The Practice of Reason: Leibniz and his Controversies

The Practice of Reason

Controversies (CVS) Controversies includes studies in the theory of controversy or any of its salient aspects, studies of the history of controversy forms and their evolution, casestudies of particular historical or current controversies in any field or period, edited collections of documents of a given controversy or a family of related controversies, and other controversy-focused books. The series also acts as a forum for ‘agenda-setting’ debates, where prominent discussants of current controversial issues take part. Since controversy involves necessarily dialogue, manuscripts focusing exclusively on one position will not be considered.

Editor Marcelo Dascal

Tel Aviv University

Advisory Board Harry Collins

University of Cardiff

Frans H. van Eemeren

University of Amsterdam

Gerd Fritz

University of Giessen

Fernando Gil †

Ecole des Hautes Etudes en Sciences Sociales, Paris

Thomas Gloning

University of Giessen

Alan G. Gross

University of Minnesota

Kuno Lorenz

University of Saarbrücken

Everett Mendelssohn Harvard University

Quintín Racionero UNED, Madrid

Yaron Senderowicz Tel Aviv University

Stephen Toulmin

University of Southern California

Ruth Wodak

University of Lancaster

Geoffrey Lloyd

Cambridge University

Volume 7 The Practice of Reason. Leibniz and his Controversies Edited by Marcelo Dascal

The Practice of Reason Leibniz and his Controversies Edited by

Marcelo Dascal Tel Aviv University

John Benjamins Publishing Company Amsterdam / Philadelphia

8

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The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences – Permanence of Paper for Printed Library Materials, ansi z39.48-1984.

Library of Congress Cataloging-in-Publication Data The practice of reason : Leibniz and his controversies / edited by Marcelo Dascal. p. cm. (Controversies, issn 1574-1583 ; v. 7) Includes bibliographical references and index. 1. Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. 2. Polemics--History--17th century. 3. Polemics--History--18th century. I. Dascal, Marcelo. B2598.P73   2010 193--dc22 2009046129 isbn 978 90 272 1887 2 (Hb ; alk. paper) isbn 978 90 272 8867 7 (Eb)

© 2010 – John Benjamins B.V. No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher. John Benjamins Publishing Co. · P.O. Box 36224 · 1020 me Amsterdam · The Netherlands John Benjamins North America · P.O. Box 27519 · Philadelphia pa 19118-0519 · usa

Table of contents

Foreword Abbreviations Contributors ������������� The principle of continuity and ����������� �������� the ‘paradox’  ���������� 1. ���� of Leibnizian mathematics Michel Serfati 2. Geometrization or mathematization: Christiaan Huygens’s critiques  of infinitesimal analysis in his correspondence with Leibniz Fabien Chareix 3. Leibniz and the vis viva controversy  Idan Shimony 4. The controversy between Leibniz and Papin:  From the public debate to the correspondence Anne-Lise Rey 5. Leibniz vs. Stahl: A controversy well beyond medicine  and chemistry  Sarah Carvallo 6. Leibniz’s conciliatory approaches in scientific controversies Marcelo Dascal and Erez Firt 7. Leibniz vs. Lamy: How does confused perception unite  soul and body? Andreas Blank

vii xi xiii

1

33 51

75

101 137

169

vi The Practice of Reason

8. Leibniz vs. Foucher: Is there anything wrong  with the Système Nouveau? Marta Mendonça

187

9. Quantification of natural and positive laws:  How to organize privileges? Pol Boucher

223

10. Leibniz’s critique of Pufendorf: A dispute in the eve  of the Enlightenment Detlef Döring

245

11. Leibniz vs. Jablonski: An intestine struggle on uniting  the Protestant camp Hartmut Rudolph

273

12. The golden rule: Aspects of Leibniz’s method  for religious controversy Mogens Lærke

297

13. Leibniz vs. Bossuet: Which reasons for Irenicism? Christiane Frémont

321

Name index Subject index

345 349

Foreword

Gottfried Wilhelm Leibniz was a philosopher, mathematician, jurist, engineer, theologian, physicist, linguist, logician, political advisor and theorist, historian – in short, a polymath. His aim, in all his endeavors, was one – to contribute to the improvement of humankind. He was also one of the first thinkers to realize that controversies have a crucial role in the growth of knowledge, as well as in progress in all branches of human activity. Much of his intellectual and practical activities consisted in participating in some of the central debates of his time (many of which are still open today). His main concern was not to ensure the victory of his own positions, however persuaded he was of their correctness. He was rather interested in learning from his opponents’ views, for he conceived the development of knowledge and the solution of man’s problems as a collective enterprise to which every bit of insight, whatever its source, was a precious, irreplaceable contribution. For him, man’s chance of progress towards happiness lies in the capacity to recognize the value of the different individual perspectives through which humans approach the world. In controversies we have the opportunity to exercise this capacity by making the necessary effort to view the opponent not as an adversary but as a teacher, from whose point of view one has much to learn and through which one can enrich and improve one’s own understanding. To his friend Placcius, who asked for his critique of a recent manuscript, Leibniz wrote in April 1695: “You should not doubt that I will be an eager and, as far as possible, a studious reader of whatever emanates from you. Nevertheless, 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, for what contributes to my improvement rather than to the other’s failure” (DA 297). It is in this Leibnizian spirit that this series was created and this book – the first in the series especially devoted to his work – is intended to provide further insight into his sui generis dialectic. Leibniz the controversialist is presented to the reader in this book through a selection of actual controversies in which he took part in different areas of knowledge and action. Of course, the practice of controversy reveals the practitioners’ beliefs about the principles that should underlie it, thereby providing a glance

viii Foreword

into their way of understanding the peculiar features of controversy’s rationality. Nevertheless, the possibility of observing the unfolding of actual controversies, the recurring strategies of argumentation used, the aims pursued, and the measure in which they are or are not reached, offers, in addition, a new perspective for understanding and assessing a controversialist’s ‘theory of controversies’. For it shows not only what a thinker thinks about how one should use reason and other tools in the conduct of a controversy, but also how he actively puts in practice the kind of rationality he preaches. It is mainly, though not only, through this perspective that the book purports to contribute to the understanding of what must be acknowledged as Leibniz’s ‘dialectic’. His unquestionable merits as a moderate and constructive polemicist notwithstanding, Leibniz was not a saint when it came to actual disputes, as he was no saint when it came to his other activities. One should not expect all the polemics he was engaged in to unfold in the benevolent spirit he claims to conform to by his nature and education. From a pluralist like him, who declares that “in a simple substance there must be a plurality of affections and relations, even though it has no parts” (Monadology §13; GP 6 608), one should rather expect a variety of ‘affections’ vis-à-vis controversies. Indeed this is the case, to judge from the sample of Leibnizian controversies gathered in this book. In this respect, the book shows how a thinker is not necessarily bound to a single model and style of debating. No wonder that the three ideal types identified in the typology of debates, which I have been using for more than a decade in my investigation of controversies (see, e.g., Dascal 1995, 1998a, b, c, d, 2001, 2004, 2008), found their way into the pages of this book effortlessly and unintentionally. Leibniz’s participation in the vis viva controversy and the Leibniz-Huygens exchange on the infinitesimal calculus (Chapters 3 and 2), for example, are close to be good examples of the ideal type I call ‘discussion’ (generally taken to be the model for scientific debate); where the objective is to determine the truth, the contenders share the assumption that this can be reached by applying a certain decision procedure, and the preferred form of argumentation is logical, mathematical, or experimental proof. The animosity of the Leibniz-Pufendorf relation, reflected in their intellectual and political positions vis-à-vis each other’s views (Chapter 10), is typical of the kind of debate I dub ‘dispute’, in which the aim is victory over the adversary, no shared method of decision of the divergence is available, and stratagems of all sorts are in use. The Sturm-Schelhammer debate is also a quite clear case of dispute, apparent, for instance, in the titles chosen for their writings against each other. Yet Leibniz’s conciliatory intervention in this dispute transforms it in fact into a ‘controversy’ (in my sense of the term). It is exemplary of his way of trying to transform the opposition between apparently contradictory positions into a milder opposition; this method permits to overcome the exclusive tertium



Foreword

non datur dichotomy, unblocking the debate and leading to the creation of an alternative which combines elements of each of the opposed positions in a sort of hybrid theory – a typical example of the contribution of the ideal type ‘controversy’ to the growth of knowledge (Chapter 6). Needless to say, actual debates can hardly be pure instances of any categories that are construed as ideal types. Debates are dynamic; they may typify different categories in different phases of their development, and even within the same phase they may display elements of different ideal types. In fact, in several of the Chapters we face debates that cannot be simply assigned to one of the ideal types. For example, the Leibniz-Papin debate, as shown in Chapter 4, is typically a ‘dispute’ in its public phase and a ‘controversy’ in its private phase – a similar phenomenon occurring in the Leibniz-Foucher debate (Chapter 8). Having briefly hinted at the richness of the material contained in each chapter of this book, which deals with relatively unknown Leibnizian controversies, I will leave it to the reader to pursue its exploration on his/her own. We have cared to make this possible by providing abundant quotations that convey not only the content but also the flavor of the arguments, by keeping the originals in French or Latin, as well as by translating them when they are not easily accessible in standard English versions, and by giving the necessary references. The origins of this book can be traced back to a 1995 project titled “Leibniz the Polemicist” and they are described in detail in DA 2006: xv–xviii. The more recent story of the book begins in 2001, with a colloquium at the Center for the Study of Modern Philosophy (CNRS, Paris), jointly organized by Christiane Frémont and myself. The topic was Leibniz’s controversies. Only some of the participants in that colloquium have submitted their contributions to the present book, but it is thanks to that indispensable initial impulse that the book has finally materialized. Other authors joined the group and gradually the intended coverage of the variety of controversies in which Leibniz was involved reached the point originally aimed at. I wish to thank the authors for their perseverance, patience, and cooperation, which collectively brought this long process to this fine result. Next, the translators who voluntarily translated or revised the translations of several chapters, especially Nikos Psarros, Joseph B. Dallet, Pol Boucher, Anna Laerke, and Edward Hughes. And most of all, Zoe Gutzeit, whose superb and dedicated editorial work produced a homogeneous volume out of disparate materials. The publication of this book was supported by the Israel Science Foundation, Grant N° 81/05.  

Marcelo Dascal Tel Aviv, September 2009

ix



Foreword

References Dascal, M. 1995. “Epistemología, controversias y pragmática”. Isegoría 12: 8–43 [English version in Tian Yu Cao (ed), Philosophy of Science, Proceedings of the Twentieth World Congress of Philosophy, vol. 10; Philadelphia: Philosophers Index Inc., 2000, 159–192]. Dascal, M. 1998a. “Controverses et polémiques”. In M. Blay and R. Halleux (eds), La Science Classique, XVIe–XVIIIe: Dictionnaire Critique. Paris: Flammarion, 26–35. Dascal, M. 1998b. “Controverse en philosophie”. In Encyclopédie Philosophique Universelle, vol. 4: Le Discours Philosophique. Paris: Presses Universitaires de France, 1583–1604. Dascal, M. 1998c. “The study of controversies and the theory and history of science”. Science in Context 11(2): 147–154. Dascal, M. 1998d. “Types of polemics and types of polemical moves”. In S. Čmejrková, J. Hoffmannová, O. Müllerová, and J. Svetlá (eds), Dialogue Analysis VI (= Proceedings of the 6th Conference, Prague 1996), vol. 1. Tübingen: Max Niemeyer, 15–33. Dascal, M. 2001. “How rational can a polemic across the analytic-continental ‘divide’ be?”. International Journal of Philosophical Studies 9(3): 313–339. Dascal, M. 2004. “On the uses of argumentative reason in religious polemics”. In T. L. Hettema and A. van der Kooij (eds), Religious Polemics in Context. Assen: Koninklijke Van Gorcum, 3–20. Dascal, M. 2008. “Dichotomies and types of debate”. In F. H. van Eemeren and B. Garssen (eds), Controversy and Confrontation: Relating Controversy Analysis with Argumentation Theory. Amsterdam: John Benjamins 27–49.

Abbreviations

Leibniz’s works A = Gottfried Wilhelm Leibniz Sämtliche Schriften und Briefe. Edited since 1923 by various Leibniz Research Centers in Germany. Currently published by Akademie Verlag, Berlin. C = Opuscules et Fragments Inédits de Leibniz. Edited by L. Couturat. Paris, 1903 (repr. Hildesheim, 1966). D = Gottfried Wilhelm Leibniz Opera Omnia. Edited by L. Dutens. Genève, 1767 (repr. Hildesheim, 1989). 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 = G. W. Leibniz Textes inédits. Edited by G. Grua. Paris, 1948. LH = Leibniz-Handschriften, Niedersächsischen Landesbibliothek Hannover. NE = Nouveaux essais sur l’entendement humain. In A VI 6 and in GP 5.

English translations DA = Leibniz: The Art of Controversies. Translated by M. Dascal, with the cooperation of Q. Racionero and A. Cardoso. Dordrecht: Springer, 2006. L = Gottfried Wilhelm Leibniz Philosophical Papers and Letters. Translated by L. E. Loemker. Dordrecht: Kluwer, 2nd ed., 1969. W&R = G. W. Leibniz Philosophical Texts. Translated by R. S. Woolhouse and R. Francks. Oxford: Oxford University Press, 1998.

Contributors

Andreas Blank is Lecturer in Philosophy at the University of Paderborn, Germany. Previously, he has taught at the Humboldt University of Berlin. He has been Visiting Fellow at the Center for Philosophy of Science at the University of Pittsburgh and Humboldt Foundation Fellow at the Cohn Institute for the History and Philosophy of Science and Ideas at Tel Aviv University. His publications include Der logische Aufbau von Leibniz’ Metaphysik (2001) and Leibniz: Metaphilosophy and Metaphysics, 1666–1686 (2005). Pol-Henri Boucher, Docteur en Philosophie, is a member of the Institut de l’Ouest, Droit et Europe (IODE), at Rennes, Bretagne. He specializes in the young Leibniz’s juridical work, within the tradition of juridical rationalism, to which Leibniz belongs. He has translated into French, commented, and annotated so far three of Leibniz’s early juridical books, Doctrina conditionum (1995), De Conditionibus (2002), and De casibus perplexis (2009), and is preparing the translation of two others: the Specimen questionum philosophicarum ex jure collectarum and the Nova methodus docenda discendaeque jurisprudentia. With the publication of these five books, he will make available to Leibniz scholars and historians of Law the core of Leibniz’s early contribution to the practice, theory, and philosophy of Law. Concomitantly, he is writing a synthetic work on juridical dialectics. Sarah Carvallo is a member of the Laboratoire d’Etudes du Phénomène Scientifique (LEPS, Lyon). Her research concerns the parallel constitution of modern European medicine with the elaboration of new scientific and philosophical representations of the living body. Her recent publications include: “La naturalisation de la compétition et la dénégation du rapport de force de Hobbes à Tocqueville” (2008), “Pourquoi ne pas être cartésien en médecine?” (2009), “Les fausses évidences: dire et représenter le vivant, en l’occurrence la mort, à l’âge classique. Hoffmann, Stahl, Leibniz” (forthcoming), “Eloge des corps mêlés” (forthcoming), “De la fabrique du corps au corps machine en passant par les automates: Jacques Vaucanson et Claude Nicolas Le Cat (1700–1768)” (forthcoming), “Stahl et les âges de la vie” (forthcoming).

xiv Contributors

Fabien Chareix is a graduate from the Ecole normale supérieure, an agrégé in philosophy, and a doctor in philosophy, specializing in the history of modern philosophy and the philosophy of science. He is at present maître de conférences at the University of Paris 4 Sorbonne. Currently, he is working on the relationships between Leibniz’s and Huygens’s theories of knowledge and is preparing a scholarly edition of their correspondance. His main field of research is the history and philosophy of rational mechanics. Marcelo Dascal is Professor of Philosophy and former Dean of Humanities at Tel-Aviv University, Israel. He is a member of the Comité Directeur of the Fédération Internationale de Sociétés de Philosophie and President of the New Israeli Philosophical Association and of the International Association for the Study of Controversies. His research includes 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. He authored La Sémiologie 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), and edited/co-edited ca. twenty books, the latest of them being Leibniz: What Kind of Rationalist? (2008). He is the founder and editor of the journal Pragmatics & Cognition and 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). Detlef Döring is director of the editorial team in charge of the edition of Johann Christoph Gottsched’s correspondence at the Sächsischen Akademie der Wissenschaften in Leipzig. For several decades he has conducted research on the history of science and universities in 17th and 18th century’s Germany. Recently, a series of English translations of his editions of Puffendorf’s works have been published, including The Divine Feudal Law: Or, Covenants with Mankind (transl. of Jus feciale, 2002); Of the Nature and Qualification of Religion in Reference to Civil Society (transl. of De habitu religionis christianae ad vitam civilem, 2002), and The Present State of Germany (transl. of De statu Imperii Germanici, 2007). Erez Firt is a PhD student in Philosophy at Tel Aviv University and holds an engineering degree in Information Systems from the Technion, Israel’s technological institute. His MA thesis focused on the concept of ‘emergence’ and its relation to scientific explanations. His current research deals with the principle of least action, its historical evolution, application in contemporary physics, and potential teleological implications.



Contributors xv

Christiane Frémont, a graduate of the École Normale Supérieure, agrégée and docteur en philosophie, is chargée de recherche of the CNRS presently at the Centre Chevrier, Université de Bourgogne. Her work has focused mainly on Leibniz’s philosophy and comprises: L’Etre et la Relation (1981, 2nd ed. 2000), Leibniz, Discours sur la théologie naturelle des Chinois (1987), Singularités: individus et relations dans le Système de Leibniz (2003), as well as three edited volumes of Leibniz texts (1994, 1996, 2001). Since 1984 she is director of publications of the collection Corpus des Oeuvres de Philosophie en langue française (whose editor in chief is Michel Serres). She has participated in the Dictionary of Seventeenth-Century French Philosophers (2008) as a contributor and supervising editor in charge of religious controversies. She has written many articles on the relationship between philosophy and literature (Voltaire, Diderot, Victor Hugo), on the philosophy of life in the 17th and 18th century, and on contemporary philosophy. Her article on Michel Serres, “Philosophie pour le temps present” is forthcoming. Mogens Lærke, PhD University of Paris-Sorbonne (2003), is a lecturer at the University of Aberdeen, Scotland. He was a Postdoc from the Carlsberg Foundation (2004–2007), from Tel Aviv University (2007), and a Harper Fellow at the University of Chicago (2007–2009). Lærke is the author of Leibniz lecteur de Spinoza. La genèse d’une opposition complexe (2008) and of numerous articles on early modern philosophy. He is also editor of The Use of Censorship in the Enlightenment (2009) and co-editor (with M. Kulstad and D. Snyder) of The Philosophy of the Young Leibniz (Studia Leibnitiana Sonderheft 35, 2009). Marta Mendonça is Professor of Philosophy at the Universidade Nova de Lisboa. Her main research interests include, among others, modalities (Megarians, Aristotle, Leibniz, Hume), early modern philosophy (Descartes, Leibniz, Hume, Kant), philosophy of nature, history and philosophy of sciences, and bioethics. Presently, she is the head of a research project on “Comprehension, Explanation and Language”, which is part of a course at the Centro de História da Cultura of the University, of which she is a founding member. Her PhD dissertation, The Doctrine of Modalities in the Philosophy of Leibniz, is about to be published. She has also published essays on modalities, causality, the ontological argument, determinism, and bioethics. She is a member of the Sociedad Española Leibniz and of the International Association for the Study of Controversies. Anne-Lise Rey is professeur agrégée of philosophy, docteur en philosophie, maître de conférences in History of Science and Epistemology at the University Lille I, and researcher at the Savoirs, Textes, Langage division of the CNRS. She is interested in Leibniz’s philosophy of nature, the relationship between science and metaphysics at the end of the 17th century and the first part of the 18th century,

xvi Contributors

and the question of style and scientific writings in modern philosophy. Her recent publications include “Diffusion et réception de la Dynamique: la correspondance entre Leibniz et Wolff ” (2007), “Leibniz et Newton dans Wolff: un précurseur pour les Lumières européeennes?” (2008), “La figure du leibnizianisme dans les Institutions de Physique de la Marquise du Châtelet” (2008), as well as “Action, perception and organisation” (forthcoming), “La chimie pour Leibniz, une pratique cognitive?” (forthcoming), and “La controverse entre Wolff et Lange: quelques précisions sur une pseudo-philosophie spinoziste” (forthcoming). 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, on the German Protestant churches and their meaning for the integration of the refugees into West-German society 1945–1972, several articles on the history of the Reformation period in early modern Germany, on the relationship between 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 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 Leibniz’s political writings. Michel Serfati holds the Higher Chair of Mathematics at the Université Paris VII – Denis Diderot. Holding doctorates in mathematics and philosophy, he has for many years directed the seminar on epistemology and history of mathematical ideas held at the Institut Henri Poincaré in Paris. His research concerns in particular algebraic supports of multiple-valued logics (Post Algebras), the philosophy of mathematical symbolic notation, and the history of mathematics in the 17th century (especially Leibniz’s and Descartes’ works) and in the 20th century (especially Category Theory and Spectral Methods). He organized many conferences on the history and philosophy of mathematics, and is the author and editor of works in both disciplines. Among his recent publications, De la Méthode. Recherches en histoire et philosophie des mathématiques (2002), La Révolution symbolique. La constitution de l’écriture symbolique mathématique (2005), and Mathématiciens français du XVIIème siècle: Pascal, Descartes. Fermat (2008). His next forthcoming publication is a book on the mathematical thought of René Descartes. Idan Shimony, a graduate of Tel Aviv University Interdisciplinary Program for Outstanding Students, is a PhD student in Philosophy. His MA thesis was on Hume’s attack on human rationality. His current philosophical research focuses on Kant’s conception of nature and antinomies. As a junior lecturer at Tel Aviv University he teaches courses on Leibniz, Hume, and Kant.

chapter 1

The principle of continuity and the ‘paradox’ of Leibnizian mathematics* Michel Serfati

1.

Introduction

On the basis of the epistemological analysis of several Leibnizian “mathematical situations”, I will first attempt to show how Leibniz’s “principle of continuity” (which is, in fact, a meta-principle) belongs to the conceptual framework of what he calls “symbolic thought”, at least insofar as its mathematical implementations are concerned. I will then show how the ambiguity of the mathematical and metaphysical status of the principle engendered controversies between Leibniz and some of his correspondents (the ‘paradox’ of Leibnizian mathematics), according to whether they were mathematicians (e.g., Varignon) or philosophers (e.g., Wolff). I will then briefly indicate the ways in which the same controversy continued after Leibniz between Poncelet and Cauchy. Finally, it will be shown how this seventeenth century “principle” remains to these days fully operational in research and teaching as a sort of internalized methodological guide. Let us begin with the following example of a well-known contemporary mathematical proposition. If un is the general term of a real sequence such that un ≥ a for every n,  and if un converges, then lim un ≥ a. n

It is clear that this statement is immediately and spontaneously accepted by contemporary mathematicians as well as by those of the nineteenth century. This is not only due to its intrinsic validity, which is doubtless, but also due to the acknowledgment of the now familiar underlying ‘mode of truth’ it relies upon – that of “proof by continuity”. One can recognize here indeed a fundamental type of ‘attitude’ or ‘behavior’ by mathematicians – currently usual – which might be informally described as follows: what is always true of the changing object (here un)



Michel Serfati

will remain true of that into which it transforms itself (here lim un ≥ a). It can be n immediately noted, however, that if we confront this admittedly valid theoretical principle with the following very close example: If un is the general term of a real sequence such that un > a for every n,  and if un converges, then lim un > a, n

then the proposition is false; that is, it deceives the same “expectation” of passage by continuity, which we have observed to be part of the mathematicians’ ‘attitude’. Therefore, the present study will be also devoted in part to a reflection on the origins and motivations, historical and epistemological, of such an ‘attitude’.

2.

“New Calculus” and “Combinatorial Game”

In this section we will return to Leibniz and focus on his “Calculus of Differences” which we will examine, however, under the aspect that interests us here, namely, the symbolic question. I will summarize the results of my earlier work (Serfati 2001, 2005), according to which one of the main epistemological lessons drawn by posterity from Descartes’s solution of the question of the representation of powers (by means of the exponent) consists in the analogical creation by Leibniz of his “New Calculus”. My conclusions, in fact, simple as they appear, seem to me to be both new in connection with the philosophical commentary of Leibniz’s mathematics and indispensable for the thesis of the present paper. Leibniz explains his claims in several texts. I will base my analysis on the Considerations (GM 5 306–308), an article published in the Journal des Sçavans 1694, where Leibniz spelled out in a particularly neat way his conception of his Calculus in contrast with those of Viète and Descartes, both reduced to their bare “five operations”. Indeed, in the older Calculus, the reciprocal relations between the five operations had been long before exhaustively analyzed (addition of products, products of additions, root of quotient, etc.). In the seventeenth century, however, with the introduction of the symbolic system, this inventory had also become exhaustive, through the combinatorial examination of the diverse possible substitutions in the ‘forms’ organized with the preexisting operational signs: ‘cross’, ‘point’, ‘trait’, ‘bar’, ‘vée’, ‘blanc’, exponent.1 To this list Leibniz thought he himself had added two one-place assemblers,2 namely the signs: d and ∫

which he interprets, respectively, as differentiation and summation. The place after the préhenseur (i.e., the one place-assembler) was first occupied by a ‘letter’ as in:

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

d x or ∫ z

Henceforth, in Leibniz’s eyes it became necessary in this “New Calculus” to reexamine combinatorially – that is, without an initial reference to meaning – the symbolic ‘forms’ obtained by effecting all possible substitutions involving both the old and the new operation signs, and then to examine their possible interpretations. Concerning the ‘d’, this is precisely what he did systematically in the first part of the 1684 Nova Methodus (GM 5 200–226), which marked, as is wellknown, the official creation of the “Calculus”. Indeed, at the combinatorial level Leibniz examined all the possible forms obtained by substituting x in d x

five of the ‘forms’ previously given in the “Calculus” of Viète and Descartes, thus obtaining: d (x + y) d (x – y) d (x · y) d (vy ) d (xa)

He then proceeded to interpret these forms as many open questions, thus inquiring what was the value of the differential of a sum, a difference, a product, a quotient, a power. For the differential of a product, for example, he observed that one has d (x · y) = x · d y + y · d x, a formula which did not appear to him spontaneously and which he had even some difficulty in demonstrating. For the power, Leibniz would obtain d (xa) = a · xa–1 dx. In modern terms, this was a formula completely literalized (a ‘canon’ in the terminology of Leibniz’s time) – one of the first in history.3 It is also clear from the context that ‘a’ was the sign of an undetermined rational number, positive or negative. Leibniz will give in what follows two numerical instantiations, the one with a = 3, whence d(x3) = 3 · x2 dx, and then with a = –3.

The system of operation rules completed in this way by the addition of the five properties was at first called by its creator the (differential) ‘algorithm’. Thus, the new concept of differential was introduced by him at the level of meaning, while ‘d’ belonged to the combinatorial level. The ‘algorithm’ included also the old Calculus. But one can easily see how the combinatorial generation of all the combination of signs contributed to this invention. For the very idea of looking for the formula of the differential of a product, for instance, had few chances of being paid attention to initially, since it had no immediate geometrical sense (one cannot represent directly as an ordinate on a figure the product of two ordinates).





Michel Serfati

The Art of Combination had thus contributed here not to find demonstrations but ideas of propositions to demonstrate, thereby exploring a new field of the Art of Discovery. Ever since, Leibniz proclaimed the advantages of his Art of Combination. He was thus touching the crucial topic of pure invention in mathematics, for which even today there are no methodical treatises. Beyond his declarations of intentions, which were quite clear, Leibniz was not able to explain the details of his own practice, e.g., how did he in fact apply the art of combination to his ‘algorithm’ as we have just proposed. In the Nova Methodus the ‘algorithm’ is in fact abruptly presented with no explication or demonstration; it is only ironically preceded by “having said this, these are the rules of the Calculus” (GM 5 220). In spite of its author’s enthusiastic declarations, the systematic procedure in question remained for a long time not understood by his colleagues. Nevertheless, ever since the “Old Calculus” had become contained in the “New”, the substitution of more complex ‘forms’ became naturally permitted, as in d (6x2 – 3x y + 5) or else � � ⋅ � �3 �4 d( + + + +et�.) 1 1⋅ 2 1⋅ 2 ⋅ 3 1⋅ 2 ⋅ 3 ⋅ 4

a combination of signs found in a letter of Jean Bernoulli (1696; GM 2 340).4 Later, Leibniz realized that, since ‘d’ was a one-place assembler (i.e., ‘préhenseur’), ‘forms’ such as d (d x) and d (d (d x))

were legitimate from a combinatorial viewpoint too. Leibniz interpreted them naturally as the repetition of the differential, called them second and third differentials, and represented them symbolically by d2 x or d3 x

In this way, the Cartesian exponent received for the first time in Leibniz a new interpretation for which he until then had no attraction, namely, to represent repetition. This use, inaugurated by Leibniz, is today common for the representation of iteration through composition.5 It was equally natural for Leibniz to perform the same substitutions upon the ‘forms’ previously obtained: d3 (6x2 – 3x y + 5)

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

Still later, he introduced summation, which he represented symbolically by ‘∫’, a second préhenseur. The iterated summation became then permitted:

∫∫ x or ∫∫∫ x which Leibniz represented, with the help of Cartesian exponents, as follows (Jean Bernoulli to Leibniz, April 20th 1695; GM 2 171) 2

3

∫ � or ∫ � which he called second and third sums. Whether for differentiation or summation, Leibniz related their origin to examples of sequences of numbers, according to an epistemological schema created in Paris based upon what is today called the Calculus of ‘finite differences’. Further substitution in these ‘forms’ in the place of the x again led Leibniz to more complex examples, such as: 3

∫ (5�

4

− 6�+7)

In many texts, of which the Considérations are just one example, Leibniz expressed his deep satisfaction in having thus revealed a double and repetitive scheme. The Leibnizian Calculus thus organized possesses a syntactical completeness – a concept that must be understood in connection with the new symbolism added by Leibniz to the earlier “Calculus”. From the moment the ‘d’ and the ‘∫’ became both préhenseurs, ‘forms’ such as

∫ dx or d ∫ x also became legitimate and interpretable in terms of the successive performance of differentiation and summation in both directions of possible execution. It is at this moment that Leibniz “establishes” the two canons

∫ dx = x and d ∫ x = x valid for whatever ordinate (as he called it) whose sign was x. As Leibniz wrote to Jean Bernoulli on October the 3rd 1696 (GM 3 802): “thus ∫ and d put together mutually eliminate each other”. This was a double formulation of considerable importance, which Leibniz proved (or believed to have proved) geometrically, once more by analogy with certain properties of numerical sequences (integers or inverses of integers), which he studied in Paris. In any case, differentiation and summation were considered by their inventor as two opposed operations – like exponentiation and root extraction – insofar as their successive performance led to identity whatever the direction of execution.6 This was an epistemological schema to which Leibniz attached great importance:





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For this method or this differential calculus serves not only for differences but also for summations which are the reciprocal of differences, more or less as the ordinary calculus does not serve only for powers but also for roots which are the reciprocal of powers. (Considérations 308)

In other texts, instead of considering this schema of successive execution of two procedures of opposed directions as primitive, Leibniz – beginning from the other pole – considered identity (accompanied by its necessary contrary, difference) as the first principle. Even then he locates at the origin of mathematics the dissociation of identity. Fascinated by his own discovery Leibniz went as far as to show that the analogy between the two couples, power-root and differentiation-summation, extended also to considerations of executability. In each of the couples, indeed, there is one of the terms which is always explicitly executable (power and differentiation) whereas the other (root and summation) generally is not. To say, however, that the summation represented a certain ‘form’ was not executable, was to say that we couldn’t provide for such a form a symbolic representation other than itself, or that it had no other interpretation than the observation that it was a certain summation. Hence, ‘forms’ initially devoid of any geometrical meaning, that is, obtained only by the pure combinatorial game of a succession of substitutions emerge, as in

∫ 6 (

� 3 + 2� 2 − 1 ) 4 � + 1

or7

∫ m�+n,d�

�� 3 +i��+k�+1

or else8

∫z d e

m

n + e ∫ z e −1d m −1ndz

These ‘forms’ were also considered as combinatorially legitimate, and were indeed put forth by Jean Bernoulli and Leibniz thereby opening up a cascade of new objects and new problems, mechanically produced regardless of their eventual meaning. One can recognize here the same structural mechanisms and the same conclusions drawn by Descartes regarding the exponent (see Serfati 2005) – only now supported by the pair differentiation-summation. In this way, the historical detachment from geometry as the only guarantor of truth was achieved de facto by the force of the game of the symbolic notation. Thus, this part of the history of mathematics – the appearance of the differential calculus – will correspond, at the epistemological level, to a separation from the ancient mathematical geometrical world. Let me repeat: this separation was coextensive with the development of

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

the symbolic notation. In any case, that every new symbolic structure should be open to substitutions became ever since a primordial demand, present in Leibniz’s practice at every page although never explicitly formulated as such. Leibniz was justly proud, then, of his “New Calculus”. In this section I have described the functioning of the “combinatorial game” in the production of assemblings of signs originally disregarding meaning. In the following section I will examine, on the contrary, the question of the meanings from the point of view of a social fact: the reception of Leibniz’s assemblings by the community of mathematicians.

3.

The Leibnizian ‘paradox’

In spite of its fecundity as purveyor of many mathematical objects as well as results, this new combinatorial methodology puts its author in a peculiar situation, which we dubbed the ‘Leibnizian paradox’. Let us recall, first, a central fact: the Nova Methodus does not contain any demonstration of the essential results it announces, results that are correct. Since its publication (1684), the constitutive elements of the fundamental paradox Leibniz faced were in place – a paradox that accompanied him for the rest of his life forming a sort of background for his quarrel with Newton. On the one hand, he was incapable of providing his “New Calculus” with any kind of ‘reasonable’ ontological foundation; this term should not be understood in some anachronistic contemporary sense, but rather by reference to the mathematical ontology of his time’s geometers, for whom Leibniz’s “explanations” about his infinitesimals by means of comparisons and analogies were largely dissatisfactory even by seventeenth century standards. On the other hand, however, once Leibniz himself or his interlocutor had admitted its confused and contradictory assumptions, the Calculus itself acquired the order of a superb mechanism. This mechanism would lead immediately to a vast field of applications of very different nature (in modern terms: rectification of curves, calculation of areas, centers of gravity, volumes, moments of inertia, etc. – all new questions full of interest in the end of the 17th century). Thus, the utility of the theory of infinitesimals was daily verifiable and actually verified. One should notice, however, that its veracity and its consistency were only anchored in its applications, at the level of utility rather than that of ontology. Since the 1690s, mathematicians naturally began to write to Leibiniz requesting clarifications about the foundation of this “New Calculus” he had invented and whose adepts they wanted to become. This was the case with young geometers like L’Hôpital (1693; GM 1 236–241), Varignon (1702; GM 4 91–97) or Grandi (1705; GM 4 210–212), as well as of recognized mathematicians such as Wallis (1697;





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GM 4 11–14) and, above all, Huygens (1690; GM 1 41–44), the old master whose endorsement of the “New Calculus” caused Leibniz so much pleasure.9 In my opinion, the paradoxical correspondence between Leibniz and Varignon testifies a situation we can retrospectively consider uncomfortable for Leibniz – regardless of the fact, as we will see, that he himself did not perceive it in this way. Leibniz was in fact unable to give a meaning to his fictions about “infinitesimals”, which were however purported to be founding ones. Yet he did not believe it preferable to openly demand from a good-willing adept to employ blindly the rules of the Calculus without worrying about its ontology – as much later de Morgan and Babbage did. Vis-à-vis his interlocutor he contented himself with a ritual discourse, where he would begin by evoking the analogy with the imaginaries, erected into a paradigm, before making him admit, on the basis of examples ever more numeral and divers, the impeccable functioning of a machine he had elaborated through the pure game of his Art of Combination. This is what we are now going to spell out.

4.

The letter to Varignon

Among the main documents related to this ‘paradox’ one should include the letter to Varignon of 1702, completed by another famous Leibnizian text, the Justification.10 This well-known letter, which cannot be studied here in detail, has often been considered to be an exposition of the essence of Leibniz’s ideas about the infinite. One should first note that it is a quite late text, written when Leibniz was no doubt an acknowledged mathematician, but when the quarrel with Newton had not yet begun, even though it was already embryonic in the critics by Fatio de Duillier (1699). The correspondence with Varignon has, however, given place to a wealth of commentaries, which seem to me to be futile, for they share the attitude of taking the text too seriously. At the moment Leibniz writes him this letter, Varignon (1654–1722) – whose name and work are today known due to an important theory on the equiprojectivity of vector fields – was (since 1688) “geometer at the Academy of Science of Paris”. For the philosophy of science, Varignon remains to this day an important figure, as one of those who were among the first who attempted to reduce the number of basic principles in mechanics. This was at that time a quite unusual procedure of abstract reduction, Euclidean, in a sense. A century later, Montucla still criticized Varignon’s habit of “generalizations”. Leibniz thus had to do with a particularly demanding partisan as well as with a deeply faithful one, for Varignon, who in fact closely followed all the positions taken by Leibniz, was one of his most fervent supporters. It is he, for instance, that opposed Rolle and refuted

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

him, and when L’Hôpital published his Treatise of 1696, Varignon welcomed it, while accompanying it by clarifications (published only in 1725) destined to correct his mistakes. This letter to Varignon is written when what has been called the ‘Paris Cabale’ against Leibniz’s discoveries is conducted by the Cartesians at the French Academy. It was led by Abbot Catelan and the mathematician Michel Rolle, and more or less supported by Abbot Galloy, a former Leibniz supporter.11 In Paris, Leibniz was first defended by L’Hôpital who died however in 1704. Varignon had then to fight for a long time and alone as Leibniz’s defender. And at one point he needed from the “master” additional information, namely, how to understand his “infinitesimals”, how to explain them? Thus, for example, he wrote him on November 28th 1701 (GM 4 89) asking for precise definitions of the infinitely big and small: I beg you, Sir, to be kind enough to send me your opinion about that, in order to stop the enemies of the calculus who thus make use of your name in order to mislead the ignorant and the simple tones… The enemies of your calculus benefit from that and disseminate in that way a neat and precise declaration of your opinion on this matter. Therefore I beg you, Sir, to send us as soon as possible this neat and precise declaration … in order to silence, if possible, or at least to confound these enemies of the truth. Mr. Bernoulli no doubt will have already mentioned to you the crude paralogisms of Mr. Rolle.

These were the requests he addressed to Leibniz, and such requests were indeed crucial for him as well as for common cause. On the other hand, if Leibniz had wanted or had been able to, he could have then benefited from a good occasion to develop publicly his positions on infinitely small magnitudes, by providing a well argued for reply. However, in Leibniz’s reply, which is the letter to Varignon here discussed. we will never discover what would have been (at long last) the foundations of his infinitesimals or of his never to be found “science of the infinite”. Leibniz rests content with a wishful, rhetorical discourse. Guided by the sole obstinate aim of making a central unique and for him crucial fact (the need of the use of infinitesimals) accepted, he is satisfied with giving, accumulating and juxtaposing unrelated arguments, sometimes contradicting each other. He begins by assuring that “there is no need to make mathematical analysis dependent upon metaphysical controversies” (GM 4 91). This is a position he often takes when he addresses mathematicians: for him, the foundations of the “New Calculus” are not to be sought outside mathematics itself. When addressing philosophers and mathematicians, in contrast, Leibniz does not hesitate to acknowledge and even to claim its metaphysical character. On the other hand, Leibniz’s argumentation about the foundations of his “New Calculus” touches



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three points. First, he says that the infinitesimals are useful for the achievement of effective results, in mathematics as well as in dynamics or in physics. This is an argument based on the primacy of utility over existence (in the present case of the constructible), which is worth what it is worth but evidently does not address the ontological question. However, Leibniz says that the infinitesimals have the same status and the same use of well grounded fictions as the imaginary quantities: one assumes their existence, one inserts them in new rules of calculus having the same form as the rules of ordinary algebra. By using them, one obtains effective results. After which Leibniz in a sense claims that one “forgets” them after having written them. Therefore, like with the imaginaries, the contradictions that might be engendered by the infinitesimals would be resolved for him in and through mathematical notation. It is natural to criticize this argument observing first that it is of the same kind as the former. The fact that one “forgets” the infinitesimals does not exonerate the geometer from the issue of the legitimacy of their prior use. It will also be observed that there is not in fact any foundation in reality for a relationship between infinitesimals and imaginaries, but only a vague underground analogy, which we might formulate in terms of the following epistemological pseudo-paradigm: neither the one nor the other of these two concepts is found in the usual, “real” calculus; therefore, says Leibniz, they resemble each other. This is an obviously sophistic argument, which, however, generations of mathematicians will continue to use.12 The third and last point in Leibniz’s argumentation is that the principle of continuity would be able to solve and arrange everything here. This crucial argument, which appears only at the end of the letter rather them at the central developments of the text, will be more explicitly presented in the Justification. We turn now to it.

5.

The principle of continuity as a solution of the paradox

The solution Leibniz proposes for the paradox can be found in the last lines of his letter to Varignon (GM 4 97) and consists in relying upon a principle of continuity firmly anchored in mathematical notation. The mechanism is based on the fact that the combinatorial game permits to form combinations of signs, such as

∫ dz and d ∫ x but wherefrom do the ideas of the properties to be demonstrated such as

∫ dx = x and d ∫ x = x come?

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

Wherefrom do the internal mechanisms of the proofs of such results come? To be sure, the first of these properties, for instance, originates in the combinatorial game providing the combination in the left (∫ dx). However, as far as the idea itself of the result as well as of its proof are concerned, Leibniz remains remarkably discreet. In his letter to Oldenburg of 1677 (B 241), he had no doubt evoked as a sort of explanation points that are “infinitely close” to each other – an expression he doesn’t dare in a printed text. In the second part of the Nova Methodus, which does not contain as pointed out any demonstration of the result it announces, he evokes in a few lines very vaguely and without preiteration “an infinitangular polygon equivalent to the curve”, which makes do as a “demonstration”. In the Historia et Origo of 1713 (GM 5 392–413), which is supposed to sum up his development in a critical moment for him, whereas he explains at length the properties he discovered in Paris about the finite series (as well as infinite ones, contained in the arithmetical and harmonical triangles), he limits himself to the short paragraph about the passage to the continuuum taking it for granted and not giving even a single property as an example. In fact, the property in question (∫ dx = x) is indisputably valid in the discrete case (that of the series of numbers, finite or not), also called finite differences, under the nowadays usual form of the sum of all differences. This result, which today we write as if �im � n = 0, then n

∑� �≥n

�

− � �+1 = � n

Leibniz had also written as ( ∫ dx = x). And it is possible indeed in modern terms to fully justify Leibniz’s writing it as follows: if to every sequence x ∈ IRIN one associates two new sequences, elements of IRIN, namely dx and ∫ x defined by: (dx)n = xn – xn + 1 and (∫ �)n =

∑�

0≤ k ≤n

k

then the formula ∫ dx = x is effectively valid (it applies therefore, once more, to the sum of all the differences), and Leibniz should be credited for having been the first to discover, certainly in connection with the harmonic triangle, an epistemological schema (the “sum of all differences”), which is valid and usual even today.13 The formula was certainly true for finite differences, but why should it continue to be true in the continuous case of geometry and curves? This analogy discrete – continuous, or infinitangular polygon – curve, Leibniz had no doubt recognized both in discrete cases and, following Pascal and Wallis, in simple continuous cases (the “paraboloid”). Nevertheless, instead of limiting himself to the recognition of this resemblance, Leibniz posits it as a general property, which he evidently does not demonstrate, but derives it from a universal principle of continuity super-ordinate to it, which could be roughly formulated as: “what is

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true of a changing form in every instance is equally true of what it becomes in fine at the end of a continuous process” (in Leibnizian terms, the terminus inclusivus transfers its properties to the terminus exclusivus). It is easy to understand how the schema might be applied here: the discrete case reaches completion in the continuous case; therefore, for Leibniz, the properties (the “affections”) that are valid in the former should transfer themselves rightfully to the latter – for which the invariance of the symbolic notation ∫ dx = x was for him the guarantor. In his reply of May 23rd of the same year (GM 4 99), Varignon does not comment on the content of Leibniz’s letter, mentioning only the need to fight against the enemies of “our Calculus”, first and almost Rolle and his “paralogisms”, before he engages quickly in a strictly technical problem concerning tangents. All the rest of the letter is devoted to questions of dynamics, regarding “centrifugal” or “centripetal” forces, entirely treated in terms of Leibniz’s differential calculus without returning to the foundational questions. Leibniz’s reply (June 20th 1702; GM 4 106) deals first with a very interesting development concerning tangents and the local properties of curves (concavity, convexity, inflection points) followed by general considerations about the places of differentiation as an operation in the calculus, which Leibniz quite naturally sees as analogous to difference in the former calculus (e.g., that of Descartes). There will be no more discussion of the justification of the calculus in the very interesting Varignon-Leibniz correspondence, which continued until Leibniz’s death.

6.

The reception of the calculus

We have just examined Leibniz’s correspondence with Varignon, the paradigmatic “young follower” who asked Leibniz to explain to him the foundations of his calculus so that he himself could make use of it. As we have seen, there was no real controversy between Leibniz and Varignon, perhaps in light of their teacher/ student relationships at a time when Leibniz was already a recognized mathematician whose calculus was generally accepted as functioning. The situation is different, however, with Bernoulli, the “candidate of the 1685s”, who had learned about the calculus through the 1684 obscure text of the Nova Metodus, about which he said, at first – and rightly so – that Leibniz’s explanation was “an enigma rather than an explanation” (GM 3, Part I, 5). Nevertheless, once he realized its interest, that same Jean Bernoulli exploited Leibniz’s discovery in an extraordinary manner, to such an extent that he must be considered one of the co-inventors of the differential and integral calculus’ praxis. As for the more experienced “candidates of the 1690s”, such as Wallis and Huygens, the question was slightly different: Newton’s methods have provided

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

them, in fact, the missing ontological foundation; they themselves presented Leibniz’s calculus as nothing but another version of Newton’s. Wallis emphasizes this point (GM 4 15). Hence, there was no need to ask Leibniz for the foundations. And Leibniz was right in avoiding any commentary about these fundamental points, so that the logical structure of these correspondences is slightly different from those with the “young followers”. In a letter of March 1697 (GM 4 11), for instance, Leibniz proposes to Wallis his “new kind of calculus”, whose interest lies in its application to the cycloid, a transcendental curve excluded by Descartes. In his reply (GM 4 15), Wallis confesses his ignorance, due to the fact that he “had not been sufficiently informed about the differential calculus, except from the fact that he had recently been told that it nearly coincided with Newton’s doctrine of fluxions”. Leibniz’s undated reply (GM 4 23–29) mentions the difference between Newton’s and his own practices (GM 4 25–28) and even claims a certain superiority for his own calculus over that of Newton’s, but he does not mention the issue of infinitesimal foundations; and it is curious to see Leibniz accepting without a word Wallis’s claim about the foundational equivalence between his theory and the theory of fluxions. Quite naturally, Wallis asks him then “to take the time to expound conveniently [his] differential calculus and Newton his method of fluxions, so that we can understand clearly both what they share and where they differ” (GM 4 30). In his reply, Leibniz ducks Wallis’s request: “in my opinion, it is better to consider the elements or instantaneous differentials as quantities in my way, rather than to take them to be as nothings. In fact, they have in their turn their differences” (GM 4 54). However, when Wallis, in a letter of January 1699 (GM 4 58), presses Leibniz with regards to the crucial issue of the precise use of the infinitesimals in the calculus, Leibniz replies in March 1699 (GM 4 63) by invoking as a decisive argument his lemma of the elimination of the incomparable which he had publish earlier in the Acta Eruditorum – a lemma which obviously could not be grounded in his own infinitesimal conceptions. A true battleground of controversies will, no doubt, arise in the debate with Newton, which was preceded by two other attacks against Leibniz, by Nieuwentijt and Fatio de Duillier. None of them was, vis-à-vis Leibniz, in a position of “candidate”, but their attitudes toward him were quite different. Fatio behaved throughout as Newton’s champion in the dispute about priority, accusing Leibniz outrightly of plagiarism. Leibniz’s sharp and well-argued answer in the 1700 Acta (GM 5 340–350) dealt therefore basically with this point, rather than with the issue of foundations. Nieuwentijt’s critique, on the other hand, addressed truly the foundations – it was virtually the only one to do so, if one foregoes Wallis (cf. Nieuwentijt 1694, 1696). He was a meticulous man, who wanted, through his critique of Leibniz’s position as well as of that of Newton and Barrow, to provide at last a rational foundation for the infinitesimal calculus. Even though his

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substantial critic was radical, as we shall see, its tone remained genial, devoid of ad hominem attacks. Leibniz was thus cordially attacked at the very heart of his system. Therefore, he decided to reply as he explained to Jean Bernoulli in June 1695 (GM 2 195): “I almost forgot to say that Bernard Nieuwentijt, a Dutch mathematician, wrote two books against our calculus, which he sent to me; but since he did so speaking about us in a honorable way, I will reply to him in the 1695 Acta in the same way”. In order to remedy the inconsequences of Leibniz’s system, Nieuwentijt in fact proposed another system instead, where the infinitely small, like dx or dy, where not null, whereas their squares, dx2 or dy2, or their products, dx · dy, were. To be sure, this procedure had the advantage of avoiding contradictions in the calculus of the infinitely small. It had, however, the serious inconvenience of being even more inconsistent than Leibniz’s: how could a non-null quantity have a null square? Jean Bernoulli, less politely than Leibniz, abruptly declared to him that Nieuwentijt’s procedures were “ridiculous”: “who could avoid laughing when he so ridiculously reasons about our calculus as a blind man about colors?” (GM 2 203).14 Nevertheless, Leibniz provides an argued answer to Nieuwentijt in the 1695 Acta (GM 5 320–328), which is, for a change, a reply about the basic issue. Addressing directly the latter’s criticism, he explains that he did not want to escape his obligations towards the République des Lettres. He lists three types of criticisms to which he would undertake to reply, the first of which is that: “my method of a differential and summation calculus would face, as the others, the usual difficulty, namely, that it would suppose that one eliminates infinitely small quantities by considering them as if they where null” (GM 5 321). Leibniz’s argumentation is two pronged. On the one hand, he easily shows that Nieuwentijt’s alternative solution did not hold water: “I don’t really see how our learned author has come to believe that a line or extension dx would be a quantity, whereas its square or the product of two such quantities would be nothing” (GM 5 322). On the other hand, in order to justify his own system he simply appeals to a new definition of equality! Leibniz declares, in fact, in this text, that for him the equality sign does not cover what it ordinarily covers (identity, numerical equality, possible superposition by coincidence, etc.) – as he himself had always used it – but, substantially, what is now called “equivalence up to an infinitely small [quantity]” (GM 5 322). From this perspective, to say that x = y is to say that x – y is an infinitely small. This is a relation that is, no doubt, a very modern equivalence relation, which we must thank Leibniz for having so remarkably conceived of; but at the same time, we must acknowledge to what extent such a creation was ad hoc within the context of its conception (see Breger 1992: 80). To be sure, to modify a symbol’s meaning is always possible, provided one applies this modification to all notations

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

where this symbol was previously included. This Leibniz certainly didn’t do, for he needed in his calculus a quality in the ordinary sense. In short, this was no doubt a remarkable technical pirouette by Leibniz the mathematician, which was unable, however, to eliminate the corresponding contradictions in the calculus’ foundations. We should note in this regard that if contemporary mathematics has been able through non-standard analysis to give a meaning (in a certain sense and at the cost of the well-known technical complications) through the Leibnizian infinitely small, curiously enough it has achieved the same regarding Nieuwentijt system – the inherent contradiction in this system only concerns real numbers (which form a field) and not what is today called the “idempotents” of a quotient ring (cf. Petitot 1997).15 As for the quarrel between Newton and Leibniz, first we should note that the real controversy dealt essentially and throughout the debate with the issue of priority and the eventual plagiarism rather than with the foundations’ issue. Since in 1710 both systems led already for nearly forty years to verifiable and verified results, there was no longer reason to enquire, except marginally, about their foundations. This is one factual conclusion to be drawn from this passionate and truly complex quarrel – proportionate in this to the personalities of the two disputants and their strategies, deliberate or not, of non-publication (see Hall 1980). Thus, it is only marginally and against the background of the priority debate that the ontological controversy emerges here. Under these conditions, one can, however, view as decisive two texts by the contenders themselves, each of them describing the steps that led their own discoveries: Leibniz’s Historia et Origo (1713) and Newton’s Account of the Commercium Epistolicum (1715). One should not forget, however, the custom of the time and the personalities of the two characters – none of these texts was publicly acknowledged by their authors: the Historia et Origo remains unpublished by Leibniz, and the Account was published by Newton only anonymously. Furthermore, they are both ad hoc texts having the form of retrospective self-justification, within the framework of a merciless war between two men and two schools. In the Historia et Origo (GM 5 392–413), Leibniz devotes many well documented and precise pages to the “discrete” case (what today would be called “finite differences”), where he explains the schemas of the arithmetical and harmonic triangle and the ensuing elaboration of his two operators ∫ and d. The passage to the continuous case of curves (the essential step in the construction) is evoked only at the end of the text, exclusively through this vague analogical sentence: “but I observed that infinitely small lines occurring in figures were nothing but momentary differences of variable lines (GM 5 407–408).16 An impartial observer would here rightly speak of tour de passe-passe.

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As for Newton, let us repeat, his “reply” and his argumentation dealt essentially with the question of the issue of priority and plagiarism. Nevertheless, he too occasionally attacked Leibniz regarding the very foundation of his discovery, i.e., the infinitesimals. Thus he writes about himself: We have no ideas of infinitely little quantities, and therefore Mr. Newton introduced Fluxions into his Method, that it might proceed by finite quantities as much as possible; it is more natural and geometrical, because founded upon the prima quantitatum nascentium rationes, which have a being in Geometry, whilst Indivisbles, upon which the Differential Method is founded, have no being either in Geometry or in Nature. There are prima quantitatum nascentium rationes, but not quantitates prima nascentes. (Newton, Account 205; Hall 1980: 295)

He further explains his own ontological schema of cinematic type as grounded on the consensus among mathematicians at that time, as well as among the ancients: “Nature generates quantities by continual Flux or Increase; and the Ancient Geometers admitted such a generation of areas and solids, when they drew one line into another by local motion” (ibid.). Although we today tend to question retrospectively the validity of these Newtonian constructions just as that of Leibniz, we must admit that Newton was right in declaring it acceptable for mathematicians of his time. And it is true that Newton’s world system, which allowed for the creation of his fluents and fluxions, did not provoke as much objections as that of Leibniz. Similarly, Newton would be quite right in saying that contrary to the Leibnizian constructions – purportedly co-extensive up to infinity – his own system took into account the infinite in a much more operational way: “When the work succeeds not in finite equations, Mr. Newton has recourse to converging series, and thereby his Method becomes incomparably more universal than that of Mr. Leibniz, which is confined to finite equations” (Hall 1980: 206). On the other hand, as all mathematicians of his time, Newton was in fact incapable of understanding Leibniz’s combinatorial thought – not that he was unwilling to comprehend, which might be understandable, but he was indeed structurally incapable, which is historically dated. When he writes “Mr. Newton doth not place his Method in Forms of Symbols, nor confine himself to any particular sort of symbols for fluents and fluxions” (Hall 1980: 294), he shows how far the symbolic system was for him irrelevant, strictly speaking, in the development of mathematics, and thereby demonstrates his total incomprehension of Leibniz’s approach in the De Arte Combinatoria (GM 5 7–88). In this, Newton merely reflected the unanimous opinion of mathematicians at that time – with the exception of Leibniz, of course – about the negligible role of symbolic representation. One will have to wait until the 1820’–1830’s and the British mathematicians of the Analytical Society, among whom Peacock, Herschel, and Babbage, whose aims

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

were to bring the advanced (symbolic) continental methods of calculus to Cambridge (see for instance Peacock 1830; Babbage 1827) in order to witness the first cracks in these beliefs. Recall that the Platonic conception assuming the reality of mathematical “ideal” objects underlies the denial of the importance of the symbolic system (see Serfati 2005). One can feel even better the ungraspable character of Leibniz’s constructions through the following comment by D’Alembert more than fifty years later: “a quantity is something or it is nothing: if it is something, it has not yet disappeared; if it is nothing, it has literally disappeared. The supposition that there is an intermediate state between these two states is chimerical” (D’Alembert 1763: 249–250).

7.

Variations about the “principle”

The Justification and the letter to Varignon are two of the many writings where he mentions his principle of continuity. The other occurrences are of interest to mathematics, too, for they clarify the various meanings of the concept of “continuity” in mathematics and should therefore be praised by mathematicians as the first in the history of our discipline. Let us recall, first, some of its previous forms in Leibniz, by means of his “Refutations” of Descartes’s Principles of Philosophy of 1697 (GP 4 350–400):17 Therefore, if two hypothetical conditions or two different data continuously approach each other (ad se invicem continue accedunt) then necessarily the results sought (quaesita) or the effects (eventa) of the two conditions also continuously approach each other (in alterum desinat), and finally join each other, and reciprocally (unum in alterum abire et vice-versa). (GP 4 375)

This conception of the principle of continuity is clearly quite close to that of the mathematical continuity of a function or of the convergence of a sequence in the modern sense. It is not, however, the closest of the conceptions supposed to underlie the passage discrete-continuous in the differential calculus examined above. There has been a second stage regarding the principle, going from the letter to Varignon of 1702 to the letter to Wolff of 1713 (GM 5 382–387). This wellknown letter, which was quite late,18 repeats in substance the former letter; we will therefore only comment on the last part of the former as well as the Justification. In this exceptionally clear text, Leibniz explains that it was in 1687 that he had for the first time proposed the principle of continuity in the Nouvelles de la République des Lettres.19 From the Justification, consider the following two passages:

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Thus, one finds in the ordinary algebraic calculus the traces of the transcendental calculus of differences … Even the algebraic calculus could not dispense with them if it should preserve its advantages … And this advantage, when applied to physics and especially to the laws of movement, consists partly in what I call the law of Continuity, which I use for a long time as a principle of discovery in physics, and as a very convenient test for checking whether certain proposed rules are all right. I had published an instance of this principle several years ago in the Nouvelles de la République des Lettres, taking equality as a particular case of inequality and rest as a particular case of movement and parallelism as a case of convergence, etc. … assuming not that the difference of magnitudes that become equal is already nothing, but that it is in the process of disappearing and, similarly, that the movement is not absolutely nothing, but that it is about to be.  (GM 4 105) Nevertheless, although it’s not rigorously true that rest is a kind of movement or that equality is a kind of inequality, just as it is not true that the circle is a kind of regular polygon, one can say that rest, equality and circle terminate the movements, the inequalities and the regular polygons, which through a continuous modification reach them while disappearing. And although these terminations are exclusive, that is, not strictly comprised in the variations they bound by them, they have nevertheless their properties, as if they were comprised following the language of infinites or infinitesimals, which takes the circle, for instance, for a regular polygon whose number of sides is infinite. Otherwise the law of continuity would be violated; i.e., since one passes from the polygons to the circle by continuous modification and without a jump, it is necessary also that no jump be made in the passage from the properties of the polygons to that of the circle.  (GM 4 106)

The second conception may be considered as definitive for Leibniz and therefore our discussion of the principle of continuity will focus on it. First, notice that if this principle had been absolutely necessary for the development of the “New Calculus”, it would have been such that for its creator the principle’s validity could only come from mathematics or logic. On the other hand, its applications having to do also, for Leibniz, with a field beyond mathematics, the principle pertained to an organically superior register. Thus, its origin and scope were both metaphysical, although Leibniz affirmed the contrary, especially in the letter to Varignon (GM 4 91). Occasionally, returning to the question in the letter to Wolff, Leibniz grants his principle a metaphysical character, this time without any hesitation: “the usage of the canons of the true metaphysics (which goes beyond verbal nomenclatures) is much larger in mathematics, in analysis and even in geometry than one usually thinks”(GM 5 382).20 Granger (1994: 234) invokes in this regard a “meta-principle governing symbolic thought”:

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

It is in fact first as a guide of symbolic thought that we have met it [the principle of continuity]. But it is a principle which, vis à vis mathematics, is really metatheoretical, originating even at a higher point, since Leibniz does not hesitate to refer to it sometimes as ‘the principle of general order’ par excellence; and if it succeeds both in geometry and in the whole of physics, it is because ‘the supreme wisdom which is the source of all things acts as a perfect geometer’.21

If we examine it from other perspectives, this Leibnizian principle is also a principle of “permanence of mathematical essences”, or, in the words of Granger (1994: 238), a principle of “existence and closure”: But Leibniz’s analysis … grants the notion of continuity a content and a generative power that make the law of continuity in mathematics a principle of existence and closure. Every natural transformation is continuous; and by making our viewpoint on the same object vary, it conserves its essence, so that the terminus exclusivus, however different it may seem to be from the stages out of which it comes, must be considered as a participant of the same nature as the termini inclusivi. Evidently such hypotheses restrict the field of Analysis, just as Cartesian algebraicity has restricted a priori the field of Geometry.

On this point, Granger is in complete agreement with Vuillemin, who had on his part spoken of “the permanence of the same reason throughout all the transition” (Vuillemin 1962: 39).22 From this viewpoint, one should notice to what extent the principle of the “conservation of inequalities through the passage to the limit”, mentioned at the beginning of this article and to be further discussed below, is a perfect illustration of the above mentioned idea of the “permanence of the same”. The “object” (for Granger) or the “reason” (for Vuillemin) are here the inequality in the broad sense of less or equal, an objectified entity that remains and maintains itself throughout all the process of change. By the way, under these conditions, the principle is interpreted by Leibniz himself as the explicit assumption of a contradiction. For rest is, in fact, nothing but a kind of movement. It is not a movement (Justification, GM 4 106; letter to Varignon, GM 4 93–94). Likewise, the circle is not a polygon. To be sure, some of the properties of the changing being are transferred sometimes to the ultimate form that achieves the change, but Leibniz wants to grant it much more when he asserts that the latter is, in all cases, of the same nature as that which precedes it. Here Leibniz, for whose mathematics the law of continuity is absolutely necessary, requires from it much more, in my opinion. In any case, everything can be seen as having evolved as if the vision of this organically overarching principle was in fact for him the assumption of the following contradiction: in part, a being is what it is not. The last aspect of our discussion leads us back more directly and perhaps more concretely to mathematics. In mathematics, the principle of continuity

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cannot deploy itself except at the symbolic level. This is an essential characteristic, albeit somewhat hidden in Leibniz, in spite of his concern for issues of notation. To invoke the law of continuity as organically superior corresponds, as we have seen, to a need dictated by the constitution of Leibniz’s mathematical calculus of differences. But the question is how to employ it effectively, how to realize it in mathematics? The above example ( ∫ dx = x) provides the answer: the combinatorial “form” of the property remains unchanged, be it in terms of sequences or of curves. Thus, the notation plays here the role of pivot, of pole, of paradigm. This is something that cannot escape, albeit negatively, someone who seriously analyzes the development of mathematical symbolism (see Serfati 2005). Within the framework of a rhetorical form of mathematical writing, à la Cardan, there wouldn’t have been in fact any effective way of embodying this metaphysical principle. Without fear of being shown to be wrong, one can affirm that there wouldn’t have been any effective future (i.e., excluding vague consequences and non-falsifiable assertions which are too general to be contradicted) for the proclamation of any Leibnizian principle of continuity in mathematics, if the latter had not been written, for 50 years already at that time, in the symbolic form that we are familiar with.

8.

Architectonics?

In light of these several examples we can now better appreciate Leibniz’s stand visà-vis a central question, underlying this study, namely the architectonic character in mathematical thought of the use of signs. Prima facie, Leibniz’s reply – belonging to his philosophy and metaphysics – amounts to the place God holds in the economy of his system. On this issue, which is coextensive with that of the infinite, I follow here the analyses of Granger (1994), Vuillemin (1962), and Dascal (1978). It is clear that, whatever Leibniz claims, the sign cannot contain all the attributes of the object. This might seem true in mathematics when the number of attributes is finite and small. Even this, however, and even in mathematics, can be contested. The issue in question here is clearly that of memory and its possible failures, that is – given that the young Descartes (Rule III) had already mentioned that the mind’s gaze cannot in any case contemplate more than two things at once (Descartes 1628: Rule III, 9).23 For the Descartes of the Regulae the intuitus can only have as its initial intuition a single attribute, and thereafter and each time its connection with another. What if, as in the example of the chiliogone (a regular polygon of a thousand sides), itself taken by Leibniz from Descartes,24 the number of attributes although finite becomes very large? Could one accept that even

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

in this finite case the sign fulfills only certain psychotechnic requirements of codification, such as remembering, recalling, and communicating? Whatever the reply might be, if the number of attributes is infinite, it is apparent that the sign used by the geometer cannot encompass all of them. What are then the function and status of the sign? Leibniz’s answer is that the noncomprehensiveness of the object’s attributes in the sign obtains only for our finite understanding. For the divine understanding, everything is grasped outside of time and the sign is a mask for us due to our human weakness. It is in this respect, however, a necessary mask, that of every “thought that moves within a system of signs” (Granger 1994: 203). Vuillemin (1962: 44) had also pointed out this fact: To know a priori the possible in transfinite multiplicities would be, at one and the same time, to distinguish an actual infinity of elementary ideas and to collect them in an intuition that only God has. Since we are finite substances, we need a substitute to compensate the insufficiency of our vision, and this substitute is the algorithm. God speaks to us. But the imagination is part of what is most essential in reasoning. One can neither grasp actual infinity in the sense of modern logicism and Cantor’s set theory, nor to reduce it to intuitively undefined processes: it is only accessible through finite systems of symbols.

Let us ask again: is the use of signs in its various mathematical modalities, e.g., that of the principle of continuity, architectonic? In order to reply, I will try to follow Granger’s analysis, which leads us, in Leibniz, to the distinction between contingent and necessary truths – the contingent truths being inaccessible for us even if for God they are analytic. Hence, the use of signs is in their case architectonic, that is, constitutive of thought in physics, for instance, since in physics all truths are truths of experience. Mathematical truths, however, belong to the domain of the necessary. Therefore, even though they “envelop” the infinite (as all those truths derived for Leibniz from his principle of continuity), they behave for us as if they were only accessible by means of signs, whose use is thus architectonic for us, or as Granger (1994: 230–231) puts it, “subjectively” architectonic. The guarantee of their correct use depends then only upon God. In this way, Leibniz himself would have resolved metaphysically the ‘paradox’ underlying his mathematical New Calculus, while at the same time he justified the validity of the notion of “blind thought”. In the following six points I will attempt to assemble and sum up Leibniz’s views on his principle of continuity and his “symbolic thought”, as we have unveiled them – explicitly in his philosophical writings and implicitly in the texts written for mathematicians. First, Leibniz claims that for any determined problem, there should be a solution. That is to say, for Leibniz, the concept or nature

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of a problem we would today call “well-formulated” is such that there is a method to find its solution. One could well describe curves whose intersection could give the solution of these problems, but I demand a solution giving me the value of the unknown. I request you, monsieur, to think about it, for you are aware that these are true determined problems and there should be a method in nature for solving them.  (Leibniz to Huygens, September 8th 1679; B 568)

Second, Leibniz forces us to admit that, however apparently ungrounded in re, the theory of infinitesimals provides the solution, for its results are in fact verifiable and exact. Nevertheless (third point), Leibniz has to resign himself to admit that we cannot ground de jure this method. But, he says, this is only due to our smallness and finitude vis-à-vis God’s knowledge. The divine understanding has no need of fictions or infinitesimals in order to perceive, for example, the true value of a quadrature. Hence, for us, the true foundation of the use of infinitesimals (fourth point) resides in the metaphysical principle of continuity, which operates in and through symbolic notation. The principle is in fact built around a simultaneous split of meaning (e.g., discontinuous-continuous) and the permanence of symbolic mathematical form (e.g., ∫ dx). In this way, “blind thought” admirably embodies the principle of continuity. It follows that (fifth point) the use of the symbolic system is necessary not only for psychotechnic reasons; it is truly architectonic, indispensable for the constitution of mathematical thought. The sixth, final and crucial point is that, under these conditions, the capacity of the mathematician to remain at the symbolic level, to continue to work at that level, retarding as much as possible the appeal to meanings, is a primordial prescription for Leibniz – deriving from what he calls the “autarchic” character of the sign: One must know that characters are more perfect the more they are autarchic, in such a way that all the consequences can be derived from them. (C 284)25

Dascal (1978: 222) comments on this statement, very to the point, as follows: “what the notion of autarchy suggests here is, above all, the independence of an adequate symbolic system – independence vis-à-vis higher mental operations”. And he adds: [Leibniz] compares the intelligent use of words (and other signs) with the use of tokens …, not by virtue of the fact that the latter refer one constantly to the ideas they are supposed to represent, but rather because one can perform with the tokens themselves every calculus operation one wishes without shifting immediately to the level of ideas. In fact, the possibility of postponing indefinitely this shift towards the ideas is what Leibniz highlights. (ibid.)

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

The validity of this capacity – so well described by Dascal – to remain at the level of the signifier by postponing as long as one wishes the return to the signified, relies, of course, for Leibniz, on the fact that “at the last moment”, the moment of returning to the meanings, the mathematician cannot fail (for him) to constantly uncover mathematically valid results. Such a certainty is grounded upon what today we would call a one-one correspondence between signifier(s) and signified(s), which, even if it escapes us (since one cannot exhaust all attributes of the thing in a sign), is, for Leibniz, ultimately ensured by God. On the other hand, this is actually the practice of mathematicians – Leibniz’s contemporaries as well as ours – a practice that does not make any reference to an explicit metaphysics, as it was the case for Leibniz. After Leibniz, indeed, mathematicians naturally arrived at the following factual conclusion: in research as well as creation, the symbolic text has become the only locus of experience or the almost only locus of mathematical work, the significations not being rendered for the most part in natural language, neither explicitly nor implicitly in the internal form of a verbally formulated thought (see Serfati 2005: 399–400). From the seventeenth century onwards, the unconscious learning of the methods of mathematical research included these necessary components: to think directly and quickly in the symbolic system, which allows one to avoid what the mathematician considers the slowness and obscurity of verbal thinking – a fact explicitly acknowledged by some ripe mathematical minds, e.g., Hadamard26 and Einstein.27 And this capacity of direct access to the symbolic is today implicitly regarded as a necessary condition for every mathematical endeavor, be it in research or teaching.

9. The principle of continuity and some of its consequences in current mathematics: The schema of “proof by continuity” Let us return to the primary question raised in our introduction: In what way can a principle which is so metaphysical and so situated in the 17th century, still continue to govern a significant part of modern mathematicians’ behavior today, through what we have dubbed an “attitude of continuity”? The answer will pass through our opening example to which four other examples will be added. In each of them we have highlighted in italics the crucial internal articulation of this very peculiar mode of organization of mathematical thought – the “expectancy of continuity”: (1a) If un is the general term of a real sequence so that un ≥ a for every n,  and if un converges, then �im u n ≥ a . n

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(1b) If un is the general term of a real sequence so that un > a for every n,  and if un converges, then �im u n > a. n

(2) If fn : I → E is a sequence of continuous functions over the interval I of IR, with values in the metric space E, and if the sequence fn converges,  then �im ��n is continuous over I. n

n+1 )è nθ 2 cos( ) if θ ∉ 2π · Z, (3) ∑ cos k θ = θ 2 0≤ k ≤n sin( ) 2 and = n + 1 if not, for example if θ = 0. Then n +1 sin( )θ nθ 2 lim cos( ) = n + 1 θ →0 θ 2 sin( ) 2 sin(

(4) The orthoptic curve28 of an ellipse is a circle whose center lies in the middle of its two foci. Therefore, it is sufficient to know one of its points. When one of the foci distances itself indefinitely along the (supposedly fixed) axis, the ellipse becomes a parabola and the orthoptic curve of a parabola is therefore a circle whose center is indefinitely far over the axis, hence a line perpendicular to the axis (x = –p), therefore parallel to the directrix, of which it is likewise sufficient to know one point.29 (5) If f is a real function, which is continuous over ]–1, 1[ such that for every a and b satisfying –1 < a < b < 1, one obtains b f 2 (t ) ∫ dt = 0, then f = 0. 1 − t2 a

In present day terms, a first approach provided by the Leibnizian principle of continuity for our various “methodological guides” could be the following, corresponding to the case of discrete sequence fn (P denotes a property): If P(fn) is true (terminus inclusivus) and if the sequence fn converges towards f, then P(f) is true (terminus exclusivus).

This formulation is appropriate for the case of sequences but not for that of the ellipse. If, then, out of our five examples, we try now to abstract a de-contextualized formulation of the “methodological guide”, we are led to our initial statement: “every property, if it is always true of a changing being, transfers itself legitimately to the last being in which it completes itself at the end of a continuous process”. However, as we have just seen in examining these six cases, this methodological

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

guide, strictly speaking, leads to results which are either true (examples (1a), (3), (4), (5)) or false (examples (1b) and (2)). Therefore, it is not a mathematical epistemological principle in the ordinary sense, and we entirely agree with Leibniz’s “metaphysical” discourse concerning the nature of the principle of continuity.

10.

The continuity schema and “mathematical intuition”

What I would henceforth call the “continuity schema” can be now characterized in terms of the four following properties: 1. The schema is different from the problematic of the “continuum” as an object (be it a Cantor object or otherwise). Continuity is here a schema, a procedure. It is not the fact of being a continuum. 2. The schema appeared in mathematics with Leibniz and was unknown before him. Euclid didn’t consider it necessary to include in his axiomatics anything related to continuity. It is only after a long historical reflection that the astute Hilbert, in the way of Klein and Pasch, adds to his axiomatics of geometry of 1899 specific axioms called axioms of continuity – including Archimedes’s axiom which did not appear in Euclid and whose necessity was imperative for the method of exhaustion. At that point, however, the procedure had not been acknowledged as deriving from the schema. Only retrospectively did it reveal itself to us as an axiom of continuity. The Archimedean method of exhaustion had certainly been a numerical approximation procedure, which was in fact extended up to the 17th century by the ‘Circle-squarers’ (those who attempted to square the circle), including Viète. But from the present viewpoint it lacked an essential element of Leibniz’s conceptualization, namely the “permanence of the same”. In the exhaustion procedure one deals with approximations; one considers the areas of the regular polygon inscribed in a circle and circumscribing it. The areas, easily calculable, of these very polygons approach that of the circle insofar as the difference may become “smaller than any given number”. But the polygons remain polygons, and the circle, a circle, contrary to the Leibnizian conception examined above. This method has been utterly refined by Viète and Ludolph leading to approximations of π of up to 30 decimals. But it didn’t allow to go further and the result could not be decisively improved other than by a change of method. This is what the introduction of the new Leibnizian infinitesimals allowed for. By foregrounding his principle, he changed the level of discourse and made obsolete the previous techniques in a way that would have been unconceivable for the earlier squarers.

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Let us repeat, emphasizing Leibniz’s glory: these epistemological procedures, this “continuity schema” seen as interiorized methodological guide, this specific conception of continuity as a regulative principle – all these concepts that are so familiar to present day mathematicians that one can hardly imagine that they were not so before, were in fact ignored before him, especially by Descartes.30 Before Leibniz, mathematicians did not think mathematical continuity. This very way of posing the issue had no sense, and what Descartes termed continuity does not belong to it. After Leibniz, they have definitely undertaken to conceive continuity as an indispensable figure of thought and to organize around it related concepts. 3. The schema developed immediately after Leibniz in geometry. To be sure, the vast set of projective properties of the conic curves, easily deduced from those of the circle through the continuity of a central projection, led the first geometers of the time to the feeling that they were applying an organically superior principle, which is always valid. Afterwards, however, even in geometry, it was an anarchic uncontrolled development. Thus, the “principle of contingent relations” of Monge (1827)31 becomes, for Jean-Victor Poncelet, the “principle of continuity” (Poncelet 1865–1866). Poncelet, attempting to build, as a pure geometer, a complex projective geometry, performed a true hypostasis of continuity, transforming it in an organically superior principle, ruling by principle and in all cases, the geometrical properties. He wanted to develop a sketch of what is now called the complex projective plane P2 (C), by introducing simultaneously points at infinity and points having complex coordinates, cyclical points and umbilical lines – a geometry, however, he wanted to study without calculations. He intended himself to extend to complex algebraic curves (complex coordinates) with complex parameters all the properties of real curves with real parameters – and this without calculations. He does not demonstrate his principle, which he places at the pantheon of higher order dispositions; but, like Leibniz, he shows many of its “experimental” verifications. The reasons for such an achievement can be easily understood today. If a property is true of a real curve, it entails a relation R(a1, a2,..., ak) = 0, which is valid for certain values of the real parameters. If R is algebraic, as R = 0 over an open subset of IRk, then R is also zero over Ck and the property remains true everywhere. Of course, this is only true for algebraic relations. Cauchy (1825–1826: 359) who was called to comment upon Poncelet’s works, as a good analyst, considered that this voluntaristic scientific strategy was merely a “strong induction” – an expression that indicates his suspicion towards metaphysical presuppositions. One can better understand Cauchy’s reticence by recalling how he himself had failed in his work due to an intuitive application – this time, false – of the schema.

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

4. The schema is today omnipresent as a framework of thought in mathematical research. It is, or it should be, an almost instinctive action for a contemporary mathematician to ask himself the question of whether a new property or form “passes to the limit”. This is, no doubt, the most essential point, which will be illustrated later. In order to formalize the “continuous process” appearing in the formulation of the schema, mathematicians have developed step by step a preliminary framework within which one can think such a process and test whether or not it is continuous. Hence the construction of topological spaces having as their main types metric and normed spaces.32 A topological space leads then to the central concept of continuous function, to which the case of the sequences is immediately subsumed. The application of the schema becomes thus coextensive with the examination of those “properties” (equalities, inequalities, relations, membership, difference, similitude), which are conserved by such a continuous function. Let us turn now to a couple of examples. The following statement is precise: the uniform convergence over every compact (of an open subset of IRn) to any other space is a metrizable concept. In all likelihood, it derives from the schema, provided one understands that what is important is that the limit be also continuous. It is not convergence as such that is decisive, but the fact that it is the convergence (the emergence) of the same. This “same” can, however, be itself different from the continuous character. Hence the question, does the convergence (in a sense to be defined) of a sequence of functions of a certain type preserve its type, is a natural one, and the replies will differ. For instance, to the question, does the uniform convergence of step functions preserve the step character, the answer is negative – there are “too little” functions of this type. If, however, one replaces the set of these functions by its adherence with respect to the uniform metric one obtains piecewise continuous functions whose character is in fact preserved. In contrast, the question whether the uniform convergence over every compact of continuous functions preserve continuity, which is just as natural, has a direct positive reply. Another example: When one defines a new concept, it is nowadays considered to be “interesting” to raise questions of continuity regarding this concept. For example, we know that if A is an invertible square matrix, the application A → A–1, is continuous. Does the same happen with pseudo-invertible matrices? Is it also the case when E is an infinite Banach space and u → u–1 (u ∈ GL(E))? As one can see, contrary to Leibniz’s views, the use of the schema not always leads to a positive answer – which is not surprising today. The principle, however, is valuable, in fact indispensable, in order to engender certain new ideas regarding properties to be demonstrated, namely those that “passed the test of ” continuity.

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The principle does institute a dialectics of passage that characterizes with precision Leibniz’s problematic. If, after the test, the property turns out to be true, one has a further property, resulting from a “proof by continuity”. If it turns out to be false, as in a famous example from Cauchy33 it paves the way towards the emergence of new concepts, e.g., uniform convergence, such that, within the new framework, the proof by continuity can still function. Thus, in Cauchy’s example, uniform convergence appears as a concept truly generated by a lack – the lack resulting from various historical counter-examples of simply convergent sequence of continuous functions, whose limit is not continuous. Nowadays, therefore, 300 years after Leibniz, the “principle of continuity” belongs to an interiorized set of methodological rules. Like the principle of symmetry (considered as normative) or that of generalization-extension (considered as a standard procedure of construction of algebraic or topological objects), they constitute part of the daily mathematical practice. Yet, they are never made explicit as such. Sometimes there is talk about this or that proof by continuity, but no manual discusses the principle of such proofs. Around such principles, that which is ordinarily called “mathematical intuition” arises. Epistemologically speaking, it seems to me important to point out that, underlying the complexity and variety of contemporary mathematical objects and structures, there are certain undisputed methodological invariants.

Notes * This chapter is a modified version of “Mathématique et métaphysique chez Leibniz: Le principe de continuité”, published in the Proceedings of the Colloquium L’un et le Multiple in honor of Jules Vuillemin (Clermont-Ferrand 2000). 1. These are the names I have given (Serfati 2005) to the operation signs regardless of considerations of meaning. For example, X + Y (cross), X · Y (point), ε (vée). 2. I propose to call such operators ‘préhenseurs’. This term can be understood as referring to the sign of a certain operation involving one argument For example, + (cross) in “X + Z” is a two-places assembler, whereas (vée) in � − 7 is a one-place assembler or préhenseur. 3. The first literal exponents, which were necessary for his notation, had been elaborated by Newton only in 1676. 4. In modern terms, Bernoulli intended to find a differential equation satisfied by the sum of a power series. 5. If E is set and f an application of E over E, current notation has it f(2) = f0 f, and, by recurrence, f(n) = f(n–1)0 f. This notation is therefore due to Leibniz. 6. “It [Leibniz’s conception of differentiation] has at least the merit of replacing incomparable quantities by operations, which can thus be inversed thereby establishing the reciprocity of differentiation and integration” (Vuillemin 1962: 32).

The principle of continuity and the ‘paradox’ of Leibnizian mathematics

7. Jacques (or James) Bernoulli to Leibniz, February 28th 1705 (GM 2 97). 8. Jean Bernoulli to Leibniz, April 20th 1695 (GM 2 171). 9. The correspondence between Leibniz and Huygens, interrupted between 1680 and 1688, continued without interruption since February 1690 within the framework of Leibniz’s “New Calculus”. 10. This text by Leibniz accompanies a letter Varignon wrote to Leibniz from Paris on May 23rd 1702 (GM 4 104–106). 11. Galloy had received the nickname chameleon due to his changing loyalties, sometimes with Leibniz sometimes with Newton. Leibniz’s correspondence with Galloy had begun already in Paris in 1675 (GM 1 176). 12. For instance, Boole (1854); cf. Serfati (2000). 13. In modern terms, this formula permits in fact to show that in all normed vector space, the nature of the sequence having as its general term un is the same as that of the series Σzn, where zn = un+1 – un. The theorem is used today in two directions (from sequences to series or vice versa). 14. “Quae mihi narras de Bernhardo Nieuwentiit, omnino lepida sunt. Ecquis a risu abstinere posset, cum ille tam ridicule de nostro Calculo, velut caecus de coloribus, ratiocinatur?” (GM 2 203). 15. Cf. Jean Petitot (1997). Written in a modern terminology, this article remarkably explains the difference between the systems of Leibniz and Nieuwentijt. 16. “Observabat autem lineas infinite parvas in figuris occurentes nihil aliud esse quam differentias momentaneas linearum variantium”. 17. Animadversiones in partem generalem Principiorum Cartesianum (GP 4 350–400). The contents of this text are close to those of the appendix to the letter to Bayle of 1687 (GP 3 51). 18. Lettre au Célèbre Christian Wolff, Professeur de Mathématiques à Halle, sur la science de l’infini (Acta Euditorum Supplementa 1713, t. V, section 6; GM 5 382–387). 19. Appendix to the letter to Bayle published by that journal (GP 3 51). 20. “Porro hoc argumentandi genus, etsi Metaphysicum magis quam Mathematicum videatur, tamen firmum est: et alioqui Canonum Verae Metaphysicae (quae ultra vocabulorum nomenclaturas procedit) major est usus in Mathesi, in Analysi, in ipsa geometria, quam vulgo putatur” (GM 5 382). 21. All of the following quotes from Leibniz are from the appendix to the letter to Bayle of 1687 (GP 3 52). 22. “The same is true of the infinitesimal calculus which is based upon the conservation of the similitude of the characteristic triangle during its disappearance, and it has been correctly pointed out that the Leibnizian continuity does not consist in being able to pass through all the intermediate steps but rather in preserving the permanence of the same reason throughout the whole transition” (Vuillemin 1962: 39). 23. Each of these two things were for Descartes minimal elements, undecomposable for perception as well as for the mind’s gaze, which he called ‘simple natures’. See Serfati (1994: 69–71). 24. “Thus when I think of a chiliogon, or a polygon of a thousand equal sides, I do not always consider the nature of a side and of equality and of a thousand (or the cube of ten), but I use

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these words, whose meaning appears obscurely and imperfectly to the mind, in place of the ideas which I have of them, because I remember that I know the meaning of the words but that their interpretation is not necessary for the present judgment” (A VI 4 587; L 232). 25. This is a quote from Leibniz’s text “On the universal language”, used by Dascal (1978: 219). 26. See particularly the section “Words and thought without words” in the chapter “Discovery as synthesis” in Hadamard (1975: 68–71). 27. On Einstein’s position, see the chapter “Scientific creation according to Poincaré and Einstein”, in Paty (1999: 241–280). 28. The set of points whence it is possible to draw two orthogonal tangents to the ellipse. 29. This example is provided by Leibniz himself following the passage quoted form the appendix to the letter to Bayle: “We know that one can assume that an ellipse can approach as much as one wishes a parabola, so that the difference between the ellipse and the parabola can become smaller than any given difference, provided one of the foci of the ellipse be sufficiently far from the other, for then the rays coming from this focus differ from the parallel rays as little as one wishes, and consequently all geometrical theorems which are true of the ellipse in general will be applicable to the parabola if one considers the latter as a ellipse, such that one of its foci is infinitely far or (avoiding this expression) as a figure that differs from some ellipse less than any given difference” (GP 3 52). 30. Descartes, however, was himself impregnated with continuity. But it was in a different sense, namely that of a certain “solidarity”, i.e., the absence of “gaps” (see Serfati 2008b). 31. For an analysis of the principle of contingent relations, see Chasles (1989: 204ff.). 32. Chronologically, the development has occurred inversely. 33. This is a well known question in the history of mathematics. See, for instance, Thompson, Bruckner and Bruckner (2001: 393): “As late as 1823 Cauchy believed that a convergent series of continuous functions could be integrated term by term. Similarly Cauchy believed that has a convergent series of continuous functions has a continuous sum. Abel provided a counterexample in 1826. It may have been Weierstrass who first recognized the importance of uniform convergence in the middle of the nineteenth century”. See also Hawkins (1975: 20–21).

References Babbage, C. 1827. “On the influence of signs in mathematical reasoning”. Transactions of the Cambridge Philosophical Society, vol. II. Boole, G. 1854. An Investigation of the Laws of Thought on which are founded the Mathematical Theory of Logic and Probabilities. London: MacMillan. [Reprinted in 1958, New York: Dover]. Breger, H. 1992. “Le continu chez Leibniz”. In J. M. Salanskis and H. Sinaceur (eds), Le labirynthe du continu. Paris: Springer Verlag, 76–84. Cartan, H. 1967. Calcul différentiel. Paris: Hermann. Cauchy, A. 1825–1826. Géométrie. Rapport à l’Académie royale des sciences. Annales de Gergonne, 16: 359.

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Chasles, M. 1837. Aperçu historique sur l’origine et le développement des méthodes en géométrie (…). Bruxelles: Hayez [Reprinted in 1989, Paris: Gabay]. D’Alembert, J. le Rond. 1763. Mélanges de littérature, d’histoire et de philosophie. Amsterdam: Zacharie Chatelain. Dascal, M. 1978. La sémiologie de Leibniz. Paris: Aubier‑Montaigne. Descartes, R. 1628. Regulae ad Directionem Ingenii. In C. Adam and P. Tannery (eds), Oeuvres de Descartes. Paris: Vrin, vol. X, 349–469. Granger, G. 1994 “Philosophie et mathématiques leibniziennes”. In Formes, Opérations, Objets. Paris: Vrin, 199–240. Hadamard, J. 1975. Essai sur la psychologie de l’invention dans le domaine mathématique. Paris: Gauthier Villars. Hall, R. A. 1980. Philosophers at War – The Quarrel Between Newton and Leibniz. Cambridge: Cambridge University Press. Hawkins, T. 1975. Lebesgue’s Theory of Integration. AMS Chelsea Publishing, Volume 282. Leibniz, G. W. 1666. Dissertatio de Arte Combinatoria. GM 5 7–88. [= Arte Combinatoria] Leibniz, G. W. 1684. Nova Methodus pro Maximis et Minimis, itemque Tangentius, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus. GM 5 220–226. [= Nova Methodus] Leibniz, G. W. 1692. Animadversiones in partem generalem Principiorum Cartesianum. GP 4 350–400. Leibniz, G. W. 1694. Considérations sur la différence qu’il y a entre l’analyse ordinaire et le nouveau calcul des transcendantes. Journal des Sçavans 1694; GM 5 306–308. [= Considérations] Leibniz, G. W. 1695. Responsio ad nonnullas difficultates ad DN. Bernardo Niewentijt circa methodum differentialem seu infinitesimalem motu. GM 5 320–329. [= 1695 Acta] Leibniz, G. W. 1700. G. G. Leibnitii Responsio ad Dn. Nic. Fatii Duillerii imputationes. Accessit nova Artis Analyticae promotio specimine indicata, dum designatione per numeros assumtitios loco literarum, Algebra ex Combinatoria Arte lucem capit. GM 5 340–350. [= 1700 Acta] Leibniz, G. W. 1702. Varignon-Leibniz correspondence. GM 4 91–97. Leibniz, G. W. 1702. Justification du Calcul des infinitésimales par celui de l’Algèbre ordinaire. GM 4 104–106. [= Justification] Leibniz, G. W. 1713. Historia et Origo Calculi differentialis. GM 5 392–413. [= Historia et Origo] Monge, G. 1827. Géométrie descriptive. Paris: Bachelier [Reprinted in 1989. Paris: Gabay]. Nieuwentijt, B. 1694. Considerationes circa analyseos ad quantitates infinite parvas applicatae principia, et calculi differentialis usum in resolvendis problematibus geometricis. Amsterdam: Wolters. Nieuwentijt, B. 1696. Considerationes secundae circa calculi differentialis principia et responsio ad virum nobilissimum G. G. Leibnitum. Amsterdam: Wolters. Paty, M. 1999. “La création scientifique selon Poincaré et Einstein”. In M. Serfati (ed), La recherche de la vérité. Paris: A.C.L. – Les editions du kangourou, 241–280. Peacock, G. 1830. A Treatise on Algebra. 2 vol. London. [Reprinted in 2005, New York: Dover]. Petitot, J. 1997. Les infinitésimales comme éléments nilpotents: actualité du débat Nieuwentijt vs. Leibniz. Preprint, Analyse et Mathématique (CAMS N° 139). Paris: Centre de Mathématiques Sociales.

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Poncelet, J.-V. 1865–1866. Traité des propriétés projectives des figures. Paris: Gauthier-Villars (2 vol.). [Reprinted in 1995, Paris: Gabay]. Serfati, M. 1994. “Regulae et mathématiques”. Theoria – Segunda Epoca 9(21): 61–108. Serfati, M. 2000. “La doctrine des chances: Le calcul des probabilités”. Mathématiques et Sciences Humaines 150: 49–79. Serfati, M. 2001. “Mathématiques et pensée symbolique chez Leibniz”. In M. Blay and M. Serfati (eds), Mathématiques et physique leibniziennes. Revue d’Histoire des Sciences 54(2): 165–221. Serfati, M. 2005. La révolution symbolique. La constitution de l'écriture symbolique mathématique. Paris: Pétra. Serfati, M. 2008a. “Symbolic inventiveness and «irrationalist» practices in Leibniz’ mathematics”. In M. Dascal (ed), Leibniz: What Kind of Rationalist?. Dordrecht: Springer, 125–139. Serfati, M. 2008b. “Constructivismes et obscurités dans la Géométrie de Descartes”. In M. Serfati and D. Descotes (eds), Mathématiciens français du XVIIe siècle: Pascal, Descartes, Fermat. Clermont-Ferrand: Presses Universitaires Blaise Pascal, 11–44. Thompson, B. S., Bruckner, J. B., and Bruckner, A. M. 2001. Elementary Real Analysis. Upper Saddle River, NJ: Prentice Hall. Vuillemin, J. 1962. La philosophie de l’algèbre. Paris: Presses Universitaires de France.

chapter 2

Geometrization or mathematization Christiaan Huygens’s critiques of infinitesimal analysis in his correspondence with Leibniz Fabien Chareix

The rise of new infinitesimal methods at the end of the seventeenth century accelerated the change of the Galilean style in natural philosophy. The historiography of this turning point in physics usually understands it as a continuous and quite fast change in the way physicists dealt with coordinates, motions, accelerations and their differential aspects. Accordingly, twenty years after Leibniz gave the rules of infinitesimal calculus, followed by Bernoulli,1 L’Hospital,2 or Varignon,3 the change was completed and gave birth to a rational or analytical mechanics, as if the end of the so called ‘geometrization’ of nature had been a change without any discussion at all.4 Letters are precisely the place for such discussions. At the time in which this revolution took place, some physicists strongly rejected the new methods,5 though using them in an informal way, because nothing could be said about the legitimacy of the infinitesimal quantities. Christiaan Huygens, in his correspondence with Leibniz and other mathematicians, was one such physicist. His attachment to geometrical methods led him to define precisely what, in his mind, was the meaning of natural philosophy. This attitude can be related to the way Huygens rejected Newton’s theory of gravity as a purely mathematical, not physical, account of matter and motion. He thus provides an original view on an internal resistance to theory change in those times of permanent scientific evolution. It is a recurrent topic in the philosophical and historical account of theory change, that the revision of belief almost never takes place in the blink of an eye. A single set of observations, providing a new class of evidence, has to be historically grounded before it can perform a massive belief revision. A common example of such a situation has been given by Albert van Helden (1983) in a well known episode of the history of technology: the birth of scientific instruments. After Galileo’s reappraisal of the function that a telescope could fulfill

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in astronomy, “the practise of astronomy, says A. van Helden, changed surprisingly little during the early decades of the telescope. The role of astronomers remained almost exclusively the measuring of positions” (ibid.: 52). The very same conclusions could be drawn from the gap between the expression of all three Kepler’s rules for planetary motion, even mixed up with confusing irrational contents, and the use of these laws as the masterpiece of modern astronomy. Galileo himself never accepted the Keplerian rules and wrote a complete book on the co­mets devoted to the refutation of elliptical motion. One possible reason for such a gap in belief revision has been given, in the case of Galileo, by Erwin Panofsky (1992) in a book which studies the relationships between Galileo’s scientific ideas and his preconceptions in æsthetics. In the case of scientific intruments, A. van Helden concludes that “only after 1640 can we say that all astronomers routinely observed the heavens with research telescopes, and not until a decade later do we notice a belief that better telescopes will reveal new phenomena in the heavens” (van Helden 1983: 52). Christiaan Huygens, though he certainly knew how power­ful was the tool he had tested on some classical problems, refused to acknow­ledge it, until his death put an end to the controversy. In this case his beliefs in the structure of physico-mathematical sciences were challenged by the newly released calculus.

1.

Infinitesimal methods in Huygens’s works

Huygens’s criticism of infinitesimal calculus can’t be explained on the basis of his own lack of knowledge on the vast range of infinitesimal techniques his century had been up to. This can be proved in, at least, two theoretical contexts: the study of centrifugal force and the mathematical analysis of isochronism. We’ll briefly address here the question of centrifugal forces.6 Having read Descartes’s statements about centrifugal force in the Principia philosophiæ, Huygens was dissatisfied with the complete lack of mathematical expressions that could be of some use in the calculation of centrifugal tension one can feel in a whirling or rotating action. Descartes studied in the Principia philosophiæ the combined motion of a released body pictured as a little mosquito or fly moving along both XXY and EA, EC, EG. But Descartes didn’t see any reliable mathematical expression of BC or FG.



Geometrization or mathematization: Huygens’s critiques of Leibniz

Galileo had also alluded to this problem in his Dialogo (1632, reed. 1890–1909),7 when examining the arguments against the rotation of the Earth. Galileo, impersonated as Salviati, starts from the correct principle: each rotating body follows, when released, a linear path along the tangent of the circle, with uniform motion (ibid.: Vol. VII: 224). At the beginning of the motion, the distance between the tangent and the circle is virtually equal to zero. In what amount of time, asks Salviati, will this body be attracted towards the center of the Earth? This action is done instantly: in the time the body is urged to act naturally in the tangent line, it is impelled to the center with a moment of descent much more powerful than the tension caused by the circular motion.

Geometry comes in only when Salviati has to face the real difficulty: light bodies, such as dust particles, should be much more rejected than attracted, because of their own weight. In the drawing, lines are momenti, i.e., quantities of force that attract/reject bodies. Imagine the mobile’s ejection at H and the effect of gravity at G, the figure HEG being infinitely small. The more H and E are near, the more HG > GE. And we know how to compare these moments of descent from the study of inclined planes: the impeto on the vertical GE is way stronger than the one on the inclined plane HG. Going even further, Galileo is able to represent all the cases of ejection/attraction in a geometrical sketch:

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Fabien Chareix

AB stands in this figure for the time of free fall, KL, HI, FG stand for the speeds acquired after AK, AH, and AF (amounts of time). DA in this figure stands for the specific weights that continuously limit the acquired speed depending on the weight (when D slides to E, weights increase). Though we could admire Galileo’s skills, the status of this ‘proof’ can be discussed and criticized. First, the specific weight doesn’t appear in the rational mathematization of free fall: speeds acquired are the same whether a body is heavy or light, rock or dust. Second, how can Galileo explain that the same axis, namely AB, can stand for both motion and time? What should have been mathematized here, GE, is in no way calculable. Centrifugal force could have been mathematically expressed on the basis of this brilliant essay in the Dialogo, but still, even though Galileo goes deeply into the mathematization of centrifugal forces vs. attraction forces, Huygens did not find here what he was looking for. Thus, judging both Descartes’s and Galileo’s results as ineffective, Huygens undertook to study this phenomenon both mathematically and empirically. C

K y

x

B

E

d/2

parabole x2=yd A

In the De vi centrifuga, a manuscript revised by the first Editors of the Œuvres complètes,8 Huygens uses a series of approximations that clearly show his mastering of infinitesimal quantities in physical sciences. First he approximates the circular path in which the released body was moving, by a parabola that has its right side (latus rectum) equal to d, the diameter of the circle. Then the equation of the



Geometrization or mathematization: Huygens’s critiques of Leibniz

parabola becomes x2 = yd, or KB2 = KF · 2AB (Yoder 1988: 16–43). These actions are restricted to an infinitely small amount of time, so that F can be part of both the circle and the parabola. Obviously, Huygens was then soon able to deal with this infinitesimal scenario in order to discover the law of centrifugal force. Whatever the reasons why, in his correspondence, Huygens was reluctant to admit the power of the Leibnizian calculus, those were not linked to a mere ignorance of the mathematical meaning and importance of infinitely small quantities.

2.

Huygens vs. Leibniz on the mathematization of physics

In the correspondence of Huygens and Leibniz, mathematics are in no way the frontmatter. In short, Huygens tries to correct all the errors of Cartesian philosophy he had read in Leibniz’s writings. The most famous controversy in this correspondence concerns the Cartesian principle of ‘conservation’. Leibniz was convinced that Descartes had made a fundamental mistake on the ‘estime de la force’ and that the French philosopher had expressed the conservation of ‘force’ by the conservation of the ‘mv’ quantity (namely the ‘quantity of motion’) in the Principia philosophiæ (see Fichant 1974, 1998). Huygens repeatedly corrects his young fellow on his reading of Cartesian physics. Both scientists share some criticism about Descartes’s definition of material substance as mere extension. But when Huygens confesses he’s attracted by the hypothesis of atoms, Leibniz endlessly urges him to give up any kind of atomism, for atoms seem to him irrational, unexplainable by the means of mechanicism and, finally, logically inconsistent. In the context of the demolition of Cartesian science, Leibniz tried to test some of the Cartesian philosophers9 by publishing a mathematical problem called De linea isochrona. Huygens gave a solution, with his own methods, in order to protect, in some way, Cartesians like Father Catelan, who was involved in a quarrel with Leibniz. Mathematics was thus introduced in the Huygens–Leibniz correspondence for a defensive purpose and Huygens always tended to oppose his own geometrical methods, sharing some sort of Cartesian philosophy of mathematics, to the rude differential notations of Leibniz. A group of five letters containing only one letter from Leibniz, apparently written in the first months of 1675, is almost entirely devoted to mathematics: the imaginary numbers of Bombelli and resolution of irrational equations.10 Leibniz alludes to the first known letter from Huygens (November 7th 1674; O.C. 7 393–395) and, almost certainly, to some live discussions with the Dutch physicist in which the latter could have advised Leibniz to publish his results on:

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[The invention] of the compass of equations, which provides, without any calculation, at one and the same time, all the roots of a proposed equation of whatever degree – be it geometrically in lines or arithmetically in approximate numbers – from which one can extract the true [roots] if they have any, without any calculation. It seems that after this instrument [is available] there is virtually nothing to be wished for the use of algebra in mechanics and in practice. It is believable that this was the goal of the geometry of the Ancients (at least of that of Apollonius) and the aim of the loci that they had introduced [in Geometry].11

Such a machine dedicated to “mechanics” and the “practice” may have not really impressed Huygens, whose comment in the final section of his letter is ambivalent: “je vous defierois d’en venir a bout si je n’avois vu desia ce que vous sçavez faire par la machine arithmétique” (‘I would challenge you to achieve this if I had not already seen what you know how to do [as in your] arithmetical machine’; Huygens to Leibniz, September 30th 1675; O.C. 7 506). Many of Huygens’s reactions to Leibniz’s ideas in that period consist in the expression of mixed-feelings filled with discontent about the desire to reduce natural philosophy to an automated process, both practically and theoretically. Huygens’s rejection of the infinitesimal calculus as the main tool to describe motion and its properties derives from his skepticism towards Leibniz’s aim to set aside mathematical intuition from the whole process of the traditional mathematization of nature. The next episode in the correspondence occurs around 1690, after Huygens had read the papers on differential and integral calculus Leibniz published in the Acta Eruditorum.12 Huygens’s dissatisfaction with Leibniz’s methods reaches its climax in his notes on a third paper of Leibniz in the Acta Eruditorum.13 The paper focused on the resistence of a given medium to a given motion. Various mistakes in physical concepts are criticized14 but the fiercest attack appears when Leibniz comes to his conclusion: Leibniz But everything corresponds to our analysis of the infinitesimals, i.e., of the calculus of summation and differentiation.

Huygens But it is not true.15

Despite the fact that Huygens seems to have little interest in a method that doesn’t seem to solve more problems than his own algebraical geometry, it is clear that all his critiques against the application of infinitesimal methods are grounded on a general hypothesis according to which there is a link between mathematics and phenomena.



Geometrization or mathematization: Huygens’s critiques of Leibniz

In the correspondence, Huygens wanted to test Leibniz’s calculus: I have seen from time to time in the Acta of Leipzig some things [you published] of your new algebraic calculus. But having found in it some obscurity, I have not studied it enough in order to understand it, as well as because I thought I had an equivalent method, both for finding the tangents of curves for which the ordinary rules are either useless or hardly helpful, and for many other investigations […]. I see that, among other uses of your new invention, you mention the inverse method of tangents, which would be of great importance if you have [developed it in such a way that], given the property or construction of the tangents, you could deduce from it the property of the curve. As if from point C of the curve ECF, having drawn the perpendicular CB = y over the straight line AD, in which are given the point A and AB = x; the tangent being CD, and BD being then equal to

yy − 2 x ; if you can find the equation expressing the relation of AB to BC, or 2x 2 xxy − aax

when BD is

3aa − 2 xy

.16

E

C

y F

x



A

B

a

D

The problem is to find the equation of the curve ECF, which is the proportion between AB = x and BC = y when this ordinate moves along the line ABD and when 2 xxy − aax (ibid.). BD is assumed to be 3aa − 2 xy Huygens built this problem, as it is clearly shown by the editors in an appendix to the letter, considering the following figure:

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40 Fabien Chareix

Where, given the equation of the curve AE (quadratum AE sit aequale rectangulo a2 y ), Huygens applies his rule17 to ex AB, BC, which can be translated in AE 2 = x determine the value of the tangent to any curve. This rule is given in a letter to J. de Witt written in 1663.18 It follows that: if 0 = xyy – aay + x3 is the equation of the AE curve,19 then the tangent SO is

2 xyy − a 2 y . By a small transformation of the yy + 3xx 2 xxy − a 2 x

, namely triangle, Huygens finds the expression of the sub-tangent OT: 3a 2 − 2 xy the condition in the problem Huygens had sent to Leibniz. Huygens knows how to deal properly with signs + and – as well as the geometrical interpretation we will also find in the paper of 1684 where Leibniz expounds the differential calculus and its rules. Huygens’s rules are in fact a geometrical method to differentiate the dx which is the value of the subtangent, though he never thought quantity y = dy about this quantity in differential terms. Geometry can deal with tangents and subtangents and, not surprisingly, Huygens’s rule makes his mastering of algebraic methods in classical geometrical problems quite clear. Except for the notable dif-



Geometrization or mathematization: Huygens’s critiques of Leibniz

ference made by the treatment of the signs (which is more general in Leibniz’s calculus), the efficiency of his “méthode des tangentes”, which could lead him to some successful demonstrations, was his first argument in rejecting Leibniz’s rules. 2 xy

In his response Leibniz finds the equation of a transcendent curve x 3 y = C ⋅ e a dx 2 x 2 y − a 2 x . The which is one of the solutions of the differential equation: y = 2 dy 3a − 2 xy 2 2 2 x y − a x dx is an equation with total differentials. It can be writequation y = 2 dy 3a − 2 xy ten y(3a2 – 2xy)dx + (2x2y – a2x)dy = 0. What Leibniz found is an integrant factor, 2

namely a function g(x,y) where gu and gv are the partial derivations of a given equation G. We thus find an equation with partial derivations which do not necessarily have solutions expressed in terms of elementary functions. The integrant x 2 − 2 xy factor Leibniz found here is g = 2 e a . The controversy that Huygens had bea gun in his prior letter allows us to understand how Leibniz deals with all kinds of transcendent curves. In the letters we only get some clues about how he possibly 2

−

2 xy

found out the quantity e a . At this stage, we can say that the correspondence between Leibniz and Huygens and the quarrels it carries all the way offer clarifications that could never be found in the public papers of both scientists. Still, Huygens seems to be unsatisfied with Leibniz’s solution and he writes to him that his own demonstration doesn’t imply any transcendent or super-transcendent equation, knowing from the beginning that the answer relied upon the equation 0 = xyy – aay + x3. Huygens started from this equation 0 = xyy – aay + x3 and, correcting the signs, his mathematical treatment of the problem led him to 2x 2 y − a2 x dx one of its soluassign to the subtangent differential equation y = − 2 dy 3a − 2 xy 3 tions. The curve 0 = xyy – aay + x he started from is precisely one of the solutions. The controversy on the signs will force Huygens to admit his initial error in the construction of the problem: 2

As for myself, I confess that the nature of this kind of super-transcendent line, where the unknown are part of the exponent, seems to me so obscure that I wouldn’t advise their introduction in geometry, unless you would notice in it some remarkable utility.20 

Again, pretending his method is more efficient, Huygens criticizes Leibniz’s calculus as an artifact maker that leads to useless “obscurity” in the application of mathematics to physics. The concept of “utilitè” is to be understood both in pure and mixed mathematics. Urged by Huygens to show his general method, Leibniz never answered precisely, and we can only see partial descriptions of such a method in various, still incomplete, papers in the Acta Eruditorum.

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Huygens’s untruthfulness is also based upon his ability to successfully deal with most of the problems that were published in various journals: the problem of the isochronous curve,21 and later, that of the “chaînette”.22 In a paper written in 1695, in response to Bernardus Niewentiit’s treatises on the differential calculus, Leibniz refers in a weird manner to the days of his correspondence with Huygens on transcendent curves: What I have also found is that if bx = y, b being constant, then b

x + dx ⋅

− b x will be

dy − 1 = x , and assuming dx and dy are 0, b 0 it yields b0 − 1 = x , or b0 – 1 = 0, or b0 = 1, which is true, since we have 1 – 1 = b

= dy; and this divided by bx gives b

x + dx ⋅

0. But in my differential calculus, such an identicism is avoided. However I con-

fess I sometimes have had cases where this method of calculation could not be neglected at all. But as Sir Niewentiit will see it, my differential method is also (and quite conveniently) extended to the equations where the unknown or undeterminated are in the exponent, which I may have been the first to introduce to the geometers when I gave my Tetragonismum Circuli Numericum in the Acta Eruditorum, in February, 1682;23 I’ll say only a few words on it here, because for many years I have already talked about it in letters to the great geometer Christiaan Huygens from then on; obviously the way to differentiate exponential equations, that did not really need to be inserted in my Algorithm, published years ago, because the rareness and unusualness of these expressions is such that even Huygens himself laboriously accepted it. As far as I know nobody has been that far and penetrated these matters that Huygens called “hypertranscendant” by joke, except the very talentuous Bernoulli, on his own initiative, without showing me anything, himself using the differential calculus. Of course, if xv = y then

dy dy dx dx and log y = ∫ . Hence v ∫ = ∫ which y x y x dy vdx . It follows that v must be given by x gives, by differentiation + dv log x = x y

v · log x = log y; however log x = ∫

and y, together or only one of them, hence it can be written dv = mdx + ndy, and m as well as y are given by x and y so that: we will have

dy vdx + log xmdx = − log x ⋅ ndy , and x y y

dx (namely the subtangent to the ordinate) equal to v . dy + m log y x

Thats’s why we have a way to trace the tangent of such a curve from the supposed quadrature ou Logarithm of the hyperbola; but for a general differenciation of the exponents no more is required in my Algorithm than the consideration of v this rule: dx v = x v ( dx + dv + dv ⋅ log x ). Then if v is a constant number such as e, x e x

e −1

it follows dx e = x e dx, which is ex ⋅ dx , namely the theorem of our Algorithm for the differenciation of powers or roots ever since admitted.24



Geometrization or mathematization: Huygens’s critiques of Leibniz

Here again, not caring to shape a general theory, Leibniz refers both to his correspondence with Huygens (where nothing like a general sketch is provided for the differentiation of transcendent equations) and to the application of the rules given in the paper published in 1684 to an exponent constant such as e. With regards to the letters and papers from 1684 to 1690,25 Huygens strictly follows a Cartesian epistemology of mathematics where geometry is the only legitimate ground for the use of infinitely small entities. Though Leibniz was certain he would manage to convert Huygens to the new calculus, we know for sure that this has never been achieved. The Marquis de L’Hospital, who discussed the new calculus with Huygens between 1692 and 1695, alludes to a letter in the hands of a friend of his, where Leibniz “assure que vous luy auez proposé plusieurs questions en ce genre, auxquelles il a satisfait au delà mesme de vos espérances” (‘affirms that you have proposed him several questions of this kind [physical questions like the ‘chainette’ one], which he has solved even beyond your hopes’; L’Hospital to Huygens, July 26th 1692; O.C. 10 305). Huygens replies instantly: “Je n’ay point trouvè d’avoir besoin pour cela de la methode de calculer de Mr Leibnits, ni je n’en trouve l’utilitè si grande qu’il semble vouloir faire accroire dans la lettre dont vous faites mention” (‘I have never felt the need of Mr. Leibniz’s method of calculation for this purpose, nor did I find its utility so great as seems to want one to believe in the letter you mention’; Huygens to L’Hospital, August 27th 1692; O.C. 10 308). Then he adds: “Il est très habile geometre d’ailleurs et s’est appliqué entre autres choses avec succès à ce qui regarde les Tangentes et quadratures des lignes courbes. C’est la dessus que rouloient les Problemes auxquels il dit avoir satisfait au de la de mon attente, ce qui est vray, mais il est vray aussi que je n’avois pas beaucoup medité alors ces matieres, m’estant tousjours plu d’avantage à chercher l’utilitè de la Geometrie dans les choses de physique et de mechanique” (‘In fact he is a very able geometrician and has applied himself with success, among other things, to the tangents and to squaring curvilinear curves. It is with such things that the problems he says to have satisfied beyond my expectation were concerned. This is true, but it is also true that at that time I had not reflected much about these matters, since the search for the utility of geometry in physics and mechanics pleased me more’. Ibid.). In Huygens’s view, the calculus did not prove its efficiency in the main matter that he is concerned with: physical science. In other words, he is persuaded that in the field of physics the method of the tangents and the calculus are only two different formal accounts that lead to the very same conclusions (as we see in the problems solved by  Huygens between 1687 and 1692). The above mentioned statements show that the

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controversy, as it manifests itself in the correspondence, is way different from the one that he opposed Leibniz and Newton (see Hall 2002; Bardi 2006). There is absolutely no need to change all traditional tools, and Leibniz only shows a superior efficiency in the resolution of minor (and useless) equations involving transcendent curves. What guided Huygens in the making of geometrical tools was their “utilité”, natural phenomena coming in first line in the process of geometrical physics. Now that infinitesimal methods have disrupted the links between given data, thus introducing the ability to build formal equations prior to any given natural problem, the making of physical laws was deeply transformed in a way Huygens and others could never accept. To summarize, we can say that Huygens, having tested Leibniz’s new calculus, refuses to admits its value, and he criticizes its complexity in the making of physics. It is important to note that his reluctance is not grounded on the rejection of all infinitesimal methods, as we saw him thoroughly exploring the field where Cavalieri, Descartes, Pascal, and the first generation of seventeenth century mathematicians and natural philosophers had already made some important discoveries. Huygens’s rejection, in our opinion, is not mathematical, but deeply physical: geometry and the motion of lines along curves, or the graphical representation of mechanical properties are so intimately linked that Huygens could not bear the ultimate goal of Leibniz’s calculus: mathematizing nature without geometry. In a way, Huygens’s classical preference for a graphical and geometrical resolution of physical matters is still sensible in Bernoulli’s analytical mechanics, Euler being the first in the middle of the eighteenth century to accomplish the design of a physics without concrete geometrical figures in motion.

3.

Conclusions

From these episodes, in which the epistemic evidence we have found only slightly changes in the end of Christiaan Huygens's scientific career, one can conclude that scientific hypotheses should not only be addressed in terms of formal theory change. Why did Huygens reject the objective simplicity of both Leibnizian and Newtonian tools in natural philosophy? The hypothesis underlying this paper is that Huygens’s attitude towards the infinitesimal calculus is the result of the strong presence, in his mind, of an idea or an ideal of what science is or should be. Knowing the very content of their letters, we can no more take for granted some of the most common statements in the history of Leibniz’s mathematical thought. For example, how could we accept that Leibniz would have “invented his new calculus between 1673 and 1676 in Paris under the personal influence of Huygens and by the study of Descartes and Pascal” (Struik 1987: 111–113).26



Geometrization or mathematization: Huygens’s critiques of Leibniz

Whatever the influence Huygens had on the young Leibniz in Paris, it certainly never went beyond analytical geometry – a fact that can only be proved by the study of their correspondence. What Huygens shows us in his private correspondence is the existence of a second – not secondary – theory change at the end of the seventeenth century. Natural philosophy, based on a corpus of geometrical tools and on the belief that geometry and the world share the very same structure, was abruptly facing its limits. Instead, new methods replaced geometry, rational mechanics being the result of a combination; abstraction and generality in mathematical tools allied to pure mathematical hypotheses that could not be grounded on mechanical picture of the world. By the end of his correspondence with Leibniz, and only then, Huygens begins to accept the value of the calculus in dealing with some physical problems: I admire ever more the beauty of geometry in the new advances it makes everyday, advances in which your contribution is so large, Monsieur, were it not only through your marvelous calculus.27

But Huygens still sees the geometrical shadow of the differential calculus, refusing to acknowledge its existence as a separate part of mathematics. Even though this calculus is efficient, it lacks something: consistency. So we can say that Huygens was reluctant to accept what Malebranche, certainly much more Cartesian than he was, fully accepted.28 Huygens could not entirely deny the power of the calculus, especially if we consider his own use and abuse of infinitesimal methods along his career. Nevertheless, there is a difference between the use of infinitesimal objects in the context of analytical or algebraical geometry and the use of differential writing of the same operations that could be dealt with the help of the old method of the tangents. The same misunderstanding occured when Huygens and L’Hospital discussed the new method. In their correspondence, while Huygens sticks to his opinion, the author of l’Analyse des infiniments petits accepts and promotes what he considers to be a real revolution in physics: geometrization is over, it is the turn of mathematization, which allows for real theoretical hypotheses. What, exactly, is the missing factor that keeps Huygens away from the growing number of mathematicians that acknowledge the necessity of changing their tools? What prevented Huygens from adopting the calculus new out of the box, and from getting rid of the laborious, though still useful, method of the tangents? The reason for such a slow-pace motion towards the calculus can only be found in his adherence to the philosophical ideal of co-development that links geometry and natural phenomena. Mechanism, in his mind, can only be expressed in the terms and mathematical forms of geometry, including infinitesimal differential

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or integral operations that could be derived from the fundamental geometrical parameters. Alluding to Leibniz29 and commenting on him, Carl B. Boyer notes that “[Leibniz] said in 1703, in a letter to James Bernoulli, that sometimes Pascal seemed to have had a bandage over his eye. This apparent lack of imagination was very likely the result of a predilection for the classical, such as later restrained the scientist Huygens also from making full use of the new procedures” (Boyer 1959: 153).30 In Huygens’s mind, the calculus was only the result of slight language alteration that could, ultimately, disrupt the link between physical and geometrical parameters. For him, this process was both useless and dangerous for the intelligibility of natural philosophy. The efficiency of the new methods did not introduce enough discrepancy between the old or classical and the new, so that there was absolutely no reason, as far as he was concerned, to adhere to the mathematical revolution that was in the making in his own time.

Notes 1. James or Jacob Bernoulli (1654–1705) and John or Johann Bernoulli (1667–1748). 2. See de L’Hospital (1696). 3. See Varignon (1687, 1725). 4. “Had he [Huygens] chosen to pursue the dynamics he sketched, exploiting the model of free fall and expressing in effect the dynamic conditions of the kinematics of descent, it is reasonable to speculate that the textbooks today would refer to Huygens two Laws of motion instead of Newton’s three, and we might discuss dynamics in terms of ‘incitation’ instead of ‘force’” (Westfall 1971: 188). 5. Such as Michel Rolle. See Rolle (1703). For a more precise account of Rolle’s ideas on infinitesimal calculus, see Blay (1992). 6. For a more complete survey on both vis centrifuga and isochronism of the simple pendulum, see Yoder (1988) and Chareix (2006). 7. There are many strong reasons to think that Huygens carefully read all that was available from Galileo during the 1650’s. This includes both the original and the Latin version of the Dialogo. 8. Huygens’s Œuvres complètes are referred to as ‘O.C., Vol., page’. 9. Assuming Huygens himself was not on their side. 10. Where Descartes spoke about the division of “quantities”. Leibniz finds more general equations. 11. “[l’invention] du compas des equations, qui donne sans aucun calcul, tout à la fois, toutes les racines d’une equation proposée de quelque degré donné qu’elles puissent estre; soit geometriquement en lignes soit arithmetiquement en nombres approchans, dont on peut incontinent tirer les veritables s’il y en a, sans aucun calcul. Il semble qu’apres cet instru-



Geometrization or mathematization: Huygens’s critiques of Leibniz

ment il n’y a quasi plus rien a desirer pour l’usage que l’Algebre peut ou pourra avoir dans la méchanique et dans la practique. Il est croyable que c’estoit le but de la Géometrie des anciens, (: au mois celle d’Apollonius) et la fin des lieux qu’ils y avoient introduits” (O.C. 7 503). The Editors of O.C. mention a manuscript in the Library of Hannover that refers to a “Constructor, Instrumentum algebraicum pro inveniendis omnium aequationum radicibus geometrice pariter et in numeris quantum libet exactis sine calculo”. Leibniz dates this invention December 1674, in Paris. 12. Nova methodus pro maximis et minimis (…), 1684, comments in O.C. 22 789; De geometria recondita et analysi in indivisibilium atque infinitorum, 1686, comments in O.C. 22 790–791. 13. Schesdiasma de resistenria medii, et motu projectorum gravium in medio resistente, 1689, comments in O.C. 22 792–795. 14. Such as ‘space’ mentioned in the fundamental law: “decrementa virium sunt proportionales incrementis spatiorum” (‘decreases of forces are proportional to increases of spaces’). Obviously, velocities are what is involved, not spaces, Huygens noted. 15. Leibniz

Omnia autem respondent nostræ analysi infinitorum, hoc est calculo summarum et differentiarum

Huygens Sed non veritati

16. “J’ay vu de temps en temps quelque chose de vostre nouveau calcul Algebraique dans les Actes de Leipsich, mais y trouvant de l’obscuritè, je ne l’ay pas assez etudiè pour l’entendre, comme aussi parce que je croiois avoir quelque methode equivalente, tant pour trouver les Tangentes des Lignes courbes où les règles ordinaires ne servent pas, ou fort difficilement, que pour plusieurs autres recherches. (…). Je vois qu’entre autres utilitez de Vostre nouvelle invention vous mettez Methodus Tangentium inversa, qui seroit de grande importance si vous l’avez telle que la propriétè ou construction des Tangentes estant donnée, vous puissiez en deduire la proprietè de la Courbe. Comme si du point C de la courbe ECF, ayant menè la perpendiculaire CB = y sur la droite AD, dans laquelle soit donnè le point A et AB = x ; la tengente estant CD, et BD alors egale à

yy − 2 x ; si vous pouvez trouver l’Equation qui exprime la relation de AB à BC, 2x 2 xxy − aax

ou bien quand BD est

3aa − 2 xy

”. Huygens to Leibniz, August 24th 1690; O.C. 9 472.

17. It can be said that Huygens follows Descartes in his reduction of infinitesimal operations to the method of tangents. Thus the study of the curves, either in differenciation or in integration, falls into geometry’s dominion. Descartes rejected transcendent equations (such as a logarithmic equation). See Vuillemin (1960: 56–73). 18. “Once all the terms of an equation are put in one part of an equation, which therefore is equal to zero, first we multiply the single terms where we find y by the number of dimensions that y has there: and this will be the quantity to divide. Then in the same way we multiply the single terms in x by the number of dimensions that x has in these terms, and we put away from all these terms one x; and this will be that should be taken as the quantity that divides the quantity to be divided that we found already. We shall have then a quantity called z or FE, from the extremity [termino] of which we drive a line that touches the curve in a given point B. It is pointless to change the signs + and –, provided we know that when the quantity of the divisor, or the divided or both of them, are under zero or negatives, we must consider them as positive; however we have to mention that when one is positive and the other negative, then z

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or FR is directed to the point A; but when both quantities are affirmative or negative, then FE is directed on the other side. For example in the curve we just talked about, since the equation is x3 + y3 – axy ∞ 0, the quantity to divide will be, according to the rule, 3y3 – axy; and the divisor 3 y 3 − axy

will be 3xx – ay. Hence z = .” (Huygens to Johann de Witt, February 25th 1663; O.C. 4 3xx − ay 312–315). a2 y

19. Since this is a triangle, i.e. → AE 2  = x 2 + y 2 , then a2y = x3 + xyy, which gives finally x  2 3 0 = xyy – a y + x . 20. “Pour moy, j’avoue que la nature de cette sorte de lignes supertranscendantes, où les inconnues entrent dans l’Exposant, me paroit si obscure, que je ne serois pas d’avis de les introduire dans la geometrie, à moins que vous n’y remarquiez quelque notable utilitè” (Huygens to Leibniz, November 18th 1690; O.C. 9 537). 21. Problem proposed by Leibniz in the Acta Eruditorum, 1687: the curve where a falling body has a constant speed of vertical fall. Huygens also gave a solution to the brachistohcrone curve: the path of minimal time of free fall. 22. Proposed by Jacques Bernoulli in the Acta Eruditorum, May 1690: “Invenire quam curvam referat funis laxus et inter duo puncta fixa libere suspensus. Sumo autem funem esse lineam in omnibus suis partibus facillime flexilem” (‘Find which curve represents a loose string freely suspended between two fixed points. I assume, on the other hand, that the string is highly flexible in all its parts’). 23. See also in the Acta Eruditorum, September 1693: “Supplementum geometriae dimensoriae, seu generalissima omnium tetragonismorum effectio per motum”. 24. Leibniz, Responsio ad Niewentiit (GM 5 324; my translation). Near the end of this paper, Leibniz announces Huygens’s death: “Ego Hugenium solo tempore Galilaeo and Cartesio postpono” (GM 5 328). 25. This could be extended to the period between 1690 and 1695; restrictions are mandatory here, but the general purpose would not be affected by the study of the late correspondence between Huygens and Leibniz. 26. The author alludes here to both Descartes’s Géométrie published in 1637 and Pascal’s Traité des sinus du quart de cercle, 1659, where the operations of small triangles and intervals allow the substitution of the curve by the tangent. 27. J’admire de plus en plus la beauté de la géométrie dans ces nouveaux progres qu’on y fait tous les jours, où vous avez si grand part, Monsieur, quand ce ne seroit que par vostre merveilleux calcul” (Huygens to Leibniz, September 17th 1693; O.C. 10 511). Huygens also confesses in a letter to Leibniz: “vostre calculus differentialis, dont je commence avoir grande envie” (Huygens to Leibniz, September 1st 1691; O.C. 10 132), a courtesy that did not prevent him from making much harsher statements in other correspondence. 28. Malebranche wrote his own Elements of infinitesimal analysis under the title Du calcul integral. This text seems to be a copy and commentary of Johann Bernoulli’s Leçons. It was edited by P. Costabel in Malebranche’s Oeuvres complètes (ed. A. Robinet, 1958–1984, Paris: Vrin, vol. XVII-2, 131–176). 29. Free quotation from the Early Mathematical Manuscripts, also in GM 3 72–73. 30. With a certain logic, Christiaan Huygens is only mentioned three times in this key contribution to the history of classical mathematics.



Geometrization or mathematization: Huygens’s critiques of Leibniz

References Bardi, J. S. 2006. The Calculus Wars: Newton, Leibniz, and the greatest Mathematical Clash of All Times. London: High Stakes Publishing. Blay, M. 1992. La Naissance de la mécanique analytique. Paris: Presses Universitaires de France. Boyer, C. B. 1959. The History of the Calculus, and its Conceptual Development. New York: Dover. Chareix, F. 2006. La philosophie naturelle de Christiaan Huygens. Paris: Vrin. Descartes, R. Principia Philosophiæ. AT 8 1–353. Descartes, R. 1996. Oeuvres de Descartes. Edited by C. Adam and P. Tannery. Paris: Vrin. Fichant, M. 1974. “La ‘réforme’ Leibnizienne de la dynamique, d’après des textes inedits”. In Akten des II. Internationalen Leibniz-Kongresses, Hannover, 17.–22. Juli 1972 [= Studia Leibnitiana Supplementa 12–15]. Wiesbaden: Franz Steiner, 195–214. Fichant, M. 1998. Science et métaphysique dans Descartes et Leibniz. Paris : Presses Universitaires de France. Galilei, G. 1632, reed. 1890–1909. Dialogo. In A. Favaro (ed), Opere di Galileo Galilei. Firenze: Edizione nazionale. Hall, R. 2002. Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge: Cambridge University Press. van Helden, A. 1983. “The birth of the modern scientific instrument, 1550–1700”. In J. G. Burke (ed), The Uses of Science in the Age of Newton. Berkeley: University of California Press, 49–84. de L’Hospital, marquis. 1696. L’Analyse des infinimens petits pour l’intelligence des lignes courbes. Paris: Jombert. Huygens, C. 1888–1950. OEuvres complètes de Christiaan Huygens. La Haye: Société hollandaise des Sciences – Martinus Nijhoff. [= O.C.] Leibniz, G. W. 1695. Responsio ad nonnullas difficultates ad DN. Bernardo Niewentiit circa methodum differentialem seu infinitesimalem motu. GM 5 320–329. Panofsky, E. 1992. Galilée critique d’art. Paris: Impressions nouvelles. Rolle, M. 1703. Remarques de M. Rolle touchant le probleme genéral des tangents. Paris: Jean Boudot. Struik, D. J. 1987. A Concise History of Mathematics. New York: Dover. Varignon, P. 1687. Nouvelle Mécanique ou Statique. Paris: Jombert. Varignon, P. 1725. Éclaircissements sur l’analyse des infiniment petits et sur le calcul exponentiel des Bernoulli. Paris: Pissot. Vuillemin, J. 1960. Mathématiques et métaphysique chez Descartes. Paris: Presses Universitaires de France. Westfall, R. 1971. Force in Newton’s Physics: The Science of Dynamics in the Seventeenth century. London: Elsevier. Yoder, J. 1988. Unrolling Time: Christiaan Huygens and the Mathematization of Nature. Cambridge: Cambridge University Press.

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chapter 3

Leibniz and the vis viva controversy* Idan Shimony

1.

Introduction

Gottfried Wilhelm Leibniz envisaged human knowledge as a common, public project. In sharp contrast to the Cartesian view of a solitary thinker who is required, as a starting point, to “doubt all things” received from others and hold them to be false, Leibniz advocated collecting and combining the old lore of the ancients and the new doctrines of the moderns, the teachings of various nations and generations, and the works of different individuals. This was not merely an eclectic assembling of materials but also a work of organizing and bringing in consistency and coherence. He warned us to “guard against being more eager to destroy than to construct”, and claimed that “if we overlook entirely the harsher things which they say against others, the writings of outstanding men, both ancient and modern, usually contain many true and good things which deserve to be collected and arranged in the public treasury of knowledge” (SD 436). Only rarely such transmissions of ideas and perspectives are smooth. As is only natural, some are at odds with others. Hence, not only organization is needed but also bringing in consistency and coherence. Open discussion and controversy were accordingly for Leibniz an essential vehicle for transforming an ever expanding aggregate of data and information into a coherent “public treasury of knowledge”. It is not for no good reason that in the recent work of Marcelo Dascal (2006), Leibniz is celebrated as a master in “the art of controversies”. Leibniz’s practice was usually in accord with this conception. He was involved in the institution of intellectual journals, societies, and academies, and engaged in vast correspondence and public discussions. It was thus no empty gesture or rhetorical lip service in writing on the occasion of publishing his New System that he had “decided upon this [i.e., publishing it] chiefly in order to profit by the criticisms of those who are informed on such matters, since it would be too burdensome to seek out and call to my aid individually those who would be disposed to give me instruction” (NS §1; L 453).

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Idan Shimony

There is a certain episode, however, in which Leibniz’s practice seems to deviate from this prima facie compelling view of the evolution of human knowledge. This involves the vis viva controversy.1 The controversy was primarily concerned with two questions. First, how to define and measure the force of a body in motion; and second, which one of the two quantities held by the parties to the controversy to be the correct measure of that force is conserved in nature. It was often thought that the controversy was a mere dispute of words. If “force” is not directly accessible but has to be defined by its observable effects, and if, further, it can be argued and shown by experiments that it is possible to measure both rival Cartesian and Leibnizian quantities as effects of forces, then there is nothing substantial to the problem and it is only a terminological sophistry. This line of thought has been attributed most prominently to Jean d’Alembert, who is conceived by many as the resolver of the dispute. Equipped with an uncompromising positivistic approach, d’Alembert sought to exclude obscure or metaphysical concepts from mechanics, the notion of force included. If anything, the word “force” can be taken to refer to the observable effects of the putative entity which presumably caused them. Now both the Cartesian and the Leibnizian quantities are in fact measurable effects. Moreover, they can be reduced to Newtonian terms: the former is the product of the Newtonian force and the period of time of its application, the latter is equivalent to the product of the Newtonian force and the distance through which it was effective. Hence, d’Alembert concluded, arguments with regard to measures of force are useless in mechanics. D’Alembert’s denunciation of the controversy in his Treatise on Dynamics of 1743 has been held by historians of science to persuade his contemporaries of its futility and to effectively put an end to it. Ernst Mach (1960: 365) thought that the controversy “lasted fifty-seven years, till the appearance of D’Alembert’s Traité de Dynamique, in 1743”. Florian Cajori (1960: 58–59) noted that “the controversy lasted over half a century, until finally, it was brought to a close by Jeanle-Rond D’Alembert’s remarks in the preface to his Dynamique”. H. G. Alexander (1956: xxxi) wrote that “the dispute about moving force came effectively to an end after the publication in 1743 of D’Alembert’s Traité de Dynamique”. Writers who do not subscribe to the view that the controversy has been a mere dispute of words also consider d’Alembert the resolver of the problem.2 Recently, Martin Schönfeld has crowned d’Alembert as “the historical winner of the vis viva debate”. He argued that “D’Alembert’s solution rested on a deliberate choice: he wanted to investigate what could be investigated quantitatively and simply ignored the rest”, the rest being the talk of forces and especially of their metaphysical aspects. This choice enabled him to clearly conceive that both the Cartesian and the Leibnizian forces “denote real and distinct aspects of physical



Leibniz and the vis viva controversy

interaction” and thus to see that “Descartes and Leibniz were both right in their own way” (Schönfeld 2000: 31–34). In what follows I would like to argue that this line of thought cannot solve Leibniz’s problem. As we shall presently see, Leibniz had already argued, half a century before d’Alembert proposed his solution, that when investigated quantitatively, indeed both forces turn out to be true and legitimate. It was precisely the metaphysical consideration, which d’Alembert undertook to bypass, that Leibniz had been seeking to bring to the fore, in order to determine which force should be given priority over the other. D’Alembert, however, could not have known this. In his public polemics against the Cartesians, Leibniz eagerly argued for his own measure, and seemed to do it at the expense of rejecting completely the quantity offered by Descartes. Due to this false impression Kant could still wrongly but justifiably write, sixty years after the initiation of the controversy and between the two editions of d’Alembert’s Treatise, that Leibniz “rejected Descartes’s law absolutely and without reservation and set immediately his own [law] in its place”.3 Indeed, Leibniz could have spared his contemporaries and successors much of the ado, had he openly emphasized the genuine nature of his problem, as he did in some of his unpublished papers.4

2.

Descartes’s principle of conservation of quantity of motion

The controversy erupted in 1686 with Leibniz’s publication of A Brief Demonstration of a Notable Error of Descartes and Others Concerning a Natural Law, According to Which God is Said Always to Conserve the Same Quantity of Motion; a Law Which They Also Misuse in Mechanics in the Acta Eruditorum, in which he attacked the Cartesian measure of force. Let us consider first Descartes’s position. Descartes’s philosophy of nature begins, as is well known, with the assertion that the essence of matter or body is extension. There is nothing inherently in material bodies save the passive geometrical property of extension. The nature of body thus does not consist in any physical or sensible qualities such as weight, hardness, or color, not to mention the four basic qualities or the forms of the scholastic tradition.5 Furthermore, since spatial extension is nothing but a property of the extended material substance (Principles of Philosophy 1.53), there can be no space where there is no body (Ibid. 2.10–12). Hence, space and body are one and the same thing, considered from different perspectives.6 Descartes goes on to draw from this statement some further conclusions: that there are no empty spaces or void in the world (Principles of Philosophy 2.16–17); that there can be no simple indivisible material particles or atoms (Ibid. 2.20, 4.202); and that the physical world consists of indefinitely extended

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uniform matter (Ibid. 2.21–22). The apparent variation and diversity in such a world is to be explained solely geometrically in terms of size, shape, and movement of parts of matter.7 Since matter in Cartesian physics is essentially passive and inert, it cannot be the source of its own motion. There must be some other cause, external to matter, from which motion originates. Descartes identifies the ultimate source of motion of matter with God. From the fact that God’s perfection is evident not only from his immutable nature, but also from his immutable and completely constant way of action, a rule of conservation of motion follows. According to this rule, God preserves at each instant of the world the same “quantity of motion”, as that which was imparted to matter in its creation. “That is why”, says Descartes, “we must think that when one part of matter moves twice as fast as another twice as large, there is as much motion in the smaller as in the larger; and that whenever the movement of one part decreases, that of another increases exactly in proportion”. That is, there are two factors relevant to the calculation of the quantity of motion: the “size” of the body and its speed. The quantity of motion which is conserved in the world is to be calculated by the product of the “size” of the body or its mass,8 and its speed (m|v|).9 However the motion of bodies may be naturally10 changed, the sum of their quantities of motion (∑ mi|vi|) will remain unaltered. In Descartes’s universe changes of motion occur only through contact. Thus, the paradigmatic case in which the Cartesian principle of conservation of quantity of motion is supposed to be most clearly evident is the occasion of impact between bodies. When two bodies collide, the sum of the quantities of motion of the two after the impact remains the same as the sum of their quantities of motion prior to their collision. Descartes supplements this general principle of conservation with three laws of nature which also result “from the immutability and simplicity of the operation by which God maintains movement in matter” (Principles of Philosophy 2.37–42), the third of which deals with bodies “coming in contact” and is specified by Descartes’s seven famous, and notably erroneous, rules of impact (Ibid. 2.46–52). Now, the force of a body in motion consists in the striving of the moving body to remain in the same state and to continue its motion, and is measured by the mass of the body and its speed. Hence the measure of force of a body in motion is the body’s quantity of motion. This quantity is never changed in the world. It is redistributed in impacts of bodies in accordance with their forces of motion and resistance, but its sum total always remains the same.11



3.

Leibniz and the vis viva controversy

Leibniz’s criticism of the Cartesian conservation principle

It is Descartes’s principle of conservation of force as quantity of motion that Leibniz takes issue with in Brief Demonstration of 1686 and in subsequent writings. The argument of Brief Demonstration is designed to present a case in which the amount of “motive force” of two moving bodies is equal and conserved through some process of change, while the “quantities of motion” they acquire in the process are not the same. From this Leibniz derives the conclusion that the motive force conserved in nature is something different from Descartes’s quantity of motion and is not to be estimated by the product of mass and speed. The “process of change” which Leibniz employs in his argument is not that of colliding bodies or impact, but rather that of free falling bodies. The argument opens with two assumptions, both of which, Leibniz believes, are acceptable to the Cartesians. The first assumption asserts that while falling unimpeded from a certain height a body acquires exactly the amount of force which is necessary to raise it back to the same height. According to the second, the force necessary to raise a body A of 1 pound to a height of 4 yards is the same as that which is required in order to raise a body B of 4 pounds to a height of 1 yard. Now from these two assumptions it follows, that two bodies, A of 1 pound and B of 4 pounds falling freely from 4 yards and 1 yard respectively, will have the same amount of force at the bottom point of their falling. For according to the first assumption A acquires in its fall from a height of 4 yards the precise amount of force necessary to raise it back to the same height; and according to the second, this amount is equal to that required to raise a body of 4 pounds to a height of 1 yard; which is exactly, according to the first assumption, the amount of force which B acquires in its free fall from a height of 1 yard. Yet although at the bottom point both bodies have the same amount of force, it follows from Galileo’s laws of falling bodies that they have different amounts of quantity of motion at that point: the smaller body A that falls from a higher position acquires a velocity twice as that acquired by the larger body B falling from a lower point; but since A is four times smaller than B, its quantity of motion is half that of the latter.12 Leibniz generalizes the consequence of his analysis of a simple case of free fall of two bodies and concludes that “[t]here is thus a big difference between motive force and quantity of motion, and the one cannot be calculated by the other… It seems from this that force is rather to be estimated from the quantity of the effect which it can produce; for example, from the height to which it can elevate a heavy body of a given magnitude and kind,13 but not from the velocity which it can impress upon the body” (BD 297).

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The amount of force is thus proportional to the height to which a body can be raised in virtue of its speed and not to the speed itself as with Descartes. In Brief Demonstration Leibniz does not go on to draw explicitly the obvious conclusion that the amount of force is proportional to the square of the velocity, as is evident from the Galilean equation. He does not state that it should be estimated precisely by the product of mass and velocity squared (mv2), nor does he entitle it there “living force”. All this will have to await the Specimen Dynamicum of 1695. Here Leibniz distinguishes between “living force” or vis viva, which is an “ordinary force combined with motion”, and “dead force” or vis mortua, which inheres in a body not yet moving and provides a solicitation to motion (SD 438). The first, Leibniz now asserts explicitly, is to be estimated by the product of mass and velocity squared.

4.

Descartes’s mistake

It is noteworthy that Leibniz employs in the above mentioned argument an analysis of a case of free falling bodies and not of impact, where Descartes’s principle of conservation of quantity of motion is supposed to reside more naturally.14 When Leibniz analyzes cases of impact in order to refute Descartes’s principle, his success relies upon exploiting Descartes’s notorious mistake of neglecting the conservation of direction and considering the quantity of motion as a scalar rather than a vector magnitude (see, for example, letter to Arnauld, November 28th/December 8th 1686; LA 97–99). This mistake of Descartes was soon to be noticed. Three decades before Leibniz’s Brief Demonstration Christiaan Huygens questioned Descartes’s principle of conservation of quantity of motion and laws of impact, commenting in his correspondence that “if all Descartes’s laws are not false, except the first, then I am incapable of distinguishing true from false” and that “Descrates’s axiom on the conservation of motion according to which the same quantity of motion always exists seemed to me formerly quite true and in conformity with reason... [b]ut I know now that it cannot always be valid and must be replaced by a more evident principle”.15 The papers on the laws of motion submitted to the Royal Society of London by John Wallis, Christopher Wren, and Huygens in 1668–1669, exposed the essential shortcomings of Descartes’s analysis of conservation of motion and laws of impact. From the works of Huygens and Wren on impacts of perfectly elastic bodies it followed that in such impacts quantity of motion as had been defined by Descartes is not always conserved. Another quantity, however, turned out to remain the same before and after collisions of perfectly elastic bodies: the sums



Leibniz and the vis viva controversy

of the products of each body’s mass with the square of its own velocity (∑ mi vi2) before and after the impact are equal. Wallis’s investigations of perfectly inelastic impacts showed that the Cartesian quantity of motion is indeed not always conserved. If, however, the direction of motion is taken into account and the quantity is considered as vectorial rather than scalar, then the quantity of motion thus interpreted can be said to be conserved in such impacts.16 As commentators have noticed, Leibniz was well acquainted with the works of Huygens, Wallis, and Wren. He was thus fully familiar with the difference between the scalar “quantity of motion” given by the product of mass and speed on the one hand, and the vector of mass times velocity, later called momentum, on the other. Accordingly, his public arguments against Descartes were intended to show the advantage of living force or mv2 over the erroneous Cartesian quantity of motion, and not to reject the valid quantity of momentum or mv.17

5.

Leibniz’s positive view – suppressing mv

It is unfortunate that Leibniz did not clearly stress this point in his public polemical writings against the Cartesians. In his unpublished critical remarks on Descartes’s Principles of Philosophy he wrote: The most famous proposition of the Cartesians is that the same quantity of motion is conserved in things. They have given no demonstration of this, however, for no one can fail to see the weakness of their argument derived from the constancy of God. For although the constancy of God may be supreme, and he may change nothing except in accordance with the laws of the series already laid down, we must still ask what it is, after all, that he has decreed should be conserved in the series – whether the quantity of motion or something different, such as the quantity of force. I have proved that it is rather this latter which is conserved, that this is distinct from the quantity of motion, and that it often happens that the quantity of motion changes while the quantity of force remains permanent.  (Critical Thoughts on the General Part of the Principles of Descartes; L 393–394)

This passage echoes the general line of Brief Demonstration but is misleading, for it gives the impression that by dismissing the Cartesian quantity of motion Leibniz argues for a unique conservation principle – that of living force or mv2. But this is not the case. As a matter of fact Leibniz did acknowledge, in addition to the conservation of living force, the conservation of the vector quantity mv, namely, momentum. In the Essays on Dynamics, written in the 1690s but published only in the 19th century, he named it “quantity of progress”.18

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He tried then to explain what seemed to be paradoxical in his position. In inelastic impacts, Leibniz argued, quantity of progress is conserved, to the effect that a body with greater force and a body with lesser force can mutually bring each other to a halt (“force” being understood here in its Leibnizian sense, i.e., as living force calculated by mv2). How can a weaker body stop a stronger one endowed with greater force? Leibniz explained it as follows. Consider a head-on collision between two bodies, A of mass 3 and velocity 2, and B of mass 2 and velocity 3. Before the collision A and B both have momentum of 6 units, but in opposite directions. That is, they have jointly a total quantity of progress or momentum of zero. If they stop one another in the collision, their total momentum is, of course, conserved. In addition, before the collision A has force of 12 whereas B has force of 18. “Although A is absolutely weaker than B”, Leibniz writes, “nevertheless in the concourse they can stop each other”. That happens because at the time of collision the bodies are not in motion, but rather static or in a state of equilibrium. Therefore, they act upon each other “only according to the laws of dead or static force[s]” which are estimated by the momenta of the bodies, which in this case are equal. Thus both A and B have a dead or static force of 6 units. By continually, mutually exhausting each other’s equal dead force, A and B eventually bring one another to a halt (ED 660).19 Yet it seems, even if Leibniz’s explanation is admissible, that there is a loss of force in this case. For before the impact bodies A and B jointly had a total force of 30, while after the impact they have none at all. Leibniz’s explanation of this apparent loss of force is tantamount to what later would be the principle of conservation of total energy. According to this explanation, the force of the macroscopic bodies is not lost but rather transferred to their molecules. In modern terms we would say that kinetic energy, in such cases, is not lost but rather transformed into heat: But this loss of total force… does not detract from the inviolable truth of the law of the conservation of the same [living] force in the world. For that which is absorbed by the minute parts is not absolutely lost for the universe, although it is lost for the total force of the concurrent bodies. (ED 670)20

6.

Metaphysical reasons for preferring living force over “progress”

Leibniz thus accepted both principles. But why did he prefer the principle of conservation of living force – the precursor of the principle of conservation of energy – over that of conservation of quantity of progress or momentum? Why did he highlight the former and suppress the latter? As I will try to show now, contrary to what was the core of d’Alembert’s positivistic solution, Leibniz had metaphysi-



Leibniz and the vis viva controversy

cal (rather than physical or mechanical) reasons for preferring the principle of conservation of living force. In the Essay on Dynamics Leibniz argued for, and gave the mathematical formulae of, three different physical laws of conservation in impact: the principle of conservation of relative velocity, according to which, given that two elastic bodies move on a straight line, the relative velocity with which they approach each other is equal to the relative velocity with which they depart after an impact;21 the principle of conservation of quantity of progress or momentum, and the principle of conservation of living force. He then commented that although he had put together the three formulae, any two of them would suffice, since any one of them could be mathematically derived from the other two (ED 658–661, 666–668). From the mathematical-mechanical point of view it was thus indifferent which would be regarded as fundamental and which as secondary. Furthermore, all Leibniz’s three principles are, from the point of view of classical physics, true. He was also keen to notice that the first applies only in elastic impacts. He correctly observed that the second is valid on the condition that no external forces interfere.22 Finally, he gave a basically correct explanation of the validity of the third in all kinds of impacts, though he did not connect the conservation of living force in inelastic collisions with the phenomenon of heat. As far as mechanics was concerned, Leibniz accepted all three principles. In particular, he acknowledged the conservation of both momentum and living force. He had no mathematical or physical reasons for granting either of the principles a privileged status over the others. Hence, as far as the controversy is concerned with the legitimacy and conservation of the revised-Cartesian and the Leibnizian quantities (i.e., of the vector mv and of mv2), if the “resolution” of d’Alembert and others which were based on acknowledging the validity of both quantities in mechanics were supposed to be an answer to Leibniz, then these writers were simply barking up the wrong tree. For as we have just seen, Leibniz had already argued for both quantities half a century before d’Alembert’s Treatise on Dynamics was published. Moreover, as historians of science have noticed, the correct mathematical expressions and relations of the quantities involved, to which d’Alembert called attention, were already known and available to Leibniz and some of his contemporaries (see Hankins 1965: 286, esp. n. 13; 1970: 209, esp. n. 3). Leibniz accepted both principles in physics. But for Leibniz, in addition to the physical discussion, the question which principle is metaphysically fundamental was crucial. In this context he was interested in metaphysical considerations, precisely of the kind that d’Alembert sought to exclude. “Besides purely mathematical principles”, Leibniz explained in Specimen Dynamicum, “there must be admitted

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certain metaphysical principles… since all the truths about corporeal things cannot be derived from logical and geometrical axioms alone, namely, those of great and small, whole and part, figure and situation, but there must be added those of cause and effect, action and passion, in order to give a reasonable account of the order of things” (SD 441). Leibniz was well aware of the physical and mathematical contributions of Huygens, Wren, and Wallis to the matter in hand, and sought for the lacking metaphysical complementary account (SD 439–440). From the metaphysical point of view it was not at all indifferent which of the principles and their appropriate formulae were to be considered fundamental. Leibniz thus sought for a solution “which satisfies at the same time the rigor of the mathematicians and the wish of the philosophers” (ED 668). And such a solution, he believed, was exhibited in the third principle and its formula, namely, in the principle of conservation of living force, mathematically reckoned by mv2. For it is only the third that incorporates nothing that has to do with relations (as in the first principle) or spatial directionality (as in the second), both of which bore the status of mere phenomena, though “well founded”, according to Leibniz’s metaphysics. Moreover, since direction is taken into account in the principle of conservation of momentum, a body can have, in relation to another, a negative quantity of momentum. Hence, if we sum up the momenta of several moving bodies the resultant momentum of the system may turn out to be zero: “it may happen that the velocity, quantity of motion, and force of bodies being very considerable, [yet] their progress is null” (ED 658). As we have seen above, head-on colliding bodies with equal but opposite momenta can stop one another. It is possible, therefore, that a system of bodies or a world in which only momentum (or any other vector quantity) is conserved will eventually run down although now we witness much motion and activity in it.23 Such a world will have to be regenerated by God. Consequently, it cannot be the best possible world and is unworthy of God’s wisdom and power. By contrast, the living force of a body, as the formula mv2 clearly shows, is a quantity that can never become negative. Hence the total amount of living force of a system of moving bodies will never nullify. Living force thus signifies something absolutely positive and real that is preserved in all occurrences of nature. A world whose motive force is equivalent to such a quantity will not run down.24 Therefore, it is living force that suits “the wish of the philosophers”.25



7.

Leibniz and the vis viva controversy

Some speculations on Leibniz’s motives

Leibniz explicitly writes in the unpublished Essay on Dynamics of 1692 that it is possible to provide an alternative explanation of quantity of motion, one that will correct the mistaken Cartesian conception: It would be possible also to give another explanation of quantity of motion, according to which that quantity would be conserved, but it is not what is meant by Philosophers [i.e., the Cartesians]. For example, in the case of bodies A and B, each moving with its own velocity, the total quantity of motion is the sum of their individual quantities of motion; and that is what Descartes and his followers understood by quantity of motion, and to be convinced of the fact, it is only necessary to look at the rules of motion which he or others, who have adopted his principle, have given. But if we wanted quantity of motion to mean, not motion taken absolutely (where no attention is paid to the direction it takes), but progression in a certain direction then the total progression (or relative motion) will be the sum of the individual quantities of motion, when the two bodies come from the same direction. But when they come from opposite directions, it will be the difference of their individual motions. And it will be found that the same quantity of progression is conserved. But that must not be confused with the quantity of motion taken in the usual sense. (Costabel 1973: 129)

Why didn’t Leibniz say so, loud and clear, in his actual public confrontations with Cartesians, such as with the Abbé de Catelan (1686–1687) and Denis Papin (1689–1691)? Why didn’t he exercise his mastery of the art of controversy and openly suggest, as he did in the unpublished Essays on Dynamics, the correct alternative “explanation of quantity of motion” and claim to acknowledge it in addition to his living force? Indeed, as late as 1710 Leibniz admitted that his views on the matter had yet to be fully published: It is known now that M. Descartes was much mistaken in his statement of [the laws of motion]. I have proved conclusively that conservation of the same quantity of motion cannot occur, but I consider that the same quantity of force is conserved, whether absolute or directive and respective, whether total or partial. My principles, which carry this subject as far as it can go, have not yet been published in full; but I have communicated them to friends competent to judge of them, who have approved them, and have converted some other persons of acknowledged erudition and ability. (T §345, 332; my emphasis)

Leibniz gave no reasons for not publishing his complete analysis. Several possible answers, however, come to mind. Let me consider briefly two of them. In the first place, if the analysis given above is correct, then Leibniz’s position here turns heavily on his metaphysics. It involves considerations with regard to the degraded

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ontological status of relations and spatial directionality. These turn out to be, in the final analysis, not real. It also obliquely makes reference to the doctrines of the divine nature and the creation of the best possible world. These highly contentious metaphysical claims were part of his forming “mature metaphysics”. Now at least at the early stages of the controversy, when Leibniz was showing special interest in the discussion, he seemed to be still hesitating to publish this metaphysics. Recall that Leibniz believed he had succeeded in persuading Arnauld of the reasonability of his metaphysics in the correspondence immediately subsequent to the writing of the Discourse on Metaphysics of 1686 (see NS §1; L 453); yet a clear, public presentation was not offered before the New System of 1695. Moreover, if Leibniz was aiming at those whose opinions mattered such as the likes of Huygens and Newton, then he had good reason to avoid introducing controversial metaphysical reflections into his discussion. Accordingly, the Brief Demonstration of 1686 is mostly technical and almost entirely devoid of metaphysical speculation. Metaphysical considerations became significant in later writings.26 A second possible answer to our query has to do with Leibniz’s argumentative strategy in the controversy. We may use Gregory Brown’s reconstruction of the argument of Brief Demonstration to illustrate the point. Recall that on Brown’s reading the primary object of Brief Demonstration was to drive a wedge between the concepts of motive force and quantity of motion in order to “prepare the way for the introduction of a new measure of motive force – one that would be consistent, as the Cartesian measure was not, with the requirement that motive force be conserved” (Brown 1984: 132–133). Now if the only quantities on the table are m|v| and mv2, then driving a wedge between quantity of motion and motive force would naturally lead one to adopt mv2 as the measure of force. If, on the other hand, an additional quantity that does conform to the requirement of conservation of motive force is offered (e.g., mv), then driving a wedge between quantity of motion and motive force will not suffice for the acceptance of mv2. The point can be made differently, independently of Brown’s reading. Since “force” was not directly accessible, certain features were used to determine the plausibility or legitimacy of the candidates. For example, it was generally held that perpetual motion was absurd. Hence, if it could be shown that a suggested definition or measure of force implied a perpetual motion, then it would mean that it should be rejected. Similarly, since conservation was highly regarded, it would invest a measure with respectability if the latter could be shown to be conserved in nature. It is thus not totally implausible that Leibniz suppressed the conservation of progress in order to highlight and bring to the fore his measure and definition of living force.27

Leibniz and the vis viva controversy



7.1

The case of Malebranche

Before I conclude, a short digression is in order. It is worth bearing in mind that in writing on the vis viva controversy, Leibniz addressed not only scientifically oriented scholars, but also thinkers with metaphysical and theological inclinations. One such philosopher was Nicolas Malebranche, a leading figure of his time, especially among French Cartesianism. Whoever his target audience was and whatever his goals and strategies in the controversy were, at least in the case of Malebranche, Leibniz succeeded. Malebranche eventually came round to Leibniz’s position. Leibniz celebrated Malebranche’s conversion at the opening of his Essay on Dynamics: The opinion that the same quantity of motion is preserved and abides in the concourse of bodies has reigned a long time, and passed as an incontestable axiom among modern philosophers… We begin now to be disabused of this opinion, especially since it has been abandoned by some of its most ancient, most skilful, and most eminent defenders, and above all by the author himself of the Search after Truth [i.e., Malebranche]. (ED 657)

Malebranche was under a constant pressure from Leibniz to reassess time and again his initial adherence to the Cartesian physics.28 He was forced, in particular, to reevaluate his acceptance of Descartes’s principle of conservation of quantity of motion and seven rules of impact. Malebranche discussed the laws of motion in the Search after Truth (Malebranche 1960: 39–44). Leibniz first publicly attacked Malebranche’s views on the matter in his answer to Catelan in the February 1687 issue of the Nouvelles de la République des Lettres. Malebranche’s rejoinder appeared later that year in the same journal. Leibniz’s next attack on Descartes’s and Malebranche’s laws of motion, in the July issue of the same year of the Nouvelles, was based on their violation of the principle of continuity. Malebranche took Leibniz’s criticism into consideration and in 1692 he published a short treatise called Des Loix de la Communication des Mouvemens. He credited Leibniz’s objections for inducing him to reconsider his former position. But Leibniz was still not satisfied. For although Malebranche rejected some of Descartes’s rules of impact and the demonstration of the principle of conservation of quantity of motion, Malebranche still did not regard the content of that principle as false.29 It took some six more years before he rejected the principle itself. Malebranche wrote to Leibniz on December 13th, 1698: While in the countryside, where I had some leisure, I reread the small, unsatisfactory treatise on the communication of motion, and wanting to verify to my satisfaction the third laws, I realized that it was not possible to make experience fit Descartes’s principle according to which absolute motion always remains the

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same. Therefore, I have thoroughly changed this treatise, for I am now convinced that absolute motion continually decreases and increases, and that only the motion from the same direction remains the same in the collision. I have therefore thoroughly corrected this treatise, but I still don’t know when it will be reprinted. I tell you this, Sir, for you to continue to be convinced that I sincerely look for the truth, and that I deserve partly by virtue of this disposition of my mind, that you continue to love me as much as I honor you. (GP 1 355–356)

Leibniz answered on March 13th/23rd, 1699: Regarding your Treatise on the Communication of Motion that you tell me, my Reverend Father, that you want to revise, in this I recognize both your penetration and your sincerity. One must be much more penetrating in order to see what must be changed in one’s own [works], than in order to discover it in others’; but one must be very sincere in order to admit it, as you already did with regard to the laws of motion in the Search after Truth, when you honored me by saying in your small treatise of 1692 that my reflections gave you the opportunity for your new considerations. However, I have found another thing in this treatise that seemed to me to face insurmountable difficulties; this compelled me to make some remarks about it; but I didn’t want to communicate them to you by fear of looking as a man who pretended to contradict you. Now that you want to rethink it, I send you these remarks, for you to reflect on those of them you think relevant. You now agree with me that the same quantity of absolute motion is not conserved, but that [the quantity of motion] from the same direction, which I call quantity of direction, is conserved. But I have to tell you that I believe that not only the same quantity of absolute force is conserved, but also that of absolute moving action, which I have found to be entirely different from what is called quantity of motion.  (GP 1 357, my italics)

Eventually Malebranche rejected the Cartesian scalar conservation principle, rules of impact, and conception of perfectly hard bodies instantaneously bouncing in impact. He came to support, instead, the principles of conservation of momentum and vis viva, and a Leibnizian conception of elastic bodies gradually rebounding in accordance with the principle of continuity. It is thus all the more puzzling, that even after the conversion of Malebranche, Leibniz still did not publish his full positive view, conveying thereby a false impression of his take on the issue.30

8.

Conclusion

Whatever the reason may be, the fact is that the Essays on Dynamics were left unpublished until the 19th century and Leibniz was misinterpreted. The controversy he had inflamed was perceived by many of his contemporaries and successors to



Leibniz and the vis viva controversy

be mainly a physical debate in which both confronting parties enthusiastically support a legitimate physical quantity that as a matter of fact is conserved in the world. This picture led historians of science to accept d’Alembert’s judgment that the controversy was a mere dispute of words. D’Alembert demanded to ban metaphysical speculations concerning force and acknowledged the adequacy of both mv and mv2. By that, it was thought, he solved the problem and ended the controversy. I have argued that Leibniz had never held this picture of the controversy. I have shown that from the outset and long before d’Alembert he had accepted both mv and mv2, that he had been convinced of the conservation of both, and that he had preferred the latter over the former for metaphysical reasons. I have also argued that the false picture is Leibniz’s fault. In what seems to be uncharacteristic of an accomplished controversialist pleading for a public treasury of knowledge, he left the clearest expositions of his views unpublished.

Notes * Earlier versions of this paper were read at a special colloquium celebrating the publication of Marcelo Dascal’s G. W. Leibniz: The Art of Controversies and Leibniz: What Kind of Rationalist?, Tel Aviv University, January 2009; and at the 23rd International Congress of History of Science and Technology, Budapest University of Technology and Economics, July 2009. I wish to thank members of the audience for helpful discussion and comments. I am particularly grateful to Marcelo for insightful criticisms on earlier drafts and suggestions which improved the content of this study. I am also indebted to him for the translations he kindly provided especially for this paper. Needless to say, the remaining mistakes are entirely my responsibility. 1. For detailed historical accounts of the actual unfolding of the controversy and specific episodes of it, see Dugas (1958: 466–483); Hankins (1965); Laudan (1968); Calinger (1968); Iltis (1970, 1971); Costabel (1973: 41–65); Polonoff (1973: 5–38); Papineau (1977); Schönfeld (2000: 19–35); Freudenthal (2002). 2. For challenges to this standard view, see Laudan (1968); Hankins (1965: 282–286, 1968: xix– xxiii, and 1970: 204–213); Iltis (1970). 3. Thoughts on the True Estimation of Living Forces, §22, Kants Gesammelte Schriften, vol. 1, 33: “[Leibniz] leugnete Cartesens Gesetz absolut und ohne Einschränkung und setzte das seinige sofort an dessen Stelle”. 4. In this respect it is important to bear in mind that Leibniz’s contemporaries and immediate successors had only limited access to his writings. In his own time and throughout the first half of the 18th century, Leibniz’s scientific and philosophical ideas were known almost entirely from the writings he published in his lifetime such as Meditations on Knowledge, Truth, and Ideas (1684), Specimen Dynamicum (1695), A New System of the Nature and the Communication of Substances (1695), and the Theodicy (1710), and from essays and letters which were published immediately posthumously such as the Leibniz-Clarke Correspondence (1717), and The Monadology (1720). Only later did major writings such as the Discourse on Metaphysics and

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the New Essays on Human Understanding, and, particularly relevant to us here, several essays on dynamics, became publicly available. 5. See Principles of Philosophy 1.68–70, 2.4, 4.201; The World, pp. 88–90/AT 11 23–27. Reference to Descartes’s Principles of Philosophy is to part and section. 6. “Nor in fact does space, or internal place, differ from the corporeal substance contained in it, except in the way in which we are accustomed to conceive of them. For in fact the extension in length, breadth, and depth which constitutes the space occupied by a body, is exactly the same as that which constitutes the body” (Principles of Philosophy 2.10). 7. See Principles of Philosophy 2.23; The World, pp. 88–90/AT 11 23–27; and especially: “That I do not accept or desire in Physics any other principles than in Geometry or abstract Mathematics; because all the phenomena of nature are explained thereby, and certain demonstrations concerning them can be given. – I shall not add anything here concerning figures, or the way in which there also result, from their infinite diversity, innumerable diversities of movement; because these things will be, of themselves, sufficiently obvious when the occasion to discuss them arises. Furthermore, I am supposing that my readers are already familiar with the rudiments of Geometry, or that they at least have capacities adequate to the understanding of Mathematical demonstrations. For I openly acknowledge that I know of no kind of material substance other than that which can be divided, shaped, and moved in every possible way and which Geometers call quantity and take to be the object of their demonstrations. And [I also acknowledge] that there is absolutely nothing to investigate about this substance except those divisions, shapes, and movements; and that nothing concerning these can be accepted as true unless it is deduced from common notions, whose truth we cannot doubt, with such certainty that it must be considered as a Mathematical demonstration. And because all Natural Phenomena can thus be explained, as will appear in what follows; I think that no other principles of Physics should be accepted, or even desired” (Principles of Philosophy 2.64). 8. Evidently, since extension is for Descartes the essence of body, the “size” of the body referred to here is its volume and not mass. However, although there was no clear concept of mass in the controversy, at the very least not before Newton’s Principia, we can ignore it as it has no bearing on the argumentative line advanced here. I shall henceforth take “size” to mean mass. On Newton’s concept of mass, see Cohen (1999: 85–95, and 2002: 58–60). 9. The expression m|v| denotes a scalar quantity where the sign or the direction of the velocity is not taken into account. Because of its importance, I shall quote the relevant section in full: “That God is the primary cause of motion; and that He always maintains an equal quantity of it in the universe. – After having examined the nature of movement, we must consider its cause, which is twofold: {we shall begin with} the universal and primary one, which is the general cause of all the movements in the world; and then {we shall consider} the particular ones, by which individual parts of matter acquire movements which they did not previously have. As far as the general {and first} cause is concerned, it seems obvious to me that this is none other than God Himself, who, {being all-powerful} in the beginning created matter with both movement and rest; and now maintains in the sum total of matter, by His normal participation, the same quantity of motion and rest as He placed in it at that time. For although motion is only a mode of the matter which is moved, nevertheless there is a fixed and determined quantity of it; which, as we can easily understand, can be always the same in the universe as a whole even though there may at times be more or less motion in certain of its individual parts. That is why we must think that when one part of matter moves twice as fast as another twice as large, there



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is as much motion in the smaller as in the larger; and that whenever the movement of one part decreases, that of another increases exactly in proportion. We also understand that it is one of God’s perfections to be not only immutable in His nature, but also immutable and completely constant in the way He acts. Thus, with the exception of those changes which either manifest experience or divine revelation renders certain, and which we either perceive or believe to occur without any change on the part of the Creator; we must not suppose that there are any others in His works, for fear of accusing Him of inconstancy. From this it follows that it is completely consistent with reason for us to think that, solely because God moved the parts of matter in diverse ways when He first created them, and still maintains all this matter exactly as it was at its creation, and subject to the same law as at that time; He also always maintains in it an equal quantity of motion” (Principles of Philosophy 2.36). 10. The qualification “naturally” is added in order to appreciate Descartes’s too often overlooked reservation that conservation in the universe obtains “with the exception of those changes which either manifest experience or divine revelation renders certain, and which we either perceive or believe to occur without any change on the part of the Creator” (Principles of Philosophy 2.36). I take “manifest experience” and “divine revelation” to be indicators of changes in the motion of bodies caused by human souls and divine miracles respectively. 11. Principles of Philosophy 2.43, 45. As Brown (1984: 131) summarizes, Descartes’s concept of motive force was “the concept of a power in moving bodies that was responsible for maintaining them in their states of motion, by which they could act upon one another in impacts, and which was transferred and conserved in impacts”. As a matter of fact, the issue is more complicated than my brief discussion here seems to suggest. For one thing, Descartes does not provide a clear, quantitative definition of force in general. For another, the notion of “remaining in the same state” is only vaguely formulated in the first two laws of nature. It can be understood thereof as maintaining the same shape, and as either remaining in a state of rest or continuing in the same direction of motion with the same speed (Principles of Philosophy 2.37–39). Since for Descartes motion and rest are qualitatively different, this suggests forces of three kinds: a force to resist a change in shape, a force to remain at rest, and a force to continue in motion. With regard to the measurement of force of a moving body there are actually four factors that have to be taken into account. In addition to mass and speed, Descartes now also speaks of “the [area of the] surface which separates this body from those around it”, and “the different ways in which bodies come in contact with one another”. He does not go on to say, however, how these four components are to be quantitatively incorporated. It is noteworthy that Descartes speaks here of a force “to continue to move at the same speed and in the same direction”. Yet, the Cartesian quantity of motion and force of moving body are regarded as scalar rather than vector quantities. For one reason, Descartes does not mention direction in the initial introduction of quantity of motion in section 36. Second, he draws a distinction between motion and “determination in some direction”. He notes in section 41 that “there is a difference between motion considered in itself, and its determination in some direction; this difference makes it possible for the determination to be changed while the quantity of motion remains intact”. Finally, in the application of the conservation principle in the rules of impact direction is not conserved. 12. From Galileo’s results it follows that v2 is proportional to h (v is the velocity acquired in descent through the height h). Therefore, if B acquires a velocity of 1 unit in its fall from a height of 1 yard, then A acquires a velocity of 2 units in its fall from 4 yards. Hence, the quantity of motion of A is 1 x 2 = 2 and that of B is 4 x 1 = 4.

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13. As Freudenthal (2002: 586, n. 13) explains, “the same ‘magnitude’ (volume) and ‘kind’ (density) together refer to ‘weight’, and hence indirectly to ‘mass’”. 14. On the relation between the analysis of impact and that of free fall in Leibniz’s dynamics, see Westfall (1971: 294–297, 302–303). 15. Huygens’s letters to Frans van Schooten Junior, October 29th 1654, and to René François de Sluse, January 3rd 1658 (quoted from Dugas 1958: 281–282). 16. For accounts of the works of Huygens, Wallis, and Wren on the laws of impact, see Mach (1960: 402–406); Dugas (1958: 280–289, and 1988: 172–180); Hall (1966); Papineau (1977: 120–122). 17. Carolyn Iltis, for example, notes that Leibniz was well acquainted with the contributions of Huygens, Wallis, and Wren, and with the difference between the scalar m|v| and the vector mv, and that his arguments against Descartes were therefore designed to establish the superiority of mv2 over the former and not over the latter (1971: 22). As I shall argue below, however, a glance at some of Leibniz’s unpublished writings on dynamics shows that this is only partly true. Indeed, from the physical point of view, Leibniz believed, mv2 was not superior to mv. Yet he thought that there were metaphysical grounds for granting the former precedence over the latter (It should be noted, however, that Iltis does acknowledge the metaphysical import of living force in Leibniz’s view in the last part of her paper). Gregory Brown (1984) criticizes Iltis for taking Leibniz to be aiming at proving the conservation of motive force and for regarding his audience as adhering to the mistaken assumption that the Cartesian quantity of motion is conserved. On his reconstruction of the argument of Brief Demonstration, Leibniz took it as a metaphysical axiom that motive force is conserved, and was primarily aiming not at showing that quantity of motion is not conserved, but rather at “driving a wedge” between the concepts of motive force and quantity of motion and showing that they are not equivalent in order to prepare the way for introducing his mv2 as an alternative measure of motive force. As support he mentions the works of Huygens, Wallis, and Wren. He then comments that “by 1686… it was fairly common knowledge… that Descartes had been mistaken in thinking that quantity of motion was conserved”, and argues that Leibniz himself was convinced that this view was prevalent at least among “those whose opinions mattered” (1984: 128–129). Thus, on his reconstruction Leibniz addressed “those whose opinions mattered” who knew that m|v| was not conserved, or those who had reservations with regard to the conservation of m|v| and would happily give it up if only they could be shown that this concession would not commit them to a rejection of the conservation of motive force. Whether or not Brown’s criticism of Iltis is fair and his reconstruction is correct, its problems serve to highlight our point. For if Leibniz appealed to those who were convinced that m|v| was not conserved, why did he try to “drive a wedge” between m|v| and the concept of motive force without even mentioning the legitimate mv? “Those whose opinions mattered” surely knew that the works of Huygens, Wallis, and Wren not only rejected the conservation of the Cartesian quantity of motion, but also offered two alternative conservation principles, the conservation of mv and of mv2. If previously there had been reasons to link motive force with m|v|, after the latter’s deficiencies were exposed it must have seemed more natural to embrace mv and not mv2 in its place. Indeed, later thinkers who assumed the Cartesian side in the controversy argued for the conservation of mv. Moreover, as we shall see below, Leibniz himself offered to replace m|v| with mv. Therefore, a wedge should have been driven between motive force and mv as well. As for those who would happily give up m|v| if only an alternative conserved quantity were provided, they should not have been waiting almost two decades for Brief Demonstration. Since, again, the works of Huygens, Wallis, and



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Wren supplied the desired alternatives. And, in their case as well, a transition to mv would be natural. In sum, whoever the audience were – the experts, the hesitators, or the dogmatists who still adhered to m|v| – a complete analysis demanded dealing with all the quantities involved. But as we shall see, mv was suppressed in Leibniz’s public discussion. 18. I refer here to two writings called “Essay on Dynamics”. The one was written in 1692 and published by L. A. Foucher de Careil in 1859 and by Pierre Costabel in 1960 (English translation in Costabel 1973). The other was published in 1860 in Gerhardt’s edition of Leibniz’s Mathematische Schriften (GM 6 215–231) and translated by Langley in his edition of the New Essays. It was dated by Gerhardt to 1691. Costabel (1973: 30) noted that it had to be written at a later date due to its reference to “the conversion of Malebranche in 1698”, but commentators writing after Costabel seem to overlook this remark, still adhering to Gerhardt’s initial dating to the early 1690s (see, for example, Iltis 1971; Brown 1984; Garber 1995: 316). In a treatise on the “communication of motion” from 1692, Malebranche rejected some of Descrates’s rules of impact and the demonstration of the principle of conservation of quantity of motion, but still did not regard the content of that principle as false. Only later did he reject the principle itself. Now, assuming that Leibniz’s essay was written in the early 1690s, Brown thinks that its reference to Malebranche is to his treatise of 1692. Consequently, he considers Leibniz’s reference to Malebranche’s conversion in the treatise of 1692 “confident” and “overly optimistic” (1984: 132, n. 37). But Leibniz, as a matter of fact, was not deluded by Malebranche’s essay of 1692 and his reference to the conversion of Malebranche was not to the treatise of 1692. As late as January 1698 he still wrote to Denis Papin of the confusion of Descartes and Malebranche with regard to the conservation of quantity of motion (A III 7 449). His correspondence with Malebranche later that year (see section 7.1 below) shows that he was aware of the shortcomings of the treatise of 1692 and of the conversion that had taken place in 1698. In short, Leibniz’s correspondence supports Costabel’s claim that the Essay on Dynamics in Gerhardt’s edition of Leibniz’s Mathematische Schriften could not have been written before 1698. It is also noteworthy that in a letter to Malebranche from March 1699 (quoted below) Leibniz referred to “action motrice” (moving action), a concept that did not appear in earlier writings such as Brief Demonstration or the Essay on Dynamics of 1692, but figures in the title of the essay under discussion. 19. See also the Essay on Dynamics of 1692, in Costabel (1973: 127–129). 20. See also Leibniz’s 5th letter to Clarke, §99: “The author [Clarke] objects, that two soft or un-elastic bodies meeting together, lose some of their force. I answer, no. ’Tis true, their wholes lose it with respect to their total motion; but their parts receive it, being shaken [internally] by the force of the concourse. And therefore that loss of force is only in appearance. The forces are not destroyed, but scattered among the small parts. The bodies do not lose their forces; but the case here is the same, as when men change great money into small” (LC 87–88). Freudenthal (2002: 574, 613, 617–618, 626) suggests that Leibniz may have arrived at this idea through his public controversy with Denis Papin between 1689 and 1691. 21. This principle was established by Huygens as the fourth proposition of his The Motion of Colliding Bodies: 579–580. 22. He writes in the Essay on Dynamics of 1692: “the ground for this maxim of progression is rather apparent, and it is reasonable, when nothing happens from without, that everything (composed of moving bodies) should not be hindered from progressing by itself as much as before” (Costabel 1973: 129). This remark shows that he was aware of the condition that the resultant momentum of a system of bodies is conserved so long as no external forces are applied.

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23. To prevent a system of bodies in which only a vector quantity is conserved from running down, God has not only to decree conservation, but also to assign it some positive value. 24. One could argue that in this case too, God has to decree conservation and to assign it a positive value. The point is, however, that a world in which living force is conserved cannot run down: either it is completely inert (i.e., lacks even the potential to be active) from the outset, or it will persist in its activity. A world with enduring motion, however, may suffer other disasters. For example, it may come to a state of “heat death” in accordance with the second law of thermodynamics. Although motion may not cease and “living force” will remain the same, it is doubtless a different form of “running down”. 25. See ED 667–668. For similar interpretations of this point, see Iltis (1971: 33); Garber (1995: 318–319). 26. This is not to suggest that Leibniz did not address speculative metaphysicians as well or that metaphysical considerations were entirely absent from his arguments. Rather, the point is that at least at the early stages of the controversy Leibniz employed more conventional metaphysical principles such as the equality of cause and effect and the law of continuity. He argued for the reality of force over and above the property of extension and for a dynamical conception of material substances, but still did not link it to the robust metaphysical conception of  material substances as constituted by substantial forms (primitive active force) and primary matter (primitive passive force). These further metaphysical contentions are present, for example, in Specimen Dynamicum of 1695. But here too, the clear analysis of the Essays on Dynamics is missing. Although the vis viva controversy is not the main issue of Specimen Dynamicum, this absence diminishes somewhat the strength of the answer offered here. 27. Freudenthal, writing on the Leibniz-Papin Controversy, argues that from the very first the range of possibilities was restricted to m|v| and mv2 (which is proportional to mh). The reason is that both quantities were drawn from statics, and it was implicitly agreed by both sides that free fall was an extension of the area of statics (2002: 582–583, 587). But if broader questions of conservation are involved and if Leibniz was interested in motive force in general and in answering how the force of a body in motion should be measured, then this is unsatisfactory. For bodies in motion do not only fall, but also roll, move horizontally, etc. In particular, they collide, and collision essentially involves mv. Impact was commonly conceived as the fundamental interaction and source of change of motion in the material world (Leibniz himself held this view with regard to the phenomenal, physical world). If so, reflections on motive force could not ignore mv. Furthermore, considerations concerning conservations had been already present in the works of Huygens, Wallis, and Wren on the laws of impact, and all the three quantities (m|v|, mv, and mv2) were discussed. Leibniz himself linked living force and impact from the very first stage of the controversy, as the letter to Arnauld of November 28th/December 8th 1686 (LA 97–99) clearly testifies. Naturally, he connected them most lucidly in the Essays on Dynamics. In short, if the vis viva controversy and the problem of impact are intimately involved, as I have tried to show they are, then the range of possibilities must have included mv, in addition to m|v| and mv2. 28. A thorough examination of the influence of Leibniz on Malebranche is beyond the scope of this study. For a detailed discussion of Malebranche’s successive revisions of his earlier Cartesianism in this context, as well as his movement towards Leibniz’s position, see Pyle (2003: 131–157). I rely heavily on his account.



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29. That Malebranche did not reject in 1692 the Cartesian principle of conservation of quantity of motion is also evident from his correspondence with Leibniz right after the publication of his treatise. See his letter from December 8th 1692 (GP 1 343–344). 30. Costabel argues that publishing against Cartesian mechanics at the beginning of the 1690s and before the conversion of Malebranche must have appeared to Leibniz “very risky” (1973: 30). This, however, cannot be regarded as a reason for not publishing the Essays on Dynamics. For despite the risk, ever since 1686 Leibniz had been publicly arguing against Cartesian mechanics. Furthermore, the unpublished Essays on Dynamics offered the quantity mv as a correction for Descartes’s m|v|, and this must have seemed to the French Cartesians more appealing than the brute rejection of the Cartesian quantity in Brief Demonstration. Finally, even if the risk can explain Leibniz’s refrainment from publishing at the beginning of the 1690s, it cannot explain the fact that Leibniz still did not publish his full view after Malebranche’s conversion.

References Alexander, H. G. 1956. “Introduction”. LC ix–lv. Brown, G. 1984. “‘Quod ostendendum susceperamus’. What did Leibniz undertake to show in the Brevis Demonstratio?”. In A. Heinekamp (ed), Leibniz’ Dynamica (= Studia Leibnitiana, Sonderheft 13). Stuttgart: Franz Steiner, 122–137. Cajori, F. 1962. A History of Physics, in its Elementary Branches (through 1925): Including the Evolution of Physical Laboratories. (Revised and enlarged edition). New York: Dover Publications. Calinger, R. 1968. “The Newtonian-Wolffian confrontation in the St. Petersburg Academy of the Sciences (l725–l746)”. Cahiers d'Histoire Mondiale (Journal of World History) 11: 417– 435. Cohen, I. B. 1999. “A guide to Newton’s Principia”. In I. B. Cohen and A. Whitman (trans), I. Newton, The Principia: Mathematical Principles of Natural Philosophy. Berkeley, CA: University of California Press, 1–370. Cohen, I. B. 2002. “Newton’s concepts of force and mass”. In I. B. Cohen and G. E. Smith (eds), The Cambridge Companion to Newton. Cambridge: Cambridge University Press, 57–84. Costabel, P. 1973. Leibniz and Dynamics: The Texts of 1692. R. E. W. Maddison (trans). Paris: Hermann. Dascal, M. 2006. “Introductory essay”. In M. Dascal, with Q. Racionero and A. Cardoso (trans, eds), G. W. Leibniz, The Art of Controversies. Dordrecht: Springer, xix–lxxii. Descartes, R. 1985. The World or Treatise on Light. In J. Cottingham, R. Stoothoff, and D. Murdoch (trans), R. Descartes, The Philosophical Writings of Descartes, Vol. 1. Cambridge: Cambridge University Press, 81–98. Descartes, R. 1983. Principles of Philosophy. V. R. Miller and R. P. Miller (trans). Dordrecht: Reidel. Descartes, R. 1964–1976. Oeuvres de Descartes. C. Adam and P. Tannery (eds). Paris: Vrin. [= AT] Dugas, R. 1958. Mechanics in the Seventeenth Century (from the Scholastic Antecedents to Classical Thought). F. Jacquot (trans), foreword by Louis de Broglie. Neuchâtel: Editions du Griffon.

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Dugas, R. 1988. A History of Mechanics. J. R. Maddox (trans), foreword by Louis de Broglie. New York: Dover. Freudenthal, G. 2002. “Perpetuum Mobile: The Leibniz-Papin controversy”. Studies in History and Philosophy of Science 33: 573–637. Garber, D. 1995. “Leibniz: Physics and philosophy”. In N. Jolley (ed), The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press, 270–352. Hall, A. R. 1966. “Mechanics and the Royal Society, 1668–1670”. The British Journal for the History of Science 3: 24–38. Hankins, T. L. 1965. “Eighteenth-century attempts to resolve the vis viva controversy”. Isis 56: 281–297. Hankins, T. L. 1968. “Introduction”. In Jean le Rond d’Alembert, Traité de Dynamique. New York: Johnson Reprint Corporation, ix–xxxv. Hankins, T. L. 1970. Jean d’Alembert: Science and the Enlightenment. Oxford: Clarendon Press. Huygens, C. 1977. The Motion of Colliding Bodies. R. J. Blackwell (trans). Isis 68: 574–597. Iltis, C. 1970. “D’Alembert and the vis viva controversy”. Studies in History and Philosophy of Science Part A 1: 135–144. Iltis, C. 1971. “Leibniz and the vis viva controversy”. Isis 62: 21–35. Kant, I. Gesammelte Schriften. Edited by the German Academy of Sciences. Berlin: Walter de Gruyter, 1900–. Laudan, L. L. 1968. “The vis viva controversy, a post-mortem”. Isis 59: 131–143. Leibniz, G. W. 1684. Meditations on Knowledge, Truth, and Ideas. L 291–295. Leibniz, G. W. 1686. A Brief Demonstration of a Notable Error of Descartes and Others Concerning a Natural Law, According to Which God is Said Always to Conserve the Same Quantity of Motion; a Law Which They Also Misuse in Mechanics. L 296–302. [= BD] Leibniz, G. W. 1686. Discourse on Metaphysics. L 303–330. Leibniz, G. W. 1692. Critical Thoughts on the General Part of the Principles of Descartes. L 383– 412. Leibniz, G. W. 1692. Essay on Dynamics. In Costabel 1973: 108–131. Leibniz, G. W. 1695. Specimen Dynamicum; for the Discovery of the Admirable Laws of Nature concerning Corporeal Forces, their Mutual Actions, and their Reduction to their Causes. L 435–452. [= SD] Leibniz, G. W. 1695. A New System of the Nature and the Communication of Substances, as well as the Union between the Soul and the Body. L 453–461. References to section number and page. [= NS] Leibniz, G. W. 1714. The Monadology. L 643–653. Leibniz, G. W. 1896. Essay on Dynamics on the Laws of Motion, in which it is Shown that not the Same Quantity of Motion is Preserved, but the Same Absolute Force, or rather the Same Quantity of Moving Action (L’Action Motrice). In A. G. Langley (trans), G. W. Leibniz, New Essays Concerning Human Understanding. New York: Macmillan, 657–670. [= ED] Leibniz, G. W. 1951. Theodicy: Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil. E. M. Huggard (trans), A. Farrer (ed). London: Routledge & Kegan Paul. References to section number and page. [= T] Leibniz, G. W. 1996. New Essays on Human Understanding. P. Remnant and J. Bennett (trans, eds). Cambridge: Cambridge University Press. Leibniz, G. W. and Arnauld, A. 1967. The Leibniz-Arnauld Correspondence. H. T. Mason (trans, ed). Manchester: Manchester University Press. [= LA]



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Leibniz, G. W. and Clarke, S. 1956. The Leibniz–Clarke Correspondence. H. G. Alexander (trans, ed). Manchester: Manchester University Press. [= LC] Mach, E. 1960. The Science of Mechanics: A Critical and Historical Account of its Development. T. J. McCormack (trans), new introduction by K. Menger. 6th edition with revisions through the 9th German edition. La Salle, IL: Open Court Publishing Company. Malebranche, N. 1960. Oeuvres Complètes, Vol. 17–1. P. Costabel, A. Cuvillier, and A. Robinet (eds). Paris: Vrin. Papineau, D. 1977. “The vis viva controversy: Do meanings matter?”. Studies in History and Philosophy of Science 8: 111–142. Polonoff, I. I. 1973. Force, Cosmos, Monads and other Themes of Kant’s Early Thought. Bonn: Bouvier. Pyle, A. 2003. Malebranche. London: Routledge. Schönfeld, M. 2000. The Philosophy of the Young Kant: The Precritical Project. Oxford: Oxford University Press. Westfall, R. S. 1971. Force in Newton’s Physics: the Science of Dynamics in the Seventeenth Century. London: Macdonald.

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chapter 4

The controversy between Leibniz and Papin From the public debate to the correspondence Anne-Lise Rey

1.

Introduction

I analyze here the still unpublished1 correspondence between Leibniz and Denis Papin (1692–1707). My analysis purports to articulate the status of formal effect, the conception of action, and the function of final causes in the demonstrative device of the dynamics.2 My objective is double: to understand in what sense and to what extent Leibniz’s dynamics can be viewed as a reform of Cartesian mechanics, from a strictly mathematical point of view and correlatively, to determine the function of this correspondence as part of a larger persuasive goal, that of convincing a learned Cartesian, familiar with experimental proofs, of the relevance of the dynamics. The question is whether this strictly mathematical presentation of the dynamics is, as Leibniz claims in this correspondence,3 entirely separable at the time from what it represents both in terms of natural philosophy and the revision of the definition of substance (the only public dimension of the dynamics). Or perhaps does it serve as an adequate language to convince Papin? This last hypothesis would illustrate the function of the controversy, and of the correspondence, in the evolution of an incipient science.

2. What kind of relation obtains between the public controversy4 and the correspondence? Four publications between 1689 and 1691 in Acta Eruditorum made the controversy opposing Leibniz and Denis Papin public. These polemic exchanges comprised two texts on the cause of gravity and two other texts more directly dealing with motive forces. In 1689 Papin published an article headed De gravitatis causa

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et proprietatibus Observationes (Acta Eruditorum, April 1689: 183–188) to which Leibniz replied in 1690 with an article headed Observatio de Causa gravitatis et defensis sententiae autoris de veris naturae legibus contra Cartesianos (Acta Eruditorum, May 1690: 228–239). Papin’s Mechanicorum de viribus motricibus sententia, asseta a D. Papino adversus Cl. GGL objectiones (Acta Eruditorum, January 1691: 6–13), followed suit, to which Leibniz answered with his De legibus naturae et vera aestimatione virium motricium contra Cartesianos. Responsio ad rationes a Dn. Papino mense januarii anni 1691 in Actis eruditorum 6 propositas (Acta Eruditorum, September 1691: 439–447). In 1695, Papin summed up the differences between his and Leibniz’s positions in Dissertationes de novis quibusdam Machinis atque aliis argumentatis philosophicis. Synopsis controversiae Authoris cum celeberrimo Viro Domino G.G.L. circa legitimam rationem aestimandi vires motrices (Acta Eruditorum 1695: 376–402). This text is the real starting point of their correspondence. I will examine this debate in order to better understand their previous exchanges and recurring differences. Dissatisfied with Papin’s summary, Leibniz wrote to him: “I must confess that when reading the summary of our controversy you propose, I cannot recognize myself my own conception of these things. And, therefore, it will be more difficult for others to understand what I mean”.5 The main theoretical point of the controversy between the two concerns the relevance of the Leibnizian estimation of the motive forces. That is, it concerns at the same time the vis viva controversy, which opposes the Cartesian principle of conservation of the quantity of movement and the Leibnizian principle of the conservation of the quantity of living force, as well as the status, in the Leibnizian demonstrative apparatus, of the formal effect. Leibniz introduces the existence of a formal effect into his various formulations of the motive forces as an effect which keeps its force, but does not consume it. Now, it is precisely in the understanding of the sense and the function of the formal effect that the ambivalence pertaining to the introduction of the notion of action as formal action can be situated. It is important, therefore, to describe the circumstances of introduction and justification of formal action. Throughout the various publications, one can observe the correspondence between the two men discuss word by word the reasons for their difference. What interests me here is the interplay between argumentative processes and theoretical opposition that characterizes this correspondence. Two recurring aspects can be said to frame this exchange. One concerns its argumentative modalities, while the other concerns the explanatory modalities used by Leibniz to convince his interlocutor. Indeed, the correspondence follows the concessions made by Papin to the Leibnizian arguments, concessions that lead Leibniz to his demonstration a priori of the principle of conservation of motive action.6 Thus, we have a phase in the



Leibniz and Papin: From the public debate to the correspondence

course of which Papin retracts and refuses – one by one – all the arguments to which he had agreed at first. This phase is structured first around Papin’s revelation of “paradoxes” (or the reduction ad absurdum of Leibniz’s arguments) which he detects in Leibniz’s letters, and the ingenuity employed by Leibniz to undo, one by one, these paradoxes; but also around the recurring necessity to “shape” the arguments (sometimes even “reduce” them) either to syllogisms, or to summaries of the presented arguments and objections. The production of specific explanations – which is aimed at convincing Papin – develops especially around the question of whether or not it is possible to agree to resort to final causes. It is from this viewpoint that reluctance to admit certain fundamental concepts of the dynamics as well as their definitions is organized. This is particularly evident regarding the discussion about the notion of living force or the debate about formal effect. Papin writes: “What’s the need to introduce a living force, since either in communicating the force or in receiving it, it is always the law of the dead force that applies?”.7 Leibniz answers by arguing that Papin’s question is absurd, for it is analogous to the question, “why to speak of times since there are nothing but moments?”.8 Also worthy of mention are the discussions starting from 1698 about the two possible senses of the word ‘action’: when Leibniz clearly distinguishes violent action from formal action, Papin resists and refuses to consider formal action as an action.9 It seems to me that it is around this question that the effect of the correspondence is most clearly revealed, not only as far as the contenders’ public positions as expressed in the learned newspapers are concerned, but also with regard to Leibniz’s defence of his own theses. Due to the interaction suited to the correspondence and the increasing hesitations of Papin, Leibniz raises numerous arguments to support the importance of the notion of action, and especially to highlight the source of its justification in efficient causes alone.10 The Leibniz-Papin correspondence, still unpublished, was commented in a major article by A. G. Ranea (1989), which emphasizes an essential aspect of Leibniz’s thought – the unveiling of the a priori reasons for the estimation of motive action. Ranea’s interpretation of this correspondence has three main aspects. First, concerning the place and the function of this correspondence in the general argumentative economy of Leibniz’s dynamics, Ranea suggests reading the exchanges between Leibniz and Papin as “the missing link” between the exposition of the a priori argument to Johann Bernoulli and that proposed to De Volder.11 Second, he points out that, although Leibniz and Papin undertake to provide an a priori demonstration of the Galilean conception of uniformly accelerated movement, the basis of their answers is different insofar as Papin relies on the causal power of gravity, whereas Leibniz rejects it. Finally, Ranea clearly

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identifies Leibniz’s singular attitude in his exchanges with Papin as stemming from his doubts about the persuasive power of his own a priori argument.12 As a result, Ranea is able to show in what sense it is necessary to understand the a priori demonstration in the dynamics:13 as what derives mechanical properties from experience, based on principles.14 Bearing in mind the useful interpretation by Ranea, I would like to raise another question about this correspondence, and examine here how the correspondence is engaged, first, in a general argumentative regime, since the a posteriori arguments about the measure of the living force have to be agreed on in order for the a priori demonstration of the principle of conservation of motive action to be “revealed”. It is also necessary to agree, beforehand, that force can be present even when there is no resistance to be surmounted. Furthermore, I would like to show how the argumentative regime governing this correspondence is also quite specific, in that it tries to demonstrate, appealing to efficient causes alone, the relevance of the dynamics. My hypothesis here is that what might appear as reservations, doubts, or lack of confidence on the part of Leibniz can be interpreted just as convincingly as the desire to relegate the arguments addressed to Papin to an exclusively explanatory domain, that of the strict appeal to efficient causes,15 i.e., to the “mathematical aspect” of the dynamics. Nevertheless, in a second period of the correspondence, this “pure” mathematical approach to the problem is placed within the framework of a “mathematization of purely ontological concepts”,16 which clarifies the importance of action in Leibnizian thought. The above considerations suggest that it is the movement between a persuasive strategy and a modality of writing specifically addressed to Papin as a singular interlocutor – a Cartesian attached to proofs based on experiments – that yields a particular structure for the proofs of the dynamics, along with some argumentative variations. A contrario, by recalling the complex links which connect the public texts and the semipublic texts that constitute this and other correspondences at the end of the 17th century,17 I would like to show how Leibniz uses the correspondence with Papin within the framework of a much larger strategy of diffusion of his dynamics which renders this correspondence a specific argumentative space within it, whose importance can only be understood with reference to Leibniz’s other correspondences (especially with Johann Bernoulli and Burcher De Volder). From this perspective, I will consider how the correspondence itself is a kind of whole text unwinding its demonstrative procedures in answer to objections, or working to round off the meaning of its fundamental concepts; I will also compare and contrast the differentiated addresses on the same subject to different correspondents.



Leibniz and Papin: From the public debate to the correspondence

My hypothesis for reading the correspondence is thus twofold: 1. The public controversy that appears in 1689–1691, the Acta Eruditorum of Leipzig, is used to introduce and to justify the link between a defence of the principle of conservation of living forces (conceived and estimated as being different from the Cartesian principle of conservation of the quantity of movement) and the architectonic principle of equality between the full cause and the whole effect. While this link is present for Leibniz from the time of his De corporum concursu (1678), it seems to work as a major public argumentative procedure only from the beginning of the 1690s. 2. The correspondence with Papin, starting from a discussion about the reasons for their divergence, is the forum for a close exchange about what constitutes the formal effect. At the same time, this discussion sheds light on how Leibniz justifies the relationship between formal effect and action. It could thus be said that, while the public controversy seems to work as the continuation of a perfectly ordinary quarrel between a Cartesian upholder of the quantity of movement and Leibniz, who defends the living force, this controversy can only be understood within the framework of the logic of the elaboration of the new science, the dynamics of action. Seen in this light, the controversy takes place in the middle of a development, starting with the Dynamica of potentia (GM 6 281–514) and continuing with the correspondence with Papin, to whom Leibniz justifies, almost always at the physical level alone, the necessity of an ‘action in itself’, required by the explanation of what is the formal effect.

3.

The obviousness of a difference

3.1

The stakes in the correspondence

For Leibniz, his controversy with Papin provides an opportunity for the implementation of an argumentative device, attached to experimental proofs and designed to convince a Cartesian. It is for Leibniz extremely important to convince this type of interlocutor. Let us recall, indeed, that at the end of the 17th century, a new natural philosophy is emerging; although it takes multiple forms, it is characterized by a concern to leave room for what experience teaches us about nature. In this respect it roughly follows what could be called the Newtonian lesson, while wanting to maintain a solid metaphysical foundation. This presentation, of course, deliberately does not take into account what Newtonian metaphysics can really mean. It is valuable, for Leibniz, to convince this type of interlocutor for at least two reasons. The first is the desire to show, on experimental grounds,

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the inanity of the Cartesian principle (this explains Leibniz’s characterization of Papin’s perspective as a fiction). The second reason is a desire to propose a new relationship between science and metaphysics, doubtless more in keeping with what many scholars were waiting for at the time. Now, the peculiarity of the dynamics is that it appears, at least in texts published in the learned newspapers of the 1690s, as a “mixed science”, both physical and metaphysical. Leibniz, as we have seen, indeed proceeds through a double path: the notion of action, with its ambivalence of being at the same time formal action and essence of the substance, makes it clear that the dynamics needs metaphysical action as a base and that, reciprocally, metaphysics needs the space of the dynamics to express the action, where express is here intended in the strong sense.18 Therefore, the correspondence with Papin is extremely interesting because Leibniz is obliged to formulate a new argumentation founded on Papin’s exigencies, insofar as it adheres to the limits fixed by Papin: a clear preference for the appeal to efficient causes “in line with reason” and a mistrust of final causes often used to justify “the incongruity of the opinions” (Leibniz to Papin, December 2nd 1697; LBr, 714, 119r). At the same time, within the framework imposed by this requirement, Leibniz uses a measure of perfection or reality which clearly places his work in dynamics, as stressed by Fichant, within “the recognition, in the most mathematically exact definition of action, of a properly metaphysical and not mathematical meaning” (Fichant 1998: 226). It is the mathematical requirement, therefore, that brings to light the ambivalence of the action, along with its fundamentally metaphysical dimension. Finally, if Papin is an interlocutor from whom it is particularly valuable for Leibniz to obtain adherence to his dynamics, it is not only because he represents perfectly the experimenter who follows Cartesian mechanics, but also because, in order to justify the coherence of his position, he is repeatedly led to amend it on questions which constitute real argumentative levers (for example, when Leibniz refers to insensible matter, as we shall see later). Leibniz weaves a close link between his various correspondences, not only by cross-references – between Bernoulli and De Volder, as well as between Papin and Bernoulli – but also by taking advantage of Papin’s resistance to some of his arguments in order to formulate them otherwise when addressed to De Volder, on the grounds that they correspond to a common type of interlocutors: a Cartesian who is open-minded to proofs by experiments. In this respect, it is fascinating to read in parallel the correspondences of Leibniz with Papin, Bernoulli, and De Volder from 1698 and to see what they reveal concerning the varieties of justification Leibniz’s employs for the introduction of formal action in his argument.



3.2

Leibniz and Papin: From the public debate to the correspondence

The objects of the public controversy reshaped  by the correspondence

What exactly is the nature of the opposition between Leibniz and Papin with respect to the estimation of the motive force? The two specific problems from which it is possible to compare the different proposals to measure the motive force are the following: how can we estimate the motive force of a body when it is in freefall according to a naturally accelerated movement? And how can we estimate the motive forces of bodies which rise to a certain height due to movement acquired in the descent, from the same height? As a good Cartesian, Papin wants to show that the forces are calculated through the quantity of movement, and in so doing he distances himself from the Leibnizian position on three counts: the first is the choice of the unit of measurement allowing the living forces to be estimated; the second is the adherence to the idea of a causal power of gravity for the estimation of free-fall or the rise of bodies (note that the first and the second aspects are intrinsically linked); and the last concerns the refusal to take into account the formal effect in the calculation of the motive forces. With regards to the question of the unit of measurement to be used in the calculation of the motive force, Papin acknowledges that we need to consider the resistance that this force has to overcome in order to develop itself, and to take into account the fact that a body moves vertically.19 This, in turn has two consequences: First, in opposition to Leibniz who argues that we should estimate the force of a body by following the distance it has covered, Papin proposes another criterion of evaluation. His Cartesian criterion20 identifies this force with the quantity of movement and bases the estimation on time rather than on the distance covered. Second, it also means that if we include resistance as a constituent of the estimation, we afford a place to the action of gravity as a causal determination of the movement. This second aspect is taken by Papin from Huygens’s conception of the cause of gravity. This is an essential point because Leibniz in his estimation refuses to give any importance to the action of gravity in the determination of the measurement of forces. The reason for this refusal is clear: it allows Leibniz to introduce the estimation of force a priori and to literally modify the formulation of the problem by suggesting that the force of a body in movement be estimated not vertically, but horizontally. Thanks to this modification of the formulation he can introduce the notion of formal effect,21 which is the effect considered in the context of a movement which develops horizontally. This leads to the third fundamental difference between Leibniz and Papin. For the latter there can be no

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question of making this unreal effect of power (an effect that keeps its force and does not consume it, as Leibniz later says in defining the formal effect.22 We can readily understand the importance of these differences, even beyond the will (shared by Leibniz and Papin) to provide an a priori justification for the definition of uniformly accelerated movement proposed by Galilee. First, it is a question of viewing science in a different way, which assumes a different way of viewing the demonstrative method. Leibniz’s refusal of considering the cause of gravity as a factor in the measure of force transforms the discussion about it into the first step in the direction of the notion of a priori, making it possible to grant a function to abstract entities in scientific measurement. Leibniz indeed suggests using as a unit of measurement an effect which is not found in the physical world – an ideal or abstract effect. But the key issue here is that this effect must be understood as formal or abstract, but at the same time be afforded efficacy. What Leibniz thus proposes to Papin as a unit of measure of force reveals a new concept of science, in which the abstract entity, built from the first notions, allows us not only to understand what the real effects are (and it is this link, metaphysically established, that is determining) but also to measure them. It is now time to compare the arguments employed in the public sphere with those that appear in the correspondence, in order to show the use Leibniz makes of the public controversy in the constitution of his scientific theories and what function he assigns to the correspondence in his multiple argumentative devices.

3.3 The principles of conservation discussed in the correspondence:  The status of “insensible matter” Leibniz employs the point of agreement between him and Papin with regards to the equivalence between the full cause and the whole effect in order to try to make the latter admit the conservation of living forces. The equivalence between the full cause and the whole effect is agreed upon already in the first letters: “It seems that you do not disapprove of my principle which consists in the equality of the cause and the effect and on which rests my way of estimating power”.23 It is accompanied by the definition of two essential concepts in Leibniz’s argumentation: quantity of power and violent effect. Leibniz has to define the former in order to show to what extent the Cartesian identification of the quantity of movement with force is senseless; he will return to this concept when discussing the definition of force. The definition of violent effect, in its turn is crucial for him to enable him to distinguish, later, this concept from that of formal effect. The quantity of power is defined as “what is determined by the number of repetitions of the same violent effect”,24 and this violent effect is



Leibniz and Papin: From the public debate to the correspondence

defined itself as “that whose production, when repeated often enough, is capable of destroying the movement in the one who produces it”. (Ibid.: LBr, 714, 18v)25 The argumentative base from which Leibniz seems to want to convince Papin thus articulates the formulation of the equivalence of the full cause and the whole effect (which allows perpetual mechanical motion to be avoided) with the definition of power. In August 1695, Leibniz wants to show Papin the contradiction, which he considers impossible to hold, between the acceptance of the Leibnizian principle of the full cause and the whole effect, on which the whole of his dynamics is based, since it is “the fundamental axiom of my reasoning” (Ibid.: LBr, 714, 18v) and Papin’s statement that the force and the quantity of movement do not differ. To prove that these two theses are compatible, Papin introduced the idea of an insensible matter that compensates for the quantity of movement which gets lost in sensible bodies. This hypothesis allows him to admit that there is indeed a loss of the quantity of movement in the case of the shock of two bodies, but also that this quantity of movement, far from disappearing, is transferred into an insensible matter, and in so doing it guarantees the conservation of an identical quantity of movement in the world.26 This is exactly what Leibniz points at, claiming that this amounts to the addition of an ad hoc entity, required by Papin in order to maintain an appearance of coherence in nature. That is why he writes to Papin that “it would be necessary, with you, to resort to some insensible matter by which nature supplies this deficiency”.27 This addition of insensible matter is backed up by Papin by the assertion that he has given a demonstration of the equivalence of the quantity of movement and force. This theoretical point interests us here for at least two reasons. First, Papin asserts that he gave this demonstration in the "synopsis" of the controversy which was published in Acta Eruditorum in 1695, so that the discussion which begins in the letters that follow is a critical comment, on the one hand, and an attempt at an explicitation, on the other, of what had already been made public. Secondly, in order to summarize the argumentation of Papin, Leibniz writes a logical outline which, considering the equivalence of the proportion of the powers of two equal bodies with the proportion of the resistances which they can overcome, leads to the conclusion that Papin is actually claiming that the proportion of the powers of these bodies is the proportion of speeds. Leibniz agrees only partially to this, since it is beforehand necessary to agree on the definition of “resistance”. It is in this context that Leibniz reaffirms, or rather reformulates, the fundamental principles of the dynamics, when he writes in the letter of December 20th 1695: “the rule of the conservation of the same effects as I established for the foundation of all the Dynamics with no need here to resort, with some difficulty, to your insensible matter” (LBr, 714, 45v). But the correspondence makes Papin change his mind

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on this point, as it is evident in the letter of February 9th 1696. Once he understands that he cannot continue to maintain both his criticism of the Leibnizian estimation of the forces, and the idea, taken from Descartes and from Huygens of compensation in the invisible matter for the loss of the quantity of movement at the time of the shocks. Papin thus gives up this invisible or imperceptible matter and promises to avoid, as far as he can, taking into account the motive power of gravity in the examples that he uses. The difference between Leibniz and Papin continues to be evident in the correspondence, where on the one hand, there is the confusion between force and quantity of movement, and on the other there is the refusal (by Papin) and the requirement (by Leibniz) of admitting the formal effect. But the correspondence has already made the interlocutors change their minds on decisive points. Papin made a valiant attempt to relinquish, without always succeeding, imperceptible matter and the cause of gravity, although it was the central point of the public debate. We can envision these concessions or, more simply, these theoretical changes, as a kind of conversion due to the Leibnizian argumentative power; but we can also understand them as a concern for a hierarchical organization of the objects of discord, and especially the objects which Papin sees as important to continue to hold in the discussion. So we see in these relinquishments a step in the reconfiguration of the discussion towards a debate centered on the a priori argument of the principle of conservation of the motive action.

4.

Leibniz attempts to bring Papin over to his dynamics

The syllogistic shaping of the arguments which begins as early as the letter of August 30th 1695, and will be further developed later on, supplies an interesting example of the means used by Leibniz to put an end to the controversy. How to come to an agreement on the terms used and to convince Papin? Leibniz proposes to achieve this by first resorting to formalization devoid of ambiguity. Now, the problem which immediately arises is that of the definition of the terms involved in the propositions of the syllogism. If “formalizing” the differences is imperative, it is because for several months, not to say several years, the exchange of arguments in the correspondence was constantly held back by rehashing things that Leibniz had considered settled. For example, Papin's agreement on the idea of the conservation of force, an agreement achieved in order to avoid the confusion between movement and force, is questioned by himself, for example in his letter to Leibniz of January 15th 1696, where he states that he has never intended to agree with anything other than the conservation of the force “in two bodies before and after the impact” (LBr, 714, 47v).



Leibniz and Papin: From the public debate to the correspondence

Moreover, Papin replies to what Leibniz took as an agreement by reminding him that by “force and effect” he does not understand the same thing as Leibniz. So, in the letter of January 15th 1696, Papin distinguishes the force which Leibniz measures “by the height where bodies can rise up” (LBr, 714, 47v) from that whose quantity is unchanging, which is measurable for Papin by the “real resistance” which it is able to overcome. It is for that reason that according to Papin, the force cannot be identified with the effect.28 It is to surmount this feeling of never finding his ideas in the words of the other that Leibniz decides to propose a formal approach to the quarrel, although he is aware of its shortcomings.29 Therefore, I believe the central point is to determine whether the syllogistic form is only an “order of justification” which merely expresses differently what has been discovered before, namely the axiom of motive action, or whether the syllogistic form can be considered as a heuristic aspect in the invention of the new science of dynamics.30 In April 1696 Leibniz sees in the rigor of the shape the opportunity “to recognize on both sides if the thesis is proved or not”.31 Papin agrees immediately in May, but suggests formalizing his arguments himself and formulating many syllogisms based on one principle, which was proposed by Leibniz and which he accepts. This principle is: “the force and its effect are always equivalent in such a way that to prove that two forces are equal, it is enough to prove that the effects which they can produce are equal”.32 Papin here apparently proposes to elaborate the formalization simultaneously on the basis of their points of convergence and of divergence: the equivalence of force and effect, on the one hand, and the sense to be given to ‘force’, on the other. The meaning of force is the point of divergence because Papin agrees to identify force and quantity of movement, whereas Leibniz proves the essential difference between them. In case it is followed, this procedure is such that if, in the following letters, the syllogistic reduction seems to be fruitful and to yield a kind of accord between the interlocutors, it is actually only delaying a discord which will reappear later on, and which will lead Papin to retract. The method used by Papin is thus to formulate the principle, to enunciate the syllogisms,33 and to wait for Leibniz's agreement before going with the description of experiments. It should be observed that there are several types of difficulties concerning Leibniz’s attempt to reach a consensus on the definitions of the key terms employed in the debate. At a first level, Leibniz points out a certain semantic wavering in Papin’s texts, for example in his use of action.34 At another level, Papin firmly contests the use and the definition of certain terms by Leibniz, particularly ‘force’ (confused with ‘movement’) and ‘formal effect’, and a strong reluctance to accept the relevance of the distinction between ‘dead force’ and ‘living force’ – which amounts to, in the context of the debate, the denial of the utility of a concept such

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as living force.35 Finally, there are a number of cases where from one letter to another, the agreement on the meaning of words vanishes, giving way to endless rectifications regarding the “common sense use” of terms. This leads Leibniz to say, in the opening to his letter of December 1695, “I do not know why we cannot agree on words, even on the points where we agree on things”.36 Thus, for the concept of force, Leibniz suggests in November 1695 to define it as the “power to produce an effect”.37 Or again, in the letter of November 18th 1698, with regards to the concept of action: “If you agreed that we call action what everybody calls action, and if you can no longer bear this word, call it what you like, this quarrel over words makes no difference to the reasoning. If you do not want this change of place in itself (the resistance of the environment set apart) to be called action, you will agree, at least, that it is a change and that is enough for me”.38 This somewhat angry remark testifies to the conceptual instability which is at play in the exchange. Where Leibniz considers that clear definitions were formulated, that they are to be shared by Papin and that he accepted them, Papin often retracts his presumed agreement. Nevertheless, it is not a question of constantly wavering over definitions. Indeed, as far as formal effect, living force, and action are concerned, all three are central notions for dynamics. What is extremely difficult for Papin to accept is that there can be something actual that is formal and, also, that it is the capacity to produce an effect that is conserved, rather than the quantity of movement. Moreover, in Leibniz’s attempts of converting Papin to the dynamics a recurring process is apparent, which amounts to reducing the controversy to a central question, which is proposed to Papin in order to know whether he agrees with it and to give him the opportunity to formulate his own argument in case he doesn’t agree with Leibniz. Leibniz reformulates by means of an example the demonstration of the principle of conservation of living force, showing once more the falshood of the Cartesian principle of conservation. This is what he does in his letter to Papin of December 20th 1695: I come to the principal and decisive point whose sole examination will be sufficient. I am happy that here our quarrel has finally been reduced to something practical, which can be verified without resorting to invisible matter. Here is my proposition: ‘a body of double speed can give the single speed not only to two but to four bodies which are similar to it in size’.39

Leibniz then presents his demonstration of the principle of conservation of the same quantity of living forces using, of course, mv2; yet, he does so by using principles shared by Papin, i.e., by trying to show him that it is in the logical inference that there is a discord between them, and not in the principles from which this inference is made.



Leibniz and Papin: From the public debate to the correspondence

The goal is to demonstrate that a body A of two degrees of speed which raises its own weight to a certain height (for example 4 feet), when coming down again from this height, can raise four bodies to one foot, so that “the body A of two degrees of speed has the power to transmit to four bodies almost identical to it, B, C, D, E, one degree of speed each”. And Leibniz concludes the demonstration in these terms: “and I took care to use principles which are common to us, in order to establish conclusions which are not” (my italics).40 Whereas Leibniz keeps to mathematical demonstration supported by experimental data, Papin proposes a reformulation of what seems to him to be decisive in the controversy. He transfers the difference between their calculations into the register of a distinction between the types of causality involved. What Papin tries to establish is that, in his demonstration Leibniz took an occasional cause for an efficient cause and, for that reason, did not really provide a demonstration.41 A final attempt at reduction of the controversy to a central question42 will be undertaken by Leibniz when a misunderstanding concerning the most important theoretical point of all the exchange arises – the a priori demonstration of the principle of conservation of motive action takes place. The misunderstanding is due to the fact that this demonstration implies the understanding of the formal action and Papin refuses, or rather misunderstands, this concept. This new attempt, in a letter of January 1699 (LBr, 714, 161r), proposes, “in order to avoid any subject of contestation and reproach”, to “return to form” and to distinguish the main arguments from the incidental arguments.43 This distinction will render the principle of conservation of motive action more explicit, and provide a development of the topic rarely found in such a detailed form. This detailed development is prompted by Papin’s hesitations. The argument that Papin uses to deny the existence of the actio in se ipsum is the necessity that all is acting, hence suffering Leibniz replies to it on two levels. First, he shows that there are acting substances without passion, e.g., immanent substances and God’s action; thus he is opposed to the universality of the principle of the reciprocity between action and passion. At the second level, he considers that, in the actio in se ipsum, the body in motion suffers for that resistance in itself which comes from its mass. Observing the various attempts at a reduction of the controversy, we note that they occur mainly at a stage in the exchange where, in order to pursue the correspondence, it is necessary to open up a new argumentative space in which it is again possible to have a dialogue with Papin, by refocusing the discussion on the nodal issue of the exchange, very often loaded with a multitude of other considerations. These few indications of the attempts to deal with disputes by reducing them to their logical forms, represent a sort of rational bringing into line, which is called into question by the fact that the various attempts of Leibniz of ‘resolving’

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the dispute – be it through logical formalization of the kernel of the difference (Leibniz often calls it ‘reduction’), or through the ‘conversion’ of Papin to Leibnizian dynamics by the compelling evidence of examples, or else through semantic agreement – end in constant failure. The Leibniz-Papin correspondence thus appears to show how Leibniz’s efforts to translate his dynamics into a language and argumentative style capable to lead to the conversion of a Cartesian attached to proofs by experiments, reveal the deep difference between two kinds of natural philosophy. In what follows, I will highlight the argumentative power which the controversy yields, on Leibniz’s view, by appealing whenever necessary to correspondences that were either contemporary with the Leibniz-Papin one, or slightly later ones that revolve around the same subject-matter. My goal is to shed some light, in the particular case here studied, on the relationship Leibniz is aware of between the various components of his extraordinarily rich epistolary practice. It is not by accident that he very rarely repeats the same arguments, for he in fact construes the exchange of letters into a space for argumentative elaboration, in which a plurality of perspectives is always open for exploration.

5.

The effects of the controversy on Leibniz’s thought

Summarizing what we might call the “effects of the epistolary controversy”, we can say that, at one level, the divergence concerning the principle of conservation induces Leibniz, in the first part of the correspondence, to clarify what he understands by power, while Papin’s refusal to admit the existence of a formal effect forces him to justify the importance he ascribes to the a priori demonstration of the principle of conservation of motive action. It seems to me that one of the first unexpected effects of the controversy with an interlocutor like Papin, is that Leibniz opts for convincing Papin by staying purely at the mathematical level of the dynamics: As for me, I do not need to care here about what takes place in the insensible nature where you take refuge, and which is perhaps the cause of gravity A of the spring. Our science is mathematical, and does not need these suppositions or philosophical hypotheses, however good they are for other purposes.44

This may seem an amazing statement, insofar as the various texts published at the same time which mention the dynamics all do so from the point of view of its importance in understanding the new concept of substance proposed by Leibniz. This suggests two considerations, each one involving a nontrivial interrogation. First, how can we understand Leibniz’s insistence on proceeding strictly by calcu-



Leibniz and Papin: From the public debate to the correspondence

lation of what conserves itself on the basis of the analysis of a limited number of cases? Second, assuming that his choice of mathematical argumentation yields a new line of support for the dynamics, what exactly is its contribution? Before exploring these questions, let us recall that, whatever its merits, this strategy fails, for in the end Papin is not convinced. Not even Leibniz’s disclosure to him – certainly in a more explicit way than he had ever done before to any other interlocutor – of the a priori demonstration of the principle of conservation of motive action is persuasive enough for Papin. To be sure, this deadlock can be explained by the deep nature of the new science of power and action, a mixed science which can be fully apprehended only by understanding the mutual dependence between the physical search for the “right principle of conservation” and the correlative metaphysical stakes which, from the notion of action, lead us to a restored understanding of the active dimension of substance. This much we can observe in the correspondence with De Volder, which begins at the end of 1698, and where both the deadlock already experienced with Papin over staying on the strictly mathematical level and the necessity to include the link between the dynamic question and the definition of substance are present. In fact, this is for me the pivotal issue of the correspondence with De Volder. Leibniz repeats, in an extremely explicit way, the level on which he wants to place his exchanges with Papin, and does so precisely when he introduces the notion of action upon itself (actio in se ipsum) by distinguishing the action from the “effection”.45 It is precisely to justify the possibility of action within a body that he states in his letter to Papin of November 1696: I cannot imagine that you would wish to resort here to the system of occasional causes as if only God acted and not bodies, because by speaking about physical actions and by estimating them mathematically, we don’t take into consideration the general Cause. And even if this system existed, we could still estimate the effort or the change that takes place in the body.46

It seems clear that Leibniz wants to convince Papin of the existence of a formal action at the level of the explanation of the movement of bodies, without resorting to its relation with metaphysical action. This Leibnizian position shows very well how far Leibniz adapted his discourse to his interlocutor, because Papin indicates in his letter of November 25th 1697 that because we know that nature does not content itself with final causes but that it always uses efficient causes to reach its purposes and a hypothesis which explains everything by efficient causes corresponding closely to reason is always preferable to opinions which, in order to support their incongruities, are obliged to resort to final causes.47

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To which Leibniz answers by asking Papin to explain in what sense his demonstration of the principle of conservation of living forces is based, according to him, on final causes (LBr, 714, 119v). Leibniz explains his point of view in the letter of December 2nd 1697, when he specifies that, according to him, “the ultimate reason for physical truths” derives from something that, according to Papin, is like a final cause; at the same time, however, says Leibniz, it is possible for him to give an abstract a priori estimation of that ‘something’, i.e., an estimation that is independent from gravity, or from the spring, or from external circumstances. In his letter of January 16th 1698, Leibniz explains this point. He chooses to present his ideas in a series of numbered items, in order to avoid losing his way. In item 6 he writes that the true amount to be estimated in motion (or, as Leibniz prefers to call it here, in action) is proportional to the force, and his demonstration is “a priori and drawn from efficient causes” (Leibniz to Papin, December 2nd 1697; LBr, 714, 119v). He emphasizes, as he often does in other correspondences, that the demonstration is handed over only to those who have shown their “ingrès” (‘agreement’) to his ideas on force. Among the effects of the controversy, we can thus see that it induces Leibniz to reveal to Papin the a priori demonstration of the principle of conservation of motive action in a type of explanation that is much more developed and detailed than that provided to Johann Bernoulli or to De Volder. This demonstration doesn’t lead to the ‘conversion’ of Papin; in fact, it has the effect of first silencing Papin. Leibniz’s reaction to this silence is a sort of irritation. Two or three letters later, we find difficulty in understanding the relationship between formal action and violent action. Finally, Papin breaks down.48 While in the letters to De Volder the ambivalence of action revealed itself from the research on the foundation of motive action, making it possible to isolate, in the heart of action, the actio in se ipsum,49 here Leibniz proposes a different approach. It can be understood from the point of view of a double exigence. First, we have a methodological demand, according to which it is not possible to keep only to experiments, and in which one needs to go beyond the geometrical laws. Second, we find a theoretical demand: the strictly mathematical understanding places at the heart of dynamics itself the need to understand what is being measured in dynamics. If there really is a possibility of measuring qualitative variations, it allows us to understand that what is measured in the dynamics of action is, indeed, “the degree of reality in things” (Fichant 1998: 221). At this point, it is due the formulation of the a priori demonstration of the conservation of motive action that the reevaluation of matter is introduced by including in it “a general force of resistance”.50 The justification for the principle of conservation of action will thus be produced, as Ranea (1989: 57) had pointed



Leibniz and Papin: From the public debate to the correspondence

out, by using the notion of natural inertia; this is what Leibniz explains in a letter to Papin of October 1698: “because a body in movement constantly overcomes its inertia by its force, and acts on itself by virtue both of the promptness and continuation (that is of intension and extension) of the given local change”.51 We see therefore that in the exchanges with Papin the redefinition of matter occurs only later, in the justification of the principle of conservation of action, so that this action on itself, estimated according to the medieval concept of latitudes of forms52– on account both of intension and extension – has an ontological bearing which can be understood only by going back to its mathematical source.

6.

Conclusion

The initial public controversy centered on a divergence, common at that time, between an upholder of the principle of conservation of the quantity of movement and Leibniz, the defender of the conservation of living forces. But the opposition between the two parties became more complex as more factors were considered and the discussion began to revolve around them: the cause of gravity, a formal effect, the respective roles of experimental evidence and a priori justification, etc. These discussions are crucial for the understanding of the argumentative strategies used by the contenders, especially of a priori argumentation as a necessary means of justification of Leibniz’s principle of conservation of motive action. They also shed light on very different natural philosophies. In trying to develop, for the specific addressee Papin, a strictly mathematical demonstration of the principles of conservation of living forces – essential in his dynamics – Leibniz deliberately decided to make use only of efficient causes. He thus made apparent the fruitfulness of the demonstrative constraint for what really mattered for him: at the heart of the mathematical treatment of the dynamics lies its metaphysical meaning.

Notes 1. I would like to thank the Hanover Library of Manuscripts at the Gottfried Wilhelm Leibniz Bibliothek, Niedersächsischen Landesbibliothek, Hannover for making this correspondence availabe to me (LBr, 714). 2. By ‘dynamics’, I mean Leibniz’s “new science of power and action”. As Michel Fichant (1998: 216–217) has shown, the dynamics are not only a new principle of conservation (made known in 1686 with the Brevis demonstratio), but also, beside the development of the concept of power, the conceptualization of “action”: “Ainsi, avant le concept d’action motrice, il n’y a pas de dynamique au sens leibnizien du mot. Celle-ci ne commence qu’à partir du moment où le dispositif conceptuel de la force et de la puissance est complété par l’extension que représente

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l’implantation de l’action dans la science du mouvement et de ses lois”. The first step then, is the text Dynamica de potentia, (GM 6 281–514), but the conceptualization of action, in its ambivalence – both as physical action and metaphysical action – occurs, essentially, in the LeibnizPapin correspondence. 3. Cf. Leibniz to Papin, November 8th 1695; LBr, 714, 33r: “Notre science est mathématique et n’a pas besoin ici de ces suppositions ou hypothèses philosophiques, bien que bonnes par ailleurs”. 4. These texts of the public controversy have been analyzed by Freudenthal (2002). In the present paper, I analyze the private dimension of the controversy, as it appears in the correspondence. 5. In the 10th undated letter, situated between the letters of the March 30th 1693 and July 18th 1694: “Je vous avoue qu’en lisant l’abrégé que vous donnez de notre controverse, je ne reconnais pas bien moi-même l’idée que j’ai de ces choses. Et ainsi il sera encore plus difficile aux autres de m’y entendre”. 6. This demonstration is given by Leibniz in the letter to Papin, April 14th 1698; LBr, 714, 137r: “Prior demonstratio hoc est: 1-Actio absolvens duas leucas duabus horis est duplum actionis absolventis unam leucam una hora. 2-Actio absolvens unam leucam una hora est duplum actionis absolventis unam leucam duabus horis. Posterior demonstratio ita habet 1-Spatium est in ratione composita temporum et velocitatum 2-Actio est in ratione composita spatiorum et velocitatum 3-Ergo Actio est in ratione composita ex simplice temporum et duplicate velocitatum”. 7. “À quoi bon d’introduire une force vive puisque soit en communiquant la force, soit en la recevant c’est toujours la loi de la force morte qui a lieu?” (Papin to Leibniz, August 20th 1696; LBr, 714, 82v). 8. “À quoi il sert de parler des temps puisqu’il n’y a jamais que des instants” (Leibniz to Papin, September 14th 1696; LBr, 714, 84r). Leibniz is probably alluding here to the link between dead force and living force and to the need to accept both, since it is the accumulation of dead force that “produces” living force. For example, in the Specimen dynamicum (1695), §6, 14: “[la force vive] naît d’une infinité d’impressions continues de la force morte”. 9. Two quotations can be given to illustrate this point. First, in the letter from Papin to Leibniz, August 18th 1698; LBr, 714, 141r: “Néanmoins comme il ne faut point discuter des mots, si vous voulez appeler ce mouvement action, j’y consens volontiers, mais en même temps aussi Monsieur, il faut que vous m’avouiez qu’il y a des actions de deux sortes; l’une qui consume la force de l’agent et l’autre qui ne la consume point”. Second, Leibniz’s answer, August 28th 1698; LBr, 714, 145r: “c’est pour cela que cette action de la première espèce pourrait être appelée formelle puisqu’elle est intime à la force et l’accompagne toujours”. 10. There’s, indeed, an argumentative interplay between Papin, who wants only a demonstration of the principle of conservation of motive action by efficient causes, and Leibniz, who denies having used final causes. For example, see Papin to Leibniz, November 25th 1697; LBr, 714, 115r: “Car on sait que la nature ne se contente pas des causes finales mais qu’elle emploie toujours des causes efficientes pour parvenir à ses fins et une hypothèse qui explique tout par



Leibniz and Papin: From the public debate to the correspondence

des causes efficientes très conformes à la raison, est toujours préférable aux opinions qui pour soutenir leur incongruité sont obligées de recourir aux causes finales”. Leibniz’s answer is in the letter of December 2nd 1697; LBr, 714, 119v: “Ainsi vous déclarez que vous avez de la peine à les [les suites de ses arguments] admettre, jusqu’à ce que je prouve mon hypothèse, non seulement par des causes finales, mais encore a priori par des efficientes”. 11. “I would like to suggest that we may discover that this is a kind of “missing link” between the expositions of the a priori argument in the correspondence with Johann Bernoulli and the letter to De Volder of March 24th 1699” (Ranea 1989: 45). 12. Within this interpretative framework, the first part of Ranea’s article underlines Leibniz’s silence regarding Papin’s claim that one cannot measure power by a horizontal effect because this is not a real effect of power (Ranea 1989: 50), the fact that he chooses not to use his a priori argument to counter Papin’s objections because “he never had faith in it”, and similar manifestations of Leibniz’s attitude towards his adversary. 13. Duchesneau (1994: 322), interprets Ranea’s move as follows: “Ultimately, the way Ranea puts it aims at highlighting a meaning of the notion of a priori argument which makes it possible to avoid the apparently radical dichotomy between a strictly formal demonstration based on the logical evidence of the premises and a system of empirically justified inferences”. It seems to me that it is all the more important to point this out since the reading of the correspondence indeed confirms the impression that Leibniz, just like Papin, is guided by two tendencies: to prove by reporting experiments and also to formulate one’s argument syllogistically. It is indeed a harmonious articulation between these two forms of “reduction” of the controversy that can guarantee the constitution of a sphere of discussion in which the a priori argument will find its proper place. 14. The letter to Papin of August 28th 1698 shows this clearly. In paragraph 6, Leibniz writes about his estimation of force by formal actions that it is “deeper and a priori. Every thing must be estimated in its source; and the source of the power capable of producing actions of the second sort is the faculty of formal actions or of the first sort” (“plus profonde et a priori. Chaque chose devant être estimée dans sa source; et la source de la puissance capable de produire des actions de la seconde espèce est la faculté des actions formelles ou de la première espèce”; Leibniz to Papin, August 28th 1698; LBr, 714, 145r). 15. As Ranea (1989: 51) notes, Leibniz is very careful to avoid dealing with the determining ontological consequences of the concept of action. 16. When Fichant (1998: 226) points out, in this connection, the double orientation of the notion of action, extensional and intensional (“It is indeed about a measure of perfection or reality, in brief about a mathematization of properly ontological concepts”), he makes use of a quotation from what Leibniz writes to Papin: “the perfection or the degree of reality in things, and particularly in movement, can be considered according to two reasons, either the extension which is here the greatness of the place or the changed space, or by the intension which is here the quickness or the speed of the change or the movement” (“La perfection ou le degré de réalité dans les choses, et particulièrement dans le mouvement, se peut estimer suivant deux raisons, savoir par l’extension qui est ici la grandeur du lieu ou l’espace changé, et par l’intension qui est ici la promptitude ou la vitesse du changement ou du mouvement”; Leibniz to Papin, after May 7th 1699; LBr, 714, 175v). 17. Semipublic because correspondence in the République des Lettres was often passed on and spread in scholarly as well as in wider circles.

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18. Indeed, the dynamics expresses the order of nature, that is, proposes to reveal the hierarchic relation between physics and metaphysics. 19. In 1691, Mechanicorum de viribus motricibus sententia, asseta a D. Papino adversus Cl. G.G.L. objectiones. 20. “I shall observe that, according to the common opinion, the quantity of force is estimated by the quantity of effect and we shall ask what quantity this can realize? Or what is its power? That is the same thing. […] therefore, a brief definition which cannot be disputed is the following one: ‘Of two bodies in movement, the one who has more power is that which can produce more effect: if there is no difference between them in this respect, then these bodies have equal forces’. But we have to note that the justifiable measure of the quantity of effect is not the distance covered by the body, nor the time through which the movement continues, but it is the resistance which is overcome. […] It follows that for the definition proposed before – what can produce more effect? – we can completely substitute this one: what can overcome more resistance? Because to produce an effect and to overcome a resistance are one and the same thing. […] Consequently, it’ll be easy to demonstrate that the quantity of forces must be estimated by the quantity of movement, following the opinion of the Cartesians” (“J’observerai que selon l’opinion commune de tous, la quantité de force est estimée par la quantité d’effet et on se demandera quelle quantité cela peut réaliser? Ou quelle est sa puissance? C’est-à-dire la même chose. […] Donc pour qu’on produise une définition brève et qui ne puisse être contestée par personne, elle sera en ce sens: ‘Duorum corporum in motu illud habet plus potentiae, quod potest plus effectus producere: si vero neutrum sit ejusmodi, illa corpora habent vires aequales’. Mais on doit noter que la mesure légitime de la quantité d’effet n’est pas la quantité d’espace parcouru par le corps, ni le temps par lequel le mouvement se continue, mais il est la résistance qui est vaincue. […] De là, on constate que dans la définition avancée plus haut: qu’est-ce qui peut produire plus d’effet, on peut tout à fait substituer cette autre : qu’est-ce qui peut vaincre plus de résistance? car produire un effet et vaincre une résistance ne sont qu’une seule et même chose. […] De là, il me sera très facile de démontrer que la quantité de forces doit être estimée par la quantité de mouvement selon l’opinion des cartésiens”; Mechanicorum de viribus motricibus sententia, asserta a D. Papino adversus Cl. G.G.L. objectiones, Acta Eruditorum, January 1691: 7–8). 21. Leibniz introduced the explanation of the relationship between action and formal effect in the Dynamica de potentia (GM 6 355), in the 4th definition: “Diffusio actionis in motu vel actiones extensio est quantitas effectus formalis in motu. Intensio ejusdem actiones est quantitas velocitatis, qua factus est effectus seu qua materia per longitudinem translata est”. He did it by introducing the medieval vocabulary of the “latitude of forms” or the quantification of qualities (with “intensio” and “extensio”). 22. For example, in the correspondance with De Volder (GP 2 191), in an undated letter between the letters of August 1699 and November 12th, 1699. 23. “Il semble que vous ne désapprouvez pas mon principe qui consiste dans l’égalité de la cause et de l’effet et sur lequel est appuyée ma manière d’estimer la puissance”. This letter from Leibniz to Papin is the third version of a non dated letter which is situated between the letters of July 18th 1694 and of August 30th 1695 (LBr, 714, 20r). 24. “…ce qui se détermine par le nombre des répétitions d’un même effet violent” (in the same letter, the 10th; LBr 714, 18v).



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25. “… celui dont la production assez souvent répétée, est capable de détruire le mouvement dans celui qui le produit”. 26. For Leibniz, this hypothesis is not explained enough, as he writes in August 1695: “As far as our controversy is concerned, you admit, Monsieur, the equivalence of the cause and the mechanical effect. You have also seen by my reasonings that in the sensible bodies this equivalence is conserved when the quantity of movement can’t be conserved in it; it seems that this point obliged you to resort to an insensible matter, and to suppose that it gains precisely the same quantity of movement which is being lost in the sensible bodies. Moreover, it would be useful to understand through a reasonable hypothesis how this alleged compensation can precisely operate” (“Pour ce qui est de notre controverse, vous reconnaissez Monsieur l’égalité de la cause et de l’effet mécanique. Vous avez vu aussi par mes raisonnements que dans les corps sensibles cette égalité se conserve lorsque la quantité de mouvement ne s’y conserve pas, cela semble de vous avoir obligé de recourir à une matière insensible, et de supposer qu’elle gagne précisément la quantité de mouvement qui se perd dans les corps sensibles. De plus, il serait bon de comprendre par quelque hypothèse raisonnable, de quelle manière se fait si justement cette prétendue compensation”; Leibniz to Papin, August 30th 1695; LBr, 714, 26r). 27. “… il faudrait avoir recours avec vous à quelque matière insensible par laquelle la nature supplée ce manquement”. And he adds: “it is only through some agreement which is not based on experience, and even less on demonstration, that one has conceived this maxim of quantity of movement” (“ce n’est que par une certaine convenance qui n’est point fondée dans l’expérience et encore moins dans la démonstration qu’on s’est formé cette maxime de la quantité de mouvement”; same undated letter, third version; LBr, 714, 20v). 28. Papin concludes this letter sharply expressing how he sees the issue at stake at this stage of the debate: “… our dispute, however, turns on things rather than on words, since it is about knowing whether the force and the effect as measured in your way are in fact the force and the effect whose quantity is unchangeable: you affirm this and I deny it” (“… notre dispute roule pourtant sur les choses et non pas sur les mots: puisqu’il s’agit de savoir si la force et l’effet mesurés à votre mode sont cette force et cet effet dont la quantité est immuable: vous l’affirmez, moi, je le nie”; Papin to Leibniz, January 15th 1696; LBr, 714, 52r). 29. “However, the lack of agreement typical of this way of disputing and the scholastic atmosphere that reigns in it, bring about that it is rarely used – which is at the cost of truth. Since I don’t recognize sufficiently my reply in your replica, I have thought that we should resort to form and see whether this means couldn’t yield agreement between us” (“Cependant le peu d’agrément qu’il y a dans cette manière de disputer et l’air d’école qui y règne, font qu’on ne s’en sert guère, mais c’est aux dépens de la vérité. Et comme je ne reconnais point assez ma réponse dans votre réplique, j’ai cru qu’il fallait recourir à la forme et voir si ce moyen ne nous pourrait mettre d’accord”; Leibniz to Papin, April 9th 1696; LBr, 714, 65r). To which he adds in the next page: “I confess that these disputes in form are somewhat boring, especially due to the repetitions (which one might however a way to avoid). Nevertheless, if one has the necessary patience for pursuing them up to the end, they provide the means to settle the affair and to avoid misunderstandings or confusions. Therefore, those who love truth are right in deciding to employ this means, especially when one debates in writing. And when one loves truth, one gladly grants oneself a little more of patience” (“J’avoue que ces disputes en forme ont quelque chose d’ennuyeux, surtout à cause des répétitions (qu’on pourrait peut-être pourtant trouver le moyen d’éviter), mais en récompense, pourvu qu’on ait la patience nécessaire pour les pousser à bout, elles donnent le moyen de sortir d’affaire, et de prévenir les mésentendus ou les brouilleries.

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Ainsi, ceux qui aiment la vérité font bien de s’y résoudre dans des cas pareils au nôtre, surtout quand on confère par écrit. Et quand on aime la vérité, on se donne volontiers un peu plus de patience”; LBr, 714, 66v). 30. This distinction between the “order of justification” and the “order of discovery”, which bears some similarity to the familiar positivistic distinction between the “context of justification” and the “context of discovery” (Reichenbach 1938: Chap. 1), is used by Ranea (1989: 55). For an interpretation of Ranea’s suggestion in this respect, see Duchesneau (1994: 320). I would like to make use of this distinction in a different way, in order to determine the inventive part present in the “order of justification”. 31. “de reconnaître de part et d’autre si la thèse est prouvée ou non”; Leibniz to Papin, April 9th 1696; LBr, 714, 65r). 32. “La force et son effet sont toujours équivalents en sorte que pour prouver que deux forces sont égales, il suffit de prouver que les effets qu’elles peuvent produire sont égaux”. Quoted in the letter from Papin to Leibniz, May 20th 1696; LBr, 714, 69v. 33. Here is an example: “Syllogism I: If body A (mass 4, velocity 1) and body B (mass 1, velocity 4) can produce both the same effect, it follow, by the above principle, that they have the same force. The antecedent is true, therefore the consequent is also true. I now demonstrate the minor by Syllogism II: If the mentioned bodies can bounce back equally equal masses that impact on them with equal velocities, all of them directly, it follows that they can produce both the same effect. The antecedent is true; therefore the consequent is true too” (“1° Syllogisme : Si le corps A (masse 4, vitesse 1) et le corps B (masse 1 vitesse 4) peuvent produire autant d’effet l’un que l’autre ; il s’ensuit, par le Principe ci-dessus, qu’ils ont autant de force l’un que l’autre. Or l’Antécédent est vrai, donc le conséquent l’est aussi. Je prouve la mineure par le 2° syllogisme. Si les dits corps peuvent réfléchir également des masses égales qui les frappent avec vitesses égales et toutes directement, il s’ensuit qu’ils peuvent produire autant d’effet l’un que l’autre. Or, l’Antécédent est vrai, donc le conséquent l’est aussi” (Papin to Leibniz, May 20th 1696; LBr, 714, 69v–70r). 34. Letter from Papin to Leibniz, November 1st 1698; LBr, 714, 151r: “Je vous supplie de vous souvenir que quand j’ai consenti qu’on appelât action, le mouvement d’un corps qui ne rencontre point de résistance, j’ai dit en même temps, à parler proprement que cela ne se devait appeler que persévérance de la même manière d’être, et jene consentais de l’appeler action qu’afin d’éviter les disputes de mots, mais puisque vous vous prévalez de ma facilité jusqu’à prétendre ne plus avoir d’instance, je crois avoir droit de me rétracter et de n’accorder plus rien”. And Leibniz to Papin, November 18th 1698; LBr, 714, 155r: “Vous dites que je me suis prévalu de votre facilité et que vous ne voulez plus rien m’accorder- c’est un reproche si visiblement injuste que je ne veux point m’y amuser. Si vous avez consenti qu’on appelle action, ce que tout le monde appelle ainsi, et que vous ne voulez plus souffrir ce mot, appelez le comme il vous plaira, cette dispute de mots ne change rien au raisonnement”. 35. See, e.g., the texts quoted in Notes 7 and 8. 36. “Je ne sais pourquoi nous ne pouvons convenir en paroles, même à l’égard des points où nous convenons dans les choses”; Leibniz to Papin, December 20th 1695; LBr, 714, 45r. Later on, in the same letter, he adds: “As for the sense you give to terms, you are allowed to understand by the words ‘force’ and ‘effect’ anything you want. But you wouldn’t be able to prove that what you mean in your way, i.e., the quantity of movement, conserves itself always the same, as what I mean conserves itself forever” (“Pour ce qui est du sens que vous donnez aux Termes,



Leibniz and Papin: From the public debate to the correspondence

il vous est permis d’entendre par le nom de la force et de l’effet tout ce qu’il vous plaira. Mais vous ne sauriez prouver que ce que vous entendez par là c’est-à-dire la quantité de mouvement, se conserve aussi toujours la même, comme ce que j’entends se conserve toujours”; Leibniz to Papin, December 20th 1695; LBr, 714, 45r). Contrary to Leibniz’s position in this respect, Séris (1987: 255), writing about the texts published in the Acta eruditorum of 1689–1690, argues that, since the controversy is real, rather than a quarrel of words, it is paradoxically easier to agree as far as the meanings of the words are concerned. 37. “Since I am sure that nature conserves always the same quantity of producible effect, I feel comfortable in calling ‘force’ the power to producing an effect (which is, therefore, also conserved), rather than the quantity of movement, whose conservation has never been verified – without, however purporting to constrain anybody about the use of the word” (“Et comme je suis assuré que la nature conserve toujours la même quantité de l’effet produisible, je suis bien aise d’appeler Force, le pouvoir de le produire (qui se conserve par conséquent aussi), plutôt que la quantité de mouvement, dont la conservation n’a jamais été vérifiée, sans prétendre pourtant de contraindre personne sur l’usage du mot”; Leibniz to Papin, November 8th 1995; LBr, 714, 33r). 38. “Si vous avez consenti qu’on appelle action, ce que tout le monde appelle ainsi, et que vous ne voulez plus souffrir ce mot, appelez-le comme il vous plaira, cette dispute de mots ne change rien au raisonnement. Si vous ne voulez pas que ce changement de place en lui-même (la résistance du milieu mise à part) se doit appeler action, vous accorderez du moins que c’est un changement et cela me suffit” (Leibniz to Papin, November 18th 1698; LBr, 714, 155r). 39. “Je viens au point principal et décisif qu’il suffira tout seul d’examiner. Je suis bien aise que par là notre dispute s’est enfin réduite à quelque chose de pratique, qui se peut vérifier sans aller chercher les matières invisibles. Voici ma proposition: ‘Un corps de vitesse double peut donner la vitesse simple non seulement à deux mais à quatre corps qui lui sont pareils en grandeur’” (Leibniz to Papin, December 20th 1695; LBr, 714, 33v). 40. “Le corps A de deux degrés de vitesse a le pouvoir de procurer à quatre corps presque pareils à lui, B, C, D, E, à chacun un degré de vitesse” … Et j’ai eu soin de me servir des principes qui nous sont communs, pour établir des conclusions qui ne le sont point” (Leibniz to Papin, December 20th 1695; LBr 714, 46r–46v). 41. “I will remark here that there is an important difference between the efficient cause and the occasional cause of a movement, since the efficient cause must have at least as much force as the force it causes, whereas the occasional force may have much less force: for example, a globe put at the edge of a well on a horizontal, well polished plane, can be pushed into the well with a small coup, and when falling it may acquire much more force that the body that pushed it and has been the occasional cause of all the velocity acquired in the fall; the same is the case in your example … I argue, therefore, that you will never prove that ‘a body with double velocity can transmit a single velocity to four bodies that are equal to it in mass’, for I do not believe that people will be ready to take occasional causes for efficient causes …” (“Je remarquerai donc ici qu’il y a bien de la différence entre la cause efficiente et la cause occasionnelle d’un mouvement car il faut que la cause efficiente ait du moins autant de force comme elle en cause, mais la cause occasionnelle peut en avoir beaucoup moins: un globe par exemple posé au bord d’un puits sur un plan horizontal et bien poli, peut par un petit coup être poussé dans ce puits et en y tombant acquérir beaucoup plus de force que n’en avait le corps qui l’a frappé et qui a été la cause occasionnelle de toute la vitesse acquise par la chute, il en est de même dans l’exemple que vous

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proposez … Je soutiens donc toujours que vous ne prouverez jamais que ‘un corps de vitesse double peut donner la vitesse simple à quatre corps qui lui sont pareils en grandeur’, car je ne crois pas que les esprits soient disposés à vouloir prendre les causes occasionnelles pour causes efficientes …”; Papin to Leibniz, January 15th 1696; LBr, 714, 48v–49r). 42. For example, Leibniz to Papin, November 8th 1695; LBr, 714, 33v: “enfin j’ajouterai qu’on peut réduire notre controverse à une considération fort simple”. Or, Leibniz to Papin, January 16th 1698; LBr, 714, 129r: “Nous allons retomber (si nous n’y prenons garde) dans ces manières de conférer où chacun a raison dans sa lettre et tant qu’il parle, à peu près comme deux armées ennemies qui ne se rencontrent point. L’une va vers la Meuse, l’autre va vers l’Escaut et chacune fait des feux de joie dans son camp. Pour y remédier, j’ai voulu réduire le tout en certains points ou articles”. 43. The new ‘shape’ punctuated by the formulation of “a principal argument”, the answer to the argument, a replica, and the answer to this replica, and the incidental question, an argument against the action, and the two first answers – all these argumentative moves constitute a device for permitting an appropriate discussion of the concept of “actio in se ipsum”. 44. “Pour moi, je n’ai point besoin de me soucier ici de ce qui se passe dans la nature insensible où vous vous sauvez, et qui est peut-être cause de la pesanteur A du ressort. Notre science est mathématique, et n’a pas besoin ici de ces suppositions ou hypothèses philosophiques, bien que bonnes par ailleurs” (Leibniz to Papin, November 8th 1695; LBr, 714, 33r). 45. Cf. Leibniz to Papin, November 1696; LBr, 714, 90v: “Je distingue l’action de l’effection. Ainsi quand un corps va dans un milieu extrêmement mince, qui ne lui résiste presque point ou quand il trouve à l’entour de son centre et, généralement quand il se meut, j’appelle cela action, de sorte que le mouvement est chez moi, une espèce d’action”. 46. “Je ne m’imagine pas que vous veuliez avoir recours ici au système des causes occasionnelles comme si Dieu agissait seul et non pas les corps, puisqu’en parlant d’actions physiques et en les estimant mathématiquement, on ne s’embarrasse pas de ces considérations de la Cause générale, et quand même ce système aurait lieu, on ne laissera pas de pouvoir estimer l’exercice ou le changement qui se fait dans le corps” (Leibniz to Papin, November 1696; LBr, 714, 91r). 47. “car on sait que la nature ne se contente pas des causes finales mais qu’elle emploie toujours des causes efficientes pour parvenir à ses fins et une hypothèse qui explique tout par des causes efficientes très conformes à la raison est toujours préférable aux opinions qui pour soutenir leurs incongruités sont obligées de recourir aux causes finales” (Papin to Leibniz, November 25th 1697; LBr, 714, 115r). 48. Papin to Leibniz, November 1st 1698; LBr, 714,151r: “...but since you take advantage of my easiness up to the point of purporting to have no need anymore of examples, I think I have the right of retracting and to concede nothing else” (“mais puisque vous vous prévalez de ma facilité jusqu’à prétendre de ne plus avoir besoin d’instance, je crois avoir droit de me rétracter et de n’accorder plus rien”). For another quote from this letter see Note 34. 49. In my dissertation, L’ambivalence de l’action. Un exemple de diffusion: La correspondance entre Leibniz et De Volder (forthcoming), I have underlined that the radical distinction between formal action and violent action has revealed the actio in se ipsum as the presence of substantiality in all forms of reality; by that, Leibniz has shown the root of being on formal action. See, for example, Leibniz to De Volder, January 20th 1700; GP 2 204–205).



Leibniz and Papin: From the public debate to the correspondence

50. This reevaluation is evident in item 30 of the January 16th 1698 letter: “… taking matter for a simple mass, indifferent to movement and to rest, it wouldn’t resist to any pression and the smallest body would carry away the largest without any delay. This is contrary to all experience and to all order. There must be dynamic principles in bodies; matter has in it the general force to resist, in addition to the particular forces to act; and there is a principle of order in all of nature, which is the ultimate reason of things” (“… qu’en prenant la matière pour une simple masse, indifférente au mouvement et au repos, elle ne résisterait point à l’impression et le moindre corps emporterait le plus grand sans être retardé. Ce qui étant contraire à toutes les expériences et à tout ordre. Il faut dire qu’il y a des principes dynamiques dans les corps, que la matière a en elle la force de résister générale, outre les forces d’agir particulières. Et qu’il y a un principe d’ordre dans toute la nature qui fait la dernière raison des choses”; Leibniz to Papin, January 16th 1698; LBr, 714, 134r). 51. “car un corps étant en mouvement surmonte continuellement son inertie par sa force, et agit sur soi-même en raison composée de la promptitude et de la continuation (c’est-à-dire de l’intension et de l’extension) du changement local donné” (Leibniz to Papin, December 14th 1696; LBr, 714, 89v). 52. Ranea (1989) has underlined that in the estimation of action the medieval vocabulary of the “latitude of forms”, particularly “intension” and “extension”, is present. This use of medieval concepts indicates the possibility to measure qualitative variations in the bodies. Their presence in the Leibnizian text is the only proof of his importing of the intellectual medieval context into dynamics: the possibility to measure the levels of reality in the bodies (Leibniz to De Volder, January 9th 1700; GP 2 204: “C’est pourquoi j’espère que, de même que ma distinction entre action libre [i.e., formal] et violente vous a satisfait, de même aussi que la distinction entre les deux intensions qui composent la quantité d’action, l’une avec l’extension à travers le temps et l’autre avec l’extension à travers l’espace, c’est-à-dire entre la puissance et la vitesse vous satisferont. Et, à la vérité, dans toute cette affaire, que vous estimiez de façon plutôt métaphysique les actions libres ou que vous estimiez de façon plutôt physique les actions violentes, toutes les raisons ont été supputées et toutes choses ont été réduites au calcul de telle sorte qu’aucune objection ne peut se présenter à laquelle je ne promette de satisfaire distinctement”. This is worth comparing with what he writes to Papin: “Ainsi si vous attribuez un véritable mouvement à quelque corps, je lui attribuerai aussi une véritable action ou mouvement que j’estimerai tant par son intension ou promptitude que par son extension […]” (Leibniz to Papin, December 14th 1696; LBr, 714, 89v).

References Duchesneau, F. 1994. La dynamique de Leibniz. Paris: Vrin. Fichant, M. 1994. La réforme de la dynamique. De corporum concursu (1678) et autres textes. Paris: Vrin. Fichant, M. 1998. “De la puissance à l’action: la singularité stylistique de la Dynamique”. In M. Fichant (ed), Science et métaphysique dans Descartes et Leibniz. Paris: Presses Universitaires de France, 205–244. Freudenthal, G. 2002. “Perpetuum Mobile: The Leibniz-Papin controversy”. Studies in History and Philosophy of Science 33: 573–637.

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Leibniz, G. W. 1686. A Brief Demonstration of a Notable Error of Descartes and Others Concerning a Natural Law, According to Which God is Said Always to Conserve the Same Quantity of Motion; a Law Which They Also Misuse in Mechanics. L 296–302. Leibniz, G. W. 1690. Observatio de Causa gravitatis et Defensio sententiae autoris de veris naturae legibus contra Cartesianos. In Acta Eruditorum, May 1690: 228–239. Leibniz, G. W. 1689–1690. Dynamica de potentia. GM 6 281–514. Leibniz, G. W. 1691. De legibus naturae et vera aestimatione virium motricium contra Cartesianos. Responsio ad rationes a Dn. Papino mense januarii anni 1691 in Actis eruditorum propositas. In Acta Eruditorum, September 1691: 439–447. Leibniz, G. W. 1695. Specimen dynamicum. Hamburg: Meiner Verlag [1982]. Leibniz, G. W. Undated. Briefwechsel: Manuscripts of Leibniz’s Correspondence. Hannover: Niedersächsischen Landesbibliothek. [= LBr 714] Papin, D. 1689. De gravitatis causa et proprietatibus Observationes. In Acta Eruditorum, April 1689: 183–188. Papin, D. 1691. Mechanicorum de viribus motricibus sententia, asserta a D. Papino adversus Cl. GGL objectiones. In Acta eruditorum, January 1691: 6–13. Papin, D. 1695. Synopsis controversiae Authoris cum celeberrimo Viro Domino G.G.L. circa legitimam rationem aestimandi vires motrices. In Acta Eruditorum, 1695: 376. Ranea, A. G. 1989. “The a priori method and the actio concept revised. Dynamics and metaphysics in an unpublished controversy between Leibniz and Denis Papin”. Studia Leibnitiana 20(1): 42–68. Reichenbach, H. 1938. Experience and Prediction. Chicago:University of Chicago Press. Séris, J.-P. 1987. Machine et communication. Paris: Vrin.

chapter 5

Leibniz vs. Stahl A controversy well beyond medicine and chemistry Sarah Carvallo

1.

Introduction

From 1706 to 1707, Georg Ernst Stahl published four treatises presenting his medical doctrine.1 In 1708 he published an overview of his doctrine under the title Theoria Medica vera (Stahl 1707–1708). Leibniz immediately questioned certain points in Stahl’s doctrine and published his disagreements. Stahl replied, Leibniz raised further objections to which Stahl replied again.2 Leibniz made two principal points: the first dealt with three general questions on the logical and metaphysical foundations of science; the second focused on certain specific statements made by Stahl in his treatises. After Leibniz’s death, Stahl collected and published their controversy, in an attempt to provide decisive replies to Leibniz’s objections (Stahl 1720). The controversy between Stahl and Leibniz can be used as a prism through which the debate within the République des Lettres about the living body can be analyzed. Leibniz’s philosophy is built as a diachronic and synchronic dialogue, whose aim is a comprehensive view of reality that is to be achieved by understanding how the numerous conflicting theories thereof integrate (Leibniz 2001: 23).3 What is at stake in the present controversy is a definition of the organism as mixed and living. The two thinkers focus on this chemical and medical issue, the study of which requires taking into account all the then existing relevant theories, along with their premises. Because their discussion takes place against the rich background of pre-existing hypotheses, a full understanding of the controversy requires, first of all, a presentation of the main theories of the living body, as well as an explanation of what Stahl and Leibniz thought about them.4 Far from being limited to the quarrel between Stahl and Leibniz, this controversy indeed implies a confrontation of a series of points of view, which 

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correspond to the authors quoted directly in the text, or otherwise indirectly referred to. The result is a multiple-entry reading method that varies according to the topics and the authors discussed. As in a city that one observes from various standpoints, one can choose to consider the concepts, the criticisms, the methods, classical medicine or current chemistry, the relationship between mathematics and experimental sciences, etc. The goal of this essay is not so much to review the topics of the controversy as it is to analyze the indispensable role of dialogue in the thought process. Admittedly, these two aspects are closely dependent. Thinking always relates to an object, the correct understanding of which always requires confrontation of different points of view. Therefore, the questions this essay deals with are: Why, and how, does Leibniz use the method of controversy to define his object, the organism, as a mixed and living body? The use of such a method reflects a search for a touchstone allowing a better assessment of the two theses concerning one and the same object. In other words, through their controversy, Leibniz and Stahl test their two incompatible philosophies of nature. Between these two fundamental ‘biologies’, which support divergent theories and practices, the more relevant explanation of the organism should prevail. That is to say, the controversy should help to establish which philosophy of nature corresponds most adequately to the contemporary state of knowledge in medicine and chemistry. To fully grasp this strategy, it will be helpful to analyze the controversy both at its medical and chemical levels, before identifying the different implications regarding the philosophy of nature.

2.

The medical controversy

2.1

Old and modern controversy concerning the concept of cause

At the origins of science and philosophy, the definition of causality triggers a polemic between two traditions: the first defends the idea of pure efficiency, the second, the idea of an alliance between efficiency and finality. For example, according to both traditions, we can see because we have eyes; but the second tradition assumes in addition that we have eyes in order to be able to see.5 This controversy is connected to the debate about the relationship between organ and function, matter and life, body and soul. Which kind of causality binds the former to the latter? In early modern thought, the progress made in mathematics and physics renews the contents of this discussion. Indeed, the Fermat principle of least time grants mathematical and physical relevance to finality, whereas Cartesian mechanics is more efficiency oriented, by its emphasis on the quantitative relation



Leibniz vs. Stahl: A controversy beyond medicine and chemistry 103

between cause and effect, as expressed in the conservation of the ‘quantity of movement’. This modern formulation of the problem of causality is transmitted from mathematics and physics to medicine, where it crystallizes the opposition between two medical theories, animism and iatromechanism, which Stahl and Leibniz, respectively, represent. The gist of this opposition is the nature of movement within the organism, the relation between the soul and the body. Animistic medicine assumes that the organism has an inherent end, i.e., life, or the soul, which directs organic movements for the purpose of its own conservation. Van Helmont, Cudworth, More, and Stahl defend this thesis. Stahl describes three aspects of organic life: (i) its subject is the soul, (ii) its object is the body, and (iii) its instruments are movements (De vita; BL 6 474). In other words, “life cannot be identified with the body which constitutes only the instrument thereof ” (De mixti et vivi corporis vera diversitate §57; BL 2 303); it transcends matter. The vital action of the soul generates the organic and chemical composition, as well as the body’s operation. This action results in “the conservation of the body mix, thanks to a principle that is inherent to the body, obviously an intangible principle, manifesting itself through an equally intangible action, i.e., through movements in general and, in particular, through secretions and excretions” (De vita; BL 6 474). Motion thus is only the instrumental cause of physical transformations, but cannot explain either their origin or their rationale. They necessarily refer back to a transcendent, non-mechanical final cause. There is thus a radical difference between the inert, deprived of any finality, and the living, always acting towards a purpose. By contrast, the iatromechanic theory reduces life to a physical phenomenon, which must be explained mechanically according to efficiency principles alone. Descartes, and later on Friedrich Hoffmann, claim to explain any organic function, starting with life itself, by the properties of matter.6 Movements explain all reality, and their laws determine any change. When Leibniz defines the body as an “igneous hydraulic pneumatic machine” (CAR 91) he resorts to the physical concepts of pressure, local movement and swirl, as well as to the chemical concept of combustion, in order to explain vital functions. In other words, the mechanics of the fluids, solids, and gases exhausts organic reality.7 However, Leibniz nuances and overcomes this radical opposition between two conceptions of instrumental or causal movements as he proposes a synthesis based on the hypothesis of Pre-established Harmony. Indeed, this hypothesis allows him to establish a parallelism between efficient and final causes.8 Trying to find a way to bridge the opposition, Leibniz focuses on each form of causality separately, and criticizes both:

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[T]he Formalists, like the Platonists and the Aristotelians, are right in seeking the source of things in final and formal causes. But they are wrong in neglecting the efficient and material ones, and to infer therefrom, as did Mr. Henri Morus in England and other Platonists, that in rejecting are some phenomena that cannot be explained mechanically. On the other side, however, the Materialists, i.e., those who attach themselves exclusively to the mechanical philosophy, are wrong in rejecting metaphysical considerations and in wanting to explain everything by what depends upon the imagination.9

2.2

The artificial and the natural

This opposition concerning causality results in a decisive disagreement among physicians about the borderline between the artificial and the natural. Animism posits a difference in nature, whereas iatromechanism posits a difference in degree. Two major consequences follow from this disagreement. The first one relates to the operation of chemical remedies. Either they act directly on health and diseases, or they only act on the body’s texture and the body mix, the soul alone being capable of acting on health. Leibniz defends the first alternative. He advocates artifice, tricks, and prosthetic devices. He holds that chemistry, of all human inventions, proves to be particularly useful at restoring the natural state of a body.10 Thus, Leibniz reduces the difference between medicine and chemistry and adheres to the iatrochemist thesis.11 In contrast, Stahl defends the second position. He refutes the iatrochemist thesis and subscribes to the Hippocratic tradition of “natura medicatrix”.12 He criticizes the effectiveness of drugs, purely material objects that are therefore heterogeneous with the vital power. In his view, chemistry does not really control the organic effects of the socalled remedies (De mixti et vivi corporis vera diversitate §100; Stahl 1707a; BL 2 339), and only nature can truly cure (Ibid. §§102–104; BL 2 341–344). The second consequence of the disagreement about the difference between the natural and the artificial relates to the status of anatomy and physiology. Whereas Stahl believes that Harvey and Descartes offer a reductionist model of the living, which is only relevant to physical, not medical anthropology, and which thus fails to capture what life is all about, Harvey and Descartes claim that their anatomy and physiology represent the mechanical model, which describes the body exactly in its reality as a machine. Harvey and Descartes describe the advent of life like a property of matter, as a result of either compressive force or chemical fermentation. Leibniz will use this animal machine hypothesis.



2.3

Leibniz vs. Stahl: A controversy beyond medicine and chemistry 105

Anatomy and physiology

The general controversy concerning the status of organic movements and the effectiveness of chemical remedies on the mix’s qualities is particularly relevant to the description of blood circulation. Indeed, its interpretation specifically illustrates the polemic concerning the status of anatomy and physiology. There are three positions vis-à-vis blood circulation: (i) the mechanic position of Harvey, (ii) the animistic conception of Stahl, and (iii) the dynamic and harmonic hypothesis of Leibniz. Although they disagree on the conception of the heart, Harvey and Descartes agree on the mechanical view of life. Admittedly, Harvey (1990: 211) considers the heart a muscle moved by the blood,13 while Descartes conceives the heart as a place of fermentation, the source of swirling blood circulation. In other words, they reverse the order of efficiency: either the blood determines systole and diastole because of the blood pressure, or the fermentation generates the alternate contraction which then causes a swirl of humors.14 However, both descriptions are limited to a strictly quantitative and material explanation of the body and do not use any extrinsic force. Whether hydrometric or chemical, blood circulation reproduces itself without any finality or any other external impulse. It is Claude Perrault (1680) in particular, who soon applies this model to all vital phenomena in the various kingdoms, animal, vegetal, etc. Stahl criticizes the relevance and the legitimacy of mechanical description for not providing the “true” cause; the mechanical model does not explain why circulation is carried out as it is and not otherwise, although nothing would prevent another type of vital function. A purely physiological interpretation neglects the final cause of circulation. Stahl distinguishes between movement, i.e., a special act of the soul designed for the purpose of life, which is an innate disposition of the body, and physical organic functions (whether vegetative, such as irritability or sensitivity, animal, such as motricity, circulation, secretion, excretion and nutrition, or human, such as will or intelligence). It is then a question of knowing how life is transformed into movement, and then into diversified organic functions. Does the sequence consist of a causal chain of a mechanical type, or is it based on a finality that transcends the parts? Stahl answers: [A]lthough this conservation finds its achievement in a formally mechanical act, it is, however, obtained and carried out in an instrumental manner through physical machines. From a long series of successive, simultaneous, synergistic acts results a supreme, unique and formal act, the conservation of the body.  (Vraie théorie médicale §6; BL 4 44)

A. L. Boyer, a vitalist physician, commentator, and apologist of Stahl in the 19th century, explains the thesis:

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You should not believe, as the iatromechanicians do, that circular movement is only achieved by the mechanical impulse of the heart and the large vessels, distended or even stimulated by the blood; the tonic force intervenes, and the soul exerts its influence by virtue of its sensitivity and its vital will. Thus blood is spread in all fabrics in variable proportion, according to the needs of the body.  (BL 4 5–6)

As an example, the phases of menstruation, lactation, and gestation constitute “a vital idea which continues and is carried out regularly in its least details” (BL 4 6).15 Leibniz’s position is halfway between these two interpretations. On the one hand, he takes into account the swirling model of Harvey; he compares organic movements to a purely mechanical circulation,16 similar to the fountains’; he explains tonic movements by elastic force (CAR 99). The body thus combines all types of motion known at the time: displacement, pressure, fermentation, gravity, and elasticity (Schneider 1993: 154–156). On the other hand, Leibniz preserves the finality of the soul, but generalizes it to all reality. However, following Fermat’s principle of least time,17 final causes acquire mathematical relevance, according to the de maximis et minimis logic, and their application is not limited to life, but extends to any physical reality. They can thus be formulated as laws of nature, similar to the law of refraction of optical rays.

2.4

The model’s status: Reduction or analogy?

Is such a description of the body as a machine equivalent to its physical reduction, hence to a neglect of its vital specificity, or does it offer a fertile analogy for the investigation of organic functions? Harvey describes his discovery of blood circulation as deriving from the simultaneous application of a mechanistic and of a vitalistic model of the body. Regarding the vitalistic model, he refers to the cosmological model of the Aristotelian Meteorologics and to the chemical concept of digestion [applied] to blood circulation (Gregory 2001: 153–168). Regarding the efficient model, Harvey transposes the methods of the mechanics to the living body. But as most of his contemporaries, Leibniz emphasizes Harvey’s mechanical analysis and neglects the vitalistic and Aristotelian references.18 Moreover, Harvey’s measurement of the quantity of blood based on specific durations, i.e., the evaluation of flows, evidences the conservation of the mass of humors through their displacement. The concept of causality thus carries an epistemology that can be defined at two different levels: mathematic and logic. On the one hand, by proposing quantitative evaluations of the flows, Harvey assumes that mathematical and mechanical analyses apply to living beings like to any other



Leibniz vs. Stahl: A controversy beyond medicine and chemistry 107

object,19 whereas the vital, chemical, and medical traditions reject the applicability of mathematics to experimental sciences. Briefly put, the concept of law of nature does not have the same meaning in both cases (see Metzger 1974: 101; cf. CAR 73, 99). On the other hand, logically, one side holds that the causes are uniform and that a given phenomenon can be understood by analogy with another one, while the other affirms the heterogeneity of the causes, which implies that the model transfer amounts to illegitimate reductionism. Thus Stahl rejects the use of the notion of law for purposes of understanding life and defends the heterogeneity between efficient and final causes; furthermore, he rejects the recourse to analogy (Metzger 1974: 168), which assumes the uniformity of natural laws. He also criticizes the relevance of efficient-cause models for understanding the vital act and consequently rejects iatromechanism: “Medical science underwent such reductionism that there is hardly any room for it nowadays” (De mixti et vivi corporis vera diversitate §59; Stahl 1707a; TM 91; BL 2 304). On the other side, following the Cartesian animal machine hypothesis, Leibniz restores homogeneity within his own system; he supports the analogies underlying the Cartesian phrase. In particular, he emphasizes the heuristic utility of fictions as a way of reaching beyond non-material differences. He also compares the body with a machine, although, from Descartes to Leibniz, as a result of the introduction of the infinite, the notion of the machine changes. He compares vital operations with chemical fermentation, as he had already done in Hypothesis physica nova (CAR 91),20 and soon modifies the metaphorical difference between them by speaking of “natural machine” (CAR 103) or “divine machine”. There is no longer room then for a tertium quid, which takes the form of an archeus, a hylarchic principle, a plastic nature, or energy. There are only differences in degree such that “The organism is formally nothing but a mechanism, albeit a more subtle and divine one” (CAR 105). If these metaphors have argumentative value in the controversy, this value is derived from their basis, which is the principle of continuity. Leibniz can compare the living to the flame, the body to a machine, the circulation of humors to sources and fountains, because he only sees a difference in degree where Stahl posits a difference in nature. From these analogies, Leibniz concludes that “the functions of the animal machine are all the more subtle as they reveal the artifice of a divine structure” (CAR 117). The difference intervenes at the level of the structure and its degrees of subtlety, which are infinite, since the presence of the infinite precisely characterizes the mark of the natural created by God in conformity with the rational laws of the best of all possible worlds.21 Leibniz asserts the continuity between the artificial and the natural, the organic and the mix, the animal and the plant and the mineral. This continuity finds its conceptual model in mathematical 

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division ad infinitum. All things are bound together, just as they are for Stahl, who denies both notions, of differences in degree and of division ad infinitum. In fact, Stahl rejects the reduction of the organism to a mechanism. The latter, for him, is a necessary but insufficient condition to life: Any organism presupposes a mechanism which constitutes the material for any body, i.e., the aptitude to really and especially perform certain movements. This mechanism effectively becomes an organism when a higher and external force [the soul] puts it into motion and directs it towards an effect as its final purpose.  (CAR 105)

For Stahl, life only abides by final causes. Of course, the mixed and physical body works according to efficient causes, but the organism as such is subjected to the ends defined by the soul. This difference in causality induces an irreducible difference in nature between the living and the inert. Far from a parallelism, there is rather a conflict between a mix that is liable to corruption and a soul that maintains the structure and the mix alive.22 When you seek to establish the borderline between the mechanical and the organical and between the reign of efficient causes and that of final causes, and attempt to identify the extent to which the mechanical is subordinated to the organical, you find out that “[it] is the very feature or necessary essence of the organism to have in itself a mechanic disposition … but it also has a formal reason that consists of its destination and an actual contribution to produce a special, unique effect” (Véritable distinction §39; Stahl 1707a; BL 2 203).

2.5 The touchstone for the passage from the machine to the living:  The infinite To escape the reductionistic error for which Cartesian theory is blamed, Leibniz introduces a new dimension into the machine: the infinite. Descartes cancels the difference between art and nature by working out the animal machine hypothesis: their apparent heterogeneity reflects merely a difference in complexity, and the parts of and relations within the body rely on the same mechanical order, although they are more numerous and complex. That is why, for that matter, anatomy does not yet master the totality of the structures (Disquisitio de mechanismi et orga­nismi diversitate §39; Stahl 1706b; BL 2 203). However, by passing from the simple to the complex, imagination makes it possible to compensate for this defect. Stahl, on the contrary, maintains a difference in nature between art and nature; in addition, he denies that matter can be divided ad infinitum. Once again, Leibniz generates a paradoxical synthesis between these two incompatible theories. He describes the organism as an infinite machine (CAR 93, 119), both at



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a temporal and a spatial level, since the preformation of organs and the envelopment of machines ad infinitum make it possible to posit a mere difference in degree between the artificial and the natural. But this understanding of the body as a real machine – though with a difference of degree – requires a new conception of the infinite and, therefore, of the machine. In this respect, Leibniz criticizes both Descartes and Stahl.23 In arithmetic as in geometry, any composition implies the infinite, and one can show the relevance of division ad infinitum with respect of the straight line or the number. Transposed to physical reality, actual division ad infinitum explains the overlap of functional machines and the complexity of chemical operations. It corresponds to a double thesis in biology: the preformation of the individuals and the envelopment of natural machines. Stahl fails to recognize the truth of the infinite at these two levels. Leibniz shows that Stahl is wrong at the level of mathematical analysis (CAR 93). But Leibniz also affirms the radical need to admit this division based on two types of arguments, one concerning the very possibility of motion, the other the logical structure necessary to explain motion. Finally, he indicates the possible applications of the concept of the infinite to the mixed and the living. Thus, Leibniz proves the continuity existing between the disciplines, as the explanatory concepts of medicine or those of chemistry come from mathematics and physics, and also from metaphysics. Consequently, the concept of the infinite confirms the relevance of the mechanical model, although both Leibniz and Stahl agree to dismiss the Cartesian animal machine thesis due to the fact that it denies any soul to animals and oversimplifies life.24 Taken to the limit thanks to the concept of an actual (temporal and numeral) infinite, the same thesis proves to be an extremely fertile ground for Leibniz. It makes it possible to preserve and explain the specificity of the living, which the hylarchic principles occulted. It thus offers a rational basis for the understanding of life. Thus, Leibniz agrees with the neoplatonician concept of form, but gives it a new meaning. Indeed, it no longer defines a hylemorphic or plastic principle,25 but the result of a serial or algorithmic operation, which wraps up the infinite: To explain the Formation of Animals, no plastic intelligences are needed to operate these wonders and form the animal freely, as a watchmaker makes his watch. It would indeed be surprising if these wise and great intelligences, after having formed it, neglected its conservation and abandoned it to the course of rough nature. All can be effected and is mechanically effected at the level of matter through the sole communication of motion; but that is thanks to a divine preformation of a machine already made long ago, which only develops or wraps itself and changes according to the occasions provided by the pre-­ordained course of nature. (Leibniz to Hartsoeker, October 30th 1710; GP 3 508)

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François Duchesneau (1999) explains the rational basis of this model that is so rich as to include the infinite.26 The form resulting from the interaction of an infinite number of machines determines a structural schematism, which is sufficient to build the model of living beings.27 And this structural composition emanates from or corresponds to a soul, which, as an entelechy, informs the body with its own finality. Thus, there is no need to appeal to plastic natures28 for understanding the form of living creatures. One principle of action is enough, if you have a correct definition of form. The form does not mean the figure, but the structure, the model, the organization, as physiology understands it, describing the laws of operation of the living. However, Stahl denies the relevance of the model for purposes of explaining the living, since he questions the value of analogies. To him, the diagrammatic model, a result of reasoning, as illustrated by anatomy, cannot coincide with the vital reality of the body. It is relevant at best to physical anthropology – not to medical anthropology – since it neglects the radical originality of life.

2.6

Medical value of the heart’s and the body’s union theory

The debate in medicine is connected with the metaphysical question about the union of the soul and the body. On this point too the debate between Stahl and Leibniz reminds the polemic between Descartes and More, Boyle and the Cambridge School (see Rogers et al. 1997; Boyle 1686), a polemic reenacted some years later by Schelhammer and Sturm.29 On the one hand, the vitalistic tradition seeks a principle of action transcending matter and acting as a cause for any new physical effect: soul, archeus, hylarchic principle, plastic nature, second or intermediate providence. On the other hand, the mechanists argue that motion must and can be sufficient to explain physical modifications: the laws of movement describe reality exactly as it is. One can summarize their point of disagreement as follows: the adversaries acknowledge the value of a mechanical description, but Stahl restricts its use to inert phenomena, while Leibniz extends it to the explanation of all reality. The animistic tradition follows the doctrine of van Helmont, who combines an inert matter and a transcending principle of action to explain phenomenal modifications (see Metzger 1923: Chapter 3). Van Helmont calls this immaterial being “archeus”: its efficiency is particularly manifest in the living creatures, through the realization of vital functions like digestion. This duality between a conception of matter as corpuscular and the assumption of a transcendent, active ingredient is resumed by the Cambridge School, although the continuity from Van Helmont to More may not be reduced to a simple transposition (see Breteau 1997). Henry



Leibniz vs. Stahl: A controversy beyond medicine and chemistry

More continues to apply Cartesian mechanics to the body, but he refers to a Spirit of Nature to explain the phenomena. This hypothesis is considered necessary because it is impossible for mechanics to explain the origin of movement without causing a regression ad infinitum. Admittedly, the mathematical model of the laws of nature makes it possible to represent the impact between two bodies, but it does not explain the nature of the cause that generates the movement in the body. This action cannot come from another body, since it would itself depend on another cause, and so on. It is thus necessary to regard the impulse as the awakening of an internal disposition of the moving body. This internal disposition characterizes the presence of life with which all living bodies are equipped.30 Ralph Cudworth confronts the same difficulty, which he solves in similar terms: on the one hand, he resumes the corpuscular hypothesis established within perennial philosophy from Moses, Pythagoras, Parmenides, and Democritus to Van Helmont, Descartes, and More; on the other, he seeks to reconcile this theory of matter with the reality of the Christian God. It is then necessary to find a principle of action that can serve as an intermediary between absolute Providence and physical transformations, since God cannot reasonably be thought to intervene directly in each detail; hence, the idea that plastic natures are the origin of all physical movements.31 Stahl takes up these categories again in a medical context that refers primarily to Hippocrates. The explanation of movement is integrated into a more specific reflection upon life, of which movements constitute only an instrumental cause. Although the corpuscular hypothesis, when joined to mechanics, makes it possible to understand how bodies are aggregated and mixed, it remains incapable of explaining life’s originality. Life is characterized by the emergence of finality within matter, since the organism tends to preserve itself in spite of corruptions and shocks to which the body is inceasingly subjected. Independent from matter, this vital purpose is carried out through the organic functions; it belongs to the soul, which constitutes the true principle of action in the living. The soul acts on the body (as mixed and as aggregate) thanks to an instrument, motion, with the purpose of perpetually restoring health. This vital or tonic movement (cf. Stahl 1692) is not restricted, therefore, to efficient causes only, although its effects fall under a series of physical modifications. The conjunction between corpuscular matter and soul acting directly on these particles characterizes these animistic interpretations of action. In contrast, Leibniz purports to both avoid the direct action of the soul on the body and escape the double risk of regression ad infinitum and negation of final causes (CAR 119). From the very beginning of the controversy, the general hypothesis of the pre-established harmony must substitute direct action of one on the other by expression between one and the other: Neither efficient nor final causes explain a particular movement or a particular thought, but the former and

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the latter correspond exactly to each other, each one finding its own raison d’être within the series of events which characterizes it, both being founded on the principle of sufficient reason. In addition to this general framework, however, Leibniz uses a principle of action derived from the substance, namely force. The general question of motion becomes, within the living bodies, the specific question of the organic functions, themselves an expression of the principle of force that is intrinsic to the animal.

2.7

The living, air, water, and places

The question of the relationship between medicine and physics does not only concern the intrinsic operation of the organism but also its relationship with external circumstances.32 In his way, Leibniz also interprets the Hippocratic legacy, but he focuses on the treatise on Airs, Waters, and Places, whereas Stahl prefers to quote the treatises included in Ancient Medicine. However, this difference in the interpretation of the Hippocratic corpus is not limited to the polemic between Stahl and Leibniz; it is present across the history of medicine and causes debates that are particularly intense in Germany at that time (Obst 1992: 10, 15). In this respect, Leibniz prolongs Boyle’s intuitions. They both refuse Cartesian reductionism, whether in medicine or in chemistry, and they both hold a strictly mechanical conception of the universe.33 Both maintain continuity between the inert and the living and, as a result, an effective analogy between the two reigns; both sustain a direct causality exerted from the environment to the organism (Boyle 1661). Later, Friedrich Hoffmann takes up the Boylean torch again at Halle University, where he teaches medicine at the same time as Stahl. After meeting with Boyle in London in 1684, Hoffmann further pursues the analysis of blood (see Boyle 1684), studies the acid and alkali couple, and writes a treatise (Hoffman 1700) linking meteorology, medicine and physics, which soon finds its institutional place at the Berlin Academy founded by Leibniz. On the other hand, Stahl considers the living as absolutely distinguishable from other material bodies. As their inner principle, life does not directly depend on external circumstances, which only affect its object, the body.

2.8

Medicine and physics: Continuity or rupture?

The debate regarding the status of the living, homogeneous or heterogeneous with matter, triggers an epistemological question: Is medicine a science that is in continuity with chemistry, physics and mathematics in accordance with a unified conception and method of science, or is it different in its object and its methods?



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The controversy relates to the specificity of the living in comparison with other bodies. This question is renewed by recent discoveries, but can be traced back to the Hippocratic thesis developed in the treatise on Ancient Medicine, which Stahl quotes in some of his works. The Hippocratic theory undoubtedly constitutes the origin of this irreducible opposition between two medical theories, vital and mechanical. Indeed, Hippocrates had already criticized the dependence of medicine on Pre-Socratic physics; Celsus later expressed the same criticism and emphasized the need to distinguish medicine and physics. Aristotle, as opposed to this, advocated a mere difference in degree between medical science and physics: [H]ealth and diseases are subjects that come within the province not merely of the physician, but so far as the consideration of their causes goes, within the natural philosopher. (…) Yet that their respective provinces are to some extent conterminous is shown by the fact that such physicians as are men of refinement and wide culture wont to talk of the laws of nature, and profess to derive thence their principles of practice, while the most accomplished of the natural philosophers rarely fail in the end to touch on the principles of medicine.  (Aristotle,  On Youth and Old Age, On Life and Death, On Breathing; 480b30, 104–105)

In the classical age, the same polemic arises between Stahl, who reasserts the Hippocratic legacy of “natura medicatrix”, and Friedrich Hoffmann, the leader of iatromechanism at Halle University, where he directly challenges Stahl (Courtès 1971). Each one comments the same aphorism in his own way: “the physician starts where the physicist finishes”. Stahl reads into this aphorism a difference in nature, and Hoffmann a difference in degree. Between Stahl’s and Hoffmann’s positions, Leibniz chooses the latter’s without hesitation. Stahl maintains a radical heterogeneity between life and physics: for him, the concept of law is inadequate to understand life. Movements are the instruments of the soul; the organic structure and the texture describe the physical order arranged and finalized by the soul. Against the conceptual model used by the mathematical and physical sciences, Stahl claims radical specificity for medicine, which lies in the idea that, far from being out of the reach of reason, the object of medicine – life – is reason itself, and can be known only through intuition, and not through reasoning. Life is pure reason, a vital act, effective awareness; reasoning emanates from reason, but cannot be identified with it. Reasoning means an organic, intellectual action that supports the rational activity in the brain. As such, reasoning can never be adequately identified with reason itself; a fortiori, the further away its object moves from life, the more reasoning is separated from reason. Such is the case of mathematics and, to a smaller extent, of physics and chemistry. Medicine constitutes, on the contrary, the rational science par excellence, where reason takes itself for its immediate object. So the living knows life,

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reason knows itself. Stahl states this distinction in a treatise entitled De Differentia λογου και λογισµου (BL 6 445–452) [R]eason, eidos, positively perceives the subtle movements of tension, trembling, excitation, irritation and fermentation, under the impression of which it operates in a rational, but not reasoned, manner suitable secretions. (BL 6 448)

This is why the only real basis for medical art lies in the intimate knowledge of secretions and excretions. Thereafter comes reasoning regarding the structure and the texture of the bodies, blood circulation, in short, anatomy, and physical physiology (Stahl 1707a; BL 2 372). Admittedly, medicine resorts to physical and chemical knowledge, but these three disciplines do not belong to the same rational order and have three distinct objects: life, the aggregate, the mixed. The proof of this radical difference between life and matter, reason and reasoning, clearly appears in the fact that, most of the time, nature does by itself all that must be done and that, very often, the physician must withdraw to let natura medicatrix, of which he is but a simple minister, operate (Defensio et vindicatio §48; Stahl 1707b; BL 2 445; De medicina sine medico; Stahl 1707c). Leibniz and Stahl carry on the opposition not only between two conceptions of the living, but also, more radically, between two definitions of reason. Animism defines an epistemology of intuition, coincidence of reason with itself in connection with the knowledge of life. Far from being integrated into a universalis mathesis of which it would constitute one among many other objects, animistic medicine, as a study of life, is reason aware of itself in action. For Leibniz, life remains a property of the substance, but its organic expression is not entirely understandable by the physical and chemical laws governing the matter. Stahl, on the other hand, transposes life into a pure essence and immediately identifies it with the soul or reason; he denies any physical equivalent to life. Separated from the body, life or reason defines the very identity of the human soul and, consequently, of man himself. In this respect, Stahl fits indeed within the revival of Platonism that animates the medical philosophy of the classical age from More and Cudworth to Stahl, and challenges the tradition of Descartes, Locke or Leibniz: [M]an is properly soul, all the body mass must be seen only as its agency... It ensues that the life of man or of the human soul consists not simply of action in general, but especially of that action exerted and performed in a body, by means of a body, on and regarding body matters, and even on the body which belongs properly to him. (Véritable distinction §51; BL 2 298)

Life does not consist of the union of the soul and the body, but in the transcendent activity of the soul on the body. To Stahl, there is neither parallelism nor occa-



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sional causes or substantial union, but animist vitalism or, according to his physician commentators in Montpellier, “vitalistic monodynamism” (Blondin 1860).

3.

Chemistry

Chemistry offers an approach that is complementary with medicine. For Leibniz or Boyle, this approach is analogous to the medical approach, but for Stahl, it is different from it. On the one hand, they are both experimental sciences. On the other hand, their complementarity results from the interweaving of the living34 and the mixed: 35 chemistry deals with masses, analyzed according to their qualities (nature and properties), while anatomy studies the structures and textures, i.e., the organization of these masses in the living. Thus, according to Stahl, chemistry logically comes before medicine in the study of the matter, as [T]he mix always comes before the structure, so that one never discovers in the body any trace of texture or structure that does not presuppose a special arrangement from all these infinitely minute atoms which, by their juxtaposition, consti(Vraie theorie médicale; BL 3 69) tute this body itself. 

3.1

The element and the mixed

Against Aristotle,36 Van Helmont, Boyle, Stahl, and Leibniz defend a corpuscular definition of the chemical element inherited from pseudo-Geber: deprived of any quality, indivisible, particles mix among themselves and cause the advent of new qualities in mixed bodies Chemistry, indeed, shows very well, proves in an unquestionable way by many examples and puts entirely out of doubt, the fact that bodies considered as physical individuals or indivisible are so minute and so tiny that their own constitution, considered separately, escapes the perspicacity and power of our senses.  (Véritable distinction §6; BL 2 259)

The chemical operations par excellence are the mix and the decomposition: corpuscles determine the limit beyond which the dissolution of mixed bodies cannot extend. While they agree on a corpuscular definition of the chemical element, Boyle, Leibniz, and Stahl diverge on the theory of the mix. This difference is marked in their respective answers to the following two questions: i. According to which rules or laws is the mix carried out? Stahl proposes a theory of affinity, while Boyle and Leibniz seek laws analogous to mechanic laws; and

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ii. Is there continuity or rupture between the mixed body and the living? Stahl asserts a rupture, but Boyle and Leibniz assert continuity.

3.2

The laws of the mix

How is it possible to pass from quality-less corpuscles to a mixed body characterized by qualities? One needs a principle for the mix that can be integrated into the physical theory of movement, while preserving the specificity of the very tiny. On the one hand, Stahl proposes a theory of affinity that enables him to escape Cartesian reductionism.37 On the other hand, Leibniz seeks to preserve a mechanistic approach at all levels of natural phenomena, while also criticizing Cartesian reductionism.38 In this respect, he over-interprets Boylean chemistry as mechanism.39 For Leibniz, the analysis of bodies is carried out, or should be carried out, simply by progressive reduction to simpler elements, so that it takes us from the organism to the flesh, the fabrics, the humors, then to the salts, vitriol, and finally to sulphur or primary metals: “Vitriolum ex sulphure aliove acido et cupro vel ferro” (‘vitriol is produced from sulphur or from another acid, with copper or iron’; A VI 4 1972).40 Moreover, the road from analysis to synthesis can be reversed,41 and it is possible to make complex bodies out of simple ones again: “quia datur circulus in compositionibus ac productionibus, ex gr. rursus potest produci sulphur ex vitriolo” (‘because there is a circle between components and composites, so, for example, you can produce again sulphur from vitriol’; ibid.). In this sense, Leibniz subscribes to a corpuscularian chemistry inheritated from Pseudo Geber and reformed by Boyle.42 If this circularity exists, it corresponds exactly to the axiom of physics, according to which the effect completely exhausts its cause. Putting aside losses by friction or dissipation, equipollence holds as much for dropping bodies as for chemical reactions in a strict mechanical context. Announcing the precept “Nothing is lost, nothing is created” makes it possible to build the idea of laws, in a somewhat similar sense to those of astronomy or movement.43 However, unlike Descartes who advocates reducing chemical laws to the mechanical model,44 and in agreement with Boyle, Leibniz recognizes the specificity, at least in practice, of chemical explanation. At the time, materials remained irreducible to purely numerical combinations and contained qualities that could not yet be analyzed using traditional instruments. Analogy and resemblance were still relevant to understanding the nature of the elements. This justified the primarily empirical situation of chemistry, which could only induce these laws, not prove them. From an epistemological standpoint, chemistry had not yet reached the degree of certainty that optics had when it demonstrated the law of the sinus on



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the basis of final causes, or that dynamics had. Nevertheless, Leibniz considers the mix following the mechanical or dynamic model of the swirl. Thus, the Leibniz-Stahl controversy still applies this fundamental divergence between two chemical theories at specific points: the explanation of fire, either by mechanics or by “phlogistic”; the explanation of salts; the explanation of phosphorus (CAR 115; see also A III 2 117–119, 231–233, 847–849; A III 3 48, 58, 268, 720; A I 8 367; see also Breger 1987: 68; Metzger 1974: 175). In each case, Stahl proposes an interpretation that is specific to chemistry, irreducible to a physical explanation, whereas Leibniz acknowledges the relevance of chemical explanation and supposes at the same time that it could be reduced to mechanical description if pushed to the limit. This divergence finds a decisive illustration in fermentation, which is like a touchstone with regard to fundamental chemistry. Leibniz summarizes the specific role of fermentation in the digestive function in a letter to Grimarest: Regarding digestion, I would be inclined to combine trituration with fermentation, or something similar, Physics with Mechanics. That is definitely Nature’s usage. One is a little too prone to make assumptions today, and even to the point of exaggerating. Archeists ban Mechanics from Medicine, & Mechanists do not see that we are not yet informed enough of the ways of nature, to explain them mathematically everywhere. I believe that the Physical depends on the Mechanical at bottom, but we could not reach that bottom. We have in Germany a Physician who denies the dependence of Physics on Mechanics, & who, banning even animal spirits, holds that the soul acts itself in the place of these spirits. That is another excess.  (Leibniz to Grimarest, February 21st 1712; D 5 63; my translation)45

Leibniz thus thinks of the difference between life and the matter, the living and the mixed, in terms of degree, not of nature; and this difference fades away as our observation skills improve. That is a simple application of the principle of continuity to the organic phenomena like secretion (CAR 117) or perspiration (CAR 109). This continuity then makes it possible to preserve the relevance of efficient causes to explain the phenomena, whatever their nature. Of course, the method of chemical analysis must adapt to the specificity of its object; but this methodological difference reflects rather the current limits of our means of investigation than the order of things. Actually, the concept of force alone should suffice to explain every thing; in fact, a distinction should be maintained between the physical level and the chemical level of analysis.46 On this point, Leibniz agrees with Boyle (see RBb 7 73–226; RBb 3 189–480), provided his corpuscularism is construed as strict mechanism.

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3.3

Is there continuity or rupture between the mixed and the living?

While Stahl follows Boyle on the theory of the element, their explanations for the mix are quite different. Stahl criticizes in particular the notion of continuity from the mixed to the living: “Chemists have not yet discovered any relationship between the mixed and the living” (Paroenesis §31; Stahl 1706a; TM 59; BL 2 158). Stahl seems to be aiming, in particular, at the experiment of the willow and the melon used by van Helmont and Boyle as a criterion for testing the continuity between the mixed and the living (RBb 2 205–378; on this experiment, see Carvallo 2002). The two chemists draw strictly opposed conclusions from the same results and observations: For van Helmont, there remains a caesura between the physical individual, an aggregate mix, and the living;47 for Boyle, physical growth of a material quantity evidences continuity between the inert and plants. Indeed, the two chemists are faced with the question of the origin of life in such mixed beings as men, animals, or plants. In line with his conception of experimental sciences, Boyle calls upon experience: like van Helmont, he compares the initial with the final masse of a plant grown and nourished exclusively with pure water. The growth of a plant indicates a production of living matter solely out of the mineral elements of air and water. This, for Boyle, shows continuity between the inert and the living, which organizes the matter. For his part, Stahl certainly acknowledges a plastic principle inherent to the plant; but he challenges the possibility of explaining the organization of air and water into a plant by the matter alone. He asserts the intervention of a vegetative soul or some vital force (Vraie théorie médicale; BL 3 72). This is confirmed by three facts: first, the mixed bodies have no intrinsic reason to last as they do; second, they even resist aggregation, although aggregation constitutes a necessary condition for the existence of living bodies; and third, they cannot reproduce themselves (Véritable distinction §7; Stahl 1707b; BL 2 262). Between the chemical and the living, Stahl maintains a difference in nature: “There is a very great difference between the mixed and the living in the human body, i.e., between the true physical constitution liable to mixing and the formal disposition of this mix to produce the acts and effects suitable for life” (Véritable distinction §11; Stahl 1707a; BL 2 267). Thus, the two chemists assume differently van Helmont’s legacy. In this legacy, Boyle separates chemistry and medicine; he adopts his chemical theory and rejects his medical explanation, whereas following J. J. Becher, his Master, Stahl proposes a new synthesis of the Helmontian vitalism, criticizing the multiplicity of intermediate beings (gas, blas, soul, archeus, spirits) which proliferated in the Helmontian treatise Ortus medicinae (Vraie théorie médicale; BL 3 58). Stahl subscribes to van Helmont’s general pretension to explain life as transcendent force acting within the matter. The radical difference between the mixed and the living



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is due to the presence of a “vital idea which goes on and is carried out regularly in its least details” (Ibid.; BL 3 6; my translation). And “it is especially in the assimilating activity of digestion that the vital force deploys at best its elective sensitivity, and that it pursues with admirable constancy the implementation of the type, the idea (eidos, idea) which preserves everywhere the mix, the texture, the shape of the organs” (Ibid.; BL 3 8; my translation). Thus, this difficulty in explaining the emergence of life from within the matter results in two distinct attitudes: either, as Boyle does, one gives up explaining life but acknowledges that the inert matter can be organized into a living being; or, as Stahl does, one resorts to a soul that uses at least intuitively chemical elements to achieve its purpose through the matter. What is Leibniz’s position in this respect and at this time? We can recognize here the question of the aggregate, which Leibniz solves at this period of his philosophy, by the metaphysical hypothesis of the dominant monad. In the controversy, Stahl challenges specifically this point: either Leibniz is of the same opinion as he is but tries to avoid its dualistic consequence by resorting to the mask of the Greek term “monad”, or Leibniz has given up, as so many others did, explaining the presence of life in the matter, even if this renouncement means reducing life to pure mechanism.48 Neither interpretation does justice to Leibnizian thought. However, Stahl correctly identifies a difficulty with Leibniz’s philosophy. In addition, he emphasizes the need to found chemistry and medicine in a philosophy of nature.

4.

Philosophy of nature

Following what criteria can a concept of nature be worked out? First, it must correspond to the interpretations of medicine and chemistry, whose results make it possible to test the validity of the assumptions governing their explanations and predictions. Thus, therapeutic success and the success of a chemical operation – or, conversely, their failure – constitute an experimental proof – or, conversely, refutation – of the theory by facts. But it is also necessary to define the general foundations of these experimental sciences by working out a philosophy of nature. Throughout his critical work regarding the materialistic or animistic theories of nature, Leibniz distinguishes a concept of nature taken in its general meaning, as the equivalent of the universe, and a concept of nature taken in a particular meaning, as the essence of beings. In respect of the former meaning, he seeks above all to reconcile final and efficient causes; in respect of the latter meaning, he proposes an autonomous principle of action that does not derogate from the requirement of rationality (Leibniz 1698, De ipsa natura §2; GP 4 504–505). If

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these two points actually prove to be complementary, the ambiguity of the term requires separating the various levels of his analysis.

4.1

Nature

The idea of nature is renewed in the Renaissance and the modern age under the impulse of discoveries and reforms operated in several fields; the principal ones relate to mathematics, experimental sciences, religion, and metaphysics (see Lenoble 1953). A scission arises between materialism and idealism, efficiency and finalism. Leibniz stands at the frontier, Stahl clearly chooses his camp. Both challenge the materialists, who attempt to entirely reduce nature to space deprived of any principle of intrinsic action. Even if Stahl grants the reduction of matter to the three dimensions of space (see Rather and Frerichs 1970: 54), he clearly separates between soul and matter. Both Leibniz and Stahl must, therefore, confer a positive content upon the idea of a nature that is undoubtedly governed by efficient laws, but at the same time, is determined by a creative act and also endowed with certain autonomy and spontaneity. In fact, Leibniz reopens the debate that Boyle (1686) had summarized about twenty years before. Three conceptions of nature prevail on the philosophical scene at the time: (i) the quasi-materialistic nature of Descartes or Hobbes; (ii) the neo-Platonic nature of Cudworth and the Cambridge School, to which Stahl can be associated; and (iii) a third intermediate position worked out to combine divine creation with the efficiency of laws immanent to the matter. By reducing nature to matter, Hobbes and Descartes consider efficient causes as the only relevant ones for understanding nature; liable to mathematical expression, natural laws correspond to the absence of will in physical matters. However, Cudworth seeks to reconcile the idea of a creative and active God with the real efficiency of natural laws. In other words, he simultaneously claims to preserve divine Providence and a relative autonomy for a nature made up of physical atoms. This reconciliation is carried out thanks to the mediation of plastic natures, which operate within the matter in an immanent manner like an art governed by laws. Of course, divine Providence is preserved in a general way, but plastic natures introduce an intermediate quasi-providence.49 Like the stoic “logoi spermatikoi”, these plastic natures indicate a properly natural principle of action, but at the same time they embody a final causality in the matter: they carry out the seal and signature of God everywhere in the world, and any material effect finds its true cause in them. Moreover, these plastics natures are organized according to a hierarchy of beings50 that, according to neo-Plotinian logic, refers to a Soul of the World situated at the top of the hierarchy. Intermediaries between God and



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the matter, plastic natures depend on the organizing force of Nature in its systematic totality. In this respect, Stahl defines nature as a synonym for the vital force or the soul, the medicatrix natura, which the physician serves; according to the Hippocratic tradition, the physician officiates as the minister of Nature. Between these two strictly opposed conceptions, Boyle chooses a middle way and simultaneously challenges Hobbes as well as the Cambridge School. In the treatise A free enquiry into the Vulgarly Receiv’d Notion of Nature (1686; RBb 10 437–571), he distinguishes nature in a general sense (or what Leibniz calls the well founded phenomena), which is regulated by laws, and nature in a particular sense (or substance, in Leibnizian terms). In this regard, Boyle appears as a precursor of the approach that Leibniz will adopt for his own account. Indeed, both criticize the idea of a Soul of the World and deprive nature of its substantial meaning. With both of them, nature becomes pure matter, organized, however, according to an infinite number of intrinsic principles of action whose effects are law-governed but which are in conformity with the providential design of God. Both give up the ambiguity of the term “nature” and attribute active power to a notion of substance endowed with force. Above all, they deny the idea of a pure soul separate from the matter. Leibniz translates this immanence by the concept of force or life: while being of metaphysical nature, force or life is in matter, although it is not matter (CAR 117). Lastly, Leibniz reconciles the efficient and final causes: the former make it possible to explain all phenomena by their immediate causes, the latter make it possible to explain all phenomena by appealing to ‘entelechies’. In De ipsa natura (1698), Leibniz summarizes these categories, following the polemic between Sturm and Schelhammer,51 in continuation of the polemic between Boyle and the Cambridge Platonists. This writing reiterates the criticism already made of the Cartesian concept of matter and promotes dynamics in its metaphysical implications. But Leibniz also puts an end to the vitalistic or animistic temptation to which Cudworth, More, and Stahl succumbed. A creative act, which is equivalent to the principle of sufficient reason, and Providence, which assigns a goal to any event without conferring a universal spirit upon nature taken in general, nor radically dissociating spirit and matter, as Stahl wishes, remains between matter and God. It now becomes possible to reconcile nature and providence better than the Ancients did. To this end, the personifications of nature must be distinguished correctly.52 That amounts to radically dissociating God and his creature, Providence and nature.53 Within the framework of a theology of creation, what is the meaning of the finality of nature, which the Aristotelian aphorisms remaining in scholastic metaphysics try awkwardly to express? How can statements such as “nature does nothing in vain” (Aristotle, De caelo II, 11) or “nature always finds the best solution” (Aristotle, De caelo II, 5; De generatione II, 10, 22) be maintained while

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asserting their compatibility with the mechanical principles of a world now conceived following the model of a clock? In accordance with faith, Leibnizian reasoning refers the will, or more exactly finality, back to a creative God. However, it enjoys a real autonomy, independent of Malebranche’s theory of occasional causes. On this point, Leibniz still adopts the same strategy as Boyle in A Free Enquiry into the Vulgarly Received Notion of Nature (1686).54 Indeed, in section III of this work, Boyle criticizes the Aristotelian definition of nature,55 and, in section IV, analyzes the various axioms or “effata” concerning nature. These axioms wrongly tend to assimilate nature to a half-god, an intelligent being, and may be kept only if they are de-personified and given strictly mechanical content. Leibniz pursues this reflection on the concept of nature from the third paragraph of the controversy with Stahl. After the first two postulates concerning the principle of sufficient reason and mechanical causality within matter, the third postulate of the controversy defines the concepts which are derived from them: nature as the reign of the efficient and final causes, action as the effect of an efficient cause and a final cause, the pre-established harmony between the matter and the form, and individual nature as entelechy. By asserting nature as the creature of God, the polemic repeats, in this respect, the results of paragraph 6 of De ipsa natura: [I]f, on the contrary, the law issued by God has left a certain trace engraved in things, if things have received by this order the arrangement which enables them to achieve the legislator’s will, then it should be acknowledged that created things contain a certain efficacy, form or inherent force, that we are accustomed to call nature and from which the series of the phenomena are derived, in accordance with the prescription of the primitive order. (GP 4 507; my translation)

Thus, Leibniz comes close to Boyle, who simultaneously defends a corpuscular philosophy of nature and an orthodox Christian theology, while stressing that the knowledge of the former leads to that of the latter.56

4.2

Natures

The controversy on the concept of nature taken in a general sense cannot but focus also on natures, monads or “plastic natures” in the Cambridge School’s terms: [Leibniz] receives from Cudworth, More and the other Cambridge Platonists the label which authorizes him to take up the “monad” in a conceptual context entirely discharged of the simplistic gravities of the atom, and oriented towards a concept of the “simple” that could benefit from all the specious new mathematical instruments relevant to his representations concerning derived forces as well as the simplicity that combined mechanism with finality.  (Robinet 1997: 194; my translation)



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To Lady Masham, Cudworth’s daughter and Locke’s protector, Leibniz confesses that he admits plastic natures in general, but remarks that “this plastic force is mechanical by itself, and consists of preformation and of already existing organs, which alone have been able to form other organs” (Leibniz to Lady Masham, July 10th 1705; GP 3 368).57 By correcting the epithet “plastic” by the expression “mechanical by itself ”, Leibniz reconciles spontaneity and efficiency within particular beings. The Leibnizian project is thus to explain what Cudworth left without explanation. The controversy with Stahl partly offers this opportunity, since it relates to this singular nature, partly autonomous and yet mechanical: the organism. Stahl calls “souls” these entities endowed with life that are still heterogeneous with the matter and that More called “hylarchic principles” and Cudworth, “plastic natures”. As a physician, he studies the manifestations of these souls within the organism in two forms: energy and tonic movement. As the ultimate principle of action and reality within the matter, these natures are not governed by the efficient causes, but direct their movements according to their own purposes: “indeed nature, the vital force, holds the structure under its absolute power” (Vraie théorie médicale; BL 3 69). The soul finds in the movement its direct instrument, and particularly in the vital or tonic movement: [T]his tonic movement is accomplished in an efficient way by the vital faculty, i.e., the vitally acting soul or, in vulgar terms, by nature. The soul applies this movement to all vital forces, the directions, the distribution, the secretions, the excretions of the mass of humors. (Du mouvement tonique vital; BL 6 519)

By prolonging the concept of nature through its organic effects, the Stahlian project exceeds the metaphysical framework to which the theories of the hylarchic principle or plastic natures were essentially restricted; it aims at the constitution of a non-mechanical science, which would correct the double Cartesian reduction of the living and the mixed to pure movements without qualities. In the medical domain, Stahl indeed works out alternative explanations based on the concepts of energy and tonic movement, which must replace mechanical descriptions. Thus, for example, the explanation of blood circulation does not depend on the model of the swirl, but on transcendent activity.58 In chemistry, fermentation does not correspond to the simple act of trituration, but to the joint presence of an acid element and an aqueous element. It is then a question of expressing correctly and precisely the relationship between the mixed and the living (Paroenesis §31). Leibniz acknowledges the practical relevance of these medical or chemical concepts, but his work consists rather of integrating them into a coherent framework compatible with experimental physics, so that the apparent heterogeneity of medical, chemical, and physical explanation principles reflects only a provisional flaw of human reason, rather than the order of things. It is

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thus a question of correcting animistic interpretations and constituting the correct metaphysics that will provide the foundation of the experimental sciences. Such is the particular and decisive stake of a correct definition of the peculiar “nature” of the living. Indeed, the second meaning of “nature”, understood as being or essence, concerns particularly the organism, which Leibniz defines in the controversy as an “igneous hydraulic pneumatic machine” thereby synthesizing the sciences of his time.59 By proposing this definition by analogy, Leibniz imposes a mechanical model governed by pressure, swirl, and heat, in the three orders of gases, liquids, and solids, to inquire into the structure or the form of the living. Thus, he takes up again a point of the prior criticism concerning a generally erroneous conception of nature and asserts that the laws of nature inscribed in matter determine an efficient causality. Consequently, it proves to be legitimate that the mechanical model should possess a heuristic function, which appears through the hypothetical status of the definition of the body as a machine. This global definition of organic operations constitutes a touchstone for validating or denying the general hypothesis concerning the definition of nature, on the one hand, thanks to a scientific theory built on the model of dynamics or celestial mechanics, and, on the other hand, thanks to experience. François Duchesneau developed this function of the model as simultaneous testing of metaphysical principles and phenomenal laws: [T]his means an analogical development of “mathematical” models to symbolize connections between, and sequences of phenomena so as to provide for their integration within theoretical frames. To form a demonstrative science about truths of fact, one has to work out such hypothetical analytic schemes.  (Duchesneau 1999: 208)60

In fact, this method of argumentation appears as early as Leibniz’s first works in physics and is applied in the controversy with Stahl. In the controversy, Leibniz operates a displacement of the medico-chemical issues towards a properly philosophical questioning designed to disclose the fundamental work of reason as expressed in experimental sciences, through such notions as cause, nature and infinite. He updates fundamental “biology” and chemistry (“rational medicine and chemistry”, as he would have put it), which support their respective practical implementations. Then, medical or chemical experiments reveal their true use: in the controversy, they constitute arguments, touchstones for testing the pre-established harmony hypothesis, and, overall, Leibniz’s metaphysical principles, through their fecundity in the interpretation of phenomena. This proof by utility legitimizes the dialogue between the physician, the chemist, and the philosopher: failing a demonstration of the intrinsic truth of



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a thesis, one can compare the respective uses of two experimental practices and induce from such a comparison the better theory. Thus, the exchange of questions and answers between Stahl and Leibniz enables the confrontation of several theories and practices in order to identify the correct ones. Far from being reduced to a polemic between two voices, the meditation shared between Stahl and Leibniz actually orchestrates a polyphonic melody, where the echoes of the Ancient times, the Renaissance, and the Modern Age can be heard. This conceptual orchestra converges on an effort to define the two concepts of nature and life, and consequently to establish the principles of rationality. Like a living mirror, the concept of monad, for that matter, constitutes the focus of the debate (CAR 217). According to the interpretation of the history of ideas that Leibniz suggests in the New Essays around that time,61 a perpetual debate characterizes the life of a diachronic République des Lettres. The unity of this Republic undoubtedly proceeds from the permanence of these so-called metaphysical open questions, which concern the soul (reason and life), God, or the world (matter and life). These questions reflect a perennial philosophy, announcement of an encyclopaedia that precisely develops through such controversies, as a counterpoint to scientific progress.

Notes 1. In the list of references these four treatises are indicated as Stahl (1706a, 1706b, 1707a, and 1707b). Their French translations figure in volume 2 of BL (1860–1864). 2. I collect, translate, and present the whole exchange in Carvallo (2004), henceforth CAR. 3. For an interpretation of the integration of the many in a philosophy conceived as a knowledge of the real, see Frémont (2003: 343–365). 4. Leibniz’s writings contain numerous references to medical and chemical theories. Concerning medicine, for example, see Mahrenholtz (1990); Duchesneau (1998, 1999). 5. See for example Epicurus, Letter to Pythocle; Aristotle, Metaphysics D; Lucretius, De natura rerum V. 6. Descartes explains life by the heart’s heat due to humors’ fermentation: “Et afin qu’on ait une générale notion de toute la machine que j’ai à décrire, je dirai ici que c’est la chaleur qu’elle a dans le cœur, qui est comme le grand ressort et le grand principe de tous les mouvements qui sont en elle… Et les artères sont encore d’autres tuyaux par où le sang, échauffé et raréfié dans le cœur passe de là dans toutes les autres parties du corps, auxquelles il porte la chaleur et de la matière pour les nourrir” (La description du corps humain; AT 11 226–227). For further analysis, see Des Chene (2001: 25–36). 7. The knowledge of organism synthetizes Archimedes’s hydrostatics, Olivier de Serres’s technics, Torricelli’s, Guericke’s, Pascal’s and Boyle’s experiments, Biringuccio’s studies on fire, Huygens’s and Denis Papin’s steam engine.

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8. Particularly: “je constitue un double et très parfait parallélisme; le premier entre les principes matériels et formels, c’est-à-dire entre le corps et l’âme; le second entre les règnes des causes efficientes et des causes finales. Le système de l’Harmonie préétablie, dont je suis l’inventeur, contient le parallélisme entre le corps et l’âme. Même si la source la plus directe de toute action est dans l’âme, comme celle de toute passion dans la matière, il ne faut cependant pas penser que l’âme fasse dévier par ses propres opérations innées – la perception et l’appétit – le moindre corps de ses propres lois mécaniques, mais plutôt qu’elle opère selon elles, et que tout est constitué dès l’origine par Dieu, créateur des âmes et des corps, pour que la série des perceptions de l’âme réponde parfaitement à la série des mouvements du corps, et réciproquement” (CAR 75–77). 9. Leibniz to Rémond, January 10th 1714; D 5 9; GP 3 607. Concerning the discussion between Descartes and Morus, cf. Cottingham (1997: 159–171), Hall (1990), Gabbey (1990). The More-Descartes correspondence can be found in Descartes, AT 5. 10. “La Chymie, armée de tous les elemens, travaille avec un succès surprenant à tourner les corps naturels en mille formes, que leur nature ne leur auroit jamais données ou bien tard. De sorte qu’il semble qu’il ne tient qu’à nous de […] rétablir la santé des corps bien plus qu’on ne pouvoit faire autresfois, puisque nous avons asseurement des remèdes, qui effacent tous ceux des anciens, et que la connaissance qu’ils avoient du corps humain, ne sçauroit entrer en comparaison avec la nostre” (Discours touchant la méthode de la certitude; GP 7 174–175). The laboratory copies nature, fire operates naturally and artificially as an instrument of analysis: “pleraque regni Mineralis corpora vera esse Laboratorii Chymici Naturalis producta per ignem actualem vel nunc subterraneum, vel olim terrae crustam involventem, alia vitrificantem, alia exhabilia expellentem. Unde maris, arenae, rupium, lapidum, terrarum, et deprehensarum in his qualitatum multarum rationes reddere docuimus” (‘most bodies of the mineral reign are in fact Natural Chemical Laboratories produced by actual fire, or by presently underground fire, or by fire which once wrapped the Earth’s crust – some vitrifying, others expelling exhalations. From this we learn the properties of the sea, sand, rocks, stones, soils, as well as how to account for many of those discovered in them’; Antibarbarus Physicus; GP 7 341). Chemists make use of ‘empirical tools’ (Organorum Empiricorum): weighing machine, thermometer, hygrometer, pneumatic pump, sensation (principally taste), microscope, mirror; they employ different effects: agitation, movement, heat, etc., and some use chemical substances as vitriol (De modo perveniendi ad veram Corporum Analysin; GP 7 267). 11. On the philosophical and scientific issues at stake in this thesis, see Fichant (2003: 1–28). 12. “Il existe une très grande différence entre le mixte et le vivant du corps humain, c’est-à-dire la constitution matérielle apte à la mixtion et la disposition formelle de cette mixtion à produire les actes et les effets propres à la vie” (Véritable distinction §11; Stahl 1707a; BL 2 267). 13. In their time, Pagel, Fleming, and Plochmann have denounced the mechanicist misunderstanding of Harvey's thesis. They reminded the Aristotelician and vitalistic hypothesis on which Harvey’s discovery was based (Pagel 1951; Fleming 1955: 319–327; Plochmann 1963: 192–210). However, as early as in the 17th century, Harvey’s discovery was read in a mechanicist way and was thus used to criticize both Aristotelism and vitalism (see Burchell 1981: 260–277). My interpretation of Stahl, however, differs from Pagel’s (1929: 44). 14. Descartes, La description du corps humain (AT 11 226–227). See his Letter to Mersenne, February 20th 1639; AT 2 524. See also Gilson (1920–1921, 1921a, 1921b); Dreyfus-Le Foyer (1937: 237–286); Rodis Lewis (1990); Bitbol-Hesperiès (1990); Duchesneau (1998).



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15. Despite this hypothesis, Stahl aknowledges the real operation of breathing as warming – and not cooling – the blood. See Carvallo (2006: 57). 16. “L’analogie entre la flamme et l’animal n’empêche pas la comparaison de la flamme avec un tourbillon de poussières agité par l’air, puisque la nature corporelle tout entière est constituée par de tels tourbillons fluides” (CAR 109; cf. De unione animae et corporis, against Perrault’s opinion; A VI 3 479–480). 17. Although Fermat did not actually give a name to his principle, he gave it a formulation as early as 1657 and then again in 1662 in his letters to Marin Cureau, from the Parliamentary: “If we consider that the thing is already made and that Nature always acts through the shortest and the easiest channels (…), this sum total [of the resistances to the environnement] must be, in order to comply with our principle, the least of all the possibilities encountered” (my translation, S.C.) (‘Si nous supposons que la chose est déjà faite, et que la nature agit toujours par les voies les plus courtes et les plus aisées, (…) cette somme [des résistances des milieux] pour satisfaire au principe doit être la moindre de toutes celles qui se peuvent rencontrer…’; Fermat (1904 II: 357). 18. According to Leibniz, the comparison between natural and artificial facts reveals the link between the sciences and technology, between theory and praxis, and leads to the growth of knowledge: “Si Galilaeus non fuisset locutus cum Hydragogis artificibus, et ab illis didicisset, aquam ultra triginta pedes in antlia aspirante attolli multum non posse, arcanum de pondere aëris et machina vacui sensibilis, et indicio tempestatum adhuc nesciremus. Harvaeus autem in suspicionem circulatori motus in sanguine deprehensi venit, cum Chirurgorum venam secantium ligaturas considerasset” (‘If Galileo had not talked with water conduit builders and had learned from them that water in an aspirant pump cannot rise above 30 feet, up to this day we would not know the secret of the air’s weight, the void-producing machine, and the barometer. Harvey had the idea of blood circulation by considering the ligatures used by surgeons for fending a vein’; De republica literaria; A VI 4 433; GP 7 69). 19. Leibniz defends the same point of view in a letter to Hoffmann, “[Like you] I am of the opinion that all corporeal phenomena take place mechanically, although we cannot always explain the particular mechanisms; in fact, even the general principles of mechanisms derive from higher sources” (Leibniz to Friedrich Hoffmann, September 27th 1699; D 2 1 260). 20. Leibniz explains fermentation in the same way from 1671 to 1709: “La force des fermentations, du froid et du chaud, de la poudre à canon etc. se peut expliquer par quelque chose d’analogique à celle des arquebuses à vent ou du ressort” (Leibniz to des Billettes, December 4th/14th 1696; G 7 453). 21. The same argument appears in the Monadology §§63–68 (GP 6 617–619). 22. “Les corps mixtes résistent à l’agrégation et à l’unité; au contraire, les vivants n’existent que sous la forme d’agrégats” (De mixti et vivi corporis vera diversitate §6; Stahl 1707a; BL 2 262). 23. “Au sujet de la doctrine des mélanges, notre célèbre auteur attribue la source du mal à la spéculation aristotélicienne, en particulier à sa théorie mathématique sur la divisibilité des corps à l’infini. A en bien juger, telle est, selon lui, la première erreur, le πρωτον πσευδοσ. Je m’étonne qu’un tel savant ait pu en venir à de telles pensées. L’ordre mathématique ne diffère du physique, que par l’abstraction qu’opère l’esprit à partir des choses concrètes. Le travail d’abstraction intellectuelle ne consiste pas à ajouter quelque chose de faux mais à retirer quelque chose de vrai, parce que nous n’avons ni la capacité de considérer tout à la fois, ni même intérêt à cette considération globale. Il est nécessaire que toute partie de l’étendue soit étendue; ce fait est

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surtout manifeste dans le cas de la ligne droite, où la partie est semblable au tout; donc une partie possède à son tour des parties. On voit suffisamment que l’auteur de cette doctrine ne fut pas Aristote. En outre, cette division a lieu non seulement en Géométrie, mais aussi en Physique; et le corps n’est pas seulement divisible à l’infini, mais divisé en acte. Par conséquent, il n’y a nulle partie de la matière, dans laquelle on ne pourrait noter à nouveau de nombreuses variétés, si la subtilité de nos sens équivalait à celle des choses” (CAR 119). See also Beeley (1996) on the history and meanings of infinitum from Aristotle to Leibniz, and Fichant (2003). 24. “Après avoir vu clairement que tous ces mouvements pouvaient procéder du seul principe corporel et mécanique, j’ai tenu pour certain et pour démontré que nous ne pourrions prouver en aucune manière qu’il y a une âme pensante chez les bêtes” (Descartes, AT V 276). 25. Leibniz analyzes this concept of form in his controversy with Stahl (CAR 85), where he refers to Cudworth (1678). As regards the importance of the neoplatonic critics of the mechanical reduction, see Roger (1963: 419–431) and Duchesneau (1998: 171–182). 26. “Leibniz is the first to use the term ‘organism’ (organismus) to designate, in contrast with man-made machines, God-devised mechanisms, namely such organic bodies as prove to be analyzable into integrative agencies unfolding to infinity. Thus, an organism always implies a complex body consisting in integrative structures and functional dispositions” (Duchesneau 1999: 206). 27. In Latin, Leibniz uses the term ‘modullum’, for example in Quid sit idea? (GP 7 263–264). Christiane Frémont (Leibniz 2001: 115) translates this term as ‘module’ in architectural, mechanical and mathematical senses, but the French term ‘modelle’ correctly renders the meaning “paradigm” presumably intended by Leibniz: “On pourroit faire en caracteres qui ne seront que des lettres de l’alphabet, la description d’une machine quelque composée qu’elles pourroit estre, ce qui donnerait moyen à l’esprit de la connoistre distinctement et facilement avec toutes les pieces et meme avec leur usage et mouvement sans se servir de figures ni de modelles et sans gener l’imagination, et on ne laisseroit pas d’en avoir la figure présente dans l’esprit autant que l’on se voudroit faire l’interprétation des caractères. On pourroit faire aussi par ce moyen des descriptions exactes des choses naturelles, comme par exemple des plantes et de la structure des animaux” (Leibniz to Huygens, September 18th 1679; A III 2 852; quoted in Dascal 1978: 215–216). 28. Plastic comes from πλαστειν, to form. 29. Leibniz participated actively in this debate, e.g. with his De ipsa natura (1698), where he refers to Descartes, Boyle, Sturm, and Schelhammer. See Palaia (1990) and Dascal and Firt (2010). 30. “The spirit of Nature therefore, according to that notion I have of it, is a substance incorporeal, but without sense and Animadversion, pervading the whole Matter of the Universe, and exercising a Plastical Power therein according to the sundry predispositions and occasions in the parts of the Matter it works upon, raising such phenomena in the world, by directing the parts of the Matter and their motion, as cannot be resolved into mere Mechanical Power” (More 1652: III, 12, §1, 254). 31. “[W]herefore, since neither all things are produced Fortuitously, or by the unguided Mechanism of Matter nor God himself may reasonnably be thought to do all things immediately and Miraculously; it may well be concluded, that there is a Plastick Nature under him, which as an Inferior and Subordinate Instrument doth Drudgingly Execute that Part of his Providence, which consists in the regular and orderly Motion of Matter; yet so as that there is also besides



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this, a Higher Providence to be acknowledged which presiding over it doth often supply the Defects of it, and sometimes overrule it; for as much as this Plastick Nature cannot act Electively nor with Discretion” (Cudworth Digression sur les natures plastiques; Cudworth 1837a: III §5, 1 213). About the theoretical context, cf. Kroll et al. (1992). Concerning the medical issues, cf. Duchesneau (1998: 315–355). 32. Stahl denies “que la flamme ne subsiste, se nourrisse, se propage et se conserve par soi, sous prétexte qu’elle a besoin d’un apport en air; de même on peut nier que l’animal n’accomplisse par soi les mêmes actes, sous prétexte que sans l’apport perpétuel et la pénétration intime des éléments environnants, non seulement la respiration n’aurait pas lieu, mais la chaleur et la fluidité des humeurs cesseraient encore […] sans même parler du mouvement tonique qu’on constate naître du mouvement des éléments environnants” (CAR 109). His argument refers to his chemical doctrine: the phlogisticon denotes a permanent entity; it burns and comes out from material combustible and dissipates into the air. See Stahl (1746: 1, 94–119). 33. Clericuzio (2000: 148) stresses that “Boyle’s actual chemical work shows that chemistry kept an independent status from physics”. 34. “Il n’y a aucune masse si grossière ou si petite soit-elle qui ne contienne en soi un corps organique” (CAR 103 §5). 35. “Les transformations qui se passent dans les humeurs animales ne ressortissent pas moins à la chimie que celle des liqueurs végétales. Par conséquent, tous les corps relèvent de la chimie, lorsqu’on les traite non pas en tant que structure mais en tant que masse” (CAR 91). 36. The Aristotelian chemical doctrine can be found in De generatione et corruptione I, 10, 328a10: “Le mélange (mixis) est donc l’union, avec altération des corps mélangés”. On the alchemical references to Aristotle, cf. Viano (1996); Obrist (1996). 37. “§4. Bien que la géométrie et le mécanisme puissent aisément nous convaincre qu’une simple apposition ou jonction très étroite et très intime, une juxtaposition, une union ou une adhésion de molécules organiques puissent former et constituer de telles combinaisons (que l’on nomme tantôt mixtions, tantôt compositions) […] il faut cependant reconnaître que la chimie expérimentale seule pourra contrôler d’une manière péremptoire toute la vérité du fait, en démontrant que les choses ne se passent pas habituellement d’une autre manière et même qu’elles ne peuvent probablement pas s’accomplir d’après un mode différent” (Véritable distinction; Stahl 1707a; BL 2 257). 38. “Cumque nihil a nobis accurate percipiatur, quam magnitudo, figura, motus et ipsa perceptio, hinc sequitur, omnia per haec quatuor debere explicari. Et quoniam de iis rebus loquimur, quae videntur sine perceptione fieri, ut reactiones liquorum, praecipitationes salium etc. ideo reliquum est, ut explicentur per magnitudinem, figuram et motum, id est per Machinam” (‘Since we may perceive nothing accurately except magnitude, figure, motion, and perception itself, it follows that everything is to be explained through these four. But because we are now speaking of those things which seem to take place without perception, such as the reactions of liquids, the precipitations of salts, etc., we have no means of explaining them except through magnitude, figure, and motion, that is, through mechanism’; De modo perveniendi ad veram Corporum Analysin; A 4, 1971; L 173). The Leibnizian interpretation of mixture corresponds to his theory of perception (cf. CAR 107), which he studied in the New Essays, a few years before. 39. According to Clericuzio (2000: 106), “Leibniz fostered this image of Boyle as a strict mechanical philosopher, and drew a sharp contrast between the latter’s and Newton’s (and the Newtonians’) theory of matter [but] Boyle did not consider chemistry as a branch of physics,

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since he did not reduce all chemical phenomena to the geometrico-mechanical affections of the particles of inert matter”. Indeed, in the third paragraph of De ipsa natura, Leibniz writes: “R. Boyle, homme remarquable, écrivit un livre sur la nature-même; son propos consiste, dans mon souvenir, à identifier la nature au mécanisme des corps. Cette identité peut être prouvée jusque dans le détail. Mais il eût fallu en distinguer les sources et les principes”. 40. De modo perveniendi ad veram Corporum Analysin; A VI 4 1972. Elsewhere, Leibniz estimates that the knowledge of elements enables to predict the effects of the whole: “Credibile est si natura corporum ejusmodi similarium nobis innotesceret non difficulter nos rationem reddituros omnium quae in ipsis apparent, imo praedicere posse omnes eorum sive cum aliis mixtorum effectus. Quemadmodum facile nobis est praedicere effectus machinae cujus structuram intelligimus” Methodus physica. Characteristica. Emendanda. Societas sive ordo. Mai (1676; A VI 3 456). 41. Stahl denies this reversible way; cf. Metzger (1974: 174–178). 42. Clericuzio (2000: 90–102, 116–135). 43. “Tria axiomata primaria: Mathematicae, totum esse aequale omnibus partibus. Physicae, effectum integrum aequipollere suae causae. Scientiae civilis, Mundum esse optimam Rempublicam, sive omnia in mundo fieri optimo modo” (‘Three primary axioms: of Mathematics – the whole is equal to all the parts; of Physics – the complete effect is equipollent to its causes; of Civil Science – the world is the best republic, i.e., everything in the world is done in the best way’; Tria axiomata primaria; 1674–1676). 44. Descartes annouced his project (in the French translation of the Abbé Picot) as follows: “On peut aussi connaître de ceci quelle est la vraie nature de l’air, de l’eau, des minéraux et de tous les autres corps qui sont sur la Terre, ainsi que je tâcherai maintenant de l’expliquer” (Principes de la philosophie IV §45; for the Latin text: AT, 8–1 231). In §63 he speaks about “Des principes de la chimie, et de quelle façon les métaux viennent dans les mines”. Here is his conclusion: “J’ai donc ici expliqué trois sortes de corps qui me semblent avoir beaucoup de rapport avec ceux que les chimistes ont coutume de prendre pour leurs trois principes et qu’ils nomment le sel, le soufre et le mercure. Car on peut prendre ces sucs corrosifs pour leur sel, ces petites branches qui composent une matière huileuse pour leur soufre, et le vif argent pour leur mercure”. Descartes criticized the Atomists as well as the Aristotelians (Principes de la philosophie IV §202; AT 8–1, 241). See also Descartes’s letter to Mersenne, July 30th 1640; AT 3 130). On Boyle’s position, see Clericuzio (2000: 3–7, 107); see also Maillard (1998). 45. Regarding the animal spirits, see CAR 101; Véritable distinction §84; BL 2 325. 46. Leibniz (1678–1679), Praefatio ad libellum elementorum physicae; A VI 4 1992–2010. 47. “Les corps mixtes sont ceux qui se forment par la combinaison des plus simples éléments physiquement indivisibles. Les corps composés, au contraire, sont constitués par l’union intime des mixtes, ou du moins par la réunion d’un nombre indéterminé de corpuscules simples et homogènes qui finissent par constituer un tout physique de cette espèce, c’est-à-dire un individu” (De mixti et vivi corporis vera diversitate §4; Stahl 1707a; BL 2, 258). 48. CAR 101, 143. For Stahl thesis dealing with life specifity, cf. De mixti et vivi corporis vera diversitate §137 (BL 2 371). 49. “And thus we have the first General Conception of the Plastick Nature, That is Art itself, acting immediately on the Matter, as an Inward Principle” (Cudworth 1678: 155).



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50. “[The Wisdom of God can] display itself abroad, and print its Stamps and Signatures every where throughout the World” (Cudworth 1678: I 3 xxxvii, §5; 1837: 213). Cf. Hutton (1997); Petit (1997). 51. Sturm wrote several treatises on this issue: Idolum naturae (1692) and De natura sibi incassum vindicata (1698). He also corresponded with Leibniz (see GP 4 504–516). Schelhammer (1697) had reacted to Sturm’s position with his Natura sibi et medicis vindicata sive De natura liber bipartitus. 52. “Cum dicimus naturam nihil agere frustra, naturam a vacuo abhorrere, naturam non aberrare, naturam ad perfectionem tendere, aliaque id genus, profecto non est intelligenda natura particularis cujusdam corporis, sed universalis illa summaque causa quae semper finem et sequitur et obtinet, quae in avibus nidificat, in fornicis hyemi providet, in omnibus rationis vestigia exhibet” (‘When we say that nature does nothing in vain, that nature abhors the void, that nature does not produces aberrations, that nature strives to perfectio, and similar things, one should not understand the particular nature of a certain body, but the universal supreme cause that always pursues an aim and reaches it – the kind of goal that in birds yields nests, in furnaces, that provides for the winter, in everthing shows the traces of reason’; Societas Theophilorum; Leibniz 1678; A IV 3 851). Then Leibniz quotes Plato’s Phedo. 53. “Deus non est quiddam Metaphysicum, imaginarium, incapax cogitationis, voluntatis, actionis qualem nonulli faciunt, ut idem futurum sit ac si diceres Deum esse naturam, fatum fortunam, necessitatem, Mundum, sed Deus est Substantia quaedam, Persona, Mens” (‘God isn’t a metaphysical entity, nor an imaginary thing, incapable of thought, of will, of actions such as certain ones suppose – so that it would be the same as if you said that God is nature, destiny, luck, necessity, the world; but God is a certain Substance, a Person, a Mind’; De arcanis sublimium; Leibniz 1676; A VI 3 474). 54. “For Boyle, it was inappropriate both theologically and scientifically to speak of Nature doing anything at all. Instead, he argued for the superior intelligibility of the mechanistic view of the world that he had championed in his profuse earlier writings, a world made up of matter acting according to properties and powers given by God. Moreover, he claimed that such a view was closely tied to a proper conception of God’s absolute power over the world, from which he saw the ‘vulgar’ view as detracting” (Hunter and Davis 1996: x). 55. “Nature is a source or cause of being moved and of being at rest in that to which it belongs primarily, in virtue of itself and not in virtue of a concomitant attribute”; Aristotle, Physica II, 192b20; translation by R. P. Hardie and R. K. Gaye). 56. The two relevant treatises are: The Origin of Forms and Qualities (1666; RBb 5) and Some Considerations Touching the Usefulsness of Experimental Natural Philosophy (1663; RBb 3 189– 480). Cf. Osler (1992). 57. Leibniz sums up his opinions on Cudworth’s system in 1705 (Considérations sur les Principes de vie et sur les Natures plastiques; Leibniz 1705; GP 6 539–555): “J’admets effectivement les principes de vie répandus dans toute la nature, et immortels … je n’ai point besoin de recourir avec M. Cudworth à certaines natures plastiques immatérielles … J’en puis dire Non mi besogna, e non mi basta, par cette raison même de la preformation et d’un organisme à l’infini, qui me fournit des natures plastiques materielles propres à ce qu’on demande; au lieu que les principes plastiques immateriels sont aussi peu necessaires qu’ils sont peu capables d’y satisfaire” (GP 6 544).

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58. T. Blondin clarifies this point more precisely: “mais il ne faut pas croire, avec les iatromécaniciens, que le mouvement circulaire s’accomplisse entièrement par l’impulsion mécanique du cœur et des gros vaisseaux, distendus ou même stimulés par le sang; la force tonique intervient, et l’âme exerce son influence en vertu de sa sensibilité et de sa volonté vitales; c’est ainsi que le sang est répandu dans tous les tissus en proportion variable, selon les besoins de l’organisme” (BL, Preface, p. 6). 59. At the same time, Leibniz uses the same comparison: “Machinam corporis humani esse, ut ita dicam Pyrobolico-Hydraulico-Mechanicam dici potest. Spiritus enim impetum facientes explosiones agere credibile est. Febrium caussam immediatam magis in spiritibus quam humoribus sitam esse puto. Vellem corpus humanum describi principio sumto a caussa finali seu officio, et dicere soleo esse machinam conservandae contemplationis gratia inventam” (‘The human body’s machine, so to speak, can be said to be pyrobolic-hydraulic-mechanic. Indeed it is plausible that the impulse of spirits provokes explosions. I think that the immediate cause of fever is located more in the spirits than in the humors. I would like the human body’s description to be based on the assumption of a final cause or function, and I usually say that the machine is invented for the conservation of contemplation’; Leibniz to Mich. Gottlieb Hanschium, December 15th 1707; D 5 163). 60. On the heuristic function of the hypothesis, see Leibniz to Conring, January 3rd/13th 1678 (A II 1 385–389, 397–402; cf. NE 4.12.10; A VI 6 453). 61. “Ce système paraît allier Platon avec Démocrite, Aristote avec Descartes, les Scolastiques avec les modernes, la théologie et la morale avec la raison. Il semble qu’il prend le meilleur de tous côtés, et que puis après il va plus loin qu’on n’est allé encore” (NE 1.1; A VI 6 71).

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Frémont, C. 2003. Singularités. Individus et relations dans le système de Leibniz. Paris:Vrin. Gabbey, A. 1990. “More and Mechanism”. In S. Hutton (ed), Henry More (1614–1687): Tercentenary Studies. Dordrecht: Kluwer Academic Publishers. Gilson, E. 1920–1921. “Descartes et Harvey”. Revue philosophique de la France et de l’étranger 90: 4324–4358. Gilson, E. 1921a. “Descartes, Harvey et la scolastique”. In E. Gilson (ed), Etudes sur le rôle de pensée médiévale dans la formation du système cartésien. 5e ed. 1984. Paris: Vrin, 51–101. Gilson, E. 1921b. “Météores cartésiens et météores scolastiques”. In E. Gilson (ed), Etudes sur le rôle de pensée médiévale dans la formation du système cartésien. 5e ed. 1984. Paris: Vrin, 102–140. Gregory, A. 2001. “Harvey, Aristotle and the Weather Cycling”. Studies in History and Philosophy of Science, Part C, 32(1): 153–168. Hall, A. 1990. Henry More and the Scientific Revolution. Cambridge: Cambridge University Press. Harvey, W. 1990. Traité anatomique sur les mouvements du cœur et du sang chez les animaux. Translated by Ch. Richet. Paris: Christian Bourgeois. Hartmann F. and Hense, W. 1988. “Die Veränderungen in Leibniz’ Plänen für eine Verbesserung medizinischer Forschung und ärtzlicher Praxis in seinen Entwürfen für Sozietäten und Akademien zwischen 1668 und 1706”. In: Leibniz. Tradition und Aktualität. V. Internationaler Leibniz-Kongreß, Vorträge, 1. Teil, Hanover, Gottfried-Wilhelm-Leibniz-Gesell­ schaft, 344–346. Hoffman, F. 1700. Observationes barometrico-meteorologicae and epidemicae Hallensis anni 1700, praemissae sub curiosae physicae medidationes circa ventorum causas... In Opera omnia physico-medica. Genève: Fratres de Tournes, 1748, vol. 5, 15–46. Hutton, S. 1997. “Cudworth, Boethius and the scale of Nature”. In G. A. J. Rogers et al. (eds), 93–100. Kroll, R., Ashcraft, R., Zagorin, P. et al. (eds). 1992. Philosophy, Science and Religion in England, 1640–1700. Cambridge: Cambridge University Press. Leibniz, G. W. 1674–1676. Tria axiomata primaria. A VI 3 427. Leibniz, G. W. 1676. Methodus physica. Characteristica. Emendanda. Societas sive ordo. A VI 3 456. Leibniz, G. W. 1676. De arcanis sublimium vel de summa rerum. A VI 3 474. Leibniz, G. W. 1677. De modo perveniendi ad veram Corporum Analysin et rerum naturalium causas. GP 7 265–269; A VI 4 1971–1975. Leibniz, G. W. 1678. Societas Theophilorum ad Celebrandas Laudes Dei. A IV 3, 849–852. Leibniz, G. W. 1687. Antibarbarus Physicus pro Philosophia Reali contra Renovationes Qualitatum Scholasticarum et Intelligentiarum Chimaericarum. GP 7 337–344. Leibniz, G. W. 1688–1690. Discours touchant la méthode de la certitude et l’art d’inventer pour finir les disputes et pour faire en peu de temps des grands progress. GP 7 174–183; A VI 4 952–962. Leibniz, G. W. 1698. De ipsa natura sive de vi insita actionibusque Creaturarum, pro Dynamicis suis confirmandis illustrandisque. GP 4 504–516. Leibniz, G. W. 1703–1705. Nouveaux essais sur l’entendement humain. A VI 6; GP 5. [= NE] Leibniz, G.W. 1705. Considérations sur les Principes de vie et sur les Natures plastiques par l’Auteur du Systeme de l’Harmonie préétablie; GP 6 539–555. Leibniz, G. W. 2001. Discours de Métaphysique et autres textes. C. Frémont (ed). Paris: GarnierFlammarion.



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Lenoble, R. 1953. “L’évolution de l’idée de nature du XVIe au XVIIIe siècle”. Revue de métaphysique et de morale 58: 108–129. Loemker, L. E. 1955. “Boyle and Leibniz”. Journal of the History of Ideas 16: 22–43. Maillard, J. F. 1998. “Descartes et l’alchimie”. In Aspects de la tradition alchimique au XVIIe siècle. Paris-Milan: F. Greiner, 95–109. Mahrenholtz, M. 1990. “Leibniz’ Literatur quellen zu einigen frühen Texten medizinalischen Inhalts”. In I. Marchlewitz and A. Heinekamp (eds), Leibniz’ Zetigenossen (= Studia Leibnitiana Supplementa 27), 350–357. MacDonald Ross, G. 1973. “Rosicrucianism and the English connection”. In K. Müller, H. Schepers, and W. Totok (eds), Studia Leibnitiana 5. Wiesbaden: Franz Steiner, 239–245. MacDonald Ross, G. 1974. “Leibniz and the Nuremberg alchemical society”. In G. Fricke, H. G. Gopfert, and H. Stubenrauch (eds), Studia Leibnitiana Supplementa 6. Wiesbaden: Franz Steiner, 222–248. MacDonald Ross, G. 1978. “Leibniz and alchemy”. In Magia naturalis und die Entstehung der modernen Naturwissen-schaften, Studia Leibnitiana Sonderheft 7. Wiesbaden: Franz Steiner, 166–177. Metzger, H. 1923. Les doctrines chimiques en France du début du XVIIe à la fin du XVIIIe siècles. Paris: PUF. Metzger, H. 1974. Newton, Stahl, Boerhaave et la doctrine chimique. Paris: Blanchard. More, H. 1987 [1652]. The Immortality of the Soul. Dordrecht: Kluwer Academic Press. Obrist, B. 1996. “Art et nature dans l’alchimie médiévale”. Revue d’histoire des sciences 49(2–3): 215–286. Obst, G. 1992. “Leibniz’ Vorstellungen über den Zusammenhang von Meteorologie und Anthropologie: ‘physica specialis cum medicina provisionalis’”. Studia Leibnitiana 24(1): 7–24. Orio de Miguel, B. 1990. “Leibniz und die physischen Monaden von Fr. M. van Helmont”. In I. Marchlewitz and A. Heinekamp (eds), Leibniz’ Zeigenossen (= Studia Leibnitiana Supplementa 27). Wiesbaden: Franz Steiner, 147–156. Osler, M. J. 1992. “The intellectual sources of Robert Boyle’s philosophy of Nature: Gassendi’s voluntarism and Boyle’s physico-theological project”. In R. Kroll et al. (eds), 178–198. Palaia, R. 1990. “Naturbegriff und Kraftbegriff im Briefwechsel zwischen Leibniz und Sturm”. In I. Marchlewitz and A. Heinekamp (eds), Leibniz’ Zeigenossen (= Studia Leibnitiana Supplementa 27). Wiesbaden: Franz Steiner, 157–172. Pagel, W. 1929. “Helmont-Leibniz-Stahl”. Sudhoffs Archiv für Geschichte der Medizin 24: 19–59. Pagel, W. 1951. “Harvey and the Purpose of Circulation”. Isis 42(1): 22–38. Perrault, Claude & Pierre. 1721. “De la Circulation de la Sève des Plantes”. Oeuvres diverses de Physique et de Méchanique. Leiden: Pierre Vander, vol. 1, 71–149. Peters, H. 1916. “Leibniz als Chemiker”. Archiv für Geschichte der Naturwissenschaften und der Technik 7: 85–108. Petit, A. 1997. “Ralph Cudworth: Un platonisme paradoxal. La Nature dans la Digression Concerning the Plastick Life of Nature”. In G. A. J. Rogers et al. (eds), 101–110. Plochmann, G. K. 1963. “William Harvey and his methods”. Studies in the Renaissance 10: 192–210. Rather L. J. and Frerichs, J. B. 1968. “The Leibniz-Stahl controversy I: Leibniz’ opening objections to the Theoria Medica Vera”. Clio Medica 3: 21–40. Rather L. J. and Frerichs, J. B. 1970. “The Leibniz-Stahl controversy II: Stahl’s survey of the principal points of doubt”. Clio Medica 5: 53–67.

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Robinet, A. 1997. “Les différentes lectures du System de Cudworth par G. W. Leibniz”. In G. A. J. Rogers et al. (eds), 187–196. Rodis Lewis, G. 1990. “Limites du modèle mécanique dans la disposition de l’organisme”. In G. Rodis Lewis (ed), L’anthropologie cartésienne. Paris: Presses Universitaires de France, 149–168. Roger J. 1963. Les sciences de la vie au XVIIIe siècle. Paris: Armand Colin. Rogers, G. A. J., Vienne, J. M., and Zarka, Y. C. (eds). 1997. The Cambridge Platonists in Philosophical Context: Politics, Metaphysics and Religion. Dordrecht: Kluwer Academic Publishers. Schneider, M. 1993. Das mechanistiche Denken in der Kontroverse. Descartes’ Beitrag zum GeistMaschine-Problem (= Studia Leibnitiana Supplementa 29). Wiesbaden: Franz Steiner. Scheel, G. 1990. “Leibniz auf den Spuren von Alchemisten in Berlin zur Zeit König Friedrichs I”. In Leibniz in Berlin (= Studia Leibnitiana Sonderheft 16). Wiesbaden: Franz Steiner, 253–270. Scheel, G. 1980. “Leibniz, die Alchemie und der Absolute Staat”. In A. Heinekamp (ed), Theoria cum Praxi (= Studia Leibnitiana Supplementa 19(1)). Wiesbaden: Franz Steiner, 267–282. Stahl, G. E. 1692. De motu tonico vitali. BL 6 475–548. Stahl, G. E. 1701. De vita. Halle. BL 6 453–474. Stahl, G. E. 1706a. Paroenesis ad aliena a medica doctrina arcendum, Halle. TM 43–64; BL 2 133–174. Stahl, G. E. 1706b. Disquisitio de mechanismi et organismi diversitate. Halle. TM 1–42; BL 177– 252. Stahl, G. E. 1707a. De mixti et vivi corporis vera diversitate. Halle. TM 65–132 [French translation, Véritable distinction à établir entre le mixte et le vivant du corps humain; in BL 2 253–388]. Stahl, G. E. 1707b. Defensio et vindicatio G. E. Stalii. Halle. TM 133–190; BL 389–504. Stahl, G. E. 1707c. De medicina sine medico. Halle. Stahl, G. E. 1737 (1707–1708). Theoria medica vera, physiologiam et pathologiam tanquam doctrinae medicae partes vere contemplativas e naturae et artis veris fundamentis intaminata ratione et inconcussa experientia sistens. Halle: Impensis Orphanotrophei. [= TM] Stahl, G. E. 1746. Fundamenta Chymiae Dogmaticae et experimentalis. Norimbergae: Impensis B.G.M. Endteri. Stahl, G. E. 1720. Negotium otiosum, seu skiamachia adversus positiones aliquas fundamentales theoriae verae medicae a viro celeberrimo intentata, enervata. Halle. Stahl, G. E. 1860–1864. La vraie théorie médicale, 6 Vols. Translated and edited by T. Blondin. Paris: J. P. Baillière. [= BL] Stahl G. E. and Leibniz, G. W. 2004. Controverse sur la Vie, l’Organisme et le Mixte. S. Carvallo (ed). Paris: Vrin. [= CAR] Viano, C. 1996. “Aristote et l’alchimie grecque: La transmutation et le modèle aristotélicien entre théorie et pratique”. Revue d’histoire des sciences 49(2–3): 189–213. Webster, C. 1982. From Paracelsian to Newton: Magic and the Making of the New Science. Cambridge: Cambridge University Press. Wilson, C. 1987. “De ipsa natura: Sources of Leibniz’s doctrines of force, activity and natural law”. (= Studia Leibnitiana Supplementa 19(2)). Wiesbaden: Franz Steiner, 148–172.

chapter 6

Leibniz’s conciliatory approaches in scientific controversies Marcelo Dascal and Erez Firt

1.

Introduction

Scientific controversies are part and parcel of science and are an important factor in the development of science. While in past decades historians have paid an increasing attention to the practical side of science, the practical aspects of controversies received less attention. However, recently there has been a growing interest in the contribution of controversies to the development of ideas, and G. W. Leibniz’s intensive participation in the scientific, philosophical, theological, juridical, and other controversies of his time has been the focus of much recent research. This paper aims to highlight and discuss one approach through which this eager participant in scientific controversies attempts to resolve them. This approach consists in trying to dispel the impression that the positions of the contenders are contradictory, and therefore irreconcilable, by constructing an alternative that actually conciliates the alleged contradictory views. We will focus on two cases of scientific controversy in which Leibniz employs the conciliatory approach. These case studies illustrate how conciliation can be achieved in different ways and at different levels. Leibniz’s attitude towards controversies was not alien to the use of conciliatory methods. For example, it is well known that one of his most important endeavors was the irenic project of reunion of Christianity; his method in this project consisted basically in a careful examination of each of the alleged contentions of the contenders with a view to showing that their alleged incompatibility was illusory. It could be overcome, he believed, if only the adversaries would moderate their perceptions of the differences between them. In this way, rather than exaggerating them into insurmountable contradictions, they would be reduced to plausible negotiable propositions. Some of them would be set aside as of lesser

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significance and thus of lesser weight in the controversy, and the remaining ones would be ‘softened’ so as to permit their eventual conciliation in a doctrine acceptable to both sides.1 While this method of reconciliation did not bring about the results Leibniz hoped for, it seems at least applicable in controversies such as those of church politics and theology – the former dependent on human decisions and desires, the latter on a large body of shared doctrinal infrastructure. But would it be applicable in scientific controversies, where each side believes its position to be supported by the facts, by mathematics, and by logic? What is of special interest in the cases we analyze in this article is precisely the fact that Leibniz applies the method of conciliation even to the supposedly unquestionably objective scientific oppositions underlying the controversies we will address in what follows. The two cases here analyzed unfold against the background of Leibniz’s attempts to overcome the alleged irreconcilability between the uses of both purely mechanistic and final cause explanations in physics. Unlike his contemporaries, who tended to espouse one position and entirely rejected the other, Leibniz believed that each of them makes useful contributions to the understanding of physical phenomena. Consequently, he undertakes to show how these contributions can be combined. “The best would be to combine the two points of view” (DM §22; A VI 4 1564; L 317), he says, in such a way that their respective benefits can be taken advantage of. While one of the debates we analyze belongs to a specific physical domain, namely, optics, the other is rather meta-theoretical and metaphysical, addressing the notion of nature itself, which depends on whether one, the other, or both focuses of physical explanations is possible or needed. In his 1682 paper Unicum Opticae, Catoptricae, et Dioptricae Principium (‘A principle shared by Optics, Catoptrics and Dioptrics’), Leibniz shows how the law of refraction (Snell’s law, see note 7) can be demonstrated through the use of either final causes or of efficient causes. In his 1698 paper De ipsa natura (‘On nature itself’), Leibniz tackles the ongoing debate provoked by Boyle’s claim that nature should be understood in purely mechanistic terms. In the former paper, he preserves the integrity of each of the two derivations of the law of refraction, recommending that each be used when it is most suitable. In the latter, he undertakes to create a middle way synthesis of the opposites: As we will see, on the one hand, he rejects the view that the non-mechanical governs the mechanisms of bodies; on the other, he rejects a purely mechanistic world view. Instead, he argues for a higher metaphysical source, inherent to “nature”, which accounts for the mechanisms of bodies – “an active created force inherent in things”. After analyzing the kind of conciliation Leibniz seeks in each of these cases, we conclude by discussing the possible reasons for the different conciliation proposed in each of them. Our suggestion is that underlying the differences observed



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one can detect a deeper metaphysical connection between the two strategies of conciliation Leibniz employs, the one focusing on the mere coexistence of the opposites, the other creating the conditions for their union and actual interaction.

2.

The disjunctive option: “Both explanations are good”

2.1

Leibniz on reconciliation

In this section we wish to demonstrate how Leibniz’s way of reconciling opposites of different philosophical traditions, or contradictory concepts, is present in his views on scientific explanations in physics. To be more precise, we wish to present the way he reconciles two forms of explanation, i.e., mechanical explanation, which is based on efficient causes, and teleological explanation, which is based on final causes. Obviously, the previous paragraph needs elaboration before we carry on to our main objective: what exactly is meant by 'reconciling', and what brought about this reconciling of efficient and final causes? The answers to these questions require, without a doubt, a much broader discussion than we can provide here. Nevertheless, we are about to provide some clues that might be useful. The term ‘reconciliation’ appears in the title of paragraph 22 of the Discourse on Metaphysics.2 In paragraph 21 Leibniz says: I find even that several effects of nature can be doubly demonstrated; once, by the consideration of their efficient cause, and again, independently, by the consideration of the final cause. (DM §21; A VI 4 1563; L 317; our italics)

This specific remark refers to the formation of an animal's tissue and the interrelation of its parts: there are those who try to explain it by mechanical means and those who refer to final causes. According to Leibniz, “Both methods are good, both can be useful … for making useful discoveries in physics and in medicine” (DM §22; A VI 4 1564; L 317). Instead of taking “diverse routes”, that is, opting for either one opinion or its allegedly opposite one, Leibniz suggests some sort of unification. By proposing this, he actually positions himself against the prevailing controversial atmosphere, where one side ridicules the other for its simplistic ideas, and the other side regards the former as superstitious and old fashioned. “The best would be to combine the two points of view” (ibid.), he says. These are not contradictory ways of thinking. One is not compelled by logical necessity to hold but one of these views. Just as Aristotle suggested that the four types of causes can be involved in explaining natural events,3 so does Leibniz suggest the possibility of cases where both methods of explanation can be used, although in

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each case, one should consider the advantages and disadvantages of each method according to the specific problem at hand:4 I find that the way of efficient causes, which is in fact the profounder and in some ways the more immediate and a priori, is on the other hand, rather difficult when one comes to details, and I believe that for the most part our philosophers are still far from mastering it. The way of final causes, however, is easier and is often useful for understanding important and useful truths, which one would be a long time seeking by the other more physical route. (DM §22; A VI 4 1565; L 317)5

2.2

The mechanistic opposition

An enlightening example of the use of final causes in physics can be found in the field of optics. Leibniz uses the discovery of the law of refraction by Willebrord Snellius, known as Snell’s law, to demonstrate how the use of the method of final causes can promote discoveries in science and physics. According to Leibniz, Snellius, and after him Fermat, followed the ancient Greeks, who applied the method of final causes to the phenomenon of reflection, and applied the same method and principles to refraction,6 whose law he discovered. The discovery was originally attributed to Descartes,7 who had done so “by the method of efficient causes”, which according to Leibniz “is not nearly so good” (DM §22; A VI 4 1566; L 318). This example is extremely significant for the purpose of evaluating Leibniz’s conciliation of efficient and final causes. Not only does it demonstrate the usefulness of final causes in physics, as will become clear presently, but it also brings together the two poles of the dichotomy, i.e., those, like Snellius and Fermat, who use final causes, and those, like Descartes, who not only adhere to methods of efficient causation but also reject altogether the concept of final causation.8 It was against this background of strong rejection that Leibniz’s reconciliation emerged. Descartes, one of the flag-bearers of the mechanistic world view, was one of many thinkers who held such extreme opposition to final causes: [I]t is no less natural for a clock constructed with this or that set of wheels to tell the time than it is for a tree which grew from this or that seed to produce the ap(PoP IV 203) propriate fruit.

Descartes’s view regarding the mechanistic nature of living things encompasses also the human body. In his Treatise of Man, he describes a human-like puppet, “an earthen machine formed intentionally by God to be as much as possible like us”. If artificial machines such as clocks, fountains, mills etc., which are created entirely by man, “lack not the power to move, of themselves, in various ways”, why



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can’t we suppose that the human automaton, created by God, “could have even more sorts of movements than I have imagined and more ingenuity than I have assigned” (Descartes 1972: 2–4). As already mentioned, many of Descartes’s and Leibniz’s contemporaries – Hobbes, Gassendi, Spinoza, Huygens, Boyle, and Malebranche, to name just a few prominent examples – held sworn mechanistic views and did not look favorably upon final causation. Thomas Hobbes forcefully expresses his thoughts on the subject, when he speaks of the mechanical nature of all things, in the first paragraphs of Leviathan: For seeing life is but a motion of limbs, the beginning whereof is in some principal part within; why may we not say, that all Automata (Engines that move themselves by springs and wheels as doth a watch) have an artificial life? For what is the Heart, but a Spring, and the Nerves, but so many Strings; and the Joynts, but so many Wheeles, giving motion to the whole Body, such as was intended by the Artificer? (Hobbes 1991: 9)

Baruch Spinoza thought that the widespread belief among men that all things in nature have a purpose or end is but a prejudice, which serves as an obstacle. In the appendix to part I of the Ethics he elaborates on the origin of this misconception and concludes with the claim that “all final causes are but figments of the human imagination” (1982: 59). Robert Boyle, to whom we shall return in the following sections, “stresses repeatedly that mechanical patterns of interaction are the only ones truly intelligible to us” (Wilson 1987: 157). In other words, in order to understand the principles of nature, we must employ mechanical explanations to explicate natural phenomena [A]s he that cannot by the mechanical affections of the parts of the universal matter explicate a phenomenon will not be much helped to understand how the effect is produced by being told that nature did it. (Boyle 1686: IV, 35)

Another good example is Christiaan Huygens.9 According to Dijksterhuis (1961: 457), Huygens’s work embodied the culmination of seventeenth-century mechanistic science: “In him the Gassendistic and Cartesian corpuscular theories found their most consistent and widest application, and the mechanistic programme formulated by Boyle its fullest realization”. In his Treatise on Light Huygens proposes to investigate light by mechanical means, since “it is inconceivable to doubt that light consists in the motion of some sort of matter”. Huygens recognizes a ‘mark of motion’ in the production and effects of light, at least, he writes, according to the true Philosophy, “in which one conceives the causes of all natural effects in terms of mechanical motions” (Huygens 1961: 3). This,

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according to him, is the only appropriate way to investigate light (or for that matter, any other field of physics), “or else renounce all hopes of ever comprehending anything in Physics” (ibid.). Last but not least is Leibniz’s bitter rival, Isaac Newton, who above all “has to be regarded as the founder of the mechanistic world-picture of classical physics” (Dijksterhuis 1961: 490). When seen against such background of widespread rejection, one may appreciate Leibniz’s conciliation as an attempt to break a largely accepted dichotomy by demonstrating how its two poles can be seen as complementary rather than contradictory.10 This attempt to reconcile these two types of causes has additional significance, which has to do with the fundamental role of the concept of cause in metaphysics and in science; any attempt to untangle the issues revolving around it is therefore a step towards clarifying “the problematic relationship between metaphysics and science” (Boudri 2002: 113). The importance of using explanations of the two kinds is implied by Leibniz himself in at least two different places: at the end of paragraph 22 of DM, where he suggests that discoveries made by using the method of efficient causes may be promoted, and sometimes even made possible, by preceding discoveries made using the method of final causes: At least we have grounds to suspect that he [Descartes] would never have found it [the principle of refraction] by this method [of efficient causes] if he had not learned anything of Snell’s discovery in Holland.  (DM §22; A VI 4 1566; L 318)11

The other passage is from the Specimen Dynamicum, quoted below, which begins by referring directly to the optical case we are discussing here: In fact, as I have shown by the remarkable example of the principles of optics… Final causes may be introduced with great fruitfulness even into the special problems of physics, not merely to increase our admiration for the most beautiful works of the supreme author, but also to help us make predictions by means of them which would not be as apparent, except perhaps hypothetically, through the use of efficient causes. Philosophers have in the past perhaps not sufficiently (GM 6 243; L 442) observed this advantage of final causes.

2.3

The optics case

In his optics example (see UP), Leibniz demonstrates how the same conclusion (i.e., the conclusion manifested by Snell’s law, that “the complementing sines will be in a reciprocal ratio to the resistance of the medium – as was claimed” (UP; D



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3 146), can be derived both from considerations of final causes and from considerations of geometry and trigonometry. Following his brief discussion of Catoptrics, Leibniz proceeds to discuss Dioptrics in the third paragraph:

Figure 1.  Refraction of light (UP; D 3, tab. 4, fig. 17)

Referring to the above figure, Leibniz wishes to answer the following question: Let IE be air, EK water, or glass, or some other medium denser than air, C a radiating point in the air, G an illuminated point beneath the water: it is asked by which path does the light shine from the former to the latter, or what is the point E on the surface of the water AB such that the ray emitted from C is to be refracted sending it to G?  (UP; D 3 145)

The method by which he proceeds to find the answer to this question is based on the presumption that “this [point] E should be taken such that the path is the easiest of all”. This presumption is based on what Leibniz calls a ‘first hypothesis’ common to the sciences of Optics, Catoptrics, and Dioptrics,12 namely, that “light radiating from a point reaches an illuminated point by the easiest path” (UP; D 3 145). Since we are dealing with different mediums, each with its own resistance coefficient, the easiest path is the path where the entire path times the resistance is a minimum.13 The calculation of the total path-difficulty (the total path traversed

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by the ray of light from point C to point G) is quite straightforward and follows from simple geometrical considerations: Path-difficulty = s = m ∙ √CH2 + y2 + n ∙ √LG2 + (h – y)2, where y stands for the segment EH, h for HL and h – y for EL; m and n represent the coefficients of resistance of the two different mediums.14 Using Leibniz’s ‘method of minima and maxima’15 we get: m ∙ 2y / 2√CH2 + y2 – n ∙ 2(h – y) / 2√LG2 + (h – y)2 = 0 If i stands for the angle of incidence and r for the angle of refraction we obtain: m ∙ sini – n ∙ sinr = 0 i.e. sini / sinr = n / m = constant, which is Snell’s Law. We have therefore reduced all the laws of rays confirmed by experience to pure geometry and calculation by applying one principle, taken from final causes if you consider the matter correctly … And so those who reject final causes in phys(UP; D 3 146) ics with Descartes err greatly.

The conciliation between the two main competing approaches to causal explanation in physics, sought by Leibniz, seems thus to be achieved. He demonstrates how Snell’s law can be derived using the method of final causes, yet at the same time espouses the use of efficient causes, when appropriate. But he seems to go even further towards conciliation. This occurs when he opposes Fermat and sides with Descartes, claiming that the velocity of light is proportional to the ‘resistance’ of the medium. In other words, Leibniz agrees with Descartes as regards the proportionality of the ratio of velocities of the ray of incidence and the ray of refraction to the ratio of the angles of incidence and refraction, from which it follows that he disagrees with Fermat’s position in this respect. Fermat used his principle of least time to derive Snell’s law (see notes 7 and 13). He looked for the path between C and G that minimizes the travel time: Time = path / velocity i.e. T = √CH2 + y2 / V1 + √LG2 + (h – y)2 / V2 To minimize T we must equal its derivative to 0 (T'(y) = 0): y / V1 ∙ √CH2 + y2 – (h – y) / V2 ∙ √LG2 + (h – y)2 = 0 Since sini = y / √CH2 + y2 and sinr = (h – y) / √LG2 + (h – y)2 we get: sini / sinr = V1 / V2

Fermat maintained that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is directly proportional to the ratio of the velocity of the ray of incidence to the velocity of the ray of refraction. Descartes claimed the opposite, namely, that the ratio of the sines is inversely proportional to the ratio of the velocities.



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The point to be noted here is that Leibniz, who opposes Descartes and concurs with Fermat as to the use of final causes, agrees with Descartes, who rejects the use of final causes in physics, as far as the proportionality of the ratio of velocities is concerned. Although contemporary optics sees eye to eye with Fermat on this matter, what is under consideration here is the issue of conciliation rather than that of physical validity. From this perspective, agreeing with one of the adversaries (Descartes) and disagreeing with the other (Fermat) in part of the account of a phenomenon is for Leibniz perfectly compatible with disagreeing with the former and agreeing with the latter in another part thereof. That is, one need not envisage scientific positions as encompassing packages of assumptions and results which one must fully purchase or decline. It is precisely this possibility of unpacking the conceptual deal that renders conciliation between otherwise irreconcilable packages feasible. To be sure, Leibniz has an explanation for supporting Descartes regarding the ratio of velocities. This issue of light’s velocity in different media is dealt with in the last paragraph of UP. His treatment of the subject relies on several definitions and one analogy: – First, the resistance of a medium is defined as being an impediment to the diffusion of light through the parts of the medium. In Leibniz’s own words, “where it [light] will communicate its own force to more insensible parts of the illuminated place, the medium will be more illuminable and less resistant to light” (UP; D 3 149). – Next, Leibniz links the medium’s resistance with its material structure: if the particles of the illuminated medium are solid, small, “or less interspersed with some other heterogeneous material not affected by light”, then the medium can be said to be more illuminated. – The analogy consists in reviewing the diffusion of light through the particles of a medium as analogous to a blow impressed at the same time on many bodies. Just as the blow “will impart less force to [each of the bodies] than if it [the blow] had been inflicted on [any single] one of them”, so does the light, when it travels through a more resistant medium where less parts are affected, affects those parts more strongly. Conversely, “in a more illuminable medium, more parts are affected, but less strongly, and the impressed impetus is weaker”. This alone explains why light moves faster in a denser medium – the material structure impedes the diffusion of light, thus “enabling” light to retain its strength and impetus and therefore, a higher velocity.16 In the remainder of the paragraph, Leibniz details how the velocity of light increases in proportion to the resistance.

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A possible complementary explanation of Leibniz’s double attitude towards Fermat and Descartes may be carved out at the meta-controversy level. It is well known that the two mathematicians were engaged in endless disputes (see Dascal 1999: 31–32). Leibniz, who at the object level overcomes the limitation he sees in both Descartes’s account of refraction using spatial variables, and Fermat’s account using time, acts as if at the meta-level, he seeks agreement with Descartes, in this case, as a token of his conciliatory approach even in the case of bitter rivals. The situation of simultaneous agreement and/or disagreement with opposed positions can be summarized as follows: Table 1.  The middle way Leibniz takes between Fermat and Descartes Ratio of science angles to velocities17

Use of methods Espouses in Final causes

inverse proportion

Leibniz

direct proportion

Fermat

Rejects Final causes Descartes

Now that we have shown how Leibniz’s conciliation approach operates in this particular case, we should inquire what is behind the scenes; what motivates Leibniz to espouse both, allegedly opposite, types of explanation? We propose that one of the answers to this question, especially appropriate for the optical problem discussed in this section, has a lot to do with one of Leibniz’s basic semiotic-metaphysical notions of expression; this answer will be spelled out in the following subsection.

2.4

Expression, signs, and conciliation

The notion of expression plays a crucial role in Leibniz’s metaphysics, as is well known. It provides the relational infrastructure of a world whose substantial units – the ‘monads’ – are ‘windowless’, i.e., are not connected by the kind of interaction that, in most ontologies, structures the universe, i.e., causal relations. Expression, in Leibniz’s system, is a relation of correspondence, of representation. Each monad represents the universe from its unique ‘point of view’; each corresponds to the same “thing”, the universe, in its own way. Through this network of representations, the monads also represent each other, i.e., are in a relation of correspondence. Our purpose here is not to pursue the global ontological facet of this relational structure, but rather its semiotic facet – the fact that the same concept of



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expression provides the basis for Leibniz’s theory of signs, or ‘characters’. Just as different monads which represent the same universe are thereby in harmonious correspondence with each other, different signs – geometrical, algebraic, logical, linguistic, or others – may represent the same object, be it concrete or abstract. If this semiotic representation is orderly, well-structured, and non-arbitrary, the sign ‘corresponds’ to its signified, for it captures the structure of the latter: There is some relation or order in the characters which is also in things, especially if the characters are well invented. (DI; A VI 4 23; L 184)

Furthermore, just as the monads correspond to each other because they represent the same universe, so too different signs representing the same object must, ultimately, correspond to each other [I]f characters can be used for ratiocination, there is in them a kind of complex mutual relation [situs] or order which fits the things …Though it varies, this order somehow corresponds in all languages … For although characters are arbitrary, their use and connection have something which is not arbitrary, namely a definite analogy between characters and things, and the relations which different characters expressing the same thing have to each other. This analogy or relation is the basis of truth. For the result is that whether we apply one set of characters or another, the products will be the same or equivalent or correspond analogously. (ibid.)

The semiotic-metaphysical notion of expression can be thus seen as underlying the possible conciliation of the different explanation and mathematical account of the same phenomenon – the motion of light – through different media. However, each of the accounts uses different mathematical methods – considerations of geometry and trigonometry as opposed to Leibniz’s method of maxima and minima – and characters. The correspondence or conciliation of these explanations, which is manifested in the fact that both yield the same law of refraction, derives from the fact that their representations of the ‘thing’ to be accounted for capture the essential elements of this thing, albeit from a different perspective. Metaphysically speaking, the “things” out there, the reality one wishes to describe or explain, in our case the motion of light, can be articulated using different sets of characters, as long as they keep a certain connection to the “things” they express or explain. The different mathematical methods, although employing different mathematical notations, come out with the same answer, for as Leibniz says, “if you apply the solution you have reached by calculation in several different ways … the answer always comes out the same” (DI; A VI 4 24; L 184). Each set of characters and reasons may highlight different properties of the “things” (for example,

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the ratios of angles and the “difficulty” of a path), nevertheless “the basis of truth is always found in the connection and coordination of these characters” (ibid.). You see then that however arbitrarily the characters may be chosen, if you observe a certain order and rule in their use, they always agree … It is always true, without any arbitrary choice of ours, that if certain characters are adopted, some definite argument must proceed, and if others are adopted whose relation to the things signified is known but different, the resulting relation of the new characters will again correspond to the relation of the first characters, as appears by substitution or comparison. (DI; A VI 4 25; L 185)

In the light of these considerations, we might better appreciate such expressions as “Both explanations are good” or “the effects of nature can be accounted for in a twofold way”. These merely reflect the harmony and non-arbitrariness of the world and the means through which we represent and get to know it. As long as we keep a certain order and relation, the phenomena of nature can be expressed in several ways, all of which are “good” and should be considered with due respect and attention. Finally, we would like to call attention to the similarity between the issues of choice of characters and choice of reasons. We have seen that in UP Leibniz demonstrates the use of both types of explanation. He derives Snell’s law using considerations of final causes and in the last paragraph, he demonstrates how Descartes’s conclusion regarding the inverse proportion between the ratio of the sines of angles of incidence and refraction and the ratio of velocities of incidence and refraction can be derived using considerations of efficient causes (i.e., the material structure, light’s impetus and diffusion, etc.). But a question arises, similar to the question of the arbitrariness of characters: is the appeal to a specific type of explanation in a specific physical problem is arbitrary? And as in the case of characters, Leibniz’s answer is negative. The choice of explanations is not arbitrary; in fact, Leibniz provides us with a meta-level rule for determining the best type of explanation out of a number of alternatives: According to Leibniz, the method of efficient causes is “profounder” and is “more immediate and a priori”. However, it is “rather difficult when one comes to details”. The method of final causes, on the other hand, “is easier and is often useful for understanding important and useful truths, which one would be a long time seeking by the other more physical route” (DM §22; A VI 4 1565; L 317). Hence, we can conclude that the method of efficient causes is harder to use. To employ it, one needs much knowledge and expertise. Leibniz himself says that “our philosophers are still far from mastering it”. Its upshot, however, is that the more effort and work one puts into a problem (by employing the harder method),



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the more effects, results and understanding it produces, since it is “profounder”, i.e., by employing it, one gets an insight of the fundamentals of things. Conversely, when confronted with a more difficult problem for which one lacks knowledge or proficiency, one should employ the method of final causes, which is easier. Employing this way, instead of seeking the solution for a physical problem for a long time “by the other more physical route”, one can reach important truths more easily and quickly, but with less results or understanding, since it is shallower, to use Leibniz’s metaphor. This relation between the two types of explanation can also be shown to be closely related to the fundamental Leibnizian division between analytic and synthetic. Analysis is analogous to the efficient cause method, for it is used to “dig out” the details of a given problem; it “goes back to principles solely for the sake of a given problem” (Leibniz 1683; A VI 4 544; 1973: 16). Synthesis, on the other hand, is analogous to the final cause method, for it is when, “beginning from principles and running through truths in order, we discover certain progressions and form tables, as it were, or sometimes even general formulae, in which the answers to what arises later can be discovered” (ibid.). Synthesis, just as in the case of the use of final causes, can be used to discover general formulae, which can be later justified or established by a deeper investigation, or analysis. For in this way [practicing synthesis] he will always progress pleasantly and easily, and will never feel any difficulties, nor be disappointed of success, and in a short time he will achieve much more than he would ever have hoped for at the outset. (Leibniz 1683; A VI 4 545; 1973: 17)

As in the case of the final cause method, the use of synthesis is easier and allows the researcher to achieve results much faster. The use of analysis, just as in the case of the method of efficient causes, is harder and lengthier, and is used to establish and better understand truths already discovered: It is better to produce a synthesis, since that work is of permanent value, whereas when we begin an analysis on account of particular problems we often do what has been done before. (Leibniz 1683; A VI 4 544; 1973: 16)

3.

Integrating the opposites

Another expression of Leibniz’s wish to reconcile two opposing scientific views can be found in an article written in 1698, as a reaction to an ongoing debate regarding the very notion of Nature.

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To understand this debate we must recall Robert Boyle’s mechanistic world view, as expressed in his A Free Enquiry into the Vulgarly Received Notion of Nature (1686). According to Boyle, God created the universe as an automaton, “and this compounded machine, in conjunction with the laws of motion freely established and still maintained by God among its parts, I look upon as a complex principle, whence results the settled order or course of things corporeal” (Boyle 1686: IV, 39–40). In Addition to this first (efficient) cause, the world is governed by rules of local motion, much like a machine or an automaton [W]hatever is done among things inanimate, which make incomparably the greatest part of the universe, is really done by particular bodies acting on one another by local motion, modified by the other mechanical affections of the agent, of the patient, and of those other bodies that necessarily concur to the effect or the phenomenon produced. (ibid.)

These ideas had a strong impact on the German mathematician, natural philosopher, and theologian Johann Christoph Sturm (1635–1703). Sturm shared Boyle’s mechanistic view regarding the natural world, which he tried to put into practice by, among other things, conducting a series of experiments in front of an audience of twenty naturae scrutatores (‘investigators of nature’), to whose judgment he subjected the phenomena produced by his experiments and on whose testimony he relied to guarantee the truthfulness and probity of his published account, the Collegium Experimentale sive Curiosum of 1679 (Ahnert 2002). This form of experimentalism was connected with the vogue of eclecticism in the last decades of the 17th century and in the first decades of the 18th, a trend that was not alien to Leibniz’s thought (see Dascal 2000). Eclectics believed that it was impossible for a single philosopher or sect of philosophers to encompass, alone, all of human knowledge, and insisted on the need of cooperation between researchers in order to understand the complexity of the world: They considered all doctrines to be provisional and open to modification. [S]o great is, on the one hand the multitude, and, on the other, the complexity, which could never be overcome even by many centuries, let alone the age or ingenuity of a single man.18

Sturm’s Physica electiva of 1697 reflects the importance he attributed to his eclecticism and experimentalism. This book “provides a defense and application of the corpuscular philosophy leaning heavily on the work of Boyle” (Wilson 1987: 165).19 Sturm’s dissertation, Idolum Naturae (1692) provoked a strong reaction by Günther Christopher Schelhammer (1649–1716), published in 1697. Sturm reacted to this critique in his De natura sibi in cassum vindicata (1698), which



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Leibniz referred to as “Dissertatio Apologetica” (‘Defensive Dissertation’). Schelhammer was a medical doctor, the personal physician of the Duke of Kiel, and a teacher at the University of Kiel. He married the daughter of the famous German jurist and Aristotelian Hermann Conring, who was also one of Leibniz’s mentors.20 Schelhammer’s Natura sibi et medicis vindicata (1697) is a discussion of Boyle’s and Sturm’s theses. Boyle (1686, 1688) had argued that, since the term ‘nature’ was equivocally used and badly misused, it should be replaced by the term ‘mechanism’. Schelhammer undertook to defend the use of ‘nature’ and to reject Boyle’s suggestion. Thus, in the first part of the book, he discusses definitions of nature by ancient and modern philosophers – including defenders of Boyle’s and Sturm’s position. Although aware of Boyle’s persuasive power, authority, and prestige, which made him a difficult adversary,21 Schelhammer did not hesitate to sharply criticize his views. In principle, Schelhammer criticizes any philosophy that proposes any sort of divine intervention in natural phenomena, on the grounds that they all lead to the loss of meaning of experimental activity and assign God an inacceptable role (see Schelhammer 1697: 56–77). The point of divergence between him and Sturm becomes the existence of a divina virtus diffusa per universum (‘a divine virtue diffused throughout the universe’), explicitly held by Sturm, but somehow – if only remotely – also present in Boyle’s theses – a position Schelhammer rejects. According to his conception of nature, God creates matter and thanks to force imparts to it motion that manifests itself according to the laws of movement. He contends that those who defend divine intervention in natural phenomena inevitably separate matter from the laws that rule it and from the forces that move it. The separation between matter and force turns out to be an irreconcilable divergence between the two German academics. It was in this debate that Leibniz intervened with his De Ipsa Natura, published in the Acta Eruditorum of September 1698. He begins by stressing that for him this topic is not new, neither personally nor historically:22 I too once gave some thought to this question … [and] was therefore all the more willing to think carefully about what is an inherently important topic, and I thought I should set out more clearly my opinion, and the whole issue, in the light of the principles which I have already presented on several occasions.  (NI §1; GP 4 504; W&F 210)23

In this article, Leibniz took the opportunity to expound his own metaphysical views concerning the inherent force which he believes to be present in things themselves, “from which their actions and passions follow” (NI §5; GP 4 507; W&F 212), and “from which the series of phenomena follows in accordance with the dictates of the original Command” (NI §6; GP 4 507; W&F 213). In this

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section we analyze the middle way Leibniz takes between the two sides and the argumentative strategy he employs in order to achieve his conciliatory aim. As we will see presently, we face here a quite different kind of conciliation, if compared with the one examined in the preceding section. Leibniz’s middle way comprises, on the one hand, the rejection of the idea that nature contains anything non-mechanical, and on the other, the belief that one should not let mechanical explanations of material things go too far. With the former claim, he positions himself on Sturm’s and Boyle’s side, whereas with the latter, he is rather siding with Schelhammer. After an initial examination of the two opposing views (Sturm’s and Schelhammer’s), as is the case in many scientific and philosophical debates, the question arises whether the issue is resolvable. Prima facie, one has indeed the impression that the two positions are irreconcilable. Nevertheless, as we shall see, it is worth to accompany attentively Leibniz’s steps in construing an acceptable alternative that allows them to live together. Leibniz’s argumentative strategy and the immediate outcome of his middle way is the ‘de-dichotomization’24 of the debate, itself a move which opens the way for alternative solutions other than the two poles of the dichotomy – exactly the opportunity Leibniz seeks for expounding his ideas on the subject. Once these two poles are no longer perceived as mutually exclusive and exhaustive alternatives, it is possible for Leibniz to propose a solution that retains some elements of both views. As already mentioned, Leibniz opposes the view that there are non-mechanical things that govern the mechanisms of bodies. He refuses to ascribe the work of nature to “created intelligences with appropriate levels of wisdom and power” such as a ‘World Soul’, Hippocrates’s omniscient heat, Avicenna’s soul-giving cholcodea, 25 or Henry More’s ‘Spirit of Nature; in his words, they “are all partly impossible, and partly unnecessary” (NI §2; GP 4 505; W&F 210). He also agrees in “broad terms” with Robert Boyle’s assertion that “we must take nature as being just the mechanisms of bodies” (NI §3; GP 4 505; W&F 211). Of course, such broad and quite vague terms do not satisfy Leibniz, and he undertakes a closer and sharper look at them, for we “must distinguish between the principles of this mechanism and what is derived from them” (NI §3; GP 4 505; W&F 211). From the rejection of the non-mechanical “created intelligences” does not follow that “we should deny that there is any active created force inherent in things” (NI §2; GP 4 505; W&F 211). Furthermore, once closely examined – Leibniz suggests – “mechanism itself has its origin not merely in a material principle or in mathematical reasons, but in some higher and, so to speak, metaphysical source” (NI §3; GP 4 505; W&F 211). This assertion clearly shows that the two polar positions can be combined in some way and that the ‘purely mechanistic’ vs. ‘wise created natures’ dichotomy should be in fact de-dichoto-



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mized, thus opening the path for an alternative capable of combining elements of both. This process of de-dichotomization and concomitant construction of such an alternative will be discussed at the end of this section. A large portion of Leibniz’s critique is directed at those who attribute ‘external denomination’ to God’s volition or command, i.e., those who believe that the first command is an external act upon a passive matter rather than inherent in the matter. He attributes this view to the occasionalists and “particularly to the most intelligent Father Malebranche” (NI §5; GP 4 507; W&F 212). He also attributes the opposite view, i.e., the view that the first command has “produced some permanent impression on things themselves” (ibid.) to Schelhammer, as well as to himself. However, as far as Sturm is concerned, Leibniz appears to think that his position regarding this important issue is unclear. Sturm adopts the theory of a first command, or “earlier-laid-down divine law” that permanently instituted the laws of nature, but Leibniz remains baffled as to what Sturm believes to be the implications of such a view: “has this volition or command, or, if you prefer, this earlier-laid-down divine law, bestowed on things merely an external denomination?” (ibid.). In any case, Leibniz’s strategy at this point is to identify the inconsistencies of the doctrine of a first command that bestows on things an externally imposed law without granting them an internal principle according to which they act: For since this earlier command does not now exist, it cannot now do anything unless it left behind some continuing effect … for if what is distant in time and place could operate here and now without an intermediary, then anything could be said to follow from anything else equally well … But if, on the other hand, the law God decreed has in fact left some trace of itself impressed upon things … then it must be admitted that things have been given a certain ability, a form or force …  (NI §6; GP 4 507; W&F 213)

In the light of these inconsistencies, one is left, according to Leibniz, with the alternative of ascribing an active force to created things, as a trace of God’s imprint. Continuing this line of thought, Leibniz presents two certainties regarding the motion of things: that “matter cannot of itself begin a motion” and that “a body considered in itself retains any impetus imparted to it, and that it remains constant in its mobility – that is, it has a tendency to persevere in whatever sequence of changes it has begun” (NI §11; GP 4 511; W&F 217). Leibniz concludes that since these cannot be just modifications of mass (since mass or matter are essentially passive), a “first subject of activity must be recognized in corporeal substance”; i.e., something additional to extension, which is purely geometrical, and to mass, which is purely material. This “substantial principle” is referred to as soul in living things, or substantial form in inanimate things, and together with

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matter, claims Leibniz, “makes up a substance which is truly one … it forms what I call a monad” (ibid.).

3.1

On what it takes to conciliate

Having presented the issue at stake, the contenders’ positions, and Leibniz’s middle way alternative, we now proceed to examine the argumentative tools he makes use of in his attempted conciliation. This examination consists in a few necessary steps. First, we shall identify the elements he chooses to preserve from each pole of the dichotomy, i.e., his agreements with each position. We have already indicated such elements with regard to Sturm’s position, and in order to complete this conciliation attempt we must look for the elements Leibniz chooses to adopt from Schelhammer’s position. To be sure, in NI Leibniz refers almost exclusively to Sturm's pole of the dichotomy; yet, besides the fact that many of these references are critical, the appearance of preferring Sturm’s ideas over those of Schelhammer is misleading, as we shall presently see, because Leibniz shares some important views with Schelhammer.26 Second, we shall examine the two positions according to several significant principles that serve as criteria in Leibniz’s examination of the positions in dispute, namely, clarity, arbitrariness, and the use of ‘external denomination’ as a method of explanation. Finally, we will observe Leibniz’s process of de-dichotomizing several dichotomies, around which this debate revolves, thus opening the way for his own suggested alternative. In the case under consideration here, Leibniz’s conciliation approach is, as we have mentioned, quite different from the case investigated in the previous section. In the optical case Leibniz regards both positions as good and useful, albeit for different purposes; in the present case he proposes an alternative uniting – at least to some extent – the opposing sides. A conciliation approach which professes to take an intermediate course between positions, must of course preserve some significant elements of both. As regards Sturm’s position, it is easy to demonstrate which elements Leibniz preserves and which ones he rejects, since he debates with Strum’s position throughout the entire paper. Beginning with Sturm, Leibniz agrees with this “man of outstanding merit in mathematics and physics” (NI §1; GP 4 504; W&F 209) in rejecting all “supposed wise created natures which produce and govern the mechanisms of bodies” (NI §2; GP 4 505; W&F 210). He also agrees in broad terms, as already mentioned, with Boyle’s saying, which represents both



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his and Sturm’s view, that nature is just the mechanism of bodies. However, he distinguishes himself from this view by claiming that these mechanisms have their origin in a higher metaphysical source, as we have seen (NI §3; GP 4 505; W&F 211). Significant parts of the paper are dedicated to Leibniz’s arguments in favor of the inherent force within things and to criticizing Sturm’s arguments against such force. In these passages he is, as it were, arguing on behalf of Schelhammer’s position. That the notion of an ‘inherent law’, which is diametrically opposed to Sturm’s “earlier-laid-down” divine law is attributed by Leibniz to Schelhammer (§5) is no minor thing in his conduct of the contest, for this notion is the backbone of Leibniz’s alternative proposal. Therefore, establishing its viability is an essential component of his strategy. No wonder that Leibniz argues that Sturm’s position doesn’t pass the test of the three argumentative and explanatory principles he makes use of in NI in order to evaluate the combating positions, as we shall see. These principles are: 1. Principle of Clarity: the clarity, intelligibility, and precision of an idea are sine qua non conditions for assigning to it an explanatory role.27 2. Principle of Non-Arbitrariness: the works of nature are not arbitrary; arbitrariness is a distinctive mark of irrationality.28 3. Principle of Inherent Force: all activity derives from inner sources; in the case of bodies, from what Leibniz calls ‘inherent forces’ (§7); external factors (‘external denomination’) cannot therefore explain activity. The first example of violating the Principle of Clarity concerns the use of external denomination as well. When examining Sturm’s view concerning the “eternal law which God has set up”, Leibniz finds his explanation not “good enough” due to its potential ambiguity, which Sturm does not care to render intelligible: For, I ask, has this volition or command, or, if you prefer, this earlier-laid-down divine law, bestowed on things merely an external denomination? Or has it really produced some permanent impression in things themselves, an ‘inherent law’ … from which their actions and passions follow …?  (NI §5; GP 4 506–507; W&F 212)

Not only doesn’t Sturm make his view sufficiently clear; one may also suspect that he supports an external denomination explanation of his position, thus increasing rather than reducing the obscurity, since this kind of explanation, says Leibniz, “is so far from making the matter more explicable that it is more like abandoning the role of the philosopher, and cutting the Gordian knot with a sword” (NI §7; GP 4 508; W&F 214).

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Another example concerns the clarification of action, or to be more precise, “whether created things can properly and truly be said to act”. Once again Leibniz confesses that he has “some difficulty in explaining the thought of the famous Sturm” (NI §9; GP 4 509; W&F 215). For, on the one hand Sturm denies the possibility of things to act for themselves, but on the other he denies the comparison between things and “an axe moved by a woodcutter” (ibid.). This renders Sturm’s claim unintelligible for Leibniz: I don’t know what to conclude from this; he seems to have explained very clearly neither the extent to which he departs from received opinions, nor what precise idea of action he has in mind. (ibid.)

It must be admitted, however, that Leibniz himself is also not so clear on the subject of action, which he supports so strongly throughout the paper. He criticizes Sturm’s lack of clarity where clarity is needed, “for, as is clear from the debates of the metaphysicians, [the idea of action] is something which is far from obvious or easy” (ibid.), but with the exception of remarking that “I have made the concept of action clear for myself ”, Leibniz does not expand upon his concept of action, rendering it entirely clear. As regards the Principle of Non-Arbitrariness, it is well known that Leibniz insisted on the primacy of reason and on the fact that the world is rationally ordered. Thus, events in our world are neither random nor arbitrary. Arbitrariness is for Leibniz equivalent to irrationality. Leibniz also believes that scientific explanations based solely on efficient causes without the considerations of final causes are arbitrary: “For I believe that God considered principles of wisdom and reasons of order when he established the laws which are observed in nature” (NI §4; GP 4 506; W&F 212). Therefore, when Sturm is promoting a purely mechanistic view, relying solely on efficient causes, he is actually saying, according to Leibniz, “that the laws of motion are arbitrary – a view which seems to me to be not entirely coherent” (ibid.). Finally, regarding the Principle of Inherent Force, we have already shown how the appeal to ‘external denominations’ is considered by Leibniz to be inconsistent. To be sure, he is not quite sure whether Sturm’s intention is to claim that the first command bestowed on things by God is merely an external denomination or that it produced some permanent impression (again a problem of clarity). However, since he explicitly attributes the latter to Schelhammer, one can conclude that the former is attributed to Sturm. The last step towards conciliation is the process of de-dichotomizing, and we shall examine how Leibniz tries to untangle several dichotomies and relations in order to create space for his middle way alternative. The following figure illustrates the different relations and dichotomies addressed by Leibniz in the NI.



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Active

(1)

Passive

Matter

Secondary

(2)

Primary

Complete

(3)

Incomplete

Substance

Figure 2.  The complex set of dichotomies in the de-dichotomization process

The process of de-dichotomizing unfolds throughout the paper, but it seems to reach its peak in the twelfth section, where Leibniz deals with one of Sturm’s arguments against the possibility of “this motive force inherent in bodies”: [I]n its nature and essentially matter is a passive substance, so it is no more possible for it to be given an active force than it is for God to will that a stone, while remaining a stone, should be alive and rational – that is, should not be a stone. Furthermore, whatever things we may suppose in body can only be modifications of matter; but … a modification of something essentially passive cannot render it active. (NI §12; GP 4 511–512; W&F 217–218)

First, we can notice the obvious dichotomy between something passive and something active (1). Second, Leibniz informs us that matter “must be understood as either secondary or primary” (2). The third dichotomy is between a complete and incomplete substance (3). When considering both (1) and (2), we can notice that matter is not simply something passive or active, since there are two types of matter, primary and secondary. Secondary matter is identified with the active pole of the dichotomy, whereas primary matter is merely passive. When adding (3) to the equation Leibniz links secondary matter with complete substance (“secondary matter is indeed a complete substance”; NI §12; GP 4 512; W&F 218), and primary matter with incomplete substance; incomplete since it lacks something: [T]here needs to be added to it a soul, or form analogous to a soul; a first entelechy, that is a striving or primitive active force which is itself an inherent law imprinted by divine decree. (ibid.)

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Leibniz continues and explains why his alternative actually de-dichotomizes the two poles and can be distinguished from each of them. “A spirit – he says – is not to be understood here, as it usually is, as an intelligent being”. He thus distinguishes himself from Schelhammer’s view, which insists on the existence of some sort of spirit in addition to passive matter. But he immediately adds: “nor is it to be understood as a mere modification, but as something constitutive, substantial and enduring” – thereby distinguishing himself from Sturm, who insisted that a mere “modification of something essentially passive cannot render it active” (ibid.). Sturm’s argument has to first refute my doctrine, says Leibniz, before it can be considered as legitimate. Furthermore, Sturm cannot claim that corporeal substance is only a modification of matter, since “the bodies of living things, according to the traditional philosophy, have in them souls” (ibid.). Sturm may hold the opposite opinion, continues Leibniz, however he cannot use it as an assumption without first proving it. Leibniz, on the other hand, believes he has such a proof or at least a very convincing argument in favor of his opinion: It is not consistent either with the order, or the beauty, or the intelligibility of things that there should be something vital or internally active only in such a small part of matter, when there would be greater perfection if it were the same in all of it. (ibid.)

Towards the end of his paper, Leibniz emphasizes even further the distinctions between him and Sturm. In addition to granting “the distinguished M. Sturm” the wisdom of keeping his distance from the “monstrosities” of the doctrine of occasional causes, he has no doubt that Sturm, at some point in the future, will either modify his view to allow some change in things, “or he will surrender to the truth” (NI §15; GP 4 515; W&F 221). In the last section Leibniz continues to exhibit his rhetoric, by contemplating on the possibility that the source of the controversy between him and Sturm is a mere misunderstanding, and perhaps Sturm’s opinion can be interpreted in such a way that “there is no longer any disagreement between us” (NI §16; GP 4 515; W&F 221). However, on second thought, and after softening his opponent and his readers, Leibniz changes his mind: But I am not confident that this is what he means since he says hardly anything like it, or that seems to follow from it, anywhere else. On the contrary, I note that things he says elsewhere are hardly consistent with this view, and also that the ‘Defence’ leads to quite different conclusions.  (NI §16; GP 4 515–516; W&F 221)29

In spite of this last burst of controversy with Sturm, Leibniz concludes the NI by stressing that there are, nevertheless, true elements in both Sturm’s and



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Schelhammer’s views and that it is possible to reconcile them by creating an alternative like his own, which combines the opposing positions and preserves the true contributions of both: If I am not mistaken, I have supplemented these things by new, more profound, and more general principles, from which there may sometime arise a restored and corrected system of philosophy, midway between the formal and the material, and combining and preserving them both. (NI §16; GP 4 516; W&F 222)

4.

The metaphysical link

In this section we wish to develop and expand our considerations on the relationship between the two cases presented in Sections 2 and 3. We believe the relation between the two cases of conciliation we have examined is not just one of coincidence or commonality (since both examples deal with the nature of Nature and the ways to explain it), but that there is a link between the two different methods used by Leibniz to reconcile opposites in scientific controversies. This link can be understood in terms of Leibniz’s fundamental ontological and semiotic classification of the main kinds of relation. In the first case, analyzed in Section 2, we referred to Leibniz’s Dialogus (1677) to account for his claim that both types of explanation, the one using efficient causes and the one using final causes, although differing in theory and in the way they mathematically express the path of light, are both ‘good’, in the sense that they correctly describe the way we perceive the reality of the light’s motion. In the second case, analyzed in Section 3, we saw how Leibniz suggests an alternative to two opposed positions, one representing the mechanistic world view, which claims that nature should be understood in purely mechanical terms, and the opposite one, which states that there is something non-mechanical about nature, be it a World Soul, a Spirit of Nature, or the like. The proposed alternative retains elements of both positions and unites them in a new theory. Here too, both positions are ‘good’, at least partly, but the conciliation goes beyond mere co-existence as good neighbors. We submit that each of the above cases corresponds to one of the basic kinds of relations identified by Leibniz, namely comparatio (‘comparison’) and connexio (‘connection’). We shall first introduce and exemplify these relations.30 Subsequently, we will propose an account of the difference between the two kinds of conciliation in terms of Leibniz’s typology of relations.

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Leibniz introduces the distinction between these two types of relation in the Nova Methodus (1667), in the context of an analysis of the relations underlying our use of signs, especially for mnemonic purposes: The foundation of mnemonics is a sensible thing called ‘note’, linked to the thing to be remembered by a certain relation. This relation can be either a relation of comparison – resemblance or dissemblance – or of connection, as the relation between whole and part, part and co-part, cause and effect, sign and signified. Hence words were invented, for otherwise it would be very difficult for humans to remember things. (A VI 1 277–278)

This semiotic-based distinction soon becomes for him, however, a general, ontological distinction between two fundamental types of relation: “A relation of a thing to another is either of convenientia (‘agreement’) or of connexio (‘connection’)” (C 434).31 It is also a fundamental classification of basic relations for later thinkers, who were not familiar with Leibniz’s distinction (see Dascal 1978: 109ff.). In addition to the examples quoted above, Leibniz mentions as examples of comparison the relations of identity, difference, opposition (of genus to species, of universal to particular), and of analogy; and as examples of connection the relations of order, one, multiple, necessity, contingence, circumstances (place, time, situation), environment, possessor-possessed, etc. Furthermore, metaphor is considered as typically based on relations of the first kind, and metonymy, of the second. The relation of comparison establishes a link between things belonging to different domains, without direct contact or dependence. From this viewpoint, it involves things that are conceptually and/or ontologically ‘distant’. The link thus established by the relation is therefore abstract in nature, even though it creates some commonality between the relata or highlights some latent, pre-existing commonality between them. It is easy to see why a metaphor such as ‘She is in the sky’, said of an absent-minded person, typifies this kind of relation. The relation of connection links things that usually belong to the same domain. The link consists in some form of direct contact, co-presence, contiguity, or dependence. The occurrence of an effect depends on that of its cause and the latter actual causation of the former; positioning a thing in some location requires their contiguity; isolating a part presumes that it can be detached from the whole of which it is a part; and so on. It is not difficult to see why a metonymy like “The White House informed that President Obama will not visit Teheran” is based on a connection relation. Let us now turn to the application of this distinction to the two cases of conciliation discussed in this paper. The relation of connection fits the second conciliation approach – integrating the opposites. As we have seen, this approach



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creates a middle-of-the-way alternative between polarized positions that were held as incompatible. The alternative, which results from de-dichotomizing this polarity, generates a space where elements of the opposed positions are in close contact and interact. It thus establishes a connection relation (other than mere opposition) between domains once separated by the abyss of alleged contradiction, which are now linked by a hybrid mediator – Leibniz’s contact generating concept of ‘inherent force’. The relation of comparison, on the other hand, fits the first conciliation approach – the disjunctive approach. In this case, Leibniz accepted both positions, that is, both types of scientific explanation, as being useful, albeit for different reasons. These types of explanation have altogether different foundations, which they keep; one is based on efficient causes, the other on final causes. However, they both reflect reality (or our perception of reality). They have nothing in common other than being two (correct) descriptions or reflections of nature. The relation between these descriptions is a relation of expression, which is essential to both Leibnizian semiotics and metaphysics, as we have seen. The conciliation this relation engenders is not based on the creation of connective links (causality, dependence, part-whole, etc.), but rather of comparative links of agreement and harmony. Ultimately, both approaches to conciliation this paper discloses are, for Leibniz, not only legitimate and useful, but also metaphysically and epistemologically necessary. And both turn out to be grounded in different aspects of his metaphysics, for the two fundamental types of relation on which they are based have the same metaphysical source. The relational structure of a universe composed of ‘windowless’ monads that do not act upon each other cannot but be a network of comparative relations. Yet, each monad’s never resting ‘inherent activity’, which continuously represents, from its particular point of view, all its counterparts, cannot but imply a tight, intimately organized dynamic universe, where everything is in fact in as close contact as possible with everything else, i.e., in a rich network of connective relations. From an epistemological point of view, it is mandatory for us humans to take advantage of the richness of this double relational network for getting to know as much as we can about the universe. Instead of being a handicap, the multiplicity of monadic perspectives is an epistemic asset, for it is through trying to put ourselves in the place or perspective of the other (DA 163–166) – as many others as we can – that we overcome the limitations of our own particular perspective. Just as monads cannot collide physically, strictly speaking their mental contents do not clash except apparently. Under close scrutiny, there is always some worthwhile truth in every position, so that conciliation, rather than conflict, is the strategy to

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be followed in controversy. And no thread made available to us by any network of relations should be neglected in our ‘multi-perspectival’ endeavor to know, since [a] multi-perspectival system, a network-like structure that highlights these multiple representations of reality and their ‘liaisons’, seems also to correspond closer, analogically, to the reality it is supposed to represent – and Leibniz, as is well-known, attaches much importance to such analogical correspondences.  (Dascal 2000: 24)

The analogy can be extended to the apparent clash between the two kinds of scientific explanation – the one based on efficient causation, the other on final causation – discussed in this paper. Just as different points of view expose different aspects of the ‘same’ phenomenon, so too the different mathematical descriptions of the motion of light, which are based on different principles or ways of understanding nature, expose different facets of the ‘same’ phenomenon, namely, of the motion of light. As Leibniz says, “both explanations are good; both are useful … for the discovery of useful facts in physics and medicine”. Both are good because both represent correctly, from their perspectives, the phenomenon they aim to describe, both use mathematical symbols to express and predict it, both correspond analogically to the variety of perspectives, which ultimately reveal nothing but aspects of a single universe. Moreover, there is another important benefit of multi-perspectivism, namely, that “it is through the comparison of the different monadic perspectives that we can discover order, invariance, lawfulness, and, ultimately, truth and unity” (Dascal 2000: 30).

5.

A final note

Leibniz’s view concerning the use of final causes in physics has since been developed extensively by many able mathematicians and physicists. Variational calculus, developed by Leonard Euler and Joseph-Louis Lagrange during the 18th century, is an example of a mathematical extension of principles such as Fermat’s. These types of principles are said to be “mathematical expressions of final cause” (Lemons 1997: 13). The principle of least action, first explicitly stated by Pierre Louis Moreau de Maupertuis, 32 and later perfected and reformulated by Carl Gustav Jacobi and Sir William Hamilton during the 19th century, is another good example. Both examples provide a mathematical basis for alternative formulations of contemporary physical theories such as classical and quantum mechanics, general relativity theory, quantum field theory, and particle physics. Consequently, one may conclude that most contemporary physical theories can be expressed



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using at least two different mathematical descriptions or, in other words, using two different sets of symbols (mathematical notations). Although the first case we presented in this paper discusses only optics and the second the question of whether the laws of nature are purely mechanic, the general implications of the issues we discussed is quite clear, and suggests that Leibniz had in mind a broader, universal interpretation of the principles involved in understanding nature and expressing its workings. That this is the case is well manifested in the following words, which are fit to conclude this article: I usually say that there are, so to speak, two kingdoms even in corporeal nature, which interpenetrate without confusing or interfering with each other – the realm of power, according to which everything can be explained mechanically by efficient causes when we have sufficiently penetrated into its interior, and the realm of wisdom, according to which everything can be explained architectonically, so to speak, or by final causes, when we understand its ways sufficiently.  (TA; GP 7 273; L 478–479)

Notes 1. Among Leibniz’s texts having to do with religious controversies, see his Methods of reunion (DA 247–262) and Controversies on sacred matters (DA 40–56), as well as Examen Religionis Christianae (A VI 4 2355–245); this last text is commented in Dascal (2003). 2. “A reconciliation of two methods of explanation, one of which proceeds by final causes, the other by efficient causes; to satisfy both those who explain nature mechanically as well as those who have recourse to incorporeal natures” (Title of DM §22; A VI 4 1564; L 317). 3. See Physics II. 2, 3, 7. 4. Regarding the use of different kinds of explanations under different conditions, Aristotle also claimed that “It is the job of the natural scientist, then, to understand all four of these causes; if he refers the question ‘Why?’ to this set of four causes – matter, form, source of change, purpose – he will be explaining things in the way a natural scientist should” (Aristotle 1996: 49, Physics II. 7 198a21). 5. It is worth noticing that Feyerabend’s ‘opportunistic’ account of the history of science does not exclude the parallel and concomitant recourse to different kinds of explanatory conceptual tools that both Aristotle and Leibniz suggest: “is it not clear that successful participation in a process of this kind [historical] is possible only for a ruthless opportunist who is not tied to any particular philosophy and who adopts whatever procedure seems to fit the occasion?” (Feyerabend 1978: 18). 6. “For it seems to me very likely that those greatest geometers Snell and Fermat – most well versed in the geometry of the ancients – extended the method that they had used in Catoptrics to Dioptrics. Indeed, I suspect that Snell’s theorem … was discovered by almost the same method” (UP; D 3 146).

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7. Snellius was the first to formulate this law mathematically in 1621, but his work was published only after Descartes had independently published it in 1637, in the Discourse on Method. Rejecting Descartes’s solution, Pierre de Fermat arrived at the same solution based solely on his principle of least time. This principle asserts that the path taken between two points by a ray of light is the path that can be traversed in the least time; the connection to the method of final causes is evident. See Goldstine (1980: 1–6). 8. “When dealing with natural things we will, then, never derive any explanations from the purposes which God or nature may have had in view when creating them ” (PoP I 28). 9. Since this part of the paper deals with the wide-scale rejection of final causation among Leibniz’s contemporaries, and the intellectual courage it took to stand against such rejection, it is worth recalling that Huygens was not only a prominent mathematician, astronomer, and physicist, but also Leibniz’s mathematics teacher in Paris. 10. For a discussion of dichotomies as used in controversies, see Dascal (2008). 11. As mentioned previously, Snellius had applied methods of final causation to discover his law of refraction. 12. A unitary principle, as the title of the paper suggests. 13. This can be compared with Fermat’s principle, or the principle of least time, which is the idea that the path taken between two points by a ray of light is the path that can be traversed in the least time. See Goldstine (1980: 1–6). 14. Also known as the coefficients of refraction, these coefficients receive a value proportionate to the density of the medium, i.e., the denser the medium the bigger their value: nvacuum = 1, nair = 1.0003, nwater = 1.33. 15. The method of minima and maxima is actually a method for finding a stationary point, i.e., differentiating and equating to zero (TA; GP 7 274–275; L 480). 16. Buchdahl (1969: 429n) considers Leibniz’s motive for agreeing with Descartes as ‘technical’. Descartes’s ‘particle-model’, he claims, “enables Leibniz to show, relying upon considerations from the theory of vis viva, that the velocity of light is proportional to the ‘resistance’ of the medium”. 17. The proportion is between the ratios of the sine of the angle of incidence to the sine of the angle of refraction and of the velocity of the ray of incidence to the velocity of the ray of refraction. 18. “[T]anta est utrobique multitudo & difficultas, cui superandae ne secula quidem multa, nedum unius hominis aevum aut ingenium, unquam suffecerit” (Sturm 1697: Chap. II, §3). 19. This reliance on a single source is in contrast with the multi-perspectivism and cooperative nature of eclecticism. At least regarding scientific cooperation, Sturm, like Leibniz, the founder of academies and initiator of cooperative scientific projects such as the encyclopedia, stressed the collective nature of scientific work. 20. It was thanks to Conring that Leibniz obtained a position in Hanover and returned from France to Germany. 21. “At hic acerrimum, maximeque formidabilem adversarium invenimus, Robertum Boyle, cuius viri tanta est auctoritas atque existimatio, ut inclinare qua vellit animus hominum, sola accessione nominis posse vediatur” (‘But here we find a very sharp and most formidable ad-



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versary, Robert Boyle, whose authority and prestige are so great that the mere mention of his name can incline the mind of men to whatever direction’; Schelhammer 1697; quoted in Palaia 2008: 435). 22. He was aware of the recent rounds of the unresolved debate he was engaging in, namely: 1. Descartes vs. Henry More regarding More’s ‘Spirit of Nature’, which Descartes believed to be superfluous and detrimental. 2. Boyle vs. the Cambridge Platonists, especially Henry More, whom Boyle censured for misinterpreting his experiments in order to endorse his ‘Spirit of Nature’ hypothesis. 3. Sturm vs. Schelhammer, the round at which Leibniz explicitly enters the debate. Note that Leibniz’s initial words for the title of his intervention echoes those of Boyle’s (1688), as if saying: I agree with Boyle, but there is more to this story. 23. Usually, in the context of a controversy, when a contender declares that he is about to present the problem to be discussed, or as Leibniz says in this passage, “set out more clearly my opinion, and the whole issue”, he in fact intends to present the problem in such a way as to fit his soon to be presented solution. However, we must recall that Leibniz enters this debate as a conciliator rather than a contender. His aim is not to place himself at one pole of the dichotomy or the other, but to seek a viable alternative to both. This he proposes to do by setting out the whole issue in light of his argumentative and explanatory principles, which will be presented in what follows. 24. See Dascal (2008) for a definition and explanation of this term. 25. Avicenna’s Cholcodea Panto-Morphe refers to the goddess of Cholchis who gives form to all things. 26. He also doesn’t spare the expression of his admiration for Schelhammer’s scholarship. For instance, referring to the notion of ‘lex insita’ (inherent law), an expression he attributes to Schelhammer, he makes a point of saying: “as M. Schelhammer, who is as distinguished in his judgment as he is in his experiments, nicely puts it” (NI §5; GP 4 507; W&F 212). 27. The young Leibniz already stresses the importance of clarity in his definitions of truth and certainty: “certainty is the clarity of truth” (A VI 2 493), “true is that which is clearly and distinctly sensible (that which can be perceived)” (ibid.). See Dascal (1978: 84–86) for a discussion of these definitions. It is worth noting that the Principle of Clarity has been adopted by 20th century analytic philosophers as the essential criterion for ‘rational philosophical discussion’ (cf. Bar-Hillel 1967). 28. This general principle is explicitly applied by Leibniz to the “principle of reduction of arbitrariness”, closely associated to his “law of expression”, both of which concern the creation and choice of the best possible semiotic systems (see Dascal 1978: 147–149, 215–216). See also Section 2.4 above. 29. ‘Defence’ is Woodfield and Franck’s abbreviation for the long title of Sturm’s (1698) reaction to Schelhammer (1697). Leibniz referred to the same writing as “Dissertatio Apologetica”. 30. For a more detailed discussion, see Dascal (1978: 104–109). 31. We make use here of the terms comparatio and connection as in the Nova Methodus quotation (also used in C 355), though Leibniz employs also other terms, roughly synonymous, to refer to the same distinction, as in the present quotation. 32. The discussion about the priority of formulation of the principle of least action has not yet been settled. See Yourgrau and Mandelstam (1979: 22–23).

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References Ahnert, T. 2002. The Culture of Experimentalism in the Holy Roman Empire: Johann Christoph Sturm (1635–1703) and the Collegium Experimentale. Unpublished Abstract: http:// sammelpunkt.philo.at:8080/308/ Aristotle. 1996. Physics. Trans. R. Waterfield. Intro. and notes D. Bostock. Oxford: Oxford University Press. Bar-Hillel, Y. 1967. “A prerequisite for rational philosophical discussion”. In R. Rorty (ed), The Linguistic Turn: Recent Essays in Philosophical Method. Chicago: The University of Chicago Press, 356–359. Boudri, J. C. 2002. What was Mechanical about Mechanics. Trans. S. McGlinn. Dordrecht: Kluwer. Boyle, R. 1686/1996. A Free Inquiry into the Vulgarly Received Notion of Nature. E. B. Davis and M. Hunter (eds). Cambridge: Cambridge University Press. Boyle, R. 1688. De Ipsa Natura, sive Libera in Receptam Natura Notionem Diquisitio ad Amicum. Geneva: S. de Tovrnes. [Latin version of Boyle 1686] Buchdahl, G. 1969. Metaphysics and Philosophy of Science. Oxford: Blackwell. Dascal, M. 1978. La sémiologie de Leibniz. Paris: Aubier-Montaigue. Dascal, M. 1998. “Language in the mind’s house”. Leibniz Society Review 8: 1–25. Dascal, M. 2000. “Leibniz and epistemological diversity”. In A. Lamarra and R. Palaia (eds), Unità e Molteplicità nel Pensiero Filosofico e Scientifico di Leibniz (Simposio Internazionale, Roma 1996). Firenze: Leo S. Olschki Editore, 15–37. Dascal, M. 2003. “Ex pluribus unum? Patterns in 522+ Texts of Leibniz’s Sämtliche Schriften und Briefe, Reihe VI, Band 4”. The Leibniz Review 13: 105–154. Dascal, M. 2008. “Dichotomies and types of debate”. In F. H. van Emeren and B. Garssen (eds), Controversy and Confrontation. Amsterdam: John Benjamins, 27–49. Descartes, R. 1644. Principles of Philosophy. In The Philosophical Writings of Descartes. J. Cottingham, R. Stoothoff, and D. Murdoch (trans). Cambridge: Cambridge University Press, 1985. [= PoP] Descartes, R. 1664. Treatise of Man. French text with translation and commentary by T. S. Hall. Cambridge, MA: Harvard University Press, 1972. Dijksterhuis, E. J. 1961. The Mechanization of the World Picture. Oxford: Clarendon Press. Feyerabend, P. 1978. Against Method: Outline of an Anarchistic Theory of Knowledge. London: Verso. Goldstine, H. 1980. A History of the Calculus of Variations from the 17th through the 19th Century. New York: Springer. Hobbes, T. 1651. Leviathan. Intro. and notes R. Tuck (ed). Cambridge: Cambridge University Press, 1991. Huygens, C. 1690. Treatise on Light. Trans. S. Thompson. New York: Dover, 1962. Leibniz, G. W. 1667. Nova Methodus discendae docendaeque Jurisprudentiae. A VI 1 259–364. Leibniz, G. W. 1677. Dialogus. A VI 4 20–25; L 182–185. [= DI] Leibniz, G. W. 1682. Unicum Opticae, Catoptricae, et Dioptricae Principium. D 3 145–150. Trans. J. K. McDonough. [= UP] http://philosophy.ucsd.edu/faculty/rutherford/Leibniz/ unitary-principle.htm



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Leibniz, G. W. 1683. De synthesi et analysi universali seu arte inveniendi et judicandi. A VI 4 538–549. In M. Morris and G. H. R. Parkinson (eds). 1973. Philosophical Writings. London: J.M. Dent and Sons, 10–17. Leibniz, G. W. 1686. Discours de Métaphysique. A VI 4 1529–1588; L 303–330. [= DM] Leibniz, G. W. 1695. Specimen Dynamicum. GM 6 234–254; L 435–452. Leibniz, G. W. 1696. Tentamen Anagogicum. Essay Anagogique dans la recherche des causes. GP 7 270–279; L 477–485. Leibniz, G. W. 1698. De ipsa natura sive de vi insita actionibusque Creaturarum, pro Dynamicis suis confirmandis illustrandisque. GP 4 504–516; W&F 209–222. [= NI] Lemons, D. S. 1997. Perfect Form: Variational Principles, Methods, and Applications in Elementary Physics. Princeton, NJ: Princeton University Press. Palaia, R. 2008. “Natura e filosofia della natura nel dibattito filosofico Tedesco”. In D. Giovannozzi and M Veneziani (eds), Natura (Colloquio Internazionale, Roma 2007). Firenze: Leo S. Olschki, 425–438. Schelhammer, G. C. 1697. Natura sibi et medicis vindicate sive de natura liber bipartitus. Kiel. Spinoza, B. 1677/1982. The Ethics. Trans. S. Shirley, Edited with Intro. S. Feldman. Indianapolis, IN: Hackett Publishing Company. Sturm, J. C. 1692. Idolum Naturae similiumque nominum vanorum ex hominum Christianorum animis deturbandi conatus philosophicus, sive de natura agentis tum universalist um particularis aliorumque cognatorum quasi Numinum supestitiosis erroneisque conceptibus Dissertatio. Altorf/Nüremberg: Henrici Meteri. Sturm, J. C. 1697. Physica Electiva sive Hypothetica. Nürenberg. Reprinted: Olms, Hildesheim, 2006. Sturm, J. C. 1698. De natura sibi in cassum vindicate, qua sentential nostra de Naturae, providentissime utique, et efficacia Divinae Virtuti contradistincta, universaliter et particulariter agentis idolo ab ignorationibus elenchi perpetuis Viri Doctissimi, mentem nostrum haud assecuti, modeste vindicator. Wilson, C. 1987. “De Ipsa Natura, Sources of Leibniz’s Doctrines of Force, Activity and Natural Law”. Studia Leibnitiana 19(2): 148–172. Yourgrau, W. and Mandelstam, S. 1979. Variational Principles in Dynamics and Quantum Theory, 3rd edition. New York: Dover.

chapter 7

Leibniz vs. Lamy How does confused perception unite  soul and body?* Andreas Blank

1.

Introduction

In a well-known passage from the mid-1680s, Leibniz claims that what is real in bodies is only the force of acting and suffering and that, therefore, the “substance of a body consists in this, as if in matter and form” (De modo distinguendi phaenomena realia ab imaginariis summer 1683 – winter 1685/86; A VI 4 1504). Moreover, he there explains that substances “have metaphysical matter or passive potency insofar as they express something confusedly, and active potency, insofar as they express something distinctly” (ibid.). As Pauline Phemister has pointed out, such a version of hylemorphism is no longer essentially Aristotelian (Phemister 2001: 79, note 41). Accordingly, she ascribes to Leibniz the view that a simple substance qua possessor of primitive active and passive force “is also, when created” a corporeal substance, because the extension of its organic body is, “to a large extent”, a modification of its primitive passive force (Phemister 1999: 72–74). The issue of primitive passive forces also bears on the role of the so-called “confusion theory of body”. Justin Smith has recently indicated some parallels between Leibniz’s use of the idea of confused perception as an explanation for the origins of “secondary matter” and the role of confused perception in the neo-Platonic emanation schemes developed by Plotinus and Nicholas of Cusa (Smith 2003: 49–56). According to his interpretation, confused perception, for Leibniz as for Plotinus and Nicholas, has the function to explain the particularity, multiplicity, and imperfection of created minds (Plotinus 1998: VI 6, 1; VI 9, 2; VI 9, 4; Nicholas 1988: 15). Moreover, Smith aligns Leibniz’s view of confused perception with Nicholas’s claim that substances are simple and composite at the same time, because the body is the “unfolding of the soul” (Smith 2003: 52; Nicholas 1988: 27).

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The purpose of the present paper is to argue that Leibniz’s small but significant controversy with the French Occasionalist philosopher François Lamy points to a more complex interpretation of the structure of corporeal substances.1 In his response to a long review of the first edition of Lamy’s De la Conoissance de soi-même, as well as in his reply to Lamy’s explicit critique of the system of preestablished harmony in the second edition of the same work, Leibniz defends a conciliatory approach to the issue of corporeal substances. His approach tries to combine Aristotelian, Cartesian, and neo-Platonic aspects rather than to reduce the theory of corporeal substance to ideas stemming from one of these traditions. In a broadly Aristotelian perspective, he objects to Lamy that the scholastic theory, according to which soul and body are, in some sense, incomplete without each other, should not be rejected. In particular, confused perception for Leibniz plays a decisive role in explaining why souls could not have the qualities they have without the qualities of their bodies, and vice versa. In a broadly Cartesian perspective, he agrees with Lamy’s claim that confused perceptions play a decisive role in the explanation of the union of soul and body. In particular, in a way similar to Lamy, Leibniz assigns to souls a location in their bodies on the basis of the functional dependence between confused perceptions and bodily traces. These Aristotelian and Cartesian components modify a neo-Platonic view of confused perceptions as the origin of the imperfection and materiality of individual objects: because the qualitative side of souls and bodies are incomplete without each other, and because bodily traces and confused perceptions are functionally dependent on each other, an organic body can never be the modification of the passive aspects of a single simple substance only (or mainly). Section 2 of the present paper uses the issues of confused perception and incomplete entities to illustrate how a conciliatory strategy shapes Leibniz’s responses to Lamy. The two subsequent sections argue that the strategy pursued in the controversy with Lamy has parallels both in Leibniz’s early philosophy and in writings from his last years. Section 3 situates the development of Leibniz’s view of the relation of soul and body in the field of theoretical options emerging from the controversy over the nature of the co-extension of soul and body in early modern Aristotelianism. Section 4 outlines some of the ways in which Leibniz’s controversy with Lamy has influenced the former’s later correspondence with the French Platonist Nicholas Rémond.

2.

Lamy vs. Leibniz on incomplete entities and confused perception

In the parts of De la Conoissance de soi-même that attracted Leibniz’s interest, Lamy is concerned with issues that are close to issues that are of importance for



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Leibniz’s metaphysics, in particular the problem of how soul and body are united, what role confused perception plays in this context, and in which sense souls can be assigned a place in their bodies. Leibniz’s response to an extended review of the first edition of Lamy’s work in the Journal des Sçavans of 1698 is an interesting combination of critical remarks and remarks that emphasize the defensible aspects of Lamy’s view of the union of soul and body. Interestingly, Leibniz’s critical remarks rather concern Lamy’s attempt to exclude an Aristotelian aspect from the theory of living beings, whereas his affirmative statements concern what he regarded to be tenable in a broadly Occasionalist theory of the relation of soul and body. To put it paradoxically: in his response to Lamy Leibniz uses techniques of controversy not so much to exclude theoretical options but rather to defend a conciliatory approach to the problem of composite entities. This use of controversy as a tool of a conciliatory approach can perhaps most impressively be observed in Leibniz’s response to Lamy’s view that the Scholastic theory of soul and body as incomplete entities should be thrown overboard. The review in the Journal des Sçavans puts Lamy’s view thus: He regards it as chimerical to pretend as they do [sc. the Scholastic philosophers] that the mind & the body are incomplete beings that have a natural & essential relation to each other. … That one suggests that they are incomplete is not more reasonable, if by this one pretends that the mind would not have all that is needed for being a true thinking substance independently of the body, or that the body would not have independently of the mind all that is needed to be a true human body. (Journal des Sçavans 26 (1698): 664)

Leibniz’s most decisive attack is not directed against Lamy’s Occasionalism but rather against this rejection of an Aristotelian theory of composite substances: The opinion of the Scholastics that soul and matter have something incomplete is not as absurd as one thinks. Because matter without souls and forms or entelechies is nothing but passive, and souls without matter would be nothing but active: the complete corporeal Substance, truly one, which the Scholastics call Unum per se (in contrast to entities by means of aggregation), as it must result from the principle of unity which is active, and from the mass that makes the multitude and which would be solely passive, if it would contain nothing but prime matter. Instead, the secondary matter or mass that makes our body has everywhere parts, which are complete substances themselves, because they are other animals or organic substances, animated or actuated separately. But the collection of these organized corporeal substances that constitutes our body is not united with our soul but through a relation that follows from the order of natural phenomena for each substance separately. And all this makes visible how on the one hand, one can say that the soul and the body are independent from

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each other, and on the other hand, that each of them is incomplete without the other, because naturally the one is never without the other. (Addition à l’Explication du système nouveau touchant l’union de l’ame et du corps, envoyee à Paris à l’occasion d’un livre intitule Conoissance de soi-même. GP 4 572–573)

As I have argued elsewhere (Blank 2003), the successive manuscript versions of this passage as well as passages from the contemporary correspondence with Johann Bernoulli suggest that what Leibniz has in mind here is not the incompleteness of active and passive aspects internal to a simple substance but rather the incompleteness of a given portion of passive mass without an active simple substance (ibid.: 7–9). Nevertheless, Leibniz’s emphasis on the role of the passive aspects of souls for the union of soul and body has close parallels in Lamy’s view of the role of confused perception. This explains why in the remainder of his reply, Leibniz tries to make clear to which extent he agrees with aspects of Lamy’s Occasionalism rather than to refute the theory as a whole. The Journal des Sçavans renders Lamy’s view of the union of soul and body as follows: This strategy to establish in the confused perceptions the union of the mind and the body, & to make known to the mind the needs of the body, & the relations the surrounding bodies have to it, appears to be the most wise to our philosopher.  (Journal des Sçavans 26 (1698): 669)

To support this claim, Lamy argues that to know clearly and distinctly the infinite relations the surrounding bodies have to mine would require a constant effort of the mind, whereas the “bare sensation of pain or bitterness, of pleasure or discontent, is a proof that is short & secure alike” (ibid.: 670). Moreover, he thinks that sensible qualities cannot be modifications of extension and, therefore, must be modifications of the mind. At the same time, Lamy’s account of the nature of the union of soul and body also has aspects that diverge strongly from Leibniz’s. For example, from the idea that sensible qualities are modifications of the mind Lamy draws the conclusion that bodies cannot have any similarities to the sensations they give us (ibid.: 672). In particular, this implies that they also cannot have any similarity to the bodily traces they are associated with: These ideas do not have any resemblance to the traces from which they result. Also, it is not at all by means of consulting these kinds of phantoms that the soul forms its ideas. The soul finds all of them formed, & God presents them to the soul as it pleases him on the occasion of the excitation of these traces. I say, as it pleases him: because although God always constantly follows the order he has established once and for all; this establishment has been so free for him, that he would have been able to make a completely different one, & e.g. attach



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the sensation of taste to the trace that results in the brain on the occasion of the excitation of the ear …  (ibid.: 674)

Lamy further explicates this view by claiming that the connection of ideas with traces, although free for God, for us is nevertheless natural and necessary, and that, in addition to these connections, we have free ones, which he calls “acquired connections” (ibid.). Finally, he holds the view that the connections between traces explain the connections between ideas: The connection the traces have among themselves consists in the easiness with which they can be mutually retraced, that is to say in case they have been formed at the same time in the brain, it is practically impossible to retrace the ones without the others, because finding open channels of communication between them, the spirits that have retraced one of them, can more easily continue their path in the routes which lead them to all the other routes than make new ones for themselves. So that, because there is a connection between the ideas of these traces, in the same way as between traces, the renewing of one single idea of a long scene is capable to recall the ideas of all the circumstances. (ibid.: 675)

Interestingly, in his response Leibniz tries to accommodate as many as possible of Lamy’s views. Most importantly, he accepts Lamy’s basic idea about the role of confused perception for the union of soul and body: Ordinarily, one conceives of confused thoughts as a kind completely different from distinct thoughts, and our author judges that the mind is more united with the body through confused thoughts than through distinct ones. (GP 4 574)

At this place, Leibniz gives to this idea a turn, which integrates it into the neo­ latonic view of confused perception as the origin of imperfection and parti­ P cularity: This is not without foundation, because the confused thoughts mark our imperfection, our passions, and our dependence on the collection of external things or on matter, whereas the perfection, force, power, liberty and action of the soul consist primarily in our distinct thoughts. (ibid.)

Moreover, Leibniz tries to reconcile Lamy’s insight concerning the role of confused perception with a not specifically Occasionalist view of Divine causation. As Leibniz points out, if expressing the states of its own body is constitutive for the soul, then even from the point of view of Divine action soul and body are naturally non-separable:

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It is true that God does not need the body, absolutely speaking, to give the soul the sensations it has, but God needs it to act in the order of nature she has established, having given to the soul and once and for all this force or tendency which causes it to express its body. (GP 4 574)

For this reason, Leibniz accepts a version of a theory of emanative causation that explains the ultimate origin of minds and sensations without assuming an immediate Divine intervention: “One agrees that these sensations cannot come originally but from God, but not immediately, except in this general manner, in which all realities emanate continually from God” (ibid.: 573). Finally, another respect in which Leibniz attempts to accommodate Lamy’s view of the relation of soul and body within the framework of his own ontology is the issue of the location of the soul. Lamy puts forth the thesis that the soul has a location only in the sense that there are parts of the body in which it immediately performs its functions. The review in the Journal des Sçavans renders it thus: He begins by remarking that the soul, because it has no extension, there can be no way to find a local residence for it; that it is neither out of nor in the body; that exactly speaking, the minds are nowhere; & that it is only a question to know in which part of the body the soul performs its functions. He pretends that this is particularly in the part of the brain, which is the source of the nerves. It is there where like in its seat it gives its orders to all the parts of the body, & where through intermission of nerves reaching out from there to the most remote parts of the body, it receives in an instant news of all that there happens. (Journal des Sçavans 26 (1698): 667–668)

Leibniz basically accepts the claim that the soul is located by means of the functional dependence of bodily states on the states of the soul, only adding an important qualification: “It seems also more exact to say that the spirits are where they operate immediately, rather than to say, as one does here, that they are nowhere” (GP 4 574). The real disagreements with Lamy concern issues that have to do with the rejection of the Scholastic theory of incomplete entities. Contrary to Lamy, Leibniz defends the view that both with respect to distinct thoughts and to confused perceptions, the states of the soul depend on the states of its body. With respect to distinct thought, Leibniz rejects Lamy’s claim that abstract thoughts can occur independently of processes in the organic body: But it seems that the body senses also our abstract thought, and experience shows that the meditations are capable of hurting it: because the most abstract thoughts use always some signs, which touch the imagination, in addition to the attention which binds the fibers of the brain. (GP 4 574)



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With respect to confused perceptions, Leibniz rejects the view that there are no structural similarities between bodily states and sensations: These confused sensations are also not arbitrary, and one does not at all agree with the opinion accepted now by several thinkers, and followed by our author, according to which there is no resemblance or relation between our sensations and the bodily traces. It rather seems that our sensations represent and express them perfectly. Someone may perhaps say that the sensation of heat does not resemble movement: Yes, without doubt, it does not resemble a sensible movement, such as that of a driving coach, but it resembles the collection of small movements of fire and the organs which are the cause of the sensation, or rather the sensation is nothing but their representation. This is like how whiteness does not resemble a spherical convex mirror, though it is nothing but the collection of many small convex mirrors such as one sees in foam when one regards it from close up. (GP 4 576)

Thus, just as whiteness has the same internal structure as the light reflected from a collection of many small mirrors, sensations have the same internal structure as the movements they represent. In this way, by stressing the importance of structural similarities, Leibniz tries to revive the idea that there is a similarity between movements in the external world, in the traces of the sensory organs, and in the sensations. This is turn gives content to the idea that perceptions in the soul could not naturally be as they are independently of the processes in the sensory organs. Rather, their representative nature depends on the existence of structural resemblances between perceptions, processes in the sensory organs, and processes in the external world represented indirectly by means of processes in the sensory organs. And it is the dependence of the qualitative side of the soul on the qualitative side of the organic body that makes the essence of the soul an incomplete essence and the soul “something incomplete”. Similar considerations in favor of a conciliatory approach to the problem of composite substances play a role in Leibniz’s response to the explicit critique of the system of pre-established harmony in the second edition of Lamy’s De la Conoissance de soi-même (1699/1701).2 One of Lamy’s objections there is that simple substances either are made for each other, or they are not. In the first case, he argues, the theory of pre-established harmony coincides with the system of Occasionalism: because in this way God, on the occasion of the series of motions, which he has foreseen will take place to the body as a consequence of the laws of nature that he has given to it, has destined a different nature to the soul, from the laws of which must arise as many diverse thoughts to respond to the diverse movements of the body. All the difference there is, thus, between this system and the

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system of occasional causes, would be that God, when he follows the occasions of the modes of one of these two substances, produces immediately the impressions in the other: whereas in the new system, God produces these impressions only mediately by endowing these substances with virtues & forces appropriate to produce them from their own interior.  (Lamy 1701, Traité Second, Vol. II: 231–232; Leibniz Review 11 (2001): 81–82)

In the second case, Lamy argues, pre-established harmony would be a result of an arbitrary decision of God. Later in the text, he adds an argument that purports to speak against the system of pre-established harmony and in favor of the system of occasional causes: Because, e.g., when a man receives a blow; I wish that one would be able to say that it is not due to this blow, nor on its occasion that the soul senses pain; but as a consequence of its own laws, it would have had the same sensation if there would have been only God and it; however, can one in the same way say, when a man gets mad, that this is not due to the reversal which takes place in his brain that his mind gets extravagant? (Lamy 1701, Vol. II: 236; Leibniz Review 11 (2001): 86)

Leibniz’s response to the second edition of Lamy’s work, dated November 30th 1702, is to a large extent concerned with what Leibniz perceives as outright misunderstandings on Lamy’s part. This renders his response less illuminating than, e.g., his contemporary replies to Pierre Bayle’s Dictionnaire Critique. Nevertheless, there are some passages that are of interest for the present issues. At the beginning of his response, Leibniz puts forth the claim that the union of soul and body is distinguished from the universal harmony among all substances only by a difference in the degrees of indirectness of representation: I respond that there is no room for doubt about which side I would choose, and that I have already declared myself in favor of the first one: therefore, one should not see any difficulty here, because it seems that one agrees that the difficulty disappears in case my system cannot accommodate what it does not have in common with the system of occasional causes. Because I hold that not only the soul and the body, but also all the other created substances of the universe are made for each other, and express themselves mutually, although one relates itself more or less mediately to the other according to the degree of the relation. (GP 4 578)

Moreover, later in the text he repeats his constitutivity thesis, according to which the expression of the body is constitutive of the soul: “I respond that I can quite well say that the soul gets extravagant because of the body, as in the other systems, because its nature is to express its body, and to be in accord with it …” (GP 4 580). Seen on the background of the claim that soul and body are related to each other only by means of a less indirect way of representation than other substances in the



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world, this thesis involves two aspects: First, it shares with Lamy’s theory of the relation of soul and body the view that everything that can explains the union of soul and body is a matter of functional dependence. Second, in contrast to Lamy’s view, it emphasizes the fact that functional dependence at the same time involves interdependence on the qualitative side. In this way, the response to the second edition of De la Conoissance de soi-même once more indicates that it is the constitutive role of the expression of bodies in souls that motivates Leibniz’s re-appraisal of the Scholastic theory of incomplete entities.

3. Leibniz and the controversy over the co-extension of soul and body in early modern Aristotelianism The idea of the incompleteness of soul and matter is well documented in Leibniz’s writings between 1698 and 1704.3 Nevertheless, although Leibniz uses the Scholastic term “unum per se” in several earlier writings (e.g., A VI 1 503–505; A VI 3 513; A VI 4 401), the idea of incomplete entities does not occur before the controversy with Lamy. Moreover, after 1704 the theory of incomplete entities seems to disappear again. Thus, it looks as if the idea of incomplete entities is not well integrated into Leibniz’s philosophical development. However, this impression is misleading, as this and the following section will argue. The present section backs up a continuity thesis by placing some of Leibniz’s early statements about the union of the soul and the body in the context of the controversy about the nature of co-extension of soul and body in early modern Aristotelianism, in particular in the work of Julius Caesar Scaliger, Fortunio Liceti, and Daniel Sennert. In a letter to Jakob Thomasius dating from 1669, Leibniz mentions both  Scaliger and Sennert as predecessors in a tradition that attempts to reconcile Aristotelian philosophy of nature with modern mechanism – a tradition in which Leibniz explicitly locates his own early metaphysics of nature. In particular, he mentions Scaliger and Sennert’s efforts to formulate a theory of animal generation that at the same time incorporates components stemming from Aristotelian and corpuscularian views of corporeal substances.4 It is true that there is no evidence that Leibniz had first-hand acquaintance with Liceti’s writings on the structure of living beings. However, in the fourth part of the Physical Remarks (1636) Sennert discusses Liceti’s views in extensive detail. Although it therefore seems plausible to assume that Leibniz was aware of the outlines of Liceti’s theory, nothing depends on this point for the present purpose. The aim of this section is not to establish textual links, but rather to make clear some of the theoretical alternatives available within the framework of mechanistic Aristotelianism, and to place Leibniz’s early views on the union of soul and body in the context of

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these alternatives. Moreover, following this interpretive approach shows the way Leibniz’s Aristotelianism modifies his Platonist learnings early on. In On the Co-extension of Souls and the Body (1616), Liceti bases his view of the location of vegetative souls on a version of a mechanistic interpretation of Aristotle’s theory of the operation of souls: That it is co-extensive with the whole body of herbs, and not contained in a single part only …, first of all is taught by nutrition; for necessarily the substance of the soul is where the operation is displayed, of which the soul is the primary efficient cause; since for Aristotle there cannot happen any operation or motion without the primary agent, and in the presence of the primary agent; because all physical action is by contact;5 but as the nutrition of a herb is an action, & a physical mutation, which proceeds from the vegetative soul, like from a principle, by means of which first of all the plant is nourished: and as everything that is nourished, according to Aristotle’s observation, is nourished with respect to even the smallest part of its body … it is necessary to confess that the vegetative soul of plants is not contained in only a part of the herb, but diffused everywhere throughout the whole body …  (Liceti 1616: 2)

Liceti develops analogous arguments for the sensitive soul dominating the vegetative soul (ibid.: 24), and for the rational soul dominating the sensitive soul (ibid.: 27). Moreover, he understands the idea of an action by contiguity and contact as a mechanistic reformulation of the idea that the soul is the formal cause of the body Liceti develops analogous arguments for the sensitive soul dominating the vegetative soul (ibid.: 4). Sennert explicitly rejects Liceti’s theory by taking up an idea formulated in Scaliger’s Exoteric Exercises (1557). According to Scaliger, souls of angels are “extended without a predicable quantity & are not moved by corporeal motions, but by the motion of an incorporeal extended thing, by changing the ‘where’” (Scaliger 1557: exercitatio 359, sect. 12). More generally, Scaliger writes, “The soul is not in a place, because it is not a quantity. Since a quantum cannot be in all parts of a quantum as a whole. But the soul is in each part of the body, which is a quantum” (ibid.: exercitatio 309, sect. 13). Sennert’s theory of the co-extension of soul and body can be understood as an explication of this view: “the form & soul per se is not a quantum, & and therefore it fills out & penetrates the whole body, it is per se indivisible, but nevertheless without quantity is co-extensive with the body” (Sennert 1676: 132–133). Therefore, Sennert compares the relation of souls to place with the relation of rays of light to space: also the presence of one ray of light does not impede the presence of a different ray of light at the same place at the same time, and an analogous observation can be made with respect to shadows. He also compares the relation of souls to place with that sensible species have to place:



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not only can more than one sensible species occupy the same place at the same time as other sensible species. They also can be at the same time in the minds of different perceivers; in this sense they can be at different places at the same time, and, in addition, have the capacity to multiply themselves (ibid.: 133). Moreover, Sennert takes up Scaliger’s view according to which the soul is extended without a predicable quantity: Here one has to distinguish between extension in the proper sense; & extension understood only analogously. Extension in the proper sense belongs to quantity & and bodies, which have parts that are disposed in way that where the one is, the other is not … However, there is not one part of the soul in the eye, another in the foot, nor is the soul bigger in the man than in the child; but as the immense & infinite God is everywhere, not having parts external to parts; also the soul in its own way fills out the whole body without having parts external to parts. (ibid.)

Leibniz’s early view of the relation of soul and body seems to come closer to Scaliger’s view that the soul is only in analogical sense co-extensive to its body than to Liceti’s view that the soul is present by contact and contiguity. It is true that in the Dissertation on the Art of Combinations (1666), he explores a theory of substantial form in purely geometrical terms. There, he puts forth the view that substantial forms understood as geometrical figures are indivisible, and thus display a structural feature traditionally associated with the formal aspect of individual substances. At the same time, the Dissertation on the Art of Combinations embraces a neo-Platonic emanation scheme that leads to the conclusion: “God is substance, a creature an accident” (Dissertatio de Arte Combinatoria 1666, Corollaria, II, 2; A VI 1 229). More specifically, in On Transsubstantiation (1668–1669) Leibniz formulates a view as to the role of passive aspects of substances that with a view to the later explication of passive potency as confused perception can well be understood as a version of a confusion theory of body: “In the idea there is ideally contained both the passive and the active potency, the active and passive intellect. Insofar as the passive intellect concurs, in the idea there is matter; insofar as the active intellect concurs, there is form” (A VI 1 512). Very early on, Leibniz’s ontology also adds to material objects displaying geometrical figure another kind of entities, which due to their immaterial nature and dynamical properties are characterized as mind-like substances. Already in On Transsubstantiation, Leibniz regards the existence of human minds or a Divine mind as a necessary condition for the individuation, and therefore the reality, of material objects:

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Whatever if considered with a concurrent mind is a substance, if deprived of a mind is an accident. A substance is the union with a mind. Thus, the substance of the human body is the union with the human mind; the substance of bodies lacking reason is the union with the universal mind or God; an idea is the union of God with a creature. (A VI 1 508–509)

Leibniz at this place characterizes both the Divine and the human mind as a “principle of motion” external to the body. The view of minds as immaterial principles of motion has the consequence that the relation of minds to space is different from that of material objects. In On Transsubstantiation he constructs the following argument to support the Thomistic view according to which minds are related to space only through their operations: All mind lacks extension. Whatever lacks extension, is not co-extensive with space. Whatever is not co-extensive with space is not at a place per se. Therefore, mind is not at a place per se. The mind operates on the body, which is in space. In this sense, therefore, it can be said that the mind is in space through  its operation. (A VI 1 509–510)

In addition, the contemporary Outline of Catholic Demonstrations (1668–1669) distinguishes the way human minds can be assigned a place in their bodies from the way the Divine mind is related to space. There, the envisaged topic of chapter 4 of the third part is characterized as “the mode of the omnipresence of GOD and the multipresence of each other mind, against Conrad Vorstius, and the Scholastic theory of the impletive, circumscriptive, and definitive ‘where’” (Demonstrationum catholicarum conspectus; A VI 1 495). Early in the 1670s, Leibniz makes the view of the multiple location of the human soul more specific by introducing the idea that in organic bodies there is some subtle matter, which he calls a “kernel of substance” (Leibniz to Duke Johann Friedrich, May 21st 1671; A II 1 108–109). About this subtle matter, he writes that it is diffused throughout the body, that it is what accounts for the regeneration of plants, and that it remains united to a soul even if the “gross” matter constituting an organic body is destroyed (De ressurectione corporum; A II 1 116–117). In the Paris years, Leibniz comes back to this issue in a short response to Robert Boyle’s alchemically inspired theory of the resurrection (Boyle 1675). There, he emphasizes his basic agreement with Boyle’s views and identifies them with his own view that a perennial “flower of substance” is what actually constitutes our body. In addition to being diffused throughout the less subtle parts of the organic body, it also is described as “containing alone in some way the form [of the body].” Moreover, the only addendum Leibniz wants to make to the theory



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of Boyle is the claim that the soul is firmly implanted in the “flower of substance” (De sede animae, February 1676; A VI 3 478–479). That at this place the flos is said to be “our body” seems to imply that it is something extended and material (Brown 1998: 582–584). At the same time, having a formal aspect distinguishes the subtle matter Leibniz has in mind here from prime matter (which at another place also is called “subtle matter” (De material prima (ca. 1670–1671); A VI 2 279–280). Moreover, in On the Union of the Soul and the Body, written possibly at the same time as the response to Boyle, Leibniz applies the idea of a subtle “flower of substance” to the problem of the seat of the soul: I have believed that there is some fluid or, if you like, an ethereal substance, diffused in the whole body, and continuous; by which the soul senses; which inflates the nerves, which contracts itself, and which explodes. … But that the soul itself agitates a vortex, is true wonder. Nevertheless, it does do this, since we act not simply mechanically, but out of those reflections, or actions on ourselves.  (De unione animae et corporis, February 1676; A VI 3 480)

Thus, according to Leibniz, subtle matter has a certain causal role in the working of the nervous system and thereby functions as the instrument by means of which the soul has sensations. Subtle matter is co-extensive to the body in the sense that it is contiguous with each part of the body. Leibniz even characterizes this subtle matter using the terminology of “form”. This implies that there is some mechanical formal cause in organic beings. Nevertheless, for Leibniz this material formal cause is not identical with the soul. The soul is an immaterial principle of force that has multiple location in the sense that, by means of subtle matter, it acts everywhere in the bodies. This amounts to the view that the soul is co-extensive with its body only in an analogical sense: the soul does not act everywhere by contact, but by acting (in a way yet to be explained) on subtle matter that acts everywhere by contact. Moreover, being co-extensive in this way presupposes the existence of entities different from the soul and its modifications. For this reason, understanding the co-extension of souls and bodies in the way outlined by Scaliger and Sennert leads to a theory of organic entities that are genuinely composite. Moreover, mind-like entities are seen as the condition for the reality of material objects. In this sense, material objects very early on are characterized as something that cannot exist independently of mind-like entities. Finally, the idea of a subtle matter acting as the instrument of the soul implies that the way souls perceive the world cannot be explained independently from the nature of bodily traces.

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4. Incomplete entities and confused perception in Leibniz’s correspondence with Rémond Leibniz’s claim that soul and body, in some sense, are incomplete without each other can be seen as a clarification and extension of ideas that were present very early on in his philosophical development. This makes it even more puzzling why he did not make more use of this strategy in his later writings. One possible explanation of this may be that Leibniz at some time gave up the view that pre-established harmony is sufficient as an explanation of the metaphysical union of soul and body (Rozemond 1997: 174–178; Woolhouse 2000: 164–170). Such an interpretation can be plausibly motivated by the response to objections put forth by de Tournemine, where Leibniz admits that pre-established harmony does not bring about a “true union” or “metaphysical union” but only gives a natural explanation for the phenomena (GP 6 595–596). On the other hand, the vinculum substantiale theory later developed in the correspondence with des Bosses explores a stronger theory of a metaphysical union involving more than pre-established harmony. Nevertheless, there is at least one significant train of thought, which has close affinities to his earlier theory of incomplete entities. Moreover, Leibniz in this context holds on to a conciliatory strategy that combines Aristotelian, Platonic, and Cartesian components. This becomes particularly clear in his correspondence with the French Platonist Nicholas Rémond in the years 1714–1715. In an undated letter to Rémond [1714], Leibniz opens the exchange with a statement of his view of the role of simple substances for the constitution of the world: One could not even conceive that it would have anything but this in the simple substances and consequently in the whole nature. The collections are what we call bodies. In this mass one calls matter or rather passive force or primitive resistance what one considers in bodies as what is passive and everywhere uniform; but the primitive active force is what one could call Entelechy, and in this mass is varying. (GP 3 622)

Moreover, at this place Leibniz emphasizes his agreement with Plato’s view that bodies are real only in a limited sense (GP 3 623). However, this does not amount to a reduction of the theory of simple substances to a Platonic version of idealism. Rather, in one of the subsequent letters to Rémond (1715), Leibniz integrates into a Platonic framework the Aristotelian aspects of his theory of composite substances. There, he argues that the transition of a soul from one organic body to another would be incompatible with the order of nature, which requires intelligible explanations and excludes leaps – two criteria that are violated by the theory



Leibniz vs. Lamy: Confused perception and the union of soul and body 183

of metempsychosis. He also outlines his alternative view of the development of living beings: Because one can conceive only the development and change of matter, the machine which constitutes the body of a spermatic animal can become a machine of the sort required to form the organic body of a human being: at the same time the merely sensitive soul must have become reasonable, due to the perfect harmony between the soul and the machine. (GP 3 635)

Thus, even at this late stage of Leibniz’s philosophical career animals are seen as genuinely composite entities: there is not only a universal harmony between simple substances, but also the relation between a simple substance and its body is seen as a special case of this universal harmony. The pre-established harmony between the soul and its organic body is more than can be explained by means of the modifications of the passive aspects inherent in the soul itself. At the same time, Leibniz integrates a Neo-platonic theory of the origin of the passive aspects of material objects into this broadly Aristotelian theory of composite substances: As to the inertia of matter, because matter itself is nothing but a phenomenon, although a well-founded one, resulting from monads, the same is the case with inertia, which is a property of this phenomenon. … But in the interior of things, because the absolute reality is only in the monads and their perceptions, it must be the case that these perceptions are well ordered, that is to say, that the rules of harmony are observed there, such as that which orders that the effect must not exceed the cause. … [B]ecause monads are subject to passions (except for the primitive one), they are not pure forces; they are the foundation not only of actions, but also of resistance or passivity, and their passions are in their confused perceptions. This is what involves matter or the infinite in number. (GP 3 636)

At this place, Leibniz embraces a neo-Platonic view according to which both the materiality and the multiplicity of individual objects derive from the confused perceptions in mind-like substances. However, at the same time he holds such a theory to be compatible with an Aristotelian theory of composite substance. The way to reconcile the one with the other is quite straightforward: the (secondary) matter associated with a given simple substance is not only a modification of the passive aspects of this substance, but a modification of the passive aspects of many simple substances standing in relations of pre-established harmony to each other. The issue of primary and secondary matter is explicitly combined with the theory of incomplete entities in one of the last letters to Rémond, dated November 4th 1715:

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I believe to have proven that each substance is active, and the soul above all. This is also the idea the Ancients and the Moderns had of it, and Aristotle’s entelechy, which has made so much noise, is nothing but the force or activity … But pure primary matter taken without souls or lives that are united to it is purely passive: moreover, to speak properly it is not a substance, but something incomplete. And secondary matter (such as, e.g., the organic body) is not a substance, but for another reason; namely, that it is a collection of several substances, like a pond full of fishes, or like a herd of sheep, and consequently it is what one calls an Unum per accidens, in a word, a phenomenon. A true substance (such as an animal) is composed of an immaterial soul and an organic body, and it is the composite of both that one calls an Unum per se. (GP 3 657)

Although this does not amount to a view of soul and body as form and matter in a genuinely Aristotelian sense, Leibniz tries to hold on to a genuinely Aristotelian notion of entelechy and the resulting view of a living being as an organic body endowed with an active principle. Interestingly, it is exactly this side of the Aristotelian theory of composite substance, which Leibniz thinks to be compatible with the philosophy of the Moderns. Moreover, Leibniz explicitly reaffirms what he had doubted in the response to de Tournemine, viz., that pre-established harmony can explain the metaphysical union between soul and body: That is why secondary causes act truly, but without any influence of a created simple substance on another one; and the souls match with the bodies and with each other due to the pre-established harmony, and not at all through a mutual physical influence, except for the metaphysical union of the soul and its body, which makes them compose an unum per se, an animal, a living being.  (GP 3 657–658)

Again, Leibniz combines this broadly Aristotelian theory of composite substances with a Cartesian theory of ideas in the human mind and a Neo-platonic account of the emanation of created beings from the ideas in the Divine mind: It suffices to consider ideas as concepts, i.e. as modifications of our soul. This is how the Scholastics, Monsieur Descartes and Monsieur Arnauld understand them. But because God is the source of possibilities and, consequently, of ideas, one can excuse or even praise this Father to have changed the terms and to have given ideas a higher signification by distinguishing them from concepts and by taking them as perfection which are in God, and in which we are participating in our knowledge. (GP 3 659)

In this sense, Leibniz can hold the view that not only in the system of Occasionalism but also in his own system “God is the only immediate external object of souls, which has a real influence on them” (GP 3 660). Finally, he points out that



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although the there is a commonly held theory of causal influence by means of species within the Scholastic tradition, the Scholastics nevertheless “acknowledge that all our perfections are a continuous gift from God, and a limited participation in his infinite perfection. Which suffices to judge that also what is true and good in our knowledge is an emanation of the light of God …” (GP 3 659–660). Thus, holding a broadly Aristotelian theory of composite substances, in the eyes of Leibniz, is compatible with a Neo-platonic emanation scheme, as well as with aspects of the Cartesian tradition. Leibniz’s reaffirmation of the theory of body and soul as incomplete entities in the correspondence with Rémond, therefore, should not be characterized as an attempt to reduce the theory of composite substance to a specifically scholastic theory. Rather, it is an attempt at integrating one particular aspect of the scholastic theory into a view of the nature of living being that reconciles elements of diverse origins. To these belongs the idea of a hierarchy of being, in which the less perfect beings differ from the Divine mind by their confused perceptions. In this sense, the primitive passive force in simple substances leading to confused perceptions can be interpreted as a principle of particularity and materiality. At the same time, however, Leibniz defends the idea that confused perceptions are something by means of which souls are united to their bodies. In this sense, confused perceptions can be seen as a feature of finite souls that makes them incomplete without their organic bodies. Thus, confused perception for Leibniz not only explains the particularity and materiality of individual things in the world, it also contributes to explaining the functional dependence between the states of a plurality of simple substances constituting a living being.

Notes * Initial research for this paper was conducted at the Center for Philosophy of Science of the University of Pittsburgh during my time as a Visiting Fellow in the academic year 2002–2003. The special collections of the Hilman Library of the University of Pittsburgh and the Staatsbibliothek Berlin provided me with rare printed sources. Earlier versions of this paper were read at the Department of Philosophy at the Humboldt University of Berlin in January 2004, and at the Annual Conference of the New Israeli Philosophical Association at the Hebrew University, Jerusalem, in February 2004. I would like to thank Ursula Goldenbaum, Ohad Nachtomy, and Pauline Phemister for their helpful comments. 1. For the history of the editions of Lamy’s work and Leibniz’s responses, see Woolhouse and Francks (1994), Woolhouse (2001). The parts of the review of the first edition to which Leibniz responded were published in the Journal des Sçavans 26 (1698): 660–668 and 669–679.

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2. François Lamy, De la Connoissance de soi-même, 2nd ed., 6 vols., Paris 1699; reprinted Paris, 1701. The passages relating to Leibniz from the 1701 edition are reprinted in the Leibniz Review 11 (2001): 73–100. 3. In addition to Leibniz’s response to Lamy, see Leibniz to Johann Bernoulli, August or September 1698; GM 3 537; Leibniz to Johann Bernoulli, September 20th/30th 1698; GM 3 541–542; Leibniz to Johann Bernoulli, December 17th 1698; GM 3 560; Leibniz to Damaris Masham, September 1704; GP 3 363. 4. Leibniz to Jakob Thomasius, April 20th/30th 1669; A II 1 14. 5. Liceti refers the reader to Aristotle, Phys., 7, 10–12; 8, 33; De an., 2, 3; 2, 24; 2, 47; De gen., 1, 35.

References Blank, A. 2003. “Incomplete entities, natural non-separability, and Leibniz’s response to François Lamy’s De la Conoi­ssance de soi-même”. Leibniz Review 13: 1–17. Boyle, R. 1675. Some physico-theological considerations about the possibility of the resurrection. London. Brown, S. 1998. “Soul, body, and natural immortality”. The Monist 81: 573–590. Lamy, F. 1694–1698. De la Conoissance de soi-même. 5 vols. Paris. Lamy, F. 1699. De la Connoissance de soi-même, 2nd ed., 6 vols. Paris [Reprinted 1701]. Liceti, F. 1616. De animarum coextensione corpori libri dvo. Padua. Nicholas of Cusa. 1998. De coniecturis. J. Koch and W. Happ (eds). Hamburg: Meiner. Phemister, P. 2001. “Corporeal substances and the ‘Discourse on Metaphysics’”. Studia Leibnitiana 32: 68–85. Phemister, P. 1999. “Leibniz and the elements of compound bodies”. British Journal for the History of Philosophy 7: 57–78. Plotinus. 1988. Enneads. A. H. Armstrong (trans). Cambridge, MA: Harvard University Press. Rozemond, M. 1997. “Leibniz on the union of body and soul”. Archiv für Geschichte der Philosophie 79: 150–178. Scaliger, J. C. 1557. Exotericarum exercitationum liber XV. De svbtilitate, ad Hieronymum Cardanum. Paris. Sennert, D. 1676. Hypomnemata physica, Hypomnema IV. De generatione viventium, ch. 6. In D. Sennert, Opera omnia, 6 vols. Paris. Smith, J. E. H. 2003. “Confused perception and corporeal substance in Leibniz”. Leibniz Review 13: 45–64. Woolhouse, R. S. 2000. “Pre-established harmony between soul and body: Union or unity?”. In A. Lamarra and R. Palaia (eds), Unità e molteplicità nel pensiero filosofico e scientifico di Leibniz. Florence: Olschki, 159–170. Woolhouse, R. S. 2001. “Leibniz and François Lamy’s De la Conoissance de soi-même”. Leibniz Review 11: 65–70. Woolhouse, R. S. and Francks, R. 1994. “Leibniz, Lamy, and ‘the way of pre-established harmony’”. Studia Leibnitiana 26: 76–90.

chapter 8

Leibniz vs. Foucher Is there anything wrong with the Système Nouveau? Marta Mendonça

1.

Introduction

The essay Leibniz published in the Journal des Sçavans in 1695, Système nouveau de la nature et de la communication des substances, aussi bien que de l’union qu’il y a entre l’ame et le corps,1 is a singular piece of work. It is a brief text, of which there are various partially corrected versions and that, in Leibniz’s own words, was very mature. Leibniz prepared the text in advance for publication, which he continuously put off. He also kept its contents largely unknown, revealing them only in a very limited and sometimes dissimulated way.2 In fact, judging by the large number of references he makes to the contents and theses of SN in the years preceding its publication, as well as by the number of variations and corrections he made to the text, it is clear that Leibniz put special care into the writing of this work. It is therefore legitimate to assume that some particularly valuable and mature aspect of Leibniz’s philosophy was made public here for the first time. This would help to explain why Leibniz referred back to this text, and to the themes he broached in it, in almost all of his subsequent philosophical work. His resistance to any private disclosing of the contents of the text as well as to making it public likens the SN to another text that Leibniz alludes to in its very first paragraph and also in his correspondence with Foucher: the Discours de Métaphysique, which he never published. In fact, the similarity between the theses defended in the SN and the treatment of the same themes in the Discours de Métaphysique is clear and allows us to identify the themes with which Leibniz was concerned in the mid 1680s, and which were made public ten years later in this short article in the Journal des Sçavans.

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In understanding why Leibniz was so cautious and reserved it is important to note that the SN in no way constitutes Leibniz’s debut in the famous French journal. Just like Foucher, with whom he held the brief public controversy that we will soon analyze, Leibniz is a frequent, almost habitual, contributor to the Journal.3 Aside from this, some of the themes developed in the SN had previously been discussed by Leibniz in the Journal, and had even given rise to an initial public correspondence between Leibniz and Foucher. These exceptional circumstances – that Leibniz was so hesitant to publish such an extensively elaborated piece, even in a journal to which he was a frequent contributor – have resulted in very different assessments of the text in recent literature. For some, it represents the culminating moment of his anti-Cartesian offensive, or the first published piece of Leibniz’s mature philosophy, presenting the themes around which all of his later philosophy would hinge.4 Those who interpret the SN in this way see Leibniz as already having won over the resistance to his ideas, and as having sufficiently prepared the public by the time of its publication; this enables him to clearly lay out his new theses, presenting them with caution but without dissimulation. According to other interpreters, however, the text is a popular one, masked by diplomacy, by Leibniz’s anxiety and preoccupation with being well received, as well as by his ambition to be seen more as Descartes’s successor than as his critic.5 Because of this, in order to be able to successfully publish his text, Leibniz was forced to camouflage his doctrines. Proponents of this claim cite both Leibniz’s confession to having written in Cartesian style and the differences between the initial version and that which was finally published. It is not easy to accept this claim wholeheartedly: saying that the compromises Leibniz made in the editing of the text makes him a populist, that it hides his philosophy more than it reveals it at the time it was published, is refuted by the very text and cannot be derived from its style. The reasons for this are twofold: on the one hand, Leibniz indicates in the SN that the reflections he presents are not likely to please popular spirits; on the other hand, if it is true that the comparison between the first versions of the text and that which was submitted for publication does reveal a difference in style – the published version being in a more Cartesian taste – it is also true that the theses presented remain relatively unchanged. There are, as we will see, omissions and additions to the final text, and some of them are even significant, but the Système is still the same. One thing is certain, however: Leibniz’s caution was not excessive, as the history of the SN’s reception shows. Immediately following its publication there were a considerable number of reactions to its content, generating two main controversies surrounding its themes – the first with Simon Foucher and the second with Pierre Bayle. The reactions were neither limited to these two, however, nor were



Leibniz vs. Foucher: Is there anything wrong with the Système Nouveau? 189

they restricted to the French intellectual climate into which they were published.6 The reactions to the SN were prolonged in time and greatly surpassed the limits of the Journal des Sçavans, carrying over into other journals and publications.7 In this paper we will only deal with the first of these public reactions: that which had as a protagonist one of Leibniz’s long-time friend, Simon Foucher. The two authors met during Leibniz’s stay in Paris, and their relationship was close enough to warrant conversations about Leibniz’s admission to the Academy of Sciences and strategies to facilitate it (cf. GP 1 407; A II 2 566). In fact, in their correspondence there is a clear and conscious distinction between a public, or publishable, level of discourse and a private level best kept hidden from outsiders (cf. GP 1 387; A II 2 133). In order to understand the nature and meaning of this brief controversy it is necessary to touch upon some of the most salient aspects of the text and the theses from which it originated, and also to follow the lead-up to the public discussion in the correspondence between the two authors.

2.

The purpose of the SN and the differences between the different versions

Among the different versions of the SN8 there are, as we have mentioned, differences that vary in significance; in some cases Leibniz does no more than to correct short sentences, in others he substantially alters the text. The oldest version of those published by Gerhardt, probably from 1694, and partially made known to Bossuet on July 2nd/12th 1694, is much shorter and written in a different style from the version published in the Journal des Sçavans, to which Foucher had access. These differences allow us, up to a point, to reconstruct Leibniz’s strategy in trying to give his text the most fitting style for its public. At the same time, they reveal the importance that Leibniz gave to the reception of this work. But the two texts also differ in particular aspects of their contents. A first difference in details is in the title: Leibniz entitled the rough draft Système nouveau pour expliquer la nature des substances et leur communication entre elles, aussi bien que l’union de l’ame avec le corps (GP 4 471). The final text has the well-known title, Système nouveau de la nature et de la communication des substances, aussi bien que de l’union qu’il y a entre l’ame et le corps (GP 4 477). In both cases the theme is clearly the same: he is presenting, in new ways, in a new system, the nature of substances and the interaction between them and also the particular form of interaction – Leibniz speaks of union – that occurs between body and soul. At this point, therefore, there are no significant differences of content; nor does the initial version reveal a clearer or more personal statement than that

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which appears in the published version. The objective of the SN is threefold, and this threefold objective is made clear in the title in both cases. The most significant aspect of the title, which is important for understanding the novelty of the SN is, in fact, kept unchanged in the two versions and is connected to the autonomy of the other two objectives of the work. It is clear that Leibniz does not interpret the question of the union of body and soul as a particular case of the interaction between substances: the problem is not to understand this particular form of “communication” that exists between two substances – body and soul – but, instead, to think the “union” between the two. To think this union requires thinking the particular nature of the body in a new way. A difference worth noting is the issue of size. While the rough draft comprises merely five paragraphs of reasonable length, the text that Foucher had access to was much longer, containing 18 paragraphs. In the draft, what Leibniz presents is essentially: a. a first biographical paragraph; b. a paragraph setting out the forseen resistance, surprise and at the same time necessity of recovering substantial forms; c. a paragraph explaining the inability of extension to ground the authentic nature of substances, even of material ones; d. a paragraph in which he characterizes substances and shows the unique nature of rational souls; e. and, finally, a long paragraph dedicated to the system of correspondence, which he presents as a corollary to the previous theses. Leibniz’s essay clearly follows the order of presentation of the objectives he sets out in the title: the first two paragraphs justify, so to speak, the characterization of the system as new by preparing the reader for the theses that Leibniz will put forth and by announcing the gist of the Leibnizian position, which implies reintroducing substantial forms; the next two paragraphs correspond to the first objective of the text – to expound and characterize the nature of substance – while the final paragraph concentrates on the other two goals: expounding the nature of the communication between substances and the particular form of union that exists between body and soul. In the published text, the sequence in which the themes are presented is substantially the same, but the themes themselves have undergone significant development. The structure is now the following: a. Three biographical paragraphs setting out the intellectual process that led Leibniz to realize the necessity of salvaging substantial forms and putting



Leibniz vs. Foucher: Is there anything wrong with the Système Nouveau? 191

them to use again. These paragraphs correspond to the first two paragraphs in the draft and have the same function in the economy of the text; b. Eight paragraphs entirely dedicated to the question of the nature of substances and their properties, emphasizing the superiority of rational souls. These paragraphs correspond to paragraphs three and four of the first version, carrying out the first objective of the title; c. Seven paragraphs dedicated to the two other objectives: expounding the nature of the union between body and soul and the nature of communication between substances. These correspond to the last paragraph of the rough draft. While it elaborates various theoretical points that were only articulated briefly in the draft, the final text does not, however, present different solutions to them. The lengthy expansion of some of the themes owes largely to Leibniz’s argumentative strategy, and also to the fact that in the version he sent to press he appealed to arguments from authority, unnecessary in the rough draft. The most noticeable differences lie not so much in the themes or questions that Leibniz explored more fully in the final version but, in fact, in the themes he omitted from his first version. The most relevant of these omissions are the references to final causality and its function as a principle for the discovery of scientific truths, and the declaration, laid down as a principle, that everything proceeds mechanically in nature.

3.

Leibniz’s argumentative strategies in the SN

As we have seen, the novelty of the SN does not lie in its themes. In it, Leibniz takes up the problems and themes that were current in the philosophy of his time and explores the critique of the Cartesian solution to these problems in a way that he had already explored, regarding the insufficiency of extension as an explanation of corporeal nature and its behavior. Foucher was well aware of this critique and shared it.9 What, then, is new about SN? And what is so shocking or valuable about it that made Leibniz take so long to prepare the published version and hesitate so much in sending it to press? And what about it was so shocking or new for it to have provoked such a chain of reactions? An initial answer to these questions can be found by reflecting on the argumentative strategies that Leibniz used in this text, particularly in the final, published version. For this purpose, it would be useful to compare the strategies he used in the different versions of the SN. The most significant alteration relates to the style of the Journal in which the text ended up being published. As he himself recognized, he adapted the text to the style of the magazine, accentuating the

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biographical dimension of the path that lead him to create the new system. However, judging from its contents, the most important alterations were of another kind. We will refer only to the argumentative strategies that Leibniz retained in the published version, as these were the strategies that Foucher knew, and to which he reacted. Of particular interest are the argumentative resources that Leibniz uses in the beginning of the text, in the “biographical” part of the SN. Leibniz presents his text as resulting from a mature reflection, which required “a long time” (GP 4 477), presumably because it had already been subject to criticism and had emerged victorious from this theoretical confrontation. Furthermore, this mature text is in agreement with other central aspects of Leibnizian thought that were broadly accepted and even applauded by critics, as was the case with his theory of dynamics. The lapse in time did not, therefore, correspond to a loss of interest in the issue, but rather to his preoccupation in avoiding precipitation at all costs. What Leibniz now presented to the public was a text that emerged victorious from many points of resistance – his own as much as those of his interlocutors. Nevertheless, it is clear that in the presentation of the theses he now offers to his readers, Leibniz lets some fear show through. He “risked” publishing a text containing reflections that were “not at all popular” and hoping for reactions motivated “by truth and not by prejudice” (GP 4 477–478). His precautions are obvious: Leibniz feared that these prejudices would seriously interfere with the reception of the text, and he defends himself against them beforehand. Anticipating prejudices and, here too, defending himself in advance against them, he proceeds to expound the initial stages of his intellectual path. The text that he now presents to the public proposes the recuperation of a scholastic notion of Aristotelian origin. In order to avoid the rejection that such a proposal would provoke, Leibniz publicly situates himself before the two main domains of influence in which this philosophical debate developed. Leibniz is a modern thinker. The “country of scholastics” that he visited in his first youth was “soon abandoned” due to the influence of mathematics and of modern authors (GP 4 478). But the abandonment of Aristotle, and even the seduction of modern philosophy, are not enough to constitute solid thought. Leibniz knows this from his own experience and confesses it publicly. His vigorous rejection of Aristotelianism and scholasticism placed him within the scope of modern philosophy, but in a philosophy that turned out to be as unable as Aristotle’s to explain what Aristotelian philosophy failed – in Leibniz’s own mind – to explain. His first adherence to the “new” philosophy was merely an illusion: an illusion that derived from the fact that atomism was satisfactory to imagination, but not to reason. In this summary of the broad sweeps of the history of philosophy, the error of Aristotelianism is presented as a methodological error more than as a theoretical



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one. The scholastic heirs of Aristotle had the theoretical resources to philosophically understand nature, but they abused these resources and ended up confusing physics with metaphysics (cf. GP 4 479). Truly understanding nature implies conserving these concepts – recovering them, now that modernity has abandoned them – but not using them outside the context in which they can be legitimately used. It was this methodological discipline that the scholastics did not respect and that ultimately discredited them. The necessity of reviving old metaphysical notions, specifically the notion of substantial form, reveals the deficiency of modern thought. This deficiency of the moderns is manifest in a different way, because the modern error is of another type. Wanting to reject the scholastic abuse of metaphysics, the moderns rejected the metaphysical notions themselves, considering them incapable of giving reason to nature. In so doing, they rejected all metaphysics, or founded metaphysics upon physical notions. But the resulting metaphysics is so deficient that it is unable to found physics itself. If the scholastics abused metaphysical notions and illegitimately transposed them to the field of physical phenomena, the moderns committed the theoretical mistake of defining metaphysics on the basis of physics. The most serious consequence of this error is that physics itself lacks sufficient foundations. Leibniz’s expository procedure brings him to place himself within the modern point of view and to invite the reader to take the same route that he had taken. He is not an adversary; he is a pioneer. It is the insufficiencies of physics and of modern ontology that Leibniz invites his modern readers to detect and to overcome with him. The unprejudiced recognition of these limitations compels him to recover notions that are particularly controversial and badly looked upon by Cartesian and mechanistic modern philosophy, namely the notions of substantial form and of force (cf. GP 4 478–479). But what the SN tries to show is that this is not an option, but a conclusion, and a necessity. Leibniz thus presents himself as a conciliator. He is a modern, an authentic modern, who is not biased against previous philosophy. He is a modern who is not partial, being thus able to see the deficiencies of modern philosophy and the hidden treasures of previous philosophies. He is the maker of the needed synthesis, and thus a precursor. Leibniz’s argumentative strategy also requires him to state his position regarding the moderns. He presents himself as a modern who does not suffer from the blindness resulting from prejudice. He has the best of intentions regarding the moderns and their philosophy, which allows him to appreciate the great contributions that gave rise to science (cf. GP 4 481). He is not blinded by the sectarian spirit he finds in some of them, nor is he paralyzed by the Cartesian heritage that impedes some of them from addressing their criticisms where they should lead

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to – a blindness that, while allowing them to see the problems does not let them see the solutions. As regards this point, just like the scholastics they so criticized, the modern philosophers were unsatisfactory in that they went “too far”: reducing everything to scientific criteria, not respecting the specific autonomy of metaphysics, they end up measuring nature by art and confusing natural things with artificial ones (cf. GP 4 481). Another of the argumentative strategies clearly present in the text is the appeal to authority. There are very few texts of the SN’s scope in which Leibniz so openly seeks recourse to the opinions of others, both ancient and modern. Once he has set out the most essential aspects of the new system, or rather, once he has set out the general thesis – substantial forms have to be re-established – Leibniz starts developing the particular aspects of his new system. And in setting them out, he openly states that he is not alone. He mentions Thomas Aquinas, Albertus Magnus, Jean Bachon, Gassendi, Swammerdam, Malpighi, Leewenhoeck, Malebranche, Regis, Hartsoeker, Democritus, Hipocrates, Parmenides, Melisso, Cordemoy, the Ancients, the Scholastics, and Aristotle. The appeal to the writings of others fits in with Leibniz’s preoccupation with presenting his position as a position based on the philosophical tradition. Leibniz mistrusts originality. He says this at various points regarding Descartes’s penchant for originality. Here he shows the reader that he is not alone in a position that would otherwise appear to be unusual. Ancients and moderns have both said something similar. And science and philosophy throughout the ages proves him right. It is particularly interesting to note the way in which he takes issue with modern writers and how he alludes to them. Why would it be odd to accept that forms last forever if Gassendi defends this same claim for atoms? Why would it be odd to accept that animals last forever if there are scientists and even philosophers who said something similar and were well accepted? What is strange about Leibniz’s “vitalism” if we know and accept the great discoveries brought about by the microscope? (cf. GP 4 479–480). This argumentative rhythm has Leibniz presenting a text with an internal unity that appears to be complete by the end of paragraph 11, but that surprisingly does not end here. Having concluded the presentation of the doctrine of substantial forms, and having justified the reasons for which it should substitute atomism, Leibniz resumes the argument about the issue of the union of body and soul and the question of the interaction between substances. In the fifth paragraph something had already been mentioned in passing regarding this, when Leibniz says that the spirits and the rational soul belong to a superior order and have particular laws, being governed in a different way than other forms or souls (cf. GP 4 479–480). In fact, this stylistic choice, which reopens an apparently concluded discussion, is not unintentional. Leibniz purports to in his own way the various



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issues dealt with in SN, expounding first his doctrine of substance and then resolving the two harder questions that any early modern theory of substance ought to handle. For him, the independent presentation of these aspects of the problem of substance ensures, on the one hand, a more favorable reception of the doctrine of substance itself, by freeing it from the understanding or acceptance of the doctrine of harmony, and, on the other, it provides sufficient grounds for the doctrine of harmony and for the explanation of the body-mind union. It is clear that Leibniz wants to clearly distinguish the objectives of the SN, first expounding his doctrine of substance and then solving the two most difficult questions that need to be answered by any modern doctrine thereof. Having understood the nature of substances by the indirect route of identifying the shortcomings of the opposite doctrine, the concomitance doctrine needs to be presented in another way because it does not have the same plausibility. Leibniz describes this methodological rupture with which he introduces the second part of the text as abandoning port and setting sail in mid sea (cf. GP 4 483). Here Leibniz describes, once again, the theoretical route that brought him from resistance and perplexity to demonstration. The strategy used in this second part has a common feature with that used in the first part of the text: it begins by analyzing a solution (the occasionalist one), which he presents as being at first view plausible but in fact unsatisfactory. But the following steps are different: Leibniz proceeds by explaining his own doctrine of the communication between substances, presenting it as a surprising solution that had been insensitively imposed on him as inevitable (GP 4 484). The next paragraphs present the stages of the argumentative route that lead from a mere hypothesis to a doctrine that should be accepted because it is more than a hypothesis. The reader is invited to follow Leibniz as he sets out the reasons that “prove” the new system and make it impossible to refuse. Finally, in the last paragraphs, Leibniz connects his new explanation with current forms of speaking, showing its compatibility with common discourse (GP 4 485).

4.

The contents of SN

As we have seen, Leibniz wants to approach three main issues: the question of the nature of substance, the question of the interaction between substances, and the question of the unity of man or the union of body and soul. These themes are not new; what is radically new is the solution that he presents to the problems he spots. This novelty explains both his cautiousness and the argumentative strategies he employs, which can be summarized in the following terms: Leibniz has already tested out the resistances readers might have to accepting the SN, and

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the SN has withstood these resistances. Apart from presenting his own system, from having the reader confront it with others and consider the value of each system, Leibniz presents it in a demonstrative way, as the only possible system of explaining nature. Aiming to present his system in this way, he pronounces a verdict against the shortcomings of the other philosophical systems, concluding that the SN prevails over them because it provides a synthesis of what is correct in the various proposals. The theses and arguments of the SN are well known and this is not the place to rehearse its main contents. The essential contribution – indeed, the novelty – of the Leibnizian answer to the first question is the substitution of physical points (physical atoms or indivisibles) by metaphysical points (atoms of substance; GP 4 482) – bearing in mind that such an atom is constituted by force and that activity is a distinctive and inseparable aspect of true substances. Attached to this essential contribution – the synthesis of the reflection that had lead him to tell Foucher many years before that he had looked for the nature of substance but did not find it, and had had to work hard to expound it himself (cf. GP 1 384; A II 2 91) – is the repeated affirmation of the existence of two different kinds of forms: brute souls or current forms belong to an order of which God is the engineer, and other forms or souls, spirits, belong to an order that has God as its lord or prince. The two orders are subordinated to different laws: spirits are subject to “particular laws” and all others are subordinate to spirits (GP 4 479–480). The conclusions or implications that follow from the nature of substance, of this type of soul whose nature is essentially active, are numerous and paradoxical. Leibniz presents with particular caution what we can call the de-ontologization of substantial changes, specifically of birth and death. There is really neither birth nor death; there is only transformation, enveloping or development of the indestructible substance. According to Leibniz, not understanding this implication had two dire consequences for philosophy: it led, on the one hand, to the aforementioned modern abuse that consisted in confounding natural and artificial things, or better said, in judging natural things by artificial ones. On the other hand, it led to an absurd concept of matter as based on the logically inconsistent reconstruction of atomism. It is interesting to observe the way in which Leibniz introduces the two following questions: the defence of substantial forms appeared to contain the answer to the great problem concerning the nature of substance and, having found a satisfactory doctrine of substance, Leibniz thought he had arrived at port. He was thrown back to sea by the consideration of the union of body and soul in light of the new doctrine of substance. Thinking about this question, for which his new doctrine did not appear to be able to provide a satisfactory answer, the more general problem of the interaction between substances arises naturally. The



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new doctrine of substance has to solve, in a more satisfactory manner than previous doctrines had achieved, the question of the unity of man and of the order of nature. By what means does the soul pass anything on to the body, and vice versa? How can one substance communicate with another? Here too, Leibniz does not subordinate the first problem to the second: the question of the unity of man is not, strictly speaking, a question of communication between substances, but the question of the communication between substances is a real problem, and his system has to find a satisfactory solution to it. The solution that Leibniz proposes is set out in paragraph 14 – the longest of SN – and consists in a presentation of the doctrine of pre-established harmony, or of concomitance. With it, Leibniz argues, the question of the unity of body and soul and the question of the interaction between substances are simultaneously solved. In the following paragraphs, and until the end of the text, the reader is led from a merely possible hypothesis to the certainty that this is the true explanation, the only good one. This is the function of the confrontation with Descartes’s concept of extension in the first part and, here in the second, the confrontation with Malebranche. Leibniz places himself within the problems that Malebranche detected, in order to approach the problem in the same terms as he did and yet to solve it with a radicalism that Malebranche did not have (GP 4 483). The final part of the text contains a particularly profound synthesis of Leibniz’s doctrine of nature and natural explanation. The systematic distinction that Leibniz establishes between the last two objectives of his text has to do with the type of solution that he proposes to the question of the union of body and soul: as we said, this question leads naturally to the question of the interaction between substances, but is not to be confused with it. In the first case, what is at stake is the connection between two orders of reality – the material, mechanical realm and the spiritual and moral realm – whose laws Leibniz sees as different. The second case, on the other hand, is concerned with a rational consideration of each of these orders and, specifically, a consideration of the dynamic character of nature. Leibniz’s solution to the first question consists essentially in de-substantializing movement and matter, which are now presented as well founded phenomena. The solution to the second question is actually the hypothesis of concomitance or harmony, according to which there is no real, effective influence of one substance upon another. The first question can, however, be brought to lead to the second; this is what Leibniz does by illustrating the advantages of his hypothesis with an example of the world of spirits: just as of any other natural substance in nature, we also say of a spirit that it, too, is like a world apart, that it is self sufficient and independent of all other creatures, etc. In this way, while not saying it explicitly, Leibniz is proposing two ways of thinking about concomitance, or agreement:

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one, so to speak, horizontal sphere that establishes simultaneously spontaneity and the agreement between the substances themselves, whether they be brutish or spiritual souls, and another, vertical sphere, that grounds the agreement between substances and their phenomenal expression in the physical world. It is in this vertical sphere that the questions of the unity of body and spirit and of the connection between the mechanic with the teleological or the moral lie.

5.

The prehistory of SN and the controversy with Foucher

The correspondence with Foucher reveals what we can call the pre-history of the SN with particular clarity and precision. This correspondence, that began as soon as Leibniz left Paris in 1676 and would only end with Foucher’s death twenty years later, is necessary for understanding the extent and the meaning of Foucher’s public reaction to this work.10 The public controversy between the two authors, published in the Journal des Sçavans, that we will analyze here is precisely the final – and culminating – stage in this epistolary exchange, which had also become public at another time, between 1691 and 1693. The controversy was in fact abruptly interrupted by the death of Foucher, who was never able to react to Leibniz’s first public response to his criticism. Because of this, the public controversy unleashed by the publication of the SN is composed of a very small number of texts: apart from the SN, there is only Foucher’s immediate reaction and Leibniz’s response to this reaction. There is also a rough draft of Leibniz’s answer, which Foucher clearly did not have access to. To these texts we could add the letter in which Leibniz announces to Foucher the upcoming publication of the SN and Foucher’s answer to this letter. However, the small number of texts exchanged between the two authors immediately before and after the SN’s publication – a number which is only explained by Foucher’s death – hardly represents the volume of correspondence between these authors regarding the new system that Leibniz made public in 1695. The first public exchange of correspondence between the two authors – motivated by the publication of the Extrait d’une lettre de M. de Leibniz sur la question, si l’essence de la matière consiste dans l’etendue (GP 4 464–466) – can only be artificially separated from the SN and its contents, and the close relationship it bears with the SN is acknowledged by both authors. Furthermore, while the private correspondence between the two is not limited to the themes of the SN, it refers explicitly to these themes at various points over the years. It is no coincidence that Foucher begins his critique of the SN by stating that the essence of its content had been communicated to him ten years before and that he had already made known his opinion of it (GP 4 487).



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The fact that the pre-history of the SN is much more extensive than its history is one of the most surprising aspects of the controversy that set Leibniz against Foucher. In fact: a. Foucher had access to the texts or to parts of the texts that made up the SN and that set out some of its central theses, and had actually been the one to lead to the publication of some of these texts; b. Leibniz had transmitted to Foucher in private many of the theses he later made public in the SN, asking him for comments and criticism; c. Foucher had received Leibniz’s letters and the theses they set out with relative enthusiasm, but had always refused to comment on them, even on those that Leibniz had explicitly asked him to; again and again, he postponed the expression of his opinion until the moment he were to know Leibniz’s claims in more detail; d. The only references Foucher made that could be interpreted as opinions suggested that his public stance would be favorable to Leibniz; e. In the whole correspondence there is only one little detail or a small reference that could help to understand the difference between Foucher’s private reaction to the contents of the SN and that which he made public: at a certain point (cf. GP 1 385–386; A II 2 131), Foucher tells Leibniz that he had sent the philosophical contents of some of his letters to various mutual friends who had expressed an interest in Leibniz’s thought. He had asked for their reaction but had made clear – as he explicitly said to Leibniz – that he did not want to judge Leibniz’s whole system, or even to comment on it, until it had been developed more fully; f. In contrast to this attitude, which he held over almost ten years, his public reaction is immediate and its very critical tone had no precedent in their correspondence and could not, in any way, be anticipated. Thus, considering all of the texts that Leibniz and Foucher exchanged, it is evident that the controversy between the two authors provoked by the SN is unlike usual controversies. Throughout almost ten years, Leibniz had provoked Foucher and asked him for a private debate; Foucher gathered Leibniz’s theses without revealing any particular opposition to them, refusing to take a stand and promising to respond in a way that would please Leibniz; when Leibniz’s text was finally published, Foucher’s public reaction, almost immediate, very schematic, and written in a hurried tone, presented a brief and very limited summary of Leibniz’s theses and a predominantly negative assessment of the importance and the content of his texts. Seen from this perspective, in order to understand Foucher’s reaction to the SN and the type of comments and critics that it deserved, it is necessary to

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take into account all of the correspondence exchanged between the two of them, both in public and in private. What is special about the SN – what is new about it, according to Leibniz, and what is wrong with it, according to Foucher – what provoked the tone of Foucher’s public reaction, is probably also what prevented him from speaking out when asked, repeatedly, in ten years of friendly correspondence.

6.

The SN and the correspondence between Leibniz and Foucher

As we have said, the correspondence began in 1675/6 when Leibniz left Paris, and was only interrupted by Foucher’s death in 1696. Not all of the letters remain, and it is possible to identify a considerable number of lost letters that are subsequently alluded to. The correspondence becomes more intensive in 1686. From the first ten years there remains only one significant letter of Leibniz, written in 1676 in response to the publication of Foucher’s Critique de la Recherche de la Verité, and four of Foucher, showing that their contact had not been interrupted but that Foucher had not kept Leibniz’s letters, and Leibniz had not considered them important enough to keep a copy for himself. These letters update Leibniz on Parisian intellectual life and give him news of the people he knew in Paris. In these letters the more or less explicit references to the content of the SN are found mainly: a. In the extract of the letter to Foucher of 1686 (GP 1 380–385; A II 2 86–93); b. In the undated letter written in response to Foucher’s letter of May 5th 1687 (GP 1 390–394; A II 2 199–207); c. In the letter of April 6th/16th 1695 (GP 1 420–421), which resumes their contact after an interruption. In this last text Leibniz announces the imminent publication of the SN and asks for comments, reminding Foucher that he had already asked him to comment on this matter; d. In Foucher’s reply of April 28th 1695 (GP 1 421–423), where he recalls that he had been told of this thesis of Leibniz approximately ten years earlier, but refuses to comment, saying that the issue needs clarification, which he asks Leibniz to send. Leibniz adds to this letter a personal note that includes elements of the SN; e. In the last two letters, one by Leibniz of July 5th/15th 1695 (GP 1 423–424) and one by Foucher’s published in the Journal des Sçavans in September 1695 (GP 4 487–490), which are written in response to the publication of the SN and are devoted to that theme.11



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Between the letters of May 5th 1687 and April 6th/16th 1695, the allusions are less explicit and direct, but not less frequent. The exchange of positions, and the underlying agreement that they both professed, centers on the issue of the insufficiency of extension as the foundation of matter. This theme is developed above all on the letters of 1691 to 1693, some of which were published in the Journal des Sçavans. As we have said, throughout the years Foucher avoided commenting on the theses that Leibniz developed in the SN. It is precisely the first reference to these theses, written in 1686, that sparked Foucher’s comment about the convenience of a distinction between the public and private dimensions of the correspondence, and his decision to defer his discussion of the issue (cf. GP 1 386–387; A II 132–133). The first and longest reference that Leibniz makes to the theses he would later develop in the SN are found in his Letter to Foucher of 1686. At the same time Leibniz was corresponding intensely with Arnauld regarding the latter’s criticism of the abstract of the Discours de Métaphysique, but he was also busy with the issues developed in the SN, namely with the larger question of the nature of substance. The contents of this letter are particularly rich in what they contribute to the history of the controversy between the two authors. Leibniz comments Foucher’s reply to Sir Robert Desgabets (Foucher 1679)12 expressing several times his agreement with Foucher’s theses. One of these occasions is his comment on page 24, where, after manifesting his agreement, he declares that Foucher is right to doubt that bodies can act upon the soul and vice versa. And he goes on to say: I have a pleasant opinion on that, one that I think is necessary and very different from the opinion of the writer of Investigation. I think every individual substance expresses the whole universe in its own way, and that its every next stage is a continuation (though frequently free) of the previous stage, as if only It and God were to exist; but since all substances are a continuous production of the sovereign Being, and they express the same universe and the same phenomena, they inter-accord exactly, which makes us say that one of them acts upon the other, because one of them expresses in a more distinct way than the other the cause or reason of the changes. (…) From that I also infer that, if bodies are substances, they cannot consist only in extension. But this doesn’t alter in anything the explanations of particular phenomena of nature, that always have to be mathematically and mechanically explained, provided that we are aware of the fact that the principles of mechanics are not exclusively dependent on extension. Therefore, I uphold neither the common Hypothesis of the real influence of one created substance on another, nor the Hypothesis of occasional causes (…) but I assert a concomitance or agreement of what happens in different substances. (…) Each

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following their own laws, one of them acting freely, the other without choice, they meet on the same phenomena. All of this is not far from a fair agreement with what you say in your answer to Dom Robert p. 26, namely that man is the proper object of his own feeling. We can however add that God is so too, being the only one who acts upon us immediately by virtue of our continuous dependence.  (GP 1 382–383; A II 2 89–90)

Here we find, clearly and concisely stated, the majority of the theses published in 1695 in the SN: the free and spontaneous character of substance, the expressive dimension of the accord between substances, the insufficiency of extension as a foundation for corporeal substances, the dependence of mechanics on nonmechanical principles, the critique of occasionalism and the presentation of the doctrine of concomitance as the essential nucleus of the new explicative doctrine of the system of nature. Apart from this long text, in this letter Leibniz also refers in passing to two themes that he would expand upon in the SN: a. The question of the nature of matter and of its real or apparent substantial character. Leibniz, who does not suggest a solution to this question, the difficulty of which he is well aware, states, however, that “we can decide such things” (GP 1 384; A II 2 91). b. The question of the nature of substance, regarding which he writes: “When people dispute whether a certain thing is a substance or a way of being, we have to define what a substance is. I haven’t found such a definition anywhere, and I was forced to work on it myself ” (GP 1 384; A II 2 91). Also characteristic, especially as regards Leibniz’s strategy, is the very small reference to the principle of inherence of the predicate in the subject, here set out as an axiom, similar to the principle of contradiction, in the following terms: “That in every true proposition the notion of the predicate is contained in the notion of the subject” (GP 1 382; A II 2 88). This principle, which provoked such a strong reaction from Arnauld at this time (cf. GP 2 15–16, 25–34; A II 2 8–9, 31–38), is here mentioned in passing as though it was self evident, and it didn’t provoke any comments from Foucher. At the same time, Leibniz makes no allusion to his bitter controversy with Arnauld: in Foucher he was looking for a supporter, not for another adversary. Foucher did not comment on Leibniz’s principle, but responded to his letter in the most flattering terms. He thanks Leibniz for his long letter and says: “I consider your wise reflections as treasures I shall preserve with care” (GP 1 385; A II 2 131). It is precisely at this point, when the essential of the Leibnizian doctrine of substance is communicated to him, that the enthusiasm with which Foucher



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received Leibniz’s show of deference is significantly and partially attenuated by what might be taken as a warning: Foucher declares that he “could not resist communicating Leibniz’s letter, or its scientific contents, to many of their common friends” and that he had already shown the letter to many “honestes gens”, being convinced that Leibniz would not blame him for that (ibid.). He further poins out that “ultimately, we are not here judging on your proposed system, and that there will be occasion for you to explain yourself further, if it suits you, on such a grand theme” (GP 1 386; A II 2 131). In the meantime, Foucher postpones any detailed analysis of or commentary on Leibniz’s theses (cf. GP 1 386, 388; A II 2 132, 133), saying, however, that should it be published he would respond “extensively and in a way that will not displease you” (GP 1 386; A II 2 131). In May 1687, Foucher again refers to Leibniz’s long letter, saying that, if it were ever published, he would respond in a way that would not displease Leibniz (cf. GP 1 389–390; A II 2 196). In a later letter (GP 1 390–394; A II 2 199–207), Leibniz returns to the theses of the SN, trying once again to bring them closer to Foucher, the French critic of Descartes. Here too, Leibniz cautions that the truth is very different from what one would imagine, for, even when a substance can be reasonably called physical and often moral cause of what happens in another substance, nevertheless, metaphysically speaking, each substance is (together with God’s cooperation) the real immediate cause of what happens in it, such that, strictly speaking, nothing is violent. And we can even say that a body is never pushed but by the force it has inside. (…) But it follows also that, in each substance that is a real substance, and not just a Machine or an aggregate of various substances, there is some I that answers to what we call soul in us, and that is unborn and incorruptible, and can’t begin except by creation. And, if animals are not simple Machines, we can believe that their generation, as well as their apparent corruption, aren’t but simple transformations of the same animal, now more, now less visible. Nevertheless, I consider that Spirits, just like ours, are created within time and exempt of such revolutions after death, since they have a very peculiar relationship with the sovereign being (…). If bodies were simple Machines, and if there was only extension and matter in bodies, all bodies would arguably be but phenomena. (…) And I seem to catch a glimpse of agreement with this in your thoughts, p. 59 of your speech on St. Augustine’s view on the Academiciens. (GP 1 391–392; A II 2 201–202; cf. Foucher 1687)

Here too, a fair number of the theses of the new system are clearly communicated to Foucher: the apparent character of generation and corruption, the ideal character of physical causality, the presentation of substance as a species of the soul, the distinction between orders of reality with the indication that spirits are

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governed by different laws, the affirmation of the phenomenal character of matter understood as extension, etc. In a later letter, where he acknowledges having received several of Leibniz’s letters at once, Foucher says that he didn’t have the opportunity to respond as quickly as he would have liked and mentions only his position regarding the essence of matter, saying that he had already expressed his opinion on the subject, and indicating that it is wrong to assume that all extension is material; he expresses his satisfaction with Leibniz’s agreement: “I’m very happy to see that you agree with me on this” (GP 1 399; A II 2 424). Later, in a letter of December 31st 1691, Foucher writes to Leibniz about Malebranche’s agreement with some of Leibniz’s theses: Malebranche had declared himself in agreement with Leibniz about the way in which nature acts, by infinitely small alterations and never in jumps. Foucher is not entirely convinced by Leibniz’s argumentation and expresses his reservations. But he continues: “If you can break the barrier between Physics and Metaphysics through your problem, as you believe you can, I’ll be grateful; in fact, the more uniformity is found in objects, the better” (GP 1 400; A II 2 474).13 Leibniz responds immediately to this letter and to the issues and difficulties that Foucher raised, in January 1692. He mentions his respect both for abstract and general investigations and for those that make specific advances in science. The reason for this double respect lies in the fact that he sees the investigation of principles as a way of advancing particular inventions (cf. GP 1 403; A II 2 491). Regarding the question of the essence of matter, a brief statement reiterates Leibniz’s conviction of the non-existence of atoms: “I can’t conceive physical indivisibles (without a miracle) and I think nature can do any smallness geometry can conceive” (GP 1 403; A II 2 492). In this letter there is also a very brief reference that is clearly connected to the SN: Leibniz refers to the scholastics, maintaining that, despite all of their barbarism, they should not be scorned, for their thoughts were very profound, although badly assimilated (cf. GP I 406; A II 2 496). Foucher answered this letter in August 1692, saying that he made arrangements for an extract of the letter to be published in the Journal, and announcing that he would respond publicly to three aspects of the text: about the Academicians,14 about the axiom according to which nature does not progress in jumps, and about the axiom Extrema in idem recidunt (‘Extremities fall back into the same’). Further, he informs Leibniz that the extract at stake was published in the Journal of the previous year and that it provoked a commentary. He briefly criticizes the nature of this objection and says: “I agree with you when you say that the essence of matter does not consist in extension, and I have proved it in my critique of the Investigation of truth and in my responses and other dissertations” (GP 1 408; A II 2 567).



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This issue begins to increasingly interest Leibniz, and his replies come faster and faster. In October 1692 Leibniz answers Foucher, commenting briefly on the objection his text on the essence of matter had been subjected to. Leibniz declares himself the winner, given that his critic inadvertently conceded to that which Leibniz meant: extension is indifferent to movement and to rest, and to explain the inertia of matter it is necessary to use another concept: that of force (cf. GP 1 410; A II 2 610). In March 1693 Foucher answers, communicating to Leibniz, among other things, the core of his own public reaction to Leibniz’s text that he himself published. The correspondence continues with Leibniz making allusions to the nature of matter, to final causality, etc., and in May 1693 Foucher complains that he still has not had access to Leibniz’s Dynamics (cf. GP 1 417; A II 2 700). Already close to the text’s publication, on April 6th/16th 1695, Leibniz decides to write to Foucher to ask him about his health. The previous interruption must have owed to his understanding that Foucher did not want to continue with their correspondence during wartime (cf. GP 1 420).15 This is a brief letter, in which Leibniz has little else to say, after circumstantial greetings, other than that he has the intention of publishing some thoughts and, among others, my system about the communication of substances and the union of body and soul, about which I sent you something before. I think it is the only one capable of giving an intelligible explanation without recurring to the divine omnipotence. (GP 1 420)

But Leibniz’s sole intention was not to announce this decision. He also wanted to provoke and prepare a reaction to the text. “I would like very much that wise people would reflect upon it, and I expect those reflections most of all from you, so as to shed light on it” (GP 1 420). He hopes that Foucher will encourage a reaction from Malebranche, who is directly implicated in the text that would soon become public. He also informs Foucher that he intends to publish all or part of his correspondence with Arnauld, owing to the affinity of subject matter (cf. GP 1 420). Foucher, who had not entirely understood Leibniz’s silence, answers quickly to this letter and to his invitation to respond to the new text. The words with which he reacts to the news of the SN’s publication are warm: It is with extreme joy that I hear from you that you are going to publish your system of concomitance. Anything that comes from such an able person as you are, Sire, cannot fail but be extremely useful to the public. You have written something to me about it nearly ten years ago, but the matter deserves elucidation, and I’m waiting for it with pleasure, provided that you fulfil your promise soon.  (GP 1 422)

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This reaction of Foucher’s is both interesting and meaningful. It reveals that it was not due to lack of interest in the content that he had not responded to Leibniz’s text and to the indications there given by Leibniz, but by a deliberate decision. The speed of the response, the precision with which he refers to Leibniz’s first revelations regarding the SN, and above all the way in which he paraphrases Leibniz’s words, referring to this new system as the “concomitance system” (GP 1 422), allow us to think that Leibniz’s words resonated more strongly with him than the lapse in his reaction would have suggested: although he did not react to them, Foucher retained Leibniz’s theses. SN was made public on June 27th and July 4th 1695. From the next day, June 5th/15th 1695, we have an incomplete draft of a letter Leibniz wrote to Foucher, in which he reveals a few of his expectations for this text. The first paragraph briefly summarizes the essential message of the SN, clarifying its fundamentals and setting out the most significant aspects of the SN: each unity expresses the whole universe in a particular way, and does this naturally, by its own laws, without receiving outside influence, except of course that of God who creates and recreates it continually (cf. GP 1 423). Leibniz cannot hide the expectations he is harboring for this text, and they are manifest in every sentence: an initial indication of these expectations can be gathered from his observations that Mons. Lantin would certainly have liked to know of these thoughts, having so well understood, years ago, the connection that united Leibniz’s physics to his metaphysics. Most significant of all is the hope that he harbored regarding the SN’s value and a positive reception of the text. If the text has a good reception he will venture to publish “also other rather peculiar thoughts I have towards suppressing the difficulties of fato et contingentia and making clear an essential difference conceivable between material forms and intelligences or spirits” (GP 1 423–424). Foucher never received this clarification of Leibniz’s; Leibniz probably did not send him the letter he prepared here in draft form. Foucher’s public reaction is published right away, in September 1695. From all of this correspondence and the way in which it anticipated the contents of the SN, it clearly transpires that, in the first phase, including that which was made public, the agreement between the two authors was assumed and explored: a. Leibniz systematically presents his positions as positions that follow from those defended by Foucher; b. The texts presuppose a certain basic agreement between the two thinkers regarding the insufficiency of the Cartesian doctrine of matter; c. The flattering tone is reciprocal;



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d. In sum, the two thinkers are on the same side; though they think about different themes, they do not clash; e. Above all it is interesting to note the recurring references that both authors make to Malebranche, whose doctrine is explicitly taken on in the SN. Through Foucher, Malebranche has access to Leibniz’s theses and reacts to them; it is also Foucher who transmits these reactions to Leibniz; f. Leibniz communicated nearly all of the theses contained in the SN to Foucher, and even some that he did not dare to develop in that text, namely the thesis of the inherence of predicates on the notion of the subject, and did not hide the originality of his own point of view.

7.

The public confrontation, or the controversy itself

Simon Foucher was the first author to react publicly to the text published in the Journal des Sçavans. This reaction, solicited by the one and promised by the other, was in the end neither the reaction that Leibniz expected, nor that which was predicted from Foucher’s words. The text is the object of a short criticism. This reaction – that Leibniz would have preferred to have been private, or to have come prior to the publication of the text – is surprising in the decisiveness of the objections and the tone in which it is written. Foucher abandons here the earlier flattering, almost venerating, style of the private correspondence and adopts a harsh and somewhat impatient criticism of Leibniz’s theses. As we have said, this reaction of Foucher’s to the SN is not the first time in which the two philosophers engaged in a public exchange of opinion. The publication, on Foucher’s initiative, of an excerpt of one of Leibniz’s letters shows the interest the French philosopher had in making public a correspondence with which he took special care and of which he was openly proud. The text in which Foucher reacts publicly to the SN takes on the usual form and style of controversies printed in the Journal des Sçavans. Foucher composes his reaction in a letter written to Leibniz. It is a brief letter, with a very clear structure. Foucher begins by acknowledging that the SN is not entirely new to him, that Leibniz had already made known to him significant aspects of its contents “more than ten years ago”, and states that, in response to that old letter, he had already communicated to Leibniz partially his feelings (GP 4 487). We shall briefly examine this introductory paragraph. To Leibniz, who had privately encouraged an intellectual confrontation on numerous occasions, just as he had done for similar reasons with Arnauld roughly at the same time,16 Foucher now says – this time publicly – that he has already shared his opinion, although not completely. The public was not familiar with the private correspondence between

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the two intellectuals. They were only minimally aware of some of the themes and texts that they exchanged. Having always postponed his reaction, while promising to react, Foucher presents himself now as having satisfied, at least partially, Leibniz’s wishes. The text continues with a critical analysis of what Foucher calls the first part of Leibniz’s text, specifically, that which was published on June 27th. Foucher reacts to this first part in only two paragraphs. He identifies two main themes, developed around a central objective, to which he reduces the whole argument of the first part (corresponding to the first 11 paragraphs of Leibniz’s text). Of particular interest, as already mentioned, is the tone and style, now significantly different from the laudatory tone of his previous correspondence. The critique is short, and relatively unsubtle. Foucher paraphrases Leibniz’s ideas, which he doesn’t even bother to quote, and evaluates them. A general analysis of the first part allows Foucher to redirect his scope and the scope of what Leibniz calls – pompously, according to this critique – a ‘new system’. Leibniz limits himself (cf. GP 4 487) to making known in all substances the unities that constitute their reality and that, distinguishing them from others, form their individuality. There follow two points that require more attentive development; the structure of Foucher’s argument is the same for both of them. He begins by acknowledging that Leibniz is right, and proceeds by questioning the pertinence of these theses and the scope of the solutions presented, making it clear that Leibniz’s reflection was not sufficiently mature to really answer these questions. The structure of the argument is as follows: a. it begins with “I still agree with you”, “You are right”, “You note very well”; b. proceeds with “yet” or “but” c. and concludes with “it is hopeless”, “I don’t think that you are right”  (GP 4 487–488). Foucher’s argument in this part is structured exactly alike regarding each of the two criticisms he makes. He concedes, he criticises, and he anticipates possible objections to his criticisms to show how irrelevant they are. Of the two themes that deserve Foucher’s critique, the first has to do with the necessity of accepting that there are first principles or primary elements that constitute the reality of extension. The Leibnizian solution appears problematic to him, but Foucher does not dwell on its analysis. He thinks that Leibniz “sleeps” (GP 4 487) on the question, which presents serious problems. The theme had already been debated, also publicly, and in the Journal des Sçavans in 1693, and because of this he does not bother returning to it.17



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The second object of Foucher’s criticism are the “unities of composition or of relation” (GP 4 488), as he calls them, which Leibniz refers to when speaking of animals and clocks, seeing them as unities. In Foucher’s view, Leibniz constructs the unity of these composites – animals and plants, for example – based on the notion of substantial form, which constitutes the principle of individuation of these composites, distinguishing them from all others. Foucher grants that Leibniz’s question is well put and that the principle of solution is pertinent but, once again, he thinks that the solution is not satisfactory. Leibniz goes too far in the concessions he makes to animals by recognizing a sensitive principle in them. If this is true – argues his critic – what Leibniz was not able to do was to sufficiently ground the difference between the souls, or substantial forms, of living organisms and substantial forms or rational souls, which in his text he had claimed were different from each other. Thus, the schematic summary of Foucher’s analysis of the first part of  Leibniz’s text is as follows. There are only two questions worth mentioning: in the first, Leibniz’s position is not new, and in the second he does not solve the problem that he attempts to solve. Both are pertinent questions, but the SN does not contribute anything, or at least anything of significance, towards their real solution. The critical analysis of the SN continues with a critique of “concomitance” which, according to Foucher, constitutes “the main and second part of your system” (GP 4 488). To this question, which Leibniz develops in seven paragraphs, Foucher dedicates a single – although quite long – paragraph. Foucher’s argumentative procedure is basically the following: a. He begins by conceding to Leibniz that his hypothesis is not impossible, or that it is not especially improbable for God; b. He goes on – here beginning the actual critique – by saying that the hypothesis is no more than an artificial and ad hoc tool for justifying an illusion: to make believe that substances act upon each other when in reality they do not. Why would we have to admit to concomitance when the same effect – exactly the same effect – that Leibniz aims to rescue with this strange artifice can be reached by simply negating the existence of bodies, those “vain and useless” (GP 4 489) masses which spirit can neither move nor come to know? c. In coming up with a line of thought created only to explain certain prejudices, Leibniz is drawn in to the same difficulties that paralyzed Descartes, which is surprising and particularly disappointing because Leibniz had other ways to solve the problem (ibid.). Which ways were these? Foucher explains them immediately afterwards, making it appear that the Leibnizian

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solution of concomitance is inconsistent with the Leibnizian defence of the active capacity of material substances, which it is not possible to think of in terms of mere extension. Foucher’s critique of this second main part of the SN thus consists mainly of declaring the Leibnizian solution to be an ad hoc solution, one that is founded on prejudice and aims to justify it: the doctrine of concomitance is a useless and incomprehensible artifice, considering the resources of Leibniz’s ontology. If Leibniz is right, if there is accord without interference between substances, and particularly between body and soul, what reason would there be not to declare bodies purely illusory, and not to see them as mere phenomena? And what need is there for grounding an accord between substances and phenomena, between realities and illusions? The Leibnizian solution is ad hoc precisely because Leibniz has the theoretical resources not to become enmeshed in a solution of the Cartesian type, a solution that is insufficient and that “we have reason to reject” (GP 4 489). According to Foucher, the theoretical resource that Leibniz uses, but does not use correctly, is recognizing or affirming that there is something in common between material and spiritual substances. This theoretical resource, which would allow him to think interaction, and the absence of which impeded Descartes from thinking it, is precisely what, for Foucher, Leibniz renders inoperative and useless with the doctrine of concomitance. At this point, it is important to note that Foucher does not distinguish between the two questions, which Leibniz approaches separately: the question of the interaction between substances, by virtue of which we can understand the dynamism of a certain plan or order of nature, and the question of the relation between body and soul, in which the interaction or the union between realities that belong to different realms or orders, is conceived: Foucher only considers the question of the union between body and soul. After analyzing the SN, Foucher concludes his reaction with a reference to methodology. Leibniz – we gather from Foucher’s now more dissimulated criticism – does not follow a rigorous methodology in the SN. Almost all the questions he takes on are questions that can only be judged by rigorously following the order which will allow us to solve them, something which – we are also led to understand – does not correspond to Leibniz’s method. Leibniz moves from the plausible to the irrefutable which, according to Foucher, is not acceptable. As a final remark, in the last paragraph Foucher acknowledges, at least in passing, that there are other themes taken on in the SN, which deserve discussion in their own right, but which he decides not to deal with (cf. GP 4 490).



8.

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Leibniz’s text and Foucher’s reaction

Foucher’s almost telegraphic reading of Leibniz’s text is surprising in the different slant that the two authors, who had known each other for around twenty years, put on the SN. The themes that Leibniz particularly valued, especially in the first part of his text, those which he surrounds with particular caution and provisos, are simply ignored or omitted in Foucher’s reading. To be sure, Foucher is perfectly aware of the importance and novelty of Leibniz’s positions; the essentially active dimension of substance, the “greatest question” (GP 4 480) of its indestructibility, the central issues in the debate between the scholastics and the moderns, the abuses of the former and the deficiencies of the latter, the notion of force (about which Foucher had asked Leibniz for details on several occasions), etc. But he chooses to attack Leibniz on a particularly feeble point. Out of all of the elaboration on the notion of substance and its implications – the real core of the SN – Foucher is interested mainly in the question of unity and plurality. This is a theme about which Foucher had already asked Leibniz for clarification (cf. GP 1 411–412; A II 2 678): how can extended things result from unextended ones? How can unextended metaphysical points be at the origin of extension? Foucher’s criticism of this point brings him, paradoxically, to compare Leibniz’s position with Descartes’s and to affirm, on two occasions, that Leibniz has no more success than Descartes had in solving the problems he takes on. This is what happens with the case of animal souls and the doctrine of concomitance. It is worth noting that Foucher makes no allusion to Leibniz’s assessment of modern philosophy, according to which the moderns confuse artificial things with natural ones. It is clear why: this principle of confusion, which keeps them focused on mechanics and prevents them from advancing to dynamics, is precisely that which Foucher is also referring to in his argument. According to him, Leibniz has just granted reason to animals. At the root of this line of reasoning is the idea that an animate principle is a res cogitans. From the second part of Leibniz’s text, Foucher retains only a general impression and it is on the basis of this impression that he comments the text. Interestingly, this position of Leibniz’s is also compared to Descartes’s, without making any reference to Malebranche and the doctrine of occasional causes, which are explicitly mentioned in Leibniz’s text and which Foucher was well aware of, and about whose reaction he had previously informed Leibniz. Here too, Foucher’s selection of themes to take on is not fortuitous. As we have seen, in the letter in which he announced the imminent publication of the SN, Leibniz asked Foucher for his reaction and suggested that it would be interesting to obtain Malebranche’s reaction as well. Foucher omits the reference to Malebranche and to the doctrine of occasionalism, which Leibniz declared to be a doctrine whose insufficiencies

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required the kind of development he himself provided. To be sure, he argues, occasionalism identified the difficulty and realized that there is no real influx between one substance and another; what it didn’t notice was that, in order to solve the problem, it is not sufficient to appeal to the general cause, which amounts to having recourse to miracle for explaining nature (GP 4 483). Leaving aside this interesting observation of Leibniz, Foucher refers back to Descartes, again to say that Leibniz’s system brings no more light than that which both rightly had fought against. Another particularly telling omission has to do with the discussion of the communication between substances. Leibniz, as we saw, distinguished clearly between the two questions: that of the communication between homogenous substances and that of the communication between realities belonging to different realms. Foucher ignores the first question and concentrates only on the second. In doing this he not only overrides a fundamental part of the Leibnizian reasoning, but he actually inverts the judgement that Leibniz had made about it. I am referring to the question of the natural character – i.e., the non-violent character – of the Leibnizian explanation. According to Leibniz, the proposal of the SN is the only one that is natural, and, as such, it is more than a hypothesis; it is a certainty. In contrast with this logical argument, Foucher calls it an ad hoc explanation, founded upon prejudice and aiming to legitimate it. The only reference to the active dimension of substances, which Leibniz developed amply in the first part of his text, is transferred to the critique of this second part, with Foucher saying that Leibniz – who was already capable of thinking of matter not in passive terms – was developing a system in which passivity was being taken particularly far, given that, for souls, bodies are useless and unknowable masses. The final criticism, regarding the order of his arguments and the correct procedure for the arguments to answer the questions, seems to have exasperated Leibniz. Here Foucher attacks the inductive style of the path Leibniz takes, which is supposed to lead one, almost unwillingly, to the country of truth that cannot be rejected. Leibniz presents his system precisely as something that has been concluded, not something from which to begin. Foucher finds in Leibniz’s text a rhetorical tool to present that which was elaborated ad hoc and based on prejudice. Foucher’s conclusion – that we do not have to take as true that which still has any obscurity, and that this should be separated from that which can be conceived clearly and sufficiently (“ce que l’on conçoit clairement et suffisamment”) (GP 4 490) – is clearly a hint that such rigor lacks in Leibniz’s argument.



9.

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Leibniz’s answer

Leibniz publicly responds to this text within Foucher’s lifetime. His response appears in the Journal des Sçavans of March 30th and April 9th 1696, a few days before the death of Foucher, on April 26th (GP 4 493–498). Leibniz’s answer was prepared with special care. He begins by identifying which of Foucher’s remarks are worth answering and he prepares his public response with a set of notes in which he points out the core of his answer (GP 4 490–493). There are six passages highlighted, identifying the topics of his answer. The first part of Foucher’s response is given two commentaries, one particularly long (occupying more than half of the whole draft) and another, briefer one. Leibniz expands on his doctrine of extension and on the relational character of space, distinguishing himself clearly from Foucher, who had made unities or points the constitutive elements of extension. On this note, however, Leibniz grants that Foucher is right in one aspect of his criticism: it is true that the whole, the composite, is a well-founded phenomenon, and that bodies are so too. But he distances himself from the conclusions Foucher draws from this statement, saying that bodies are neither futile and useless entities nor unknowable realities. The second question of the first part of Foucher’s argument was granted much less importance. It is clear that the living organisms of brutes are not capable of theoretical reasoning, nor of good or evil in a moral sense. Interestingly enough, the question of concomitance, around which Foucher’s most radical criticisms revolve, does not merit a very developed response. What Foucher considers to be a useless artifice is actually something necessary in order to naturally understand the natural world. Leibniz briefly recalls the capacity of the SN to account for phenomena: we can continue to say that substances act upon each other, but we should understand exactly what this means or else redefine the meaning of this statement. The last two paragraphs approach the singularity of nature as a whole, as Leibniz understands it. God does not substitute nature, acting in its place; God produces everything (mediately), producing a nature that produces (immediately) its own modifications in an ordered way. Foucher’s last argument shows that he did not understand the nature of substances and their natural activity: certainly, corporeal substances are capable of movement and of effort. But here too, we are using an imprecise, though useful, way of speaking. Effort and activity happen “indoors” (GP 4 493); they are tendencies towards change according to their own laws. Foucher did not have access to these notes nor were they made public. The published text is written in quite a different style, made up of short paragraphs

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that function almost as a gloss on Foucher’s text, except for a few more developed paragraphs, particularly the last one. Unlike the draft, in which he broadly developed the question of the unity of substance and the relational character of space and extension, in the published text Leibniz chose to react mainly to the criticisms of the second part of his text. In a brief introductory paragraph he discreetly reveals his perplexity regarding the tone of Foucher’s response. He does this by reminding his interlocutor, but really revealing to the public, that he does not remember having received any objections from Foucher when “many years ago” he told him of his “Hypothesis of Philosophy” (GP 4 493). If these had been presented to him, Leibniz would have considered them. Just as he would do, without reservation, should Foucher decide to present a pertinent and precise objection to any of the theses of the SN, which does not appear to have been the case: judging from the published text, Foucher simply wanted to give Leibniz the opportunity to deepen some of his statements. From an argumentative point of view, the gist of Leibniz’s strategy is concentrated in these few lines: to an incisive, yet from his perspective, tardy and misplaced criticism, Leibniz reacts by saying that he does not find in Foucher’s text any precise or pertinent critique. To the first round of criticism, related to the questions of the principles of unity of extended substances, Leibniz answers with a reduced set of brief notes in which he distinguishes his position from Foucher’s interpretation of his text. In the first four paragraphs almost all of the arguments are presented negatively: Leibniz shows that he did not mean to present principles of the unity of extension, that the unity of the clock is not that which Foucher said it to be, that the sensitive principle of animals does not reside in the disposition of organs, etc. This last observation serves to accuse Foucher of using an irrelevant argument: what he presents as a criticism is not contrary to what Leibniz affirms, and what he infers from Leibniz’s position does not in fact follow from his theses. The most fully developed part of Leibniz’s published response is that which refers to harmony. Leibniz dedicates 16 paragraphs to this aspect of Foucher’s critique, and uses a wide and varied range of resources to defend the SN. Recognizing Foucher’s reluctance to accepting his thesis, Leibniz begins by responding to some particular objections regarding the utility and the advantages of his solution. The answers are clear: the question of utility does not make sense when what is at stake is the demonstration of a necessary system (GP 4 494–495). As for the advantages, they are obvious: the system of harmony explains – and is the only one that does so naturally – the communication between substances and the unity of body and soul. The second level of his argument is aimed at Foucher’s objection that the Leibnizian solution rendered bodies actually useless, given that the soul neither



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knows nor interacts with them. Leibniz’s response points out to an argument not used in the SN: the moral dimension of divine action and the reasons that motivate that order. “God wanted it”, “God thought it good”, “substances concur for God’s designs” (GP 4 495). Having dealt with the objection in its deeper level, Leibniz returns, as he had done in the SN, to the common manner of speaking of nature: we speak of reciprocal action, of the knowledge of bodies and of acting upon them, and we are right to do so. The Copernicans also spoke of the movement of the sun. It is not common language that we have to change; what we must change is the comprehension of the scope of these statements: causality is real, but it is ideal, not physical. The final set of arguments used to respond to the alleged uselessness of bodies refers to the supposed passivity that, according to Foucher, follows from Leibniz’s position. We have seen that this was Foucher’s main criticism, the reason why the solution presented in the SN appeared so disappointing to him. Foucher did not understand Leibniz’s position, and he did not understand the SN: not only did Leibniz never admit the passivity of bodies, he also claimed that “there is action everywhere” (GP 4 495). Here we find the most radical level of opposition and divergence between the two authors. Leibniz’s system is disappointing to Foucher because Leibniz thought of substance in terms of activity, but was unable to explain interaction in the same terms: causality and movement become ideal and are only ways of speaking. Leibniz, on the other hand, feels that he has been misunderstood by Foucher because from his point of view “there aren’t bodies without movement or substances without effort” (GP 4 495). The Leibnizian solution does not deprive the natural world of activity, nor does it deprive physics of mechanics; it simply refers mechanics back to dynamics and, in so doing, redirects it to metaphysics: the world of activity and force is the world of substances, the world of physics is the world of phenomena, and movement is the phenomenal expression of substantial activity. The understanding of the true meaning of movement and body is not incompatible with the establishment of its phenomenal character; more than that, having understood substance, it is compatible only with it. In the second part of his answer, published on April 9th (GP 4 496–498), Leibniz attacks Foucher’s methodological objections: the observation – Foucher presented it as an objection – that the Leibnizian system is ad hoc should be interpreted as a mark of excellence, not as an objection. It is true that it is a system that was built a posteriori, in order to save phenomena, but this is how systems are, and should be built. Considering the possible meaning of Foucher’s statement, according to which Leibniz has pre-established motives – prejudices – that he wants to save by proposing his new system, Leibniz presents in new terms what he sees as the most important reason for accepting the hypothesis of harmony:

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this hypothesis is founded on a priori reasons but these reasons are good reasons; because there is no other way to explain emanative action in accordance with the laws of nature, we can consider the hypothesis he proposes demonstrated by its principles. Leibniz avows that he thought he could present the utility of his thesis by showing the problems that other theories faced in trying to explain what his explains naturally (the natural is here situated between the violent and the supernatural). A brief rhetorical argument, still regarding Foucher’s methodological reservations about the SN, appears in paragraph 19: Foucher appears to accuse Leibniz of superficiality or lack of rigor when he says that it is necessary to ask many other questions before answering those which Leibniz takes on and resolves briefly in his text. Ironically, Leibniz asks him to admit the possibility that he had already asked those questions. In the final paragraph, which is by far the longest, Leibniz prepares the continuation of the controversy, redirecting the argument into a field that was particularly dear to him at the time, and appealing to an argument that reinforces the credibility of the SN, but that does not respond directly to any of Foucher’s objections. “I will add one more reflection” (GP 4 497), he writes. The argument that reinforces his previous theses consists in saying that his is the only system that does not violate two general laws of nature: the principle of conservation of the quantity of force, with which he corrected Descartes’s principle of the conservation of the quantity of movement, and the principle of conservation of the quantity of direction. Put simply, only his system respects “all the natural laws of bodies, despite the changes that occur in them as a result of the changes of the soul” (GP 4 498).

10.

Conclusion

The analysis of the set of texts that contain the scientific exchange between Leibniz and Foucher allows us to look at the SN with some surprise. Is there really a controversy between the two authors that was generated by this text? Foucher died very soon after the publication of the SN and had time only to react energetically to the text, without being able to reply to Leibniz’s response to his criticism. At the same time, Leibniz had communicated, before publication, nearly all of the significant contents of the SN to Foucher, having asked him for a private reaction, which Foucher refused to produce. In this sense, there was not really a controversy between the two authors. In the first, private phase, because Foucher did not want one, and in the second,



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public phase, when Leibniz was no longer asking for it, because Foucher could not continue the controversy that he himself had started. The controversy was not announced – it was in fact announced that there would not be one – but it began when it was no longer either wanted or foreseen. In this exchange many of the ingredients that would allow us to see it as a real controversy are lacking. The main reason is that neither one of the interlocutors considered themselves as belonging to opposing sides. Their positions diverge on essential points, but they coincide on even more essential ones, namely on the nature of matter and in their criticism of Descartes. The very rhythm of controversy is somewhat inverted here. There is a long period of provocation, not taken up or recognized by the interlocutor, and an explicit avoidance of reaction. Then, almost abruptly, there is a public reaction disproportionate to the relative indifference that Foucher had previously revealed. It would appear that the two authors use their correspondence, less as a way to exchange opinions, than as a way of letting each other know what they were working on, which, while having some overlap, was also very different: Foucher was occupied with academic philosophy; Leibniz with the notion of substance and the elaboration of dynamics. In reality, both were looking for the right time, one to present his philosophy, the other, to react to it. Again, we find here, so to speak, a certain inversion of the dynamics of the controversy: instead of moving from private debate to the public arena, reaching a high point and gradually dying out, the relation between Leibniz and Foucher is different: as we have seen, Foucher avoids private debate, and then publicly attacks Leibniz’s text with an intensity that had no precedent in his private correspondence. It is impossible to anticipate how Foucher would have responded to Leibniz’s public reply to his criticism. This atypical style could have taken on the form of a more authentic public debate, with partisans on each side. Foucher’s death did not allow this to happen. From the point of view of its contents, the important question is the following: what was so new about the SN for Leibniz to have surrounded it with so much caution and care? And what was so shocking about it to have provoked such a violent reaction from Foucher? A brief answer to the first question, which would be necessary to nuance a little more than it is possible to do here, could be the following: the SN proposes that physics be overcome as the model of knowledge because it denounces its methodological insufficiency. Proposing the recovery of substantial forms, Leibniz “deontologizes” the material world and its movements, declaring the resources of Cartesian ontology (the substantial nature of extension, the substantial reality of movement, the possible passivity of material substances) to be unsatisfactory, and

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proposes to replace it with a phenomenalization of the resources of mechanical physics: we can continue to speak of interaction between substances, of bodies and their movement; we can speak of physical causality, but we should understand the meaning and the reach of these statements. On the other hand, the SN presents itself as the only possible way of overcoming the difficulties stated in its title: there is no other way of explaining the interaction between substances, no other way of understanding the union between soul and body. But it is not possible not to look for an answer to these questions. Not doing so means making nature and its dynamism incomprehensible, and any ontology that does not find a satisfactory explanation is, for that very reason, itself unsatisfactory. The nerve of the Leibnizian argument, that which gives the SN its systematic character, is at this point the notion of the natural: the doctrine of influence is incomprehensible; occasionalism is not convenient enough. Were it possible, the former would be the source of a violent – and as such non natural – explanation of nature; occasionalism is clearly another non natural explanation of nature, not because it is violent, but because it is miraculous. The natural world, which is neither violent nor supernatural, is precisely what only harmony can sufficiently – that is, naturally – explain. From this perspective, Leibniz’s expectations for the SN are really many and quite understandable: he is not proposing yet another modern doctrine; he is presenting himself as a pioneer and as a successor of Descartes, who he once wrote had been detained “in the antechamber of truth”. The answer to the second question – what is shocking about the SN – is more difficult to find. Foucher shared Leibniz’s reservations regarding Descartes. Like him, he recognizes the necessity of establishing a connection between physics and metaphysics. What shocked him most was probably the phenomenalization of the physical world, namely of physical movement and activity.

Notes 1. Henceforth SN. 2. Leibniz’s reservation in publishing the SN might be partially due to the reaction that his communication of the summary of the Discours de Métaphysique had provoked in Arnauld. 3. On Leibniz’s and Foucher’s publications in the Journal des Sçavans, cf., respectively, volumes 6 (pp. 312–320) and 4 (pp. 741ff.) in Journal des Sçavans, Table Générale des Matières …. 4. Cf. for instance Palaia (1996: 122): “The Système nouveau comprises one of the highest points in the search for a balance between the autonomy of natural laws and the principles of the metaphysical system, for Leibniz the most fundamental reason behind all his research”. 5. Cf. for instance Brown (1996: 40): “The New System, I conclude, was intended as a popular piece and should not be taken as a definitive statement of Leibniz’s philosophy at the time”.



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6. Besides Foucher and Bayle, Lamy and des Maizeaux also reacted to the SN. 7. On the several reactions to the publication of the SN, cf. Palaia (1996). 8. On the different versions of the SN and the possible reasons for them, cf. Brown (1996). 9. On Leibniz and Foucher’s agreements regarding their criticism of Descartes and the nature and scope of the theses they share, cf. Brown (2004). 10. Cf. GP 1 369–427; A II 1 245–249, 422–423, 468–469, 542–543, 548–549; and A II 2 86–93, 130–133, 158–162, 194–197, 199–207, 217–218, 282–285, 290–292, 421–424, 473–476, 489– 496, 565–568, 609–610, 676–681, 699–700, 708–711, 719–721, 726–727. There are 12 remaining letters from Leibniz and 16 from Foucher. Only the last four letters (two from each; GP 1 420–427), all from 1695, aren’t yet published in A II. In A II 2 there is a so far unpublished letter from Foucher to Leibniz (nº 67); furthermore, this volume acknowledges as addressed to Foucher the letter of 14 April 1687 (nº 158), which Robinet had wrongly taken to be addressed to Bayle; moreover, it corrects the letters’ orders, and dates as from the end of June 1693 the undated letters published by Gerhardt (GP 1 414–416). On the history of the relationship between Leibniz and Foucher, cf. Brown (2004), Popkin (1966), and A II 2 l–liii. 11. Gerhardt publishes this text twice in GP, once when presenting the correspondence between Leibniz and Foucher (GP 1 424–427), and again after SN, and as a reaction to it (GP 4 487–490). I will follow the GP 4 edition. 12. Leibniz annotated this text, which includes the reply to Desgabets. See A VI 3 312–326. 13. The letter presumably begins with an allusion to Galileo’s problem of the chainette, which Leibniz analyzed in an article of 1692. But Foucher’s allusion to Leibniz’s conviction that he can overcome the barrier between Physics and Metaphysics doesn’t seem to refer to this text, but rather to the letter Leibniz sent Foucher and regarding which Malebranche manifests his agreement and Foucher his doubts. Unfortunately, according to the editors of A II 2, this letter is lost (see A II 2 473). 14. Foucher presents himself as “an Academician in the Platonic style” (GP 1 388; A II 2 194) and the ideas of academic scepticism are present in virtually all his correspondence with Leibniz. In fact, it was this topic that motivated Leibniz’s first letter, where he expresses his agreement with Foucher on some fundamental issues: the need to examine once in a lifetime all our assumptions (GP 1 369; A II 1 245), the impossibility to demonstrate the external world’s existence, and the need, defended by the Academicians, to block the mind’s spontaneous movement that rushes towards “fabricating what we call matter and body” (GP 1 372; A II 1 248), etc. Leibniz’s profound interest in Foucher’s work, and their agreement in this shared background, lead Foucher to inform Leibniz about the publication of his books, to send them to him and to discuss them with him. In this spirit, Foucher sent to Leibniz the second volume of his Dissertations sur la recherche de la verité ou sur la philosophie des académiciens (cf. GP 1 401; A II 2 475) and Leibniz asks him to clarify another issue in which both agree already back in 1675 (GP 1 374; A II 1 249), namely, that the requirement to examine all assumptions up to the end didn’t lead the Academy – as several scholars had thought – to oppose the advancement of science; on the contrary, such a requirement does not prevent the progress of scientific knowledge, even in the absence of a proof of the truth of all propositions that are susceptible of proof, Leibniz argues (GP 1 402; A II 2 490).

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15. It is hard to determine to which war Leibniz alludes here, and the text doesn’t provide hints to it. It could be the so-called Nine Years War, where Louis XIV was involved – which might explain, in Leibniz’s eyes, Foucher’s fears; but this war ended only in 1697, so that it wouldn’t help to explain the continuation of the correspondence in 1695. It could also be a reference to the conflicts in Hanover, including Maximilian Wilhelm’s and Otto von Moltke’s conspiration of December 1691, after the death of Duke Friedrich Augustus, and the events of the following years; yet this could hardly justify, for Leibniz, Foucher’s desire to interrupt the correspondence. 16. From Arnauld Leibniz wanted a private evaluation of the Discours de Métaphysique, before its eventual publication; from Foucher, of the Système Nouveau. When he didn’t receive from Arnauld, in the latter’s first letter, the careful reading he expected, Leibniz protested and, in the following letters Arnauld payed much more attention to the young man’s arguments. See Dascal (1995) and DA 148. 17. Cf. Extrait d’une letter de M.D.L. pour soutenir ce qu’il y a de luy dans le Journal des Sçavans du 18. Juin 1691. Journal des Sçavans, January 5th 1693, 7–8 (GP 4 466–467); Extrait d’une lettre de M. Foucher Chanoine de Dijon, pour répondre à M. de Leibniz sur quelques axiomes de Philosophie, Journal des Sçavans, March 16th 1693, 93–95 (GP 1 410–414; A II 2 676–681); and Reponse de M. de Leibniz à l’extrait de la lettre de M. Foucher Chanoine de Dijon, inserée dans le Journal du 16. Mars 1693, Journal des Sçavans, August 3rd 1693, 279–280 (GP 1 415–416; A II 2 711–713).

References Brown, S. 1996. “Leibniz’s New System strategy”. In R. S. Woolhouse (ed), Leibniz’s ‘New System’. Florence: Leo S. Olschki, 37–61. Brown, S. 2004. “The Leibniz-Foucher alliance and its philosophical bases”. In P. Lodge (ed), Leibniz and His Correspondents. New York: Cambridge University Press, 74–96. Dascal, M. 1995. “Strategies of dispute and ethics: Du tort and La place d’autruy”. In Aken der VI. Internationalen Leibniz-Kongress. Hannover: Leibniz Gesellschaft, vol. 2, 108–116. Foucher, S. 1679. Nouvelle dissertation sur la Recherche de la verité, contenant la Critique de la Critique de la Recherche de la verité. Foucher, S. 1687. Réponse a la Critique de la Recherche de la Vérité sur la Philosophie des Académiciens: Seconde Partie: Où il est parlé du Sentiment de S. Augustin touchant les Académiciens. Paris. Foucher, S. 1693. Extrait d’une lettre de M. Foucher Chanoine de Dijon, pour répondre à M. de Leibniz sur quelques axiomes de Philosophie. Journal des Sçavans, March 16th 1693, 93–95; GP 1 410–414; A II 2 676–681. Foucher, S. 1695. Réponse de M. S. F. à M. de L. B. Z sur son nouveau sistême de la communication des substances proposé dans les Journaux du 27 juin et du 4 juillet 1695. Journal des Sçavans, September 12th 1695, 349–352; GP 4 487–490. Journal des Sçavans. 1754, 1756. Table Générale des Matières contenues dans le Journal des Savans, de l’Édition de Paris. Depuis l’année 1665. qu’il a commencé, jusqu’en 1750, inclusivement, avec les noms des Auteurs, les Titres de leurs Ouvrages, et l’extrait des Jugemens qu’on en a portés. Paris: Briasson, Libraire, Vol. 6, 312–320 and Vol. 4, 741ff.



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Leibniz, G. W. 1692. De la chainette, ou solution d’un problème fameux, proposé par Galilei, pour servir d’essai d’une nouvelle analyse des infinis, avec son usage pour les logarithmes, et une application a l’avancement de la Navigation. Journal des Sçavans, March 31st 1692; GM 5 258–263. Leibniz, G. W. 1693a. Extrait d’une letter de M.D.L. pour soutenir ce qu’il y a de luy dans le Journal des Sçavans du 18. Juin 1691. Journal des Sçavans, January 5th 1693, 7–8; GP 4 466–467. Leibniz, G. W. 1693b. Reponse de M. de Leibniz à l’extrait de la lettre de M. Foucher Chanoine de Dijon, inserée dans le Journal du 16. Mars 1693. Journal des Sçavans, August 3rd 1693, 279–280; GP 1 414–415; A II 2 711–713. Leibniz, G. W. 1695. Système nouveau de la nature et de la communication des substances, aussi bien que de l’union qu’il y a entre l’ame et le corps. GP 4 477–487. [= SN] Leibniz, G. W. 1696. Eclaircissement du nouveau systeme de la communication des substances, pour servir de réponse à ce qui en est dit dans le Journal du 12. Septembre 1695. Journal des Sçavans, March 30th and April 9th 1696, 136–138 and 138–140; GP 4 493–498. Palaia, R. 1996. “The ‘New system of the nature of substances’ in the philosophical journals of the seventh century”. In Woolhouse (ed), 113–122. Popkin, R. H. 1966. “Leibniz and the French skeptics”. Revue Internationale de Philosophie 76– 77: 228–248. Rutherford, D. 1995. Leibniz and the Rational Order of Nature. New York: Cambridge University Press. Woolhouse, R. S. (ed). 1996. Leibniz’s ‘New System’. Florence: Leo S. Olschki.

chapter 9

Quantification of natural and positive laws How to organize privileges? Pol Boucher

1.

Introduction

In Chapter 7 of the De Casibus Perplexis, Leibniz mentions, among many others, the name of Nicolas Vigel, a jurist of the 16th century, which he calls solidissimus (‘very reliable’), who wrote a book entitled Methodus juris controversi (‘On the controversy about the method of law’). This book is not unique but very characteristic of a period that aimed to organize laws as a whole and to reach a system in which there should be no conflicts between norms and rules. Of course, this plan was designed to build a general method for the elimination of all juridical controversies. It is thus understandable that Vigel also wrote many books whose titles contained the word ‘Method,1 and also that Leibniz’s project of reorganizing Law in the Nova Methodus was directly connected with the De Casibus Perplexis intention. Of course, the processes of both authors are the same: confronted with juridical controversial cases, they said that the judge is obliged to conclude the case, not by drawing lots nor favoring his friends, but by researching undoubted reasons or at least highly probable reasons. However, they differ in one point and this point constitutes the Leibnizian specific contribution. Both of them, as jurists of the same epoch, try to resolve ‘perplex’, i.e., ‘hard’ cases, in that part of the Law where their elimination seems to be impossible, i.e., in safety and privilege rights, because the perplexity results from the gathering of different legislator’s wills. But when Vigel, as many jurists in Leibniz’s time like Rauchbar,2 Carpzov3 or Berlich,4 decides on the impossibility of rational elimination of these cases, Leibniz proves that this elimination is possible if we organize the norms according to Natural Law and the evaluation of benefits. There is thus an implicit controversy between Leibniz and contemporary jurists regarding how to deal with a special type of hard cases, which is very instructive about Leibniz’s approach to hard cases in general.

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2.

The safeties and privileges theory

Safeties are put to the disposal of debtors and their creditors by the legislator to allow the first to obtain a credit, and to guarantee to the second the payment of their claim. This double function is so important that we could consider it as the raison d’être of being of all the improvements that have taken place over the centuries and that have led to the actual safeties system and their organization, thanks to rules such as prior tempore potior jure and generi per speciem derogatur. By multiplying secured debts (possessory lien, pledging, preferential right and mortgage) next to personal debts (surety-bond and guaranty), Law has gradually conferred to the obligations an existence independent from the contracting parties.5 Instead of only being guaranteed by the creditor’s personal and direct power over his debtor or his representative, the obligations’ content has been guaranteed by the debtor’s possessions, either really held (pledge) or potentially held (mortgage). All that was then required was the advertising of these two juridical instruments, to create the possibility conditions of a general credit6 system, that would overcome the fortuitous case(s) and allow an increase of the general flow of wealth. It is for that reason that the use of the rule generi per speciem derogatur was generalized, allowing credit for all the facilities that we can find in societies where economical, juridical, and social relations are more and more complex. If the holder of a general safety was preferential and could recover his claim by alienating at his good will all or some of the debtor’s possessions up to the limit of the debt, the holders of particular privileges who would come into concourse would in all only possess an incidental debt, and would then most certainly renounce offering this credit possibility. It was therefore inevitable, in the interest of creditors, debtors, and the society in a whole, to progressively try, either to temper the general liens priority over the special privileges, or to completely inverse the order of priority, with an exception to the super privilege of salaries, and general liens of court costs and copyright. It is so in the case of real property liens where we see prevalence of the special liens,7 or also in the case of a concourse between a multiple mortgage concerning a number of immovables and different unique mortgages each concerning only one immovable. Indeed the indivisibility of the mortgage allowing the multiple mortgage holder to choose the possessions that he wishes to discuss first, and that till complete payment of his debt, in spite of the effects of his choice on the content of his concurrents’ unique mortgages, we would end up with the despoilment of some of them, unless we applied the generi per speciem derogatur rule and unless the jurisprudence did not intervene to prevent it, either by applying the abuse of right theory, or by obliging the multiple mortgage holder to withdraw, in each possession, an amount that preserves the debts of his competitors, or to discuss in priority the later mortgages (see Cabrillac and Mouly 1997: 721).



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But the complexity of juridical bonds created by this multiplication of safeties, and most of all, the necessity of their constant adaptation to contradictory requirements of personal and collective interests, and of equity and legality, demands constant revision of the safeties’ subordination order. In some circumstances a privilege can find itself prevailing over a second privilege, although in other circumstances it would be subordinated to the second, occupying the latter’s initial place. Inevitably perplex cases result from this situation, so that jurisprudence must intervene to compensate the Law’s hesitations. But what rules must we apply to reorganize Law? Should we favor much simpler, general safeties, at the cost of special safeties, as they prohibit personal interests? Or should we do the exact opposite, with the risk of multiplying exceptions, in order to respond to social evolution and adapt the Law to the settlement of concrete cases? More generally, which principles can we use to resolve perplex cases, i.e., to definitely demonstrate the coherence of the Law system, rather than eliminating them by introducing a motion applicable to the circumstances? In other words, which are the fundamental norms that underlie the Law, that would allow to combine the richness of its effects with the simplicity of its solutions, and to make every juridical case decidable, regardless of its complexity? Such are the questions raised by some dipositions in today’s safety law, and such are also the questions that Leibniz resolves throughout the De Casibus Perplexis and the Elementa Juris Naturalis 121, by using a method for analyzing perplex cases in which the respect of logical laws, the peculiarity of the juridical context, and the jusnaturalistic hierarchy of norms are combined. The analysis of a few examples from the De Casibus Perplexis, contrasted to the actual safety Law, will demonstrate this.

3.

The problem to solve

In Chapter 35 of the De Casibus Perplexis, Leibniz analyzes a situation where three elements, formed one after the other, come into concurrence as follows: A a tacit mortgage, B the Treasury, and C a dowry. These terms design, of course, juridical realities, the characteristics of which are those of the Justinian law within which Leibniz evolves, but we can easily link them to similar dispositions in our own legislation, thereby underlining the topical character of his argumentation. We thus obtain the following correspondence: “the tacit mortgage” would correspond today to the ancient “secret mortgages”, i.e., the one of the ward and the one of the married woman which were made explicit by the law of July 13th 1965, when the rights of these people were no longer opposable to a third party except by the date of their registration (French Civil Code, art. 2121). Consequently, it

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represents a general legal mortgage. On the other side, the right of the Treasury would designate today the privilege of the Treasury on “all tax payers’ immovables” (French General Tax Code, art. 1929) which allows it to reimburse itself with priority on the tax payer’s properties. Therefore, it is also a general privilege. Finally, the right that the married woman has on the husband’s belongings due to the dowry could have a certain similarity with the present legal mortgage that a wife holds, which starts on the day of her registration and gives her priority over her husband’s creditors (French Civil Code, art. 2134). But a similarity only, certainly not an equivalence, as the privilege of the dowry is far less extended in today’s legislation than it was in the times of the Corpus Juris Civilis, due to the fact that today it begins on the day of its registration, while since the Justinian constitution of 531 it possessed a retroactive effect (see Mazeaud 1999: 324). As Mazeaud perfectly reminds us, Justinian transformed this privilege in 530 [which before belonged to the wife and allowed her to “prevail over her husband’s chirographical creditors”] into a mortgage starting on the day of the marriage; it was objected that the reform compromised the husband’s credit, which did not stop the Emperor, to whom was given the epithet uxorius, from making in 531 this safety a privileged safety prevailing over all mortgages issued by the husband’s initiative, even prior to the marriage; unmarried men themselves were affected in their credit as they were potential husbands! (Ibid.)

The dowry privilege becomes therefore similar in its extension to the salary’s present day super-privilege that prevails over any other safety. We can then easily see how a perplex case could arise, if each of these three general safeties came to claim priority over the others in an attempt to establish a hierarchy, since each would have reasons overcoming those of the other two. That is exactly what happens when the three components of this perplexed case are expressed as follows: – the anterior tacit mortgage is preferred to the intermediary Treasury – the intermediary Treasury is preferred to the posterior dowry – the posterior dowry is preferred to the anterior tacit [mortgage] The first proposition is justified by C.4.53.1 which declares: “it is not forbidden to the tutors or curators to alienate their own properties with its cause, although in the capacity judged at the title [of tutors or curators] they become debtors [of those of whom they have the charge]. Consequently, your curator can have mortgaged his property with its charge to the benefit of the Treasury”. This means that a ward’s general occult mortgage prevails over the general privilege of the Treasury in case of concourse, as the tutors or the curators are first of all the ward’s debtors before being the Treasury’s debtors.



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The second proposition is justified by C.7.73.2 that gives priority to the Treasury’s general privilege, whose date of constitution precedes the one of the dowry, by saying: although your husband is obliged at one point, thanks to the dowry, to give you something, the rights of the Treasury prevail over your cause if he engaged himself towards the Treasury before his possessions were mortgaged to your benefit. Because if he starts to be obliged [towards the Treasury] after his possessions were mortgaged [to your benefit], the privilege of the Treasury is no longer applicable to his properties.

Finally, the third proposition is justified by the Justinian law in C.8.17.12 which gives the dowry’s privilege a retroactive value: We have been disturbed by the constant withdrawals on the wife’s [possessions], by which they deplore the loss of their dowry and [which are operated] on the husbands’ possessions by anterior creditors [to the marriage]. That is why we have considered the ancient laws which provide in personal actions at law, an important prerogative to the rei uxoriae action,8 in order to give the wives, a privilege against nearly any personal action at law, and to allow them to pass before the other creditors, even if they were anterior” … “it was more acceptable when husbands were in a situation towards their creditors in which by their own possessions alone, they satisfied their obligations, and not by the means of the wife’s dowry that she possesses for her belongings and her food and that is her own or has been given to her by someone else.

The circularity of this order is now quite manifest as the mortgage prevails over the Treasury that prevails over the dowry, which in its turn prevails over the mortgage. As the mortgage once again will prevail over the Treasury in an endless process, it becomes impossible to determine an indisputable hierarchy of these three safeties, as each one claims primacy over the others. Nevertheless, an order must be given since, by law, a judge has the obligation to judge, the denial of justice being forbidden. If we forbid ourselves for now from choosing a hazardous or arbitrary criterion to eliminate perplex cases, two solutions seem a priori possible: we can hope to eliminate these cases either by demonstrating their sophistical nature, or by stating the normative foundations of a strict safety hierarchy. The first solution would therefore be logical, the second normative, and both would potentially have the same effectiveness. In reality, the first solution eclipses before the second, because a perplex case is not a sophism that we could refute with the Aristotelian method, by demonstrating that surreptitiously a term is given an extension that is not its own to falsely conclude even more (Aristotle, Soph. Refut. §18). Indeed,

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the relative extension of the terms of each element does not contain in itself any contradiction; and although we cannot conclude in this way owing to the circularity of the implications, it is not logically contradictory to find ourselves in such a position of undecidability. The difficulty does not come from the fact that we mistook the meaning of a law and that we attributed to a safety an extension that was not its own in the context of a positive law. Rather, the difficulty comes from the fact that this law actually exists in the Code, although it leads to a circular subordination of safeties. To resolve a perplex case one must not try to refute it, but rather to eliminate its possibility conditions by proposing a new extension to the terms in conformity with the requirements of a strict order relation. Put differently, resolving a perplex case where different elements have priority over its followers in a circular way, supposes that we examine the norms that they express and break the circularity by attributing to one of them an absolute priority over the others, despite the fact that one of them nevertheless prevails over it. But the simplicity of this solution must not hide the major difficulty, which is the justification of the choice taken on the element to be privileged. If three elements are disposed in such a way that the first prevails over the second, the second in its turn over the third, and the third over the first again, the logical properties of each element are the same as if they all are superseded by the previous element, and supersede the following one. In consequence, it would be illegitimate to choose one over the other as absolute reference for a decreasing order of privileges9 if there was no reason to ignore the arguments giving priority to its predecessor. The central difficulty is now to unearth those reasons. So we can easily understand that the De Casibus Perplexis undertakes long developments, discussing the solutions proposed by the Commentators and the Glossators of Civil and Canonic Law. Indeed could one really content oneself with circumventing the difficulty as some doctors did, by adding to the transitive rule “If I defeat the one who has defeated you, I have defeated you too” applicable to the whole of the claims and safeties, the clause logically devoid of sense “even if in other respects you defeat me”, with the intention of separating logical laws from the juridical situations in which they are expressed, to obtain more than ever, from a partial identity of the people implied in both cases, an unacceptable conclusion? And could we really add that clause knowing, on the one hand, that the genius of the Romans was of introducing that logical rule into law10 in order to apply it in the case of claims and ranks transfer, as well as in compensation (French Civil Code, art. 1295), mortgage, or subrogation problems (French Civil Code, arts. 1250 & 1251), where it allows, for example, a debtor to compensate the debt he has towards a creditor by the cessation of an equal claim he possesses over a third creditor, as if the creditor of a creditor of a debtor became the direct creditor of the debtor11 (or vice versa, as if the debtor of a debtor of a creditor became the direct



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debtor of the creditor); and knowing, on the other hand, that the added clause is even against reason as it claims to reverse the logical order of priority obtained in a certain situation, under the pretext that an opposite order can be obtained in another, preferred situation? Leibniz is perfectly clear on this point. One cannot resolve a perplex case by sacrificing logic for the benefits of arbitrary decisions. On the contrary, it can only be resolved by using Natural Law’s universal rationality12 to conciliate the context’s juridical characteristics and the indisputable validity of logical laws.13 One difficulty appears nevertheless, which makes the solution a lot less evident than it seems. In the perplex case that we have just seen, each argument relies on a different law (C4.53.1, C.7.73.2, and C.8.17.12) that appeared at one point of the history of law with the purpose of providing a classification of privileges which corresponds to the needs and the norms of the time. But one of these laws found itself confronted with the ambiguous situation of having to fit into a preexistent classification and at the same time, of introducing as an exception elements of a new order. This is of course C8.17.12, the latest, through which Justinian gives priority to the dowry over the creditor’s occult mortgage (but not over the Treasury), though by transitivity it continues to come after the dowry in conformity with what the two previous laws impose. The perplexity here results from an opposition between the terms of this new law and the logical consequence of the two previous ones. But at the same time it seems that even though there is a conflict of reasons, there is all the same no conflict of laws, since they are not in direct contradiction. Of course we can regret that, for the difficulty would be much easier to eliminate because all we would need to do would be to introduce a general rule that would abrogate any anterior law if opposed to the prescriptions of a new law, or on the contrary, establish a rule that nullifies any new law that contradicts with any anterior law. Yet it is clear that it is not the use of logic alone that will allow us to resolve a perplex case, even though the given solution must be logically valid as it should definitely represent a reorganization of safeties where transitivity will once more be possible. It is also clear that perplexity did not occur when we had only the two first laws because the legal hierarchical organization of the three terms was in conformity with logic and gave us the set – occult mortgage, Treasury privilege, and dowry. Nor would it occur if Justinian had given a true super privilege to the dowry so that it would have then preceded the occult mortgage in virtue of C.8.17.12, and the Treasury’s privilege by transitivity. The problem is that he gave only a partial privilege, allowing it to prevail only over the creditor’s occult privilege, but once again refusing its prevalence over the Treasury privilege by maintaining C.7.73.2, and forbidding in this way to definitively organize safeties by transitivity. How must we then consider this Constitution, which introduces circularity and makes

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this case perplex? Must we eliminate it, knowing that it represents a concrete case that upsets the safeties hierarchy that we obtained with the anterior laws, or should we on the other hand enlarge its range, giving therefore the dowry the super privilege necessary for a reordering of law? Should we, in other words, favor the laws’ preexistent hierarchy at the expense of their innovative counterpart, or should we do the opposite? To put it even more generally, should we either adopt the maxim generali per speciem derogatur (cf. Rolland and Boyer 1999: 296) in the interpretation of Law and the elimination of perplex cases or proceed in the opposite way and take for rule: generali per speciem non derogatur?

4.

The way to resolve the problem

If the presence of perplex cases results from a distortion between a certain legal hierarchical organization and the requirements of a logical hierarchical organization of Law, and if in fact, it all comes down to a classification problem, then the elimination of these cases will imply that we specify both the relation of the particular to the general in a hierarchy of norms, and the treatment reserved to exceptions. Of course this problem is not new, since it was already the subject of discussion at the end of the thirteenth century between the founder of Montpellier’s law school, Placentin, and Azon’s master, Johannes Bassianus.14 And it was even less of a novelty that the rule allowing to favor the specific designation when in concurrence with a generic designation, is stated on numerous occasions15 by the Roman Law thanks to a very simple consideration: the specific designation being a complementary information added to the generic designation, our respect of the settlor’s or the legislator’s intention obliges us to give it priority over the generic designation. Moreover, precision in juridical matters is always preferable to generality when this generality conveys incertitude, since it is the law that is responsible for the fulfillment of obligations.16 And this is so true that the opposite solution is only adopted when it is manifest that the species has wrongly been mentioned in the place of the genus.17 But these solutions are not adapted to the actual situation for they require the inclusion of the species in the genus, while in the examples of the De Casibus Perplexis the concrete cases are precisely opposite to the genus. Consequently, the term derogatur of the rule must receive the meaning of rupture and not the one of continuity, since there is no question here of specifying the general rule by the enunciation of its specific difference, but rather of affirming the existence of a new safety, regarding which we ask ourselves if it should not benefit from a more general privilege than the safety that prevailed over it in the previous order. Leibniz is therefore perfectly right to declare that a “particular right departs from the common right. And from this derogatory will from the one



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who establishes the decree, we have a principle from which we can start” (De Casibus Perplexis, Chap. 30). But to avoid an arbitrary choice, he must at the same time imperatively justify the super privilege he gives to this exception. Because after all why give authority to the derogatory will of the one who establishes the decree, if this will can err? It is perfectly clear that it is certainly not for any positivist type of reasons. The obedience to power is not justified by the fact that it is an established power, but by the fact it is a reasonable power. Neither is it for internal reasons to a given codification of positive law, as in this case it is a matter of giving juridical value to a norm which is unfamiliar with this codification. So it is then only for reasons external to positive law, i.e., for reasons of Natural Law, that we can do it. We have the immediate indication of this when we survey of the expressions used in the examination of certain cases, as they contain terms such as: “the Laws reason” (Chap. 26), “it is more suitable that” (Chap. 29), “it is better that” (Chap. 32). But we have the most definite proof of this at the beginning of Chapter 10 when Leibniz declares that: “the ruled judgment of the judge follows the rules of charity, equity, humanity, convenience, usefulness, etc., where the case can not be settled in accordance with [positive] law”, or when he declares in Chapter 11: But because in accordance with the civil Law’s reason, the positive laws rely on Natural Law and the Law of Nations on a direction for exception’s determination and a more particular direction for restriction, it follows that this Natural Law and Law of Nations will prevail in certain circumstances, till the opposite is approved by a law, as if it was the people’s universal agreement (because as the Prince can produce laws, [this agreement] coming from the people expresses itself into him by consensus). And consequently if the interpretation is then uncertain, we should add the interpretation rules of natural reason and although equal rules and presumptions militate in favour of each party, we should judge against the one who relies on any positive law which cannot be sufficiently justified, although approved. It becomes therefore obvious that even Bachoff von Echt will acknowledge that every case, in which nothing is uncertain, can always be resolved by means of the simple Natural Law and Law of Nations.  (De casibus perplexis 157)

Nevertheless we could say that in matters of safety conflicts, to ground the decision on competences such as the judge’s “natural reason” or his sense of “equity”, would be to unduly privilege approximation. And this seems all the more regrettable since we presented Leibniz’s approach as a model of a steady reasoning in the reorganization of Law. Can we still defend it, if the treatment of perplex cases only comes down to being a vague sprinkle of jusnaturalistic themes? The answer to this question is complex. It obliges us to confront both Leibniz’s and the contemporary approaches in matters of safety classification, and at the

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same time link the De Casibus Perplexis to the Elementa Juris Naturalis 122, in order to underline more than ever the necessary convergence of reasons implied in the reorganization of Law. But at the same time such a complex endeavor possesses two considerable advantages: (1) it allows to show to what extent modern law would benefit from Leibniz’s inspiring approach, to rationalize its way of resolving privilege conflicts. (2) it allows to accurately connect the detail of civil legislation to general principles of Natural Law by detailing the intermediary degrees that are much too often left in obscurity, due to a lack of knowledge concerning how to determine them. For these purposes, let us examine a modern safety law treatise. In it we will constantly discover the use of a vocabulary that we could believe issued from the Justinian compilation or from Natural Law theoreticians: when a justification must be given for any pre-eminence of such or such privilege, the notions of equity, justice, personal or general interest are called upon.18 But the extension of each of those notions and the definition of their relations remain very informal in spite of the fact that the very technical character of the organization of privileges where we distinguish with precision the finalities of each one, their basis and their limits, should impose the opposite. Furthermore, the progressive multiplication of privileges seems to go against the formulation of strict organizational rules, as Cabrillac and Mouly (1997: 701) remind us: No disposition of the Civil Law allows us to determine a precedence between the two categories of preferential rights [general and special]. This gap in the law developed a doctrinal controversy at the beginning of the 19th century, which was settled by an order of the “Cour de Cassation” [i.e. the Supreme Court] dating from the 20th of March 1849 in favour of the special privileges justified by the generi per speciem derogatur principle. This solution has been constantly reaffirmed; but jurisprudence has renounced to base it on an adage that would make this primacy a primacy by nature and which would give it an absolute value, hardly compatible with the ever more numerous exceptions it required. The primacy is now founded on the respective qualities of the claim and the priority is justified, for each special privilege, by the reason that justifies its existence.

Nevertheless, privilege conflicts do not lack justification. Far from it, they result from very precise tensions between the legitimate right of each person to obtain his due (lessor’s privilege for example), the obligation of the society to protect the persons against excessive complaints (the limitation of general liens in real estate), and the right of that same society to insist upon both the general interest over particular interests and the fundamental personal right over secondary collective interests (the case of the super-privilege of salaries). An equitable resolution of a conflict between creditors and debtors will therefore imply that we take



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into consideration the three components of these situations, i.e., the parties (one or several creditors in concourse, one or several debtors jointly held or not), the immovable or movable nature of what is in dispute, and the existence of a general or special privilege. It would indeed be iniquitous that a creditor who would benefit from a general lien over the immovables could use it as a pretext to sell all the debtors’ movables, whilst a partial sale would have been enough to satisfy himself off and, what’s more, would not have injured the second rank creditors. So we obtain in this way a balance between the contracting parties’ mediate and immediate interests and the society, whereby a certain representation of what is the legitimate order is expressed. Therefore, in our Civil Code the classification of privileges obeys the following principles: when creditors are in the same rank, conflicts in immovables matters are resolved by concourse, but when some of them have general liens, priority goes to the salaries super privilege, then to the court costs privilege, and finally to the privilege of copyright. It is legitimate to keep the priority of the rights of those who have increased the common asset by their work and guarantee at the same time the recovery of the court costs which benefits the creditors’ community (cf. French Civil Code, arts. 2095, 2104, and 2105). When there is a conflict between general liens and special privileges concerning real property, the first prevails (French Civil Code, art. 2105), if the movables have already been allocated, because if they could unconditionally prevail over the special privileges, it would be in no one’s interest to give a claim guaranteed by real property that an anterior general lien could reduce to nothing. It is then in the debtors and creditors general interest, i.e., the society as a whole, to proceed in such a way that the credit possibilities are not reduced by an excessive priority given to general liens. When there is a conflict between general liens concerning real property, the difficulty here is also to establish a legitimate order between the safeties which guarantee the creditors, debtors, and the community’s respective interests. The article 2101 of the Civil Code defines it by the following order: 1/ salaries 2/ court costs 3/ Treasury 4/ funeral costs 5/ last medical expenses. When there is a conflict between general and special privileges concerning real property, the second prevails over the first, with an exception to the super privilege of the salaries and to the privilege of the legal court that guarantee the individual’s fundamental rights and the rights of the community, for it is clear that the first meaning of the generi per speciem derogatur rule is applied here. Indeed a general privilege on movables is equivalent to a claim on each piece of them, and so would correspond to a genus whose special privilege would be a species, as it would confer a determined claim on a particular movable.

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Finally, when there is a conflict between immovables’ special privileges, the priority order between creditors must be determined by a simultaneous consideration of the nature of their claims and of their actions in the preservation of the possession.19 When these creditors are pledgees and benefit of the same privilege, we apply the prior tempore prior jure rule to know which one prevails over the others. However, if they have all participated in the preservation of the property, the last one is preferential in accordance with the opposite posterior tempore prior jure rule, because without him, the others might not have anything at all. Finally, when one is a pledgee and the other, the one who keeps the property in good condition, the privilege of the second one will prevail over the privilege of the first one if his action followed the constitution of the pledge, as it is legitimate that it comes first in the order of priorities by the fact that it was profitable to the first. Of course in the opposite case the argument is reversed. If the details of these rules are set aside and we try to summarize their underlying principles, we immediately see that they are all founded on the idea of a search of balance in a system of opposed forces where either multiple personal rights, actual or potential, legal or legitimate, or multiple personal rights and the common good, are in conflict. And we notice at the same time that the solution to each of these conflicts is obtained by relating the claims of each party to the common good that results from the preservation or the improvement of the common property. This is the case with the three general privileges (movable or immovable), which must necessarily prevail over the special privileges as they guarantee to all an optimal exercise of their rights. It is also the case with the credit given by the priority of special and multiple mortgages over the general mortgages, as it increases the happiness of all and allows at the same time the compensation of fortuitous cases.20 And finally, it is also similar in the case of the pledgee keeping the property in good condition; his right must legitimately prevail over the others’ since his action guarantees their claims. It is now clear that a consistent theory of the organization of safeties and privileges cannot make do without an eudemonist oriented philosophy, where the definition of just and legitimate would result from an organization of duties and rights connecting each person to the others and to the society as a whole, and whose first and final principles were those stated by Leibniz in the Elementa Juris Naturalis 122 (A VI 1 433) when he declares: The just is: My benefit accompanied by another’s no-benefit. The compensatory allowance. My absence of “dolus” accompanied by another’s “dolus”. My necessity accompanied by the sacrifice of another’s necessity.



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The unjust is: My benefit accompanied by another’s “dolus”. My absence of “dolus” accompanied by the sacrifice of another’s necessity. My absence of benefit accompanied by another’s no-benefit.

And when he adds: “indeed the City is a secure Society, i.e., a multitude of men living with the knowledge of security that they procure to each other” (A VI 1 446). We could indeed try to deduce from this a safeties classification in accordance with Natural Law, and draw from it the rules allowing us to harmonize personal and collective interests, in compliance with the requirements of the Political Body whose aim is the maximal happiness compatible with the safety of each person.21 This is because the different privileges are all in all nothing more than institutional ways to prevent the abuse of right. But this becomes impossible when the determination of the balance point between creditors’ and debtors’ respective interests takes as a rule, not to unconditionally respect the suum cuique tribuere formula as if there was no difference between the jus fruendi and the jus abutendi, but to apply the neminem laedere formula, whose effect is to delimit the different parties legitimate rights by combining the following couples of terms: necessityutility, benefit-“dolus”, no-benefit-absence of “dolus”. We obtain in that way, for one same positive right, a graduation of its practice, as the no necessary benefit of one contracting party gives way to the effective “dolus” of the other party, who obtains by that means a dispensatory privilege, which would legitimately prevail if it became necessary or if it did not bear one “dolus”. But one question still remains, which seems, if not to weaken the very principle of a quantitative determination of safeties right, at least to subordinate it to the possibility of a total quantification of Law, i.e., to Universal Justice. Since the privileges organization rules aim at the formation of an optimal balance between the personal and the collective rights, they also reflect some conceptions of the fundamental personal rights. But the problem is to know whether the definition of the norms defining the legal status of a person comes under a quantitative approach similar to the one we have just examined. Of course, this question did not arise when the intention was to justify the primacy accorded to the special privileges over the general liens in order to increase the general happiness, since the effects produced by the introduction of this primacy – thanks to the generi per speciem derogatur rule – are immediately measurable and are closely limited to the safeties domain. But does it mean that it will be the same when it comes to the question of the legal status of a person? How could we indeed quantitatively justify the modification of a woman’s legal status and the grant of the Justinian’s super privilege when it is perfectly clear that a diminution of the

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husband’s credit results from it? But that seems impossible as this law looks at first sight like an economical aberration. So pressing reasons were then needed to impose it, and not only reasons concerning the immediate economical interests of some party. What are we then to do with such a law when it proves to be the source of a perplex case? Should we eliminate it in the name of an approach limited to an immediate detailed account of rights, or on the contrary, accept that Law contains norms whose effects, although real, exceed our computing capacity? And in that case, how can we avoid the disappearance of the “principle of reason” in favor of a neutral principle of imputation ratifying the arbitrariness of juridical decisions? Of course the difficulty is considerable as it finally comes down to asking ourselves if, in an eudemonist vision of Law, it is possible to gather in the same computation, all the norms derived from the right governing things and contracts – in which we can quantify the positive impact they have on the party’s material situation since they concern property distribution – and all the norms derived from personal rights, for which we can only suppose that they will have effect by the compensation of their immediate negative aspects. Let us look from this perspective at the case 19 of the De Casibus Perplexis, in which a tacit anterior mortgage, an express intermediary mortgage, and a posterior dowry are opposed. The circular precession of these terms will be the result of the following juridical constraints: – The anterior tacit mortgage of which Leibniz talks about (either general or special) corresponds today to a legal mortgage, i.e., to the safety that the law automatically confers to people whose property is used by another, like in the case of a money-lender whose money is used to restore a building. This simple mortgage, issued from a very general disposition of the law and not from any judgment or convention, has naturally no need to be registered (except in the case of the married woman or of the ward since 1955) in order to prevail over all the other simple mortgages which are posterior to it because, in accordance with the prior tempore potior jure rule, the simple mortgages priority order is defined by their day of registration (or of constitution when they are secret). – Justinian’s Constitution as stated in C.8.17.1222 gives a privilege to the woman anxious to claim her dowry in the case of a divorce, and gives her priority over the personal actions that the husband’s creditors can institute. But it does not give her this privilege when the action instituted by creditors is real and exists even if ownership changes. However, an explicit mortgage (i.e., by contract, in today’s terminology) conferring chattels which are real like all mortgages, the privilege of the explicit intermediary mortgage will therefore prevail over the privilege of the dowry.



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– Last, we know that the Authentic 9723 gives a privilege to the dowry over the money-lender legal mortgage, whether it was constituted before the dowry or not, because it is suitable to compensate the “feminine weak nature”. We obtain in this way a perplex case where the anterior legal mortgage prevails by temporal priority over the intermediary conventional mortgage (1st position), which in its turn prevails over the posterior dowry as its privilege is limited to personal actions (2nd position), and the dowry prevails over the anterior legal mortgage as the “feminine weak nature” has to be protected (3rd position). But at the same time we see that such a perplexity results from the ambiguity of the woman’s juridical status generated by the incoherence of the Roman laws which seem to be trying to transform her in a sui juris by granting her a super privilege, and at the same time, in other aspects, to maintain her in her initial state of subordination. It becomes therefore obvious that the perplexity will not be removed until we eliminate the composite nature of her juridical status and until we renounce to obtain the impossible agreement between the principles of two opposite legislations. But on the other hand, saying this is not sufficient to eliminate the problem, for many different legal solutions have historically been proposed in Justinian and Saxon and in ordinary law, and all seemed reasonably justifiable. Indeed all the different balance solutions they proposed between rights and duties, things and persons, seemed equally acceptable in the absence of knowledge of the best one to choose by a definitive computation of all the components of the problem. And as Leibniz reminds us, This perplex case is resolved in favour of the dowry by Bartolomeo Saliceti in [his commentary] of the Authentic “quo jure” in C.8.17,24 and by Nicolaas Everaerts, Andreas Rauchbar, Daniel Moller, Benedictus Carpzov; Matthias Berlich leaves these cases to the judgment of the judge; the former correctly [conclude] according to the Saxon law’s point of view, in accordance with the end of §.31,25 but in the ordinary law’s point of view, [the parties] will concourse for proportional parts in accordance with the end of §.20 and §.27. Because Justinian’s law is as much in favour of the 3rd position as the use in our time is in favour of the 1st and 2nd [position]. (De casibus perplexis 201)

Can we then conclude that the definition of the woman’s juridical status is only a simple matter of agreement, and that we must accept indifferently either of these solutions on the pretext that each one offers to positive laws a balanced state? Or on the contrary, should we not try to search for a solution that is legitimate because it is optimal?

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Leibniz’s answer implies that we come back once more to the Constitution uxoriae and that we try to acknowledge the complex interplay between economical, institutional, and normative constraints which preceded its establishment. Indeed the perplex case would never have emerged if we had not tried to compensate the negative effects that the woman’s juridical status had on her possibilities of getting her dowry back, by giving her a super privilege, and at the same time, tried to maintain some juridical consequences from her original status. Because when she found herself in the subordinated position defined by the ancient law, the coherence of the privileges priority order was ensured by the succession . And oppositely, if Justinian’s innovations had provided a perfect harmony between personal rights and material rights, or in other words, if the dowries privilege had been accompanied by general modification of status, we would have had the following indisputable order: <dowry, anterior legal mortgage, intermediary express mortgage>. The fact that this case appeared, then, shows only that it was clumsy to want to void a juridical inferiority concerning personal status by giving an exorbitant privilege, whilst maintaining in other respects prescriptions implying this inferiority by transitivity. In no way does it demonstrate the intrinsic perplexity of Law, but only the necessity to consider it as a system of material, institutional, and normative constraints which we must harmonize to obtain the maximal goodness possible. It demonstrates even less that we can freely satisfy ourselves with an unconcerned liberty in the choice of a solution. Because if it is possible to privilege the 1st or the 2nd solution, in conformity with the “use” of a later period – as the different mitigations brought to the woman’s juridical status allow to reestablish either the legal mortgage’s or the explicit mortgage’s priority – nevertheless it does not imply the equivalence of these solutions. Far from having to resort to the common law’s rule which says that “all applicants to something divisible or transmissible are admitted in proportional parts, when a perplex concourse occurs” (De Casibus Perplexis §27), the comparison of juridical systems must be based on a rule similar to justice is the charity of the wise, to try to obtain the best possible balance between rights and duties, pleasures and pains, claims and debts, benefits and frauds. But this gathering of quantitative and qualitative, of safety right and person right, implies of course the possibility of a Universal Justice, of which G. Grua said that it could not be distinguished from prudence, the art of goodness or personal happiness, reasonable action of each one for his happiness, and consequently, the act cannot be defined by public interest, without giving priority to the subject, at least for his salvation or necessity. Justice is a constant effort towards common happiness, not in the absolute, but at least when our own happiness is saved”.  (Grua 1953: 168)



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The resolution of perplex cases is therefore, for Leibniz, a normative process focused on the status of people, which leans on a quantitative approach of rights and duties stated in the Elementa Juris Naturalis 122, but which at the same time transcends it in its ultimate finalities. This is because the refutation of controversies is in last resort an enterprise of “universal benevolence, which is accomplished by the wise man in conformity with measures taken by reason, in the aim to obtain the biggest goodness” (Leibniz to Arnauld, March 1690; GP 2 136), and because this goodness is the one of a Republic of wise spirits and not simply the one of a merchant society. We therefore easily understand the reasons why the fundamental principles of a privilege hierarchy formulated in the De Casibus Perplexis are opposed to a strict economical vision of safety right. We also understand even better why Leibniz would not have accepted the contemporary development of collateral securities offered to ordinary persons, whose impoverishment is such that secured debts can no longer be obtained, since the credit given by these collateral securities is primarily concerned with the profit of creditors, whilst equitable is “what is consonant with reason in the distribution of properties amongst people”, or in other words, what aims to “make the happiness of another while preserving one’s own, and to prevent another’s misfortune while trying not to suffer either” (A VI 1 455–458).

Notes 1. Methodus regularum utriusque juris, Basel, 1584; Methodus observationum Camerae Imperialis, Basel, 1588; Methodus juris feudalis, Hanovre, 1597; Methodus universi juris Pontificii absolutissima in quinque libros distincta, nunc demum additionibus methodi juris controversi aucta, Basel, 1597. 2. Rauchbar (1599): 1st part, quaestio 4, nota 33. 3. Carpzov (1638): 1st part, Constitutio 28, definitio 180. 4. Berlich (1644): Conclusio 72, nota 6. 5. “Secured debts appeared only after personal debts. Indeed they need a law system evolved enough to establish a distinction between the thing, and the right that concerns that object” (Mazeaud 1999: 14). 6. “The Revolutionaries, understanding what the Nation’s credit could have gained with a good land organization, instituted the mortgages advertising … Later, the desire to facilitate credit made the legislator improve the mortgage system by improving its advertising, particularly by eliminating the exceptions of our right concerning general advertising rules (the secret nature of statutory liens of the married woman and the ward) and by diminishing the number of privileges that were not submitted to advertising (decree of the 4th January 1955)” (Mazeaud 1999: 14).

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7. “At the time of the wording of the Civil Code, this rule [art. 2105, which gives priority to real estate general liens over real estate special privilege] did not present any serious inconvenient for the building credit, as the general liens on movables and immovables guaranteed only paltry claims. But when the legislator gave such privileges to the Treasury and to the Social Security, credit was affected. It is for that reason that recent texts have considerably limited the numbers of general liens applied to immovables. Today, preference given to court costs is justified by the necessity of ensuring the liquidation of the debtor’s property, and the one given to salaries and copyrights by imperious social reasons. All the other general liens, because only concerning immovables as simple mortgages, eclipse themselves in front of the immovables special liens” (Mazeaud 1999: 269). 8. It concerns an action which is “given to a woman with which she can reclaim to her husband what she must equitably recover of her dowry” in case of divorce (Girard 1978: 1012). 9. Cf. De Casibus Perplexis §23: “Consequently, each time that that is objected to them due to another point of view, i.e., when they themselves argument in such a way that: the posterior dowry precedes the anterior tacit mortgage, and this one precedes the intermediary explicit mortgage, so the dowry too precedes the intermediary explicit mortgage; and that we object: on the contrary start by the explicit mortgage in such a way that: the intermediary express mortgage precedes the posterior dowry, the [posterior] dowry [precedes] the anterior tacit [mortgage], so the first one always precedes the last one; or otherwise: the anterior tacit mortgage precedes the intermediary explicit [mortgage] which [precedes] the posterior dowry, so the first precedes the last one), they immediately reply that that rule, “if I defeat, etc.”, is wrong in its two last connections. Why then is the first connection not false either when you are favorable to the dowry? Maybe they would reply, because we must give reason to the dowry in doubtful case, D.50.17 beginning of 85. But such favors must only be added when the decision can not be obtained otherwise, which sometimes occurred in doubful cases in matters of facts, and it is for them that the law 85 is to be understood and not in doubtful cases in matters of law, which can always be accurately resolved”. 10. Cf. D.44.3.14.3: “And if you give me something as pledge, and if I have given as pledge that same thing, my creditor uses your accession time to property just as well against a third party than against you, until you repay me. Because if I am your superior, my superior prevails all the more over you. But if you pay me back, in that case he does not use your accession time to property”. 11. “The surrogated solvens acquires the rights of the paid creditor, especially the mortgage that guaranteed the claim” (Mazeaud 1999: 526). 12. De Casibus Perplexis §21: “The first in relation to a first is first in relation to a second. [A rule] that ensues from the heart of philosophy, and that can be even more abstract at a superior level, because the cause of the cause is the cause of the caused, and the genus of the genus is the genus of the species, and the required of the required is the required of the requiring, and the condition of the condition is the condition of the conditioned, and the model of the model is the model of the modeled, and the subject of the subject is the subject of the predicate, and a part of a part is a part of the totality. These rules can be all inversed, for example: the totality of the totality is the totality of a part, the predicate of the predicate is the predicate of the subject”. 13. De Casibus Perplexis §22: “in the same way, if instead of first and of close we say precedent and follower, then this perfectly true proposition will appear: “the follower of the follower is the



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follower of the precedent”, or if inversed: “the precedent of the precedent is the precedent of the follower, of course, in “the same series”. Understood in such a way, this rule has no limit, and the contrary implies contradiction”. 14. Cf. in the Dictionary of Canonic Law, the article dedicated to Dyno Rossoni (alias de Mugello), editor of the chapter De regulis Juris in the Sextus of Boniface the 8th, and mentioned by Leibniz in Chap. 28 of the De Casibus Perplexis, where we learn that it was “a question debated between Joannes (probably Bassianus) and Placentin to determine if the exceptions to the rule are or are not understood in the rule”. 15. In particular D.50.17.80: “The species case deviates from the genus in all the Law, and everything that concerns the species is considered preferential”. D.34.2.1: “If we bequeath to one the clothes, and to another the feminine clothes, we will owe the first what is left once the feminine clothes have been taken away and given to the person whom they are attributed to”. D32.99.5: “If slaves are bequest in general to someone, and litter carriers particularly to another, and that some are at the same time slaves and litter carriers, they are part of the litter carriers. Indeed the species always deviates from the genus”. 16. See in particular D.18.6.8, and the case of transactions where the sale of a particular object and not only generic, implies the use of precise designations in the interest of these same parties: “It is necessary to know when the sale is perfect because we know upon whom the risk is incumbent; indeed, when the sale is perfect, the risk is incumbent upon the buyer, and if concerning what is sold, it appears what it is, which one it is and in what quantity, and that it exists and that it is sold, then the purchase is perfect”. 17. Cf. D.33.10.9: “One can not deviate from the movables general legacy by a special legacy where species are enumerated by a lack of knowledge of the totality”. 18. We can find for example in Mazeaud (1999) an explicit use of the Ars aequi et boni concerning general liens such as court costs: “it is equitable that the person who advanced the expenses necessary for the forced sale of the debtors’ property, should not be exposed to the law of concourse in the refunding of these expenses. The proceedings which come from the forced sale of the debtors’ property benefit all the creditors; it is therefore fair that all should bear the charge of it” (p. 225) … “Therefore it is equitable that his privilege concerns all his patrimony” (p. 226). Idem for the privilege of the creditors allowing a business to continue its activities: “this privilege is justified by fairness and usefulness” (p. 228). For the one of the medical expenses: “the human foundation of this privilege is in its own a sufficient justification” (p. 231). It is the same in the case of special privileges like the one linked to preservation and increase of the debtor’s patrimony thanks to the creditor: “it is equitable that he is paid by that value before the other creditors” (p. 252). Idem for the furniture seller (p. 255). Idem also, the case of the victim of a fraud against the one who committed it (p. 262). Idem finally in the cases of competition between privileges of the same type or of different types, because “reasons of rights and of equity” intervene to give priority to one or another (pp. 273, 274). We also find similar expressions in Cabrillac’s and Mouly’s writings (1997: 487): “the privilege now lays on the more general idea that work, not being merchandise, its payment deserves a special treatment which is a projection on the pecuniary field of human dignity and the protection of what is due to him”. Idem (p . 488): “… a considerable difference which, even if justifiable, is not equitable…”). 19. Cf. Mazeaud (1999) and Cabrillac and Mouly (1997: 271): “The drafters of the Civil Code did not lay down the rank of immovables special privileges – unlike they did for the general liens in the article 2101 – nor did they give any general principle; the article 2102 of the Civil

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Code gives only a few detail solutions. Therefore the settlement of conflicts between immovables special privileges is very delicate. To carry out a classification, we will have to recourse to general rules. It is therefore necessary to group together these privileges by taking into account their foundation, in aim to fix the preference amongst each group depending on the quality of the claim (art. 2096 of the Civil Code). But inside each group, the concourse law enacted by the article 2097 of the Civil Code clashes with the rules of possession or of equity, in such a way it is put aside”. 20. Cf. the analogous case of insurances in Sève (1994: 173): “But do we want to let people fall into misfortune and transform entire families into beggars; if we want that, then the country must feed these beggars, who are non-productive social members, they may be even corrupt, which will have for only consequence that they will cost more to the State than if we decided to compensate fortuitous cases whose compensation will support an honest man who will want to earn his means of subsistence”. Cf. also Knobloch (1999: 543–558) concerning Leibniz’s calculation of the right amount of the intermediary interest in the reimbursement of a debt and the calculation of pensions and annuities for a given life expectancy. 21. Cf. Grua (1953: 168, 169): “But public utility does not make the wise or the prudent man, forget or sacrifice his own.” … “It would indeed be foolish to neglect one’s own utility, and Grotius is not satisfactory when only alleging the desire of society.” … “The science of law shows indeed how it is our happiness to procure happiness to another, as much as possible as long as ours is safe”. 22. C.8.17.12: “We have been disturbed by the constant withdrawals on the wife’s [possessions], by which they deplore the loss of their dowry and [which are operated] on the husbands’ possessions by anterior creditors [to the marriage]. That is why we have considered the ancient laws which provide in personal actions, an important prerogative to the rei uxoriae action [“given to a woman with which she can reclaim to her husband what is equitably hers of the dowry” in case of divorce (cf. Girard 1929: 1012)], in the aim to give the wives, a privilege against nearly any personal action, and to allow them to pass before the other creditors, even if they were anterior” … “it was more acceptable that husbands were in a situation towards their creditors where by their own possessions only, they satisfied their obligations, and not by the means of the wife’s dowry that she possesses for her belongings and her food and that is her own or has been given to her by an another”. 23. Authentic 97: “…when a woman who reclaims a privilege on an ancient dowry … wants to prevail over older creditors and a posterior creditor comes forward claiming that a ship, or a house, or a field was bought or repaired with his money, or that the aforesaid privilege must be his own with regard to what has been bought or repaired with his money, we ask if it is acceptable for the dowry to prevail over such a [legal mortgage]” … “therefore many people questioned these cases, and we do not believe that a woman should give to another such a privilege” … “Consequently, we do not want it to be possible to oppose such privileges to women if someone renovated a house or bought a field, as we have sufficiently acknowledged the weakness of feminine nature and that they are easily tricked; therefore, we do not allow their dowry to be diminished in any way”. 24. Authentic, C.8.17: “Which right [of priority of the dowry over the anterior mortgages] is used against those who have a personal privilege, like [those] of money which bought or renovated something, putting aside those who are not subjected to this privilege “thanks to a



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new Constitution, like for example, those who lend to the husband in order to acquire military equipment”. 25. That is, the rule set forth by the founder of Saxon Law, Johann Georgius the 1st (1666: t. 43, fol. 590, 1st part): “But if we can not establish an order in the repayment of creditors’ claims, we first subtract from the net estate, all possessions brought to the household by the wife, then the other properties in management, then the Treasury is reimbursed, and finally all the other creditors come into concourse”.

References Aristotle. 1950. Sophistical Refutations. J. Tricot (trans). Paris: Vrin. Berlich, M. 1644. Conclusiones practicabiles, secundum Divi Augusti Constitutiones Saxonicas. Arnheim. Cabrillac, M. and Mouly, C. 1997. Droit des sûretés. Paris: Litec. Carpzov, B. 1638. Jurisprudentia forensis romano-saxonica, secundum ordinem constitutionum D. Augusti Electoris Saxonicae exhibens Definitiones judiciales succinctas rerum et quaestionum in foro praesertim saxonico occurentium, et in dicasterio saxonico, quod vulgo scabinatum lipsiensem appellitant. Frankfurt. Girard, P. F. 1978. Manuel élémentaire de Droit Romain, 8th edition. Paris: Duchemin. Grua, G. 1953. Jurisprudence universelle et théodicée selon Leibniz. Paris: Presses Universitaires de France. Johann Georgius the 1st. 1660. Corpus Juris Saxonicum. Dresden. Knobloch, E. 1999. “Les finances”. Studia Leibnitiana Supplementa 34: 543–558. Leibniz, G. W. 1666. Disputatio de casibus perplexis in jure. A VI 1 233, 256. Leibniz, G. W. 1669–1671. Elementa Juris naturalis. A VI 1 431, 485. Leibniz, G. W. 2009. Des cas perplexes en droit. P. Boucher (trans). Paris: Vrin. Mazeaud, H. L. et al. 1999. Leçons de Droit Civil, 7th edition, 3rd tome, 1st Vol. Paris: Mont­ chrestien. Rauchbar A. 1599. Quaestionum quinquaginta ad jus Saxonicum partes duae. Frankfurt. Rolland, H. and Boyer, L. 1999. Adages du droit français, 4th ed., Paris: Litec. Sève, R. 1994. Le droit de la raison. Paris: Vrin. Vigel, N. 1599. Nicolai Vigelii de Dreisa Hessorum jurisconsulti Methodus juris controversi in sex libros distincta … cum ratione juris controversi, cum judicio legendi et in judicando sequendi, operi praefixa. Basel.

chapter 10

Leibniz’s critique of Pufendorf A dispute in the eve of the Enlightenment Detlef Döring

1.

Introduction

The spiritual life of the Baroque era was marked by severe, often polemical literary disputes in the fields of theology, philosophy, and the other scientific disciplines. The scientific community of that time was for a long time often involved in such quarrels that reached far beyond national borders. A well known example is the dispute between Leibniz and Newton concerning the priority for the invention of the infinitesimal calculus. A less known controversy is that between Leibniz (1646–1716) and his Saxon compatriot Samuel von Pufendorf (1632–1694). Like many scientists of the Baroque, both were polyhistorically oriented thinkers, with Leibniz expressing this inclination at a higher degree than Pufendorf. Leibniz opposed Pufendorf in almost every field of thinking they shared, from philosophy of law to history, from theology to politics, from reflections about the state of the Holy Roman Empire to considerations about the German Nation. Leibniz’s entire correspondence and private notes – from his younger days up to old age – is soaked with criticism of Pufendorf. This criticism, however, was never published under Leibniz’s name during his lifetime. The main tune of Leibniz’s statements against Pufendorf is always the same: He is a superficial, not serious, vulgar popularizing thinker who lives mainly from plagiarism and who is undeservedly liked by the public.1 Leibniz’s rather atypical aversion for Pufendorf has always astonished the scholarly community. Already Gottschalk Eduard Guhrauer, Leibniz’s first modern biographer, stated that: “there was probably no other scholar except Pufendorf against whom Leibniz displayed such a profound aversion, not only as a philosopher, but also as a historian and as a person” (Guhrauer 1846: 15). Paul Ritter, the initiator in the 20th century of the ‘Academy Edition’, planned to

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comprise all Leibniz’s writings was of the opinion that during his entire scholarly life Leibniz felt a “profound opposition” to Pufendorf (A IV 1 xxxi). On the other hand, it is completely unknown to us if and how Pufendorf was familiar with Leibniz’s personality and work and if he was aware at all of his criticism against him.2 Neither his publications nor his correspondence contain any reference to Leibniz, with the sole exception of the very few letters he exchanged directly with him. As far as we know, both men never met.3 There may have been a chance for such an encounter during Pufendorf’s studies in Leipzig (1650–1658), but an age difference of almost fourteen years makes it improbable that Pufendorf had any contact with the young Leibniz who entered the university in 1660. In November 1667 Leibniz moved to Frankfurt/Main and some months later to Mainz. Both places are not far from Heidelberg where Pufendorf had a chair since 1661. But there is no evidence that during the time he spent in the Palatinate he had any contact with his, at that time quite unknown, compatriot.4 In the summer of 1668 Pufendorf moved to the newly founded university of Lund in Sweden. He lived for twenty years in Sweden where he finally became a historian appointed by the court. It is known that during that time Pufendorf travelled once to the Netherlands (1684) following an itinerary that brought him to Hanover. There was, however, no meeting with Leibniz who was in the Harz mines where he was probing his wind-driven water pumps. In 1688 Pufendorf was appointed professor in Berlin following an invitation by the elector, prince Friedrich Wilhelm. Leibniz visited the capital of the electorate of Brandenburg for the first time in 1698, i.e., four years after Pufendorf’s death. However, Leibniz was in closer contact with Pufendorf’s elder brother Esaias, who was also in the Swedish public service.5 Since the brothers were on very close terms with each other, it is very probable that Esaias told his younger brother Samuel about his discussions with Leibniz. It is remarkable, however, that Leibniz, who was regarded by his contemporaries as an assiduous correspondent, addressed only four letters to Pufendorf, two in 1690 and two in 1693. The latter did reply to the first letter on each of these occasions, but did not react to Leibniz’s replies. The contents of those six letters (four written by Leibniz and two by Pufendorf) are of lesser importance and do not reveal the fundamental differences that separated the two scholars (A I 5 610–611, 625–626, 655–657; A I 5 380–382, 428–430; GW 1 1274–1276, 1281–1282, 1356–1360). Leibniz’s criticism on Pufendorf has not been articulated in his published work. It is documented only in private correspondence,6 in unpublished records,7 in memoranda addressed to political decision makers,8 in anonymous publications,9 and in poems. This reluctance against publicity probably derives from Leibniz’s general shyness towards disputes carried out in print. The spectrum of publications that appeared during his lifetime does not contain any significant



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polemical texts, since Leibniz was always interested in harmonizing extreme positions. Pufendorf was in this respect the absolute opposite. His numerous polemical writings make up a significant part of his oeuvre. Leibniz found this kind of disputes disgusting. To his friend Placcius he described Pufendorf’s famous polemical edition Eris Scandica as “parum amabile” (‘not gentle’) and lacking moderation.10 Furthermore, certain considerations forced him to be very careful towards any public confrontation with Pufendorf, or with any publicly articulated criticism against him. Firstly, Pufendorf had managed during his entire life to gain the sympathy and protection of the mighty ones, consolidating his position in the various European courts. Secondly, his enemies often experienced this circumstance very painfully and so that they had always to consider very carefully whether an attack on him would serve their own interests or not. In the last quarter of the 17th century Leibniz made great efforts to improve his contacts with Berlin, something that a position in the service of the House of Brandenburg would certainly help. The succession of Pufendorf as the Court Historian was in this respect an important motivation. However, before the fall of the influential minister Eberhardt Danckelmann in December 1697, who was Pufendorf’s main protector, any criticism on the latter wouldn’t be useful. Nevertheless, especially during that time, Leibniz endeavored to disclose and to demonstrate to the public the mediocrity of his recently deceased rival. A subtle example of this attitude is an anonymous defamatory poem against Pufendorf, which circulated after his death and was taken up and enhanced by Leibniz. In that poem Pufendorf is characterized as a lunatic who escaped with great pains his incarceration in Stockholm, and would have faced the same fate in Spandau if he hadn’t died before (Entner 1999). At the same time, the already mentioned anonymous Epistola ad amicum was published aiming at proving Pufendorf’s mediocrity and unimportance in almost every scholarly field. The printing of this pamphlet, which raised some attention and provoked some journalistic response, took place under very clandestine circumstances. Leibniz’s authorship, which was confirmed only at the end of the 20th century, was known only to a small circle of handpicked persons. Leibniz’s contemporaries already conjectured that his aversion to Pufendorf was based on personal motives. This opinion is grounded on a statement by Leibniz, which he made long after Pufendorf’s death. He had asked Pufendorf to intervene for a personal affair for him in Sweden; but Puffendorf not only didn’t do what Leibniz had asked, in spite of having promised to do so, but rather tried to obstruct the whole affair.11 It can be hardly assumed that this vague incident was the actual cause of the grudge Leibniz harbored against Pufendorf.12 The real reasons for that should be sought in Leibniz’s personality.

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Despite the great care with which any psychological explanation must be treated, there is some evidence in this direction. Leibniz regarded his compatriot as a scholar of a far lower academic level compared with himself, since he regarded himself as a philosopher who investigated the very depths of being – an attitude that we will encounter often in our analysis. Pufendorf’s success in life stood, according to Leibniz, in a sharp contrast to his scholarly mediocrity. Leibniz’s jealousy went so far that after Pufendorf 's promotion to the rank of baron by the King of Sweden, Leibniz arrogated to himself the title of baronet (Freiherr), since he couldn’t obtain it by any other means. This desperate action can be explained by the importance the society at that time attributed to such matters. Another point of rivalry between him and Pufendorf was the fact that Leibniz never managed to leave Hanover to enter the service of one of the more important courts, e.g., Berlin or Vienna, in contrast to Pufendorf, who moved apparently without any great effort from one political center to the other: from Heidelberg to Stockholm and then to Berlin. His salaries exceeded by far those of Leibniz.13 Pufendorf was a secret counselor, Leibniz just counselor of the court. Finally, Pufendorf published one best-seller after the other, while Leibniz accumulated unpublished torsos, since he couldn’t manage to finish a work because of his job and his constant attraction to new projects.14 He regarded his unfinished works, however, as much more solid than the allegedly hastily compiled, flat writing of Pufendorf’s. It would be wrong, however, to reduce the differences between Leibniz and Pufendorf to envy or to the personal antipathy of the younger towards the older, for it is more deeply rooted. In spite of the fact that both lived and created in the early Enlightenment, they did not share a common viewpoint and their work points to different directions. It is this observation that makes Leibniz’s criticism of Pufendorf interesting. This hypothesis is supported by the fact that there is a second case of strong aversion that was close to disdain against a contemporary scholar by Leibniz – who under normal circumstances was a harmony seeking person – namely, Christian Thomasius, who was on good terms with  Pufendorf and could be regarded as his pupil. Leibniz’s statements about Thomasius are not so numerous, as compared with those about Pufendorf, but quite clear. Thoma­sius’s philosophy, Leibniz argues, is “sylvestris … et antipodialis”,15 superficial, flat, without tradition.16 This is the crucial point: Contemporaries like Pufendorf and Thomasius live in Leibniz’s eyes in a different world, which has nothing in common with his. There cannot be any disputes with them at a peer level. These fundamental differences between Leibniz and Pufendorf deserve a closer look. Both were raised and educated in Saxony: Pufendorf studied at the Prince’s school at Grimma and at the University of Leipzig. Leibniz was educated solely in Leipzig. However, the results of both educations were very different. Later in



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his life, Leibniz gave an account of his education in a famous letter addressed to Nicolas Remond. He studied intensively Aristotle and the Scholastics, something that he never regretted.17 Later he turned to mechanics and mathematics. But, as he grasped the last principles of mechanics, he realized that the laws of motion cannot be found in mathematics, but rather in metaphysics, to which he then returned. As a result of those reflections he developed the monadology. According to this testimony, metaphysics was always the main topic in Leibniz’s broad and multifaceted work. Its development is rooted not only in the intensive study of Aristotle, but also in the reception of the works of the medieval and of the modern German and Spanish Scholastics. For Leibniz, it was always very important to refer to philosophical authorities who could support his opinions (Leibniz to Kästner, August 21st 1709; D IV 3 261). Central to his thinking were the concepts of monad and pre-established harmony. These ideas, however, would appear to the following thinkers of the Enlightenment as quite strange and “bulky”.18 What they regard as important in Leibniz’s philosophy is its method of reasoning, with the principle of sufficient reason becoming the kernel of the Leibniz-Wolffian Philosophy,19 which was quite widespread until the second half of the 18th century. Its main thesis is that nothing happens without a cause; all events are ordered in this sense. Christian Wolff remarked that the best trait of Leibniz’s philosophy is the fact “that the interconnection of the one with the other becomes evident and that we arrive to quite clear concepts without realizing it. Thus we obtain a degree of astuteness that cannot be arrived at with other means”.20 Pufendorf, on the other hand, gives us a completely different picture of his development: He studied Aristotle for a long time, regarding him as the peak of wisdom, until growing doubts forced him to reject the doctrines of his teachers, as he reports in a letter (Pufendorf to Johann Christian von Boineburg, January 13th 1663; GW 1 24). He didn’t rely on authorities. The doctrine of “habemus expressum textum in Aristotele” (‘we have an explicit text in Aristotle’) was overshadowing when he was a student, and he compared its commentators to beetles that would eternally continue to roll the “Aristotelian horse-dung” if a few good heads hadn’t succeeded in throwing away its yoke.21 His main aversion is directed towards metaphysics, which he despises as useless quibbling. It should be sufficient for a student to know “what kind of creatures are a proposition, a syllogism and the rest of the genera argumentandi”. All that could be learned in a couple of hours and “if one understands only a dozen of terms like causa, effectus, subjectum, adjunctum, actus, potentia then one has no reason for mourning if all other metaphysics vanished” (Pufendorf 1995: 548). In his disputes with the numerous vices stemming from the ranks of orthodox Lutheranism, Pufendorf always mocks their closeness to metaphysics: It is a shame when a person who up to then swam in the swamps of metaphysics would presume to speak about natural law and

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suggest the use of logic and metaphysics as a prerequisite for studying Grotius.22 Pufendorf’s starting point is the observation of the real world. What, for example, is an honorable deed cannot be conceived a priori by means of reason, but only by observing carefully the way humans live (Eris Scandica; GW 5 164). In Leibniz’s eyes, this rejection of philosophy in favor of empiricism appears as a declaration of the intellect’s bankrupcy. Leibniz frowned at such statements of Pufendorf’s against metaphysics, and this may explain the following negative judgment about him that has been often cited: “Vir parum jurisconsultus, minime philosophus” (‘A man who is a small jurist and a very small philosopher’; D VI 3 261).23 Leibniz repeatedly accuses Pufendorf of being an inconsequent and not stringent thinker. His writings had a popular character and were read by many people; they lacked however any philosophical depth. In lieu of deep considerations one finds compilations of others’ works.24 Pufendorf’s texts were superficial and flat regardless of the topic they dealt with.25 This contrasting attitude towards philosophy and especially metaphysics is of great importance for understanding Leibniz’s and Pufendorf’s opposed ways of thinking. This becomes evident if we focus our attention on the topic of religion and the church, which was still a central issue in the late 17th century. Both regarded this problem as very important during their lifetimes. Their differences concerning this issue bring us to the kernel of their contrast. The religious disputes at that time were centered on the relationship between the confessions, on the necessity for an ecclesiastical reform, and on the need for the renewal of religious life. Both Pufendorf and Leibniz belonged to the numerous lay theologians who in the outgoing 17th century participated in the religious debates arguing that the “quarrelsome theologians” were not able to bring about religious peace and the long expected renewal of religious life in the spirit of Christianity.26 The criticism of the theologians of the emerging enlightenment is already felt by Pufendorf and Leibniz, but they are attracted to the issues of religion in a way and degree that are not found any more among the enlighteners of the 18th century. Both also still regard as evident the fundamental dogmas of the traditional Christian doctrines,27 an attitude which was given up by the ensuing Enlightenment. These dogmas include the doctrine of the sacrifice of Christ in the name of humanity, the doctrine of the original sin, and the undoubted evidence of the revelation. The difference between Pufendorf and Leibniz lies in the way they try to justify their ideas. Pufendorf promotes the idea of a “naïve Christianity” that is based solely on the Holy Scripture and rejects explicitly any philosophical treatment and logical justification of the divine revelations. He stresses the point that it was remarkable “that in the whole New Testament one cannot find the slightest vestige of philosophical material, so that one is in a position to understand it thoroughly without any sense of philosophy besides common sense



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and natural logic” (Unvorgreiffliches Bedencken: 437). Those Lutheran theologians who concern themselves with “scholastic philosophy” in order to become abler to dispute with the Catholics are criticized sharply (Eris Scandica; GW 5 132). Revelation and reason have to be sharply separated: God has not revealed himself to men in order to confirm any a priori conceptual truths, but in order to show them the way to eternal salvation, something that they never could deduce from pure reason. Philosophy and revealed religion are thus two completely different things; a Philosophia Christiana is not possible.28 The foundation of every theology is the Holy Scripture, the meaning of which can be accessed immediately.29 With these ideas, Pufendorf opposes not only his adversaries in the ranks of the orthodox and intellectual Lutheran theologians; he also tacitly opposes Leibniz. For the main aim of Leibniz is exactly to prove the coincidence of reason and revelation, the harmony between religion and philosophy. Theology has thus to use the aid of philosophy in order to justify the Christian dogmas. Leibniz thinks that on this ground he can resolve one big problem that concerns his entire life – the quest for the reunification of the separated confessions (see Rudolph 1999b). Leibniz’s efforts were to settle the seemingly irresolvable dogmatic controversies with the aid of philosophy. An example of such a controversy was that about the Holy Communion. Pufendorf’s claim that one had simply to believe in the presence of Christ’s flesh and blood in the Holy Communion and that the dispute about the mode of this presence was solely a matter of empty “curiositas”30 had to be regarded by Leibniz as an attack against the kernel of his own efforts.31 Such an argumentation, he replied, could have only a palliative effect, but it would be unable to put effectively aside the real differences between the confessions. This would be possible only by means of reason, i.e., only by means of a thorough criticism of the Cartesian concept of substance, because the unjustifiable application of this concept in explaining the presence of Jesus’s body created not only the intra-protestant disputes but also the dissent with the Catholic Church.32 In contrast to Pufendorf, Leibniz sticks to the goal of uniting the Christian churches, especially the reunification of the Protestants with the Catholic Church, which was of great importance for him, and he pursues this aim in countless discussions and in an intensive correspondence. He hopes to achieve it negotiating with high ranking ecclesiastical and worldly decision makers. The utilization of philosophy serves the same purpose: The burning dogmatic questions should be resolved by means of reason in such a way as not to pose obstacles to the reunification endeavor. This is the practical application of Leibniz’s idea that man will do the right thing as soon as he has intellectually recognized it. This attitude is completely opposed by Pufendorf’s stance:33 The sole aim of the Catholic Church was the unlimited growth of its power and wealth. The belly, however, has no ears;

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arguments of reason do not reach it. The dogmas of the papal church were tailored to fit this goal. They had nothing to do with real Christian faith. Thus it appeared that all efforts to try to rebut the representatives of the papal church with argument will be in vain, since their actions weren’t motivated by reason, but by the will, and this will consisted in unrestrained greed for power. Any negotiation with the pope and his representatives is thus in Pufendorf’s eyes not only pointless, but also very dangerous, since there is always the threat of the subjecting of Protestantism to the rule of the “Antichrist”. So it is not surprising that in one of his historical works Pufendorf concludes a report about some interconfessional negotiations with a very sharp judgment, namely that all those who advocated the co-existence of Catholics and Protestants were either swindlers or didn’t have a clear mind.34 Fiddling around with apparently irrefutable philosophical theorems, be it for safeguarding religion, for interconfessional negotiations, or for promoting the Christianization of everyday life, could lead to the decline of Christianity itself. The alternative was for Pufendorf a biblical theology that recognized only one source, namely the revelations of the Holy Scripture. Man has to take them seriously and remodel his life according to the commandments and demands set up by Jesus Christ.35 Pufendorf’s last work (Jus feciale) was devoted to the outline of such a biblical theology, which should be derived from a very small number of fundamental principles. To these belonged especially the doctrine of the regeneration (rebirth) of the baptized man that provides the notoriously weak human intellect with new and novel energies. The observation of the Christian commandments comes into effect as a result of this inner rebirth that gives one the necessary power for doing this. The divine laws are fulfilled not by force, but “è spontaneo Spiritu Deo filiale obsequium praestant è viribus per generationem collatis” (‘by the spontaneous filial obedience to the divine spirit contributed by generations of men’; Jus feciale: 187; GW 9 57). A true Christian life conduct can be thus achieved only through a change of the will by means of rebirth, but not by means of the operations of the intellect. However, it is up to one’s choice if one accepts or denies the way of rebirth. Man is free like God, who acts also freely and is not limited by any law. If the latter were the case then miracles would be more or less impossible and also prayers would have no effect, since God could not fulfill these pleas. If God were bound by compelling laws, so Pufendorf, then he would not act freely and could not intervene in the course of the world (GW 4 1 165). Starting from these premises Pufendorf sharply attacks the Calvinist doctrine of predestination, which according to him threatens the state.36 In contrast, Leibniz is able to find an arrangement with the doctrine of predestination because it fits his idea that God never acts arbitrarily, but is always conducted by reason. The predestination of someone for salvation and of someone else for condemnation



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does not occur without thinking, but out of God’s “ex altitudine divitiarum et sapientiae” (‘richesses and wisdom coming from above’; Leibniz 1709: 105).37 But if God acts according to immutable laws that cannot be influenced by Him, then the acceptance of miracles becomes difficult and the sense of prayers problematic. Thus miracles are practically ruled out by Leibniz and his successor Wolff,38 a circumstance that evoked the violent resistance that the Leibniz-Wolffian philosophy encountered. The demand for a “naïve Christianity” that is rooted in the Bible and rejects any dogmatic dispute that is interwoven with philosophy is one of the great matters of concern at that time. It is found also in Pietism to which Pufendorf was an adherent, though a critical one,39 and it is also found in the thinking of Christian Thomasius who, as mentioned above, was also the object of Leibniz’s aversion. Thomasius shares with Pufendorf the criticism of the connection of philosophy with theology. Theology is rotten because of its mixing with philosophical “artificial words”. It would be better to follow the “naïve method” of Apostle Paul, namely explaining the faith with “juridical words”. This was Pufendorf’s way and from “such comparisons could one understand the matter much more clearly than by means of a lot of disputing and subtle distinctions that since the beginning of the reformation were practiced due to the Aristotelian and the scholastic philosophy” (Pufendorf 1696: 178). However, Thomasius goes a step further and comes closer to the spirit of the Enlightenment because he definitively rejects Pufendorf’s attempt to set up a universally binding fundamental theological system: “We can set up a system, but we cannot bind the people to it, since then it would become a formula concordiae. A politician should consider that such a thing is impossible: He can advise, but he cannot force his advice upon someone because such a thing is against reason”.40 Thus the controversial interconfessional debates are in the era of the Enlightenment no longer an issue. A second point that separates Pufendorf from the Enlightenment is his sharp comments against religious romantics.41 It is with Thomasius that a modern concept of tolerance begins to develop. The sharp contrast between Leibniz and Pufendorf in the assessment of the relationship between reason and revelation is not an isolated phenomenon, but belongs to a set of disputes that can be traced well into the 18th century’s Enlightenment. The main representative of the rejection of Leibnizian rationalism combined with a promotion of a biblical theology is Christian August Crusius, professor at the University of Leipzig (1715–1775). Crusius is not only a theologian, but also an indirect disciple of Christian Thomasius’s philosophy. The sort of philosophy he’s an adherent of attacks Leibniz and Wolff, pointing to the limits of reason. The backbone of Leibnizian philosophy, the principle of sufficient reason, is decisively rejected, while in contrast the freedom of will is underlined: “Some people try to succeed using human wisdom, thinking that

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if the correct motives were to be made understandable by means of the exact and sharp utilization of philosophy then people would act accordingly”. However, what actually matters is the “proper force”, “the healthy state of the soul” (Crusius 1756: 27). The utilization of the Leibnizian philosophy for the purpose of sustaining Christian religion is also criticized. This would lead inevitably to the decline of religion since this philosophy is erroneous. The result of such an amalgamation would be an eclectic religion, which would consist of arbitrary Bible citations and of figments (cf. Crusius 1752). As a countermeasure Crusius sets up a so-called “prophetic theology” that stands completely in the tradition of the Biblical theology that was propagated by Pufendorf some decennia earlier. No wonder that Crusius was one of the sharpest philosophical opponents of the Leibnizian Johann Christoph Gottsched (1700–1766) who also lived and worked in Leipzig. Gottsched brings to an end what is rather outlined in Leibniz’s philosophy, namely the overcoming of revelation by reason (Hirsch 1964: 16): The fundamental doctrines of Christianity still appreciated by Leibniz are given up, e.g., the doctrine of the original sin and the doctrine of satisfaction (Christ’s sacrifice for humanity’s guilt). According to Gottsched, man can achieve salvation without Christian revelation. Man's doctrine can be appreciated only if it coincides with the commandments of reason (natural theology); miracles are thus from this point of view impossible. In Gottsched’s view Christianity becomes a mere cultural phenomenon, the continuation of which depends on the perfection of culture (Döring 2000). What Pufendorf had anticipated as a result of the reduction of the system of the dogmas is thus now achieved: The pursuers of this reduction aim at mutating Christian religion “into nothing else than a cute moral philosophy” (Pufendorf 1695b: 894). Turning our attention to the doctrine of natural law, another important issue in which Leibniz also opposed Pufendorf, we encounter lines of contrast similar to those encountered in the theological disputes. With respect to this issue the impact of reason is also of paramount importance to Leibniz (Schneider 1967). Reason enables us to recognize that justice is a transcendental idea that holds also in a world which is void of humans (See, e.g., Elementa Juris Naturalis; A VI 1 460). The rules of goodness and justice are, according to Leibniz, older than God’s commandments. Even God himself is subject to these laws that he hasn’t issued.42 When he created man, he had to do it in such a way that man resulted as he should be, i.e., as capable and inclined to pursue to a virtuous life.43 Voluntarism, i.e., the idea that the definition of good and evil are subject solely to God’s arbitrariness is vehemently rejected by Leibniz, because if it were so God would lose the title of being the Good One and mutate into a tyrant. If the existence of all virtues relied solely on a divine imperative then one could do also the opposite as soon as God withdrew his initial orders. Leibniz stresses that



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he shares this standpoint with many contemporary theologians, Protestants as well as Catholics (Theodicy §182; GP 6 223). Those who deny the transcendental character of justice are thoroughly irrational. Pufendorf shares this opinion, but this could be neglected since he never thought deeper. The polemics against the absolute decree of the Reformed (something that Leibniz considers as tolerable under a certain interpretation) concealed that Pufendorf, even in his theory of natural law, adheres to the ideas of those who present God as a despot.44 Concerning the issue of the justification of natural law, Leibniz also here claims that it is reason that proves that the laws of justice exist per se. It is possible to grasp the rules of justice with the help of reason in the same manner as it is possible to justify the doctrines of faith. The norms issued by God didn’t stem from His free will; they are in accordance with the eternal truths, so that the theologians have been right in opposing Pufendorf who didn’t realize that eternal justice couldn’t be attributed to God if he were supposed to derive the law from His free will.45 A further argument against Pufendorf picks up this thread of God’s essential justice: Only the presupposition of their existence renders men able to observe the laws because of their love to God and to their fellow human beings and not because of their fear from punishment. The result of the acceptance of this presupposition is that a concept of justice, linked to theology, which is far better than the concept that results from Pufendorf’s ideas, is established.46 The ultimate goal is merging natural law with Christian doctrine: “Atque hoc sensu recte a viris doctis inter desiderata relatum est jus naturae et gentium traditum disciplinam christianorum…” (‘In this sense scholars correctly list as one of their desiderata the inclusion of the law of nature and peoples among the Christian disciplines’; D IV 2 297), for ultimately, theology is nothing but a “sacra jurisprudentia” (‘Holy jurisprudence’; GR 377).47 Pufendorf, on the other hand, bases his derivations of the natural law on an empirical ground, namely the nature of man.48 Since natural law has to be valid for all humans regardless of their particular mood of worshipping God it cannot be treated “secundum disciplinam christianorum”. It cannot be reconstructed from reason either, but it has rather to be obtained using methods similar to those of the natural sciences, namely by setting up hypotheses derived from the observation of nature.49 If this method is applied then it soon becomes clear that the fundamental human trait is the helplessness resulting in the necessity for humans to form communities. The rules that govern the life in the community make up the universally valid natural law. The fact that man is created to live in community goes back to Divine will. If this is so then natural law is also rooted in God’s free will because if one sets up an aim he defines also the means, by which this aim can be achieved.50 Thus for Pufendorf natural law doesn’t rely on taking over rational laws that exist independently of God, but has to be regarded as something that

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has been set up arbitrarily and is justified solely by God’s totally free will, wishing to create man as he actually is. Pufendorf so attacks Leibniz’s position and also the doctrines of other dissenters, according to which man possesses exactly this nature because he cannot have any other51 – God is not in a position to act otherwise and to create a human being that does not comply with the concept of being human – the existence and the essence of man have been created simultaneously. For Pufendorf, however, God is not a tyrant who imposes vices on humans declaring them as commandments, but his action is guided by His goodness, which knows no other goal than the perfection of human life. Natural law is thus restricted to this world; it is up to faith – and not to reason – to make any statements about the hereafter. The mundane restriction of natural law and reason is vehemently rejected by Leibniz, who claims that natural law is founded on the transcendental laws of reason embracing at the same time the totality of human nature. He also denies Pufendorf’s idea that accepting the immortality of the soul and expecting the final judgment are solely matters of faith (Monita quaedam ad Samuelis Puffendorfiis principia §2; D IV 3 276–277). Leibniz regards both ideas as completely rational. Nobody could deny that God’s aim consisted in rewarding the good and punishing the evil. This corresponds necessarily to the order and harmony of the world. Another – at that time hotly debated – issue where Pufendorf and Leibniz act on completely opposed backgrounds is the character of the Holy Empire of the German Nation.52 Here too it can be observed that Leibniz argues from a theoretical point of view, while Pufendorf is empirically oriented. For the latter, a metapolitical use of the concept of the “Reich” (in the meaning of empire) has been rendered obsolete: He explicitly rejects the doctrine of the four reigns and the theory of translatio, claiming that the Roman Empire has gone and that the so called Holy Roman Empire of the German Nation is not by any means its sucessor. The label “Roman” results solely from the contingent fact that the Emperor rules also over the Patrimonium Petri. In the same manner as Switzerland derives its name from one of its cantons, the new state is called “Roman” because the Kaiser claims rights upon the City of Rome.53 In later writings Pufendorf further expands this position, claiming that the title of Emperor is an empty label,54 and rejects the Rome campaigns of the previous Emperors because they have not been of great use to Germany.55 The Medieval Ages are an era that lies beyond the scope of Pufendorf’s interests.56 Therefore he is quite reluctant against the efforts of a number of scholars who tried to establish in the eighties of the 17th century an “Imperial Historical College” (see Döring 1996: 87–88). Finally, during his entire life Pufendorf viewed the Imperial House of Habsburg with suspicion because of its egoistic and for Germany disastrous ambitions that threatened the independence of the Reichsstände (the federal political forces of



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the Reich). Until the seventh decade of the 17th century Pufendorf feared that the House of Habsburg strived to establish a Europe-wide universal monarchy, a task that was near its fulfilment during the Thirty Years War. A universal monarchy would mean the oppression or even the elimination of Protestantism, the protection of which plays a central role in Pufendorf’s political concepts. In this respect the House of Habsburg has failed, since instead of positioning itself as the vanguard of the reformatory movement it has favored Catholicism because of dynastic considerations.57 A central issue in the 17th century debates about the constitution of the Empire was the relationship between the Holy Empire itself as political entity and its various territories, which in the aftermath of the Peace of Westphalia began to strengthen their sovereignty. The positions in these debates ranged from defining the Holy Roman Empire explicitly as a monarchy to the declaration of the total independence of the States from the Empire. Pufendorf has taken position on this issue in his renowned reflections on the constitution of the Empire that were published under the pseudonym ‘Monzambano’. His statement, that the Holy Roman Empire was like a monster, became quite famous and can be found in almost every work on the history of this political entity, but it doesn’t match exactly the proper definition of its character. According to Pufendorf, the Holy Roman Empire of the German Nation is an irregular state that comes very close to a system of unequal allies (systema sociorum inaequaliter foederatorum). The Electors are not subjects but rather allies of the Emperor. Nevertheless they cannot aim at the dissolution of the Empire and the abolition of the Emperor because this would destroy all the States of the Empire. Monzambano’s (i.e., Pufendorf’s) goal was to defend the freedom of the States of the Empire and to strengthen Protestantism.58 That the Princes were never subdits of the Emperor is rooted in the beginnings of the history of the Holy Roman Empire. Pufendorf justifies this independence with the (historically not founded) argument that the Emperor had not enfeoffed to the Princes their territories, but that they originally belonged to them (feuda oblata). Their enfeoffing by the Emperor was a mere symbolic act. A transformation of the Empire according to the model of the centralistic western European states is unthinkable for Pufendorf. Therefore he rejects all reformatory plans because this “crooked figure [i.e., the Empire] is so hardened that it would rather break than become straight again” (Pufendorf to Landgraf Ernst von Hessen-Rheinfels, November 1st 1691; GW 1 333). Only the gradually increasing threat for the Empire by France and the Ottomans at the end of the 17th century evokes in Pufendorf certain patriotic feelings towards the former Empire, which resulted, however, only in a number of practical demands like the ban of separate treaties between France and single German territories, but not in a reformatory plan for the entire Empire. Pufendorf’s insistence on the historically rooted sovereignty and the freedom of the States of

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the Empire as well as his critical judgment of any plan for reforming the Empire are certainly connected to the fact that during his entire lifetime he was in the service of single states being thus forced to provide theoretical arguments sustaining their independence against the imperial power.59 Nevertheless, his realistic attitude was also an important motive for his sober judgment of the relationship between the Emperor and the States of the Empire and for his lack of interest for the restitution of the old imperial power. In Leibniz’s thinking we find a completely contrasting attitude that is evidently still moving in the tracks of medieval imperial concepts (Hammerstein 1974). Emperor and Pope are for him the Heads of Christianity with the Emperor taking a unique position among the nations because of his sacral dignity as defender of the Church.60 The Empire (which needs, however, to be reformed) makes up the center of Europe, its destiny being to establish universal peace. His “profession would be to stand by every Christian suffering from unjustified violence and sustaining the peace in Europe in order to unify the mundane with the spiritual Head of Christianity under one aim, namely to exercise the office of the advocate of the Church, in order to seek the universal good and to keep the swords in the sheaths without exercising any military force”.61 Thus Europe pacified by Germany can and would point its weapons against the outlandish barbarians, enlarging thus Christ’s Empire.62 Leibniz’s efforts to reunite Christianity fits this way of thinking since the overcoming of the religious schisms is a prerequisite for the proposed harmonization of Europe. With enough good will and with proper reforms – that Leibniz does not deny at all – the flaws of the Empire can be repaired as well as the religious schism. In contrast to the sceptic Pufendorf, Leibniz has repeatedly submitted proposals for improving the state of the Empire bringing it to a position to achieve these great goals. It is evident that because of his view of history Leibniz can by no means share Pufendorf’s secular concept of the Holy Roman Empire of the German Nation. Its sacral dignity and its universal aim are given up by the latter; Monzambano rejects even its nature as a state. On the other hand, Leibniz faces the same difficulties as Pufendorf: He is also in the service of single States (Mainz, later Hanover) and has to support their particular interests, which very often are opposed to the interests of the Empire. On the other hand, Emperor and Empire are not only a sort of extraordinary and especially dignified facts, but they are also meaningful and necessary for guaranteeing the further existence of the States of the Empire. Leibniz’s answer is thus superficially similar to that of Pufendorf’s but in detail quite different from it. Leibniz has twice commented extensively on Monzambano’s ideas: in Specimen demonstrationum politicarum pro eligendo rege Polonorum (1669) and in a memorandum that was published only in the 20th century, but was written also



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around 1670 (In Severinum de Monzambano; A IV 1 500–502). According to Leibniz, Pufendorf’s statements regarding the constitution of the Empire are confused by containing imprecise definitions. Here we also encounter Leibniz’s standard complaint, that Pufendorf is a confused thinker. Namely, at no point does he declare exactly what were civitas, societas, or respublica irregularis. Leibniz would declare a state as irregular only if the establishment of a general will weren’t possible,63 i.e., if in the case of the Holy Roman Empire of the German Nation there were differences between the Emperor and the States. This is, however, not the case since the Empire is a functioning civitas. Regarding the States comprising the Empire, they are regarded by Leibniz as real fiefs and not as feuda obleata in Pufendorf’s sense. This means that the Princes of the Empire are indeed subdits of the Empire, and this includes the Holy Roman Empire with all its institutions as a whole and not only the Emperor.64 The Empire is not a mere societas or foedus, but rather a civitas or res publica. Nervetheless, Leibniz cannot deny that the parts of the Empire enjoy certain sovereignty as it is acknowledged in the conclusion: “ergo falsum est Principem Germaniae statim Imperii et Imperatoris subditum esse” (‘therefore, it is false that a German Prince is entirely a subdit of the Empire and of the Emperor’) in Leibniz’s essay on the election of the Polish King that was directed against Monzambano. According to this claim, Leibniz declares that the Princes of the Holy Empire are sovereigns, a fact that is recognized by all foreign powers.65 In order to describe this quite strange political construction of a state that is both a civitas and a federation of sovereign Lords, Leibniz uses expressions that resemble those of Pufendorf. The Empire – according to Leibniz – is a “family” of particular states, “a systema civitatum foederatum”.66 His fundamental idea is, however, that the Holy Roman Empire of the German Nation is not a mere mundane political power, but an entity that is grounded on transcendental principles that is profanized by Pufendorf’s definition of it as a mere federation. On the other hand, both Pufendorf’s and Leibniz’s definitions of the Empire as “systema sociorum inaequaliter foederatorum” and “systema civitatum foederatum” laid the seeds for the development of the federal state as it has been proposed especially by Johann Stephan Pütter in the 18th century. Although Leibniz and Pufendorf both belong to the beginning of the Enlightenment they represent two different ways of thinking that unfolded in the following decades. Both can be regarded as representing a transitory period: They anticipated future developments, but at the same time they stood on traditions that cannot be related directly to the Enlightenment, being nevertheless important for its development. The situation as a whole is somewhat obscure and cannot be analyzed up to the last detail. Pufendorf recurs to a critical stance against scholasticism, which can be traced back to Humanism, by claiming that there are no necessary and transcendental truths, a stance whose upshot is a sort of

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empiricism. The laws of human coexistence, for example, cannot be derived from transcendental laws that exist independently of the existence of man, but rather from the observation of the conditio humana. Also, the interconnection between reason and revelation is rejected by him. They are two different issues that have to be strictly separated from each other. The source for revelatory knowledge is solely the Holy Scripture that in a sense makes up the empirical basis for acquiring religious knowledge. Faith is not a rational but an act of the will, which is weakened by the original sin making human rebirth necessary. Only faith makes man capable to obey Christ’s commandments. Rebirth is, however, linked to the acceptance of certain elements of faith, like the doctrines of trinity and the deputy death of Christ, an attitude that underlines the separation of faith from philosophy, since the latter would never accept those doctrines. This is a clear rejection of the developments of the 18th century that will result in a continuous reduction of the doctrines of Christianity. This distance from any transcendental attitude marks also Pufendorf’s view of the Holy Roman Empire, which he regards as a confederation of states that is nevertheless of great importance for the preservation of the political equilibrium in Europe. Even if Pufendorf appears to be an explicit empiricist, an enemy of the traditional metaphysics of scholasticism, a critic of the linking of reason to revelation, and a sober observer of the events of his time – in other words, even if he appears as a thinker who stands nearer to the Enlightenment than Leibniz – we can find also traits pointing in other directions. Despite the separation of faith and reason, he regards the Christian religion in its Lutheran version as the central issue for understanding the world and man. This includes the idea that man is coined by the original sin and can free himself from its claws only by rebirth, which is not a rational, but a deliberate act. The German Enlightenment will not – with few exceptions – take an irreligious turn, but in its main stream it will nevertheless try to reshape faith according to the rules of reason and to maintain an optimistic picture of humanity, following Leibniz’s paradigm and not that of the sceptic and pessimist Pufendorf. The latter is situated, however, in a tradition of religious renaissances that will dominate the following centuries, but also in a philosophical tradition that will lead away from Leibniz, via Thomasius and Crusius, to the philosophy of Kant. Leibniz, who is still rooted in the tradition of Aristotelian and medieval philosophy, and who seems more conservative than Pufendorf, is nevertheless standing at the very beginning of a movement that in the following era of the Enlightenment will restrain faith in favor of reason, regarding the latter as being able to justify irrefutably its doctrines. Its application can therefore render possible the settlement of dogmatic controversies. Leibniz insists thus until his death that the confessional controversies can be overcome if the appropriate men, i.e., the mighty ones, would negotiate on a rational basis. He shares with Pufendorf



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the view that dogmatic differences are relative, but not on the same background: All differences could be settled if all these questions were treated rationally. In contrast, for Pufendorf they lose their importance in view of the demand for a religious rebirth that can be achieved only by the will enabling the real Christian life. Leibniz’s linking of faith to reason results instead in the rationalization of Christianity. Leibniz’s concept of natural law accords with his rational optimism because in the system of this great speculative thinker natural law is only an element of a perfect universe that is constructed according to transcendental laws, at the same time proclaiming the glory of its Creator and founding the Happiness of its denizens. They do not obey a law issued by an invisible God, but observe it because they wish to imitate divine justice. Leibniz always regarded himself primarily as a philosopher, struggling to achieve a rational worldview embracing the totality of the world, which could be constructed only on a metalevel that was inaccessible to Pufendorf, thus evoking Leibniz’s aversion against him. Leibniz is a more thorough recipient of ancient traditions so that many of his ideas could not have a future, for example his insistence on a medieval concept of the Holy Roman Empire linked with the idea of the reunification of the churches, or his concept of a Christian natural law. Nevertheless, he strongly influenced future developments and this was not only in the field of the natural sciences. His worldview, manifested especially in the Monadology and the Theodicy, has determined for a long time the philosophy of the Enlightenment, mainly in the form given to it by Christian Wolff. A central element of this system is the principle of sufficient reason, demanding the necessary logical consequence of everything that happens: … et il ne souffre aucune exception, autrement sa force seroit affaiblie. Aussi n’estil rien de si faible que ces systèmes où tout est chancelant et plein d’exceptions. Ce n’est pas le défaut de celuy que j’approuve, où tout va par règles générales, qui tout au plus se limitent entre elles. (Theodicy §44; GP 6 127)

Consequently, God has lost his almightiness since the course of the world obeys imutable and inabolishable laws. Miracles are impossible. Thus both Pufendorf and Leibniz, important personalities of the German and the European spiritual life, point in two directions, in the past and in the future, each one in his own manner.

Notes 1. Here are a few examples of Leibniz’s general evaluation of Pufendorf’s intellect and of his contributions: “semper judicavi passim popularia potius quam solida, interdum et non satis tuta ab eo afferri” (‘I have always considered that the thoughts he put forth indistinctly were more popular than solid, and sometimes insufficiently expounded’; Leibniz to Johann Paul

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Kress, May 1712; LBr, 506, Bl. 1). “M. Pufendorf avoit de l’esprit et du talent pour les matieres populaires, mais il n’estoit rien moins que meditatif ” (‘Mr. Pufendorf was witty and talentous for popular affairs, but he was far from being capable of meditating’; LH XI 1 3 Bl. 6). Pufendorf was very popular among the academic youth, “quod popularius exposuisse videri queat quae a Grotio Viro Summo sublimius erant pertractata nec a juvenibus tam facile capiebantur” (‘[because] he was capable of expounding in a more accessible way subject matters that were sublimely treated by the venerable Grotius and yet were not so easily understood by the young’; Epistola ad amicum: 15–16). 2. Pufendorf’s library contained the following works of Leibniz: Caesarinus Fürstenerius, Nova methodus discendae docendaeque Jurisprudentiae, and Ratio Corporis Juris reconcinnandi (Palladini 1999: 237–238). It has to be taken into account that Leibniz hadn’t published much until Pufendorf’s death in 1694. However, Pufendorf’s book about the constitution of the German empire was openly criticized by Leibniz in his Caesarinus Fürstenerius. Interestingly, Pufendorf did not react to it despite the fact that he normally did not shun the occasion for a polemic. 3. Leibniz confirms this: “Samuelem Pufendorfium videre mihi non datum est …” (‘I have not had the opportunity of seeing Samuel Pufendorf’; GR 376). 4. Christian Habbeus reports in 1670 to Leibniz that Pufendorf expressed the wish to correspond with him (Habbeus to Leibniz, September 24th 1670; A I 1 214). 5. Leibniz and Esaias Pufendorf met in the 70’s and the 80’s several times. In this context it is relevant that Esaias’s widow, Veronica, asked Leibniz for support for her and her children. 6. In his first preserved letter, Leibniz already mentions Pufendorf in a critical manner. He alleges that Pufendorf compiled his Elementa jurispudentiae from Erhard Weigel’s manuscripts (Leibniz to Jacob Thomasius, September 2nd 1663; A II 1 3). 7. His critique of Pufendorf in a report to Severinus de Monzambano (A IV 1 500–502) was first published only in 1864. 8. Leibniz proposes in Mainz the establishment of a committee that should prohibit the publication of dangerous books, such as Pufendorf’s book on the constitution of the Empire: “Man weis was bisweilen ein baar bücher für schaden gethan. Der Hippolytus à Lapide vor diesen, der Monzambano und Burgoldensis unlängst, haben gewislich die gemüther nicht wenig verstört und exulcerirt” (January 1670; A I 1 500). 9. Leibniz criticizes Pufendorf 's famous book on the constitution of the Empire in the following publications that appeared under pseudonym: Caesarini Fürstenerii de Jure Suprematus ac Legationis Principium Germaniae (A IV 2 65, 67) and Specimen demonstrationum politicarum pro eligendo Rege Polonorum (published under the pseudonym Georgius Ulicovius Lithuanus (A IV 1 61). The most important criticism in this context is the Epistola ad amicum super exercitationes posthumas Samuelis Puffendorfii De consensu et dissensu protestantium that was published after Pufendorf’s death (see Döring 1993: 176–197, which contains also the text of the Epistola). 10. “Nescio, to cl. viri, Samuelis Pufendorfii, librum legeris, Eridis parum amabili titulo inscriptum... Ego scriptoris ingenium colo atque exosculor, sed vellem moderari sibi nonnihil, minusque acriter invehi in dissentientes” (‘I don’t know whether you have read the book of this illustrious man, Samuel Pufendorf, a book with a not so attractive title, Eris Scandica … I honor and praise the author’s talent, though I would like him to moderate himself somewhat,



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and be less abusive towards those who do not agree with him’; Leibniz to Placcius, May 10th 1687; D 6 45). 11. Receperat aliquando in se curationem negotii cujusdam mei in Suecia, sed per amicos didici, contraria omnia ab eo acta fuisse” (‘Some time ago he was in charge of a certain affair of mine in Sweden, but I learned through friends that he did exactly the opposite [of what I wanted]’; Leibniz to Bierling, October 28th 1710; D 5 358). 12. A remark that goes back to the chancellor of the University of Halle, Johann Peter Ludewig, is more credible, namely that Pufendorf had advised the Elector of the Palatinate not to appoint Leibniz at the University of Heidelberg (Ludewig 1721: xxv). Ludewig Markus Detlev Friese indicates as a source for this information a friend of Pufendorf’s. This remark was recorded long after the alleged incident and cannot be confirmed independently and has thus to be treated with care. 13. Leibniz complains to the Elector Georg Ludwig of Hanover about Pufendorf’s quite high income (K I 9 299). 14. Pufendorf himself had pointed out to Leibniz the fragmentary character the latter’s work: ‘All scientific efforts are more or less futile (frustra insumatur) if one cannot present any results’ (Pufendorf to Leibniz, March 31st 1693; GW 1 357). 15. Leibniz to Kästner, January 30th 1711 (D 4 3 264). The transcription “archipodialis” is incorrect. Dascal, accepting Dutens’s transcription, translates the whole sentence as: “Yet, his [Christian Thomasius’s] philosophy is to this day still immature (sylvestris) and, so to speak, pedestrian (archipodialis)” (DA 72). 16. Leibniz’s correspondence with Thomasius was even more meager than that with Pufendorf. There exists only one letter from Thomasius addressed to Leibniz and his response (see Heinekamp 1979: 92–97). However, it is very reasonable to think that they have known each other personally since Leibniz was a student of Christian Thomasius’s father, Jakob, with whom he kept in touch for a long time. 17. “Etant enfant j’appris Aristote, et même les Scholastiques ne me rebutérent point; et je n’en suis point faché presentement” (‘As a child I studied Aristotle and even the Scholastics were not unpleasant to me; and I don’t regret it today” (Leibniz to Remond, January 10th 1714; GP 3 606). 18. These ‘strange sounding’ elements for them are therefore either interpreted not as intended by Leibniz or else they are simply omitted. It is, however, symptomatic that the Berlin Academy, which was founded by Leibniz, awarded a prize to a manuscript that rejected the Monadology. The Academy had announced a prize for the best manuscript on the question whether the doctrine of monads was valid. The winner was Johann Heinrich Gottlob Justi’s Unter suchung der Lehre von den Monaden und einfachen Dingen, which was published in Berlin by Haude et Spener, in 1748. 19. This expression should be put actually in quotation marks, since we are dealing with two different systems. However, it was in common use in the 18th century. 20. Christian Wolff to Graf Ernst Christoph von Manteuffel, January 27th 1741; University of Leipzig Library, Ms 0346, Bl. 90. 21. “Ac nisi bona quaedam ingenia fraenum istud pedanticum abrupissent, ad mundi usque finem Philosophi poma Aristotelica ad scarabaeorum instar in circulum volvissent, scientia rerum naturalium ne hilum quidem promota” (Eris Scandica; GW 5 270). Ethics and politics

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too would undergo similar progress – Pufendorf continues – were it not for his, Pufendorf’s, enemies (he refers concretely to Valentin Alberti) who tried to throw back these sciences in the old prison of Aristotelian philosophy. 22. “Et sane quid indignius est, quam quod homo, qui nihil aliud quam per plusculos annos Jenae in lacunis Metaphysicorum volutatus est [referring to Valentin Veltheim, professor at Jena], apud nos aliquid de studiis hiscere velit? Quod enim luculentius specimen esse poterat triobolaris eruditionis, quam quod ad lectionem Grotii adspiraturo, fundamenta Logices et Metaphysices potissimum commendat …” (Pufendorf, Specimen controversiarum circa Jus Naturale ipsi nuper motarum; GW 5 179–180). Some pages later Pufendorf complains that he was accused in Jena of insulting the majesties because he allegedly had insulted the “Sacred Metaphysics” (p. 184). 23. Leibniz pronounces this verdict with respect to the discussion about the scope of validity of natural law. He claims that he stays completely in the trail of the phiosoophical and juridical tradition, in contrast to Pufendorf. 24. “Quum tamen pleraeque sententiae in progressu non admodum principiis cohaerentur, neque ex iis tamquam caussis deducantur, sed potius aliunde ex bonis auctoribus mutuo sumantur …” (‘However, since most of the ideas developed do not fit completely the principles, and are not deduced from them, but are rather borrowed elsewhere from good authors, nothing prevents this little book from containing many good things …’; Monita quaedam ad Samuelis Puffendorfii principia; D IV 3 275). Pufendorf’s books on natural law “non sunt magni momenti jurisprudentiae quippe ac solidioris philosophiae non usque gnarus” (‘have no great importance in jurisprudence inasmuch as [they] do not reach the level of a more solid philosophy’; Epistola ad amicum: 197). There are numerous repetitions of these allegations. 25. Leibniz’s criticism is targeted also against Pufendorf’s works in history, something that cannot be pursued further here. However, the tenor of the criticism is always the same: Pufendorf’s historical works were hastily compiled, they contained a lot of plagiarism, they were erroneous and totally superficial. 26. “… il me semble, qu’il ne faut pas qu’elle [die Religionsgespräche, D.D.] passe par les seules mains de Messieurs les ecclesiastiques, qui ont leurs maximes, et leurs veüs à part, les quelles ont quelque fois plus de rapport à leurs preventions et à leurs passions, qu’au bien de l’Eglise …” (‘… it seems to me that they [the religious discussions] should not be only in the hands of the ecclesiastics, who have, each, their principles and their wishes, which in turn are more related to their prejudices and their passions than to the good of the Church …’; Leibniz to Herzog Anton Ulrich von Braunschweig-Wolfenbüttel, November 7th/17th 1698; A I 16 23). Pufendorf’s criticism is directed against the “malady of the preachers”, the righteousness that was always connected with the patronization of laymen by the theologians: “...sie glauben, Gott sey keinem gnädig, der nicht praecise alle distinctiones adoriret, die sie in ihren patribus et pl. reverendis praeceptoribus gelesen” (‘… they believe that God is not a gracious being who adores exactly all the ornaments that they [the clergymen] have read in their patribus and revered teachers’; Pufendorf to Thomasius, March 24th 1691; GW 1 310). 27. “In hoc quippe Articulo de tribus personis in unâ divinâ essentiâ residet fundamentum genuinæ Religionis Christianæ, quo subruto et hæc collabitur, et nil remanet, nisi accurata quædam Philosophia moralis” (‘Certainly in this article [of faith] about three persons in one divine essence resides the foundation of the genuine Christian religion. If it is undermined



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and ruined, nothing remains except a certain precise moral philosophy’; Pufendorf, Jus feciale: 174; GW 9 54). 28. “Sane enim veritates philosophicae non sunt objectum revelationis divinae, seu Deus non ideo peculiari modo hominibus se revelare voluit, ut ipsos talia doceret, quae antea per rationem, et inspecta rerum natura cognoscere dabatur; sed ut viam salutis aeternae rationi incognitam eis ostendere … Igitur cum revelatio divina, et Philosophia circa diversa objecta versentur, haec cum illa conformari nec potest, nec debet …” (‘Indeed, philosophical truths are not the object of divine revelation, i.e., that God did not want to reveal himself to men in this special way in order to teach them things in such a way that he could previously know through reason and the inspection of natural things; but rather to show them a way of eternal salvation unknown to reason … Therefore, since divine revelation and philosophy deal with different objects, the latter neither can nor should conform to the former …’; Pufendorf, Commentatio super invenusto pullo; GW 5 267). 29. “Nam ubi datur principium fallere nescium, quale in Theoligicis controversiis est sacra Scriptura, non potest non demum controversiarum eo spectantium exitus reperiri. Nec minus ad extremum genuinus Sacræ Scripturæ sensus erui potest, ex quo omnis controversiarum decisio promanat, si legitima interpretationis adminicula adhibeantur” (‘For there is no trace of failure, in theological controversies, of the infallible principle which is the Sacred Scripture; one cannot fail to find the solution of controversies examined through this principle. Nor is it possible that it does not lead at the end to the true sense of the Sacred Scripture, wherefrom the decision of all controversies emanates, if the legitimate yardsticks of interpretation are employed’; Jus feciale: 29; GW 9 15). Along with the discussion about a work on variants of the Biblical text, Pufendorf claims: “Ist aber doch dabey Gottes sonderbare providentz zuerkennen, daß diese variae lectiones uns keinen glaubens artickel verwirren, und die rechte lectio leicht zufinden ist” (‘However, God’s special providence is recognized in the fact that these various readings do not confuse us, and the correct reading is easy to find’; Pufendorf to Adam Rechenberg, October 8th 1690; GW 1 288). 30. “Circa quam observandum est, eam quatenus circa modum præsentiæ versatur, fere plus curiositatis quàm fructus habere, dummodo super ipsa Sacramenti substantia ejusque fine, et usu consentiatur” (‘As to what is to be observed, insofar as this concerns the mode of presence it is a question more of curiosity than of bearing some fruit, as far as above it there is agreement about the substance of the sacrament, its aim, and its use’; Jus feciale: 21; GW 9 66). 31. In his Debate with Leibniz concerning the reunification of the churches, the Brandenburgian Preacher of the Court Daniel Ernst Jablonski refers to Pufendorf when he turns to the discussion of the Holy Communion and cites the abovementioned passage of the Jus feciale. This was reason enough for Leibniz to react fiercely (cf. Rudolph 1999b and 2010). 32. Cf. Rudolph’s (1999b) detailed and convincing analysis of this complex topic. 33. There are numerous pieces of textual evidence for this. I refer only to one passage of the posthumously published work Jus feciale: “Huc delapsi hominis conditio tanto miserior erat, quod nec intellectus ejus viam dispicere posset Deum placandi, et voluntas in prava proclivis non posset non aversari eum, cujus iram metuebat, et à quo nihil propitii expectare dabatur, nisi novo gratiæ pignore accepto” (‘On this side the condition of the fallen man was so lamentable that not even his intellect was able to discern a way to placate God, and his will, in its tortuous inclination, was unable to avert he whose ire it feared and from whom nothing propitious was to be expected, unless in exchange for a new pledge’; Jus feciale: 112; GW 9 37).

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34. “Et experientia constat, eos qui circa Romanenses cum Protestantibus conciliandos sategerunt, aut impostores fuisse, aut judicio mentis parum polluisse” (‘Experience shows that those who have endeavored to reconcile Catholics and Protestants were either impostors or had their judgment somewhat disturbed’; Pufendorf, De rebus gestis, Buch XIV, Chap. 20). Notice that Pufendorf is usually very reluctant to draw conclusions in his historical works. 35. Life under Christ’s commandments is completely different from pagan life: “Nam professio fœderis in Christo aliam vitam, alios mores postulat, quam quos Ethnici, et qui instinctum carnis; seu corruptionis ex peccato originali ortæ sequuntur” (‘For the profession de foi dans le Christ implies another life and other customs than the those of the pagans and those instigated by the carnal instinct, i.e., those that follow from the corruption stemming from the original sin’; Jus feciale: 171; GW 9 53). 36. “Frustra autem leges istae civiles feruntur, et inique poena ob easdem violatas exigitur, nisi penes cives sit eas observare aut violare. Huic dogmati adversantur, qui actiones humanas, super quibus in foro civili ratio solet exigi, fatali cuipiam necessitati, et quae usum liberi arbitrii in hujusmodi rebus plane extinguit, subjiciunt. Quod dogma Calvinianis quibusdam tribuitur: ac Reipublicae sane est perniciosissimum” (‘However, these civil laws would be made in vain, and the punishment for their violation would be unjustly demanded, unless it is in the power of the citizens to observe or to violate them. To this dogma are opposed those who submit human actions, for which one usually demands reasons in a civil tribunal, to a sort of fatal necessity, which completely eliminates the use of free will in this kind of affairs. And this [contrary] dogma, attributed to certain Calvinists, is obviously very dangerous for the State’; Pufendorf, De concordia verae politicae cum religione Christiana §16, p. 494). 37. Furthermore, one should not forget that God never acts sine ratione: “Es sind demnach rationes die gott bewegen einem seine gnade auff solche weise zu geben, daß sie nicht ermanglen bey ihm anzuschlagen dem andern aber nicht. Aber die rationes muß man nicht in unsern guten qualitäten suchen … sondern in harmonia universi …” (‘There are thus reasons that move God to bestow on someone his grace in such a way that it does not fail to be made known to him, whereas this is not the case with another. But we must not look for the reasons in our good qualities, but rather in the harmony of the universe’; Leibniz to Albrecht Philipp von der Busche, February 1st 1697; A I 12 536). However, with this claim Leibniz does not comply with the predestination doctrines of the Dordrecht Conventions. 38. Theodicy, Discours Preliminaire §2 (GP 6 50); see also, Part I, §54: God has foreseen every single prayer and thus has taken care that it is fulfilled (GP 6 132). 39. With regards to Pufendorf’s relationship to Pietism, see Döring (1992: 103–111). The Pietist regarded Pufendorf as a Theologian (see Lange 1744: Preface). Lange, who after Francke’s death became the leading Pietist in Halle, expresses his high esteem for Pufendorf’s Jus feciale and announces a new edition that was not printed because of his death. Lange was in contact with Rüdiger and Hoffmann who taught a philosophical system that was anti-Leibnizian and anti-Wolffian (see Döring 1999: 108). 40. Thomasius (1701: 193). Thomasius argues that Pufendorf is wrong in believing that the normalization of the Christian faith can be achived by the power of the state, since there exists no neutral judge on this matter (Thomasius 1701: 123). Pufendorf expresses this view in De habitu 1687: §49.



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41. These people were regarded by some enlighteners as mere confused people and as dreamers, but were not attacked because of their deviation from the central dogmas of the major churches. 42. Also regarding this topic Leibniz can be placed at the beginning of the development of a modern secular worldview, since the existence of justice and the virtues without God’s actual support renders Him in principle redundant – a view that, of course, he himself didn’t hold. 43. “Les vertus ne sont vertus que parce qu’elles servent à la perfection, ou empêchent l’imperfection de ceux qui sont vertueux, ou même de ceux qui ont à faire à eux; et elles ont cela par leur nature et par la nature des créatures raisonnables, avant que Dieu décerne de les créer” (Theodicy §181; GP 6 222–223). 44. Theodicy §182; GP 6 224. Pufendorf appears also here as a “shallow thinker”. 45. “Et vero justitia servat quasdam aequilitatis proportionalitatisque legis, non minus in natura rerum immutabili divinisque fundatas ideis, quam sunt principia Arithmeticae et Geometriae” (‘And, indeed, justice follows certain rules of equality 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 of geometry’; Monita quaedam ad Samuelis Puffendorfii principia; D IV 3 280). 46. “Atque huc ducunt meliora universalis jurisprudentiae principia, quae etiam cum sana theologia conspirant, et ad veram virtutem excitant. Tantumque abest, ut, qui non spe aut metu a superiore, sed propensione animi recte agit, juste non agat, ut ipse potissimum juste agat, quadam divinae justitiae humana imitatione” (‘To this lead the best principles of universal jurisprudence, which collaborate also with wise theology and bring about true virtue. Thus he who acts well, not out of hope or fear, but by an inclination of his soul, is so far from not behaving justly that, on the contrary, he acts more justly than all others, imitating, in a certain way, as a man, divine justice’; Monita quaedam ad Samuelis Puffendorfii principia; D IV 3.280). 47. “… de quo generatim ita sentio: totam mentium universitatem esse unam civitatem maximam sub monarcha Deo, qua nulla potest intellegi perfectior, ut quod de optima Repubblica vel votis vel figmentis pro modo nostro designamus, in rem ipsam contulerit suprema intelligentia, caeteris creaturis in id unum conditis uti inserviant gloriae regis et civium felicitati” (‘… in general, my conception [of  ‘sacred jurisprudence’] is this: the entire community of minds is a great city under the monarch God; this city cannot be better understood than as the best Republic, which we so designate either following our wishes or our imagination, as having been put together by the supreme intelligence, the other creatures in it having one purpose – to serve the king’s glory and the citizens’ happiness’; GR 377). 48. Pufendorf describes his plans for a “De jure naturae et gentium” in a letter to Johann Christian von Boineburg of Januay 13th 1663 (GW 1 27): “In priori agendum de fundamentis Juris universalis, ubi consideranda venit natura entium moralium in genere, moralitas actionum, impositio, imputatio, qualitates et quantitates morales rerum et personarum, obligatio, imperium, lex, meritum, poena et similia. Inde Systema aliquod componendum, in quo specialia juris capita ex dictis fundamentis demonstrentur, cui insignia ornamenta possunt accedere et testimoniis autorum, variorum populorum institutis, et controversiarum illustribus exemplis” (‘First of all, what must be treated are the foundations of universal Law, which consist in the examination of the nature of moral beings in general, the morality of actions, as well as the imposition and the imputation of moral qualities and quantities of things and persons, obligations, sovereign power, law, merit, punishment, and the like. Afterwards, a certain system should be composed, in which the particular chapters of Law are

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demonstrated from the foundations, and its remarkable illustration can be obtained from the testimony of authors, from the institutions of various peoples, and from examples of famous controversies’). 49. “Neque enim opus erat [he refers to the development of natural law as a scientific discipline], ut isthaec propositio esset ex earum numero, quae communiter natura notae novantur, seu quarum evidentia citra ratiocinationem intellectui sese adprobat. Sed sufficiebat eam ex ejusmodi extructam observationibus, quas ipsa natura rerum et hominis suppeditat, et quae a nullo sanae rationis compote in dubium vocari possunt. Haec porro propositio licet eundem in disciplina juris naturalis usum praebeat, quem in physicis et astronomicis exhibent hypotheses, eadem tamen hypothesis proprie dicta non est, ideo quod non dumtaxat tanquam vera supponatur, non definitio utrum revera cum natura rerum congruat, to minus; sed ejus veritas et existentia manifestis et certis demonstrationibus utique subnitatur” (‘Indeed, there is no need that that proposition [the development of natural law as a scientific discipline] be among those that are part of those provided by nature, i.e., among those whose evidence reveals itself before reasoning. It was sufficient that it be the result of observations that the nature of things and of men provides with abundance, and that no rational person can doubt. Furthermore, even if that proposition has the same use in the discipline of natural law as those of the hypotheses used in physics and astronomy, it is not, strictly speaking, a hypothesis, for it is not only supposed to be true until the definition no longer really corresponds to the nature of things, but its truth and its existence is always grounded upon evidend and certain demonstrations’; Pufendorf, Eris Scandica; GW 5 142). 50. “Cum autem non aliter, quam observata lege naturali, id obtineatur; intelligitur quoque a Creatore obligatum hominem ad isthanc servandam; tanquam medium non ex arbitrio hominum inventum, ac ex eorum libidine mutabile, sed expresse ab ipso Creatore huic fini procurando constitutum. Qui enim alicui pro imperio injungit finem, censetur quoque eundem obligasse ad usurpanda illa media, sine quibus finis non potest obtineri” (‘However, since that cannot be obtained except by observing the natural law, it is understood that the Creator also obliges men to observe it, insofar as it consists in a means conceived not by the arbitrariness of man and modifiable according to his will, but as a means expressly created by the Creator himself for this purpose. In fact, whoever imposes an end to another by virtue of his own power is taken to constrain the other to make use of those means without which that end cannot be achieved’; Pufendorf, De jure naturae, II, III, 20; GW 4 155). 51. In the same manner that a triangle consists necessarily of three angles man has necessarily been created as a rational animal (Zentgraf 1678: 129). 52. Detailed accounts of Pufendorf’s understanding of the nature of the Empire can be found in Döring (1996 and 1999). 53. Pufendorf develops these ideas for the first time in a talk given on July 21st, 1655 to the learned society of the Leipzig Collegium Anthologicum (Quomodo respublica Germanorum Imperii Romani nomen sit adepta, et quidnam cum eo proprie ad Germanos pervenerit?; Pufendorf, Kleine Schriften: 24–28). 54. “Denn es hat zwar Teutschland ein Haupt/ so den Titel eines Römischen Kaysers führet; welcher Titel in seiner ersten Bedeutung nichts anders als die Souverainität über die Stadt Rom … importiret … Wiewol vorlängst die Realität den Teutschen Königen von den Päbsten entzogen/ und ihnen nur der Nahme übrigblieben” (‘For Germany has indeed a Principal, so that it can bear the title of a Roman Emperor – a title whose original meaning consists in assuming



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sovereignty over the city of Rome … How much does reality inebriate the German kings, leaving them with nothing but the name?’; Pufendorf, Einleitung, 612–613). It is noteworthy that Charlemagne’s coronotation in the year 800 is not even mentioned in the Einleitung. 55. Pufendorf, Einleitung: 570. Later it is stated there that Germany had sent in vain soldiers and money to Italy. 56. It was not very sensible for Pufendorf to state to Leibniz, who was immensely interested in medieval history and had been assigned the task of writing the history of the House of Brunswick-Lüneburg, that he had refused the offer to write a history of the beginnings of the Hohenzollern family because he (Pufendorf) was concerned only with contemporary history (Pufendorf to Leibniz, March 31st 1693; GW 1 358). 57. Cf. Pufendorf, Einleitung, 618f. and Pufendorf, De statu Imperii germanici, Chapter 8, §7. 58. “‘Monzambano’s’ intention was that the “statum Germaniae … esse conservandum, nec contra eam quidquam novandum. Quo ipso et libertatem Ordinum Germaniae, et securitatem religionis Protestantium inniti, coecus sit qui non videat” (‘Monzambano’s intention was that the German constitution should be preserved and that nothing new should be introduced against it. Hence, whoever did not see that this implied the freedom of Germany’s States of the Empire and the security of the Protestant religion, was blind’; Epistola ad amicos; GW 5 92). 59. Sweden, in the services of which Pufendorf stood for the longest part of his professional life, was also a State of the Empire because of its possessions in Germany. Its politics concerning the Holy Roman Empire of the german nation were in principle also aiming at the attenuation the imperial power. 60. “Iam Imperator est Advocatus Ecclesiae Romanae. Ergo Imperator habet id ius in orbem terrarum, quod Advocatus in res Ecclesiae” (‘Now, the Emperor is the Advocate of the Roman Church. Therefore, the Emperor has the same right in the Earth as an Advocate in ecclesiastical matters’; De jure imperatoris romani in orbem terrarum; A IV 1 503). At another place we read: “Die Majestät unsers Kaisers und der teutschen Nation wird von allen Völkern annoch erkennet … Er ist das weltliche Haupt der Christenheit und der allgemeinen Kirche Vorsteher” (‘The majesty of our Emperor and of the German nation will be recognized again by all nations … He is the worldly Principal of Christendom and the general Leader of the Church’’; Ermahnung an die Deutschen, ihren Verstand und ihre Sprache besser zu üben; Leibniz 1916: vol. 1, 6). 61. Bedenken welchergestalt Securitas publica … (A IV 1 167). Heinrich von Treitschke describes correctly Leibniz’ ideas about the state: “… in the focus of his thinking was not the real existing state in his limited and needful existence, but … ‘God’s Empire’, the ideal unity of humanity. The existence of a mundane state is for him important only insofar such a state is part of a universal spiritual order” (Treitschke 1929: 347). 62. Bedenken welchergestalt Securitas publica … (A IV 1 166). 63. “Mihi mos est eas Civitates irregulares vocare, quae casu consistunt, id est in quibus una voluntas haberi cum opus est, certo semper non potest” (‘I usually call irregular those cities where chance prevails, i.e., cities where it is always impossible to attain a single will when it is necessary’; A IV 1 501). 64. “Ideo negat [Monzambano, D. D.], Imperium unam Rempublicam constituere, sed foedus multarum. Sed cum territoria Principum omnia sint Imperii feuda, necesse est ipsum directum Dominum territoriorum Imperii esse” (‘Consequently, [Monzambano] denies that [an] Empire constitutes a single state and holds that, on the contrary, it is in fact an association of many.

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But since the territories of the princes are all fiefs of [an] Empire, it is necessary that the direct control of the territories belong to the Emperor’; Specimen demonstrationum politicarum pro eligendo Rege Polonorum; A IV 1 61). 65. “Caeterum Principes Germaniae non minus quam Italiae, omnes etiam exteri... entre les Souverains referunt, cum iis in foedera ineunt, connubia contrahunt, breviter, ut pares, ut consanguineos colunt” (‘Besides, the German princes, not less than the Italian ones, as well as all the foreign ones, are soon respected by the Sovereigns, once they enter in alliances with them or contract matrimony, be it as peers, be it as parents’; Specimen; A IV 1 61). 66. “Imperium est familia civitatum. Seu civitas imperans, cui aliae parent. Etsi accurate loquendo non sit nisi una. Et ita esset imperium systema civitatum foederatarum” (‘An empire is a family of cities; in other words, a commanding city to which the others obey. Accurately speaking, therefore, there is only one. Therefore, an empire is a system of federated cities’; Elementa juris naturalis; A VI 1 445).

References Crusius, C. A. 1752. Epistola ad Ioannem ernestum L. B. ab Hardenberg de Summis Rationis Principiis. Leipzig. Crusius, C. A. 1756. Erweckungspredigt welche an dem allgemeinen Buß- Bet und Fast-Tage am 12. Nov. 1756. in der Universitätskirche gehalten. Leipzig. Döring, D. 1992. Pufendorf-Studien. Beiträge zur Biographie Samuel von Pufendorfs und zu seiner Entwicklung als Historiker und theologischer Schriftsteller. Berlin: Historische Forschungen, Bd. 49, 103–111. Döring, D. 1993. “Leibniz als Verfasser der “Epistola ad amicum super exercitationes posthumas Samuelis Puffendorfii de consensu et dissensu protestantium”. Zeitschrift für Kirchengeschichte 104: 176–197 [includes the text of the “Epistola”]. Döring, D. 1996. “Das Heilige Römische Reich Deutscher Nation in der Beurteilung Samuel von Pufendorfs”. In Samuel Pufendorf filosofo del diritto e della politica. Atti del Convegno Internazionale Milano, 11–12 novembre 1994 a cura di Vanda Fiorillo. Naples, 73–106. Döring, D. 1999. “Der Westfälische Frieden in der Sicht Samuel von Pufendorfs”. Zeitschrift für historische Forschung 26: 349–364. Döring, D. 1999a. Die Philosophie Gottfried Wilhelm Leibniz’ und die Leipziger Aufklärung in der ersten Hälfte des 18. Jahrhunderts. Stuttgart/Leipzig (Abhandlungen der Sächsischen Akademie der Wissenschaften. Phil.-hist. Klasse, 75. Bd, 4. Heft), 108f. Döring, D. 1999b. “Der Westfälische Frieden in der Sicht Samuel von Pufendorfs”. In Zeitschrift für historische Forschung 26. Bd. (1999), 349–364. Döring, D. 2000. “Johann Christoph Gottscheds Bedeutung für die deutsche Aufklärung”. In D. Fratzke and W. Albrecht (eds), Lessing. Kleine Welt – Große Welt. Kamenz 2000 (Erbepflege in Kamenz, 20. Jahresheft), 143–164. Entner, H. 1999. “Leibniz und Pufendorf. Bemerkungen zu zwei Gedichten”. In M. Fontius, H. Rudolph, and G. Smith (eds), Labora Diligenter Potsdamer Arbeitstagung zur Leibnizforschung, 1996 (Studia Leibnitiana, Sonderheft 29). Stuttgart: Franz Steiner, 186–196. Guhrauer, G. E. 1846. Gottfried Wilhelm Freiherr v. Leibnitz: Eine Biographie. Breslau: Hirt.



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Hammerstein, N. 1974. “Leibniz und das Heilige Römische Reich deutscher Nation”. Nassauische Annalen 85: 87–102. Heinekamp, A. 1979. “Der Letterwechsel zwischen Leibniz und Christian Thomasius”. Studia Leibnitiana 11: 92–97. Hirsch, E. 1964. Geschichte der neuren evangelischen Theologie. Gütersloh: Gerd Mohn. Lange, J. 1744. Lebenslauf, zur Erweckung seiner in der Evangelischen Kirche stehenden, und ehemal gehabten vielen und wehrtesten Zuhörer, von ihm selbst verfaßet. Halle & Leipzig. Leibniz, G. W. 1668–1672. In Severinum de Monzambano. A IV 1 500–502. Leibniz, G. W. 1709. Tentamen expositionis irenicae trium potissimarum inter protestantes controversiarum. In Spener, P.J., Consilia et Judicia Theologica Latina. 1. Teil. Frankfurt/M, 105–113. Leibniz, G. W. 1916. Deutsche Schriften. Edited by W. Schmied-Kowarzik. Hambutg: Felix Meiner. Ludewig, J. P. Opuscula oratoria. Halle 1721. Palladini, F. 1999. La Biblioteca di Samuel Pufendorf, Catalogo dell’asta di Berlin del settembre 1697. Wolfenbüttler Schriften zur Geschichte des Buchwesens 32. Wiesbaden: Harassowitz. Pufendorf, S. 1678a. Specimen controversiarum circa Jus Naturale ipsi nuper motarum. Upsalla: Daniel van der Mylen. Pufendorf, S. 1678b. De concordia verae politicae cum religione Christiana. In S. Pufendorf: Dissertationes academicae selectiores. Frankfurt/M. & Leipzig: Christian Weidmann, 465– 497. Pufendorf, S. 1687. De habitu religionis christianae ad vitam civilem. Bremen. Pufendorf, S. 1688. Commentatio super invenusto pullo. Frankfurt/M: Friedrich Knoch. Pufendorf, S. 1695a. De rebus gestis Friderici Wilhelmi Magni, Electoris Brandenburgici commentariorum libri novendecim. Berlin. Pufendorf, S. 1695b. Einleitung zu der Historie der vornehmsten Reiche und Staaten so jetziger Zeit in Europa sich befinden. Frankfurt/M. Pufendorf, S. 1695c. Jus feciale divinum sive de consensu et dissensu Protestantium. D. Döring (ed). GW 9. Pufendorf, S. 1696. Das Recht Evangelischer Fürsten in Theologischen Streitigkeiten ... und wider die Papistischen Lehrsätze eines Theologi zu Leipzig vertheydiget von Christian Thomasen und Enno Rudolph Brenneysen. Halle. Pufendorf, S. 1994. De statu Imperii germanici. In H. Denzer (Editor and Translator), Die Verfassung des Deutschen Reiches. Frankfurt/M. & Leipzig: Inselverlag. [Text originally published under the Pseudonym ‘Severinus de Monzambano’]. Pufendorf, S. 1995. Unvorgreiffliches Bedencken wegen Information eines Knaben von Condition. In D. Döring (ed), Samuel von Pufendorf: Kleine Vorträge und Schriften. Texte zu Geschichte, Pädagogik, Philosophie und Völkerrecht. Frankfurt/M: V. Klostermann, 537–550. Pufendorf, S. 1996–. Gesammelte Werke. Edited by Wilhelm Schmidt-Biggemann. Berlin: Akademie Verlag. [= GW] Pufendorf, S. 2002. Eris Scandica. F. Palladini (ed). GW 5. Ritter, P. 1931. Einleitung. A IV 1 xvii–xxxviii. Darmstadt: Akademie Verlag. Rudolph, H. 1999a. “Leibniz’ Bemühungen um eine Reunion der Kirchen”. In H. Otte and R. Schenk (eds), Die Reunionsgespräche im Niedersachsen des 17. Jahrhunderts. Göttingen: Vandenhoeck & Ruprecht, 156–172.

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Rudolph, H. 1999b. “Zum Nutzen von Politik und Philosophie für die Kirchenunion. Die Aufnahme der innerprotestantischen Ausgleichsverhandlungen am Ende des 17. Jahrhunderts”. In M. Fontius, H. Rudolph, and G. Smith (eds), Labora diligenter. Potsdamer Arbeitstagung zur Leibnizforschung (= Studia Leibnitiana Sonderheft 29). Stuttgart: Franz Steiner, 108–166. Rudolph, H. 2010. “Leibniz vs. Jablonski: An intestine struggle on uniting the Reformed camp”. In M. Dascal (ed), The Practice of Reason: Leibniz and his Controversies. Amsterdam: John Benjamins, 273–296. Schneider, H.-P. 1967. Justitia Universalis. Quellenstudien zur Geschichte des “christlichen Naturrechts” bei Gottfried Wilhelm Leibniz. Frankfurt/M: V. Klostermann. Thomasius, C. 1701. Dreyfache Rettung des Rechts Evangelischer Fürsten in Kirchen-Sachen... aus des Herrn Thomasii Lectionibus publicis mit Fleiß zusammen getragen von Johann Gottfried Zeidlern. Frankfurt/M. Treitschke, H. 1929. “Samuel Pufendorf ”. In his Aufsätze, Reden und Lettere, Vol. 1. Meersburg: J.W. Hendel. Zentgraf, J. J. 1678. De origine, veritate et immutabili rectitudine Juris naturalis secundum disciplinam Christianorum. Straßburg.

chapter 11

Leibniz vs. Jablonski An intestine struggle on uniting  the Protestant camp* Hartmut Rudolph

1.

The problem

Two projects have brought Leibniz and the court chaplain Daniel Ernst Jablonski together: a plan for a learned society and the effort to reconcile the divided Protestant denominations, Lutherans and Calvinists. And both these undertakings yielded the Hanoverian court counselor’s involvement in the government affairs of Brandenburg-Prussia. The role of Leibniz in the founding of the Berlin Society, i.e., the future Prussian Academy of Sciences, has already been the object of frequent discussion and documentation (e.g., Brather 1993). And scholarship has not been inattentive to the endeavors aimed at drawing the Calvinists – to whom, since the conversion of Johann Sigismund in 1613, the ruling House of Brandenburg felt itself to belong – closer to the Lutherans, who included the great majority of Brandenburg subjects (Dalton 1903; Delius 1970; Hübener 1990; Selge 1990). Nevertheless, there is an apparent justification for looking once again at these events. The work on Leibniz’s manuscripts for the Akademie-Ausgabe, editing the correspondence and the writings, has been bringing to light new sources and thus new understanding. Research up to now has, admittedly, been addressing the sequence of occurrences; but in so doing, it has given only indirect, or in fact no consideration at all, to the fact that the two outstanding Protestant ecumenical figures of their day, Leibniz and Jablonski, were not only concerned with finding a resolution of the one-hundred-seventy-five-years-old controversies within Protestantism and with bringing to an end the confessional split between these Protestant groups, but saw, in addition, that at the bottom of their common planning there lay quite conflicting ideas on the way in which “Zion’s breaches” should be healed (D. E. Jablonski to Leibniz, March 5th 1698; A I 15 412: “die brüche Zions

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… geheilet zu sehen”). This controversy, more precisely, the Leibnizian position in a controversy about the solution of this controversy, will be explored in what follows, on the basis of one of Leibniz’s writings from 1699.

2.

Impulses of an intra-Protestant reconciliation around 1697

At around the same time, that is, 1696/1697, the two figures, Leibniz and Jablonski, both turned to the question of how an easing of the confessional disagreements within Protestantism could be attained. Two events in the year 1697 had led to a weakening of the position of European Protestantism. These events gave a new urgency to the attempt to do away with the denominational split between Lutherans and Calvinists and, if possible, to include the English church as well in these efforts at union. On the one hand, with the Treaty of Rijswijk (1697) an agreement was reached on regulating denominational relations in the territories being exchanged between France and the German Empire that weakened the Protestant side; on the other, the conversion of Friedrich August I, Electoral Prince of Saxony – this territory being the very heartland of the Lutheran Reformation – strengthened the Roman Catholic Church at the expense of the Protestants. Representing the latter in the Empire now essentially became the responsibility of the Electoral Princes of Hanover and Brandenburg. The ruling house of Brandenburg was interested in a softening of denominational differences, if only with regard to its own territories; after all, the religious policies of Friedrich Wilhelm I (1640–1688), the Great Elector, had led to considerable tensions vis-à-vis the Lutherans. In a document addressed to the Brandenburg state secretary Johann Jacob Julius Chuno on October 7th 1697 (A I 14 590–599; see esp. pp. 593–595), Leibniz set forth a three-stage plan for overcoming the conflicts within Protestantism. As a first step, the Protestant states, including the Netherlands and England, should form a political alliance which would serve the interest of all concerned; next, as an important factor for strengthening this alliance, the divided Protestant denominations should tolerate one another and not go on apostrophizing each other as God’s enemies deserving damnation; finally, the signatories should make an effort to solve the controversies in order to reach a “union des sentiments”, a unification of the denominations whose separation persisted – this being the whole point of the thing. This, Leibniz noted, is easier than it might seem. As his further correspondence with Chuno shows (cf. esp. Chuno to Leibniz, November 20th 1697; A I 14 765–767), Leibniz’s reflections were met with a corresponding readiness of the Electoral court in Berlin. In addition, a further initiative of Leibniz’s, aimed at the King of England, found understanding on the part of the English emissary in Hanover.1 The first result of these endeavors in Berlin



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is a lengthy position paper of the Calvinist court chaplain Daniel Ernst Jablonski, A brief exposition of the AGREEMENT and the DISTINCTION in the faith of the two Evangelical, so-called Lutheran and Reformed, churches – from which it also becomes clear that such distinction by no means attacks the basis of Christian belief (henceforth KV).2 The diplomat of Electoral Brandenburg, Ezechiel Spanheim, delivered this document to Leibniz in December 1697, who later received from his Electoral Prince the commission to work out an answer together with the Abbot of Loccum, Gerhard Wolter Molanus. In addition, before being urged to do so by the Privy Council in Hanover (cf. A I 15 8), Leibniz had Jablonski’s paper sent to theologians in Helmstedt. In spite of repeated impatient inquiries from Berlin, another year elapsed before the position paper worked out by Molanus and Leibniz, Non-commital Considerations of a Written Work called Brief Presentation of the Unity and the Difference in the Faith of the two Protestant Churches [henceforth UB], was sent to Berlin.3

3.

Jablonski’s Kurtze Vorstellung (1697)

In its method, Jablonski’s Kurtze Vorstellung had relied on the Leipzig Discussion of Union. In 1631, Calvinist and Lutheran theologians from Saxony, Brandenburg, and Hesse had come together for a “private conference”.4 The creeds on both sides were compared with one another; the consensus established by this means and the articles that diverged from one another were carefully recorded. With regard to the points that remained controversial between the two denominations and which could yield no coming together in discussion, one contented oneself in Leipzig with a call for giving the brotherly mutuality of the divided denominations precedence over a stubborn insistence on the exclusivity of one’s own position. This appeal had an effect, to be sure, on all Irenicists and all socalled Syncretists. The young Leibniz – as shown by an exchange of letters with his brother and brother-in-law in the year 1669 (see Leibniz 1934) – also belonged to this Protestant splinter group (one essentially shaped by the Helmstedt theologian Georg Calixt). However, appeals of this kind failed to impress the strict denominationalists. They viewed the tolerance promoted by the Irenicists as threatening some of the core areas of their own creeds that were never to be relinquished. Leibniz took the refusal to tolerate Christians belonging to another denomination and the refusal to recognize them as members of the community of Christians, as a deficiency of love. For him, what constituted the cause of schism in Christianity was not the objective differences between the denominations but, rather, a petty mercenary spirit (“amour mercenaire”),5 loveless and obstinate dealings with the

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dissidents, and jockeying for positions of power. In the 1690’s he had extracted from church history and the history of dogma (in dealings with, say, the Arians) a number of examples of the toleration of far greater differences within the Church6 than could possibly be represented by the confessional differences dividing the Roman Catholic Church and the Protestants – a historical argument a majore ad minus for the tolerantia ecclesiastica he demanded. On this point there were most likely no differences of opinion between Leibniz and Jablonski. Strictly speaking, though, in using these arguments one was still pegged at the first and second levels of the process of unification, whereas with Jablonski’s KV and Leibniz and Molanus’s UB, the way to go towards attaining true oneness was meant to have as its basis an approximation of the positions content-wise and, at the end of the day, the elimination of confessional differences. Just like the participants at the Leipzig conference back in 1631, Jablonski based his KV on a church-historical construct: on the route leading from the three creeds (Symbole) of the early church and the fundamental articles of faith formulated by four ecumenical councils, recognized by every Christian denomination including the Roman Catholic Church;7 another creed, knowingly binding on both Lutherans and Calvinists, namely, the Augsburg Confession of 1530, had been used by the protesting States of the Empire to articulate their theological position at the imperial Diet.8 If Protestants from both denominations already have at their disposal a common creed, one surely only need to take up one article after the other “and with each article first show the consensus, and in what respect or respects the two Evangelical divisions are in agreement. Secondly, when a particular article comes up in which the parties differ, one wants to spell out such dissent and what this dissent consists of: And then, thirdly, one wants to demonstrate that such dissent does not reside in fundamentals or topple the basis of Christian Evangelical belief”.9 The points of dissent are seen by Jablonski as lying in the areas of Christology (Confessio Augustana (1530), art. III) and the Doctrine of the Sacrament (Confessio Augustana (1530) art. IX and X), as well as in the understanding of Confession and Penance (Confessio Augustana (1530), art. XI and XII) and here, as well as in the doctrine of Predestination and Grace, possibilities of going back to a specific article of the Confessio Augustana are blocked. These are in fact the essential postulates standing at that time in the way of an understanding within Protestantism. In every one of these cases Jablonski formulates the elements of consent and dissent in order to produce the proof that, in a “momentum dissensus”, in the exposition of the motive, the motivation of the dissent, the “Grund des Glaubens” (‘the foundation of believing’), as he puts it, is not challenged. The tools of his argumentation are, on the one hand, the appeal to formulations in the creed with which the multiplicity or, better put, the spread of the spectrum



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of interpretation in Lutheranism is to be shown so as to allow the objective distance between the two denominations to appear as slight as possible. On the other hand, there was the appeal to the linguistic approximation of the positions, in order to be able to assume a congruence of content that is as far-reaching as possible. This may be illustrated with a presentation of the difference in the Lutheran and Calvinist Christological doctrines of the Two Natures: Both sides hold that Christ, in His pure, unchangeable, indivisible, and inseparable unio hypostatica as God and man, participates in the divine attributes, i.e., omnipotence, omnipresence and/or ubiquity and omniscience. In several variant versions (cf. Sparn 1988: 4–7) orthodox Lutheranism had sharpened this statement to the point where, they argued, these divine qualities must be conceded to pertain as well to the humanity, the human nature of Christ. The actual basis for this doctrinal development had been provided by the differences between Lutherans and Calvinists, dating from the very beginning, in their respective understanding of the real presence of Christ in the Eucharist, as one can see from Article VIII of the Konkordienformel (1579, BSLK: 1017–1049). Jablonski narrows down the objective difference to the formulation: Both parts …, the one denying and the one affirming, preserve equally the true personal union of the two natures in Christ; since the Reformed party, when they have reservations about ascribing divine qualities to human nature, hereby separate the two natures just as little as the Lutherans, when they ascribe the divine qualities to humankind, thereby mix the two natures.10

Then he points to a number of doctrinal utterances in Lutheranism which do not follow the declaration of a ubiquity of Christ according to his humanity, on account of which they have been denied in all other parts of Christianity, “wie sie gegen morgen und abend sich ausbreitet” (‘as it spreads eastwards and westwards’), even though not excluded “aus der Lutherischen Kirchen-Gemeinschafft” (‘from the community of the Lutheran Churches’), and asks “wie könten dann umb derselben willen die Reformirten mit fug ausgeschloßen werden?” (‘how then could the Reformers justifiably be excluded for the same reasons?’). The limitation of this method – if one takes a look at the history of the arguments between the Lutherans and the followers of Zwingli in the Reformation period – becomes apparent at the most sensitive point of the conflict, the socalled manducatio impii, i.e., the question whether godless people taking part in the Last Supper receive in actuality the true Body of Christ. In the Wittenberg Konkordie of 1536, for the sake of softening the cutting edge of this question, agreement had been reached between Upper Germans and Lutherans on the Pauline formulation in 1 Corinthians 11: 27, according to which the “unworthy” also truly eat the Body of Christ (indignos manducare; Bucer 1988: 124), and in this

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way succeeded in avoiding the statement of a manducatio impiorum (the godless enjoy the Body of Christ). However, a year later the Schmalkaldic Articles destroyed this reconciliation of the Reformed and the Lutherans, one that had been achieved through all that effort (BSLK: 451).11 Accordingly, the Upper German theologians, above all Martin Bucer, though intent on reconciliation, refused to sign. Not even the Konkordienformel, which, to be sure, had been inserted in the Wittenberg Konkordie,12 was sufficient to reverse this hardening of positions completely (BSLK: 64). Jablonski believed that he could reconcile both sides at the level of content, by proving that the Calvinist reservations vis-à-vis a manducatio impiorum (‘eating by the reprobates’) did not contradict the formulation of article X of the Augsburg Confession in the Latin version, where it was simply noted that “the body and blood of Christ are truly present and are distributed to those eating in the Lord’s Supper”.13 The Calvinistic understanding of the Body of Christ (so he argued) has a better basis in the words of the Augsburg Confession than does the contrasting Lutheran one. It is particularly from this issue in the controversy that one can perceive the limitations of the method chosen by Jablonski as, likewise, by the above-mentioned “Privat-Conferentz” in Leipzig, decades before. The point in time when the Augsburg Confession was drawn up was, in objective terms, too far away from the controversy between Lutherans and Calvinists to acquire relevance for resolving the oppositions at the end of the 17th century. In Augsburg, the Protestants were concerned with explaining their own positions vis-à-vis the Emperor in accord with the catholic, i.e., universal Christian church. By their use of Holy Scripture and the history of its interpretations, they tried to prove that these positions, which stood in manifest contradiction to the teachings of the Roman Catholic Church, were actually orthodox. In contrast, the extremely sharp conflicts that had been smoldering the camp of the Reformers for six years came to seem less pressing. All the same, it was precisely in this connection, when it was a question of interpreting the articles of the Augsburg Confession, that they weighed in, as is shown by the history of the “Variata” created in 1540 by Melanchthon, the understanding of which (as indicated above) Jablonski felt himself obliged to bring up in his prologue.

4.

The position of Molanus

The criticism of Molanus takes off precisely from here, as one can deduce from his draft of “Antwort Ger[ardi] Abb[atis] Luccensis et Domini de Leibenitz auff die Kurtze vorstellung, … Dominorum irenicorum Berolinensium” (‘Answer by



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Ger[ard] Abb[ot] of Loccum and by the noble sir, G. W. von Leibniz to the Brief Exposition … of the irenic Berlin masters’; LH I 9, fol. 106r–167r), Admittedly, he too states that he sees no dissent in the fundaments between the contending Protestant confessions (LH I 9, fol. 106r–167r); at the same time, however, he names the title of a polemical treatise of the Wittenberg theological faculty, “Kurtzer und gründlicher Beweis, das der Reformirten lehre, der seeligkeit nachtheilig und verdamlich sei …, darin zugleich erwiesen, das sie im grund des glaubens … irren …, allen frommen Christen, sich für solcher gefährlichen secten zu hüten, … nebenst einem anhange, der einfeltiger beistimmung, unserer Evangelischen Kirchen, wegen verdammung der Reformirten lehre” (‘Brief and thorough proof that the doctrine of the Reformed is spiritually disadvantageous and to be condemned …, in which, at the same time, is proven that … in the fundamentals of their belief … they err …[;] to all pious Christians to guard against such dangerous sects … together with an appendix which [contains] the unanimous approval of the damnation of the … [Calvinist] doctrine by our … [Lutheran] churches’; Wittenberg (Mevius) 1663), a reaction of the strict Lutherans to the religious conference in Kassel in 1663. The only way of interpreting this reference is as a reflection of the mind of the Abbot of Loccum (incidentally a pupil of Georg Calixt’s): his belief in the necessity of confronting each and every precipitous feeling of irenic euphoria with the negative experiences of earlier attempts at conciliation, which is to say, confronting it with the harsh reality of confessional conflict in its implacability. In part, these were actually personal experiences of the Lutherans with the consequences of the above mentioned Kassel conference, an agreement reached there between Lutherans and Calvinists for mutual tolerance.14 Following the religious conference in Kassel, in which a tolerantia ecclesiastica was agreed on between the Lutherans of Calixtian persuasion and the Calvinists – an agreement which, however, was retracted by the Hessian landgrave – the Lutherans had felt compelled, contrary to the arrangements on the side of the Calvinists, to turn the university over.15 Thus Leibniz writes on the 16th of November 1698 to D. E. Jablonski: Molanus is “von Rinteln her noch allezeit in Sorge, daß man des Friedens zu der Evangelischen [= Lutheraner] Nachtheil sich Reformirter Seite zu bedienen gewohnet” (‘Molanus, “<writing> from Rinteln, is worried the whole time that people on the Reformed side are making use of the peace to the disadvantage of the Evangelicals [Lutherans]. He, Leibniz, however, has “spoken encouragingly” to the Abbot (Leibniz to D. E. Jablonski, November 16th 1698; A I 16 293). This experience wasn’t the last thing to cause Molanus to warn against a mere reciprocal toleration of the two confessions (unio virtualis; ‘a virtual union’) and to vehemently demand unio actualis (‘an actual union’) through which the division “could be totally 

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removed, and one could again be brought, assembled, to one church and one altar”. Molanus considers Jablonski’s first step, defining the consent necessary for this along the lines of the articles in the Augsburg Confession as unsuitable. These are “opposed above all to the Roman Church” (LH I 9, fol. 107v/108r); hence it is not surprising that the Calvinists and Lutherans – Molanus calls them “Evangelici” – are of one mind about these articles. Molanus also has reservations regarding Jablonski’s expert’s report (LH 108/109) with respect to the Leipzig “Privatkonferenz” of 1631 and the attendant handlings by the Calvinists of the results striven for there, especially the alleged impairment of the discretion agreed on with the Lutheran theologians.16 Molanus would like to see a strengthened consideration given to the negative experiences of the Lutheran-Calvinist dialogue in the 17th century at the coming negotiations for a settlement, strengthened beyond what is considered in the Berlin court preacher’s expert’s report, which doesn’t devote a single word to fears of this kind on the Lutheran side. When, following the reading of the UB at the court in Berlin, there developed the view that the two experts’ reports provided a suitable basis for a religious discussion, it was Molanus who expressed intense second thoughts, and not only for the reasons mentioned up till now. Within Protestantism (he held), suspicion would arise towards the Irenicists; among the Lutherans, particularly in Electoral Saxony, one would stir up resistance at universities and among the ministers, and also awake the suspicion of a desire to split Lutheranism. This would particularly be the case if, as happened after the Leipzig Conference, the results were to be spread around openly, counter to the agreements. On this last point, reference is made to a person who counts as one of the leading Irenicists of the 17th century in Europe and whose activity was judged in one way by Jablonski and in a completely different way by Molanus and Leibniz: the Scottish born Presbyterian John Dury (Duraeus). Jablonski had met him when he was still in his father’s house and realized, as he wrote in March 1697 to Gordon, that the man had “in meinem Herzen das [scil. ökumenische] Feuer entfacht” (‘had “kindled the <ecumenical> fire in my heart’; Sykes 1950: 10f.). As late as Feburary 22nd 1698, the court chaplain expressed the wish that a phoenix might rise from Dury’s ashes and, with the same gifts and same intensity, but with a more fortunate hand and more success, complete the task of union (Sykes 1950: 10–11). Molanus’s reservations towards Dury had already been addressed. Leibniz let Jablonski know his misgivings about the irenic efforts of the Scot with unsual clarity. He declined quite expressly to join in Molanus’s disapproval of the publication of the report on the Leipzig Conference, making the point that the complaints still heard about the matter from the Lutheran side (Leibniz calls them the “Evangelischen”) are no longer in accordance with the times. “Vielmehr hat Duraeus damit ein guth werk gethan” (‘On the contrary Dury has done a good



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thing in this’; Leibniz, 2nd half of September 1698; A I 15 833). There is more to Leibniz’s reservations about Dury and the results of the Leipzig Conference. For him, neither this conference nor the striving of the dedicated Irenicist from Scotland could succeed in creating a viable basis for the unity of the divided confessions that was sought for; rather, they came to a halt when still far from this goal: Thus it is simply a supplication in a legal dispute, or what the jurists call confirming the war rightfully, to be sure, just a liquidation of the prevailing demands, and belongs to the tractates, but is still all too far from peace. Nor has the good, well-meaning Duraeus been able to advance things any farther; not to suggest that perhaps he wasn’t equal to task.17

However, now Leibniz sees that the time has come to aim for progress, not the least because at this point excellent and expert politicians are involved (Leibniz to D. E. Jablonski, September 1698; A I 15 833–834). And fittingly, a year later he will also support, unlike Molanus, the beginning of talks and, at the same time, in order to promote them, he brings Molanus’s reservations to the attention of the Reformed side in Berlin (BSLK 64). We owe our knowledge of the reasons to Leibniz, who, though not following Molanus on this point, nevertheless strove for the objections’ being taken into consideration in the discussions with the Brandenburgers. The difference between Leibniz and Molanus did not consist in the former’s having striven merely for the tolerantia ecclesiastica (‘toleration of the churches’), i.e., for a unio virtualis (‘virtual union’), whereas, for the latter, any agreement not amounting to a true union of the two Protestant confessions would have appeared as damaging to the unity of the churches of the Reformation (Hübener 1990: 133). Leibniz, too, through his UB wants emphatically to make possible the unio realis (‘actual union’) as Molanus had formulated it – a union to the effect that the division could be “gentzlich aufgehoben” (‘totally removed’) and “people could be brought and gathered once again” “zu einer kirche und einem altar” (‘to one church and one altar’). Therefore he sees his argumentation as having as its goal the proof that the conflict within Protestantism cannot be a “rechtmäßige ursach” (‘legitimate cause’) “das Schisma zu unterhalten und die völlige unionem communionis in Sacramento Corporis Dominici mutuae zu ver­hindern” (‘to support the schism and to hinder on both sides the total union of the communion in the sacrament of the body of the Lord’), as the final sentence of the UB (LH I 9, fol. 314v) has it.18 It seem rather that the Abbot of Loccum had judged the prospects for success with more skepticism and estimated the dangers threatening the struggle for a lifting of the schism as greater than his opponent in Hanover and the Calvinist partner to the discussion in Berlin had. Leibniz and Jablonski saw for the first time a veritable historical chance and, independently of one another,

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had taken the initiative. There are no visible reasons for distinguishing the goal of the most recent efforts by Leibniz from the unio actualis (‘actual union’) of Molanus. And herein he differs from the court preacher of Berlin and his felllow Calvinist comrades-in-arms. They are, as Jablonski says at the end of his KV, in fact only working towards a “dwelling peaceably together” (‘friedliches beysammen wohnen’) of the separate doctrines and therewith towards the “ecclesiastical toleration” (‘tolerantia ecclesiastica’) which allows “gradually, through God’s blessing, the truth to be shown more clearly” (‘nach und nach, durch Gottes Segen die Warheit klärer zu erhellen’). Jablonski goes no farther than attempting to lead the divergent notions to a middle way (‘Mittelstrasse’). This is the best concept for characterizing his ecumenical strategy. In the KV he inserts it at a crucial place, i.e., in the Doctrine of Election, where, evidently, there can be no settlement between the particularists, with their double predestination, and the universalists. Here he wants to keep to “a middle way between these two” (‘Mittelstrasse zwischen diesen Beyden’) like the one represented by a whole row of Calvinistic churches in Europe – as also in Brandenburg (KV 150–151). In 1698, in opposition to Leibniz, he confesses his sympathy for the Anglican Churcn for its choosing “a devout middle way […] between the superstition of the Papists and the indifference of the Calvinists” (‘eine andächtige mittelstrasse […], zwischen der Papisten Aberglauben vnd der Calvinisten Kaltsinnigkeit’; D. E. Jablonski to Leibniz, October 15th 1698 (after his return from Hanover); A I 16 224).

5.

Leibniz’s method

Without abandoning the diplomatic elegance that characterizes Leibniz’s argumentation in every controversy, it is quite clear how far he, the Hanover courtier, is from Jablonski’s picture of things. In his foreword, Leibniz does also speak of the efforts on the Hanoverian side to lead the points at issue between both sides “on the basis of the divine word and both parties’ confident basic understanding […] into the middle […] (‘aus götlichem wort und beeder Partheyen zuversichtlichen grund-Verstandt […] ins Mittel’; UB: LH I 9, fol. 175v); but this must happen in such a way that the settlement striven for in those possibly ensuing counter-explanations (‘in denen etwa erfolgenden Gegen-Erklärungen’) be recognized “as acceptable” (‘vor annehmlich’) and, if it should really lead to a unification, be free of all “palliation” and “Zwey-Deutigkeit” (‘double meaning’; ibid.).19 Leibniz is not striving for a minimum of agreement; he won’t content himself with a resumé of the results reached up until then in conversations on union. Rather, like Molanus, he views the attempts hitherto (including those undertaken by Jablonski) as insufficient. The above-mentioned20 interchange on the



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figure of the Irenicist John Dury in 1698, that is, in the year when Molanus and Leibniz were working on an answer to the KV and were for that reason repeatedly bothered by Jablonski, was intended to communicate the criticism actually pertaining to Jablonski’s KV. Admittedly, Molanus and Leibniz take over essential arguments from the KV, as when, for example, in agreement with Jablonski’s reference (KV: 143) to Pufendorf’s Jus feciale divinum (‘the divine law of war and peace’; Pufendorf 1695: 225), they make the point that one could avoid the quarrel about the real presence if one were to suppress curiosity about the way in which this real presence would be explained; that is, if one left aside the way in which things happen in the divine mysteries (quomodo in divinis mysteriis) and simply retained, in line with the words of Holy Scripture, the truth of the thing at all times (rei veritas alle zeit).21 In addition, Leibniz takes over, for example, Jablonski’s allusion to the whole well-known formulation in Confessio Augustana X (UB: LH fol. 260v). But a certain number of the controversial points were not treated so intensively in the KV; thereby the causes hindering the Lutherans from drawing closer to the arguments of the Calvinists could have been swept aside. In addition, themes in the KV were passed over which on the side of the Lutherans were usually regarded “alß hochwichtig” (‘of high importance’; UB: Prolog, LH fol. 175r). If these are still not more than hints, the decisive instrument of Leibniz’s critique is his manner of procedure in the UB itself. Contrary to Molanus’s draft, Leibniz holds back from evaluating the connection with the Leipzig “Privatkonferenz” that was, for Jablonski, of fundamental methodical importance, i.e., connecting with an orientation on the articles of the Augsburg Confession that went as far as possible. Molanus’s draft just makes visible an intention that was probably originally present, one dividing up the points of controversy according to three “classes”, and discussing these one by one: an initial class in which the disagreements simply concerned concepts but where, objectively considered, unity prevailed; a second class in which differences grounded in objective matters were present, but the differences were such that they had no bearing on the fundamentals of the faith and could be worked out among the contestants; and, finally, a third class of controversial positions which cannot be resolved. In the UB one can only find a few traces of this approach.22 Leibniz was obviously convinced that following this strategy (also applied to the controversial points in Jablonski’s KV) no substantial basis could be found for the unio realis: writing up the various doctrinal utterances in this manner leaves one at a level at which those who call the other party heretics cannot be reached because, in their minds, such extension of the fault of the adversaries endangers the fundamentals of faith. In the end, one gets nowhere by placing in opposition utterances of the quarreling parties such as are contained in creeds or theological treatises and then evaluating the measure of dissonance according to the pattern

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mentioned. With a method like this, one doesn’t reach those segments of the parties holding views that differ from that of the Irenicists (Leibniz, Molanus, and Jablonski consider themselves as such Irenicists), for whom a smoothing over of the bases of the faith without endangerment seems impossible. But the efforts at unification can only be successful if the opposition of the strict confessionalists is overcome.23 This requires a discussion of the motive for the allegedly heterodox doctrine, the reasons for its coming about and, on the other hand, the causes of the exclusion from orthodoxy of the opponent and the justification of a verdict of this sort. To seek for this is already commanded ex lege humanitatis et charitatis (‘by the law of humanity and of charity’; UB: LH fol. 177v): as beings endowed with reason we know about our weakness and imperfection, which includes the pronitas errandi (‘readiness to make mistakes’); as Christians we know, further, that we practice love towards our neighbor and, according to the regula aurea (‘golden rule’), should do nothing to the other which we do not want done to us by others.24 By no means does that mean relativizing the truth or reducing the creeds to general basic truths undeniably accepted by all – Leibniz did not subscribe to the consensus quinquesaecularis (‘of five centuries’) – the assumption of a consensus in all essentials of the creed among the Christians of the first five centuries. On the contrary, he held that, in and for himself, a Christian would not like to be a heretic; nevertheless, as a reasonable being he can at times be led by philosophical or theological premises to conclusions which can willy-nilly bring about a heterodox consequence. As an example of a mistake induced by a misleading of this sort Leibniz cites the teaching of the Gnesiolutheran Matthias Flacius (Illyricus), according to which original sin is no accidens but, rather, a substantia of man. Without question from this thesis, stemming as it does from a “fehl-tritt in der philosophie” (‘misstep in philosophy’), it follows an heterodox Manichaeism and the consequent elimination of essential elements of Christian belief. But while he lived, Flacius spoke out against such heresy “mit hand und Mund” (‘with the hand and the mouth’). Thus it is (Leibniz argues) an infringement of aequitas, of fairness, to accuse Flacius of heresies, even though they follow “deutlich aus seiner lehre” (‘clearly from his teaching’; LH fol. 178). Leibniz names such views, which result from mistaken premises, “ungestandene Ketzerei” (‘unconfessed heresy’) – a heresy that he does not attribute to himself, of course. In the discussion of basically contentious themes dividing the confessions, a double question arises: 1. Ob dies eine ketzerliche meinung sey, daraus eine ungestandene ketzerey folget und wie weit ein theil dem andern eine solche ungestandene ketzerey mit gutem gewißen beymessen könne? (‘Whether this is a heretical opinion out of which



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an unconfessed heresy follows and how far one part can, in good conscience, attribute to the other such an unadmitted heresy?’) 2. Ob einige der Unserigen genugsahme Uhrsachen gehabt oder nicht, solche conseqventien aus der Lehre aller oder einiger Reformirten zu ziehen (‘Whether some of our own had sufficient cause or not to draw such conclusions from the doctrine of all or of certain of the Reformed?’; LH fol. 177r).

Whereas Jablonski, who cites the history of dogma and of theology to illustrate the breadth of the spectrum in order to produce in the adversaries the ecumenical spirit of tolerance required for unity, Leibniz cites the positions in each case in order to test them with regard to their orthodoxy. Balancing the divergent declarations in the realm of the doctrine of divine attributes and the decretum dei absolutum (‘God’s absolute decree’) follows more geometrico by means of the syllogism. Herein he arrives at determinations which rule out the orthodoxy of certain positions within Reformed theology, because, say, following the logic of a declaration of the existence of God or one of the divine attributes, e.g., omnipotence or goodness, would have to be negated: If God chose one part of mankind as elected, the other part as reprobated, and decrees the reprobates to go to hell, then his omnipotence means that God is able to do this and that his decision is infallibly to come to pass. But would God not have acted then in contradicition to other attributes of his, namely his perfect goodness, his perfect justice, and would this not be a contradicition to the perfection of his creative work? But none of the controversial theologians intends, or knowingly accepts to bargain about such a result. Rather, the procedure applied by Leibniz points to an unrecognized slight error at one stage of the thinking process; and in the “ungestandener” (‘unadmitted’) result of this error “wegen connexion aller wahrheiten” (‘due to the connection of all truths’) and with the application of the proposition that contradictoria cannot be true at the same time, a serious error, a heterodox teaching can be entailed (UB: LH I 9, fol. 179v–180v). To this kind of more geometrico argumentation one could attach the hope that an objectively based unity of confessional declarations may be reached among the opponents, reasonable beings that they are, for rational reasons. Where this is (still) attainable, Leibniz would like to illuminate the controversial positions to the degree that at least “ein theil den andern beßer vorstehen möge” (‘one side [or: part] may understand the other better’), which at least leads to the result that no-one attributes to another a position which shatters the foundations of Christian belief and which thus excludes the very possibility of a fellowship of the churches. Yet, the fact that every adversary can evaluate the error found in every opponent’s argument or conclusion “unter dem favor der dunckeln reden” (‘undermines the favor granted to obscure talking’). Thus, in place of accusations of heresy one would make the effort, owed to

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Christian love, to warn one’s fellow Christian, to lead him to the path of truth by giving him insight into the undesired consequences of his statement (UB: LH I 9, fol. 183v/184r; see also UB: LH I 9, fol. 180v/181r; see also the above the two quotations from fol. 183v/184r).25 Leibniz’s extensive argumentation concerning the decretum dei absolutum (‘God’s absolute decree’) and the divine attributes (UB: LH fol. 184r–257r) constitutes the attempt to introduce such an insight into the discussion of the universalism and particularism of divine Election, which was being violently disputed between Lutherans and Calvinists and also within the Calvinist churches. What resulted is an almost comprehensive exposition of the problem of theodicy in which Leibniz of course regards universalism as the only possibility of grasping divine Election by Grace that is compatible with the divine attribute.26 Respect is given to particularism as a logical consequence of the idea of Election – which also in a “historical” sense cannot be denied. That is to say, God in His eudokia27 chose Petrus, whereas the eudokia passed Judas by. And this must have in God, “der die Weißheit und beständigkeit selber ist” (‘who is wisdom and permanence itself’; UB: LH I 9, fol. 252r), a causa impulsiva praedestinationis (‘the cause that acts as the grant and the thrust of predestination’), which, say, with Luther, is ascribed to the deus absconditus, the unfathomable. However, Leibniz declines to appeal to this, for every speculative assertion of a double predestination, of a limiting of the universalism of Election by Grace to only one part of humankind, necessarily leads to a contradiction, since this Election by Grace could no longer be the decretum dei absolutum (‘God’s absolute decree’) 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 ad infinitum, unless, turning things around, one were to connect à 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 the Holy Scripture, where the “causae impulsivae voluntatis et decretorum divinorum … per bonam consequentiam, wenn nicht a priori, wenigst[ens] a posteriori” (‘impulsive causes of the divine will and decree’ can be found, ‘be it by the biblical wording itself be it by looking on the good aftermath, if not a priori then at least a posteriori’; LH I 9, fol. 138v) can be found. Leibniz draws a parallel between the refusal to base the damning of the “reprobati” speculatively in the decretum absolutum and the cognitive rules of natural science: the former theological-philosophical speculation is just as little indicated as “man in Physicis befugt ist ad qualitates occultas seine Zuflucht zu nehmen, so lang die Uhrsach des natürlichen dinges sonst zu ergründen ist”(‘in physics one is free to take refuge in [or fall back on ] hidden qualities as long as the cause of the natural thing can be accounted for in another way’; LH I 9, fol. 138v).28



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It is especially with this point that 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 a use of reason. The corresponding means for creating a sufficient basis for the ecclesiastical unity sought for is the argumentation more geometrico (see Rudolph 2004: 269f.). Leibniz makes use of a method like the method he had already developed and promoted in his early writings for solving political problems. The arguments in the UB, which rely on syllogistic the form precisely in the sections on the attributes of God and the divine Election of Grace, rest on a conviction he had explained in the Nova methodus discendae docendaeque jurisprudentiae of 1667. In this early exposition there is a reference, in the context of the giving of reasons for natural right, to a mathematically certain (mathematica certitudine) proof of God’s existence; more precisely, of God as a being endowed with the highest wisdom and might, on the basis of which the claims spread by the atheists can be dissolved (A VI 1 345). Leibniz’s argumentation in the UB continues this line of thought and also holds to the presuppositions he had listed in a fundamental work for the reunion of the Protestants with the Roman Catholic Church from the 1680’s: he who devotes himself to this task must not be indebted to anyone; instead, as a person newly arriving from a new world, he has, as it were, to follow solely what Holy Scripture, pious Antiquity, ‘right reason itself’ (ipsa recta ratio), and the appropriate consideration of the historical facts (rerum gestarum fides) show to a person who approaches the subject with the recommended impartiality (Examen religionis Christianae; A VI 4 2356). Just as a deficiency of love causes schism,29 so, as is explained by Leibniz himself in the UB, it is often relatively small errors, conclusions fallaciously arrived at, that are pregnant with heresy. By tracing such consequences, not intended by supposed heretics, to those less significant mistaken passages, critics are able to react to the controversial teachings in a way other than denying their proponents their community within the church. Thus the method of a detailed and logico-philosophical analysis of the statements at issue does not simply rely on the well-known lofty position of reason in his metphysics; rather, it also results consequentially from his analysis of the causes, as well as the controversies themselves, and also of their handling between the confessions. Quite differently from Jablonski, Leibniz thus employs the entire philosophical potential at his disposal. This can be seen, even more than in the case of the controversies over the divine Election by Grace, in Leibniz’s discussion of the real presence of the body and blood of Christ (interpreted in a controversial way by Lutherans and Calvinists) according to the words of consecration in Matthew 26: 26–28 (UB: LH fol. 258r–314v).30 With his anti-Cartesian metaphysics of substance, which he developed in an effort to come to terms with the Roman Catholic

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conception of transubstantiation (see Goldenbaum 1998: 172ff.), Leibniz tries to break down the Calvinistic reservations, now recently nourished by the Cartesian concept of the body, about a substantial presence of the body of Christ. That is to say, he tries to join the Lutherans, who insisted on the essential real presence of the body of Christ, philosophically possible for the Calvinists. In so doing, he is concerned to prove that there is no need for a new philosophy; what is needed is simply the ‘received doctrine’ (doctrina recepta) and the ‘healthy reason’ (gesunde vernunfft).31 The emphasis on the ‘old’ (alten) philosophy, the old definition of the body as an accident, used as a basis for the clarification of the controversial problem, derives from a discussion which had come up in 1698 – still before the two Hanoverians sent their UB to Berlin – and lasted until the beginning of 1699. Following Jablonski’s orders, Leibniz had sent a shorter text to Berlin.32 Preserving the anonymity of the author, Jablonski made this provisional position paper of Leibniz and Molanus available to several Brandenburg clerics, and gave Leibniz a report on their critical reaction.33 The possible peace between the confessions and their unification was being endangered, “wenn sie auf die Vereinigung in der Philosophie und derselben application zur Theologie gegründet werden müste” (‘if it should be based on the union between philosophy and its application to theology’; D. E. Jablonski to Leibniz, January 1st 1699; A I 16 446). For the theological settlement that was being sought, the agreement of the opponents was predicated (this was the objection of the Brandenburg Calvinist theologians) upon a “completely new philosophy [scil. promoted by the Hanoverians, H.R.] which one was not yet accustomed to” (‘gantz neue Philosophie […], deren man in thesi noch nicht gewohnet’; D. E. Jablonski to Leibniz, January 1st 1699; A I 16 446). The new philosophy, so the argument goes, compels the Cartesians, who hold the upper hand among the Calvinists and who have a number of representatives among the Lutherans, to renounce their ideas. But Georg Calixt issued warnings of such a way already. One will scarcely be able to bring the opponents to the point of a “vollkommenen Uebereinstimmung in ihren Meynungen oder Concepten” (‘complete agreement in their [philosophical] intentions or concepts’); nor is this a necessary precondition for the agreement; enough is achieved by the proof, as Jablonski writes (invoking Philippians 3: 15f.),34 that “die diversitas nicht die essentia sey” (‘the diversity is not the essence’; A I 16 446 ll. 19–22 and 447). Leibniz probably saw this criticism as striking at the heart of his concept of union. He asked himself, as he replies to Jablonski on January 8th,35 whether he might wish “eine eitele Ehre mit neuen philosophischen Grillen hiebey suchen” (‘to seek for a vain honor with new philosophical whims’) and whether he wouldn’t have to give up all such arguments (Leibniz to D. E. Jablonski, January 8th 1699; A I 16 471).



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One senses indeed a certain injured feeling in his letter.36 This exchange at the start of 1699 reveals, above all, the fundamental methodological difference in regard to the negotium irenicum between Jablonski and Leibniz. For Leibniz, the solution was to be found in having what he diagnosed as the cause of the controversies between the confessions, namely false philosophical conclusions, recognized as precisely that, philosophical. That is, his concern was not that of Jablonski, which, one might say, was with a moving closer together by the confessions merely on the level of protocol towards a midway tolerable on both sides; Leibniz was concerned with feeling out the places in everybody’s philosophical preconception where a switch could occur, places that could lead to positions in a confession that would strike the other side in each case as heterodox. Since with the opponents it is a question of matters of reason, since there can be only one truth, since the unity longed for can only persist salva veritate, in rational philosophical discourse – the successful elimination of the causes of the controversies has to work. Leibniz saw no alternative to this procedure, which – in distinction to all earlier attempts, including (for Leibniz) Jablonski’s KV – enables, without any palliation and free from continuing inner contradictions (cf. UB: LH fol. 224r, quoted above in note 22), a true ecclesiastical unification of the presently still divided confessions. In the whole history of ecumenism this concept was no more than an episode. However, Leibniz is not the sole ecumenical spirit who failed in his exertions on behalf of the unity of Christians.

Notes * My sincere thanks go to Dr. Joseph B. Dallett (Ithaca, N.Y.) for his English translation of this essay. 1. On this as well as on the foregoing, cf. also Gerda Utermöhlen’s Introduction to A I 14, pages xlv–xlviii. 2. This text, written in 1697, was for the first time critically edited by the author of the present essay. A preliminary edition is available in Jablonsky (1999). 3. Written in 1698–1699. Partial edition of the first draft, Hanover, Niedersächsischen Landesbibliothek, LH I, 9, fol. 106r–167r, here: 130r–137v, in W. Hübener (1990: 147–167); copy of a second draft with a few further corrections by Leibniz in Hanover, Niedersächsischen Landesbibliothek, LH I, 9, fol. 174r–314v; first complete edition in: A IV 7, pre-edition (PDF-Datei n. C3 142, 71 pages; current state accessed at http://leibniz-potsdam.bbaw.de/potsdam/). The draft contains passages in the hand of Molanus and modifications as well as extensive amplifications by Leibniz – which mirror a further controversy, namely, the discussions between the two Hanoverian protagonists of Lutheran irenicism concerning a viable agreement with the Calvinists. This controversy requires an investigation of its own, which will have to wait for a collation of the second and first manuscripts in a critical edition of the text.

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4. As phrased in the title of the report edited by the Calvinist theologian Johannes Bergius in 1636: “Account of the private conference which was held in Leipsic in the year 1631 among theologians of Electoral Saxony, Electoral Brandenburg, and of the Principality of Hesse” (Relation der Privat-Conferentz, welche … zu Leipzig im Jahr 1631 … zwischen den … Chur­Sächsischen, Chur-Brandenburgischen, vnd fürstlichen Hessischen Theologen gehalten worden; Berlin [s. n.] 1636). 5. Cf., for example, Leibniz to Kurfürstin Sophie, August 1697; A I 14 53–60. 6. Cf., for example, Sur Pellisson, Reflexions sur les differends de la religion (A IV 4 511–517; DA 309–324) or De arianismo Vandalorum (A IV 4 517). 7. For the Lutherans, see “Formula Concordiae, Epitome”, in BSLK: 768; for the Calvinists see, e.g., Confessio Sigismundi (1614), in Müller (ed), 836. 8. Müller (ed), 836. Cf. Johann Heinrich August Ebrard, Das Bekenntniß des christlichen Glaubens, dem Kaiser anno 1530 zu Augsburg übergeben, wie solches 1540 im Druck erschienen, 1541 und 1546 zu Worms und Regensburg von den vereinigten Ständen neu dem Kaiser vorgelegt, 1554 durch Kurfürst Ottheinrich in der Pfalz, 1555 in Sachsen eingeführt, 1558 auf dem Convent zu Frankfurt und 1561 auf dem Fürstentag zu Naumburg neu bestätigt; von Calvin und Olevian unterzeichnet und beschworen worden; enthält die Lehre, worin die beiden evangelischen Kirchen von je übereinstimmen und worauf sie sich vereinigt haben. (‘The Confession of the Christian Faith, presented to the Emperor in the year 1530 in Augsburg, as it appeared in print in 1540, was presented anew in 1541 and 1546 in Worms and Regensburg to the Emperor by the united Estates, introduced in 1554 in the Palatinate by Prince Elector Ottheinrich, in 1555 in Saxony, in 1558 at the Assembly in Frankfurt, and confirmed anew in 1561 at the gathering of the Princes in Naumburg; signed and sworn to by Calvin and Olevian; contains the doctrine which the two Evangelical churches have always agreed on and the basis on which they have united’). In his “Relatio”, Bergius, Jablonski’s immediate predecessor in the office of court preacher at Berlin, reports: “Da dann anfänglich die Chur-Brandenburgischen vnd Fürstliche Hessische Theologi sich freywillig erkläret / daß sie mit Mund vnd Hertzen zu der Anno 1530 … zu Augsburg … vbergebener Confession sich bekenneten” (‘Since then originally the theologians of Electoral Brandenburg and the principality of Hesse voluntarily declared that they with voice and heart […] agree with […] the [Augsburg] Confession [of 1530]’; BSLK 43f.). Here there is no need to go into more detail regarding the problematic of the relationship of the so-called Variata (changes introduced by Melanchthon in 1540) to the 1530 version of the Invariata. Jablonski’s opinion is like that of a succession of Calvinists: that the later version does not display any objective variation on the earlier one; he bases his exposition on the text of the articles of 1530 (KV 129f.). 9. “[U]nd bei jedem Articul zuerst den Consensum, und worinn beyde Evangelische Theile einig sind, anzeigen. Zweytens, wann einiger Articul kommt, worinn man discrepiret, will man solchen Dissensum, und worinn selbiger besteht, ausführen: Und dann drittens will man darthun, daß solcher Dissensus nicht in fundamentalibus bestehe, oder den Grund Christlichen Evangelischen Glaubens umbstoße” (KV 130–131). 10. “Beyde Theile …, der verneinende und bejahende, behalten gleichmäßig die wahre Persöhnliche Vereinigung beyder Naturen in Christo; allermassen die Reformirten, wann sie die Göttliche Eigenschaften der Menschlichen Natur zuzueignen bedenken tragen, damit die Naturen eben so wenig trennen; als die Lutherischen, Wann sie die Göttliche Eigenschaften der Menschheit zueignen, damit die Naturen vermischen” (KV 134; Jablonski’s emphasis).



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11. Cf. further, in the Konkordienformel, Epitome VII, BSLK: 796ff. 12. Konkordienformel, Solida declaratio, VII, BSLK 1015. 13. “[Q]uod corpus et sanguis Christi vere adsint et distribuantur vescentibus in Coena Domini”. BSLK: 64; emphasis by H.R. 14. Cf. with this Hübener’s (1990: 133) allusion. 15. Later, Molanus, pressured by Leibniz, wrote a detailed account of the events in Rinteln. He notes that at the colloquium in Kassel on both sides men of “ungemeiner erudition, moderation u. aufrichtigkeit” (‘exceptional learning, moderation, and probity’) had come together. In this way one was hoping for the church and the University of Rinteln “daselbst stabilirten beiderseitigen tolerantz u. brüderlichen Vereinigung … ein aureum seculum” (‘for a Golden Age [developing] from the tolerance and brotherly union, as they had been established there [in Kassel] on both sides’). Instead, tolerance was exploited by the Calvinists for driving away the Lutheran professors, “um proselytos zu machen” (‘in order to make proselytes’; Molanus to Leibniz, January 4th 1700; A I 18 265–266, pre-edition; accessible at http://www.nlb-hannover. de/Leibniz/Leibnizarchiv/Veroeffentlichen/II8A.pdf). 16. Starting with John Dury (Durie): De pacis ecclesiasticae rationibus inter Evangelicos usurpandis, et de theologorum fundamentali consensus in Colloquio Lipsiensi inito … sententiae (n.p., 1634); then with J. Bergius (as in n. 11). 17. “Ist also nur eigentlich eine Litis contestation, oder was die Juristen den Krieg rechtens befestiget nennen, halt zwar in sich eine liqvidation der habenden forderungen, und gehöret zu den Tractaten, aber vom frieden ist es noch alzu weit entfernet. Es hat auch der guthe wohlmeynende Duraeus es weiter nicht bringen können; denn zugeschweigen daß er vielleicht dem Werck nicht genugsam gewachsen gewesen“. Leibniz, September 1698; A I 15 834. 18. In the prologue to the UB Leibniz accords the KV his “praise” for introducing “viel dienliches” (‘much that is useful’) which can further not only a “Tolerantia Ecclesiastica” but also a true “concordia” (LH I 9 fol. 175r). 19. “So hat man nicht umbhin gekont, beederley, nemblich sowol berührte, alß auch einige noch in der Vorstellung [= KV] unberührte, doch an sich selbst bedenckliche controversien, in der ‘furcht des Herren’ [cf. Proverbs 1: 7, 9, 10] zu überlegen. Man hat sich auch anbey bemühet, aus götlichem wort und beeder Partheyen zuversichtlichen grund-Verstandt solche Erklärungen ins Mittel zu bringen, welche, da sie in denen etwa erfolgenden Gegen-Erklärungen vor annehmlich erkennet werden solten durch gottes seegen dem Werk ohne palliation, und ZweiDeutigkeit ab zuhelfen, zulänglich seyn mögten” (‘Thus one could not avoid […] giving consideration in the “fear of the Lord” [cf. Proverbs 1: 7, 9, 10) to the two, that is, the controversies already touched on as well as several not touched on in the KV but in and for themselves serious controversies. In this, one also strove, following the Divine word and the confident basic understanding of both parties, to make central such explanations as should be sufficient, since in any resulting counter-explanations they ought to be recognized as acceptable, through God’s blessing, without being remedied by means of palliation or ambiguity’; UB: LH fol. 175f.). 20. Cf. above, pp. 280–281. 21. UB: LH fol. 262v/263r. In his outline, Molanus named “die menschliche curiositet in glaubenssachen” (‘the human curiosity in matters of faith’) and the “Nicodemische Quomodo, oder wie mag das zugehen” (‘Nicodemian Quomodo, or how can that happen’) as the reason

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for the regrettable contentiousness of the Reformers which threatens the entire program of the Reformation (UB: LH I 9, fol. 107). 22. At the beginning of the section “Von der ewigen Gnadenwahl” Leibniz had originally written: “Unter die streitigkeiten, welche nicht verbales, sondern reales, dabey aber also beschaffen seyn, daß sie den grund des Glaubens nicht auffheben, sondern salva unitate Ecclesiae wol toleriret werden können, zehlet man billig und fürnemlich die fragen, so aus dem Articul der ewigen Gnaden Wahl entspringen oder damit verbunden. Wann nur einige harte unleidliche sententiae oder Reden, vermieden werden, welche die Attributa divina selbst aufrichten und bereits in der ersten Class nehmlich bey den streitigkeiten die man nunmehr bloß pro verbalibus halten zu können hoffet mehreren theils bemercket worden, doch auch wiederumb in etwas alhier berühret werden müßen”; but in the corrected version he limited himself to an objective description of the positions (‘Among the controversies, which are not only caused by a different use of words but by essential differences, and which do not abrogate the basic principles of our faith but which can be tolerated in order to keep church unity, one justly counts above all those items dealing in one way or another with the eternal divine election of grace. One should only avoid some hard and unacceptable statements dealing with the divine attributes, which had already been mentioned within the first class of controversies, namely those, which now, we hope so, by a larger majority can be counted as only caused by verbal differences, and which have to be touched to a certain extent in the present context’; LH fol. 224r). 23. “Welches nicht Unserthalben [i.e., Lutherans of an irenic persuasion], sondern in ansehen derjenigen untersuchet werden muß, die aus einigen der Reformirten Lehren solche heterodoxiam gefolgert, und deshalber die Reunion beeder kirchen für unmüglich ausgegeben” (‘Which must be investigated, not for our sake [i.e., Lutherans of an irenic persuasion] but, rather, in consideration of those who have concluded such heterodoxy from a few of the doctrines of the Reformed, and for that reason have declared the reunion of both churches to be impossible’; LH I 9 fol. 177r). 24. I have attempted to demonstrate this elsewhere (Rudolph 2004). 25. Notice that this thought makes the above-mentioned two leading questions of ecumenical dialogue coincide. 26. For a summary of his judgment, see UB: LH fol. 247v–251v. 27. Leibniz translates this concept as “beneplacitum zu teutsch Guth befinden” whereby he emphasizes “bene” and “Guth” (UB: LH fol. 247r). 28. For Leibniz the analogy lies in the circumstance that the soul-saving faith (that of Peter, say, in contrast to Judas’s lack of faith) was either fixed in God’s foreknowledge or that this faith has to be the “causa impulsiva externa”. The double result of the divine absolute will does not lie grounded in this itself but, rather, is a component of the execution of this will: predestination is a decree; justification and eternal salvation are the execution of such a decree (UB: LH fol. 252v/253r). 29. Cf. above, pp. 275–276. 30. The author has also followed the argumentation of Leibniz elsewhere (Rudolph 1999: 120– 125). See also Hübener (1990: 137f.). 31. “Weil nun die letzterwehnte [i.e., Cartesian, H.R.] definitio corporis dadurch seine Essentz in tribus dimensionibus nude gesuchet wird, eigentlich nur das corpus mathematicum und nicht physicum angehet, in physicis selbst auch von vielen vor unzulänglich gehalten wird,



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geschweige daß in hyperphysicis dadurch der allmacht Gottes schrancken zu setzen, so wäre zu sehen, ob vielmehr definitio antiqua et recepta beyzubehalten, und also zu erläutern, ut per eam distingvatur, 1o Corpus a substantia tanquam species a genere. 2o a Spiritu seu anima, tanquam species a specie disparata. 3o a spatio tanquam contentum a continente. Wann nun eine solche erklärung der Natur des Cörpers also bewandt, daß sie nichts in sich hält, so multiplicatae corporis praesentiae zu wieder, so würde auch alle diesfals den Unserigen, und fast gantzen Orient- und Occidentalischen kirchen vermeintlich auffgebürdete [scil. by the Calvinists, H.R.] absurditas dadurch klärlich auffgehoben werden. Solches nun ist aller dings thunlich, und hat man dazu nichts alß doctrinam receptam, und die gesunde vernunfft selbst von nöhten. Und kan dieses in andern fällen zum exempel dienen, daß man den mysteriis a Deo revelatis ex praetensa ratione contraria nicht wiederspreche; Dan wan man alles in der furcht des herren gebührend überleget, pfleget Gott die gnade zu geben, daß sich mittel zeigen alle vermeinte absurditäten aus dem wege zu räumen” (‘Now, since the last-mentioned [i.e., Cartesian, H.R.] definition of the body – in terms of which its essence is sought in only three dimensions – pertains only to the corpus mathematicum and not the physical body, and in physics itself is considered by many as insufficient – to say nothing of the fact that, in the realm of what transcends physics, barriers are set to the omnipotence of God – one should examine whether, on the contrary, the old definition (corresponding to [that in] scholastic philosophy) should be retained, and thus be interpreted as the means to allowing the following three distinctions: first, the distinction of body from substance, just as species is distinguished from genus; secondly, that of spirit (spiritus) from soul (Spiritus or anima), just as one species is distinguished from another; thirdly, that of the body from space, just as the contained (contentum) is distinguished from the container (continens). When, then, such an explanation of the nature of the body is so constituted that it contains nothing in itself which contradicts the multiple presence of the body, the absurdity, thereby clearly perceived, that has allegedly been thrust, in this case, upon our people and nearly all the Eastern and Western churches [scil. by the Calvinists, H.R.] would be eliminated. This is now in any event doable, and for this one needs nothing but the traditional doctrine and sound reason itself. Indeed, this can serve in other cases, too, for example, that one, starting with a supposedly contrary argument (or application) from reason, not contradict the miracles revealed by God. For if one gives appropriate consideration to everything in the fear of the Lord, God customarily gives grace so that means are shown for disposing of each and every alleged absurdity’; UB: LH I 9, fol. 268v/269v). 32. Tentamen Expositionis Irenicae trium potissimarum inter protestantes controversiarum (1698); on this cf. Hübener (1990: 167–169). 33. Jablonski to Leibniz, January 1st 1699; A I 16 445–447. 34. “Let us therefore, as many as be perfect, be thus minded: and if in any thing ye be otherwise minded, God shall reveal even this unto you. Nevertheless, whereto we have already attained, let us walk by the same rule, let us mind the same thing. Brethren, be followers together of me, and mark them which walk so as ye have us for an ensample”. 35. Leibniz to Jablonski, January 8th 1699; A I 16 467–474. 36. Should his course of action “statt des Nutzen Anstoß und Schaden bringen: hoc ipso renuncire ich darauf solennissime, quantum ad praesens negotium. Man schlage beqvemere vergnüglichere Redens-Arten vor [i.e., ones closer to satisfying the demands], ich will der erste seyn zu applaudiren. Nur daß man nicht palliative, sondern realiter verfahre. Denn wir haben mit Leuten zu thun, da es ohndem hart genug halten wird” (‘give offense or bring

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about damage instead of usefulness: I renounce it most solemnly however much it pertains to the current business. Let one propose easier and more pleasant turns-of-phrase [i.e., ones closer to satisfying the demands], and I shall be the first to applaud. Only that one should not proceed in a palliative way but, rather, realistically. For we have to deal with people, since it is difficult enough in any case’; Leibniz to Jablonski, January 8th 1699; A I 16 471).

References Bekenntnissschriften der evangelisch-lutherischen Kirche. 1982. 9th printing. Göttingen: Vandenhoeck und Ruprecht. [= BSLK] Bucer, M. 1988. Martin Bucers Deutsche Schriften, Vol. 6,1 Edited by R. Stupperich, M. de Kroon, and H. Rudolph. Gütersloh: Mohn. Brather, H.-S. 1993. Leibniz und seine Akademie. Ausgewählte Quellen zur Geschichte der Berliner Sozietät der Wissenschaften 1697–1716. Berlin: Akademie Verlag. Dalton, H. 1903. Daniel Ernst Jablonski. Eine preußische Hofpredigergestalt in Berlin vor zweihundert Jahren. Berlin: Martin Warneck. Deichert, A. 1999. “Zum Nutzen von Politik und Philosophie für die Kirchenunion. Die Aufnahme der innerprotestantischen Ausgleichsverhandlungen am Ende des 17. Jahrhunderts”. In M. Fontius et al. (eds), 108–166. [= BSRK] Delius, W. 1970. “Berliner kirchliche Unionsversuche im 17. und 18. Jahrhundert”. Berlin-Brandenburgische Kirchengeschichte 45: 7–121. Ebrard, J. H. A. 1853. Das Bekenntniß des christlichen Glaubens, dem Kaiser anno 1530 zu Augsburg übergeben, etc. Speyer: Kranzbuehler. Fontius, M., Rudolph, H., and Smith, G. (eds). 1999. Labora diligenter. Potsdamer Arbeitstagung zur Leibnizforschung, 1996. (= Studia Leibnitiana Sonderheft 29). Stuttgart: Franz Steiner. Goldenbaum, U. 1998. “Leibniz as a Lutheran”. In A. P. Coudert, R. H. Popkin, and G. M. Weiner (eds), Leibniz, Mysticism and Religion. Dordrecht: Kluwer Academic Press, 169–192. Hübener, W. 1990. “Negotium irenicum. Leibniz’ Bemühungen um die brandenburgische Union”. In H. Poser and A. Heinekamp (eds), 120–169. Jablonski, D. E. 1697. Kurtze Vorstellung der EINIGUNG und des UNTERSCHEIDES, im Glauben beyder Evangelischen so genandten Lutherischen und Reformirten Kirchen: woraus zugleich erhellet, daß sothaner Unterscheid den Grund Christ[lichen] Glaubens keinesweges anfechte. In M. Fontius, H. Rudolph, and G. Smith (eds), 144–166. [= KV] Kapp, J. E. 1745. Sammlung einiger Vertrauten Briefe. Leipzig: Breitkopf. Leibniz, G. W. 1667. Nova methodus discendae docendaeque jurisprudentiae. A VI 1 263–364. Leibniz, G. W. 1934. Lettres et fragments inédits. Edited by P. Schrecker. Revue Philosophique de la France et de l’Etranger 118: 57–83. Molanus, G. and Leibniz, G. W. 1698. Unvorgreiffliches Bedencken über eine Schrifft genandt Kurtze Vorstellung der einigkeit und des unterscheids im Glauben beeder protestirenden Kirchen. LH I 9, fol. 174r–314v (will be published soon in A IV 7). [= UB] Müller, E. F. K. (ed). 1903. Die Bekenntnisschriften der reformierten Kirche. Leipzig: A. Dei­ chert. Poser, H. and Heinekamp, A. (eds). 1990. Leibniz in Berlin (= Studia Leibnitiana Supplementa 16). Stuttgart: Franz Steiner.



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Pufendorf, S. 1695. Samuelis Lib. Bar. De Pufendorf Jus feciale divinum sive de consensu et dissensu Protestantium exercitatio posthuma. Lübeck. Rudolph, H. 1999. “Zum Nutzen von Politik und Philosophie für die Kirchenunion. Die Aufnahme der innerprotestantischen Ausgleichsverhandlungen am Ende des 17. Jahrhunderts”. In M. Fontius et al., 108–166. Rudolph, H. 2004. “Ansätze einer Friedensethik bei Gottfried Wilhelm Leibniz”. In N. Brieskorn and M. Riedenauer (eds), Suche nach Frieden: Politische Ethik in der Frühen Neuzeit III. Stuttgart: Kohlhammer, 267–289. Selge, K.-V. 1990. “Das Konfessionsproblem in Brandenburg im 17. Jahrhundert und Leibniz’ Bedeutung für die Unionsverhandlungen in Berlin”. In H. Poser and A. Heinekamp (eds), 170–185. Sparn, W. 1988. “Jesus Christus V”. In Theologische Realenzyklopädie, XVII. Berlin: Walter de Gruyter, 1–16. Sykes, N. 1950. Daniel Ernst Jablonski and the Church of England. A Study of an Essay towards Protestant Union. London: S.P.C.K.

chapter 12

The golden rule Aspects of Leibniz’s method  for religious controversy* Mogens Lærke

1.

Introduction

“I have spent much time and applied myself much to controversies”, Leibniz writes to Paul Fontanier-Pellisson in 1692 (FC 1 378). There is nothing surprising in this statement. Leibniz was introduced very early, still an adolescent, to controversialist religious literature, especially Martin Luther and Laurentius Valla (GP 3 143 481; Baruzi 1907: 192, 238). His own involvement in controversies dates from his arrival at the Court of Mainz. It was stimulated by, for example, his discussions with the Baron Von Boineburg concerning the Socinian doctrines of Andrej Wissowaty and Daniel Zwicker, and by his conversations with the Catholic brothers Walenburch at the Court (A VI 1 518–535; K 3 272–273; Baruzi 1907: 203–209, 218). Leibniz’s grand project Demonstrationes Catholicae from the late 1660’s and early 1670’s testify to these first steps as a controversialist. Later, in the 1690’s, Leibniz’s correspondences concerning the reunification of the Christian Church constitute a privileged field of investigation regarding religious controversies. Finally, we find samples of his controversialist work scattered around in a number of other correspondences, in short fragments and in annotations written throughout his life. Leibniz’s involvement in religious controversy is constantly paralleled by theoretical reflections on the nature of controversy itself. From the early sketches in the Demonstrationes Catholicae to mature writings like the Nouveaux essais, Leibniz develops a subtle, pragmatic logic for conducting disputes – a general ars controversiarum. Marcelo Dascal has often stressed the importance of this metacontroversial layer in Leibniz’s texts. Part of this “art of controversies” concerns religion and theology.1

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In relation to his ecumenical project, Leibniz’s interest in theory of controversy must be explained from the fact that he considered one of the primary obstacles for a reunion of the Church to be the lack of an adequate method for discussing religious matters: 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)

Indeed, in many of Leibniz’s ecumenical texts, controversy itself is the object of controversy. This is for example the case in the correspondence with Bossuet, where Leibniz compares Rojas y Spinola’s “method of suspension” to the French bishop’s “method of exposition” for solving religious disagreement. In the following I discuss some fundamental features of the normative theory of controversy that governs Leibniz’s reflections on religious debate. First, I will discuss in some detail the historical and theoretical situation that the theory is supposed to help changing, i.e., I will determine the dangers inherent in the very form of religious dispute and the ways in which such disputes should not be conducted. I do this through an analysis of Leibniz’s notion of “sectarianism”, especially in relation to his critique of “innovation” in philosophy and religion. Second, I discuss one of the fundamental principles of Leibniz’s counter­strategy. His theological methodus disputandi is governed by two precepts or, more precisely, two procedural rules. The first is the obligation to love God (Amor Dei). This implies the obligation to do everything in our power to promote the glory of God (Ad majorem Dei gloriam). I have developed some of the background for this rule elsewhere, and will leave aside any further investigation of it here (Lærke 2007). The second precept is the so-called “golden rule” i.e., the rule according to which I should not do unto others, what I do not wish others do unto me. Stressing the importance of the golden rule in relation to religious disputes is far from original in the 17th Century. It places Leibniz among the late heirs to the irenic thinkers of the Renaissance but it also makes him a precursor of the Enlightenment partisans of the doctrine of “tolerance”. But the rule receives a special interpretation in Leibniz, distinct from the one that can be found in other authors. It is this special interpretation that I will analyze in the final sections of this paper. I am not the first to point out that the golden rule plays a very prominent role in Leibniz’s ethics (see, e.g., Gil 1984; Dascal 1993: 394–397; Robinet 1994: 87, 116, 119–120, 150–153; Ausin and Roldán 2004). What I wish to contribute to the discussion is the following. The golden rule is most often considered to be the formalized expression of the fundamental Christian precept of caritas, i.e., the obligation to love our fellow man. But according to Leibniz, I will argue, the full meaning of the rule can only be grasped as a specific relation between charity and

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prudence (caritas/prudentia). Prudence plays the role as a sort of “moderator” of charity. This serves to conceptualize the golden rule as a jurisprudential rather than ethical rule for conducting controversy and resolving disputes. Thus, I will point out that for Leibniz, the golden rule is not exactly an ethical rule, but rather a law of justice.

2.

The satanic stratagem

In a Relation pour la Cour impériale, Leibniz gives the following brief, defeatist outline of the religious disputes of his time: “The parties have been completely opposed [ont esté dans les extrémités contraires]: they have persecuted each other with iron and fire; they have treated each other as heretics, as idolatrous, as excommunicated, as damned” (FC 1 17). It is of some importance to understand exactly what Leibniz means by “extrémités contraires”. Notably, the expression bears upon an action rather than a state of affairs: this “complete opposition” expresses less how the parties are situated in relation to each other as it expresses how they do situate each other by mutually condemning each other. To this effect, Leibniz quotes the sayings of some French bishops on the occasion of a Papal visit: “Si excommunicaturus venit, excommunicatus abidit” (‘If he comes to excommunicate, he will himself depart excommunicated’; A I 6 167). Leibniz’s observations on this point are of course commonplace. We can find many similar statements in philosophical, theological, or political texts from the Reformation to the Enlightenment. I will quote two representative passages that have the advantage of stating clearly and in strikingly similar fashion the formal properties of mutual religious condemnation. The first is a passage from Salvianus’s De gubernatione Dei that Hugo Grotius quotes in the last paragraph of Meletius (1611); the second is a remark from John Locke’s Letter Concerning Toleration (1689): Thus, they are heretics, but without knowing it. Furthermore, they are heretics for us, but not for themselves. They think that they are catholic to such a degree that they confer the infamous name of “heretic” upon all of us. And so what they are for us, we are for them […]. So the truth is on our side, but they think it is on theirs. (Grotius 1991: §92, 325) For every Church is orthodox to itself; to others, erroneous or heretical. Whatsoever any church believes, it believes to be true; and the contrary thereunto it pronounces to be error. So that the controversy between these churches about the truth of their doctrines, and the purity of their worship, is on both sides equal […]. (Locke 2003: 225)

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According to these texts, it is the dichotomy orthodoxy/heresy which governs the “logic of exclusion” (Lagrée 1991a: 65). The use of such logic among Christians had become a particularly acute problem since the beginning of the Reformation, but the problem was of course not new. Christianity was always threatened by internal schism, the proliferation of sects and opinions. In Civitas Dei, Saint Augustine quotes Varro, who deduced no less than 288 possible sects from their diverging conceptions of the highest good (Augustine: III, Chap. 19, 93–99). Isaac d’Huisseau reminds us in the preface to La réunion du Christianisme (1670) of Saint Epiphanius who enumerated no less than eighty different heresies among Christians in the third century (d’Huisseau 1670: 5). Erasmus complains to Jean Schlecta that one cannot “imagine anything extraordinary that does not have its partisans”, and “nowadays one makes six hundred articles out of a single one” (Letter 1039, Erasmus 1970: 125, 130; Lagrée 1991a: 47). Leibniz himself has recourse to a proverb to express something similar: “There are as many opinions as there are heads” (autant de sentiments que de têtes; GP 7 180). As we have seen, the logic of exclusion consists in construing the orthodoxy of oneself through denouncing the heresy of the other, and vice versa. However, as many writers since the beginning of the Reformation have pointed out, schismatic behavior is in itself a sign of heresy, because condemning your fellow man is a violation of the only divine law that all Christian sects can agree upon, namely the law of charity. To take a significant example, we can quote Erasmus’s De amabili concordia ecclesiae (1533). According to this text, the greatest heretic of all was Core who opposed Moses and divided the tabernacle (Numbers 16; Erasmus 1992: 783–785, 792). Religious division is by definition wrong, because, as Erasmus says it, “the summit of our religion is peace and full agreement” (summa nostrae religionis pax est et unanimitas; Letter 1334, Erasmus 1970: V, 220; Lagrée 1991a: 48–50). Insofar as the search for true religion has degenerated into disputes, this search has itself become the reason why we have lost true religion. “One puts forward the defense of Catholic faith, and sometimes personal passions get mixed up in it, and under the banner of Christ one undertakes the works of Satan”, Erasmus writes to Jean Carondelet in 1523 (Letter 1334, Erasmus 1970: V 228). Jacob Acontius dramatically designated this problem a “satanic stratagem” (Satanae stratagemata) in his book from 1565 (Acontius 1927; Jacquot 1954: 193–195). Leibniz argues in a similar fashion: “Because of religion one destroys the most fundamental religion, which is to honor and fear God” (GR 206–207). In a certain sense, Leibniz’s entire project of reuniting the Christian churches is one great effort to break the vicious circle of the satanic stratagem. His critique of sectarianism and religious division prolongs the humanist critique of “mad disputing” (rabiosa contentio) that Erasmus formulated (Letter 1039, Erasmus 1970: IV, 123–131). It

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is an effort to put out “this fire of disputes that heats up more than it lights up”, as Leibniz puts it (A VI 6 2159). For, as he writes in a letter to Madame de Brinon, It is in these rash 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 it is not to love to precipitate oneself to judge that he will soon be on his way to Hell with the Devil to stay there eternally as an enemy and blasphemer of God.  (FC 2 92)

3.

Schism and innovation

Most often, Leibniz writes, sects are right in what they defend and wrong in what they reject (GP 3 607). Therefore, as he remarks to Pierre Coste, “I follow this general maxim to hold only a few things in contempt and to profit from that which is good everywhere” (GP 3 384, 562). “Les choses ont tant de faces” (‘Things have so many faces’), Leibniz exclaims in the Conversation du Marquis de Pianese et du Père Emery Eremite (A VI 4 2281; DA 194). Even the most confused mystics hold Leibniz’s esteem if only their zealous religiosity is correctly understood, the grain separated from the straw and the gold from the dirt (GP 3 384, 624). Doctrines like Cabbalism still hold their part of the truth (A I 5 109; GP 6 625). What such ways of praising God lack in cognitive clarity, they may possess in suggestive power: “Their thoughts are most often confused, but as they use beautiful allegories, or touching images, this may serve to render the truths more acceptable, if only one confers a reasonable meaning [bon sens] on these confused thoughts” (GP 3 552; see also GP 7 497). The only doctrines that he rejects completely seem to be juridical astrology and – at least in texts written after he read the Ethics in 1678 – Spinozism (GP 3 562; GP 4 523–524). Leibniz refuses almost nothing, neglects almost nothing: “[…] I admit that the most sure is not to neglect anything, and even that true love commands it” (A I 6 119). Indeed, one should not condemn too hastily, but one must attack vices without showing spite against the persons. It seems that one could work for the propagation of truth and piety with a meekness worthy of true piety, instead of adopting the sectarian and schismatic spirit of those who burst out against deceit …  (GR 143–144)

There is ideally something like a “good” inclusive sectarianism, where different sects work towards a common goal, but each of them from a particular point of view (Baruzi 1907: 396). “Very often I think that all parties are right, when there is mutual understanding”, Leibniz writes (FC 1 373). The problem is, of course,

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that in practice a plurality of perspectives on religion almost always leads to “bad” exclusive sectarianism. But it is important to point out that Leibniz does not, contrary to many of his contemporaries, consider the proliferation of sects to be a bad thing in itself. What he criticizes is a sort of dogmatic backlash in the sectarian spirit which stems from the will to human glory. This will first of all manifest itself as a pretension of innovation. It is telling that in his description of those who “break the union” Leibniz does not simply speak of those who oppose “prejudices to prejudices”, but of those who set “innovations against innovations” – nouveautés contre nouveautés (FC 1 176). Leibniz writes the following about innovators: What they search for is much more glory than truth, and to dazzle the others rather than to enlighten themselves. In order to get us out of this mess we must renounce on the spirit of sects and the fondness of innovation. One must imitate the geometers, where there are no Euclideans or Archimedeans. They are all in favor of Euclid, and all in favor of Archimedes, because they are all in favor of the common master who is the divine truth. (GP 3 158)2

Linking schism to innovation is not an unusual move. Accusations of “innovating” religion is an important element in the logic of exclusion, for the Protestants and the Roman Catholics were mutually accusing each other of “inventing” a new Christianity grounded in human interests. As Leibniz remarks, “tragic exclamations” against innovation were heard on both sides of the religious divide (GR 57). He comments further on these mutual accusations in the Nouveaux essais: […] it was possible to publish ‘legitimate presumptions’ on both the Roman Catholic and the Protestant sides. Ways have been found, for example, to bring forth accusations of innovation against certain aspects of each of them: when the Protestants mostly abandoned the old form of ordination of clergy, for instance, and when the Roman Catholics altered the old canon of the Books of the Old Testament […]. Thus, since these accusations flow in both directions, innovation is not a clear proof of error in these matters, even though it arouses suspicion of it. (NE 4.15.6; A VI 6 459)

The Roman Catholics accused the Protestants of breaking with the ecclesiastical tradition that goes back to the time when Saint Peter handed the power of the keys to Heaven over to the Church (potestas clavium). According to them, by establishing a new church, the Protestants violate a prescription, i.e., a legitimate presumption of truth grounded in tradition and in favor of the Roman Catholic Church.3 The Protestants, for their part, accused the Roman Catholic Church of abusing the ecclesiastical powers invested in them by inventing new dogma disfig-

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uring the original Christian faith (clave errante). We can find arguments of this type – only to mention two good examples among innumerable texts dealing with this issue – in La réunion du christianisme from 1670 by the Saumur theologian Isaac d’Huisseau and in the leading Huguenot theologian Pierre Jurieu’s Examen de l’eucharistie from 1682 (d’Huisseau 1670: 62; Jurieu 1682: 18).4 Leibniz himself argues in a similar way to refute bishop Bossuet’s defense of the decisions of the Council of Trent concerning the Biblical canon: It is at least clear that our opinion [i.e., the Protestant opinion] concerning the canon of the divinely inspired book has all the characteristics of a catholic doctrine, whereas the innovation introduced by the assembly of Trent has all the characteristics of a schismatic uprising. For when innovators proclaim the invariable doctrine of the Catholic Church to be anathema, this is the clearest charac(FC 2 343) teristic of rebellion and schism that one can imagine.

It would be too hasty, however, to place Leibniz unequivocally on the side of the Protestants in this debate about “innovation” of doctrine, for “prejudices are opposed to prejudices, innovations to innovations, Fathers to Fathers; but the balance fit for weighing them against each other is not in the hands of everybody, and it is not easy to handle” (FC 1 176). In fact, he sees no point in ascribing guilt for the schism to one party or the other: One can say with some justification that there is guilt on both sides when it comes to schism. The Reformers ought to make an effort to maintain the ecclesiastical union and the Pope and the Bishops should not pass so promptly to excommuni(GR 188) cation and other ways of rigor.

Leibniz has no doubts as to the presence of abuse within the Roman Catholic Church (FC 1 175–176). He does, however, agree with the Roman Catholics that following the prescription for the ecclesiastical tradition is a weighty argument: “[…] that which has always been taught in the universal Christian Church in a continuous line of tradition ought to be believed and followed […]” (GR 215). But it remains a condition for the validity of this prescription that one must first establish the legitimacy of the ecclesiastical body claiming to hold the key power, i.e., one must have some certainty that the condition clave non errante is fulfilled (FC 1 205; GR 191–192). For, if the key power has been usurped and placed in the wrong hands, and if the Church “makes new articles of faith”, God does not ratify the decisions made by the ecclesiastical body (GR 215–216). Nevertheless, Leibniz believes that the Protestants go too far when proclaiming the Pope to be the Anti-Christ. Only extreme abuse justifies schism, and one should employ all means to bring unity back to the Church.5

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If we take a step back and consider as a whole this sequence of arguments concerning the problem of “innovation”, it becomes clear that Leibniz oscillates dialectically between the opposed positions. This is, I believe, a general feature of his approach to religious controversy: in his practice of controversy, it is not always clear whether he should be placed on the Catholic or the Protestant side of the divide. Even though he always (and sincerely so, in my opinion) remains a Protestant, Leibniz often poses as a Catholic. The most famous example is the Systema theologicum (or Examen religionis christianae) from 1686 (A VI 4 2356– 2455). Some commentators have even mistaken the text for a proof of conversion. In reality, as also Marcelo Dascal points out, such Roman Catholic essays are part of a dialectics of reconciliation (Dascal 2003: Sect. 5.3).

4.

Innovators in philosophy and theology

As I have argued in the preceding section, Leibniz refuses to identify either the Roman Catholic Church or the Protestant Church as the veritable “innovators” who cause schism and “bad” sectarianism. But who should we then identify as the innovators of religion? It is here helpful to take a look at whom Leibniz considers to be innovators in philosophy. In spite of the title of his famous text from 1695, Système nouveau, Leibniz’s ambition was never to “innovate” (a term which, as we have seen, has strong pejorative connotations for Leibniz) but rather to “reform” philosophy (see Mercer 2004: 31–33). Thus he praises those who try to develop a “demonstrative philosophy capable of eradicating the innovators” (A VI 4 1484). In 1686, he writes to Arnauld: […] I do not aspire to the glory of being an innovator, as it seems he [i.e., Arnauld] has understood my opinions. On the contrary, I usually find that the oldest and most broadly received opinions are the best. And I do not think one can be accused of being so (of being an innovator) when one has produced only some new truths, without overthrowing the established opinions.  (GP 2 20–21; A VI 4 454–455, 731, 977)

In philosophy, to discover new truths, one must paradoxically renounce the pretension of innovation and search for support in tradition. For truth does not reveal itself to a single man, but gradually through the history of philosophy. Each philosopher has “produced some new truths”, but none of them detains true philosophy alone. Leibniz is far from believing in the renewal of philosophy announced by Descartes. He does not endorse the “radical doubt” that characterizes the Cartesian method. It is too easily abused (GP 5 181; GP 7 164). The Cartesians’ conviction of being above the entire tradition is an expression of pride

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and self-glorification. Descartes is “too sure of his glory” (Leibniz 2001: 104–105). He has only “haughty contempt” for the arguments of his adversaries and he has “tarnished [his] good qualities by an enormous ambition of being the leader of a sect” (Leibniz 2001: 104–1055; A VI 4 1483–1484; GP 3 656). It is this unfortunate attitude that the Cartesians praise, doubting everything except the words of Descartes himself, who has become master of their sect: “I find that nothing is more harmful to the sciences than the spirit of sectarianism and servitude, and in fact the Cartesians discover almost nothing new and they hardly advance” (FC I 334); “I know that it is rather difficult for the Cartesians to rid themselves of the prejudice of their master’s infallibility” (A VI 4 2197). Spinoza, an “extremely corrupt” Cartesian, represents the extreme case: he is not only an innovator but, even worse, the most recent one (le dernier novateur), as Leibniz calls him in the Discours de métaphysique (GP 3 545; A VI 4 1532; GP 4 201). ‘Innovator’, however, is more than just a generic term for a group of philosophers with Descartes at the origin and Spinoza at the summit. In all these texts, the innovator finally stands out as something like a conceptual function or structural feature. The innovator is a sort of conceptual person,6 in whom an exclusive conception of truth is intrinsically linked to a will to human glory, thus giving rise to sectarianism. The pretension of innovation is methodological rather than psychological. It is not exactly the new philosophers themselves who are the bearers of the innovative character, but rather their methods. The innovator does not manifest himself in Descartes’ or in Spinoza’s individual minds, but inside the structures of Descartes’ “radical doubt” or in Spinoza’s method more geometrico. Descartes becomes an innovator by systematically refusing to take into account the philosophical tradition; Spinoza takes the pretension of innovation as far as to reinventing language – that the Dutch Jew writes in an obscure, private language is indeed one of Leibniz’s major objections to the Ethics (GP 1 142–143, 147; A VI 4 1372). In the same way as the innovator is a conceptual person, innovation as such is not so much a temporal and historical category as a logical or archeological category. It is opposed to the law of nature rather than to antiquity, because the law of nature is the “deepest” layer of thought. This point becomes clear in a passage from the Parallèle entre la raison originale ou la loy de la nature, le paganisme ou la corruption de la loy de la nature, la loy de Moyse ou le paganisme réformé, et le christianisme ou la loy de la nature rétablie, where Leibniz criticizes the principle according to which antiquity may serve as proof for religious truth: This language is also that of the Papists against the Protestants, and the latter are just as keen as the others to make tragic exclamations against change and innovation without dreaming of how many absurd doctrines, inconvenient and

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barbarian, we would be obliged to follow if the practices of our ancestors should be the rule of our actions. If antiquity is the mark of the truth, it is clear that the law of nature has won its cause, because it has begun with the human race […].  (GR 57)

Because it is a structural feature rather than a psychological one, the “pretension of innovation” is not only present in the new theories of modern philosophers who do indeed perceive themselves as innovators. The “deceit and make-believe of the innovators” can be found where one least expects to find it (A VI 4 1850). An innovator can be a rationalist as well as a mystic, a theologian or a scientist, a recent thinker or a Greek philosopher. Innovative pretensions can contaminate a philosophical system that claims to invent a new truth; they may come to expression in the possessed mind of a mystic who believes to have received new revelation directly from God; they may manifest themselves in the arguments of an orthodox Roman Catholic having too much faith in the decisions of the latest Church Council. To mention an important example of how Leibniz’s critique of innovation is put to use in his religious controversies, he manages to turn bishop Bossuet, a committed guardian of the ecclesiastical tradition, into a novateur. In a letter to Leibniz, Bossuet objects to the very notion of Reformation by maintaining that “yesterday, one thought like this, consequently, today, one must believe the same thing” (FC 1 385). Leibniz returns the argument as follows: “It happens that one believed differently the day before yesterday! Must one always canonize the opinions that are to be found as the last ones?” (FC 1 389; Baruzi 1907: 385–386). Thus, Leibniz dissolves the identification of Reformation and innovation established by Bossuet by showing ad hominem that Bossuet himself defends a methodological principle with inherent tendencies to innovation by always holding on to the (new) decisions of the Council of Trent. This example, incidentally, also allows us to realize that the relation between innovation and schismatic sectarianism can be established in both directions. Whereas in the case of the Cartesians it is the pretension of innovation that leads to sectarianism, in Bossuet it is his Roman Catholic orthodoxy that leads him to defend an argument with an implicit pretension of innovation. But, moving in one direction or the other, from innovation to sectarianism or vice versa, the result is similar: “bad” sectarianism, or the establishment of a logic of exclusion. This explains the subtitle of a sketch from 1679–1786 (GR 30), bearing the speaking title Apologia fidei catholicae ex recta ratione (‘Apology of universal faith from right reason’), to which he adds: contra novatores (‘against the innovators’).

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5.

The method of the ignorant

What form does a sectarian dispute take? Certain texts by Leibniz could lead one to think that the schismatic logic of exclusion entails religious controversy without rules. For example, in a Promemoria zur Frage der Reunion der Kirchen sent to Ernst Von Hessen-Rheinfals in November 1687, Leibniz expresses in the following terms his regret that religious controversies often quickly degenerate: […] the disputing parties rant to the winds, busy themselves in punctilious discussions, swerve from the issue in digressions, change the order, answer only to that which they find convenient, mask the adversary’s objections or solutions, try to escape them through derision or invectives, employ repetitions, do not distinguish the job of the respondent from that of the opponent nor that of the one who must prove from the one who must not. (A I 5 11)

The participants argue according to their own private principles; they all repeat incessantly their own arguments and ignore those of the others; they digress in al directions, “for which reason colloquia and conferences are usually fruitless, and are often only good to turn spirits sour and to give rise to new controversies” (A I 5 11). As Leibniz says: “One gets lost in a labyrinth of disputes” (A VI 4 2249). An early text denounces it as the “vice of confused disputes” (A VI 2 387–389; DA 1–6).7 But the sectarian form of controversy is not simply chaotic. It has its own argumentative strategies. It follows an identifiable, albeit perverse, logic that leads inevitably and necessarily to the deepening of religious schism. Indeed, there is a whole argumentative complex grounded in the combination of sectarianism and the pretension of innovation; a complex that can be considered as a self-amplifying construct with its own internal logic, i.e., a “satanic stratagem” in the sense of Acontius. Leibniz speaks of a “method of the ignorant”, sometimes of “a certain spirit of contradiction” (FC 1 86; A VI 4 2250). A fundamental feature of the method of the ignorant is the refusal to examine the premises of an argument, mocking not only the adversary, but refusing all possible argumentative exchange. This explains why Leibniz, in his annotations to Spinoza’s reply to the critique of a converted Catholic named Albert Burgh, exceptionally defends the Dutch Jew against Burgh’s somewhat fanatical attacks: I admit that those who always ask us: How do you know that you are not mistaken because so many others have a different opinion? are mocking us, or themselves. Because it is the same thing as replying to my argument: How do you know that your conclusion is true? without wanting to examine the premises. (A II 1 302)

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The method of the ignorant is a method where adversaries dispute while refusing to settle from the outset on a common criterion of truth, all insisting on the truth they deduce from their own particular principle.9 Such fundamental disagreement on the very criteria of truth is without doubt a more acute problem in the domain of religious controversy than in any other type of controversy (political or scientific). There is an inherent tendency in religious thought towards multiplication of the principles of interpretation of its statements, that is to say, of the criteria of religious truth: we have already cited Saint Augustine, Epiphanius, Erasmus. This problem of the criterion of religious truth and the “rule of faith” was amply discussed in the 17th Century as the problem of the “judge of controversies” (A VI 1 548). Albert Burgh has recourse to the method of the ignorant because, as Spinoza writes to him, he has already learned to argue by insulting his opponents, but mainly because he refuses to acknowledge that there can be other criteria of religious truth than the one he defends himself. If Burgh is a sectarian, it is because he believes that the problem of the judge of controversies can be resolved simply by stating your own principle, without taking into account the argument of the opponent. It would be wrong, however, to believe that the method of the ignorant is reserved for religious fanatics or headless sectarians. In a certain sense Spinoza himself is a corrupt Cartesian who in his feigned and unintelligible geometrical demonstrations in the Ethics has become a victim of the very method of the ignorant that he himself rejects in Albert Burgh’s argumentation (GP 1 139–152; GP 3 259, 592; GP 6 531; A II 1 413, 535; A VI 4 705, 967, 2197–2198, etc.). For, according to Leibniz, it is common to both Burgh and Spinoza that they refuse to examine the premises of the truth they defend by the principles of any authority other than their own.

6.

The method of moderation

The primary condition for overcoming disputes, including those concerning religion, is “a method that will surely always terminate them, following the principles of an incontestable prudence” (A VI 4 2260; DA 180). Leibniz’s goal is to construct a methodus disputandi that excludes the argumentative strategies of the sectarian, i.e., argumentative short-cuts, redundancies, omissions, the negligence of the other’s argument, etc. (A VI 4 576–578; DA 155–157; Olaso 1975). Therefore strict rules for the practice of controversy must be established. First of all, one must begin with the question of the judge of controversies, that is to say, by stating the primary rules that must govern the exchange: “The way of disputation or

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discussion is ineffective, as there is no judge or regulated form that the disputing parties are obliged to follow exactly” (A I 5 11; DA 248). An ordered controversy is first of all characterized by being moderate: “There must be limits and moderation in everything” (D 5 355); “nothing renders a dispute more recommendable than the moderation of those who dispute” (K 4 430). Obviously, moderation concerns each of the individual participants and their individual attitudes towards their opponent, insofar as people sometimes are ready to dispute even the evident, because they are blinded by their passions and their interests. Some people even quarrel about geometry, a science in itself certain and precise (A VI 4 2258; DA 178). But moderation must also work in spite of the participants, i.e., it must be inscribed in the form of controversy itself, as part of “a certain new logic” (FC 2 32, 529). Leibniz states this quite clearly when he explains that ideally “the nature of the dispute obliges people to speak moderately in spite of themselves” (FC 1 83). The participants must be forced by the form of the method itself: Those who fight would have their arms tied up so much, that they would not be able to move themselves except in an ordered and measured way, and they would be drawn forward by machines that would carry everything out, like in a naval combat where the movement of the vessel and the force of the canon gives the law to those who fight. Moreover, that anger should be out of season, when one would no longer be able to distinguish the friend from the enemy. (FC 1 83)

It is important to stress the almost mechanical character of the method of moderation. In this respect Leibniz’s method for religious controversy is similar to the method for scientific controversy he elaborated under the name of a characteristica universalis, which would eventually allow solving all disputes concerning natural things through simple calculation: Calculemus! (GP 7 188–200; GP 3 605). Surely, because of the difference in nature between the objects of controversy, scientific and religious controversies do not follow the same rules. The object of religious controversy, i.e., revelation and Scripture,9 requires other less formal means of proceeding than simple calculation. But this does not mean that these “other means” are any less constraining or that they rely any more on the opinions or attitudes of the individual participants. In religious controversy, the opponents have their arms tied up as much as in scientific “calculation,” but the ropes are different. The rules of religious controversy are essentially conceptualized by Leibniz according to a juridical model. He compares them 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; A VI 4 2162; DA 62). It involves the use of juridical or semi-juridical principles that govern a “softer” form of reasoning, partly grounded in a calculus

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of probabilities, but which also contains important elements of casuistic reasoning (Dascal 2001).10 In this context, I will limit myself to discuss the rule of rules, so to speak, namely the so-called golden rule. In controversy, the golden rule is a principle of moderation and following it is an indispensable condition for avoiding that argumentative exchange degenerates into violent dispute, schism and sectarianism.

7.

The golden rule I: The first test of generalization

The “golden rule” is stated in Matthew 7: 12 (positively) and in Tobias 4: 15 and Luke 6: 31 (negatively): Quod tibi non vis fieri, alteri ne feceris – ‘do not do unto others, what you do not wish others do unto you’. For Leibniz, the rule implies that “[…] one must maintain […] a spirit of charity towards those from which one is separated” (FC I 199). This moral requirement is formulated mutatis mutandi as an obligation to place oneself in the situation of one’s opponent: “The true meaning of the rule is that the right way to judge equitably [juger équitablement] is to adopt the point of view of other people [la place d’autrui]” (NE 1.2.4; A VI 6 92; A VI 3 903–904; GR 699–701; DA 164). It is necessary to perform an “exchange of places in thought”, as he writes in a small annotation from around 1695 (GR 648). From a strict Leibnizian point of view such an enterprise is of course metaphysically doomed: monads such as human souls have no windows and therefore nobody can, strictly speaking, look into the soul of somebody else, even less put himself in the place of the other. Our very individuality depends on our perspective on the world: from the metaphysical point of view, literally placing oneself in the place of the other would be equivalent to become the other. But we may imagine ourselves in the other’s place and thereby try to bridge the difference of perspective, for this difference is not only the ground of individuality, but also the root of dissent. Leibniz writes in the Conversation du Marquis de Pianese et du Père Emery Eremite: […] this is what gives rise to this diversity of opinion, everybody considering the objects from a certain side: only very few people have the patience to go all the way round the thing [fr. faire le tour de la chose] until they are on the side of their opponent, that is to say, people who will examine the pros and cons with equal zeal and with the spirit of a disinterested judge in order to see to which side the balance must lean, because time is needed for this, and our passions or distractions hardly give us any.  (A VI 4 2250; DA 173)

One must “faire le tour de la chose”. As Marcelo Dascal has pointed out, it is important to stress the generalization of the other that this involves: “Leibniz in fact

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immediately adds to his formulation of the principle that it is not the place of a single other that we should try to occupy, but that of all others” (Dascal 1993: 403). A long passage from the Méditation sur la notion commune de la justice from 1702 leads us towards a similar conclusion: It could maybe be said that not harming anybody, neminem laedere, is the precept of the law called jus strictum, but that equity also demands that we do something good, when this is suitable [lorsque cela convient], and that it is in this that consists the precept, which demands that we grant everybody what belongs to him, suum cuique tribuere. But this suitability [convenance] or “that which belongs” is known as the rule of equity or equality: Quod tibi non vis fieri aut quod tibi vis fieri, neque aliis facito aut negato. It is the rule of reason and of our Lord. Put yourself in the place of the other and you will be at the true point of view to judge what is just and what is not. Some objections have been made against this great rule, but only because it is not applied everywhere. It is for example objected that a criminal can claim to be pardoned by the sovereign judge in virtue of this maxim, because the judge would wish the same thing if he found himself in a similar position. The reply is easy. It is necessary that the judge places himself not only in the place of the criminal, but also in the place of those others who have an interest in the crime being punished.  (DR 123–124, italics mine)

Whereas the first part of the quotation states the primitive rule of charity (putting oneself in the place of the other), the second part clearly states that the golden rule should be considered as a principle for procuring general felicity (putting oneself in the place of all others).11 Thus, there is a test of generalization for any act of charity. One must ask: if this is a charitable act towards this other (to spare this criminal, for example), is this also charitable towards everybody else (the victims of the criminal, for example)? When considering the case of a criminal being judged at a tribunal, the pertinence of this principle of generalized charity appears fairly obvious. But Leibniz also applies it in his critique of philosophical and theological sectarianism, for “charity must distance us from that which smells of sects and increase dissension” (GR 93 105). Also in the “tribunals” of philosophical and theological controversy all possible positions must undergo the test of generalization, meaning that one should not put oneself in the place of one particular other. Simply putting oneself in the place of Descartes, for example, is to become a member of the sect of Cartesians, or to adopt Martin Luther’s perspective as one’s own is to become a member of the sect of Lutherans. For this reason, “one is wrong to call oneself a Lutheran” (FC 1 196 note; Baruzi 1907: 354, note). Leibniz’s rejection of sectarian particularism is accompanied by an affirmation of the universality of religion without ambiguity (Grua 1956: 228). Universal religion (religio catholica)

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is for the glory of God, sectarianism for the glory of men: “[…] it is exactly to be in a sect, when one relies too much on the authority of men and on the cabbala of a certain party” (FC 2 87, 546; FC 1 273). In this sense, Leibniz considers himself a “Catholic” even though he adheres to the Augsburg Confession, because by the Catholic (i.e., universal) faith he “does not mean the Roman one, but the opinion which has been transmitted all the way to us from antiquity” (Leibniz cit. in Robinet 1994: 151; FC 1 235–236).

8.

True love and prudence

Before taking the analysis of Leibniz’s conception of the golden rule any further, we must briefly consider his definition of love. He strongly objects to the quietist notion that true love implies completely disregarding our personal motives and wishes. No love is completely disinterested in this absolute sense: “[…] it is impossible to renounce on the consideration of our own good […]” (DR 50). Leibniz rejects, however, that love of ourselves is something bad in itself, but he makes a difference between a “good” and “natural” amour de soi-même and a “bad” or “egoistic” amour-propre, here borrowing a distinction from the Traité de l’amour de Dieu de Saint François de Sales: “Self-love is a very good and very pure passion that the author of nature has given to us […]. One can only want something because it appears to contribute to one’s good, either by facilitating some pleasure or by preventing some pain” (DR 41; Lafond 1983: 76–89). True, disinterested love exists where the felicity of the other is not the objective that replaces our own felicity, but where the felicity of the other becomes a condition of ours. This is the background for Leibniz’s famous definition of love as the pleasure taken in the felicity of the other: “Amare est felicitate alterius delectari” (GP 3 207; GP 7 73; A VI 4 1357, 2793, etc.). This definition is constant in Leibniz’s writings. We find it as early as in the Specimen demonstrationum politicarum pro eligendo rege Polonorum from 1669 and in the Elementa juris naturalis from 1670–1671 (A VI 1 34, 464. See also A II 1 173–174, A VI 2 485). Almost forty years later, in 1708, Leibniz still writes in the Réflexions sur l’Art de connaître les Hommes: “The love of our fellow man […] is a propensity to find pleasure in the felicity of that which one loves. It is in this way that the felicity of the other enters into ours […]” (DR 42). This aspect of Leibniz’s theory of pure love is most often considered in relation to his conception of the love of God (amor Dei). In that context, Leibniz’s conception of love gives rise to the moderate theological utilitarianism of the fatum christianum that he opposes to the passive religiosity of quietism in his contributions to the querelle du pur amour. This aspect of Leibniz’s theology has been studied by Emilienne Naert (1959) in a wonderful study. What has been less

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noticed is that this special conception of true love also has important implications for his conception of charity and the golden rule. When we love somebody, be it another person or God, the love of ourselves is always involved in one way or another. The question is whether we are conscious of it or not, i.e., whether we take this fact into account in our relations and exchanges with the loved one. Consciousness of our own interests in love relations is what Leibniz designates by the concept of “prudence” (prudentia). Prudence is the concern for one’s own felicity: “Prudentia est ars vivendi, seu ars procurandae sibi felicitatis” (A VI 4 456; GR 755). Leibniz also explains this very clearly in the Elementa juris naturalis: Prudence, furthermore, cannot be separated from our own good, and any statement which contradicts this is empty and foreign to the actual practice of those who utter it, whatever they may say against it. There is no one who deliberately does anything except for the sake of his own good, for we seek the good also of those whom we love for the sake of the pleasure which we ourselves get from their happiness. To love is to take pleasure in the happiness of another.  (A VI 1 461; L 134)

To take into account one’s own good does not, however, express the full meaning of being “prudent.” In the Elementa juris naturalis Leibniz also considers prudence to be closely connected to the use of “right reason” (recta ratio) and to justice: But the right reason for our actions is the same as prudence. It follows, therefore, that there can be no justice without prudence. […] Justice will therefore be the habit of loving others (or of seeking the good of others in itself and of taking delight in what is good for others), as long as this can be done prudently (or as long as this is not cause of greater pain). For even the joy that we take in our own good must be curbed by prudence, lest it sometime become the cause of greater pain; how much more then the joy we take in that of others.  (A VI 1 461–465; L 134–137)

According to this argument, prudence counterbalances the love of the other by making this love a just love or a measured love, for “justice is prudence in producing the good of the other or in not producing the bad” (A VI 1 435; A VI 1 454). Insofar as it is linked to the concept of justice, prudence concerns not only our self-love (amour de nous-mêmes) and our own pleasure and pain, but it implies a reflection on the overall outcome of pleasure and pain from a more global perspective. It is in this sense that Leibniz also links prudence to the consideration of universal harmony, to universal justice and to equity (Robinet 1994: 84). Justice is not simply caritas, but caritas sapientis (‘the charity of the wise’) or caritas recte ordinate (‘correctly ordered charity’), and the way in which charity becomes “wise”

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or “well ordered” is exactly by being moderated by prudence, as caritas prudentis (‘the charity of the prudent’; A I 6 108; A VI 4 2758; GR 604–605). Following this analysis, prudence figures as a sort of “moderating reason” which ensures a balanced exercise of charity, and which allows us to judge with justice and equity. This should not lead us, however, to believe that immoderate charity lacking prudence should be considered outright unjust: “[…] if somebody is said to have violated prudence from exaggerated love, he is not said to be unjust” (A VI 1 434). The reason for this asymmetry in the relation caritas/prudentia can be found in Leibniz’s complex notion of justice. Exaggerated love harms nobody (neminem laedere) and is therefore not unjust from the point of view of strict law (jus strictum). But it is not equitable, because it does not grant to everybody what belongs to them (suum cuique tribuere).12 In this sense, procuring equity in the exercise of charity is the role of prudence.

9.

The golden rule II: The second test of generalization

We note at this point that the concept of prudence appears strangely ambiguous. It is linked to the consideration of our own good and to our self-love. But it is also linked to a consideration the totality of the context, or the general outcome of pleasure and pain, i.e., to the notion of equity. So to be prudent in relation to the other involves, at the same time, a reflection on a particular interest (that of ourselves in relation to the other) and on a general interest (that of everybody else than the other). What this double meaning of prudence reveals, is that we are dealing with a sort of twin principle of charity and a second test of generalization. Charity is, it will be recalled, the obligation to “go all the way around the thing” (faire le tour de la chose) in order to assume the perspective of the opponent conceived as a generalized other. Prudence reverses this movement: it is an obligation, whilst being charitable towards the other and trying to put oneself in his place, to take into account all other perspectives besides the other’s, including our own. This is why prudence presents itself as both representing our own interest and a general interest. Prudentia is a principle for moderating charity in such a way that our love of ourselves is taken into account, but only insofar as we take part in a generalized other of the other, which includes our own perspective as well as that of any particular other. Thus, there is a second test of generalization: Not only should we put ourselves in the place of the generalized other (the test of caritas); but we should also put ourselves in the place of the other of the other, i.e., a generalized “self ” (the test of prudence). Only in this fashion is charity (caritas) and self-love (amour de soi) balanced in an equitable manner, in accordance with the requirements of a

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more general, if not universal, principle of justice. It is only when we acknowledge that reciprocal love also involves this second test of generalization, both caritas and prudentia, that the golden rule acquires its full meaning, namely as a rule of justice: “Omnis caritas est virtus, sed non est justitia nisi cum prudentia accessit” (‘every charity is virtue, but there is no justice unless it is joined to prudence’; A VI 4 2793; GR 614).

10.

Conclusion

The golden rule constitutes the first principle of the method of moderation that Leibniz proposes to avoid the exclusivist logic of “innovators” and the sectarian method of the ignorant. As already mentioned, stressing the importance of the golden rule in the context of religious controversy is by no means uncommon in the philosophical and theological discourse of the 17th Century. As Jacqueline Lagrée shows, the minimalists among the theologians of the 17th Century, such as Sebastien Castellio or Hugo Grotius often appeal to this “law written in the hearts of men” (2 Romans 2:15). The neo-Stoical theologians of the early modern period sometimes compared the rule to Cicero’s notion of natural law (Castellio 1981: 54; Castellio 1996: 83–84; Grotius 1991: §68, 318; Lagrée 1991a: 212–218; Lagrée 1991b: 46). We find references to the rule in texts by many philosophers, for example in Thomas Hobbes’s De Homine (XIV, §5) and De Cive (III, §26) or in Samuel Pufendorf’s De jure naturae et gentium (1672) (Pufendorf 1998: IV-2, Chap. V, §13, 546). Charity, or reciprocal love, is also the most important precept in Spinoza’s notion of true religion in the Tractatus theologico-politicus (Spinoza 1999: XIV, 464–481). But this should not overshadow the fact that Leibniz conceptualizes the rule in an original manner. We may summarize this originality in three points. First, Leibniz considers the golden rule as a procedural rule. In controversy, the golden rule must be used to “tie up the arms of the participants” in such a manner that they do not succumb to the vice of confused disputes and argue according to their own particular principles. It exercises a structural constraint on the opponents which forces the opponents to “speak moderately in spite of themselves” and to put aside their (explicit or hidden) pretensions of innovation. Second, the rule is traditionally viewed as a simple formalization of the precept of caritas. Leibniz, on the contrary, defines the golden rule as a rule of “measured” or “balanced” love, as a hybrid principle which combines both caritas and prudentia.13 For this reason, Leibniz considers the golden rule to be a rule of justice rather than simply a rule of love. Finally, Leibniz conceives the rule as involving a double test of generalization which obliges us to shift not only between our own

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“place” (A) and that of the other (B), but also to take into account the place of the generalized other (non-A) and that of the generalized other of the other (non-B). Leibniz’s method of moderation requires that we shift dialectically between these various “places,” particular and general, in order to finally determine “to which side the balance must lean” (A VI 4 2250; DA 173). In this way the golden rule is a procedural principle of optimization and of generalization that serves to lead controversy towards a conclusion which is maximally equitable.

Notes * The Carlsberg Foundation has funded research for this paper. I thank my sister Anna Lærke for her help with the English language. Any remaining blunders are entirely my own. 1. According to a typology that Leibniz implicitly makes use of in the Commentatiuncula de judice controversiarum (1669–1671; A VI 1 548–559; DA 7–24), there are three fundamental types of controversy: religious, theoretical, and practical (A VI 1 554; DA 16). The typology he considers for his “method of establishments” (theological, philosophical, and juridical; GP 3 194; DA 366) in a letter to Thomas Burnett (February 1st 1697; A I 13 547–559; GP 3 186–197; DA 359–372) is mutatis mutandis the same. 2. Voltaire will use exactly the same argument in the article on “sects” in the Dictionnaire philosophique (Voltaire 1967: 385). 3. The origin of this argument is Tertullian’s De praescriptione haereticorum. In Leibniz’s lifetime, Pieter and Adriaan Van Walenburch, among others, reused it in their Tractatus generales de controversiis fidei (1670). Leibniz annotated this text in 1677 (A VI 4 2471–2472), but he had already discussed religious matters in person with these two Catholic brothers in Mainz. Leibniz’s remarks on the notion of the “judge of controversies” in the long fragment Commentatiuncula de judice controversiarum from 1669–1671 (A VI 1 548–559; DA 7–24) are partly directed against their prescriptive argument for the infallibility of the Roman Catholic Church (A VI 1 294, 547; GP 3 481; GR 199, note). He also discusses the principle of prescription in a letter to Paul-Fontanier Pellisson and in the Nouveaux essais (A I 6 77; NE 4. 15.6; A VI 6 458–459). 4. The fact that these two authors agree on this particular point does not make them similar otherwise. Pierre Jurieu denounced the dogmatic minimalism proposed by Isaac d’Huisseau as simply “criminal”, in an anonymous book from 1672 (Jurieu 1672: 8–9). 5. Leibniz argues in a parallel manner when discussing the obedience a subject owes to the Sovereign and the legitimacy of rebellion. Formally, the argument stems from Hugo Grotius’ De jure belli ac pacis (1625) (Lærke 2005: 55). 6. I borrow this useful notion of a “conceptual person” from Gilles Deleuze and Félix Guattari, Qu’est-ce que la philosophie? (Deleuze and Guattari 1991: 62–65). 7. The following surprisingly skeptical passage in the Conversation du Marquis de Pianese et du Père Emery Eremite also leads in this direction: “I have acknowledged indeed that at present we are all ignorant, that all our reasoning is founded only on suppositions, that we lack principles for judging things; that there is no measure of truth, that everyone holds on to his particular opinions, and that there are almost none that we have in common” (A VI 4 2257; DA 178).

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8. Leibniz writes in a text from 1679 on the uses of his universal characteristic, once it has been established as a general methodus disputandi: “One will no longer hear [once the universal characteristic is fully elaborated, ML] this impertinent objection that people harass each other with today, and which turns everybody away from the will to reason, and because of which we do not respond to the argumentation of the other by examining his arguments as much as by replying in a general fashion: “From where do you deduce that your reason is more upright than mine, what criteria of truth do you have?””(GP 7 187–188). 9. I leave aside here the question of natural theology which Leibniz tends to identify with metaphysics. 10. Leibniz gathers all this under the heading of a “balance of reason” (trutina rationis). Thus, he cites a Roman proverb: rationes non esse numerandas sed ponderandas – ‘reasons should not be counted but weighed’ (GP 7 521; DA 381). The metaphor of a “balance” is already carefully elaborated in the Commentatiuncula de judice controversiarum from 1669–1671 (DA 7–24), but is present in numerous texts written throughout his entire life. Cf. A VI 1 548–559; A VI 4 2250, 2259; DA 173, 179; C 210–214, 337–339, GP 3 191–194; GP 7 187–188; FC 2 32; GP 5 192 446–448, etc. See also Dascal (1996: 14). 11. This is also what Leibniz’s use of the French verb “convenir” and the noun “convenance” suggests. André Robinet has pointed out how Leibniz uses these terms when speaking of universal harmony (Robinet 1994: 112). 12. Neminem laedere and suum cuique tribuere constitute the two first principles of the threestep notion of justice borrowed from Ulpianus that Leibniz defends as early as in the Nova methodus discendæ docendæque Jurisprudentia (1667). These two principles correspond to the levels of justice called, respectively, “strict law” and “equity.” The third and highest principle of justice, “living honestly” (honeste vivere), corresponds to the level of “piety”. This triple concept of justice can be found in a numerous texts. See A VI 1 343–345; A VI 4 2850–2871, 2930; DR 123–124, 163–164; GR 566–567, 606–621; GP 3 387–389. For a commentary, see Robinet (1994: 104–116). 13. The notion of “hybrid concepts” has been suggested to me by Marcelo Dascal in personal correspondence.

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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, 387–409. Dascal, M. 2001. “Nihil sine ratione → Blandior ratio”. In H. Poser (ed), Nihil sine ratione. Proceedings of the VII Internationaler Leibniz-Kongress. Berlin: Leibniz Gesellschaft, 276–280. Dascal, M. 2003. “Ex pluribus unum? Patterns in 522+ Texts of Leibniz’s Sämtliche Schriften und Briefe VI, 4”. The Leibniz Review 13: 105–154. Dascal, M. 1996. “La balanza de la razón”. In O. Nudler (ed), La Racionalidad: Su Poder y sus Límites. Buenos Aires: Paidós, 363–381. English version, “The balance of reason”, in D. Vanderveken (ed), Logic, Thought and Action, Dordrecht: Springer, 2005, 27–47 [Access din http://www.tau.ac.il/humanities/philos/dascal/papers]. Deleuze, G. and Guattari, F. 1991. Qu’est-ce que la philosophie? Paris: Minuit. Erasmus, D. 1970. La correspondance d’Erasme. P. S. Allen, H. M. Allen, and H. W. Garrod (eds). Bruxelles: Presses Académiques Européennes. Erasmus, D. 1992. De amabili concordia ecclesiae. C. Blum, A. Godin, J.-C. Margolin, and D. Ménager (eds), Erasme. Paris: Robert Laffont, 822–883. Gil, F. 1984. “Leibniz, la place d’autrui, le principe du pire et la politique de la monadologie”. Passé Présent 3: 147–164. Grotius, H. 1991. Meletius. In J. Lagrée, La raison ardente. Paris: Vrin. Grua, G. 1956. La justice humaine selon Leibniz. Paris: Presses Universitaires de France. Hobbes, T. 1839. Opera philosophica omnia. W. Molesworth (ed). London: John Bohn. d’Huisseau, I. 1670. La Réunion du Christianisme ou la Manière de rejoindre tous les Chrétiens sous une seule Confession de Foy. Saumur: René Pean. Jacquot, J. 1954. Acontius and the Progress of Tolerance in England. Genève: Droz. Jurieu, P. 1672. Examen du livre de la reunion du christianisme. Jurieu, P. 1682. Examen de L’Eucharistie. Rotterdam: R. Leers. Lærke, M. 2005. “Jus circa Sacra. Elements of theological politics in 17th century rationalism: From Hobbes and Spinoza to Leibniz”. Distinktion 10: 41–64. Lærke, M. 2008. “Apology for a credo maximum. On three basic rules in Leibniz’s method of religious controversy”. In M. Dascal (ed), Leibniz. What kind of Rationalist?. Dordrecht: Springer, 397–407. Lafond, J. 1983. “Avatars de l’humanisme chrétien (1570–1710). Amour de soi et amour-propre”. In Albert Heinekamp (ed), Leibniz et la renaissance. Studia Leibnitiana Supplementa XXIII. Wiesbaden: Franz Steiner, 76–89. Lagrée, J. 1991a. La raison ardente. Religion naturelle et raison au XVIIe siècle. Paris: Vrin. Lagrée, J. 1991b. La religion naturelle. Paris: Presses Universitaires de France. Leibniz, G. W. 1994. Le droit de la raison. Ed. R. Sève. Paris: Vrin. [= DR] Leibniz, G. W. 1996. New Essays on Human Understanding. P. Remnant and J. Bennett (trans). Cambridge: Cambridge University Press 1996. (The Pagination in this translation follows that of A VI 6.) [= NE]. Leibniz, G. W. 2001. Opuscules philosophiques choisis. P. Schrecker (ed). Paris: Vrin. Locke, J. 2003. Two Treatises of Government and A Letter Concerning Toleration. I. Shapiro (ed). New Haven, CT: Yale University Press. Mercer, C. 2004. “Leibniz and his master: The correspondence with Jacob Thomasius”. In P. Lodge (ed), Leibniz and his Correspondents. Cambridge: Cambridge University Press, 10–46.

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Naert, E. 1959. Leibniz et la querelle du pur amour. Paris: Vrin. Olaso, E. de. 1975. “Leibniz et l’art de disputer”. Studia Leibnitiana Supplementa XV: 207–228. Olaso, E. de. 1995. “¿Como discutir con les escépticos? El caso de Leibniz”. In J. A. Nicolas and J. Arana (eds), Saber y conciencia. Homenaje a Otto Saame. Granada: Comares, 323–332. Pufendorf, S. 1998. Gesammelte Werke. Berlin: Akademie Verlag. Robinet, A. 1994. G. W. Leibniz. Le meilleur des mondes par la balance de l’Europe. Paris: Presses Universitaires de France. Spinoza, B. 1999. Traité théologico-politique. F. Akkerman, J. Lagrée, and P.-F. Moreau (eds). Paris: Presses Universitaires de France. Voltaire. 1967. Dictionnaire philosophique. Paris: Garnier.

chapter 13

Leibniz vs. Bossuet Which reasons for Irenicism? Christiane Frémont

“The art of conferring and disputing needs to be completely re-founded” (NE 4.7.11) – who was better placed than Leibniz to express this requirement and perhaps even to provide a way of subscribing to it? His career as a jurist and advisor to princes, as well as his work as a philosopher, accustomed him to various kinds of writing, among which dialogue (real or fictional) finds a preponderant place, since only in a confrontation of different points of view truth is to be found. Leibniz was wary of conferences that favored eloquence and the skill of making a good impression (see, e.g., Vices of mingled disputes §8; DA 3), and of any use of language which restricted itself to rhetorical artifice; that is why Leibniz the writer, whilst acknowledging the theoretician and controversialist in Bossuet’s writings, criticizes him for using the eloquence of the pulpit. But if there is such a thing as an art of controversy,1 it obviously has to do with rhetoric, and Leibniz wished to give rhetoric’s technique full legitimacy as a means to achieve knowledge. And yet, how vain were all those controversies that became entangled in the accumulation of prefatory questions, annexes and appendices, which were then replicated and duplicated, taken up again, or irrelevantly reactivated, and thus interminable. Leibniz liked to tell the following story: One day M. Casaubon the elder was taken into an old room at the Sorbonne and told that debates had been taking place there for more than three hundred years. He replied, ‘And what has been decided?’.2

We ought to take the question seriously. What has been decided? That is what it is really about: we need to reach a decision. The word ‘decision’ does not necessarily refer to a demonstration of the truth more geometrico – even less to an ecclesiastical authority – but indicates in general the incontestable establishment of a thesis on which agreement can be reached. But by what procedure?

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It remains to be seen whether the decision procedure identifiable in the correspondence exchanged between Bossuet and Leibniz can possibly be applied to all controversies, whatever their object or discipline. Could the art of controversy that they put to work give us a more general model of a method for finding the truth, variously applied elsewhere in specific modalities, and sometimes enabling exceptional successes? Might the mathematical kind of demonstration be a particular case of argumentation where, since the constraints are determined as narrowly as possible, the results are most certain – to the point of becoming necessary?

1.

Controversy or negotiation?

The controversy in question is remarkable in that, in the period which concerns us here, it no longer has any object or theological content on which the participants disagree, which needs to be debated to make the reunion of the Churches possible. There is no longer any real theological controversy because matters have already been discussed throughout two centuries of controversy, involving theologians from both sides, and there is practically no argument or method which has not been tried. Above all, many fundamental questions reconsidered since the 1670s have recently been settled by the writings of Bishop Rojas y Spinola and Abbé Molanus. Consequently, Leibniz and Bossuet work on documents that have already defined and solved the problems in question. It is striking, too, to notice the reduction not only in the number of controversies, but also in their weight: Leibniz often returns to this point (see Leibniz to Bossuet, April 8th/18th 1692; A I 7 312), stating that the remaining differences between the two parties are really less serious, “even less considerable”, than those tolerated within the Roman Church itself (divided over probabilism, pure love, and Gallicanism). Rather than controversialists, therefore, Leibniz and Bossuet are in the position of commentators on the controversy; it is up to them to decide whether the proposed solutions are sufficient to conclude the project undertaken between Rome and the Empire: Is reunion formally possible on this basis? The dialogue between Leibniz and Bossuet takes place in an intricate context of a political and diplomatic affair, where there are different and multiple interests: France – Gallican and politically unified – obviously does not have the same objectives as the German Empire, which is both politically and religiously divided; this explains the changes of attitude on Bossuet’s part (since he not only represents the French Church but is also concerned about Roman orthodoxy) as well as that of Leibniz, the servant of the Duchy of Hanover, which is linked to the Empire. However, it would be too simple to oppose (as Foucher de Careil does) Leibniz the political negotiator and Bossuet the theologian-controversialist, and



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to conclude that reunion did not take place because the political negotiation had failed; the negotiation proposed by Leibniz and Molanus had also had theoretical content, as well as theological and religious implications, and was to become in its turn an object of controversy. So what we have is a negotiation which encompasses a controversy (about questions left to one side), wrapped in a meta-controversy (about the establishment of points for debate); but also a controversy about negotiation (its meaning, its possibility, its pertinence, and its conditions), and a negotiation which turns into controversy (engaged by Leibniz over the question of ecumenicity, in particular that of the Council of Trent). Hence the complexity of the dialogue, which oscillates ceaselessly between controversy and negotiation. It is notable, however, that the logic – or rather the rhetoric – of controversy is not so different from that of negotiation, since in both cases it is a question of a principle which seeks the optimum, the most probable knowledge. It is not so much a question of defining truths as of establishing the conditions for truth in the matter of religion, and finding sufficient grounds to construct the catholicity of Christian Europe – without underestimating the sufficient as opposed to the necessary, postulated by Bossuet, since sufficiency is firmly founded on the recognition of an infallible truth. On Leibniz’s side, too, there is intransigence over what he considers irreducible. The drive to irenicism is nonetheless based on good reason, since in the matter of religion we are fortunate to have a fixed point known to be absolutely true – infallible, because revealed; if one were to renounce infallibility, said Pellisson, one would render religion as uncertain as physics! It is quite rare in a controversy dealing with philosophy, science, law, morals, etc., that one can be sure of the conclusion in advance – sure, that is, of the necessity of arriving at real agreement – in a domain where nonetheless no truth is demonstrable. Therein lies, perhaps, the singularity, if not the paradox, of religious controversy.

1.1

Negotiation: An “expedient”

The two most illustrious thinkers involved in this affair are irreducibly opposed over a simple but fundamental question: of controversy and negotiation, which of the two is the condition of the other? The theologian-bishop founds the communion of the churches on a complete resolution of all controversies; the philosopher-diplomat reckons that a reunion before such a complete resolution is possible and would help to smooth out the differences. The urgent need is to obtain the reunion of the churches; that has been the goal of both popes and princes, already fraught with a long history, anticipated since 1648 – the peace of the Church (not the search for truth) figures in the program

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of the Treaty of Westphalia. The philosopher’s role is to make the bishop understand “what is singular and considerable” in the program drawn up by Spinola and Molanus (see Leibniz to Marie de Brinon, December 1691; A I 7 212): the Protestants do not seek mutual civil toleration, but real intellectual agreement on the truth; indeed they believe many of the truths of faith sufficiently established and clarified in Bossuet’s Exposition de la doctrine catholique (1671) – but as it also contains others whose “way of explanation” has not convinced them, reunion seems impossible. That is where negotiation is needed in order to re-establish communion, notwithstanding certain differences which may be left to one side (“the way of suspension”), if however (and only if) they encompass nothing which could be considered heretical in the eyes of either party; the Protestants already recognize the Pope and the hierarchy of the Church, as well as the authority of a future ecumenical council, where they and the Catholics would sit as equals, charged with resolving the final controversies. (One should note in passing the very advanced stage the affair has reached at this time; it will never be so close again to being resolved – the Pope himself is in favor of the stratagem.) Leibniz tries to convince Bossuet of the legitimacy and efficacy of this “expedient” (Leibniz to Marie de Brinon, May 1694; A I 10 126) as being the only one capable of contributing something new to an unresolved or irresolvable question. The term “expedient” suggests, in mathematics for example (cf. Parmentier 1989: 8–9, 22–25), a change of method, a new choice as to the conditions for resolving a problem: one departs from the general method as being inoperative under certain conditions or in a certain case, because there is a means of reaching a solution by inventing an appropriate and singular procedure, which approaches things from a different angle, which may be longer, more costly and unrepeatable elsewhere, but which works. Explaining this negotiation to Landgrave Ernest (who thought highly of Leibniz, although he was a somewhat intransigent Catholic), Leibniz makes it clear that he had first proposed it to Bossuet as a question of principle, regardless of content and circumstances: it is not a question of deciding whether it can be applied immediately, but whether it is “feasible and licit in itself, … possible – I say, possible – as a legal possibility” (Leibniz to Landgrave Ernst, October 9th/19th 1691; A I 7 164–165). Thus begins a controversy whose ramifications come to occupy the whole of the correspondence: Can the Church allow the principle of re-establishing ecclesiastical communion notwithstanding disagreements that one undertakes to reduce later on? Leibniz judges this “reasonable” (Leibniz to Bossuet, October 1693; A I 10 196), since it is fair to both parties, who remain equal; neither is obliged “to give up in advance their principles or their symbolic books” (ibid.). But Bossuet immediately upsets the balance, requiring a commitment in advance from the Protestants that they will submit to the decisions of the Council of Trent. Bossuet



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then explains those decisions in such a way as to show that it was the Protestants who were in the wrong for wanting the separation in the first place. Does the expedient not hide, as many have said following Foucher de Careil, a logical circle that justifies Bossuet’s refusal? That is, in order to reunite the churches it would be necessary to solve all controversies in an ecumenical council; but for that to happen, the council would have to include the Protestants, that which would presuppose that they had been absolved of heresy. But Leibniz’s argument puts the principle of reason first: the convergence of reasons supporting a provisional reunion proved retrospectively that there had never been sufficient reasons for the separation. Negotiation would work immediately, expediting the problem, reaching its goal directly and deciding on a new state of things that would favor a definitive solution. One would be able to arrive, for the time being, at a state of civil equality between the faithfulness of both confessions and at a real doctrinal tolerance never before obtained, since Lutheran doctrine would no longer be condemned – it would rather be a subject to debate in the same way as certain contested ideas within Catholicism – and all without prejudice for faith or for piety. As far as sufficiency is concerned, the expedient is justified, since the reasons for supporting it are incomparably stronger than those for rejecting it: First of all, it is incontestably licit. The Church has already practised it in comparable circumstances. On this point, Leibniz introduces a historical method to show “examples of this temper”, since, as he writes to Pellisson, “examples have great weight in this matter” (Leibniz to Pellisson, May 6th 1692; A I 7 327; see also Leibniz to Marie de Brinon, May 1694; A I 10 128; Leibniz to Bossuet, July 3rd 1694; A I 10 132). As contingency provides no necessary reasons, an argument in a religious controversy is more juridical than demonstrative: the “defendant” appeals to cases that can establish a precedent – which doubtlessly demonstrate nothing to do with the present litigation but which have weight, incidence, and influence capable of determining the decision one way or the other. The philosopher happily follows this method in order to weaken the (theologian’s) dogmatic reasons and the (bishop’s) arguments from authority. The recurring example is that of the Calixtines in Bohemia, for whom the Council of Basel had suspended a decree of the Council of Constance concerning communion in two species, ordinarily reserved for priests, without denying the truth upheld in the Church, but putting off the question of dogma for a future decision, and on the minimal condition that the Calixtines declare their belief in the doctrine of concomitance, which affirms the entire presence of Christ in each species. In practice, tolerance was achieved (depending on which particular habit seemed preferable) founded on a single doctrine. Agreeing to concomitance, the Calixtines recognized the validity of communion in a single species but were not

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obliged to recognize its necessity; and where a thing is valid but not obligatory, the possibility remains open for one thing or the other to be thought better. “This is our case in terminis”, Leibniz affirms (Leibniz to Bossuet, July 3rd/13th 1692; A I 8 122; cf. Leibniz to Marie de Brinon, September 1693; A I 9 187; Leibniz to Bossuet, October 13th/23rd 1693; A I 9 195); and it has greater value, and is even more deserving of comparable treatment, as it is a question of half of Europe, not just of a small group of Bohemians. The expedient also applies the rule of the optimum, since the suspension of a controversy would be a small evil for a great good, a condition sine qua non; separation is a greater sin than reunion achieved at the cost of suspending certain controversies whose real final outcome is unknown, since it is impossible to decide on the distribution of error and truth (Bossuet contests this postulation, but for Leibniz it is a fundamental working hypothesis). Reunion is in conformity with Christianity itself: schism is an injury to charity and renders vain the promise made to the Church, the key for salvation (not to mention the other advantages that have to do with the political construction of Germany and Europe, and the religious organization of the earth). But as it is not necessary, reunion is not obligatory at any price; there is no absolute reason, either dogmatic or doctrinal, to become a Roman Catholic: I have given much time and application to controversies, but as I have not yet been able to find any absolute necessity which would oblige us all to be in the Roman communion at whatever price, I find it sufficient to do all for the re-establishment of that communion which one believes oneself able to do, following one’s conscience. (Leibniz to Pellisson, July 27th/August 6th 1692; A I 8 157)

But negotiation reveals a disagreement on principle, which for both parties justifies their method and indicates their solution; Leibniz treats the separation as a schism, Bossuet in terms of heresy (what is more, formal heresy). One should not oppose, as it has too easily been done following Foucher de Careil, reason and free enquiry to tradition and authority, but rather the jurist, who takes into account an event in history (the Reformation, which gave birth to the churches of the North – German, Danish, Swedish, English, and Scottish) and ponders the origin and legitimacy of that new fact, and the theologian, who measures the universal Church by the yardstick of a particular church, and refuses all others the respect they are due. Treating the question in terms of schism presents several advantages from the strategic point of view. If there had been schism, it would be passive; but Rome can be accused of active schism – Leibniz adopts Claude’s formula, “we did not leave, we were chased out”, and that merely for having sought to reform abuses, not to change the faith. If the reformed church is schismatic, there is every reason to



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deal with it as the Roman church did in an earlier age with the Greek and eastern churches, on an equal footing. Here again the jurist appeals to cases that establish a precedent: at the Councils of Florence and Ferrara, eastern Christians were invited with the title of “separated” Christians, “on an equal footing with the Latins” (Reply to Abbé Pirot, June 15th 1693; A I 9 134), whereas the Protestants at Trent were invited as “already condemned”, treated as suspect, even as accused. If one were to consider, on the other hand, the existence of a separated Protestant church, nothing would prevent the calling of a new, truly ecumenical council made up of both the Roman and the Northern churches (Molanus here repeats Luther’s demand), where the Romans would not be judge and party at once, which is juridically unacceptable for vice of form. Moreover, there is every reason to claim that there had not in fact been a Protestant schism; the Council of Trent created it by presupposing what it ought to have examined – that the Protestants were separated Christians (see Leibniz to Marie de Brinon, April 18th 1695; FC 2 90–96; cf. Leibniz to Pirot, July 27th/August 6th; A I 8 157; and the Relation pour la Cour, art. 28–30, FC 1 30). On this point, Leibniz develops a long argument showing that there was not in his day, any more than there had been before, any reason for the separation. It is enough to contemplate the state of the various controversies at the time, taking into account the mutual concessions made by Spinola and Molanus, and Bossuet’s Exposition: they are either non-existent or purely verbal (hence void), either simply philosophical (hence without importance for faith) or real, either resolvable, and in large part already resolved (on points as important as the Eucharist, justification, grace and merits) or, finally, insoluble – but in these cases their solution can be delayed since they do not involve salvation. Bossuet accepts all of this. In short, there is no more reason for schism with the Protestant church (prepared as it is to recognize the Pope and the church’s hierarchy, as well as the authority of ecumenical councils) than there is for schism with the Gallican church. To force the theologian to acknowledge the non-existence and the illegitimacy of the schism, Leibniz hypothetically brings a case from the past into the present, just as jurists invent fictional cases to fill in gaps in jurisprudence: Go back before the Council of Trent; suppose the separation had not taken place; if certain Christians now held the views we hold on points of dogma and practice, would you consider it right to exclude them from the Church? If you were Pope, he asks Landgrave Ernest, would you exclude us? The general case, which encompasses the fictional case and the real one, was the following: without considering Lutheranism or Calvinism (the philosopher refuses sectarian words ending with “ism”), if a protestant recognizes the principle of catholicity, and agrees that one should never separate oneself from the Church when it has expressed itself in a truly ecumenical council, is that protestant to be considered heretical or schismatic?

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If it were a question of schism, the Reformation would become by rights the object of a negotiation; and if there is “diplomacy” in that, it is based on a rigorous and theologically informed examination of the terms of separation. But Bossuet derives the schism from a previous cause; there was, first and foremost, heresy – we should remember his verdict on Leibniz: “a man with those sentiments is heretical and obstinate” (Bossuet to Pellisson, December 27th 1692; A I 8 214). Pellisson and Bossuet tend to harden the notion of heresy, demanding external communion as well. The Protestants are material and formal heretics, they are mistaken as to the dogma, and deliberately refuse the doctrines declared by the Church, making themselves their own judges and guardians of doctrine; hence they wanted separation. The reunion of the churches can take place only if the Protestants return to communion like lost sheep, like prodigal sons, etc. On doctrine, the bishop distinguishes true and false following his invariable method of exposition of the faith, and following the explanation of the truth held by divine right by the Roman church. It follows that, treated as a heresy, the Reformation continues to be the object of a vast theological controversy, in dogma as well as in discipline, the resolution of which logically precedes any project for reunion. In consequence, Bossuet refuses to suspend the controversies Leibniz considers insoluble at present but inessential, as well as the principle of a future council that would be able to solve them. The affair was to fail on these two propositions, and this is where the hypothesis of negotiation itself falls into controversy: Bossuet does not accept that there are any articles that are inessential to salvation, and he rejects the necessity for a new council, since Trent has already defined everything and solved everything. The Protestants, although they admit the principle of conciliar authority, do not admit the legitimacy of Trent. This question was to derail, and to close, the whole discussion.

1.2

Controversy: The obstacle

The discussion is not so much about dogmatic content as about the status of truth in matters of religion, that is, the legitimacy of the word concerning faith. Curiously, what might seem the weightiest problem – the dogmatic disagreement persisting since the Reformation – according to Leibniz counts the least: “three decades” of controversies either resolved or tolerable, on which the Church has no need to decide (Projet de Leibniz (au nom de l’abbé de Lockum) Pour faciliter la réunion des Protestants avec les Romains Catholiques, August 27th 1698; FC 2 172–193). Bossuet’s new ‘concillation’, completed in 1701 for Pope Clement XI (Bossuet to Leibniz, August 12th and 17th 1701; Bossuet 1864: XVIII 321–350),



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agrees on the majority of the results; concerning transubstantiation, for example, Bossuet welcomes Leibniz’s doctrine of the force which sustains the real presence and multi-presence; as for the serious question of justification and merit, it is not disqualifying. By contrast, Leibniz, more as a religious man than as a theologian, is more demanding with respect to Roman abuses. He considers certain points of discipline (such as the worship of images and relics) as more consequential than doctrinal differences, because they go against piety; practice and morality, more than theological speculation, call the essence of piety into question. Nonetheless, an agreement on this point is possible, since Bossuet concedes that those particular practices are not obligatory (Bossuet to Landgrave Ernst, September 2nd/12th 1691; A I 7 146ff.). The real controversy concerns two questions of law: the principle of faith and that of catholicity. As the correspondence continues, the discussion comes up against two objects: fundamental articles of faith, and ecumenicity (the latter encompassing a factual question as to the ecumenicity of the Council of Trent). The juridical point of view replaces dogmatic analysis, since it alone can decisively settle the question of truth in matters of religion.

1.2.1 Fundamental articles It is easy to agree on a good definition of faith: faith consists of that which is necessary and sufficient unto salvation. Leibniz tends to reduce the doctrine of salvation to a single fundamental article, the love of God, since that is the source of piety and charity. His letter to Bossuet of December 11th 1699 proposes the following classification: certain articles declared at the time as being matters of faith have not been directly revealed; as the Church added them illegitimately, one has the right to deny them. The veritable matters of faith, revealed and declared as such, are more or less important according to their connection with the doctrine of salvation: there are “articles which are so fundamental as to be necessary” (not following them would endanger salvation) and articles which are not necessary but are important to various degrees, according to their connection with those which are necessary. The connections between the articles do not follow the logical sequence of implication or deduction; they are approximately calculated according to the articles’ degree of incidence on salvation. In some cases, that incidence is negligible or nil; hence the reduction in number of veritable controversies. Let us recall that the distinction between fundamental and non-fundamental articles was the basis for reunion schemes among Protestant churches, some of which were successful. Bossuet, who accepts the distinction in his reply of January 9th 1700, finally includes secondary articles in the category of fundamentals because of their possible results. Moreover, he tends to transform connections

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into necessary sequences within a general demonstration, following the principle that the Church is never mistaken and says nothing which is not to the purpose, because “everything holds together”. The slightest loosening of a detail leaves the whole in doubt; thus, for example, the episode of Tobias’ dog has no direct importance for salvation but must be believed so as to avoid doubting the book of Tobias altogether; and in the same vein, one who denies the distinction between the baptism of Jesus and that of John rejects at the same time the belief in the divine institution and in the efficacy of the sacraments. Whence the inflation in the number of subjects of controversy, as well as the justification of a great many of the anathemas of Trent. For Leibniz, however, the connections are not deductive sequences from antecedent to consequent; if the formula “everything holds together” has any meaning, it is in a composition of arguments (drawn from history, from practice, and from the consideration of the presumed purposes of God) which support each other with a view to a result which is perhaps rather a “resultant”. To find a way out from an otherwise interminable discussion, the legal question needs to be asked – and answered – by the historical method. The legal question concerns the status of the word that speaks the Faith; where does it get its legitimacy from? Defining the problem as a jurist, Leibniz displaces the customary opposition between Protestant free enquiry and Catholic tradition in order to call on authority as well: if there is enquiry, it relates not to the content or the interpretation of dogma, but to that which founds them in law, their “authorization”, their authentication. It is not a matter of denying the Church’s authority, but of ascertaining that the Church is speaking de jure divino on all articles that it declares as matters of faith. The criterion is: any article is a matter of faith if it has been explicitly and officially decided to be so since the revelation and from the primitive church onwards (Leibniz to Landgrave Ernst, February 23rd/March 5th 1691; A I 6 176). This is, to the very letter, the rule of perpetuity of faith backed up by the authority of tradition – which is why Leibniz, turning the tables, writes to Bossuet that variation was on the Catholic side, perpetuity on that of the Protestants (this is not a new argument, as protestant controversialists from the end of the sixteenth century onwards claimed tradition in their support). To the formula “one should believe today what one believed yesterday” Leibniz retorts “but what are we to say if it turns out that one believed something else the day before?” (Leibniz to Bossuet, October 1st/11th 1692; A I 8 171), since we can always find examples in history to counter the rule, questions which were not asked in the primitive church and on which rulings were made later (this is elaborated in the following paragraph). For the promise made to the Church not to be vain, it is necessary that whatever is essential for salvation be the object of a direct, immediate revelation; it is not the tradition that counts, but the original,



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explicit and official declaration. However, Bossuet usually opposes perpetuity of fact (rather than of law) and a vague notion of the “universal Church” spread throughout Christianity, with an uncontested consensus on the part of eminent doctors and councils: all things which do not constitute an “authorization”. Leibniz (the librarian) then devotes himself to the historical work of searching the sources of acts and of official declarations which authenticated beliefs from the outset, and which obliged the faithful to believe them; and, as a good jurist, he calls on decisions made at an assignable date on questions which had not yet been defined before that date, even though they were the uncontested objects of consensus in the Church: sometimes there were “entirely new questions on which nothing had as yet been established”, such as the worship of images and the question of monothelitism (Leibniz to Landgrave Ernst, November 1692; A I 8 183; Leibniz to Bossuet, October 1692; A I 8 171, and March 1693; A I 9 83). These examples sufficiently invalidate the principle that “the Church has never defined anything which had not previously been judged Catholic” – in both senses of the verb “to judge”. Nevertheless, Bossuet questions the historical method, that is, the search for an assignable moment and a motive for a decision, since “nothing shall be sifted anew” (Bossuet to Leibniz, July 1692; A I 8 136). The historian is in fact applying to Roman orthodoxy the same method of investigation he uses with respect to sects and heresies (see Cogitationes de externae religionis professionis mutatione, 1686/1687; A IV 3 305–309): tracing the point when the split – the mutatio – occurred in order to examine its legitimacy; was it the rectification of an error (and therefore a return to the original) or a variation of a dogma? Did it bear on a point already defined as a matter “of faith” or not? – and so on for the whole series of mutatio, mutatio mutationis, mutation mutatae mutationis, etc. The rule is not to designate the introduction of a doctrine or usage as a fixed point, but to return to the canonical decision which imposed it as an article of faith; this, Leibniz invariably repeats, is a question of law which can be resolved by citing authentic documents, whereas the universal consent of the infallible Church is an artifice to avoid the real question (Leibniz to Bossuet, October 1693; A I 9 200). Bossuet, accustomed to winning,3 reasons without taking account of the status of the arguments he uses, whereas Leibniz builds up a detailed dossier in order to instruct a legal procedure. On the basis of an example about the canonicity of the books of the Old Testament, Leibniz announces the discovery of the critical moment, the root of all the variations: Innocent I, whose equivocal terminology in AD 405 was to give credit later to illegitimate definitions.4 The Leibnizian method in question supports a strategy that can immediately be applied to certain definitions of the Council of Trent which were denounced as novelties (Abbé Pirot’s defence of them itself provides examples of dogmas

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which had perhaps always been believed and followed, but never declared), with a view to lifting the anathemas and the accusation of heresy against the Protestants – once there is a sort of “theological void” concerning the contested points; formal heresy is a crime against canon law only if the object of litigation has been authenticated as an article of faith.

1.2.2 Ecumenicity The Council of Trent’s ecumenicity becomes the main point of the controversy after the evaluation established on August 27th 1698. It is a question of fact which involves a question of law: a council is truly ecumenical if it brings together the totality of Christians, including those who are presumed to be separated. Although Bossuet accepts the evaluation of August 27th, he refuses the “method of abstraction or suspension”, which is supposed to cover the unresolved questions until the calling of a new council. This is the irreducible point where irenic negotiation turns out to be impossible, since the bishop anticipates the discussion and declares that the judge in the controversy would obviously decide in favor of the doctrine currently defined as catholic by the Council of Trent, which has definitively decided the Faith. The paradox of the dialogue resides in the fact that Leibniz accepts the doctrine of Trent for the most part, with the exception of the anathemas (they are unjustified since they concern “non-declared” points). As he writes to Duchess Sophie: “I am myself of the mind of the Council on many things, but that does not mean that I accept its authority or its anathemas” (Leibniz to Sophie, January 1691; A I 6 162; and July 1694; A I 10 139). To Marie de Brinon he writes that, in essence, the decisions of Trent are “not so contrary to the Protestants as people think”; Grotius judged them to be fairly close to the Augsburg Confession. As acknowledging the possibility of a future council amounts to accepting the principle of negotiation and of reunion in advance, Bossuet has no other means than to affirm the legitimacy and validity of the Tridentine decisions, and Leibniz has no other strategy than to ruin them, putting the Council on trial. In fact, Leibniz’s arguments are not entirely new: first, there was vice of form since the Roman Catholics were at once judge and party; secondly, the Council was more of a “synod of Italians” (Leibniz to Landgrave Ernst, December 1692; A I 8 208) than of the Christian Church since neither the north of Europe nor the Eastern Churches were represented in it (Leibniz does not fail to wonder that a Gallican bishop should support “a troop of Italians”); finally and above all, the Council was illegitimate for lack of official recognition by all the nations represented, since the Electorate of Mainz and, mainly, France (this is the weightiest argument here) did not accept it.



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With respect to this last argument, Leibniz objects to Abbé Pirot’s (De l’Autorité du Concile de Trente, 1692), Pellisson’s, and Bossuet’s view that the Council was accepted in reality since it was not contested, and was indeed put into practice; even if they were incontestable, he claims, they were nonetheless without value. According to Leibniz, it is not legitimate to derive law from fact, and juridically speaking, the Council was not ratified by the nation; there was no declaration by the French ambassadors present at Trent, nor by the King, nor by the Third Estate; nor did Catherine de Medicis accept what it had to say about faith itself, for fear of irreparable schism with the protestants in the Kingdom. To these facts Leibniz adds as final proof Henri IV’s profession of faith (the one the King made in person at Saint-Denis, which is different from the one Cardinals d’Ossat and du Perron made in his name at Rome, drawn up by Pius IV): the fact that the French prelates removed the two passages referring to the Council indicates that the Council had not been accepted. For “ordinarily a fact can only be established by a detail” (Leibniz to Bossuet, February 5th 1702; FC 2 433) and this one is decisive; it shows that the Church had indeed taken pains to avoid making a king say something which had not been authenticated by the nation.5 Faced with the impossibility to resolve this ultimate controversy, the irenic negotiation came to an end in 1694, just as it did again after 1699. And yet: “est in potestate nostra ut controversias finiamus”.6

2.

The art of controversy

At first sight it may seem that there is no reason to look for a specific logic for resolving controversies other than the general method that reduces all problems to a form of calculation. This is the lesson to be drawn from all the prefaces and outward appearances of general science: one should apply the precept “calculemus” (‘let us calculate’; A VI 4 913, GP 7 200, DA 266) and observe that “omnes nostri errores sint tantum errores calculi” (‘all our mistakes are nothing but mistakes in calculating’; C 221) in order to conclude that all disciplines, even medicine and politics, may be treated by the same method (cf. A VI 4 975; C 221; GM I 181, 186); one may thus achieve the same success as mathematicians derive from their formalism (argument in forma, syllogistic or otherwise, serves as a connecting thread to verify the validity of reasoning, as well as the use of the characteristic – of a logarithm, etc. – which, by dividing notions into simple terms, gets rid of impossible notions), since “the majority of philosophico-theological controversies” derive from the absence of correct definitions.

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2.1

From controversy to conversion

‘Controversy’ is an interesting word because of its Latin etymology, which connects it to the analysis of sites: two antagonists who occupy two opposite places, as far apart as one could wish, are brought together by dialogue (irenic, both on principle and because truth requires it to be so) until they become neighbours or even identical and thus interchangeable, passing through various mutual conversions or inversions, by each situs turning towards the other, in sum (or at the end of the conversation) by a rotation of the situs vers all directions. The term ‘controversy’ indicates that it is the object which is debated, with emphasis on the contra, whereas Leibniz’s method considers rather the position of the subjects – who are indeed face to face but may be prepared to turn round, versus: what is most important is not contra-diction but the reversal of situations. Such is the structure of the Des Controverses, dated from 1680 (A IV 3 204–212; DA 201–208). A takes B’s place, and by multiplying the number of places and displacements, by a rotation (vertere) of every place towards (situs vers) all directions, one will end up occupying every possible scenario, reaching at infinity the ichnographic point where they merge together; the universal is the sum total of all versions – so it may well be by means of the art of controversy that truth can be attained. From the same family of the word “controversy” comes the word inconsistency, a failing of which Leibniz was accused, and which perhaps has less to do with morality than with knowledge. Faced with a Cartesian he would play the Aristotelian, but if someone were to run Descartes down he would raise him up:7 since each party thought he belonged to the other, who was he, really? In the same way, before his Protestant prince he would speak as a Catholic, but would champion the Reformation in front of the converted duke. Fakery, or the expression of truth always at work? Versus: from controversy to conversion, the word is still from the same family: “when we have made all the Protestants into Catholics, we shall find that the Catholics have become Protestants” (Leibniz to Marie de Brinon, September 1693; A I 9 187). Not as a result of syncretism or eclecticism, but because in the end, analyzing the various situs each party will recognize his own in that of the other. Controversy is obviously an interesting object for a philosophy of communication: the world is an infinite, unconnected ensemble of points of view which actively represent the overall point of view of God – the world, that is, bodies, souls, spirits, and hence also thought, philosophy, history, religions, and within those religions, sects, heresies and schisms. Reminding Arnauld in 1671 of the trouble he had taken to study all the controversies, Leibniz suggests that it is divine providence itself which led authors to oppose each other, so that the reader, comparing and judging, might construct for himself “a real system worthy of admiration”



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(Leibniz to Arnauld, November 1671; Leibniz 2001: 62). Even so, controversies would not melt away in a harmonious reconciliation of points of view just under the power of reason; irenic discourse demands work, a technique of argument, a stratagem even: hence the invention of the sort of debating machine proposed to duke Johann Friedrich. The Des Controverses – whose main points are summed up in the Conversation du marquis de Pianèse et du P. Emery, Ermite (1679/1680; A VI 4 2250; DA 173) – develops a technique for exposing an argument, governed by a spatial arrangement whose very form is the reason for its efficacy: it forces opponents (“drawn by machines which would carry everything out” A IV 3 211; passim) to occupy a situs other than their own, so that the controversy is carried on without them, or despite them, thus producing automatically an impartial exposition of the appropriate arguments which support opposing theses; it forces the controversialists to “go all round the matter until they put themselves on their opponents’ side; with equal application and a disinterested spirit, to examine the points for and against, to see which way the balance ought to swing”, so that the readers would be unable “to judge which side the author supported” (Des Controverses, ibid.). We must not be misled by the vocabulary of “for and against”. Of course Leibniz knows the method of the scholastic disputatio, but his is different, based on a fiction which causes a variation, not in opinion, but in the identity of the enunciator: the separation of subject and discourse means that the supposed author does not seek to defend at any price the thesis he is obliged to pronounce, but supports it as if despite himself, for reasons he is forced to acknowledge – a good way of removing the pernicious effects of rhetoric from the conference or the lecture-hall, or the talent of someone like Bossuet – who was no readier than Pellisson, Arnauld, or Nicole to “look at the other side of the coin…” (Leibniz to Marie de Brinon, October 1690; A I 6 118). Leibniz apparently applies this strategy in 1686 in a text called Examen religionis christianae or Systema theologicum (A VI 4 2355) and in 1694 in the Judicium Doctoris Catholici (A I 10 156–169; DA 329–340),8 which sets out and supports the Catholic point of view on the controversies without giving any clue that the author is in fact a Protestant. Far from being (as Emery, Broglie, or Lacroix would have it) the religious testament of the author, it should be included with all the other texts in his religious negotiation, as an experiment that applies the third of the six rules of the Des Controverses, i.e., to put oneself in one’s opponent’s place. Leibniz takes it up again in 1694 in order to send it to Spinola under the title Judicium doctoris catholici de tractatu reunionis cum quibusdam protestantibus, emphasizing that it is an “expedient”, an “innocent address” drawn up in concert with Molanus.

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One can recognize behind the machinery of the Des Controverses the rule of “the other’s place, that true point of perspective in politics and morality” (A IV 3 903; GR 699; DA 164) which, as much as it is a strategy to see into the opponent – or even more so – as well as being a law of justice so that everyone gets a fair hearing, is a means of, and a benefit for, knowledge: “a place fit to make us unearth considerations which would otherwise never have occurred to us” (A IV 3 904; GR 700; DA 165); for whatever we would find unjust if we were in the other’s place has every chance of really being unjust in our place, in other places, in multiple places, or indeed in any place whatsoever; in the same way, whatever we judge to be true or false in matters of philosophy or religion has some probability of really being true or false if we still claim it to be so when we occupy the other’s place; since taking the other’s place has the automatic effect of showing up whatever remains invariable despite all the variations of situs. The arrangement suggests that each opponent could just as well be the other, that each in fact is possibly the other from a certain point of view – in keeping with the metaphysic of harmony, which requires that each situs should include all others in a certain way, since they all have the same referent: the truth which resides in God. Such a method, according to Bossuet, leads to indifference in matters of religion; but for Leibniz it produces truth, for it manifests in every doctrine whatever its contradictors acknowledge to be true. For the Protestant would play the Catholic “taking things at their worst”, without doing any favors to a thesis he had no interest in supporting; leaving aside, then, all complacency and all rhetoric, he would only retain those arguments he was forced to allow, showing up whatever withstood criticism. The Catholic would proceed in the same way with regard to the Protestant, and thus emerges the incontestable. We can call a thesis “incontestable” if its reasons are incomparably more solid than any rationally preferable other, and if one cannot reasonably refuse to accept it. It remains to be seen whether the machinery of the Des Controverses can be applied to all controversies or whether, as its title suggests, it only works “in matters of religion”. Let us suppose that it is specific, even though connected to a more general method that includes various procedures for achieving knowledge, depending on the type of truth concerned.

2.2

The logic of controversy

Only arguments in forma are valid, admittedly – but what form are we to recognize as valid? For, if the Projet et essais pour arriver à quelque certitude pour finir une bonne partie des disputes, et pour avancer l’art d’inventer (A VI 4 963–970; DA 275–283) reaffirms the same requirements ten years after the plans for the general



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science, it also suggests a different model, that of Roman jurisconsults in whose work we find “fine samples of demonstrative reasoning”; and a rule different from that of dividing a difficulty into little propositions (which wearies the spirit), i.e., “distinguishing the more important propositions from the lesser” – that is, weighing rather than counting, comparing reasons in order to estimate their weight. The letters of 1694 were to develop the method suggested two years earlier: “dry, fleshless reasoning with neither charm nor beauty, which would lead us to the truth by a way like that used by people who keep account books, or by land surveyors, with regard to numbers and lines. The way is rough but it is straight” (Leibniz to Marie de Brinon, July 1692; A I 8 125). The way is straight because it advances towards its goal without hesitation, repetition, or omission; but it is rough because it passes through every asperity (facts, details, cases), retains meticulously everything that has been advanced, stops at the least unexamined thing, to arrive at a result which is not a demonstration stricto sensu, but a proof; unpolished, it does not have the elegance and economy of a geometrical demonstration. The essential thing is, first of all, to keep an exact account of everything which has weight in the discussion by giving each argument its value once and for all before passing on to something else or drawing any consequences (Leibniz notes many times that Bossuet neglected certain instances without giving any reason, for example the argument of the Council of Basel9), since it is not sufficient to neglect a datum, a document, an item in a file which might modify the state of the question: jurists, accountants, and surveyors establish exact evaluations. In fact, the reference to geometricians (surveyors) refers to an in forma procedure, without however indicating a demonstrative sequence or syllogism; accountancy and surveying – one the ancestor of arithmetic, the other of geometry – both tend to use algorithmic techniques, and follow an accumulative method which arrives at a result, an evaluation of what does or does not count: “when I start playing the logician or the calculator … these solid, important things do not quite lead to the conclusions one would like to draw” (Leibniz to Marie de Brinon, July 1692; A I 8 125). Accumulating, demonstrating. These two approaches, at first sight so opposed, are nevertheless equally operative. But perhaps in the end we have to say, like Casaubon, that this accumulation is sterile – three centuries at the Sorbonne, some thousand pages written on the matter of reunion, with what result? In 1694, after an interruption of six months and before a rupture lasting four years, it was clear that there were two ways, and only two, out of the impasse: either to leave the controversy to be negotiated or to find the right method of closing all controversy, since negotiation itself had become the object of controversy. Leibniz, meditating on the undecidable, wrote to Marie de Brinon:

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[O]ne single controversy, if one were to persist stubbornly in wearing it out, could become a legal trial which would take a man’s whole life to discuss … and when all is said and done what would happen would be what we see in difficult trials, that in the end one would be in as much of a mess, or even more so, than in the beginning.  (Leibniz to Marie de Brinon, May 30th/June 9th 1694; A I 10 126–127)

Now this comparison, pejorative to begin with, is turned in favor of the juridical model, since trials do reach verdicts because judges impose “a certain order” which enables progress towards a decision. The same goes for a controversy; there will be no end to it “unless we can agree on a certain new Logic, which remains to be invented, and which ought to do for controversies what the rulings of judges do during a trial”. Was this an importation or an invention? Whilst the writings of 1677–1680 invite the extension of demonstrative models that are efficacious in mathematics and metaphysics, this is the first time we find mention of a “new” logic, and the author here says very little about it. His goal is not so much knowledge as decision: “to determine visibly which party one ought to choose” – not which party is demonstrably right, but which reasons present themselves visibly and lead such a party to prevail over other possibilities. Therefore, it is a technique of choice, governed by the principle of the optimum, which also operates on the knowledge that precedes the choice. It requires, first of all, a kind of survey, an account of the reasons, however small they might be (even if they disappear to infinity), of possible states of affairs, of certain details which give meaning; and “a balance of reasons” which test or gauge the incidence and truth value of the arguments advanced from one side and the other, an “estimation” where weighing is more important than counting. Leibniz later insists on the newness of the logic in question (“a new species of logic quite different from what we have had up to now”; “a new kind of logic which would deal with degrees of probability” (Leibniz to Marie de Brinon May 30th/June 9th 1694; A I 10 126–127) and accords it increasing importance for human knowledge and practice: more sublime, finer, more difficult than the vulgar logic which only deals with the necessary, and which a mediocre genius can master, this logic, so far almost unused, but visible at least in the form of some fine samples of juridical argument, would be able to demonstrate things beyond the limits of the previous logic, since it would deal with reasons for the contingent. It would be a “science of proofs, fit to verify historical facts and to give the meaning of texts”; but the problem was that logicians of the time did not yet know how to estimate degrees of proof – they lacked that “Art of proofs which is the veritable Topic or Dialectic” (Leibniz to Burnett, July 17th/27th 1696 and February



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1st/11th 1697; GP 3 183 and 193; NE 4.3.20 and 4.7.11; Théodicée §§27, 28, 31; GP 6 77, 167–173). This new logic has one thing in common with ordinary logic: the application of a “method of establishments”, characteristic of mathematicians, and of which it is also a particular kind: “by Establishment I mean when one determines and completes certain points, and puts certain theses beyond dispute, so as to gain ground and to have foundations on which one can build” (Leibniz to Burnett, February 1st 1697; GP 3 192; DA 364–365). The method is general and consists in finding the exact definitions of terms and in drawing propositions from them which cannot be doubted, and which in their turn will be the elements composing an argument; but it is also distinctive in its applications according to the certainty it authorizes: “geometrical” when the process of establishment provides a demonstration whose sequences are absolutely necessary and incontestable, because they can be reduced to identical propositions; “moral” when there is no absolute necessity amid the consecutions; a certainty which, unlike the other, must be said to be non-necessarily incontestable and hence a possible object of controversy, for here we have a certainty where we cannot demonstrate the impossibility of opposing some other, stronger certainty. There is certainty by the accumulation of reasons that do not follow one another stricto sensu, there is as it were some leeway between them – and therefore room for some incidence, positive or negative – but they support, confirm and reinforce each other to the point that the whole is decisive. However, this new logic also differs from ordinary logic – illa logica vulgaris per saltem incedens – in that it is a technique of continuity – analysis gradaria10 – it works intensively, in the increase or decrease of the degree of probability, of plausibility (the qualitative term is more adequate), it evaluates the degree of sufficiency, measures the variation in importance of a datum within an argument, in a procedure which passes continually from the uncertain to the certain.11

2.3

Controversy in matters of religion

The logic of the probable applies to controversies concerning the truths of faith, which are a particular kind of factual truths, appropriate to the chosen world. The common usage of the term indicates a comparable intellectual operation: “one can compare faith with experience”, and even incomprehensibility does not prevent us from believing certain natural truths; we owe “a kind of faith to the witness of the senses”, “we add faith to the wonders brought back from China” (Théodicée §§1, 5, 36, 41). The same goes for historical truths based on the analysis of monumenta, and for everything where assent relies on “motives of credibility” (NE 4.16–4.18).

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Religious faith is more than belief in the fideist sense, since it is rational, similar to a form of knowledge: again it is a question of truth. But what kind of truth is reality susceptible to? For although there is one single notion of truth defined by the formula “praedicatum inest subjecto, otherwise I do not know what truth is” (Leibniz to Arnauld,12 July 1686; GP 2 56), contingent propositions have this specific feature: even if they have a priori proofs (because the sufficient reason of the predicates is contained in the subject), they cannot be the object of “demonstrations” properly speaking (“reduction to the identical”) since their analysis is interminable even for God (who “sees [the whole series] at once” but can no more reduce a contingent proposition to a necessary one than he can turn a surd into a rational number). Within truth there is both the demonstrable and the indemonstrable, not because of weakness of understanding, but by the very nature of the object (see the end of De Libertate; A VI 4 1658; see also Frémont 2001: 333). The demonstrable does not exhaust the rational, and that alone is enough to open up the field of controversy, since it contains truths that, a parte rei, resist demonstration and make room for contestation. This is why religious controversy is a good case to illustrate method in controversy – a special case, admittedly, but an excellent case, a privileged case because of the type of truth which is its specific object: an infallible truth, a truth known in advance to be absolutely certain. It is indeed absolutely true once it is known to be authentically revealed, or presumed true when it is expressly connected to the foregoing; and yet neither one nor the other can be demonstrated. Because they belong to the realm of the contingent, in order to know what we acknowledge to be infallibly true, only controversy allows us to establish their non-demonstrable truth: rare are the dogmas which cannot be debated, for we know neither absolutely nor generally, as Bossuet wished, what in the doctrines developed by the Church is directly related to saving faith – as is shown by the number and duration of disputes, variations on all sides, division into sects, and the appearance of heresies. In order to know and to prove, we only have at our disposal (apart from simple demonstrations of possibility which are the minimum that can be required of truth) the balance of reasons as they increase towards the emergence of a prevailing view. This brings us back to surveying, which classifies proofs (particular marks, distinctive signs, catalogues of miracles, facts and meanings established by exegesis), and the weighing of arguments taken separately and then accumulated into a result which is finally decisive (that is, incomparably stronger than any other) and withstands every contrary argument. For, if a well-supported thesis is doubtlessly “considerable”, there is still the possibility that its opposite might be equally or even more so (Leibniz to Bossuet, May 14th 1700, §46 (actually written in February); FC 2 322): the whole question is how to put whatever is more considerable



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“beyond attack”. Because we are not in the realm of the demonstrable, there is room for contrary arguments which might be probable or more convincing, but which can be brought down by yet more conclusive arguments: “each party will always find plausible arguments in Scripture, in Tradition or in Reason” (Leibniz to Bossuet, May 30th/June 9th 1694; A I 10 124) – unless we apply the new logic which will teach us to reach conclusions even about the non-demonstrable. Controversy is possible, and indispensable, just like the methodological displacement of situs, because there is no absolute necessity to occupy this or that place, but only better reasons – even on a dogma as fundamental as transubstantiation and multipresence; its possibility, established in the Demonstrationes Catholicae (A VI 1 494–517), and based on the dynamic notion of force (which Bossuet approves) is not enough to legitimize it as a necessary object of belief, since other ways of operating are perhaps better; this, indeed, could be debated, which is why Leibniz prefers to stick to the Protestant doctrine of consubstantiation. But as the reasons here are not necessary ones, there is no call for anathematization… So, on this point as on grace and justification, communion in one or two species, and the worship of images, he sees no reason to become Catholic; conversion is something to be weighed: I can well see, he says, advantages to being Catholic, but I can also see stronger reasons which make me think that your side could be a danger to salvation (Leibniz to Marie de Brinon, February 18th/28th 1695; A I 11 292; FC 2 85). The doctrine of Trent is “tolerable” on most points, but “not everything which is tolerable is necessarily veritable” – one can be mistaken without danger – and “not everything which is veritable is always necessary” – one can fail to follow something which is true (so, for example, communion in two species, authorized exceptionally in Bohemia, and desired by the Protestants unless the forthcoming council should decide in favor of the Catholic practice). Once there is no necessity there is choice – except for what has been directly and distinctly revealed as salutary: the division between true and false, here, is determined exclusively in relation to salvation, and for the rest there is indeterminability in controversies since the promise made to the Church is not to make us know everything we would wish. Reasons for converting are only persuasive if it turns out (and this remains to be proved) that the Church, which is not the only way, is nevertheless “the best way to be saved”, since it would be dangerous to neglect ordinary ways to salvation (confession is surer, because thanks to the sacrament it only requires attrition, not contrition, which is more difficult). There is above all no reason to convert “at any price”. In order to conclude a religious controversy we need to find the right situs, one which reveals the criterion that encompasses and surpasses, which brings out in every case reasons that, though strong, are not sufficient – sufficiently 

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overwhelming, that is, always to prevail against all others. The rule is to be sought in a ratio which is “the measure of revelation present at the time in the Church”: its degree of inspiration, its proximity to the divine source – that alone makes an article a matter of faith and justifies a canonical decision. It remains to determine the standard, the fixed point in relation to which one measures the ratio: Leibniz accepts none other than the doctrine of salvation, i.e., whatever is explicitly stated in Scripture as being necessary to salvation. This allows the reduction of fundamental articles, and hence controversies, to a very small number – in fact to just one, the love of God, since the only damnable thing (this is the Confessio Philosophi) is to hate God. Here, irenicism is not seeking a prudent, minimal agreement between the churches, but trying to make out the hard core of revelation, the few rare articles which are incontestably and directly connected to salvation, that being the only sufficient reason which encompasses all others: immeasurably stronger than all those brought along by theologians in support of their doctrines. Any controversy which is not directly related to salvation, and so to the love of God, and so to charity, is negotiable – in sum, for Leibniz, almost all the decisions of Trent: which is why the affair could begin with negotiation, itself justified by a reason stronger than the concern to resolve controversies: ending the schism, which is an injury to Christian charity. A conclusion in the form of a hypothesis is unavoidable: if controversy is indispensable for knowledge of the truth, particularly in “human affairs which do not allow for metaphysical precision”, it is because reality itself is as it were controversiable:13 the nature of knowable objects derives from that very procedure, because those objects demand more than a strictly demonstrative knowledge. Knowledge of the real, then, comes via rhetorical and juridical argument – which is why the Théodicée, a book of controversy, which puts God on trial, is also the great book of the world as it is, the book which explains the chosen real world. Since there can be no demonstration of propositions of existence, the real – all that belongs to this world, contingently chosen by the divine will – is susceptible to moral certitude: true, but with a kind of truth that means that its opposite is not impossible but also arguable, defensible, and plausible. And thus the field of controversy is open; once what is true is not absolutely true, we must say that it, rather than anything else, is true; that it relies on stronger reasons, much stronger … incomparably … infinitely stronger: whatever we can say is “incomparably more probable than the opposite” (Leibniz 1903: 515) is certain and thus beyond the reach of all contestation. So all in all it is not surprising that reality as a whole should be controversial, since the world is the object of a choice: this one rather than that one – and let us emphasize that there is no way of demonstrating that this world is the best



Leibniz vs. Bossuet: Which reasons for Irenicism? 343

(De Contingentia; A VI 4 1652). As sufficient reasons recede to infinity, and optimization applies even to means, every element of the created world is subject to an evaluation: what has the most right to exist? Only that which would be invariable throughout all possible worlds is stricto sensu demonstrable and not subject to controversy. Controversy is thus the broadest model of knowledge of the real, since it constitutes a search for the best reasons to endorse a particular proposition, and that is called proof, a genus of which demonstration is a particular species – we can understand why Leibniz had such respect for the wisdom of jurists. That this knowledge is not based on demonstration in no way compromises the assurance that there is a truth which can be attained: controversy is the best means to avoid skepticism in matters of philosophy and indifference in matters of religion, since human reason, which goes with God’s reason, can always, if it follows the right logic, finish any controversy.

Notes 1. The word “controversy” (controverse in French) in this text is used both in the sense of a specifically religious controversy, and that of debate in general, and would thus normally be translated “debate” in most contexts. It has, however, consistently been translated “controversy” in order to preserve the integrity of the author’s observations. 2. Leibniz to Burnett, February 1st/11th 1697; GP 3 192; DA 365; see also Théodicée §353; GP 6 325. 3. “You always suppose that one should recognize that the Church has decided” (September 3rd 1700; FC 2 376). 4. Leibniz to Bossuet, May 14th 1700 (FC, II, 349); in order to distinguish them more clearly from the Apocrypha, Pope Innocent I is said to have named as “canonical” books which the early church (and Protestants) considered merely “ecclesiastical” but which the Roman Church has ever since considered canonical. 5. Even if the French Church did eventually recognize the Council of Trent, the Kings of France never incorporated its decisions into the constitutional laws of the Kingdom. 6. ‘It is in our power to end controversies’ (C 417). 7. Leibniz to Conring, March 19th 1678 (A II 2 402; Frémont 2001: 146); and to Philipp, January 1680; A II 1 508; GP 4 286. 8. See Foucher de Careil, letter to Lescoeur, published in le Correspondant, September 25th 1852, vol. XXX (the Systema was announced in the Des Controverses). 9. On this important Council, which began in Basel and continued in Ferrara and Florence, see DA 260 note n and the corresponding text. 10. Mathesis universalis, Praefatio; GM 7 51.

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11. It is worth recalling here Chaïm Perelman’s thesis (1958) that juridical logic is the counterpart of formal logic, which he shows by formulating the corresponding logical relationships and quasi-logical relationships. Bossuet applied a “hard” logic, by implication, where Leibniz brought to bear a “soft” logic, by co-incidence: so for example in the interpretation of Tobias it was improper to translate an incidence into an inference. Or again, compatibility does not mean identity: for Bossuet, “not obliging us to depart from our principles” was the same as entering into our principles; for Leibniz, that meant recognizing other principles but not following them. 12. In Leibniz’s manuscript, this letter is dated June 1686, while in Arnauld’s printed correspondence it is dated July 14th 1686. 13. Or debatable; but, as already stated, the word controversy and its derivatives have been preferred.

References Bossuet, J.  B. 1671. Exposition de la doctrine catholique sur les matières de controverse. Paris. Bossuet, J. B. 1864. Recueil de Dissertations et de Lettres concernant un Projet de réunion des Protestants d’Allemagne, de la Coinfession d’Augsbourg, à l’Église Catholique. Œuvres complètes, vol. XVIII. Paris: Vivès. Leibniz, G. W. 1680. Des Controverses. A IV 3 204–212. Leibniz, G. W. 1688–1690. Projet et essais pour arriver à quelque certitude pour finir une bonne partie des disputes, et pour avancer l’art d’inventer. A VI 4 963–970; DA 275–283. Leibniz, G. W. 1698. Projet de Leibniz (au nom de l’abbe de Lockum) Pour faciliter la reunion des Protestants avec les Romains Catholiques. FC 2 172–193. Leibniz, G. W. 1903. Introductio ad Encyclopaediam Arcanam. C 511–515; A VI 4 525–531; DA 219–224. Leibniz, G. W. 2001. Discours de metaphysique et autres textes. Edited by C. Frémont. Paris: Garnier-Flammarion. Parmentier, M. 1989. Leibniz: Naissance du calcul différentiel. Paris: Vrin. Pirot, Abbé. 1912. De l’Autorité du concile de Trente. Unpublished dissertation, first edited and published by Ch. Urbain. Paris: L. Letouzey. Perelman, C. and Olbrechts-Tyteca. 1958. Traité de l’Argumentation: La Nouvelle Rhétorique. Paris: Presses Universitaires de France.

Name index

A Ahnert, T.  150, 165 Alberti, V.  263 Alexander, H. G.  52, 70 Apollonius  38, 46 Archimedes  25, 125, 302 Aristotle  112–113, 115, 121, 125, 127–128, 139, 163, 165, 178, 184, 192–194, 227, 248–249, 262 see also Aristotelian Arnauld, A.  56, 61, 70, 184, 201–202, 205, 207, 218–219, 239, 304, 334–335, 339, 343 Augustine  203, 300, 307 Ausin, T.  298 Avicenna  152, 164 Azon  230 B Babbage, C.  8, 16 Barrow, I.  13 Baruzi, J.  297, 301, 306, 311 Bassianus, J.  230, 241 Bayle, P.  29, 176, 188, 218–219 Becher, J. J.  118 Beeley, P.  127 Berlich, M.  223, 237, 239 Bernoulli, Jakob  29, 46, 48 Bernoulli, Johann  4–6, 12, 14, 28, 29, 77–78, 80, 90, 93, 172 Bernoulli, Jakob & Johann  33, 44 Biringuccio, V.  125 Bitbol-Hesperiès, A.  126 Blank, A.  169, 172 Boineburg, P. W. von  249, 267 Bombelli, R.  37 Boole, G.  28

Bossuet, J.-B.  189, 298, 303, 306, 321–333, 335–337, 340 Boucher, P.  223 Boudri, J. C.  142, 165 Boyer, A. L.  46, 105, 230 Boyle, R.  110, 112, 114–118, 120–122, 125, 128–130, 138, 141, 149–152, 154, 164–165, 180–181 Brather, H.-S.  273 Breger, H.  14, 116 Breteau, J. L.  110 Brown, G.  62, 67–68, 70 Brown, S.  181, 218–219 Bucer, M.  277–278, 293 Buchdal, G.  164 Burchell, H. B.  126 Burgh, A.  307–308 C Cabrillac, M.  224, 232, 241 Cajori, F.  52 Calixt, G.  275, 279, 288, 325 Cantor, G. F. L. P.  21, 25 Carondelet, J.  300 Carpzov, J. B.  237, 239 Carvallo, S.  101, 117, 125–126 Castellio, S.  315 Catelan, F., Abbé de  9, 37, 61, 63 Cauchy, A.-L.  1, 26–27 Cavalieri, F. B.   44 Celsus, A. C.  113 Chareix, F.  33, 46 Chuno, J. J. J.  274 Clericuzio, A.  128–130 Costabel, P.  48, 61, 65, 68–70 Crusius, C. A.  253, 260, 269 Cudworth, R.  103, 110, 114, 120–122, 127–128, 130–131

D D’Alembert, J.  16–17, 52–53, 58–59, 64–65 Dalton, H.  273 Danckelmann, E.  247 Dascal, M.  20, 22, 29, 51, 65, 128, 137, 145, 150, 159, 161–165, 262, 297–298, 304, 309–310 Davis, E. B.  131, 165 De Duillier, F.  8, 13 Deleuze, G.  316 Delius, W.  273 Democritus  111, 194 De Morgan, A.  8 Des Bosses, B.  182 Descartes, R.  2–3, 6, 12–13, 17,  20, 25, 29, 34, 36–37, 44, 46–48, 52–57, 61, 63, 65–70, 84, 103–105, 107–108, 110–111, 114, 116, 120, 125–128, 130, 140–142, 144–146, 148, 163–164, 184, 188, 194, 197, 203, 209–212, 216–219, 304–305, 311, 334 see also Cartesian Des Chene, D.  125 Desgabets, R.  201, 219 Des Maizeaux, P.  219 De Tournemine, R. J.  182, 184 De Volder, B.  77–78, 80, 89–90, 93–94, 98 De Witt, J.  40, 48 D’Huisseau, I.  300, 303, 316 Dijksterhuis, E.  141–142 Döring, D.  245, 254, 256, 262, 266, 268 Dreyfus-Le Foyer, H.  126 Duchesneau, F.  93, 96, 109, 124–128

346 Name index

Duraeus, J.  280–282, 291 Durie, Dury  see Duraeus E Einstein, A.  23, 29 Entner, H.  247 Erasmus van Rotterdam, D.  300, 308 Euclid  8, 25, 302 Euler, L.  44, 162 F Fermat, P.  102, 106, 127, 140, 144–146, 162–164 Feyerabend, P. K.  163 Fichant, M.  37, 80, 90–91, 93, 126, 128 Firt, E.  128, 137 Flacius  284 Fleming, D.  126 Foucher, S.  68, 187–192, 196, 198–221, 322, 325–326, 343 Frémont, C.  125, 128, 321, 324, 340, 343–344 Frerichs, J. B.  120 Freudenthal, G.  65, 67, 69–70, 77, 92 Friese, L. M. D.  262 G Galilei, G.  33–36, 46, 55–56, 67, 127, 219 Gallois, J.  9, 29 Galloy  see Gallois Garber, D.  69 Gassendi, P.  141, 194 Gil, F.  298 Gilson, E.  126 Girard, P. F.  240, 242 Goldenbaum, U.  185, 287 Goldstine, H.  164 Grandi, G.  7 Granger, G. G.  18–21 Gregory, A.  62, 68, 106 Grimarest  117 Grotius, H.  242, 249, 261, 299, 315–316, 332 Grua, G.  238, 242, 311 Guattari, F.  316 Guericke, O. von  125

H Habbeus, C.  261 Hadamard, J.  29 Hamilton, W.  162 Hankins, T. L.  59, 65 Harvey, W.  104–106, 126–127 Helden, A. van  33–34 Helmont, J. B. van  103, 110–111, 115, 118 Hilbert, D.  25 Hippocrates  104, 111–113, 152 Hirsch, E.  254 Hobbes, T.  120–121, 141, 315 Hoffmann, F.  103, 112–113, 127, 266 Hübener, W.  273, 281, 289–290, 292–293 Hunter, M.  131 Hutton, S.  130 Huygens, C.  8, 12, 21, 28, 33–34, 36–48, 56–57, 60, 62, 67–70, 81, 84, 125, 128, 141, 163 I Iltis, C.  65, 68–70 J Jablonski, D. E.  265, 273–283, 285, 287–290, 293 Jacobi, C. G.  162 Justinian  225–227, 229, 232, 235–238 K Kant, I.  53, 260 Kepler, J.  34 Knobloch, E.  242 L Laerke, M.  297, 298 Lagrange, J.-L.  162 Lagrée, J.  300, 315 Lamy, F.  169–177, 185, 219 Lantin, J. B.  206 Lemons, D. S.  162 Lenoble, R.  120 L’Hôpital, G. F.  7, 9, 33, 43, 45, 46 L’Hospital  see L’Hôpital Liceti, E.  177–179

Locke, J.  114, 122, 299 Ludewig, J. P.  262 Ludolph de Cologne  25 Luther, M.  286, 297, 311, 327 M Mach, E.  52, 68 Mahrenholtz, M.  125 Maillard, J. E.  130 Malebranche, N.  45, 48, 63–64, 69–70, 121, 141, 153, 194, 197, 204–205, 207, 211, 219 Masham, D.  122 Maupertuis, P.-L. M. de  162 Mazeaud, H. L.  226, 239–241 Mendonça, M. de  188 Metzger, H.  107, 110, 117, 130 Molanus, G.  275–276, 278–283, 288–289, 291, 322–324, 327, 335 Monge, G.  26 Montucla, J.-E.  8 More, T.  103–104, 110–111, 114, 121–123, 126, 128, 152, 165, 178–179, 225 Morus  see More Moses  111, 300 Mouly, C.  224, 232, 241 Monzambano, S. de  257–259, 262, 268–269 see also Pufendorf N Nachtomy, O.  185 Naert, E.  312 Newton, I.  7–8, 12–13, 15–16, 28–29, 33, 44, 46, 52, 62, 66, 79, 129, 142, 245 see also Newtonian Nicholas of Cusa  169 Nieuwentijt, B.  13–15, 29, 42, 48 Niewentiit  see Nieuwentijt O Obrist, B.  129 Oldenburg, H.  11 Osler, M. L.  131 P Pagel, W.  126



Palaia, R.  128, 165, 218–219 Panofsky, E.  34 Papin, D.  61, 69–70, 75–98, 125 Parmenides  111, 194 Parmentier, M.  324 Pascal, B.  11, 44, 46, 48, 125 Peacock, G.  16 Pellisson, P. F.  290, 297, 316, 323, 325–326, 328, 333, 335 Perelman, Ch.  344 Perrault, C. & P.  105, 127 Petit, A.  130 Phemister, P.  169, 185 Placcius, V.  247, 262 Placentin  230, 241 Plato  131, 182 see also Platonism and neoPlatonic Plochmann, G. K.  126 Plotinus  169 see also neo-Plotinian Poncelet, J.-V.   1, 26 Popkin, R.  219 Pseudo Geber  115–116 Pufendorf, S.  245–269, 283, 315 see also Monzambano Pythagoras  111 R Ranea, A. G.  77–78, 90, 93, 96 Rather, L. J.  70, 120, 175, 182, 185, 228, 282, 285, 322 Rauchbar, A.  223, 237, 239 Rémond, N.  126, 170, 182–183, 185 Rey, A.-L.  75 Ritter, P.  245

Name index 347

Robinet, A.  48, 122, 219, 298, 312–313 Rodis Lewis, G.  126 Rogers, G. A. J.  110 Rojas y Spinola, C. de  298, 322 Rolland, H.  230 Rolle, M.  8–9, 12, 46 Rozemond, M.  182 Rudolph, H.  251, 265, 273, 287, 292 S Scaliger, J. C.  177–179, 181 Schelhammer, G. C.  110, 121, 128, 130, 150–156, 158–159, 165 Schlecta, J.  300 Schneider, H.-P.  254 Schneider, M.  106 Schönfeld, M.  52–53, 65 Selge, K.-V.  273 Sennert, D.  177–179, 181 Serfati, M.  1–2, 6, 17, 20, 23, 28–30 Sève, R.  242 Shimony, I.  51 Smith, J. E. H.  169 Snell, W.  138, 140, 142, 144, 148, 163, 164 Snellius  see Snell Spinoza, B. de  141, 301, 305, 307–308, 315 Stahl, G. E.  101–105, 107–130 Struik, D.  44 Sturm, J. C.  110, 121, 128, 131, 150–158, 164–165 Sykes, N.  280

T Thomasius, C.  248, 253, 266 Torricelli, E.  125 U Utermöhlen, G.  289 V Valla, L.  297 Varignon, P.  1, 7–10, 12, 17–19, 29, 33, 46 Varro, G. T.  300 Viano, C.  129 Viète, F.  2, 3, 25 Vigel, N.  223 Voltaire  316 Vorstius, C.  180 Vuillemin, J.  19–21, 28–29, 47 W Walenburch, A. & P. van  297, 316 Wallis, J.  7, 11–13, 56–57, 60, 68, 70 Wilson, C.  136, 141, 150 Wissowaty  297 Wolff, C.  1, 17–18, 29, 249, 253, 261, 263 Wren, C.  56–57, 60, 68, 70 Y Yourgrau, W.  165 Z Zentgraf, J. J.  268

Subject index

A a priori  19, 21, 76–78, 81–82, 84, 87–91, 93, 140, 148, 216, 227, 250–251, 286, 340   see also argument abrogate  229, 292 absolute – decree  255, 286 – disinterested love  312 – motion  61, 64 see also action – power  123, 131 – priority  228 – providence  111 – reality  183 – reason  326 – reference  228 – value  232 – will  292 abstract  147, 160, 204, 240 – a priori estimation  90 – effect  82 – entity  82 – formulation  24 – mathematics  66 – thought  174 acid  112, 116, 123 Acta Eruditorum  13, 38, 41–42, 48, 53, 75–76, 79, 83, 94, 97, 151 actio in se ipsum  79, 87, 89–91, 98 action  77, 79, 86, 91, 96–97, 99, 103, 178, 299 absolute moving  64 – and passion  60, 87 – and effection  89, 98 aware of itself in  114 desperate  248 direct  111

divine  87, 173, 215, 256 emanative  216 express the  80 formal  77, 79 – libre  99, 173 – of gravity  81 in itself  see actio in se ipsum instantaneous  35 instinctive  27 intangible  103 least  162, 165 moving  see motive motive  69, 76–78, 84–85, 87–92 power and  89, 91 rei uxoriae  227, 240, 242 rotating  34 violent  90, 98–99 ad hoc  14–15, 83, 209–210, 212, 215 adversary  93, 110, 137, 145, 151, 164, 193, 202, 251, 283, 285, 305, 307, 308 affection  12, 130, 141, 150 aggregate  51, 111, 114, 118–119, 203 agreement  84–86, 90, 95, 146, 160–161, 182, 192, 197–198, 201–204, 206, 219, 231, 237, 265, 274–275, 279, 288–289, 329 see also disagreement air  95, 112, 118, 127, 129–130, 143 alchemy  135, 180 algebra  10, 18, 26, 28, 38–40, 45, 147 algorithm  3–4, 21, 42, 109, 337 amour – de soi  312–314 – mercenaire  275

– propre  312 querelle du pur  312 analogy  2, 5–8, 10–11, 15, 106–107, 110, 112, 116, 124, 145, 147, 160, 162, 292 analysis  9, 16, 18, 33, 38, 44–45, 55, 109, 116–117, 149, 203, 208–209, 216, 225, 312 – gradaria  339 anatomy  104–105, 108, 110, 114–115 animal  105, 109, 112, 117, 127, 129–130, 139, 177, 183–184, 203, 211, 268 see also brute – machine  104, 107–109 animism  103–105, 110–111, 114–115, 119, 121, 124 anonymous  246–247, 288, 316 anthropology  104, 110 anti-Cartesian  188, 287 see also Cartesian Antichrist  252, 303 antiquity  287, 305–306, 312 aqueous  123 see also water arbitrary  147–148, 154–156, 165, 175–176, 227, 229, 231, 236, 254, 268 see also principle of non-arbitrariness architectonic  20–22, 79 argument  10, 13, 28, 41, 55–57, 62, 68, 77–78, 80, 84, 86–87, 93, 98, 127, 129, 148, 158, 176, 180, 194, 208, 211–216, 218, 229, 234, 240, 252, 255, 257, 276, 285, 288, 293, 303, 306– 308, 313, 316, 322, 325, 327, 330, 332–333, 335, 337–340, 342 argumentation  9–10, 14, 16, 80, 82–83, 89, 91, 124, 204, 225, 251, 276, 281–282, 285–287, 292, 308, 322, 344

350 Subject index

argumentative  62, 66, 76–80, 82–84, 87–88, 91–92, 98, 107, 152, 154–155, 165, 191–195, 209, 214, 307–308, 310 Aristotelian  103–104, 106, 121–122, 128–130, 150–151, 169–171, 177–178, 182–185, 192, 227, 249, 253, 260, 263–264, 334 arithmetic  109, 267, 337 art  108, 120, 130, 179, 228 – of discovery  4 – of combination  3–4, 8, 10–11, 45, 116, 171, 179, 307 – of conferring  321 – of controversy  51, 61, 65, 297, 322, 333–334 – of goodness  238 – of proofs  338 – of reconciliation  120 articles of faith  276, 303, 329 fundamental  276, 329, 342 non-fundamental  329 artificer  141 artificial  104, 107, 109, 127, 140–141, 194, 196, 209, 211, 253 astronomy  34, 116, 268 atom  122, 196 atomism  37, 192, 194, 196, 204 Augsburg Confession  276, 278, 280, 283, 312, 332 automaton  141, 150 axiom  25, 56, 60, 63, 68, 83, 85, 116, 122, 130, 202, 204 B balance  218, 232–235, 237–238, 303, 310, 316–317, 324, 335, 338, 340 barbarian  258, 306 Baroque  245 benefit  9, 122, 162, 226–227, 230, 232–235, 241, 336 best possible world  60, 62, 107 biblical  252–254, 265, 286, 303 see also Scripture biology  102, 109, 124 blind thought  21–22 blood  105–106, 112, 114, 123, 127, 251, 278, 287

body  34–36, 48, 52–58, 60, 66–67, 70, 81, 86–87, 89, 91, 94, 96–97, 101–112, 114–116, 118, 124, 128, 131–132, 138, 140–141, 153, 157, 169–186, 189–191, 194–198, 203, 205, 210, 214–215, 218–219, 235, 251, 277–278, 281, 287–288, 293, 303 see also corporeal and subtle brute  71, 196 see also animal C Cabbala  301, 312 calculus  2–10, 12–15, 17–18, 20–22, 29, 33–34, 37–46, 48–49, 162, 245, 309 Old  3–4 Calvinism  252, 266, 273–275, 276–283, 286–291, 293, 327 Cambridge Platonists  121–122, 165 see also Platonism caritas  298–299, 313–315  see also charity Cartesian  4, 9, 19, 37, 43, 45, 51–55, 57, 59, 61–64, 67–68, 70–71, 75–76, 78–81, 86, 88, 94, 102, 107, 109, 112, 116, 121, 123, 141, 170, 182, 184–185, 188, 191, 193, 206, 210, 251, 287–288, 292–293, 304–306, 308, 334 casuistic  310 Catholic  180, 251–252, 255, 257, 266, 274, 276, 278, 287, 297, 299–300, 302–304, 306–307, 312, 316, 324–326, 330–332, 334–336 Catoptrics  138, 143, 163 Causa impulsive externa  292 causal  77, 81, 103, 105, 144, 146, 181, 185 causality  87, 102–104, 106, 108, 112, 120, 122, 124, 161, 191, 203, 205, 215, 218 causation  140–141, 160, 162, 164, 173–174 cause  9, 54, 60, 66, 70, 79, 81–84, 88, 94–95, 98, 102, 110, 115–116, 131–132, 160,

175, 181, 183, 201, 203, 226–227, 240, 247, 249, 275, 279, 285–286, 289, 304, 306, 313, 328 efficient  41, 45, 77–78, 80, 87, 89–92, 97, 103–104, 106–108, 111, 117, 119–124, 138–140, 142, 144, 148–150, 156, 159, 161–163, 178 final  22, 38, 62, 75, 77, 80, 87, 89–90, 92, 103–108, 111, 117–122, 138–146, 148–149, 156, 159, 161, 164, 188–189, 197, 205, 210, 212, 215–216, 234, 256, 281, 298, 324, 326, 333 centrifugal  12, 34, 36–37 centripetal  12 chaînette  42, 43, 219 character  9, 15, 17–18, 20, 22, 27, 147–148, 197, 202–204, 212–215, 218, 225, 232, 250, 255–257, 263, 305, 309  see also sign Characteristica  130, 309 charity  231, 238, 284, 298–300, 310–311, 313–315, 326, 329, 342 see also caritas chemistry  101–107, 109, 112–113, 114–119, 123–126, 129–130 chiliogon  20, 29 Christian  29, 111, 122, 248–255, 258, 260–264, 266–267, 275–276, 278, 284–286, 290, 297–298, 300, 303, 323, 332, 342 Christianity  137, 250, 252–254, 258, 260–261, 275, 277, 300–302, 326, 331 reunification of  251, 261, 265, 297 Christianization  252 Christology  276–277 Church  138, 250–252, 258, 264, 269, 274, 276, 278, 280–281, 287, 291–292, 297–299, 302–304, 306, 316, 322–333, 340–343 circle-squarers  25 circular  35–36, 106, 228, 236



circularity  116, 227–229 circulation  105–107, 114, 123, 127 see also blood and heart civitas  259, 300 clarity  154–156, 165, 198, 280, 301 Clave errante  303 codification  21, 231 coexistence – of opposites  139, 149 co-extension – of souls and bodies  170, 177–181 combinatorial  2–4, 6–7, 10–11, 16, 20 see also art of combination combustion  103 see also fire commentators  57, 69, 115, 228, 249, 304, 322 communication – between substances  65, 187, 189–190, 212 – of movement  63–65, 69 comparatio  see comparison comparison  113, 125, 127, 148, 156, 159–162, 165, 188, 238, 338 compensation  84, 95, 228, 234, 236, 242 complementation  60, 115, 120, 142, 146, 230 composite  116, 169, 171, 175, 181–185, 209, 213, 237 composition  4, 103, 109–110, 209, 330 concession  68, 76, 84, 209, 327 conciliation  137–140, 142, 144– 147, 152, 154, 156, 159–161, 229, 279 see also reconciliation and irreconcilable conciliator  165, 193 conciliatory  137, 146, 152, 170–171, 175, 182 concomitance  195, 197, 201–202, 205–206, 209–211, 213, 325 Confession  188, 250–251, 276, 278–281, 283–284, 287–289, 312, 325, 332 see also Augsburg Confession

Subject index 351

confused  7, 61, 179, 197, 259, 267, 301, 307, 315 – perception  170–177, 182–185 connection  20, 159–161, 164–165, 285 connexio  see connection consensus  16, 85, 231, 275–276, 284, 291, 331 conservation  19, 29, 37, 53–65, 67–71, 76, 78–79, 82–84, 86–92, 97, 103, 105–106, 109, 216 consubstantiation  341 context – of discovery  96 – of justification  96 contingent  21, 26, 30, 256, 325, 338, 340 continuity  1–2, 10–11, 17–30, 63–64, 70, 107, 109–110, 112, 116–118, 177, 230, 339 continuous  11–12, 15, 17–19, 22, 24, 27–28, 30, 33, 181, 185, 201–202, 260, 303 contradiction  10, 14–15, 19, 83, 137, 161, 202, 228–229, 241, 278, 286, 289, 307 contradictory  7, 137, 139, 142, 225, 228 controversiable  342 controversial  62, 139, 193, 223, 253, 275, 283, 285, 287–288, 297, 342 controversialist  65, 297, 321–322 controversy  1, 9, 12–13, 15, 34, 37, 41, 44, 52–53, 59, 62–64, 66, 68–73, 75–76, 79, 81–84, 86–88, 90–93, 95, 97, 101–102, 105, 107, 111, 113, 117, 119, 122–125, 128, 137–138, 146, 158–159, 162–166, 170–171, 177, 188–189, 199, 201–202, 207, 216–217, 223, 232, 239, 245, 251, 260, 265, 268, 274, 278, 282–283, 287, 289, 291–292, 298–299, 304, 306–311, 315– 316, 323–330, 332, 335–344  see also art of controversy convenientia  see comparison

conversion  63–64, 69, 84, 88, 90, 273–274, 304, 334 corporeal  60, 66, 127, 150, 153, 158, 163, 169–171, 177–178, 191, 202, 213 see also body correspondences  13, 78, 80, 88, 90, 162, 297 cosmological  106 Council  275, 303, 306, 323–325, 327–329, 331–333, 337, 343 Creator  67, 261, 268 criticism  14, 34, 37, 51, 55, 63, 65, 68, 84, 102, 113, 121, 124, 192–193, 198–199, 201, 207– 217, 219, 245–248, 250–251, 253, 262, 264, 278, 283, 288, 336 curve  7, 11–13, 15, 20, 22, 24, 26, 39–44, 47–48 D damnation  274, 279 de maximis et minimis  106 debate  13, 15, 52, 65, 75–77, 84–85, 95, 101–102, 110, 112, 120, 125, 128, 138, 149–152, 154, 156, 165–166, 192, 199, 211, 217, 250, 253, 257, 265, 298, 303, 321, 323, 325, 343 see also argument decision  176, 201, 205–206, 231, 240, 246, 251, 265, 285, 321–322, 325, 331, 338, 342 decomposition  115 de-dichotomization  152–154, 156–158, 161 see also dichotomization and dichotomy deduction  329, 330 demonstrable  323, 340–341, 343 see also indemonstrable demonstration  4, 7, 10–11, 27, 41, 53, 55–57, 62–63, 66, 68–69, 76–78, 83, 86–93, 95, 116, 124, 138–139, 180, 195, 214, 216, 268, 308, 321–322, 330, 337, 339–340, 342–343 demonstrative  75–76, 78, 82, 91, 124, 196, 304, 325, 337–338, 342

352 Subject index

de-ontologization  196, 217  see also ontology de-personified  122 derogatory  119, 230–231 de-substantializing  197 dialectic  28, 304, 338 dialogue  87, 101–102, 124, 280, 292, 321–323, 332, 334 dichotomization  152–153, 157–158 see also  de-dichotomization and dichotomy dichotomy  93, 140, 142, 152, 154, 156–157, 164–166, 300 differential  3–4, 6, 12–14, 16–17, 28, 33, 37–38, 40–42, 45 differentiation  2, 5–6, 12, 28, 38, 42–43 diffusion  78, 98, 145, 148 digestion  106, 110, 117, 119 dioptrics  138, 143, 163 diplomacy  188, 282, 322, 328 disagreement  104, 110, 146, 158, 298, 308, 326, 328 see also agreement discovery  6, 12, 16, 18, 30, 96, 106, 126, 140, 142, 162, 191, 331 see also art of discovery discussion  12, 18–19, 33, 37, 51, 59, 62, 65, 67, 69–70, 77, 79, 82–84, 87, 91, 93, 98, 101–102, 126, 139, 143, 151, 164–166, 189, 194, 201, 210, 212, 230, 246, 251, 264–265, 273, 275, 280– 281, 284, 286–289, 297–98, 307, 309, 328–330, 332, 337  see also argument disinterested  310, 312, 335 disputatio  243, 335 see also dispute dispute  13, 52, 65, 87–88, 95–97, 146, 154, 202, 233, 245–251, 253–254, 281, 297–301, 307– 310, 315, 321, 336, 339, 340, 344 see also argument, disputatio, and disputing disputing  95, 253, 300, 307, 309, 321 see also argumentation and art of disputing dissent  251, 276, 279, 310

divine  21–22, 62, 67, 107, 109, 120, 151, 153, 155, 157, 173–174, 179–180, 184–185, 205, 215, 250, 252, 254–255, 261, 264–265, 267, 277, 282–283, 285–287, 291–292, 300, 302, 328, 330, 334, 342 dolus  234–235 dowry  225–227, 229–230, 236–238, 240, 242 dualistic  119 dynamics  10, 12, 46, 52, 57, 59, 61, 63–64, 66, 68–70, 75, 77–80, 83–86, 88–91, 94, 117, 121, 124, 192, 205, 211, 215, 217 E eclecticism  150, 164, 334 ecumenical  273, 276, 280, 282, 285, 289, 292, 298, 323–325, 327, 329, 332 effata  122 effect  35, 46, 55, 58, 60, 70, 75–77, 79, 81–86, 88, 90–91, 93–97, 103, 108, 110, 116, 120, 122, 130, 141, 150, 153, 160, 183, 209, 226, 235–236, 251–252, 275, 281, 299, 336 effection  89, 98 efficiency  41, 43–44, 46, 102– 103, 105, 110, 120, 123 see also cause, efficient elastic  56, 59, 64, 69, 106  see also inelastic elector  246, 257, 263, 274, 290 electoral  274–275, 280, 290 ellipse  24, 30 eloquence  321 emanation  169, 174, 179, 184–185, 216 Emperor  226, 256–259, 268– 270, 278, 290 Empire  166, 245, 256–262, 268–270, 274, 276, 322 empiricism  250, 260 encyclopaedia  125, 164 energy  58, 107, 123 Enlightenment  72, 245, 248– 250, 253, 259–261, 298–299 entelechy  110, 121, 122, 157, 171, 182, 184

entity  19, 43, 52, 82–83, 123, 129, 131, 170–171, 174, 177, 179, 181–183, 185–186, 213, 257, 259 envelopment  109 epistemological  1–2, 5–6, 10–11, 25–26, 43, 106, 112, 114, 116, 161 epistolary  88, 198 see also correspondences equation  16, 28, 36–44, 46–48, 56, 157 equity  225, 231–232, 241–242, 311, 313–314 evangelical  275–276, 290 exception  16, 67, 156, 224–225, 229–233, 246, 260–261, 332 excommunication  303 excretions  103, 105, 114, 123 expectancy  23, 242 expedient  323–326, 335 experience  21, 23, 63, 67, 78–79, 95, 118, 124, 144, 174, 192, 266, 279, 339 experiment  118, 335 experimental  26, 75, 79, 87, 91, 102, 107, 115, 118–120, 123–125, 131, 151 explanatory  76, 78, 109, 155, 163, 165 expression  11, 26, 30, 34, 38, 40, 66, 111–112, 114, 120, 123, 146–147, 149, 161, 165, 176–177, 198–199, 215, 263, 298–299, 304, 306, 334 extension  14, 28, 37, 53, 66, 70, 91, 93, 153, 162, 169–170, 172, 174, 177–182, 190–191, 197, 201–205, 208, 210–211, 213–214, 217, 226–228, 232, 283, 338 external  54, 59, 69, 90, 105, 108, 112, 153–156, 173, 175, 179–180, 184, 219, 231, 328 F faith  93, 122, 252–253, 255–256, 260–261, 264, 266, 275–276, 283–284, 290–292, 300, 303, 306, 308, 312, 324–333, 339–340, 342 see also articles of faith



federation  259 fermentation  104–107, 114, 117, 123, 125, 127 finalism  120 finality  102–103, 105–106, 110–111, 121–122 finite  5, 11, 15–16, 20–21, 185  see also infinite fire  117, 125–126, 175, 280, 299, 301 see also combustion and igneous flattering  202, 206–207 flesh  116, 251 fluxions  13, 16 force  6, 34–37, 41, 46, 49, 52–54, 56–59, 64–65, 69, 73, 76–79, 82–86, 90–97, 104–106, 108, 112, 117–119, 121–123, 127, 138, 145, 151–153, 157, 161, 169, 173–174, 181–182, 184–185, 193, 196, 203, 205, 211, 215–216, 252–254, 258, 261, 309, 327, 329 motive  55, 60–62, 67–68, 70, 75, 81, 157 of attraction  35–36 formal  43–44, 75–77, 79–82, 84–91, 93–94, 98–99, 104–105, 108, 118, 159, 178–179, 181, 299, 309, 326, 328, 332, 344 formalists  104 formalization  27, 84–85, 88, 315 formula  3, 11, 29, 59–60, 149, 235, 253, 290, 326, 330, 340 formulation  5, 24, 27, 76, 81, 83, 90, 98, 103, 127, 162, 165, 232, 276–278, 283, 311 foundation  7, 9, 10, 12–13, 15–16, 22, 79, 83, 90, 101, 119, 124, 160–161, 173, 183, 193, 201–202, 227, 241–242, 251, 264, 267–268, 276, 285, 316, 339 function  17, 21, 24, 27–28, 30, 33, 41, 75–77, 82, 102–103, 106–107, 110–112, 117, 124, 169, 174, 181, 191, 197, 214, 224, 305 G Gallican  322, 327, 332

Subject index 353

generality  45, 230 generalization  8, 28, 310–311, 314–316 generation  3, 16, 44, 177, 203 Generi per speciem derogatur  224, 232–233, 235 geometer  8, 10, 19, 21, 26, 42 geometrical  3, 6, 16, 26, 30, 33, 35, 37, 40, 44–46, 53, 60, 90, 144, 147, 153, 179, 308, 337, 339 geometrization  33, 45 geometry  6, 11, 16, 18–19, 25–26, 35, 38, 40–41, 43–45, 47, 66, 109, 143–144, 147, 163, 204, 267, 309, 337 German  72–73, 150–151, 245, 249, 256–262, 269–270, 274, 278, 322, 326 Glossators  228 God  20–23, 53–54, 57, 60, 66–67, 70, 87, 89, 107, 111, 120–122, 125, 128, 131, 140–141, 150–151, 153, 155–157, 164, 172–176, 179–180, 184–185, 196, 201–203, 206, 209, 213, 215, 251–256, 261, 264–267, 269, 274, 277, 282, 285–287, 291–293, 298, 300–301, 303, 306, 312–313, 329–330, 334, 336, 340, 342–343 see also divine Golden Rule  284, 297–299, 310–316 grace  266, 276, 286–287, 292–293, 327 gravity  7, 33, 35, 75, 77, 81–82, 84, 88, 90–91, 106 see also force Greek  119, 306, 327 H hard cases  223–243 harmony  103, 111, 122, 124, 148, 161, 170, 175–176, 182–184, 195, 197, 214–215, 218, 238, 248– 249, 251, 256, 266, 313, 336 health  104, 111, 205, 254, 288 heart  14, 90–91, 105–106, 110, 125, 141, 240, 280, 288, 290 heresy  284–285, 287, 300, 325–326, 328, 332

heretic  283–284, 287, 299–300, 324, 327–328 heterodox  284–285, 289  see also orthodox heterogeneous  104, 107–108, 112–113, 123, 145 see also homogeneous heuristic  85, 107, 124 Hippocratic  104, 112–113, 121 history  3, 6, 17, 30, 33, 44, 48–49, 65, 112, 125, 128, 163, 185, 188, 192, 198–199, 201, 219, 229, 245, 257–258, 264, 269, 276–278, 285, 289, 304, 323, 326, 330, 334 homogeneous  107, 112 see also heterogeneous humanism  259 humanity  231, 250, 254, 260, 269, 277, 284 humors  105–107, 116, 123, 125 hybrid  161, 315 hydraulic  103, 124 hylarchic  107, 109–110, 123 hylemorphic  109 I iatrochemist  104 iatromechanim  103–104, 107, 113 ideal  17, 44–45, 82, 203, 215, 269 idempotent  15 igneous  103, 124 see also combustion and fire imagination  21, 46, 104, 108, 128, 141, 174, 192, 267 immanent  87, 120 see also inherent impact  54–59, 63–64, 67–70, 84, 96, 111, 150, 236, 254 imperceptible  84 imperfection  169–170, 173, 267, 284 implicit  223, 306 incomplete  41, 157, 170–172, 174–175, 177, 182–186, 206 inconsistency  153, 334 inconsistent  14, 37, 156, 196, 210 indemonstrable  340 see also demonstrable

354 Subject index

individual  51, 61, 66, 109, 115, 118, 122, 170, 179, 183, 185, 201, 233, 305, 309 individuation  179, 209 induction, strong  26 inductive  212 inelastic  57–59 see also elastic inert  54, 70, 103, 108, 110, 112, 118–119, 130 infallibility  305, 316, 323 infinitangular  11 infinite  8–9, 11, 16, 18, 20–21, 27, 29, 31, 66, 107–110, 121, 124, 172, 179, 183, 185, 334 see also finite actual  109 infinitely  9, 11, 14–16, 30, 35, 37, 43, 115, 204, 342 infinitesimal  7–10, 13, 16, 18, 22, 25, 29, 33–34, 36–38, 44–48, 245 inherent  15, 103, 118, 122, 138, 151–153, 155–157, 161, 165, 183, 298, 306, 308 see also immanent innovation  298, 301–307, 315 insensible  80, 82–83, 88, 95, 98, 145 integral  12, 38, 46, 48 integration 28, 47 intension  91, 93 interaction  53, 70, 77, 110, 139, 141, 146, 189–190, 194–197, 210, 215, 218 interpretation  3–4, 6, 30, 40, 70, 77–78, 96, 105–106, 111–112, 117, 119, 124–126, 129, 163, 169–170, 178, 182, 214, 230–231, 255, 265, 277–278, 298, 308, 330, 344 intransigence  323–324 intra-protestant  251, 274 intuition  20–21, 25, 28, 38, 113–114 invisible  84, 86, 261 irenic  137, 275, 279–280, 284, 292, 298, 332–335 irenicism  289, 321, 323, 342 irrational  34, 37, 255 irrationality  155–156

irreconcilable  137, 145, 151–152 see also conciliation irreducible  108, 113, 116–117, 323, 332 isochronism  34, 42, 46 J Journal des sçavans  2, 171–172, 174, 185–189, 198, 200–201, 207–208, 213, 218, 220 juridical  137, 223–225, 228–231, 236–238, 253, 264, 301, 309, 316, 325, 329, 338, 342, 344 jurist  151, 223, 250, 281, 321, 326–327, 330–331, 337, 343 K kernel  88, 180, 249–251 kinematics  46 L La place d’autrui  310 Last supper  277 law  67, 70, 153, 157, 236, 245, 249, 252, 254–256, 261, 264, 267–268, 299–300, 323 see also hard cases Canonic  241 Inherent  155 Justinian  237 – of conservation  58 – of expression  165 – of nature  53, 231, 306, 315 – of refraction  138, 140, 142, 144, 148, 163–164 positive  223, 231 quantification of  223, 235 reorganization of  223, 225, 229, 231–232 Roman 230 Saxon 237, 243 laws of motion  46, 61, 64, 151 legitimacy  10, 33, 59, 62, 105, 303, 316, 321, 324, 326, 328, 330–332 life  7, 102–114, 117–119, 121, 123, 125, 130, 141, 200, 242, 245–252, 254–256, 261, 266, 269, 297, 338 see also living

light  12, 20, 35–36, 79–80, 88, 91, 141–145, 147–148, 151, 153, 159, 162, 164–166, 175, 178, 185, 196, 205, 212, 273 see also optics linguistic  147, 277 literal  3, 17, 28, 81, 310 living  56–62, 65, 68, 70, 76–79, 81–82, 85–86, 90–92, 101–104, 106–119, 123–125, 140, 153, 158, 171, 177, 183–185, 209, 213, 235 see also life logic  18, 30, 48, 79, 120, 138, 229, 250–251, 285, 297, 300, 302, 306–307, 309, 315, 323, 333, 336 hard  344 maximis et minimis  106 new  338 right  343 subtle  217 vulgar  338 logical  13, 60, 83, 86–88, 93, 101, 109, 139, 147, 212, 225, 227–230, 250, 261, 286, 305, 325, 329, 344 logoi spermatikoi  120 love  64, 95, 255, 275, 284, 286–287, 298, 301, 312–315, 322, 329, 342 Lutheran  251, 260, 274–275, 277–280, 289, 291, 311, 325 Lutheranism  249, 277, 280, 327 M machine  8, 38, 103–110, 124– 128, 140, 150, 183, 203, 309, 335 see also animal machine, mechanical, mechanistic mad disputing  300 see also dispute manducatio impiorum  278 material  37, 53, 66, 70, 104–105, 107–108, 112, 118, 120, 129, 145, 148, 152–153, 159, 179–181, 183, 190, 197, 204, 206, 210, 217, 236, 238, 250, 328 materialistic  104, 119–120 mathematical  1, 6–7, 9–10, 17, 19–23, 25–28, 30, 33–34,



37–38, 41, 44–46, 48–49, 59–60, 66, 75, 78, 80, 87–91, 102, 106–107, 109, 111, 113, 120, 122, 124, 128, 147, 152, 162–163, 322 mathematician  1–2, 7–9, 12, 14–17, 21–23, 26–27, 33, 44–45, 60, 146, 150, 162, 164, 333, 339 mathematics  1–2, 4, 6, 9–10, 15–20, 23, 25, 30, 32, 37–38, 41, 43, 45, 48–49, 66, 102–103, 107, 109, 112–113, 120, 130, 138, 154, 164, 192, 249, 324, 338 mathematization  33, 36–38, 45, 49, 78, 93 matter  9, 33, 43, 53–54, 57, 60–61, 63, 65–67, 69–70, 80, 82–84, 86, 88, 90–91, 95, 102–104, 108–112, 114–115, 117–125, 128–131, 141–142, 144–145, 151, 153–155, 163, 169, 173, 177,  179–184, 196–197, 200– 206, 212, 217, 219, 231, 237, 251, 253, 266, 280, 323, 325, 330–331, 335, 337, 342  see also material primary  157, 183 prime  171 secondary  157, 183–184 subtle  180–181 mechanical  44–45, 59, 78, 83, 95, 103–106, 108–110, 112–113, 115–117, 122–124, 128–130, 138–139, 141, 150, 152, 159, 163, 181, 197–198, 202, 218, 309  see also machine mechanically  6, 103–104, 109, 127, 163, 181, 191, 201 mechanics  8, 33, 38, 43–45, 52–53, 59, 75, 80, 102–103, 106, 111, 117, 124, 162, 201–202, 211, 215, 249 mechanism  7, 10, 45, 107–108, 116–117, 119, 122, 128–129, 151–152, 155, 177 see also subtle mechanistic  106, 116, 131, 138, 140–142, 150, 152, 156, 159, 177–178, 193

Subject index 355

medical  101–104, 107, 110–111, 113–115, 118, 123–125, 129, 151, 233, 241 medicine  101–104, 109–110, 112–115, 117–119, 124–125, 139, 162, 333 medieval  91, 94, 249, 256, 258, 260–261, 269 medium  38, 142–145, 164, 268 meta-controversy  146, 323  see also controversy metaphor  107, 149, 160 metaphysical  1, 9, 18, 20, 22–23, 25–26, 52–53, 58–60, 62–63, 65, 68, 70, 79–80, 89, 91–92, 101, 104, 110, 119, 121, 123–125, 131, 138–139, 146–147, 151–152, 155, 159, 161, 169, 182, 184, 193, 196, 211, 218, 310, 342 metaphysics  18, 20, 23, 60–62, 65, 79–80, 94, 109, 120–121, 124–125, 139, 142, 146, 161, 171, 177, 193–194, 204, 206, 215, 218–219, 249–250, 260, 264, 287, 338 meta-principle  1, 18 see also principle metempsychosis  183 meteorology  112 method  6, 13–14, 16, 22, 25, 38–43, 45, 47, 82, 85, 102, 112, 117, 124, 126, 137–138, 140, 142–144, 147–149, 154, 163– 164, 210, 223, 225, 227, 249, 253, 255, 275, 277–278, 282, 284, 287, 297–298, 304–305, 307–309, 315–316, 322, 324– 326, 328, 330–337, 339–340 méthode  see method methodology  1, 7, 24, 26, 28, 90, 117, 192–193, 195, 210, 215–217, 289, 305–306 metonymy  160 mind  20, 29–30, 33, 44–46, 61, 63–65, 78, 83, 131, 156, 158, 163, 165–166, 171–173, 176, 179–181, 183–185, 192, 195–196, 219, 252, 279–280, 293, 306, 332  see also soul minimum  143, 282, 340

miracle  67, 204, 212, 218, 252–254, 261, 293, 340 misunderstanding  45, 87, 126, 158 mix  103–105, 107–108, 115–119, 277 mixed  34, 38, 41, 80, 89, 101–102, 108–109, 111, 114–118, 123, 300 moderation  247, 291, 308–310, 315–316 modern  3, 7, 11, 14, 17, 21, 23, 28–29, 34, 49, 51, 58, 63, 102–103, 120, 125, 151, 170, 177, 192–196, 211, 218, 232, 245, 249, 253, 267, 306, 315 moment  5, 7, 8, 11, 23, 35, 77, 91, 188, 199, 331 momentum  57–60, 64, 69, 276 monad  73, 119, 122, 125, 146– 147, 154, 161, 183, 249, 263, 310 see also windowless monadology  65, 127, 249, 261, 263 moral  197–198, 203, 213, 215, 254, 265, 267, 310, 339, 342 mortgage  224–229, 236–240, 242 motion  16, 33–38, 44–46, 52–58, 60–64, 66–72, 83, 87, 90, 103, 106, 108–112, 128–129, 141, 147, 150–151, 153, 156, 159, 162, 178, 180, 225, 249 see also force, motive, and movement movement  18–19, 54, 66–67, 70, 76–79, 81–86, 89, 91, 93–97, 103, 105–106, 110–111, 116, 123, 126, 151, 175, 197, 205, 213, 215–219, 257, 260, 309, 314 see also motion multiplicity  118, 161, 169, 183, 276 mutatio  331 mystic  306 N Natura medicatrix  104, 113–114 nature  16, 19, 52, 54–55, 62, 79, 83, 89, 92, 95, 97, 99, 104, 107, 113–126, 131, 138–141,

356 Subject index

150, 152, 155–157, 159–163, 182, 189–191, 193, 196–197, 202, 204–205, 212–213, 218, 267, 305, 312, 340 insensible  88, 98 – of body  53, 127, 130 plastick  128–130 singularity of  213 necessity  25, 45, 77, 79, 87, 89, 131, 139, 160, 190, 193, 208, 218, 225, 234–235, 238, 240, 250, 255, 266, 279, 323, 326, 328, 339 negotiation  252, 322–326, 328, 332–333, 335, 337, 342 neo-Platonic  109, 120, 128, 169–170, 173, 179, 183–185 neo-Plotinian  120 Newtonian  16, 44, 52, 79 non natural  218 notation  6–7, 10, 12, 14, 20, 22, 28, 37, 147, 163 see also sign Nouvelles de la République des Lettres  17–18, 63 numerical  3, 5, 8, 14, 25, 109, 116 O objection  16, 63, 77–78, 93, 101, 175, 182, 204–205, 207–208, 214–216, 281, 288, 305, 307, 311 Occasionalism  153, 170–173, 175, 184, 195, 202, 211–212, 218 ontology  7–8, 10, 13, 15–16, 78, 91, 93, 146, 159–160, 174, 179, 193, 210, 217–218 see also  de-ontologization operation  2–3, 5, 12, 22, 28, 45–48, 54, 103–104, 107, 109–110, 112, 115, 119, 124, 127, 178, 180, 339 optics  106, 116, 138, 140, 142– 143, 145–146, 154, 163 organic  102–108, 111–114, 117, 123–124, 128, 169–171, 174–175, 180–185 organism  101–103, 107–108, 111–112, 116, 123–125, 128 orthodox  122, 249, 251, 277– 278, 284–285, 299–300, 306, 322, 331 see also heterodox

P papal  252, 299 papist  282, 305 parabola  24, 30, 36–37 paraboloid  11 paradox  1, 7–8, 10, 21, 77, 323, 332 paradoxical  8, 58, 108, 196 parallelism  18, 103, 108, 114 paralogism  9, 12 Paris Cabale  9 particle  35, 53, 111, 115, 130, 145, 162, 164 passion  60, 87, 126, 312 see also action passive  53–54, 70, 153, 157–158, 169–172, 179, 182–185, 212, 312, 326 path-difficulty  143–144 peace  250, 257–258, 279, 281, 283, 288, 300, 323 perception  29, 126, 129, 137, 161, 169–175, 179, 182–183, 185–186 perfection  54, 80, 93, 158, 173, 184–185, 254, 256, 267, 285–286 perpetual  62, 83, 125, 330–331 perplex case  195, 214, 223, 225–231, 236–239 personal  44, 151, 189, 200, 224–225, 227, 232, 234–239, 242, 247–248, 277, 279, 300, 312 perspective  14, 19, 51, 53, 78, 80, 88, 145, 147, 161–162, 170, 199, 214, 218, 236, 302, 310–311, 313–314, 336 perspiration  117 phenomena  34, 36, 38, 44–45, 59–60, 66, 103–105, 107, 110–111, 116–117, 121–122, 124, 127–128, 130, 138, 140–141, 148, 150–151, 162, 171, 182–184, 193, 197, 201–203, 210, 213, 215, 253–254 see also well-founded phenomenon phlogistic  117 physical  33, 36, 38, 43–46, 52–53, 59–60, 65, 68, 70–71, 79–80, 82, 89–90, 92, 102– 106, 108–111, 113–118, 120, 123,

138, 140, 145, 148–149, 162, 177–178, 184, 193, 196, 198, 203–204, 215, 218, 293 physiology  104–105, 110, 114 Pietism  253, 266 plagiarism  13, 15–16, 245, 264 plastick  see nature Platonism  103–104, 114, 121–122, 165, 170, 178 see also Cambridge Platonists and neo-Platonic plausible  132, 137, 177, 195, 210, 342 pluralism  318 plurality  88, 185, 211, 302 pneumatic  103, 124, 126 polemic  53, 57, 75, 102, 105, 110, 112–113, 121–122, 125,245, 247, 255, 262, 279 see also argument and argumentation politics  138, 235, 245–246, 248, 256–257, 259–260, 263, 269, 274, 287, 299, 308, 322–323, 333, 336 polygon  11, 18–20, 25, 29 Pope  252, 258, 303, 324, 327– 328, 343 see also papal positive  see law potency  169, 179 potentia  79, 92, 94, 249 power  2–3, 6, 19, 28, 37, 42, 45, 60, 67, 77–78, 81–83,  86–89, 91, 93–94, 97, 104,  115, 121, 123, 128, 131, 140, 151–152, 163, 173, 224, 231,  251–252, 258–259, 266– 269, 276, 298, 301–303, 335, 343 motive  84 predestination  252, 266, 276, 282, 286, 292 pre-established  103, 111, 122, 124, 170, 175–176, 182–184, 197, 215, 249 preformation  109, 123, 131 prejudice  141, 192–193, 209– 210, 212, 215, 264, 302–303, 305, 325 pre-Socratic  113 pressure  63, 103, 105–106, 124 presumption  143, 231, 302



principle(s)  see meta-principle Descartes’s  53 Fermat’s  102, 144, 165 – of clarity  154–155 – of conservation of quantity of motion  53, 65, 67 – of continuity  1, 10, 17, 23 – of inherent force  122, 151, 154–155 – of least time  164 Other principles  344 Our principles  344 Prior tempore potior jure  224, 236 priority  13, 15–16, 53, 165, 224, 226–230, 232–234, 236–238, 240–242, 245 private  45, 92, 187, 189, 198– 201, 207, 216–217, 245–246, 275, 290, 305, 307 privilege  223–227, 229–242 probability  30, 310, 336, 338–339 probable  223, 246, 323, 339, 342 proof  1, 11, 28, 36, 75, 78–80, 88, 114, 119, 124, 158, 172, 219, 231, 276, 279, 281, 287–288, 302, 304–305, 333, 337–338, 340, 343 see also art of proofs – by continuity  23–25 Protestant  251–252, 255, 266, 269, 273–276, 278–279, 281, 287, 302–305, 327–330, 332–336 Protestantism  252, 257, 273– 274, 276, 280–281, 343–344 prudence  238, 299, 308, 312–315 psychotechnic  21–22 public  41, 51, 53, 57, 61–62, 65, 69, 75, 77–79, 81–84, 91–92, 187–189, 192, 198–201, 205– 207, 213–214, 217, 238, 242, 245–247 see also private Q quantity  14, 17, 37, 40–41, 47–48, 53–72, 76, 79, 81–86, 91, 94–97, 103, 106, 118, 178– 179, 216, 241 quantum  47, 162, 178, 293

Subject index 357

quarrel  7–8, 15, 31, 37, 41, 79, 85–86, 97, 101, 245, 283, 309 R rabiosa contentio  300 rational  3, 13, 33, 36, 45, 87, 107, 109–110, 113–114, 124, 157, 165–166, 178, 190–191, 194, 197, 209, 223, 255–256, 260–261, 268, 285, 289, 340 rationalist  32, 65, 306 rationality  119, 125, 261 reason  14–15, 19, 29, 34, 45–46, 51, 56, 62, 64, 67, 70–71, 80–81, 85, 87, 89–90, 108, 112–114, 118, 121–125, 131, 156, 174, 180–181, 184, 192–193, 201, 204, 210–211, 215, 217–218, 224, 228–229, 231–232, 236, 239–240, 249–256, 260–261, 265, 283–284, 286–289, 291–293, 300, 306–307, 311, 313–315, 323, 325–327, 333, 335, 337, 340–343 reasonable  7, 46, 60, 69, 95, 171, 183, 190, 231, 238, 263, 284–285, 301, 324 reasoning  21, 30, 83, 86, 110, 113–114, 122, 211–213, 231, 249, 268, 309–310, 316, 333, 337 reception  7, 12, 188–189, 192, 195, 206, 249 reconciliation  111, 119–121, 123, 138–140, 142, 149, 159, 163, 173, 177, 183, 185, 266, 273–274, 278, 304, 335 see also conciliation reductionism  104, 107–108, 112, 116 Reformation  253, 274, 277, 281, 292, 299–300, 306, 326, 328, 334 reformed  116, 255, 258, 275, 277–279, 281, 285, 292, 326 refraction  106, 138, 140, 142– 144, 146–148, 164 Regula Aurea  see Golden Rule relations  2, 26–27, 30, 59–60, 62, 108, 146–147, 156, 159–162, 172, 183, 224, 232, 274, 313

religion  120, 163, 258, 250–253, 254, 260–261, 264, 269, 274, 279–280, 290, 297–300, 302, 304–309, 311, 315–316, 323, 328–329, 335–336, 339–343 Religionsgespräche  264 remedies  14, 104–105 representation  2, 4, 6, 16, 44, 122, 146–147, 162, 175–176, 233 Republic  125, 130, 239, 267 République des Lettres  14, 17–18, 63, 93, 101, 125 resistance  33, 38, 54, 78, 80–81, 83, 85–87, 90, 94, 127, 142–145, 164, 182–183, 187–188, 190, 192, 195–196, 253, 280 revelation  67, 77, 250–251, 253–254, 260, 265, 306, 309, 330, 342 rhetoric  9, 20, 51, 158, 212, 216, 321, 323, 335–336, 342 see also argument and argumentation Roman  166, 230, 237, 245, 256–261, 268–269, 280, 287, 306, 312, 322, 327–329, 331–332, 337, 343 – Cathoic  see Catholic rule  3–4, 8, 10, 18, 20, 28, 33–34, 39–43, 48, 54, 61–64, 83, 148, 150–151, 223–225, 228–236, 238, 239–242, 252, 284–286, 293, 297–299, 306– 316, 326, 330–331, 335–337, 342 see also Golden Rule S Sacrament  265, 276, 281 safeties  223–232, 233–236, 238–239 salts  116–117, 129 salvation  238, 251–252, 254, 265, 292, 326–330, 342 satanic  299–300, 307 schismatic  300–301, 303, 306–307, 326–327 scholastic  53, 95, 121, 170–171, 174, 177, 180, 185, 192–193, 251, 253, 293, 335 scholastics  171, 184–185, 192– 194, 204, 211, 249, 259–260, 263

358 Subject index

science  8–9, 29, 37, 43–44, 49, 52, 59, 65, 75, 79–80, 82, 85, 88–89, 91–92, 98–99, 101–102, 107, 112–113, 123–124, 130, 137, 140–142, 146, 163, 185, 193–194, 204, 219, 242, 286, 309, 323, 333, 337–338 Scripture  250–252, 260, 265, 278, 283, 286–287, 309, 342  see also biblical secretion  105, 114, 117, 123 sect  150, 178, 304–305, 311–312 sectarianism  193, 298, 300–302, 304–308, 310–312, 315, 327 secured debts  224, 239 semiotic  146–147, 159–160, 165 sensation  126, 172–176, 181 series  11, 16, 28–30, 36, 57, 90, 101, 105, 111–112, 122, 150–151, 175, 241, 331, 340 sign  2–5, 7, 10, 14, 20–23, 28, 30, 40–41, 47, 66, 146–147, 160, 174, 278, 300, 340 skepticism  38, 221, 258, 260, 281, 316, 343 Snell’s law  see law of refraction Socinian  297 sophistic  10 see also argument and argumentation soul  67, 72, 102–106, 108–111, 113–114, 117–121, 123, 125, 152–153, 157–158, 159, 169–186, 189–191, 194–198, 201, 203, 205, 209–212, 214, 216, 218, 254, 256, 267, 292–293, 310, 334 see also spirit space  24, 27, 29, 47, 53, 66, 78, 80, 87–88, 93, 120, 156, 161, 178, 180, 213–214, 293 spatial  53, 60, 62, 109, 146, 335 species  160, 178–179, 185, 203, 230, 233, 240–241, 293, 325, 338, 343 spirit  111, 117–118, 121, 128, 130, 152, 158–159, 165, 173–174, 188, 193–194, 196–198, 203, 206, 209, 219, 239, 250, 252–253, 275, 285, 289, 293, 301–302, 305, 307, 310, 334–335, 337  see also soul

spiritual  197–198, 210, 245, 258, 261, 269 strategy  26, 62, 78, 89, 102, 122, 152–153, 155, 161, 170, 172, 182, 189, 191, 193, 195, 202, 214, 282–283, 298, 331–332, 335–336 stylistic  194 substance  17, 21, 37, 53, 65–66, 70–75, 80, 87–89, 112, 114, 121, 126, 128, 131, 153–154, 157–158, 169–172, 175–181, 182–187, 189–191, 194–198, 201–203, 205, 208–215, 217–218, 251, 265, 287, 293 see also communication and subtle subtangent  40 subtle – body  180 – logic  217 – matter  180–181 – mechanism  107 – movement  114 – substance  181 suffering  87, 169, 258 summation  2, 5–6, 14, 38  see also integral super privilege  224, 229–231, 233, 235, 237–238 super-transcendent  41 suspension  298, 324, 326, 332 swirl  103, 105–106, 117, 123–124 syllogism  77, 84–85, 96, 249, 285, 287, 333, 337 symbol  14–16, 21, 162–163  see also sign symbolic  1–3, 6–7, 12, 16–23, 32, 257, 324 syncretism  275, 334 synthesis  30, 103, 108, 116, 118, 138, 149, 193, 196–197 synthesizing  124 T tangent  12, 30, 39–40, 43, 45, 47, 49 teleological  139, 198 temporal  109, 237, 305 tension  34–35, 114 terminus – exclusivus  12, 19, 24 – inclusivus  15, 24

The other’s place  see La place d’autrui theologian  150, 250–251, 253, 255, 264, 266, 275, 278, 280, 285, 288, 290, 303, 306, 315, 322–323, 325–327, 329, 342 theological  63, 137, 253–254, 265, 276, 279, 283–284, 286, 288, 298–299, 311–312, 315– 316, 322–323, 328–329, 332–333 theology  121–122, 138, 245, 251–255, 267, 285, 288, 297, 304, 312 Thomistic  180 tolerance  253, 255, 275, 279, 285, 289, 291, 298, 325, 328 tolerantia ecclesiastica  276, 279, 281–282, 291 topological  27–28 traces  18, 131, 170, 172–173, 175, 181, 283 transcendent  41–44, 47, 103, 110, 114, 118, 123 transitivity  229, 238 transubstantiation  288, 329 treaty  274, 324 truth acceptable  301 agreement on the  324 contingent  21, 60 see also contingent defining  323 divine  302 enemies of  9, 302 error and  326 finding the  322 important  149 infallible  323, 340 knowledge of the  342 lovers of  64, 95 mark of the  306 mathematical  21 new  304, 306 non-demonstrable  340 – of experience  21 – of fact  124 – of faith  324, 339 only one  289 part of the  301 production of  340 religious  305, 308



surrender to  158 type of  336, 340 type  1, 16, 27, 79–80, 90, 105, 119, 148, 193, 196–197, 199, 210, 223, 231, 241, 303, 308, 336, 340 U uniform  27–28, 30, 35, 54, 107, 182, 204 unio  see also union actualis  279, 282 hypostatica  277 realis  281 virtualis  279, 281 union  72, 110, 114–115, 129–130, 139, 170–173, 176–177, 180–182, 184, 187, 189–191, 194–197, 205, 210, 218, 274–275, 277, 279–282, 288, 291, 302–303 unit  58,67, 81–82, 146

Subject index 359

unity  125, 154, 162, 171, 194–195, 197–198, 206, 209, 211, 214, 251, 269, 273, 275, 281, 283, 285, 287, 289, 292, 303 universal  11, 16, 30, 66, 87, 121, 131, 141, 160, 163, 176, 180, 183, 229, 231, 235, 238–239, 257– 258, 267, 269, 278, 303, 306, 311–313, 315, 326, 331, 334 unum per se  171, 177, 184 usefulness  44,132, 140, 231, 241 utilité  see usefulness V vacuum  see void vegetative  105, 118, 178 violent  77, 82, 90, 94, 98, 203, 212, 216–218, 253, 310 virtue  151, 267, 315 vis mortua  56 vis viva  51–52, 56, 63–64, 70, 76, 164

vital  103–107, 110–111, 113, 118–119, 121, 123, 158 vitalism  106, 115, 118, 110, 115, 121, 126, 194 void  53, 127, 131, 164, 238, 254, 327, 332 voluntarism  135, 254 W water  112, 118, 127, 143, 246  see also aqueous well-founded phenomenon  213 well grounded fictions  10 windowless  146, 161 see also monad wise  109, 152, 154, 172, 202, 205, 238–239, 242, 267, 276, 313 Wittenberg Konkordie  277– 279 World Soul  152, 159

In the series Controversies the following titles have been published thus far or are scheduled for publication: 7 6 5 4 3 2 1

Dascal, Marcelo (ed.): The Practice of Reason. Leibniz and his Controversies. 2010. xvi, 359 pp. Eemeren, Frans H. van and Bart Garssen (eds.): Controversy and Confrontation. Relating controversy analysis with argumentation theory. 2008. xiii, 278 pp. Walton, Douglas: Dialog Theory for Critical Argumentation. 2007. xviii, 308 pp. Dascal, Marcelo and Han-liang Chang (eds.): Traditions of Controversy. 2007. xvi, 310 pp. Frogel, Shai: The Rhetoric of Philosophy. 2005. x, 156 pp. Eemeren, Frans H. van and Peter Houtlosser (eds.): Argumentation in Practice. 2005. viii, 368 pp. Barrotta, Pierluigi and Marcelo Dascal (eds.): Controversies and Subjectivity. 2005. x, 411 pp.