). “[. . .] mais j’ai d´eja r´epondu que tout sentiment est la perception d’une verit´e, et que le sentiment naturel l’est d’une verit´e inn´ee, mais bien souvent confuse, comme sont les experiences des sens externes: ainsi on peut distinguer les verit´es inn´ees d’avec la lumiere naturelle (qui ne contient que de distinctement connoissables), comme le genre doit estre distingu´e de son espece, puisque les verit´es inn´ees comprennent tant les instincts que la lumiere naturelle”. This is just how, two decades later and without any knowledge of Leibniz’ Nouveaux Essais, Christian Wolff solved the problem of Christian Thomasius, who in his theory of affections found no way from “unreasonable love” to “reasonable love”, since due to Thomasius’ concept of affections the will cannot be guided in a rational manner, but has to follow the affections. “PH. Ils [les bandits] n’observent les maximes de justice que comme des regles de convenance, dont la practique est absolument necessaire pour la conservation de leur societ´e. – TH. Fort bien. On ne sauroit rien dire de mieux a` l’´egard de tous les hommes en general. Et c’est ainsi que ces loix sont grav´ees dans l’ame, savoir comme les consequences de nostre conservation et de nos vrais biens”. “Car la felicit´e n’est autre chose qu’une joye durable. Cependant nostre penchant va non pas a` la felicit´e proprement, mais a` la joye, c’est a` dire au present; c’est la raison qui porte a` l’avenir et a` la dur´ee”. “Or le penchant exprim´e par l’entendement passe en precepte, ou verit´e de practique: et si le penchant est inn´e, la verit´e l’est aussi, n’y ayant rien dans l’ame qui ne soit exprim´e dans l’entendement mais non pas tousjours par une consideration actuelle distincte”. “[. . .] une necessit´e morale; et c’est tousjours une heureuse necessit´e, d’ˆetre oblig´e d’agir suivant les regles de la parfaite sagesse”. “[. . .] la necessit´e morale porte une obligation de raison, qui a tousjours son effect dans le sage. Cette espece de necessit´e est heureuse et souhaitable, lorsqu’on est port´e par de bonnes raisons a` agir comme l’on fait”. “[. . .] la necessit´e morale, qui oblige le plus sage a` choisir le meilleur” (Th´eodic´ee, § 367; GP 6 333). “Mais cette maniere de necessit´e, qui ne detruit point la possibilit´e du contraire, n’a ce nom que par analogie; elle devient effective, non pas par la seule essence des choses, mais par ce qui est hors d’elles, et au dessus d’elles, savoir par la volont´e de Dieu. Cette necessit´e est appel´ee morale, parce que chez le sage, necessaire et dˆu sont des choses equivalentes” (Abreg´e de la Controverse reduite a` des Argumens en forme, 3eme Objection; GP 6 386). See above, n. 40. “Cette necessit´e morale [. . .] est une necessit´e heureuse. Plus les creatures en approchent, plus elles approchent de la felicit´e parfaite. [. . .] Et une volont´e, a` laquelle il est naturel de bien choisir, merite le plus d’ˆetre lou´ee” (Abreg´e de la Controverse reduite a` des Argumens en forme, 3eme Objection; GP 6 386). “Est autem jus quaedam potentia moralis, et obligatio necessitas moralis. Moralem autem intelligo, quae apud Virum bonum aequipollet naturali [. . .]. Vir bonus autem est, qui amat omnes, quantum ratio permittit”. “Justitia est caritas sapientis; Caritas est habitus amandi omnes”.

References Kulstad, M. 1991. Leibniz on Apperception, Consciousness, and Reflection. M¨unchen: Philosophia. Lamarra, A. 1995. Notes on reason and instinct in the Nouveaux Essais. In Leibniz und Europa. VI. Int. Leibniz-Kongeß, Vortr¨age II. Hannover: Leibniz-Gesellschaft, pp. 198–205.

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Leibniz [DM] = Discour s de Metaphysique. In A VI 4 and GP 7. Locke [Essay] = An Essay concerning H uman U nderstanding. Ed. by P.H. Niddich, Oxford: Clarendon Press, 1982. McRae, R.. 1976. Leibniz. Perception, Apperception, and Thought. Toronto: University of Toronto Press. Poser, H. 2001. Leibnizsche Handlungsmodi zwischen Ontologie und Deontologie. In: Th. Buchheim, C.H. Kneepkens, and K. Lorenz (eds), Potentialit¨at und Possibilit¨at. Modalaussagen in der Geschichte der Metaphysik. Stuttgart: Frommann-Holzboog, pp. 273–292. Poser, H. 2006. Leibniz et la potentialit´e des id´ees inn´ees: un probl`eme modal. In F. Duchesneau and J. Griard (eds.), Leibniz selon les Nouveaux Essais. Paris: Vrin / Montreal: Bellarmin, pp. 21–33. Poser, H. Forthcoming. Innate ideas and the foundation of rationalism. In T. Ben Guiza (ed.), Les enjeux du rationalisme moderne. Carthage: Acad´emie Tunisienne des Sciences des Lettres et des Arts 2007. Riley, P. 1996. Leibniz’ Universal Jurisprudence. Justice as the Charity of the Wise. Cambridge, MA: Harvard University Press. Ripalda, J.M. 1972. Instinkt und Vernunft bei G.W. Leibniz. Studia Leibnitiana 4: 19–47. Ripalda, J.M. 1975. Die geschichtliche Bedeutung der Instinkttheorie bei Leibniz. In Akten des II. Int. Leibniz-Kongresses, Bd. 3 (= Studia Leibnitiana Supplementa 14). Wiesbaden: Steiner, pp. 175–186. S`eve, R. 1983. En quel sens les v´erit´es morales et juridiques sont-elles dans la pens´ee de Leibniz, e´ ternelles et n´ecessaires? In: Leibniz – Werk und Wirkung. IV. Int. Leibniz-Kongreß, Vortr¨age I. Hannover: Leibniz-Gesellschaft, pp. 708–715. Wolff, Chr. 1720. Vern¨unfftige Gedancken von der Menschen Thun und Lassen, zur Bef¨orderung ihrer Gl¨uckseeligkeit [so-called Deutsche Ethik]. Halle: Renger.

Chapter 32

Causa Sive Ratio. Univocity of Reason and Plurality of Causes in Leibniz Stefano Di Bella

The hendiadys “causa sive ratio” could well be taken as the cypher for that age of Western thought mainly labeled as “Rationalism”. In the analytic as well as in the hermeneutic tradition, it is also taken as emblematic of an alleged identity of thought and being, or of logic and world. From this perspective, the historical evaluation of Heidegger, who reconstructs the epoch-making emergence of the “grand principe” between Descartes and Leibniz, is not so far from the one presupposed by this remark of G.H. von Wright: Philosophers have long been accustomed to making a distinction between the relation of cause and effect on the one hand and the relation of ground and consequence on the other. The first is factual and empirical, the second conceptual and logical. Before the distinction became current, it was often ignored or blurred – particularly by the rationalist thinkers of the seventeenth century (Von Wright 1971: 34).

Because he is the recognized father of the “principle of reason”, Leibniz is commonly held to be especially committed to the causa/ratio collapse. As a matter of fact, however, the cause/ratio equivalence is not so hastily subscribed to by him. Thus, in one of the first drafts devoted to the principle of reason, we read: “Surely, nothing is without a reason, but this does not mean that nothing is without a cause” (Elementa verae pietatis; A VI 4 1360). In order to understand what is at stake here, we should consider the intensive reflection of this age on causality, starting from the reshaping of the ancient Aristotelian paradigm of “four causes”. As has been correctly observed, the Greek aitia covered a wider scope than our “cause”, to embrace any answer to a “why-question”. In this perspective, the plurality of “causes” – or, alternatively, their reduction to one only – and their relation to the intelligibility need, expressed by the terminology of “reason”, offer a good terrain to test the flexibility of a model of reason.

S. Di Bella Scuola Normale Superiore, Pisa, Italy

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1 Intelligibility and Efficiency: Changing Paradigms 1.1 Metamorphoses of Efficiency: From Scholastic Tropes to Scientific Intelligibility As a matter of fact, already in the Aristotelian “scire per causas”, the ontological necessity of essences went hand in hand with the necessity of scientific explanation. But here, the central role was played by essence, which furnished the real ground of all properties on the one hand, and the principle of our demonstrative knowledge on the other. Hence the primacy of formal cause within the famous scheme based on the plurivocity of the four senses of “cause”. Scholastic tradition was basically faithful to this scheme – going back ultimately to Posterior Analytics – though modifying it. Thus, the Aristotelian “moving cause” was expanded into the idea of an “efficient cause”, i.e., of a productive one, connected with divine power as its original source and model on the one hand, and with existence as its typical effect on the other. Suarez’s detailed treatment of causal concepts in his Disputatio XII can be seen as the mature result that Scholastic tradition presented to the rising modern philosophy. As a matter of fact, Suarez gives expression to the primacy that efficient cause had assumed. In 1670 the young Leibniz edited an anti-Scholastic work by the Italian humanist Nizolius. The Preface to Nizolius’s work gives him the occasion to sketch a vigorous program for the renewal of the philosophical style, whose pivotal idea is a kind of linguistic therapy applied to traditional philosophical jargon. The notion Leibniz chooses for illustrating his criticism of Scholastic language is that of “cause”, as defined by Suarez: [. . .] Whether terms are popular or technical, they ought to involve either no figures of speech or few and apt ones. Of this, the Scholastics have taken little notice, for, strange though this sounds, their speech abounds with figures. What else are such terms as ‘to depend’, ‘to inhere’, ‘to emanate’, and ‘to inflow’? On the invention of this last word Suarez prides himself not a little. The Scholastics before him had been exerting themselves to find a general concept of cause, but fitting words had not occurred to them. Suarez was not cleverer than they, but bolder, and introducing ingeniously the word ‘influx’(influxus), he defined cause as what flows being into something else, a most barbarous and obscure expression. Even the construction is inept, since ‘influere’ is transformed from an intransitive into a transitive verb; and this influx is metaphorical and more obscure than what it defines. I should think it an easier task to define the term ‘cause’ than this term ‘influx’, used in such an unnatural sense (GP 4 148; L 126; italics mine).

Suarez’s attempt, notice, aimed at giving a unitary definition covering all genera of causes. For Leibniz, however, the alleged definition turned out to be nothing but an example of the undue application of metaphor – i.e., of a rhetorical device, suited to literary style – to the field of philosophical analysis. Now, the criticized metaphorical term of “influence” (influxus) was that by which Suarez’s definition intended to capture the dimension of “efficiency” as the central one for the notion of cause. Precisely this aspect, however, is felt “obscure” from the point of view of an austere conceptual analysis, such as Leibniz puts forward in the Preface to Nizolius.

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Leibniz published his anti-Scholastic manifesto for a new philosophical style together with a letter addressed to his teacher Jakob Thomasius (GP 1 15–27), where he sketched an interesting attempt at reconciling the Aristotelian tradition with modern “scientific” philosophy. In practice, Aristotle’s conceptual framework – purged of Scholastic overinterpretation – is submitted to a translation into the language of the mechanistic program. It is hardly surprising that Leibniz’s main efforts are devoted here to the reinterpretation of the doctrine of “four causes”. “Mechanical philosophy” – whose first and main model is represented for the young Leibniz by Hobbes’s De Corpore – radically challenges the role of essences (especially if intended as “substantial forms”) and final causes. Thus, the primacy of efficient cause becomes absolute, whereas the other types of causes are simply dismissed. At the same time, the understanding of efficient cause is entirely reduced to two explanatory paradigms: mechanical impact and geometrical deduction. Leibniz’s conciliatory attempt in the letter to Thomasius does not diverge from these leading ideas of “moderns”, insofar as all Aristotelian types of causes are reduced to motion as efficient cause; formal cause is nothing but the shape that is configurated by motion itself. The suggestion of the geometrical model is also present, indeed. Echoing a big debate on the epistemological status of mathematics that had occupied Aristotelian circles between the sixteenth and seventeenth century, he takes sides with the thesis most favorable to mathematics. His argument, running on the assumption of the causal nature of the scientific enterprise, points precisely to the causal character of geometrical knowledge: The Scholastics, in fact, thought so meanly of mathematics at first that they made every effort to exclude it from the number of the perfect sciences, chiefly on the ground that it does not always demonstrate from causes. But, if we consider the matter more accurately, it will be seen that it does demonstrate from causes. For it demonstrates figures from motion; from the motion of a point a line arises, from the motion of a line a surface, from the motion of a surface a body. The rectangle is generated by the motion of a straight line along another, the circle by the motion of a straight line around an unmoved point, etc. Thus the constructions of figures are motions, and the properties of figures, being demonstrated from their constructions, therefore come from motion, and hence, a priori, from cause. Geometry is thus a true science [. . .] (GP 1 21; L 98).

Besides the Euclidean model of geometric demonstration, geometric construction plays an important role in the new philosophy as a paradigm for genetic definitions. In this way, the De Corpore chapter on scientific methodology offered some interesting hints towards a causal reinterpretation of the notion of essence itself, or the nature of a thing: The names of the things that are known to have a cause must contain in their definition this cause or way of generation: so, we define the circle as the figure that arises by rotating a straight line on the plane, and so on (OL I 72).

This type of definition will provide a good model for “real definition”, a topic on which Leibniz, at least from the end of his Paris stay, will rely, precisely in order to cope with Hobbes’s conventionalist challenge. Besides this semantic content, Hobbes’s De Corpore did provide a kind of logical syntax of the notion of cause, through a conditional analysis in terms of requisita.

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Within this framework, Hobbes sketches a deterministic theory according to which the whole sum of the (necessary) conditions for the production of an effect is also infallibly sufficient to bring it about, and is qualified as its “cause”. Now, Leibniz’s basic adoption of the Hobbesian framework for causation is evident since the early seventies. In Leibniz’s transcription, the whole sum of requisita becomes the “reason” (ratio) – or, almost indifferently, the “whole cause” for the existence of something.1 Notice that this metaphysics of requisites, in the context of the Paris notes and the writings related to the Spinoza meeting, runs into some trouble insofar as they play the double role of elements of the essence and conditions for existence. Thus God, as the “last reason of things”, seems to work also as their essence. But in order to grasp this problem, we have to consider the new contamination of efficient and formal cause within the causa sui and related topics.

1.2 Eidos and Efficiency: Causality Beyond Intelligibility in Hobbes and Descartes In Suarez’s Disputations, on the one hand, efficient cause appeared coextensive with the space of existence; on the other, the essences of things and the related eternal truths acquired a relevant ontological autonomy within God’s mind – here also, a line of Scholastic thought found its achievement. Moreover, this role of essences in divine understanding was a heritage of Platonic eidos which was able to survive the crisis of Aristotelian embodied forms, and to still inspire the mathematical essentialism of new science. Thus, the emphasis laid on geometry made the status of “eternal” [read now: mathematical] truths a burning issue also for the pioneers of new science. The most revolutionary theories were put forward by Hobbes himself and by Descartes – both submitting the rationality of mathematical essences to a grounding act of power. As is well known, Hobbes gave to eternal truths a linguistic (hence conventional) status, locating their ground in human will. Since the Preface to Nizolius, Leibniz’s critical assessment of Hobbes implies the rejection of this conventionalism. Descartes, for his own part, links great ontological appreciation of mathematical essences with the bold statement of their being created by God – the famous “creation of eternal truths”. Questioned by Mersenne about how this divine causality should be thought of, Descartes answers: “as an efficient and total cause” (Descartes to Mersenne, May 27, 1630; AT I 151–152). Efficiency, or productive power transcending our intelligibility, appears as the true name of cause. Thus, the radical equivocity of cause with respect to God is accompanied by as much a radical weakening in the traditional plurality of the different types of causes. Also the balance of the two great explanatory paradigms underlying the classification of causes – the eidetic one, grounded on the form or essence, and that of efficiency – is profoundly reshaped. As has been shown by the studies of J.L. Marion (see especially Marion 1991: 231–263), the explanatory paradigm for our

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basic contact with the world – i.e., sense knowledge – is no longer the intelligibile one, based on similarity (ressemblance), of the sharing of some “eidos”, but is the causal one, marked by “dissemblance”, of the establishment of a “code”. The Cartesian project is marked, however, by a strong ambivalence, as far as the relationship between intelligibility and causality is concerned. On the one hand, intelligibility is submitted to a foundation that radically transcends it; on the other hand, within the “code” – once this has been established – strong explanatory univocity rules, where causal explanations possess the conceptual transparency of geometry. Descartes’ ambivalence culminates in his handling of the divine Ground itself. In the First Replies, he states the “great principle” in order to apply it to God’s existence. This is another revolutionary idea: for the whole tradition, God was the first cause; but the first cause as such was itself free of the rule of causality: accordingly, He was called “ens a se” only in a negative sense. Descartes, on the contrary, risks calling God causa sui in a positive sense. In this way, the maximum of univocity – God as submitted to causal rationality – goes on a par with the maximum of equivocity – i.e., with the incomprehensible idea of self-causation.

1.3 The Leibnizian Reception: From Causa Sui to Ratio Sui In Leibniz’s letter to Magnus Wedderkopf of May, 1671, the quest for the causal antecedents of human action is pursued until divine will is reached: For it is necessary to refer everything to some reason, and we cannot stop until we have arrived at a first cause – or it must be admitted that something can exist without a sufficient reason for its existence, and this admission destroys the demonstration of the existence of God and of many philosophical theorems. What, therefore, is the ultimate reason for divine will? The divine intellect [. . .] What then is the reason for the divine intellect? The harmony of things. What the reason for the harmony of things? Nothing. For example, no reason can be given for the ratio of 2 to 4 being the same as the ratio of 4 to 8, not even in the divine will. This depends on the essence itself [. . .] (A II 1 117; L 146).

Apparently in a neat contrast with Descartes’s great principle, no further reason can be given for the “harmony of things”. Leibniz’s conclusion somehow echoes Silesius’s “Ros ohne warum”, cherished by Heidegger as the radical alternative to the great principle. Anyway, the quest for a reason is ultimately satisfied, but within the eidetic paradigm of essences, taken in its Platonic-Pythagorean version: that is to say, within the sphere which Leibniz was eager to defend against Hobbes’s conventionalist challenge.2 Only some years later, however, Leibniz is faced with the Cartesian “causa sui”. When considered in its productive sense, the notion is firmly rejected by him. Leibniz, however, clearly accepts the Cartesian claim of extending to God himself the jurisdiction of the “principle of reason”. In his Fourth Objections, Arnauld attacked Descartes’ causa sui from a traditional point of view: a first uncaused cause has to be admitted, at the risk of either falling into the contradictory notion of selfcausation or being involved in infinite regress. In the Elementa verae pietatis – a

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metaphysical writing that is based on the principle of reason – Leibniz poses to himself the same objection, to solve it by the remark I quoted at the beginning: But one will object: if nothing is without a reason, then there will be no first cause, and no final end. My answer is: surely, nothing is without a reason, but this does not mean that nothing is without a cause. A cause, in fact, is the reason for a thing insofar as it is external to the thing itself, that is to say it is the reason for its production. The reason of a thing, however, can also be internal to it. And this turns out to be the case in all things that are necessary, like mathematical truths, that do contain their reason in themselves; and like God, who alone among actual beings is the reason of His own existence (Elementa verae pietatis; A VI 4 1360; italics mine).

By this seemingly innocuous terminological move, Leibniz achieves his reception of the Cartesian novelty. The need of a positive reason even for God’s existence is fully accepted; by the same move, however, the causa/ratio distinction is ready to eliminate any reference to the (incomprehensible) idea of self-production. Leibniz’s decision for univocity paves the way for the final interpretation of the ontological argument as the logical implication of God’s existence by His essence. But this is a story I don’t want to tell here (see Di Bella 1995). Rather, I am interested in verifying how the rejection of the metaphysical primacy of efficiency – together with the acknowledged absoluteness of the principle of reason – determines a new assessment of the doctrine of causes and of the subtle balance between the eidetic model and that of efficiency; consequently, also of the understanding of the “series of things”.

1.4 The Reason Beyond the Cause The surplus of reason with respect to the cause, and their connection, are not only decisive for the inner structure of divine Ground, but also for its relationship with all the rest. Both in Leibniz and Descartes we find the idea that the last explanation marks a discontinuity of type with respect to the chain of ordinary causal explanations, implying a neat original distinction between the metaphysical and scientific whyquestions, respectively. This is also the reason why for both thinkers the possibility of an infinite causal chain of world states is irrelevant for the further leap to a First Cause. As a consequence, in order to conclude with the latter, they needn’t deny the possibility of infinite series, that on the contrary are expressly held by them to actually exist. For Descartes, however, the transcendence of the First Cause with respect to the world series is precisely a strictly causal one, again, consisting in the power of producing existence. In this perspective, it is crucial to submit to the causal claim even those realities – like eternal truths – that seem to be excepted from it, insofar as they hold independently of the existence of concrete beings. In Leibniz, on the contrary, the decisive leap is from the series of causes to a first reason, as results from the writing On the Radical Origin of Things: Even if we should imagine the world to be eternal, [. . .] the reason for it would clearly have to be sought elsewhere, since we would still be assuming nothing but a succession

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of states, in any one of which we can find no sufficient reason, nor can we advance the slightest toward establishing a reason, no matter how many of these states we assume. For even though there be no cause for eternal things, there must yet be understood to be a reason for them (De rerum originatione radicali; GP 7 302; L 486).

Even if taken as a whole, the infinite series would still need a reason for its explanation, and the same would be true for eternal (uncaused) realities, like essences. In any case, the reason for an existent thing must lie in another existent being. Hence, also the laws, insofar as they actually hold, are in need of an existential basis. But it is only their holding, and not their content, which does depend on God’s existence. The denial of the creation of eternal truths is a central piece of Leibniz’s philosophical battle, indeed. For him, the rational code of essences, far from being produced by a causal act, represents a kind of common ground that embraces God as well as finite minds. In this sense, the absoluteness of the “code” stated in the letter to Wedderkopf is not abandoned. Its being uncaused is no longer interpreted as absence of reason, but as self-foundation according to the logic of the ratio sui.

1.5 Reason and the Plurality of Causes In Leibniz, therefore, the space of “reason” exceeds that of “causes”. In Descartes, the emphasis laid on the incomprehensibility (“equivocity”) of divine causation was accompained by the breakdown of the Aristotelian theory of causes and by the primacy of efficiency. Surprising as it may be, in Leibniz, on the contrary, the univocal need for a “reason” makes room for a rehabilitation of the plurivocity of causes. On the other hand, Descartes, when pressed by Arnauld’s objections – the latter insisting on the need of sharply distinguishing the case of essence from that of existence, and to assign efficient cause only to the latter – went as far as to rely, following the Aristotelian tradition though in a different way, on the flexible tool of analogy, in order to connect the formal and efficient sense of cause within his causa sui. In Leibniz, instead, analogy is replaced by a clear-cut classification under the common concept of ratio. The formal cause, conceived of according to a geometric paradigm, preserves its autonomy, but is excluded from the existential sphere – with the exception of the limiting case of God, of course. “Causes” in the strict sense maintain their privileged relationship with existence. In a dialogue of the same period as the Elementa, also centred around the principle of reason, the interlocutor, the Catholic bishop N. Stensen, observes: “The principle “Nothing is without a reason” is understood with reference to efficient, material, formal and final cause” (Conversatio cum Stenone; A VI 4 1375). It is a transcription of the ancient doctrine of four causes in the language of reason. This could be subscribed to by Leibniz, and no longer in the form of a forced translation, as was the case in the claimed “conciliation” of his Preface to Nizolius. In the mature Leibniz, in fact, some types of causes are rehabilitated, that are not included in the framework of mechanical science. Needless to say, the most relevant case is

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the revaluation of final cause, from both the epistemological and metaphysical point of view. For Leibniz, the field of contingent truths is dominated by “raisons de convenance”. The role of final causes in the unfolding of the existing world corresponds to the primacy of moral and esthetic axiological grounds in the laws which build up the basic structure of the world. Leibniz accepts, notice, Suarez’s subsuming of the working of “final cause” under the efficient one, via the notion of moving ground in the mind of an agent. But in the explanatory order, the hegemony of final cause is stated. On the whole, therefore, the “causes” are clearly taken as a subset of “reasons”,3 exactly marked by their relationship to existence. They maintain a relative irreducibility, insofar as they remain bound to the production of existing beings and of their states. Their subordination to “reasons”, however, means that the ultimate ground has always to be looked for in a conceptual space. Thus, a mere act of will can never provide a satisfying answer to a “why question”.4 Moreover, the primacy of eidos is originally restated in a quite general way, even beyond the twofold reassessment of mathematical and finalistic rationality. Let us consider, again, the Cartesian establishment of “code”, whose locus classicus was the relationship between mechanical motion and sensible quality (the qualia of contemporary debate), or in general the heterogeneous mind/body connection. After Descartes, the main stream of Cartesians – Malebranche and other so-called Occasionalists – had taken the step of simply giving away efficiency, while emphasizing the aspect of institution, although they tended, on the other hand, to dissociate the idea of institution from that of arbitrariness, by stressing in the former the characters of generality and “convenance”. Now, Leibniz aims at reducing more radically the space of arbitrariness, by directly challenging the original intuition concerning dissemblance, e.g. in the doctrine of so-called “primary and secondary qualities”: One should not imagine that such ideas as those of colour or pain are arbitrary and deprived of any natural connection with their causes: God is not accustomed to act with so little order and reason. Rather, I would say that there is a kind of likeness, that is not complete or, so to say, in terminis, but expressive, or according to an ordered relation, in the same way as an ellipse, and also a parabola or a hyperbole are somehow similar to a circle, of which they are the projection onto a plane: because there is some exact and natural relation between what is projected and its projection, given that each point of the one corresponds to each point of the other according to some precise relation. This has not been grasped by Cartesians, and on this point you have conceded to them more than you usually do and more than you should have done (NE 2.8.13; GP 5 118–119).

The concept of “expression”, as is well known, has been elaborated by him in order to explain our possibility of grasping and expressing objective truths through linguistic systems that are built up from conventional signs. Causation – i.e., the correspondence of an effect to its cause – is explained in the same way as truth – i.e. the correspondence of a proposition to the world:5 cause and effect, as well as proposition and world, do share the same structural arrangement – we would say, their logical form: and this is precisely what “expression” amounts to. One might

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be puzzled in imagining what having a logical form means for a cause or an effect. But puzzlement, maybe, could be mitigated if we conceive of both cause and effect as states-of-affairs. The well-ordered correspondence does also offer, as is well known, the means to spell the intersubstantial cause-effect relation by substituting physical influence. In this way, the weakening of efficiency under the primacy of the eidetic paradigm seems to find its achievement. And the cause-effect relation seems to be simply reabsorbed into a conceptual relation. Better, an epistemological one, insofar as only an explanatory constraint can provide the required asymmetry in the causeeffect relation, which cannot be assured by the mere concept of correspondence. As Leibniz explains to Arnauld, we attribute to the sea waves the role of cause for the ship’s movement, and not vice versa, because the first relation is more easily understandable. Now, in general, post-Cartesian thinkers – after eliminating the anomaly of Descartes’s instauration – are eager to reduce, within their “way of ideas”, causal dependence to a conceptual one. Leibniz will meet this approach especially in Spinoza’s ontology and epistemology. Interestingly enough, however, he will challenge precisely this reduction of ontological dependence to the conceptual one. Let us see how.

2 Series of Causes and Series of Reasons 2.1 Causal Production, Geometrical Demonstration, and Parallelism In his private 1678 notes to Ethica, Leibniz lingers on proposition 25 of the first part, where Descartes’ idea of the divine production of essences is echoed: God is the efficient cause not only of the existence of things but of their essence as well. Otherwise the essence of things could be conceived without God, by Axiom 4 (On the Ethics of Benedict de Spinoza; GP 1 147; L 203).

In post-Cartesian philosophy, Spinoza is a bold supporter of the causa/ratio identification. At the same time, his reception of Descartes’ ideas assumes a quite different form from its Cartesian model: in the world of Ethica, in fact, efficient causation collapses into geometrical deduction, insofar as he combines the Cartesian thesis of the causal establishment of the “code” with the idea of the unchangeable necessity of the code itself. Thus, the isomorphism between causal science and geometry becomes full assimilation: “[F]rom divine power, i.e. from infinite nature, infinite things in infinite ways necessarily arose, or they necessarily follow, by the same necessity by which from the triangle’s nature it follows that their angles are equal to two right angles” (Ethica I, prop. 17). Needless to say, Leibniz is eager to contrast this kind of assimilation of “causa” and “ratio” as strongly as the opposite one of Descartes. To this aim, his neat distinction between essential and existential connections assumes a modal connotation.

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Thus, he vigorously challenges the extension of geometric entailment to cover the field of efficient causality, by emphasizing his discovery that the basic physical laws are irreducible to geometric axioms: in other words, they are not logically necessary. The sharp distinction between logical and nomological necessity is indeed a major theme in Leibniz’s criticism of Spinoza’s philosophy. At any rate, the interpretation of Spinoza’s stance is rather controversial. Some years ago, E.M. Curley (1969) put forward an updated reading of Spinoza’s world in terms of a “model metaphysics”, i.e., of a picture of world as built up from a chain of states-of-affairs, whose connections are ruled by some nomological facts. Let that be as it may, Spinoza’s view of the “geometric” structure of the causal process implied a perfect correspondence between the (causal) order of things on the one hand, and the (causal) order of ideas on the other, expressed by the so-called “parallelism” of Proposition 7 of Ethica II: “[T]he order and connection of things is the same as the order and connection of ideas”. In the so-called “model metaphysics”, this means – once assumed that the corresponding “ideas” are a kind of propositions which express the related states-of-affairs – nothing but this: “[I]n general, wherever there is a relation of logical dependence among propositions, there is a relation of causal dependence among the corresponding facts” (Curley 1969: 54). Now, once Spinoza’s blurring of logical and nomological necessity has been dismissed, one might say that the model metaphysics view is not so far from Leibniz’s. Thus, that model could well capture the chain of world states sketched in the De rerum originatione, with the transitive causality of the chain of particular things plus the underlying nomological structure rooted in God’s mind (of course, without taking here into account the fact that Leibniz’s world states are not abstract entities like our states-of-affairs, nor modifications of a unique substance like Spinoza’s modes, but are series of modifications rooted in a plurality of individual substances). If taken in this way, the ground-cause parallelism also seems to be wholly accepted by Leibniz. Nevertheless, Leibniz does criticize proposition 25 of Part I by questioning the content of Axiom 4, which is, notice, the only basis for Spinoza’s parallelism: But this proof carries no weight. For even admitting that the essence of things cannot be conceived without God, by proposition 15, it would not follow that God is the cause of their essence. For the fourth axiom does not say that ‘the cause of a thing is that without which it cannot be conceived’. (This would be false, for a circle cannot be conceived without a centre, or a line without a point, yet the centre is not the cause of the circle, nor the point of the line.) The fourth axiom says merely that ‘the knowledge of the effect involves the knowledge of the cause’, which is something far different. Nor is this axiom convertible – not to mention the fact that to involve something is one thing and to be inconceivable without it is another. The knowledge of the parabola involves the knowledge of its focus, yet the parabola can be conceived without it (On the Ethics of Benedict de Spinoza; GP 1 147; L 203).

I have dealt elsewhere with this interesting remark by Leibniz (Di Bella 2001) so I am limiting myself here to summarizing my conclusions. In general, Leibniz does not question here the conceptual interpretation of causality as such, nor the related isomorphism between the series of reasons and the series of causes. He

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only challenges the inadequate form this interpretation received in the context of the Cartesian way of ideas. In Spinoza’s definitions, in fact, Leibniz saw the full expression of the Cartesian attempt of reducing ontological dependence to a generic conceptual one, the latter being interpreted in its turn as a kind of conceptual need (indigentia conceptus alterius; in Cartesian terms, sine alio concipi non posse). (a) Against this Cartesian understanding, Leibniz’s remark contains a first warning, concerning the adequacy of our intuitions. He wants to stress this point by emphasizing the difference between “A being not conceivable without B” and “A involving B”. The first is merely an epistemic criterion, open to subjectivistic drift; the second one determines the objective logical space of a concept. (b) Even if cleaned from the epistemic flavor of Cartesian intuitionism, conceptual equivalence is criticized. To say that Axiom 4 is not convertible means that we cannot pass from a generic conceptual implication to the holding of a causal one. The comparison to other places in the Leibnizan corpus confirms that a causal relation always has some conceptual content; however, the nature of this content has to be further specified. Otherwise, causality could collapse into inherence. This is likely to be Leibniz’s worry, in the context of a discussion of Spinoza’s stance. Actually, Leibniz’s own metaphysics of conditions in the preceding years had bordered this collapse, given the ambiguous role of requisite as a condition both for essence and existence.

2.2 Beyond Geometric Construction A final remark (c) on Leibniz’s criticism. He cites here the case of the circle – a classic example of genetic definition – to give an example of conceptual connection that cannot be mistaken for a causal connection. Not every intelligibility condition is by this very fact a causal condition. After accurately distinguishing causality from the model of geometric demonstration, Leibniz distances himself from the other geometric model of construction. In the late 70s, in effect, when he closely investigates the topic of real definition, Leibniz comes to distinguish the ideal production from the real one; in this context, geometrical construction shows an increasing difficulty in capturing causal processes. In the interesting text De Synthesi et Analysi, we are faced with the difference between constitution and generation, the former expressing a possible way of production (for instance, one of the possible ways of construing an ellipse), whereas the latter reflects the actual one: [. . .] it is useful to have definitions involving the generation of a thing, or, if this is impossible, at least its constitution, that is, a method by which the thing appears to be producible or at least possible [. . .] to set up a hypothesis or to explain the method of production is merely to demonstrate the possibility of a thing, and this is useful even though the thing in question often has not been generated in that way. Thus the same ellipse can be thought of either as described in a plane with the aid of two foci and the motion of a thread about them or as a conic or a cylindrical section. Once a hypothesis or a manner of generation is found,

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one has a real definition from which others can also be derived, and from them those can be selected which best satisfy the other conditions, when a method of actually producing the thing is sought (GP 7 292–298; L 230–231).

As a first step, the problem of the plurality of possible constructions can be solved by referring to the simplest ones; this can work well for providing genetic definitions of types (or species) of objects (e.g., the circle, the ellipse). But when we are interested in the genesis of a determinate circle, a problem of existence arises, and the criteria of selection should be different: So De Synthesi invokes the compatibility with the whole context of surrounding things. Since the end of his Paris stay Leibniz had discovered that only abstract objects – like mathematical ones – do admit a plurality of possible constructions, or, better, they are undetermined with respect to their genesis. Real (i.e., concrete) beings, on the contrary, should involve within them the causal trace of their genesis. A draft of that period, the Meditatio de Principio Individui (A VI 3 490–491), comes to this conclusion starting from the selfsame causal axiom discussed in the Ethica notes. Finally, the embodiment of a genetic track into the individual’s nature will find its achievement in the complete concept theory of 1686. This also means the rehabilitation of formal cause in the Aristotelian sense of substantial form, or principle of action. But I cannot dwell on this point here. Anyway, several of these ideas which emerged within the critical assessment of the current models of conceptual dependence – I mean the irreducibility of existence, the unicity and full determination of the related construction, and the distinction between ineherence and causal relation – are preserved within the framework of Leibniz’s theory of conditions.

2.3 Consequence and Cause: Towards a Leibnizian Theory of Conditions As an alternative to the Cartesian intuitionistic theory of causality, and to the related inadequate view of conceptual dependence, Leibniz elaborates in the succeeding years a theory of conditions, which develops the old Hobbesian model no longer towards a metaphysics of requisita, but towards a kind of formal ontology of causal relation. I cannot dwell here on the details of this theory, which is documented in several of Leibniz’s drafts devoted to the inquiry into categorial schemes. Let me only briefly show how Leibniz tackles, within this framework, the task of providing a unitary definition of cause, capable of taking into account its different interpretations, as well as the task of rethinking the cause-reason isomorphism in a more adequate way than the Cartesian approach managed to do. In this perspective, the following text is worth quoting: One notion can be more general than another, though being not simpler. This is the case for the notion of a concurring factor, that embraces the concepts of antecedent, requisite, cause; notwithstanding, its notion includes that of antecedent, as usual for terms that stand in a relation of analogy [. . .] As far as the antecedent is concerned, I define it in the following way: it is a term such that, if it is given, another does follow, which I label as consequent

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[. . .] Provided only that it be prior for nature: that is to say, provided it is a real antecedent, and not a merely logical one (Potest aliqua notio esse generalior; A VI 4 303; italics mine).

Leibniz is trying to capture through his logical notion of “condition” the general concept of “cause” that Suarez failed to capture through his metaphorical language. Notice that he also somehow relies on analogy, insofar as the relevant notion of “concurring factor” (conferens) works as a kind of “focal meaning”. But what I am more interested in is the unusual contrast of “logical” and “real”. Leibniz is here considering the first difficulty one is faced with when seeking to provide a conditional analysis of causality. I am alluding to the fact that the logical notions of necessary and sufficient condition cannot account for the asymmetry of causal relation. In a logical or inferential system, if proposition p is a sufficient condition for q, then q is a necessary condition for p. But if the relation of condition is given a causal sense, then the inference does not hold. This asymmetry marks the distance between the causal structure of reality and the inferential patterns we are following in our inquiry: we could say – relying on a traditional dichotomy – between the order of being and the order of knowledge. In the latter, in fact, it is quite usual to pass from the knowledge of the effect to the knowledge of its cause. The need to impose an ordering relation is the more urgent, as, for Leibniz, on the ontological level too we have a plain equivalence of cause and effect, given the fact that all of the necessary conditions do work infallibly as sufficient ones. In order to capture causality, the logical skeleton of consequence has to be implemented by a new notion, that of “order of nature”. Adding priority of nature to the logical concept of necessary condition (conditio), we obtain the notion of requisite – the key concept of Leibniz’s theory, in particular that which plays the role of causal factor. Not accidentally, the Notes to Spinoza also present a detailed remark on the order of nature, where the Dutch philosopher is criticized for having neglected this notion. But how to understand the order of nature? The Cartesian criterion of one-sided dependence (A can be conceived without B, but B cannot be conceived without A) is not reliable, for the grounds we already know. The great postulate of the combinatorial project can suggest a more satisfying answer: according to it, all concepts can be in principle resolved into simpler ones, until the simplest are reached, from which all the remaining are built up. Consequently, the combinatorial order of increasing complexity is the objective or natural order, which determines the direction of causal relation. The Leibnizian drafts show that this concept is worked out on the terrain of the meta-theoretical problem of the organization of an axiomatic deductive system of science. In particular, the order of nature is thought of to handle with a plurality of equivalent definitions and to order theorems hierarhically. A little known episode in the later history of philosophy and logic could help us in grasping the significance of these Leibnizian ideas. I am thinking of Bolzano’s theory of the “consequence” (Abfolge) relation, as it is introduced in the second part of his Wissenschaftslehre (Bolzano 1837, II, §§198–222; pp. 339–390). This notion

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is not a purely logical one, insofar as it is distinguished from that of “deducibility” (Ableitbarkeit, the true ancestor of our Tarskian “consequence”), and properly holds only for true propositions. It aims at capturing the old Aristotelian distinction between explanations oti and dioti, hence it is an objective asymmetrical relation of “grounding” among propositions “an sich”, which is accurately distinguished from epistemical inference. On this basis, Bolzano is well entitled to quote the NE passage which contains the Leibnizian version of the cause/reason isomorphism: Reason is a truth known to us, whose connection with a less known truth has the effect that we give our assent to the latter. It is especially called ‘Reason’, however, when it is the cause not only of our judgement, but also of truth itself: what is also labelled as ‘a priori Reason’; and a cause within things corresponds to a reason on the level of truths” (NE 4.17.3; GP 5 457).

“Cause” is taken here in its most general conceptual core of consequence plus order of nature. But there is an allusion to the shift from an understanding of “cause” as a relation connecting propositions, to a relation directly connecting things, or maybe better states-of-things. The peculiar link of “cause” to existent beings is not dismissed, indeed. “Cause” in the strictest sense is defined as a requisite which contributes to the way of production according to which the effect is actually and succesfully brought about (conferens cum successu).6 Moreover, the order of nature is applied to a temporal series of states: be this conceived of more abstractly, like in the model of the series-of-things, or as the concrete series of states of an individual substance, as is the case in Leibniz’s mature metaphysics. As we read in an interesting text devoted to this topic: It is somehow difficult to explain, what is prior for nature. For, exactly as the subsequent state of a substance involves the previous, so conversely the latter does involve the former: each of them, indeed, can be known from the other one. Hence, it seems to follow that the previous is not simpler than the subsequent, but both involve the same elements, and are to be somehow equated. The solution to this puzzle, however, could be illustrated by an elegant example. We know, in fact, that there are often many properties of one and the same object, one of which is easier to find and to demonstrate than the other, while being nevertheless reciprocally deducible, hence all involving the same elements [. . .] In the same way, two states of the world – although each of them involves the other – nevertheless are not understood with equal ease, nor explained from their sources. Therefore, prior for nature is the one, whose possibility is more easily demonstrated, i.e. that is understood more easily. From two states that are reciprocally contradictory, the one that is prior for nature is also prior in time (Quid sit natura prius; A VI 4 180–181).7

Far from explaining the asymmetry of causation, like in post-Humean approaches, temporal order itself is grounded by Leibniz on the causal order, hence ultimately on the order of nature. In this way, Leibniz sketches a logically-minded conceptual account of causality, flexible enough to translate different epistemological and ontological relations without blurring them together or with logical consequence. In this framework, the irreducibility of existential and temporal dimensions is somehow preserved, though being subordinated to conceptual dependence.

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Notes 1. In a 1676 draft we read: “The whole sum of requisites is the full cause of a thing. Nothing is without a reason, because nothing is without the whole sum of its requisites” (De existentia; A VI 3 587). And in a draft of the first Hannover years: “Nothing happens without a reason. Nothing exists, indeed, unless all requisites of its nature do exist. Now, the existences of all the requistes, taken together, are the reason of the thing” (Deus nihil vult sine ratione; A VI 4 1388). 2. The refusal of Hobbes’s thesis is made clear since the Preface to Nizolius. 3. The plurivocity of Leibniz’s meaning of “cause” and the subordination to “reasons” are recognized in Mates (1973). As we shall see, we are not faced, however, with an unnoticed confusion, but with a conscious attempt at articulation. 4. The locus classicus for this statement is Leibniz’s late discussion with Samuel Clarke on the principle of reason. Whereas for Clarke it is quite natural to invoke divine will as a well-suited candidate to satisfy the need for a reason, for Leibniz such an arbitrary will, far from satisfying the principle, does directly fly in the face of it. 5. Notice, moreover, that the causal relation that is considered here – between sensation and perceived body – is a cognitive relation, posing a problem of cognitive correspondence. For expression as the key concept for a theory of language and truth, see the 1677 Dialogus (GP 7 190–193; A VI.4, 20–25). 6. “A cause is a factor which contributes successfully [conferens cum successu], i..e. if the result is the actual existence of the thing, of which it poses a condition, according exactly to this way of production [actually followed]” (A VI 4 940). “A conferens is a requisite for some way of production according to which a thing can be brought about. A cause is a requisite for the way it is actually brought about” ( A VI 4 630). 7. On this text, see Rauzy (1995).

References Bolzano, B. 1837. Wissenschaftslehre. Repr. 1929. Leipzig: Felix Meiner. Curley, E.M. 1969. Spinoza’s Metaphysics. Cambridge, MA: Harvard University Press. Descartes, R. 1963–1974. Oeuvres. Ed. C. Adam and P. Tannery. Paris: Vrin [= AT]. Di Bella, S. 1995. L’argomento ontologico moderno e l’ascesa dell’ens necessarium. Annali della Scuola Normale Superiore di Pisa. Classe di lettere e Filosofia. Serie III, vol. XXV, 4: 1531–1578. Di Bella, S. 2001. Nihil esse sine ratione, sed non ideo nihil esse sine causa. Conceptual Involvement and Causal Dependence in Leibniz. In H. Poser (ed.) Nihil sine ratione (VI. Internationalen Leibniz-Kongresses).Berlin: Leibniz-Gesellschaft, pp. 297–304. Hobbes, T. 1839–1845. Opera Latina. Ed. W. Molesworth. London: Bohn (repr. Aalen, Scientia, 1961) [= OL]. Marion, J.L. 1991 Sur la th´eologie blanche de Descartes. Analogie, cr´eation des v´erit´es e´ ternelles et fondement, 2nd ed. Paris: Presses Universitaires de France. Mates, B. 1973. Leibniz and the Phaedo. In Akten des II. Internationalen Leibniz-Kongresses. Wiesbaden: Steiner, pp. 135–148. Rauzy, J.B. 1995. Quid sit natura prius? La conception leibnizienne de l’ordre. Revue de m´etaphysique et de morale: 31–48. Von Wright, G.H. 1971. Explanation and Understanding. London: Routledge & Kegan Paul.

Index

A Abfolge, 507 Abstract, 5, 9, 18, 19, 23, 24, 25, 86–87, 92, 111–112, 116, 117, 118, 146–147, 164, 174, 207, 209, 232, 238, 242, 244, 247, 283, 298, 299, 301, 302, 306, 309–310, 316, 373, 380, 424, 438, 504, 506 mathematics, 92, 111, 144, 147, 309 physics, 474 reason, 438 abstraction, levels of, 4, 146–148 Achilles, 349 acroamatic, 23 act, 7, 26, 100, 116, 142, 186, 192, 319, 335–336, 337, 367, 473 action, 6–8, 20, 27, 40, 51, 55, 77, 100, 111, 113, 114, 117, 118, 124, 132, 146, 148, 163, 175, 177, 179, 186–187, 190–191, 192, 194–195, 196, 205, 243, 282–283, 287, 289, 293, 297, 302, 303–304, 308, 310–311, 329, 335–336, 339, 344, 345, 349–350, 352–353, 357, 358–359, 360–361, 362–363, 365–367, 368, 369, 384, 426, 429, 431, 453, 455, 456, 467–468, 470, 471, 475, 483, 484, 486, 489, 499, 506 impedible, 467 Adam, 30, 332, 414, 416–420 Adams, R., 79, 385, 398, 406, 449, 453 adversarial, 53 adversary, 52, 56, 64, 67, 102, 321, 325 aesthetic, 147, 310, 311 aesthetics, 362 See also beauty affect, 334, 357–358, 361, 452 affectio, 430 affection, 76, 332, 334, 346, 471, 487, 489, 492

African, 412–413 agreement, 41, 90, 93, 168, 169, 174, 190, 191, 195, 196, 239, 244, 346, 351, 352, 360–361 Albert, H., 232, 245 alchemist, 113, 115, 118 algebra, 63, 94, 138, 148, 170–171, 173 algebraic, 131, 145, 149, 150, 172–173, 479 algorithm, 89, 127–128, 135, 173, 378 algorithmic, 265 alphabet of human thoughts, 41, 63 altruism, 318, 320 See also other American Native, 411, 412, 417 amphibology, 213–227 analogical, 5, 113, 231, 240, 242, 259, 335, 432, 437 analogic intelligence, 423 analogous, 174, 348, 350, 379 analogy, 28, 76–77, 93, 113–115, 116, 117, 121–122, 123, 129–130, 133, 135, 147, 151, 175, 178, 207, 220, 238–239, 241, 242, 267, 269, 297, 302, 304, 434–437, 446, 457, 474, 488, 501, 506–507 legal use of, 242 See also hermetic and topics analysis, 28, 49, 53, 90, 142–145, 155–166, 179–180, 267–278, 364, 379–381, 485 of the Ancients, 275 of concepts, 78, 174, 217 dialectical, 159 regressive, 268, 269 situs, 145, 147, 148, 365 of transcendants, 137, 150 analytic, 22, 51, 53, 93, 163, 322 Anselm, 221

511

512 Anselmian, 282, 287 Antitrinitarian, 389–390 Antognazza, M.R., 438 apagogical, see Proof apologetic, 386, 424, 426, 449 apperception, 300, 304 appetite, 7, 192, 303, 307, 335, 487 Aquinas, Th, 45, 224, 284, 452, 466 Arab, 69, 113, 416 arbitrariness, 50, 181, 245, 480, 502 arbitrary, 5, 125, 179–180, 186–187, 194, 209, 284 arbitrio, 68, 276, 277, 278, 446 Archimedes, 144, 464 architectonic, 51, 90, 116–117, 190, 469 argumentation, 12, 17, 40, 45, 52, 55–56, 61–62, 63, 66, 67, 92, 144, 146, 148, 157–158, 160, 161, 189, 192, 199, 232, 235, 237, 239, 247, 282, 286, 315, 349, 444–445, 446 conclusive, 40 argumentative, 3, 37, 42, 52, 61, 66, 199, 210, 215, 235, 251–266, 322, 331, 474 loci, 61 order, 52 Arian, 387 Aristotelian, 10, 162, 343, 344, 346, 352, 390, 400, 442, 469, 495, 496–497, 501, 506, 508 Aristotelianism, 19, 352, 471 Aristotle, 21, 27, 69, 167, 177, 269, 284, 295, 343, 374, 470, 497 arithmetic, 41, 120, 130, 146, 163, 171, 213, 217–218, 280, 286, 317, 339, 363, 413–414, 428, 442, 450, 457, 480, 482–483 binary, 450, 457 quadrature of the circle, 126, 134 Arnauld, A., 332, 501 ars analytica, 163 combinatoria, 125, 126, 128, 132–134 formularia, 148 inveniendi, 63, 89, 93, 128, 209, 385 iudicandi, 209 art of controversies, 37, 40, 63 of dialectic, 156, 157, 159 d’inventer, 211 of discourse, 155, 159 of discovery, 210 of infallibility, 170 of judgment, 349

Index machines of, 118 of reasoning, 60, 155, 267 assembler, 127, 129, 131, 133, 137 assensus, 384 assertabilism, 296, 297, 300, 301, 302 atheist, 49, 388, 452, 463, 469, 480 atom, 101, 113, 114 attraction, 99, 100, 101, 106, 110, 272 Augsburg Confession, 406, 441, 446, 454 See also Protestant Augustine, 282, 284, 288, 331, 402, 406, 414, 432 Augustinian, 8, 282, 399, 401, 405, 432, 441 authentic, 151, 234, 308, 310, 436, 437 authenticity, 293–312 authority, 9, 49, 55, 233, 235, 384, 441–447 autonomy, 132, 192–193, 208, 293–312 Averro¨es, 393, 466 Avicenna, 466, 476 axiological, see rationality axiom, 6, 24, 45, 113, 114–115, 116, 141, 143, 146, 161, 162, 164, 171–172, 201, 215, 218, 219–220, 226, 232–233, 268, 279–281, 334, 466, 484, 503–505, 506 of Alphenus, 233 axiomata legum, 232 axiomatic, 57, 163, 209, 231–234, 235, 507 quasi-axiomatic, 49, 51 axiomatization, 40 Ayer, A.J., 177, 178 B Babbage, C., 135 Babylon, 417 Bachovius, 47 Bacon, F., 209, 420 balance, 8, 12, 31, 54–55, 56, 61, 66, 68, 69, 71, 100, 176, 207, 308, 312, 321, 337, 338, 340, 357–358, 360–361, 362–363, 366, 367–368, 388, 399, 406, 476, 498, 500 of reason, 7, 31, 51, 54, 66, 357, 368, 398, 399, 406 of reasons, 40, 361 of rights, 46 See also scales Balde, 241 Bartole, 231, 246 Bayle, P., 119, 120, 121, 330, 362, 390–393 beautiful, 114–115, 145, 147, 148, 286, 306–307, 330, 366, 401 beauty, 114–115, 147, 286, 306–307, 330, 366, 401

Index Beck, L.W., 454 Beeley, P., 4, 80, 85, 86, 96 Belaval, Y., 5, 46, 379 belief, 52, 121, 135–136, 178–179, 336–337, 413, 435, 456–457 Bentley, R., 151 Bernouilli, Jacques, 130 Bernouilli, Jean, 131 Bernoulli, Johann, 114, 117, 120 Bible, 9, 414, 441–447, 450, 456 authority of, 9, 441–447 witness of, 444 See also Scripture Biblical, 9, 54, 419, 426, 442, 447, 454, 456, 458 exegesis, 9, 447, 454 Bierling, F.W., 90, 91, 399 binary, see arithmetic Blank, A., 155 blend, 200, 207, 208 Bolzano, B., 507, 508 Bossuet, J.-B., 285 Boucher, P., 6, 11, 46, 49, 51, 65, 231, 235, 255 Bouquiaux, L., 5, 99 Bourguet, L., 92, 339, 452 Bourignon, A. 401 ´ 57, 69 Boutroux, E, Bouvet, J., 141, 414, 415, 458 Boyle, C., 151 Boyle, R., 89, 99 Breger, H., 4, 125, 141, 143, 144, 147, 148, 149 Br´ehier, E., 38, 39, 62, 63 Brobro, M., 477 Brown, S., 456 Bruy`ere, N., 166 Buber, M., 315 Bucer, M., 447 bucket experiment, 103–104 Buddhism, 414 Buffon, G.-L.L., 420 burden of proof, see proof Burnett, Th, 31, 57, 70, 71, 101, 289, 333, 363, 371, 397, 447 Buxtorf, J. (senior and junior), 442 C cabbalistic, 112, 404 Caesar, 294–300, 302, 304–307, 309, 311, 350, 372 Cajori, F., 131 calculation, 8, 18, 22, 31, 39, 41–42, 43, 53, 54, 55, 116, 135, 142, 144, 149, 158, 176, 210, 237, 245, 343, 344, 348, 349, 350, 352, 353, 357, 360, 472

513 calculus, 4, 37, 41–42, 57, 61, 63, 80, 81, 89, 91, 111–112, 114–115, 116, 119, 120, 126, 127, 128, 130, 131, 135, 137, 143–144, 145, 147, 150, 173, 176, 298, 299, 348–350, 352, 362, 367, 369, 398, 415, 442 differential, 4, 115, 119, 130, 145, 362 infinitesimal, 89, 114, 126, 143, 144, 352 integral, 137, 145, 173 new, 22, 125, 126–131 old, 128 of variations, 362, 369 See also logical Calov, A., 442 Calvinism, 287, 390, 406, 445 Calvin, J., 281, 288 cannibal, 389, 412 Cantiuncula, C., 239, 240, 246 Cardan, G., 132, 150 Cardoso, A.D., 7, 329, 332 caritas, see charity Caroline, 101 Carraud, V., 477 Cartesian, 5, 24, 56, 87, 94, 107, 117, 129, 134, 145, 150, 169, 171, 215, 216–217, 225, 288, 310, 321–322, 325, 330, 333, 386, 388, 389, 390, 391, 454, 480, 482, 499–500, 502, 503, 505, 506–507 method, 56, 390 order of discovery, 322 case circular perplex, 244 law, 174, 175 perplexed, 236, 244, 255 Cassirer, E., 427 Castellio, S., 399, 400 casuistry, 231, 235, 245, 275, 386 Catholic, 32, 44, 176, 333, 372, 373, 384, 388, 397, 405 Catholicism, 44, 377 Cauchy, A.-L., 144 causa integra, 466, 471 sui, 469, 498, 499–500 causality, 10, 164, 185, 296, 302–303, 308, 310, 312, 329, 331, 335, 337, 466–467, 468–470, 475, 476, 477, 495, 498–499, 504, 505, 506–508 immanent, 475 mechanic, 470 moral, 335 of will, 337

514 cause and effect, 87, 88, 92, 495, 502–503, 507 efficient, 190, 196, 330, 344, 496, 497, 498, 501, 503 final, 88, 195, 273, 274, 303, 330, 344, 363, 469, 497, 501, 502 first, 190, 196, 243, 499, 500 formal, 469, 496, 497, 498, 501, 506 immanent, 190, 191, 329, 470, 475 its own, see causa, sui mechanic, 90, 116, 469 moving, 496 precise, 469 required, see requisite sine qua non, 467, 468, 470 whole, 466, 498 causes plurality of, 495–509 series of, 500, 503–508 centrifugal, 103, 104, 106–108, 110 certainty, 24, 32, 40–41, 43, 47, 54, 57–59, 69, 70, 161, 218, 219–220, 232, 241, 252, 254–255, 257–258, 261, 263–264, 265, 267, 270–271, 274, 282, 301, 312, 351, 386, 413, 429, 481 moral, 24, 58 character, 38, 41, 79, 92, 108, 133, 155, 157, 187, 188, 189–196, 215, 216, 217, 334–337, 415, 502 Characteristica universalis, 18, 22, 41, 141, 151, 398 charity, 2, 8, 47, 284–288, 317–320, 321, 324, 325, 334, 388, 393, 399, 400, 402, 488–489 of the wise, 284, 288, 317, 319, 488 Charron, P., 332–333, 340 Chemla, K., 181 Chemnitz, M., 442 China, 58, 176, 411, 412, 414, 420, 458 Chinese, 69, 411, 412–416 See also sinology Christ, 332, 333, 406, 413, 414, 416, 436, 441, 445, 446 Christendom, 332, 376, 411, 417, 457 Christian, 8–9, 34, 49–50, 284, 288, 319, 331, 332, 333, 334, 343, 376, 377, 384, 400, 406, 412, 413, 414, 415, 443, 444, 445, 450, 453, 454, 455 Church, 42, 49, 55, 66, 332, 333, 384, 386, 388, 397, 400, 405, 406, 442, 443, 445, 482 Cicero, 63, 280, 479

Index circular, 46, 103, 104, 106, 109, 149, 222, 234, 235, 243, 244, 280, 316, 466 circularity, 149, 222, 280, 316 Clarke, S., 416, 455, 509 classification, 17, 165, 175, 185, 190, 191, 200, 203, 205, 208, 214, 216, 219, 231, 236, 240, 464, 501 Clatterbaugh, K.C., 477 Clemens of Alexandria, 413 Co¨effeteau, 331, 339 cogitatio caeca, 148, 223 cognition, 18, 29–30, 214–215, 216, 217–218, 220, 224, 225, 226, 299, 301, 305, 358, 362, 367, 441, 443, 447, 484, 487 adequate, 214–215, 217, 218, 224 intuitive, 213, 214–215, 216, 217, 218 combination, 42, 47, 75, 77–78, 126, 170, 215, 237–238, 366–368 combinatory, 53, 75, 79, 80, 92–93, 126, 127, 132, 148, 237, 379–381, 466 common sense, 43, 157, 184 communication, 53, 63, 99, 192, 199, 283 adversarial, 53 communis opinio doctorum, 245 compatibilist, 475 comperception, 405, 406 complex number, 150 term, 222 compossible, 337 comprehensibility, 21, 392, 501 See also intelligibility computability, 40 compute, 361 concept, 21, 28, 51, 60, 79, 89, 109, 122, 147, 183, 188, 195–200, 218–223, 268–271, 295–296, 305–307, 479–480, 487 analysis of, 78, 174, 217 cluster of, 39 complete, 7, 21, 77, 122, 294, 295, 296, 298, 303, 471, 472, 473, 476 composed, 78, 217 distinct, 215, 216–217, 488 empirical, 298, 302, 306, 307 extension, 240 formation, 306, 307, 308 general, 294, 295, 306, 403, 496, 507, 508 innate, 157, 165 legal-logical, 242 meta-, 53 primitive, 41

Index simple, 216, 217, 299 singular, 294 conceptual cluster, 39 containment, see in-esse dependence, 10, 506, 508 domain, 200, 206, 208 integration network, 200, 210 concession, 9, 38, 44, 90, 107, 270, 271, 360, 361, 473 conciliation, 4, 37, 57, 59, 96, 501 See also reconciliation conclusive, 40, 62, 242, 308, 315, 474 concourse of creditors, 236 of safeties, 237 condition, 32, 79, 89, 176, 195, 204, 214, 232, 234, 243, 252–258, 259–260, 261, 270, 276, 437, 470, 507 conditional, 28, 46, 162, 237, 251–252, 256–258, 267, 268, 269–270, 272–273, 349 conditionality, 234, 252, 254, 255, 258, 262, 273, 276 conditioned, 234, 244, 253, 254, 255 conditionee, 253, 261, 276 conditioner, 253, 261, 262 conflict, 17, 38, 45, 85, 91, 177, 180, 242, 259, 298, 319, 357, 364, 389, 474 Confucius, 414, 415 conjecture, 54, 68, 92, 162, 176, 273, 300, 301, 369, 389 Conring, H., 160–162, 275 conscience, 220, 346 consciousness, 118, 331–332, 336, 337 consequentialist, 343, 359 consubstantiation, 405–406 contingency, 27, 184, 297, 475, 484 contingent, 21, 27–28, 60, 86, 87, 265–278, 298, 472, 482, 484 continuity, 8, 39, 45, 91, 113, 114, 118–119, 472 See also principle, of continuity continuum, 58, 86, 88, 91, 141, 202, 203, 318 contract, 45–46, 236–239, 243, 273, 374 of agency, 237–238 tacit, 45–46 contractualist, 231 contradiction, 4, 19, 40, 60, 74–76, 146, 220, 480, 481 See also principle, of contradiction contradictory, 37, 100, 135, 138, 184, 244, 499 noncontradictory, 39

515 contrary, 3, 9, 12, 44, 56, 57, 65, 69, 100, 103, 116, 117, 149–150, 194, 221, 253, 334, 470 controversialist, 397, 405 controversies judge of, 42, 49, 50, 51, 54, 55, 66, 393, 435 resolution of, 43 theological, 8, 49, 50, 66, 68, 390–393 controversy, 4, 8, 43, 49, 54, 101–102, 151, 216, 383–394, 397–407, 441 convention, 138, 374, 432, 434, 437 conventionalism, 498 conversation, 42, 340, 351, 352 convolute, 113, 114, 117, 118, 119, 121, 451 Cook, D., 420, 449, 457, 458 cooperation, 2–3, 8, 11, 38, 56, 57, 60, 69, 117, 200, 204, 209, 366 C¨oppel, J.L., 236, 245 Coras, 242, 244 cosmic, 5, 112, 115, 117, 119, 469 cosmogeny, 450 cosmology, 175, 206, 467 cosmos, 186, 190, 453 See also World, universal Coste, P., 335, 338–340, 485 Council Lateran, 441 of Trent, 44, 442 counterfactual, 474 creation, 9, 20, 26, 28, 56, 59, 61, 76, 125, 126, 127, 186, 188, 206, 282–283, 329, 337, 338, 350, 375–376, 387, 415–416, 417–418, 426, 447, 449, 450–451, 453–455, 456, 457, 458, 468, 474–475, 498, 501 continued, 475 ex nihilo, 415, 451 from nothing, 450 Platonic, 451 creationism, 419, 474 cr´edibilit´e, 444 credibility, 23 creditor, 231, 236 credo maximum, 397–407 credo minimum, 399, 400 criticism, 1, 30, 56, 171, 193, 325, 331, 424, 496, 505 Cudworth, M., 416 Curley, E.M., 504

516 curve transcendent, 91 transcendental, 149, 150, 179 Cyrus, 349 D Daniel, S.H., 155 Dante Alighieri, 414, 437 Dascal, M., 1, 3–4, 11–12, 17–18, 22–23, 26–33, 37–38, 42, 55, 63–64, 66–67, 69–70, 73, 121, 210–211, 265, 293, 308, 315, 319, 321, 324, 357, 368–369, 383, 392, 394, 398–400, 406, 435, 476 Dascal, V., 63 Dasen, G., 236, 245 Dear, P., 277 debate, 8, 37–40, 45, 65, 66, 160, 192, 215, 225, 322, 323, 325, 375, 428, 442, 454, 466 debater, 41, 325 de Carcavy, P., 87 decision, 2, 8, 20, 26, 27–28, 32–33, 37, 42, 43, 46–47, 50, 54, 60, 66, 109, 147, 149–150, 174–175, 177, 254, 257, 267, 268, 269, 270–271, 273, 274, 277, 284, 310, 315, 329, 348–350, 357, 358, 359–360, 361–363, 366, 367, 371–382, 378, 379–381, 407, 435, 474, 476, 481, 500 making, 8, 40, 268, 271, 310, 357 procedure, 42, 43, 47, 50, 381 decisions, calculus of, 37 declarative, 8, 147, 383–394 deduction, 5, 20, 40, 168, 174, 350, 378, 385–386, 472, 476, 483, 497 deductive, 5, 6, 29, 32, 46–47, 86, 90, 91, 93, 114, 116, 142–144, 151, 210, 232–233, 234, 268, 351 See also topics defendant, 46, 391 defensibility, 23 definiendum, 187, 220, 221, 234, 236, 240 definiens, 220, 221, 234, 236, 240 definition adequate, 221, 222 genetic, 497, 505, 506 nominal, 39, 216, 221, 234 precise, 40, 85, 199 real, 39, 75, 218, 221, 222, 225, 497, 505 de Gaudemar, M., 343, 346, 353 degenerationist, 418

Index deist, 400, 442 See also theistic de La Fontaine, J., 371 de la Hire, P., 143 de La Loub`ere, S., 96 de l’Hˆopital, G.F.A., 120, 135, 138, 141 deliberation, 6, 55–56, 59, 68, 70, 74, 174–177, 181, 269, 273, 293, 302, 309, 310, 357–358, 359, 360, 362–364, 366, 367–368, 374, 474–475 ethical, 302, 309 de Maupertuis, P-L. M., 420 de Mendonc¸a, M., 183 democracy, 302, 308, 373, 374, 375 de Molina, L., 340, 467, 473, 477 demonstrability, 23, 469 demonstrate, 5, 17, 18–19, 21, 23, 39, 44, 57, 92, 93, 102, 114, 116, 142, 143–145, 148, 161, 171, 174, 176, 191, 220, 225, 237, 268–269, 274, 276, 277, 279, 281, 283, 286, 335, 346, 362, 367, 372, 383, 387, 389, 391, 413, 415, 430, 443–444, 450, 452, 454, 456, 464, 465, 466, 469, 483, 497, 505, 508 demonstration, 6, 19, 31, 42, 46, 49–50, 53–54, 58, 60, 66, 70, 75, 94, 95, 97, 99, 100, 114, 143–144, 161–162, 172, 174, 176, 187, 189, 205, 206, 211, 215, 218, 221, 225, 234–235, 236, 239, 251, 258, 268–269, 275, 276, 277, 279–283, 285–286, 288, 289, 296, 311, 334, 346–347, 350, 371–394, 403, 445, 465–467, 480, 482–483, 487, 490, 497, 499, 503, 505 chain of, 42 circular, 46, 234, 235 mathematical, 46, 66, 251, 279 moral, 57, 280 Platonic, 286 political, 371 demonstrative force, 54 knowledge, 160, 161, 162, 496 metaphysics, 31 de Montaigne, M., 412 de Monticelli, R., 437 De Morgan, A., 135, 138 deontic, 235, 482, 488 de Oviedo, F., 477 dependence, 10, 23, 42, 258, 503–506, 508 de Reyger, A., 233, 245, 246

Index de Roberval, G.P., 369 Derrida, J., 315 des Billettes, G.F., 90 des Bosses, B., 226, 312, 337, 402, 406, 457 Descartes, R., 96, 223 method of analysis, 91, 93, 163, 269, 271, 272, 275, 322 notion of dialogue, 322–324 description, 155, 238, 239–240, 368, 436 determinism, 26, 27, 59, 467, 498 de Volder, B., 114, 117, 120 Dewey, J., 312 d’Huisseau, I., 400 dialectic, 3, 8, 12, 31, 37–71, 155, 156, 159, 203, 434, 442, 450 interaction, 52 meta-, 51 non-confrontational, 57 redundancy, 53 relevance, 53 two-pronged, 37–71 unity of, 38 varieties of, 40 dialectical, 11, 45, 52–54, 59, 64, 157, 159, 434, 450 analysis, 159 form, 52, 53, 62 dialogue, 209, 322, 323, 501 Di Bella, S., 10, 477, 495, 504 dichotomy, 191, 196, 215, 270, 303, 329, 507 differentiation, 127, 129, 130, 133, 150, 444 Diodorus, 27 diplomacy, 176, 177 Disalle, R., 106, 107 discovery, see art, of discovery discursivit´e, 62 discussion, 3, 12, 37, 59, 101, 158, 247, 364, 398, 441, 446, 457–458 disposition, 7, 10, 18, 46, 47, 115, 188, 347 disputant, 9, 42, 45, 64 dispute, 18, 19, 23, 25, 31, 39, 41, 42, 43, 44, 45, 46, 51, 52, 53, 57, 58, 67, 101, 177, 322, 383, 386, 390, 391–392, 398, 496 divine, 18, 21–22, 73–81, 90, 185–186, 285, 286–287, 358, 389–390, 444–445, 498–499 election, 337, 445 See also grace prescience, 471 providence, 100, 384, 387 rationality, 19, 73, 79–80

517 See also God division of labor, 2, 40, 53, 55–60 dogma, 50, 122, 384, 387, 389, 390, 399, 400, 401, 403, 404, 406 dogmatism, 89, 90, 94, 167, 346, 383, 386, 399, 400–401, 403 Dostoevskij, F.M., 424 Dreyfus, H., 142 duality, 129, 130, 318, 386 Dummett, M., 296, 297, 312 Durant, G., 245 dynamics, 5, 89, 106, 107, 108, 111, 119 E Earman, J., 101, 108 ecclesiastical, 444, 445, 446 eclecticism, 33, 56, 57 ecumenic, 9, 397, 441, 444, 446, 447 effect, 7, 12, 25, 88, 103, 104, 108, 114, 120–121, 187, 207, 253, 257–258, 268, 271, 273, 466, 471–472, 474 egocentric, 321 egoism, 318 Egypt, 22, 415 eidos, 498, 499, 502 Einstein, A., 101, 104, 105, 106, 108–109 elasticity, 111, 113, 114, 119 election, 8, 337, 371, 374, 375, 378, 380, 445 Elster, J., 362, 369 emanation, 20, 24, 272, 287, 320, 451, 474 emotion, 43, 367, 431 empathy, 8, 316, 317, 320, 325 empiricism, 22, 107, 116, 146, 167, 177, 178, 305 encyclopaedia, 27, 56, 63, 66, 69, 199, 200, 202–203, 205, 209, 210, 211 England, 175, 416 entelechy, 111, 114, 118, 119, 121, 124 enthusiasm, 10, 43, 44, 167, 174 enthymeme, 157, 158 Epicurus, 19, 281, 284, 288 epistemic, 111, 117, 252–258, 263, 296, 301, 302–303, 505 epistemology, 1, 5, 10, 29, 30, 55, 56, 60, 102–103, 178, 199–212, 296, 508 epsilontics, 144 equipollence, 105, 110, 114, 117, 472 equipotent, 114, 119, 122, 123 equity, 47, 318, 347 Erasmus, D., 393, 399 eristic, 43 esoteric, 23, 24, 25, 34, 414

518 essence, 25, 74, 113, 239, 240, 277, 295, 324, 388, 414, 451, 469, 473, 496, 497, 498, 501 ether, 87–89, 104 ethical, 8, 62, 302–303, 309–311, 317–320 ethics, 8, 55, 163, 164, 269, 280, 286, 309–310, 348, 483 ethnography, 411, 413, 419 Euclid, 4, 148, 149, 167, 171, 172, 173, 268, 275, 497 Eudoxus, 167 Evangelical, 406 See also Protestant Evathlus, 242, 243, 244 Everhardus, N., 239, 240, 241, 246 Everitt, N., 450 evidence, 54 evil, 9, 18, 55, 59, 302, 304, 312, 316, 336, 339, 340, 358, 364, 367, 397, 401–402, 413, 423, 424, 426, 427, 428, 432–433, 436, 437, 455, 485 commensurable, 428 incommensurable, 428, 432, 433 physical, 432 presentification of, 423, 433 exactness, 42 excommunication, 388, 398 exercise, 7, 56, 156, 338, 373 exhortation, 55 existence, 5, 10, 25, 26, 29, 30, 37, 49, 75, 101, 103, 107–108, 186, 244, 329 exoteric, 21, 23, 24, 214, 215 experience formal, 5, 11, 167, 177–181 inner, 334, 487 sense, 92, 172, 479, 482 explanation, 5, 25, 86, 128, 183–197, 337, 429, 508 exponential, 125, 134 expounder, 43 expression, 9, 40, 42, 43, 54, 63, 113–115, 373, 403, 434, 471, 502–503 F factual, 269, 446, 468, 472, 474 Fage, R., 413 faith, 9, 43, 50, 58, 332–333, 339, 351, 384–385, 431–432 feeling, 6, 7, 8, 151, 186, 190, 302, 329–340, 346, 430 Felden, J., 162 Fichte, J.G, 426 fides, see faith

Index figurism, 414, 420 finitary, 173 flexibility, 45, 46, 47, 199, 203, 208, 345, 501 form, 26, 41, 52–53, 61–62, 130, 134, 167–181, 261, 298, 322, 433, 437, 502–503 arbitrariness and impertinence of, 181 correct, 61 of disputing, 62 force of, 61, 62 formal, 5, 22, 52, 74, 79, 115, 143, 144, 157, 167–170, 177–181, 209, 469 formalism, 5, 46, 53, 126, 170, 177, 238–239 formality, 45, 167, 177, 386 formalization, 4, 5, 40, 42, 61, 169, 176, 351 formula, 41, 61, 133–134, 150, 307, 335, 398, 447 Foucault, M., 62 Frankel, L., 464 free action, 27, 30, 132, 329, 468 will, 7, 26, 116, 273, 335, 336, 349, 445, 467, 473 freedom, 10, 18, 21, 26, 29–31, 47, 58, 100, 102, 184, 297, 299, 303, 308, 310, 311, 329, 331, 335–337, 338, 387, 390, 467, 475, 477, 484 of indifference, 338, 467 Friedman, G., 424 Friedman, M., 108 Fritz, G., 67 fulguration, 451, 475 G Gaius, 237 Gale, G., 369 Galganetto, L., 245 Galilean, 107, 108 Galileo, 105, 109, 123, 369 Gallois, J., 94, 96 Gammarus, P.A., 239, 240, 246 Garber, D., 81, 369 Garver, E., 181 Genesis, 130, 132, 160, 329–340, 451 geometer, 42, 92, 133, 135, 172, 267, 280 geometric, 114–115, 131, 145, 148, 267, 269, 277, 283, 331, 497, 503, 505–506 G´erard, V., 223 Gerhard, J., 442, 446 German, 53, 67, 420, 442 Gleissemberg, M., 236, 245

Index Gnosticism, 113, 387 Goddu, A., 377 God City of, 285, 343, 347, 351, 352, 353 See also divine Goldenbaum, U., 63, 95, 458 golden rule, 348, 399–400, 404 Goldstine, H.H., 369 grace, 186, 282, 331, 338, 363, 445 election by, 445 Gracia, J.E., 65 grammatica rationis, 34 Grandi, 135, 138 Granger, G.G., 132, 138 Greece, 69, 144, 414, 426, 430, 457 Gregory, J., 150, 369 Griard, J., 8, 371, 373 Grosholz, E.R., 5, 169, 170, 173, 180, 326 Grotius, H., 318, 326, 373, 382, 399, 400 H habit, 185, 317, 334, 336, 346, 358, 363, 400 Hansch, M.G., 281, 288 happiness, 202, 317–319, 336, 377 hard cases, see case rationality, see rationality hard-soft distinction, 37 harmonization, 87, 90, 95, 445 harmony, 4–5, 9, 21, 25, 28, 33, 57, 113, 114, 115, 116, 117, 133, 188–189, 190–191, 193, 194–195, 196, 197, 286–287, 312, 320, 337, 344, 346, 376, 390, 424, 444, 445, 469, 489, 499 of minds, 116 of things, 116, 499 heathen, 413, 444 Heath, T.L., 275 Hegel, G.W.F., 434, 435 Heidegger, M., 308, 315, 425, 495, 499 Hellenic, 113 See also Greece Herbert of Cherbury, E., 400 heresy, 8, 383, 384, 386–389 formal, 387 material, 387 heretic, 49, 372–373, 386, 387, 388, 417 half-, 386 hermeneutics, 31, 50, 58, 274, 426 scriptural, 50 hermetic, 5, 111–124 enlightened, 117

519 See also analogy heuristic, 40, 150, 315, 316, 319, 357, 363, 364, 366, 386, 401 Heyting, A., 312 hierarchy, 5, 173, 200, 203, 209, 214, 217, 218, 232, 241, 242, 244, 294, 300, 347 hieroglyph, 415 Hilliger, O., 245 Hintikka, J., 181, 275 Hobbes, Th., 10, 27, 263, 281, 284, 286, 288, 318, 326, 411, 456, 466, 467, 468, 471, 473, 497, 498–499 holistic, 116, 123, 469 Holmes, O.W., 180, 181 Holy Ghost, 388 homo patiens, 428 Hostler, J., 318, 325, 326 Huet, D., 393 Huggett, N., 104, 105 human, 1, 3–4, 8, 19, 21, 22, 26, 28, 29, 41–42, 52, 55, 59, 60, 62, 63, 73–81, 89–90, 93, 99, 116, 117, 118, 151, 155, 156–159, 161, 162, 164, 165, 167, 175–177, 178, 180, 183, 185, 186, 189, 206, 209, 210, 220, 267, 281, 283–284, 285, 297–298, 299, 301, 302, 304–305, 311, 315, 318, 320, 321, 324, 329, 331–333, 339, 340, 343, 344–345, 346, 349–350, 357, 358, 363, 366, 367, 385, 387, 390, 397, 411, 412, 417–419, 424, 428, 431, 437, 442, 444, 457, 475, 480, 481–482, 484, 486, 498, 499 origins, 411, 417, 419 Hume, D., 5, 122, 167–181, 284, 419 Husserl, E., 213, 306, 315, 425, 436 Huygens, C., 85, 86, 95, 105, 112, 114, 120, 121, 134, 135, 138, 146, 176 hypothesis, 28, 33, 40, 87, 89, 112, 123, 189, 191–193, 194–196, 214–218 hypothetical, 28, 161, 244, 252, 262 I I Ching, 415 icon, 170, 172, 173 idea, 1, 4, 23, 25, 28, 33, 39, 40, 41, 43, 65, 66, 79, 90, 92, 115, 126, 132, 141, 150, 164, 168, 169, 170, 179, 180, 213, 214–216, 218–219, 222, 323, 368, 470, 479–492 identity, 10, 25, 39, 101, 122, 130, 209, 220–223, 350, 426, 471

520 idolatry, 414 imaginary number, 150 imagination, 87, 91–92, 97, 101, 113, 126, 172, 179, 205, 207, 293, 305–311 anchored, 305, 306 productive, 305 reproductive, 305 unanchored, 306–308, 309 immanent, 6, 190, 191, 245, 329, 347, 470, 475 immediacy, 92, 219, 222, 223, 427–428 impanation, 405, 406 imprecision, 40 impression, 7, 179, 300, 305, 335, 338, 479, 483, 488, 489 improvement, 33, 56, 167, 168, 177, 203, 348, 349, 351 incalculable, 348, 350 incarnation, 332, 390, 413, 437 inclination, 7, 26–27, 156, 304, 335–336, 344, 357–358, 362, 363, 472–476, 485, 491 incliner sans necessiter, 21, 26 incline without necessitating, 40, 62, 474 incomplex, 222, 226 incompossible, 474, 475 incomprehensibility, 21, 392, 394, 501 inconsistency, 40, 45, 102, 103, 105 inconsistent, 77, 100, 138, 222, 283, 472, 475 incorporeal, 164, 411 indemonstrable, 121, 220, 334, 487 indicantia et contraindicantia, 31 individual, 1, 7, 10, 19–20, 21, 25, 26, 28, 29–30, 34, 45, 56, 77, 111, 122, 141, 144, 148, 150, 151, 167, 184, 207, 215, 233, 236, 238–242, 243–245, 294–297, 298, 299, 302, 303–304, 305, 306, 308, 311, 312, 323, 338, 348, 349, 351, 353, 361, 398, 412, 418, 423, 424, 425, 428–429, 437, 438, 446, 454, 470, 471–472, 481, 482, 504, 506, 508 identity, 10, 472 individualization, 430 individuation, 20, 44, 65, 430–431, 438 induction, 20, 58, 70, 90, 91, 96, 157–158, 162, 171, 172, 277 See also topics inductive, 90, 91, 162, 165, 231, 240 See also topics ineffable, 431, 437–438 inertia, 104, 105, 106, 107, 108, 109, 111, 113, 114, 119, 120, 121, 169, 178 in-esse, 110, 121–123, 124

Index inference, 6, 52–53, 167, 168–169, 170, 177, 233, 267, 268, 273, 350, 380, 472, 507–508 oblique, 61 infinite, 20, 21, 28, 29, 62, 87, 91, 107, 111–112, 114, 117, 126, 136, 137, 151, 173, 294, 297, 299, 304, 319, 339, 503 infinitesimal, 89, 91, 96, 113, 114, 135, 143–145, 150, 349 influxus, 28, 496 in forma, 17–18, 19, 52, 64, 67 modus disputandi, 64 ingenium, 145 See also insight injective, 378 innate concept, 157, 165 idea, 479–492 instinct, 485, 489 principle, 345, 483, 484 truth, 483, 487 innate ideas, kinds of concepts, 482 moral principles, 482–483 notiones communes, 482 principles of arithmetic, 482 principles of geometry, 482 principles of logic, 482 innateness, 22, 479, 482, 485, 486 inquisition, 24, 388 insight, 26, 28, 29, 30, 142, 156, 165, 305, 319, 420, 482 instinct, 10, 343, 346, 480, 483, 484–488, 489 intellect, 91, 97, 161, 216, 217, 296, 316, 334, 350, 387, 394, 475, 486, 499 intellectual, 6, 19, 20, 23, 116, 147, 297, 301, 316, 319, 320, 323, 336, 398, 420, 458 intelligence, 156, 196, 346, 423, 432 intelligibility, 4, 66, 73–81, 111, 116, 123, 169, 183, 186, 188–189, 195, 276, 277, 278, 329, 330, 331, 337, 344, 349, 403, 435–436, 470, 495, 496–497, 498–499, 505 moral, 330 natural, 330 intelligible, 73, 74, 75, 76, 79, 80, 87, 91–92, 117, 171, 179, 192, 216 interpretation, 2–6, 11, 24, 26, 27, 29, 40, 45, 47, 50, 56, 63, 66, 93, 94,

Index 105–106, 108, 126, 129, 130, 132, 161, 220, 232, 244, 246, 253, 256, 260, 266, 269, 270, 271, 275, 277, 278, 334, 348, 369, 380, 383, 401, 402, 404, 405, 406, 415, 423, 436, 441, 443, 447, 454, 456, 472, 500, 504–505, 506 figurative, 50 pragmatic, 40 Intorcetta, P., 415 intuition, 5, 116, 145, 169, 213–227 invention, 121, 128, 157, 163, 280–281 See also art, d’inventer irenic, 9, 23, 49, 388, 400 irony, 12, 122, 415 irrational, 40, 126, 145, 146, 149, 384, 387 Islam, 417, 456 J Jammer, M., 109 Jansenius C.O., 402 Jaquelot, I., 193, 281 Jesuit, 8, 201, 332, 388, 399, 402, 405–406, 411, 414–415, 419–420, 458 Job, 31, 65, 143 Jolley, N., 123, 449, 450 Judaism, 417, 444, 456 judge of controversies, 42, 50, 54–55, 393 disinterested, 56, 400 judgement, 196, 222, 232, 334–337, 340, 358, 363, 369, 401, 425, 508 Jungius, J., 165 juridical condition, 251–252, 253–256, 257–258, 259–262, 263–266, 268, 276 logic, 6, 61, 252, 262, 267, 270, 274 jurisprudence, 6, 31, 46, 58, 155, 161, 162–164, 267, 268, 271, 273, 274, 279–281, 284–287, 288, 315, 345, 385, 389, 398, 399, 450 juris, 5–6, 12, 45, 47, 54, 60, 61, 70, 176, 267, 268, 270–271, 273, 369 jusnaturalist, 242 jus naturae, 484 naturale, 484 justice, 6, 18, 62–63, 163–164, 166, 176, 180, 279–288, 289, 309, 317–320, 321, 324, 326, 362, 380, 385, 399, 400, 426, 433, 480, 481, 488, 490, 491, 492

521 justification, 4, 173, 193, 237, 244, 296, 300, 302, 303, 321–322, 373–375, 389, 427, 466, 473–474 justitia universalis, 484, 488–489 K Kant, E., 284, 293, 294–301, 302–303, 304, 305, 306, 307–308, 309–311, 312, 335, 346, 348, 427 Kaplan, B., 435 Kauppi, R., 311 Kemp, C., 178–180 Kepler, J., 120 Kestner, H.E., 285 Kierkegaard, S., 311 Kircher, A., 415 Kline, M., 369 knowledge classification, 199–200, 208 confused, 334, 357–358, 436, 484, 487–488 declarative, 147, 383, 385–386 demonstrative, 160, 161–162, 496 distinct, 296, 479, 484, 488 divine, 220 of God, 320, 324, 332, 411, 413 management, 200, 205–206 organization, 202, 205, 209 a priori, 411 procedural, 383 revealed, 161 sociology of, 443 tacit, 142, 146–147, 149, 151 Knuuttila, S., 362 Koch´anski, A.A., 96 Koistinen, O., 368 Koyr´e, A., 100 Kulstad, M., 479 L labyrinth, 91–93, 97, 200, 336, 340, 398 Lactantius, 426 Lady Masham, 91, 191 Laerke, A., 406 Laerke, M., 9, 397, 404, 406 Lagr´ee, J., 400 Lamarra, A., 484–486 Lambert, P., 232–233, 245, 247 La Mothe le Vayer, F., 332 language, 5, 9, 11, 33–34, 42, 62, 79–80, 114, 121, 122, 133, 138, 155–156, 160, 165, 170, 171–173, 196, 199–200, 204, 207, 208, 210, 216, 316, 343, 351–352, 390, 418, 432, 433, 435–436, 496–497, 501, 507, 509

522 formal, 171, 199, 207 natural, 5, 11, 33–34, 133, 170, 172–173, 204, 207 See also lingua La Peyr`ere, I., 417–419, 420 Laplace, P-S., 100 Lariche, R., 428 latitude, 259–260, 261, 266, 365 law conditional, 233–234, 237, 242, 244, 247 of continuity, 39, 91, 112, 118–119, 136, 207, 318, 472 external, 243 of homogeneity, 133 inertia of, 106–107, 109, 119–120 Justinian, 231 moral, 10, 309, 344–345, 480, 481 of motion, 85, 87, 95, 106–107, 109, 331, 339 of nature, 85, 86, 89, 94, 116, 151, 186–187, 191, 333, 383–384, 389 philosophy of, 177–178 positive, 6, 47, 51, 66, 233, 235, 237, 271, 284 of preservation, 191 Roman, 46, 69, 232, 235–236, 245, 257, 280, 284–285 Romano-Saxonic, 241 Saxon, 231 substantive, 233, 235–245 legal axiom, 231–235 humanism, 231 rationalism, 6, 12, 231–235, 238, 242, 244–245, 246 reasoning, 6, 239–240, 270 substitution, 236 See also rationality legitimacy, 4, 50, 129, 131, 132, 138, 144, 148–150, 195, 216, 240, 244, 270, 273, 299–301, 331, 426, 452–453 Leibniz criticism of Descartes, 11, 89, 90, 91, 94, 97, 172, 316, 323 formula, 53, 113, 133–134, 163, 347, 481 and the other, 315–324 Levi, E., 181 liberty, 17, 26, 59, 375 See also freedom limits, 87, 89–90, 91, 116, 150, 156, 163, 206, 208, 235–236, 267, 279, 348–350, 351, 367, 368, 375, 398, 411, 427, 428, 466

Index lingua mentis, 34 philosophica, 34 loci, see argumentative Locke, J., 5, 22, 25, 69–70, 119, 167–170, 171–172, 174–177, 219–220, 225, 279, 281–283, 345, 411, 418–419, 479, 480–481, 482, 483, 488 logic of choice, 475 composite, 46 formal, 51–52, 67, 168, 274, 428 juridical, 6, 61, 252, 262, 267, 270, 274 new, 6, 31, 61–62 non-monotonic, 40 standard, 40, 42, 46, 59 true, 27, 54, 164 vulgar, 59 logical concept, 164, 242, 345, 507 conditional, 252, 256, 271–274, 276, 428, 468 meta-, 464 syntax, 497–498 logicism, 213, 464 logodicea, 427 logos, 413–414, 416, 427–430, 433, 436 love, 8, 26–27, 46, 99, 143, 284–288, 317–320, 324, 325, 326, 338, 339, 348, 349–350, 351, 399, 400, 401, 402–404, 437, 445, 485, 488–489 enlightened, 403–404 Lutheran, 9, 44, 397, 406, 441–442, 446 See also Protestant Luther, M., 386, 393–394, 397, 441, 444–446 lying, 4–6, 40, 55–56, 59–60, 107–108, 159, 176, 186, 188–189, 193, 210, 221–222, 271, 287, 310, 312, 318, 323, 333, 335–336, 348, 349, 390, 425, 433, 442, 470, 488, 501 M Mach, E., 101, 104–106, 108–109 Machiavelli, N., 177 McRae, R., 483, 484 machine, 100, 109, 118, 145, 185, 298, 352, 368, 398, 414, 455 Mahnke, D., 131, 213 Mahometan, see Islam Maier, A., 476, 477 Maimonides, 454 Malebranche, N., 28, 70, 94, 192, 193, 211, 214, 215–216, 217, 224, 225, 502

Index Malpighi, M., 89 mandate, 46, 237 Manichaeism, 387 Marco Polo, 414 Marion, J-L., 322, 498–499 Marquard, O., 426 Marras, C., 5, 166, 199, 210, 476 Marsilius of Inghen, 477 martyrdom, 388 Masullo, A., 431, 438 materialism, 88, 112 Mates, B., 509 mathematical equation, 5, 115, 116, 119–121 mathematics, 1, 4–6, 8, 11, 18, 22, 28, 40, 45, 51–52, 55, 57–58, 63, 69, 80, 86, 89, 92, 93, 96, 97, 111, 113, 123, 125, 128, 130, 134, 138, 142–145, 146–147, 148–149, 150–151, 167, 168, 170, 172–174, 175, 177–181, 279–280, 282, 286, 288, 301, 309, 317, 330, 339, 363, 369, 372, 376, 378–379, 381, 384, 497 as an art, 178 application of, 86, 372 See also geometer matter, 5, 7, 19, 24, 30, 31, 42, 44, 46, 52, 56, 58–59, 61, 68, 69, 70, 88, 100, 102, 103–104, 105–106, 108, 111–112, 114, 119, 122, 123, 124, 130, 135, 144, 155, 158, 161–162, 164, 168–169, 170, 171, 174–176, 178, 181, 183, 185, 187, 192–193, 194, 195, 209, 215, 217, 219, 233, 239, 242, 244, 267, 269, 270, 276, 286, 296, 298, 300, 304–305, 316, 332–333, 335, 338, 349, 350, 364, 372, 388, 389, 397, 402, 413, 442–443, 446, 451, 495, 496–497, 501 eternal, 451 See also materialism maxim, 6, 21, 31, 33, 168–170, 174, 220–221, 279, 281, 283–285, 302, 304, 308, 309, 334, 339, 347, 348, 352, 455 Mayno, 241 meaning definite, 39 disjunctive, 50, 403, 407, 435 literal, 50 See also common sense mechanicism, 195, 470

523 mechanism, 6, 11, 54, 87–90, 100, 112, 115, 116, 117, 118, 121, 125, 135, 185, 232, 236, 239, 240, 242, 243, 245, 247, 330, 337, 340, 432, 466 mediacy, 427–428 Melanchthon, P., 446 Melchiorre, V., 435–436 Mercer, C., 81, 457, 469 Merleau-Ponty, M., 425, 434 Mersenne, M., 498 metamorphosis, 126, 133 metaphor, 5, 17, 23, 24–25, 27, 28, 31, 47, 66, 86, 90, 115, 121–123, 199, 200–201, 204, 206, 207, 208–210, 357, 360–361, 369, 398, 476, 496 metaphysics, 1, 5, 9, 10, 11, 18, 22, 23, 24–25, 28, 29–31, 34, 42, 45, 55, 58, 73–74, 86–92, 118, 121, 142, 143, 148, 163, 192–193, 195, 199, 279–280, 286–287, 293, 297–298, 300–301, 302, 333, 362, 385, 418, 441–442, 444, 449, 452, 453, 458, 465, 470–471, 473–474, 481, 487, 498, 504–505, 506, 508 method, 4, 18, 19, 41–44, 57–58, 114, 137, 162–164, 268–278, 322, 357, 365, 373–375, 444, 446 comparative, 164–165 of Establishments, 57 Methodenstreit, 425 Mexican, 417 middle term, 167–168, 170, 347 mind, 3, 7, 11, 17, 18, 21, 25, 27, 29, 33, 38, 44, 45, 52, 62, 65, 66, 74, 76–78, 79–80, 90, 114, 115–116, 121–122, 142, 155, 156–158, 162–165, 169, 172, 174, 178–181, 183, 216, 217, 219, 222, 256, 281–285, 287, 297, 298, 301, 305, 306, 318, 320, 321–322, 324, 330, 335–337, 338, 339, 340, 344, 345–347, 348, 350, 351, 357, 358, 361, 362, 363, 367, 376, 383, 385, 411, 442, 451, 455, 458, 467, 469, 471, 472, 477, 479, 483, 486, 498, 501, 502, 504 eternal, 287 philosophy of, 45, 305, 351, 357, 362 miracle, 5, 99, 106, 184, 186, 188, 191, 192, 194, 196, 282, 384, 416, 434, 449, 450, 451, 453–456, 458 miraculous, 183, 185–186, 191, 192, 193, 194, 453, 454, 456

524 mirror living, 115, 121–123 missionary, 8, 414, 415, 419–420 modal, 32, 120, 183–184, 329, 473, 479, 481, 490, 503 modality, 8, 27–28, 32, 54, 57, 128, 202, 235, 243, 253–256, 257, 333, 344, 488 moderation, 42–43, 64, 398, 402, 405, 446 moderator, 43, 52, 53 See also expounder modularity, 206–208 modus operandi, 60 Modus Ponens, 53 Mohammedan, see Islam Molanus, G.W., 96 monad, 2, 20, 21, 24–25, 34, 56, 111–112, 114, 115, 123, 293, 295, 297, 298, 299, 300, 303, 304, 312, 363, 376, 414, 418, 456 monogeneticism, 418, 419 monological, 321–324 moral causality, 335 certainty, 24, 57–58 conditional, 267, 270, 271–272, 274, 276, 277 consciousness, 336 deliberation, 293, 310, 359, 360 demonstration, 280 improvement, 343, 351–352 instinct, 10, 486, 489 law, 10, 309, 344–345, 480, 481 necessity, 58, 330, 337, 338, 480–481, 484–485, 488 principle, 248, 333–334, 419, 479–489 science, 483, 484 subject, 117, 329, 334, 336 morality conditional, 270, 271–272, 274 philosophical, 331–334 rationalist, 329 moralization, 8, 344, 345–347, 348 more geometrico, 22, 288, 334, 445 Morell, A., 326, 333, 334 More, Th., 416 Moretto, G., 426 Moses, 386, 394, 401, 413–414, 417, 423, 458 mos italicus, 231, 233 motion, 339, 340, 358, 463, 497, 502, 505 motivation, 62, 311, 329, 335, 337, 343, 348, 350, 351, 473 motive, 1, 7, 100, 302, 304, 308, 312, 317, 322, 329, 335–337, 340, 363, 388, 468

Index Mulvaney, R., 288 mystery, 42, 123, 184, 282, 332, 391–392, 431, 445, 449, 453, 456 Eucharist, 389, 455 of faith, 9, 23, 50, 394, 423, 431–432, 433, 435 Trinity, 389 mystic, 106, 401, 403, 420, 456 N Naaman, N., 8, 315, 319, 321, 323, 326 Nachtomy, O., 3–4, 73, 75, 81 Napoleon, 100 Natoli, S., 429 natural abilities, 343, 345–347, 352 appetite, 335 dialectics, 156 explanation, 5, 183–197 immortality, 281–282, 289 inclination, 27, 31, 156, 329, 351, 486 language, 5, 11, 33–34, 133, 170, 172–173, 204, 207 law, 6, 47, 51, 248, 279–289, 333, 389–390 light, 332, 351, 383, 427, 483, 484, 487 machine, 100, 185 normativity, 345 philosophy, 103, 272, 274, 416, 454, 463, 468, 475 priority, 470, 477 reason, 47, 66, 191, 271, 281, 331, 333, 338, 339, 441, 443 science, 1, 4, 11, 19, 34, 83, 89–90, 151, 443, 445–446 selection, 125, 132–134 understanding, 441 See also praeternatural, supernatural naturalism, 346, 386 nature, 5, 9, 37, 45, 49, 55, 58, 65, 69, 78, 80, 81, 86–87, 97, 109, 112, 123, 124, 130, 156, 163, 166, 184, 188–189, 194–195, 263, 276, 277–278, 289, 329–331, 337, 390, 397, 416, 418, 424, 508 machines of, 118 material, 101, 187, 337 order of, 86, 163, 186, 188, 507–508 necessary See also truth necessitarianism, 10, 121, 329, 465, 473, 475 necessitation, 472–475 necessity conditioned, 10, 255, 480

Index geometrico-metaphysical, 330 happy, 325, 329, 404, 412, 485, 488 hypothetical, 27, 481, 488, 489 logical, 158, 237, 272, 330, 389, 473, 484, 496, 504 metaphysical, 57–58, 114, 330, 480 moral, 58, 280, 330, 337, 338, 480–481, 484–485, 488–489 nomological, 504 physico-moral, 330 Nef, F., 383 negotiation, 27, 40, 62, 65, 315, 317, 361 neo-Platonic, 450 See also Plotinian Nestorian, 414 neutral, 40, 43–44, 121, 336, 361, 480 Newman, J-H., 394 Newton, I., 5, 99–100, 101, 103–105, 106–107, 108–109, 112, 121, 125, 130, 131, 134, 135, 143, 150 Newtonian, 4–5, 99–101, 107–108, 117, 119, 134, 454 Nicene creed, 418 Nizolius, M., 23, 70, 155, 164–165, 166, 496, 498, 501, 509 nominalism, 5, 45, 169, 223, 242, 244–245 norm, 46–47, 51, 66, 68, 243, 270, 271, 274, 347 normativity, 272, 345 notation, 4, 40, 80, 125–126, 127, 131, 173, 199, 457 nothingness, 450 notio completa, 28, 121 notion primitive, 78, 216–217, 218, 224 number, 29, 37, 41, 54, 60, 63, 74, 75, 76, 78, 79, 81, 86, 88, 92, 115, 125, 134, 138, 144–145, 147, 149–150, 151, 166, 169, 172–173, 174, 179, 185, 194, 205, 217, 220–222, 225, 231, 233–234, 236–238, 239, 244, 247, 259, 281, 287, 340, 360, 363, 366, 373, 399, 415, 441–442, 457, 466, 481, 484, 497 numerical, 11, 53, 63, 136, 158 Nussbaum, M., 343, 346, 352 O obligation, 45, 100, 237, 239, 267, 270, 272–273, 274, 312, 380, 384, 393, 400, 402–404, 480, 482, 485–486, 488–489, 492 oblique, see inference

525 occasionalism, 28, 186, 187, 188, 189–191, 193, 194, 196, 502 Ockham, W., 466–467, 469, 476, 477 Oecolampadius, J., 441 of Reyger, see de Reyger Oldenburg, H., 85–86, 94, 95 Ong, W.J., 157, 166 ontic, 235 ontology, 59, 111–112, 113, 115, 117, 118, 122, 135, 155, 189, 209, 214, 297, 299, 301, 302, 303, 431, 434, 451, 496, 498, 500, 503, 505, 507, 508 onus probandi, 45, 65, 454 See also proof charge of operation, 7, 8, 41, 63, 77, 78, 127, 129, 130, 150, 171, 188, 196, 215, 220, 237, 240, 321, 329, 337, 364, 423, 425, 432, 456, 466 opponent, 8, 45, 65, 102, 122, 144, 317, 323–324, 357, 391–392, 441 optimization, 362 optimum, 116, 124, 339, 351, 359, 362–363, 366–367, 369 organic, 111, 112–113, 115, 123 organism, 113, 118 organon, 41, 63, 202, 203, 420 Origen, 413 Orio de Miguel, B., 111 Orphic, 414 other place of the, 8, 315–326, 346–347, 348, 353 otherness, 38, 315, 320, 324 overdimension, 5, 119–121, 122 P Paganism, 9, 331–332, 339–340, 387, 394, 411–458 pain, 219, 281, 283, 325, 390, 424, 428–429, 430–434, 502 Papinian, 235 Pappus, 268–269, 275 paradox, 38, 45, 125, 135–136, 349 parallelism, 92, 97, 324, 503–505 Parmentier, M., 369 Pascal, B., 146, 176, 386, 393–394 passion, 7, 54, 319, 331, 358, 364, 427, 485, 486, 491 pathicity, 430–431, 437, 438 Paul, 245, 288, 345, 406, 444 Pauline, 8, 284, 399, 400, 405 Pellisson-Fontanier, P., 8, 387–388, 394, 403, 404 perception, 7, 25, 77, 111, 115, 169, 173, 178, 216, 220, 222, 224, 241, 300–301,

526 305, 306, 307–309, 312, 326, 334–335, 337, 344, 352, 363, 418, 419, 434–435, 443, 487, 491, 492 perfectible, 18, 338, 343 perfection, 22, 29, 77, 114, 115, 118, 119, 146, 184, 187, 284, 286–287, 289, 315, 317, 320, 325, 326, 332, 338, 339, 343, 344, 347, 348, 352, 359, 361, 363, 366, 369, 403, 433, 445, 451, 481, 485, 489, 490 perfectionism, 8, 245, 286–287, 343, 347, 349, 352 Perkins, F., 412, 420 peroration, 52 perplex, 169, 243, 268, 271, 277, 278 See also case Persian, 69, 412 person, 45, 50, 52, 68, 177, 232, 237, 246, 251, 252–253, 254, 255, 256, 257, 260–261, 270, 273, 296, 316, 326, 348, 351, 366, 374, 377–378, 379, 397, 406–407, 412, 429, 430, 437, 482 perspicuity, 159, 161, 165 petitio principii, 102, 108, 117–118, 121 Phemister, P., 451, 456 phenomenalism, 85, 86–87, 111–112, 113, 116, 121, 122, 123, 177–178, 298, 299, 312, 338 Phenomenology, 7, 9, 195, 293, 300, 307, 308, 309–310, 423, 430, 434–435, 436 phenomenon, 11, 17, 34, 45–46, 53, 63, 70, 85, 86–90, 105, 111–112, 114–115, 116, 124, 186–187, 189, 192–193, 194, 195, 196, 299, 312, 331, 344, 351, 443, 474, 488 Phillibert, 245 philosophy aims of, 89 physics, 5, 11, 17, 34, 45, 86–89, 92, 95, 96–97, 99, 101, 107–108, 111–112, 113, 114, 123, 130, 147, 149, 192–193, 194–195, 303, 310, 330, 339, 362, 432, 445, 452, 469 abstract, 474 concrete, 474 Pichler, A., 388, 443, 447 Picon, M., 5, 213, 223, 225 piety, 285, 326, 339, 340, 399, 403, 443 Piro, F., 10, 81, 463, 466 Piron, E., 404 plaintiff, 46

Index Plato, 19, 156, 280, 283–285, 287, 288, 345, 346, 414, 450, 457, 458, 479, 482 Platonic, 213, 280, 281–283, 284, 286–288, 289, 319, 414, 451, 498, 499 Plotinian, 25, 118 plurality, 2, 5, 10, 33–34, 76, 93, 111, 113, 188, 190, 203, 206–208, 209, 337, 402, 404, 417, 476, 495–509 pluri-multidimensional, 200, 208 Poincar´e, H., 172, 173–174 Poland, 8, 371, 372, 373–375, 376–381 Polanyi, M., 142, 149 polemic, 10, 12, 171–172, 321–324, 424 political, 2, 9, 23, 44, 56, 112, 161, 163, 176, 287, 333, 348, 360, 361, 367, 372, 373, 378, 379, 381, 411, 458 politics Church, 55, 66 polygeneticism, 419 Poma, A., 426, 434 Pope, A., 427 Popkin, R.H., 417, 419, 420 Poser, H., 10, 420, 479, 482 possibilia, 25, 29, 224, 225, 274, 473–475, 482 possibilities, 25, 27, 49, 74–75, 76–79, 80, 89, 125, 126, 127, 173, 190, 196, 218, 223, 237–238, 245, 306, 308, 335, 350, 365, 404, 425, 426, 441, 451, 474, 479 See also possibilia possibility, 8, 21, 25, 27–28, 42, 49, 57, 62, 74, 75–76, 78–79, 193, 207, 220–223, 435, 488 possible worlds, 21, 25, 26, 29–30, 32–33, 60, 76, 77, 121, 207, 284, 330, 339, 349, 350, 351, 358, 362, 363, 369, 427, 455, 474, 476, 480–481, 485 Post-Glossators, 231–232, 236 postulate, 21, 25, 29, 79, 107, 143, 172, 268, 391, 507 Posy, C.J., 7, 293, 312 practice, 4, 8, 23, 47, 50–51, 55, 59, 62, 65, 80, 89, 93, 125–138, 175, 178, 204, 206, 268–269, 271, 273, 305, 307, 309, 321, 323, 330, 333, 340, 345, 348, 384, 386, 401, 403, 419, 425, 430, 444, 447, 455, 497 praeternatural, 184–185, 296 pragmatic decision, 142, 148–150 organization, 53 rationality, see rationality role, see syllogism

Index pragmatics, 351 pragmatism, 480 pre-Adamism, 416–418, 420 precision, 56, 57, 59, 288, 391 See also imprecision predestination, 390, 445–446 pre-established harmony, 5, 28, 190–191, 193, 194–196, 312, 344, 455 prejudgment, 59 prescription, 241, 378, 405 presumption, 22, 29, 32, 40, 45, 47, 50–51, 54, 58, 59, 61, 66, 68, 161, 176, 360–361, 369, 384–385, 389, 398, 405, 417, 477 presumptuousness, 332, 340 principle of the best, 21, 26, 28–29, 76, 330, 464, 475, 480, 481, 485–486, 488–489 of calculability, 57 of causality, 464–465 of conciliation, 57 of continuity, 39, 112, 118–119, 135–136, 207, 318 of contradiction, 4, 40, 60, 74–76, 81, 146, 220, 480 in-esse, 121–122 of extremality, 337 of grounds, 464 of harmony, 115, 116 of the identity of indiscernibles, 102, 311 of indiscernability of identicals, 20 of individuation, 20, 44, 65, 431, 471 of infallibility, 28, 386, 481 innate, 345, 483, 484 mechanical, 88, 187, 207 moral, 333–334, 348, 419, 479–492 new metaphysical, 121 other’s place, 315, 317, 324, 325 overdimensional, 5, 119–120, 122 plausibility of, 21 of plenitude, 466 of reason, 22, 74, 162, 164, 192, 194, 464, 489, 495, 499–500, 501, 509 of reasoning, 164 of reasons, 192, 194, 293, 319, 381, 464, 495, 499–500, 501, 509 of reduction, 34 reversibility of, 116–117 of substitution, 234, 240, 242 of sufficient reason, 4, 10, 28–31, 60, 74, 101, 102–103, 146, 192, 452, 463–476, 488

527 of truth, 60 of uniformity, 118 universal scientific, 115 of variety, 315 principles innate, 345, 483, 484 of jurisprudence, 162 moral, 333–334, 348, 419, 479–485, 487, 488–489 of motion, 85, 87, 95, 107, 339 multiplicity of, 188, 384 reversibility of, 116–117 priority, 21, 50–51, 130, 236, 276–277, 283, 470, 507 probabilities probability, 27, 31, 54, 58, 68, 161–162, 175–176, 256, 258–260, 261, 262, 265, 266, 278, 281–282, 357, 359, 360–361, 364, 385, 388 theory of, 31, 32 probable, 162, 174, 260, 273, 350, 365 probatio, 53, 65 See also proof problem-solving, 40, 172 procedural, 8, 147, 242, 348, 383–394, 398–399, 470, 477 Proclus, 268, 275 proof apagogical, 144 burden of, 38 See also onus probandi charge of, 45–46 See also onus probandi degrees of, 31, 54, 70, 360 of the Pythagorean theorem, 168–170 specular, 117 See also demonstration prophecy, 412, 414, 458 Protagoras, 242–244, 247, 283 Protestant, 9, 44, 176, 400, 405, 406, 417, 446 Protestantism, 441 providence, 100, 281, 332, 339, 384, 387, 456 prudence, 156–157, 176, 331, 333, 352, 376, 378, 380, 393, 398–399, 400, 406 Pufendorf, S., 287, 317 Pythagorean, 168–170, 172–173, 281 Q quantification, 40, 296–297 quantity, 100, 104, 107, 120, 135, 138, 144, 150, 246, 339, 366, 369, 378, 451 quasi-geometric, 284

528 R racism, 419 radical, 3, 5, 6, 18, 29, 38, 39, 54, 55, 73, 88–89, 117, 126, 185, 208, 286, 288, 332–333, 379, 386, 406, 417–419, 424, 429, 498–499, 502 Ramism, 155, 160, 166 Ramus, P., 155, 156–159, 160, 162, 165, 166 ratio, 18, 19, 25, 55, 65, 67, 68, 70, 71, 73, 97, 149, 173, 231, 234, 236, 239, 241, 242, 245, 259, 274, 393, 398, 443, 476, 477, 484, 486, 492, 495, 498, 499–500, 501, 503 legis, 231, 241, 242 recta, 65, 68, 73, 245, 443, 484, 490 scripta, 236 sui, 501 rational, 2–6, 8, 12, 21, 24, 25, 26, 27, 28, 29–30, 31, 33–34, 37–38, 40, 60, 74, 85, 86–87, 116, 126, 132, 138, 145, 146–147, 151, 164, 165, 167–169, 173, 175, 183, 220, 231, 233, 235, 238, 243, 245, 274, 284, 319, 331, 333, 335, 336–337, 343, 344, 346–347, 351–352, 357–369, 375, 383–394, 424, 426, 446, 450, 453, 455, 456, 457, 482, 485–487, 489, 492, 501 power, 37, 336 rationalism, 1–6, 10, 11, 12, 17–35, 37, 38, 39, 73, 80, 85–98, 111–124, 141–142, 210, 231–248, 315–326, 343, 379, 383–385, 393, 454, 456, 457, 465, 479–492, 495 strict, 18, 20, 21, 23, 24, 32, 34, 90, 91–93 rationalist, 1–3, 10, 17–22, 29, 33, 59, 80, 91, 93, 125, 236, 329, 411, 449, 454, 458, 465, 483, 495 rationality axiological, 346 calculative, 8, 350, 352 divine, 19, 73, 79–80, 81 dogmatist, 22 empirical, 85–98 God’s, 18 hard, 6, 8, 37, 40–41, 45–46, 55, 62, 80, 368, 383 Hermetic, 112–123 human, 22, 73, 79–80, 81, 183, 366 instrumental, 352 juridical, 6, 46 legal, 6, 12, 231–248 level of, 146, 344–345, 353

Index mathematical, 4, 111, 116, 141–152, 179 moral, 8, 343–353 pagan, 411–420 perfect, 18, 19 perfectible, 18 plastic, 474 practical, 5, 117, 293–312, 357, 358, 362, 367 soft, 10, 11–12, 17, 22, 23, 27, 29–30, 32, 33, 34, 38–39, 40, 43, 45, 51, 55, 59–60, 62, 73, 80, 293, 308, 311, 367, 383, 384–385, 392, 465 strong, 17–35, 483 See also hard rationalization, 232, 235, 236, 241, 245, 248 346, 388, 442 Rawls, J., 286 realism, 45, 213, 214, 242, 244–245, 299, 343 reason balance of, 7, 31, 40, 51, 54, 66, 166, 357, 361, 368, 398–399, 406–407 calculating, 22, 31, 41, 111, 142, 158, 233, 260, 343, 346, 349–350, 352, 360, 369, 378, 472 computing, 40 demonstrating, 142, 452 and faith, 58–59, 331–332, 444 fragmentation of, 384 inclining, 26, 60, 188 its own, see ratio and mystery, 445 pathic, 9, 423–438, 433 philosophical, 427 pragmatic nature of, 385 and revelation, 442–444, 446 right, see ratio univocity of, 495–509 reasonable, 40, 54, 55, 62, 86, 118, 135, 174, 273, 285, 311, 339, 348, 364–365, 368, 437, 442, 445–446, 454, 488, 492 reasonableness, 5, 11, 58 reasoning deductive, 76, 86, 89, 91, 93, 116 hermetic, 117–123 legal, 6, 239, 270 reasons evaluation of, 8, 372, 376, 379 inclining, 26, 60, 188 necessitating, 188 series of, 503–505 weighing of, 6, 40, 158–159, 165, 166, 357, 367, 368, 398

Index reconciliation, 38, 43, 57, 86, 87, 176, 177, 181, 298, 299, 318–319, 326, 497 recta ratio, see ratio reductionism, 238 reflection, 1, 10, 51, 56, 77–78, 101, 165, 169–170, 220, 308, 331, 344, 348, 376–377, 378, 381, 384, 397, 419, 479–480, 487, 489, 495 reform, 177, 199, 205, 267, 274, 373, 386 Reformation, 447 Reichenbach, H., 101, 104, 105–106, 108 relational, 101, 105, 109, 348, 390 relativity, 101, 104–105, 106, 107, 108–109, 120, 419, 480 religion universal, 389 vraie, 386 re-memory, 479 Remes, U., 275 repartee, 52 repetition, 64, 120, 128–129, 169, 171, 425 replica, 53 representation, 18, 43, 53, 64, 79, 115, 116, 126, 129, 130, 132, 170, 172–174, 178, 235, 299, 334, 336, 340, 344, 353, 405, 406, 423, 431, 435 requirement, 39, 46, 55, 131, 187, 233, 234, 235, 239, 324, 376, 399, 449–450, 476 requisite, 10, 183, 195, 207, 217, 272, 325, 349, 463, 465–468, 470–471, 472–475, 476, 477, 498, 506–508, 509 Rescher, N., 369, 449, 476 respondent, 45, 65 resurrection, 384, 389, 455 retort, 47, 53, 216 reunification, 42 reunion, 443–444 revealed, 7, 42, 54, 161–162, 195, 283, 304, 384, 404, 405, 414, 424, 449–450, 457, 458 revelation self-, 442 rhetoric, 174, 176, 441 rhetorical, 134, 155, 157, 165, 210, 235, 252, 277, 441, 442, 496 Ribas, A., 416 Ricoeur, P., 432 rights, 6, 46, 54, 58, 236, 245, 251, 267, 271, 276–277, 278, 372, 373 rigor metaphysicus, 30

529 Riley, P., 6, 279, 289, 317–320, 326, 385, 452, 458, 488, 491 Ripalda, J.M., 484–485, 487 Robadey, A., 181 Robinet, A., 91, 166, 382, 403–404 Roinila, M., 8, 357 Rousseau, J-J., 284, 373 Rudolph, H., 9, 415, 420, 441 rule declarative, 8, 383–394 ethical, 316 golden, 348, 399–400 See also other, place of the moral, 347, 480–481, 482, 483, 488–489 Pauline, 399 procedural, 8, 242, 383–393, 398–399 Stoic-pragmatic, 480 Russell, B., 141, 371, 385, 406, 452, 453, 456, 458 Rutherford, D., 368 S safeties theory, 231 salvation, 18, 50, 285, 332, 387, 388, 404, 442 Sartre, J-P., 312, 315 savage, 9, 411, 412–413, 417, 457 scales, 12, 27, 31, 40, 360–361, 369 See also balance Scarafile, G., 9, 423 Scepticism, 22, 30, 143 scheme, 79, 125–126, 128–129, 130, 137, 301, 302, 303, 310, 346–347, 474, 496, 506 Schepers, H., 3–4, 11–12, 17, 38, 63, 73, 81, 96, 121, 123, 263, 268 schism, 373, 386, 388, 390, 397, 398, 400–401 Scholasticism, 10, 19, 23, 24, 30, 41, 61, 88, 134, 169, 189, 193, 231, 244, 245, 295, 386, 466, 467, 469–470, 471, 473, 477, 496–497, 498 Schrecker, P., 451 science general, 41, 55, 75, 202, 206, 211, 214, 223, 366 See also scientia generalis specular, 117 scientia generalis, 18, 21–22, 23, 24, 27, 92, 202, 205, 206, 215, 364, 486 Scotus, D., 45, 477 Scriptural, 50, 315, 412, 416, 419 See also hermeneutics

530 Scripture, 9, 49, 50, 54, 65, 66, 283, 384, 414, 417, 442, 443, 444, 456 historicity of, 443 See also Bible sectarianism, 398, 400, 446 self acting, 302–305 -awareness, 7, 305 composite, 303 -discovery, 310 -interested, 316 -knowledge, 305, 308, 310 metaphysical, 311 semantics, 4–5, 50, 53, 74, 122, 232, 296–297, 299, 300–301, 302, 303–304, 312, 430, 497 semiotics, 42, 53, 63, 113, 251, 472 Senault, F., 331, 339 sense figurative, 50–51 improper, 50 proper, 50, 159 See also meaning Serfati, M., 4, 125, 127, 130, 133, 134–135, 136, 137, 138 Sertillanges, A.D., 424 Shaftesbury, A.A.C., 485 Sherman, N., 325 sign expressive, 436 similarity, 57, 88, 115, 148, 160, 165, 236, 241, 256, 269, 337, 415, 499 sin original, 332, 427 sinology, 415, 420 See also China Skepticism, 42, 59, 172, 178, 388, 412 See also Scepticism Sleigh Jr., R.C., 449, 476 Smith, J.E.H., 411 Socinianism, 387–388, 390, 397 Socrates, 280, 282, 284 Sophie, 95, 206, 353 Sophie Charlotte, 91 sophism, 54 soteriology, 441 soul, 26–27, 49, 58, 169, 186–187, 190, 191, 192, 193–194, 196, 281–282, 285, 304, 321, 326, 344, 357–359, 362–363, 366, 386, 416, 428, 455–456, 479, 482, 486–487 South, R., 414

Index space, 5, 62, 74, 101, 102, 103, 104, 105–107, 108–109, 115, 186, 195, 200, 203, 287, 299, 301, 325, 429, 437, 470, 472, 498, 501–502, 505 speech act, 351 Spener, C., 457 Spinoza, B. de, 353, 503, 504 Spinozism, 10, 59, 194, 343 spontaneity, 100, 122, 187, 307, 335, 346–347 Stahl, D., 468 Stensen, N., 501 Stoicism, 285, 331–332, 338, 339, 343, 345, 386, 471, 480 strategy of argumentation, 55 argumentative, 37, 199, 331 of controversy, 144 cooperative, 56 multi-perspective, 56 negotiation, 37 Strauch, J., 235 Strickland, L., 457 Suarez, F., 28, 467, 468–469, 477, 496, 498, 502, 507 subject, 12, 21, 25, 26, 27, 28, 29, 33, 44, 56, 75, 76–77, 78, 86, 87, 89, 91, 105, 115, 117, 118, 119, 121, 122, 134, 157, 164, 168, 170, 176, 179, 181, 184, 187–188, 193, 220–223, 241, 244–245, 247, 270, 280, 311, 319, 322, 329, 334, 335, 336, 338, 344, 352, 369, 371, 373, 379–380, 391, 428, 437, 463 subordinate, 95, 148, 186, 330, 344, 444, 455, 508 substance, 7, 20–21, 25, 28, 95, 111, 113, 115, 117–118, 119, 122, 134, 138, 141, 161, 181, 184, 187, 190–191, 192, 193–194, 195, 196, 246, 282, 289, 295, 297, 311, 312, 326, 339, 376, 389, 432, 451, 454–457, 470, 471–472, 486, 504, 508 substitutability, 126, 132 substitution, 125, 126, 127, 128–130, 131, 133, 145, 234, 236, 239–240, 242, 246, 255–256, 260–262, 456 suffering, 9, 351, 423–424, 428–430, 433 summation, 127, 129–130 sunkatabasis, 399 See also tolerance supernatural, 184–186, 194, 332, 339, 416, 427, 449, 453, 456 surjective, 8, 378

Index syllogism, 41, 65, 69, 157, 158–159, 165, 167, 168–170, 171, 352, 390, 391, 473 syllogistics, 19, 27, 45, 46, 57, 63, 74, 92, 168–169, 170, 172, 241 symbolic, 40, 53, 57, 79, 113, 125–126, 127, 129, 130, 131, 132, 133, 134, 135, 138, 170, 172, 173, 214–215, 218, 223–224, 343, 348, 349, 426 inventiveness, 125–138 notation, 40, 125–126, 127, 173 pre-symbolic, 5, 213, 218 synopsis, 64, 235 synthesis, 2, 39, 93, 142–145, 163, 202, 204, 268, 285, 300, 380 Switzerland, 442 Syria, 414 T tabula rasa, 207, 482 Tannery, P., 275 Taoism, 414 Taylor, Th, 275 teleology, 346 term complex, 222 incomplex, 222, 226 Tertullian, 405 textualism, 50, 54 theistic, 449, 457 Theodicy, 114, 183, 184, 285, 312, 330, 335, 337, 339, 340, 423, 454, 456, 459 theodicy, 9, 423, 424, 426, 427–428, 432–433, 438, 445 theologian, 44, 59, 64, 86, 90, 287, 298, 332, 375, 387–388, 400, 441–443, 447, 452, 454 theology, 1, 2, 8, 9, 11, 18, 20, 24, 26, 30, 31, 42, 46, 49–50, 55, 58, 59, 61–62, 66, 68, 89, 280–281, 285–286, 333, 351, 383–384, 385, 386, 388, 389, 390–393, 399, 400, 407, 411–412, 415, 416–417, 419, 441–443, 444, 445, 449–450, 453, 454, 456, 457, 458, 464, 469, 474–475, 480, 483 ancient, 412, 457, 458 early Christian, 411, 413 natural, 24, 31, 46, 280–281, 285–286, 333, 385, 390, 412, 415, 416–420, 449–450 philosophical, 9, 445, 449–458

531 prisca, 412, 415, 416–417, 458 rationalization of, 442 revealed, 42, 449–450 theopneumatics, 442 theorem, 24, 46, 65, 119, 142–143, 150, 163, 168–170, 172–173, 201, 233, 234–235, 246, 248, 258, 263, 268–269, 271, 275, 276, 277, 464, 479, 482, 499, 507 Thiercelin, A., 6, 251 Thomasius, C., 281, 282, 386, 393, 394, 399, 492 Thomasius, J., 65, 469, 497 Thomist, 466 Tisias, 242, 244 Toland, J., 403 tolerance, 62, 175, 399 See also moderation topics, 61, 63, 157, 163, 231–232, 238, 498 Torricelli, E., 369 transcendent, 91, 130–131, 138, 149–151, 179, 184, 300–301, 320, 324, 434, 443, 500 transcendental curve, 149–150, 179 magnitude, 149, 151 transcreation, 456 transformation, 1, 41, 115, 118, 147–148, 188, 239, 265, 434, 467, 476, 479 transubstantiation, 312, 389, 405–406, 441, 454–455 See also mystery Trinitarian, 389–390 Trinity, 281, 285, 287, 389, 469 See also mystery trope, 208, 496–498 See also metaphor truth analytic doctrine of, 463 contingent, 6, 21, 28, 29, 32, 60, 86, 121, 162, 298, 464, 472, 474, 480–481, 483, 484, 502 eternal, 141, 281–282, 283, 284, 286–287, 317, 320, 346, 351, 427, 450–451, 481, 489, 498, 500–501 of fact, 118 See also factual necessary, 6, 21, 46, 50, 58, 60, 79, 91, 176, 272, 281–282, 286–287, 297, 298, 472, 479, 481, 482–483 of reason, 6, 28, 29, 60, 222, 320, 334, 482–483, 489 Tyson, E., 417–418, 420

532 U uncertainty, 6, 40, 103, 251–278 understanding, 33, 37, 39, 43, 59, 67, 75, 79, 80, 86, 92, 93, 114, 119, 132, 142, 147, 148, 151, 159–160, 168–169, 170, 191, 196, 205, 208, 210, 218–219, 222, 223, 225, 245, 267, 282–283, 287, 299–301, 303, 307, 309, 311, 316, 317, 320, 324–325, 329, 334–335, 337, 338, 340, 345, 248, 358, 361, 362–363, 367, 411, 414–416, 423, 425, 427, 429, 431–432, 435, 437, 441, 443–444, 447, 450, 456–457, 465, 472, 479, 481–482, 483–484, 486–488, 497, 498, 500, 505, 508, 3–4 unity endemic, 304 universal, 45 expression, 10, 471–472 universality, 42, 170, 171, 312, 346–347, 351, 353, 412 universalization, 9, 302–303, 309–310, 348 V vacuum, see void Vagetius, J., 216, 224 Valla, L., 397 Van Fraassen, B.C., 177, 181 van Leeuwenhoek, A., 93 van Wallenburch, A., 405 van Wallenburch, P., 405 Varani, G., 162–163, 166, 211 Vargas, E., 6, 267, 275 Varignon, P., 135, 138, 143 vectorial, 8, 361–366, 367–368, 369 verisimilitude, 59 See also probability verity, see truth verstehen, 425 See also understanding Vieta, see Vi`ete Vi`ete, F., 125—127, 131, 143, 147 Viotti, B., 160–162 vir bonus, 10, 273, 480, 482, 485, 488–489, 490, 491, 492 visualization, 91 Viviani, V., 146 void, 101, 392, 450 volition, 316, 337, 340, 357–359, 364 voluntarist, 281, 287–288

Index von Anderten, H.E., 236, 245 von Boineburg, J.C., 371 von Tschirnhaus, W., 92, 126 von Wright, G.H., 495 vraisemblance, 68, 70, 388 See also probability W Wachter, J-G., 447, 484, 485–486 Wagner, G., 31, 142 Wallis, J., 86, 91, 93, 94, 96, 135, 138, 369 Wedderkopf, M., 473, 499, 501 Weigel, E., 274 weighing, 6, 12, 18, 27, 40, 44, 59, 61, 158–159, 165, 166, 176, 304, 307, 350, 357, 358, 361–362, 367–368, 388, 398 See also reasons weight, 7, 27, 40, 54, 55, 59, 91, 134, 172, 360–361, 362–363, 367, 406, 429, 443, 504 Weil, S., 428 Werner, G.C., 93 whole and part, 87, 92 will causality of, 337 complete, 337 determination of, 329–447 genesis of, 283, 334 Wilson, C., 458 wisdom, 9, 100, 114, 185, 194, 196–197, 280, 283, 284–285, 287–288, 317, 319–320, 321, 324, 325, 330, 333, 339, 365–366, 378, 388, 393, 399, 411, 412–416, 420, 441–445, 454, 481, 485, 488–489 Wolff, C., 480, 492 world eternity of, 452 See also cosmos Wren, C., 85, 94 Y Yakira, E., 180 Yi Jing, see I Ching Z Zanardi, A., 429 Zarka, C.-Y., 467 Ziegler, J., 245 Zwingli, U., 386, 441