Themes from Early Analytic Philosophy: Essays in Honour of Wolfgang Künne

THEMES FROM EARLY ANALYTIC PHILOSOPHY

Grazer Philosophische Studien INTERNATIONAL JOURNAL FOR ANALYTIC PHILOSOPHY

FOUNDED BY Rudolf Haller EDITED BY Johannes L. Brandl Marian David Maria E. Reicher Leopold Stubenberg

VOL 82 - 2011

Amsterdam - New York, NY 2011

THEMES FROM EARLY ANALYTIC PHILOSOPHY ESSAYS IN HONOUR OF WOLFGANG KÜNNE

Edited by

BENJAMIN SCHNIEDER AND MORITZ SCHULZ

Die Herausgabe der GPS erfolgt mit Unterstützung des Instituts für Philosophie der Universität Graz, der Forschungsstelle für Österreichische Philosophie, Graz, und wird von folgenden Institutionen gefördert: Bundesministerium für Bildung, Wissenschaft und Kultur, Wien Abteilung für Wissenschaft und Forschung des Amtes der Steiermärkischen Landesregierung, Graz Kulturreferat der Stadt Graz

The paper on which this book is printed meets the requirements of “ISO 9706:1994, Information and documentation - Paper for documents Requirements for permanence”. Layout: Thomas Binder, Graz ISBN: 978-90-420-3362-7 E-book ISBN: 978-94-012-0059-2 ISSN: 0165-9227 E-ISSN: 1875-6735 © Editions Rodopi B.V., Amsterdam - New York, NY 2011 Printed in The Netherlands

TABLE OF CONTENTS

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Wolfgang Künne: Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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I. Truth and Assertion Ian RUMFITT: Truth and the Determination of Content: Variations on Themes from Frege’s Logische Untersuchungen . . . . . . . . . . . . .

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Manuel GARCÍA-CARPINTERO: Truth-Bearers and Modesty . . . . .

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Edgar MORSCHER: Logical Truth and Logical Form . . . . . . . . . . . .

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Mark SIEBEL: “It Falls Somewhat Short of Logical Precision.” Bolzano on Kant’s Definition of Analyticity . . . . . . . . . . . . . . . . . . . . . . . .

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II. Concepts and Propositions Hans-Johann GLOCK: A Cognitivist Approach to Concepts . . . . . . . .

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Andreas KEMMERLING: Thoughts without Parts: Frege’s Doctrine . . .

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Stephan KRÄMER: Bolzano on the Intransparency of Content . . . . . . .

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Nick HAVERKAMP: Nothing but Objects . . . . . . . . . . . . . . . . . . . .

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III. Cognition and Volition Peter SIMONS: Cognitive Operations and the Multifarious Reifications of the Unreal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Kevin MULLIGAN: Meaning Something and Meanings . . . . . . . . .

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John HYMAN: Wittgenstein on Action and the Will . . . . . . . . . . .

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IV. Reference and Existence David WIGGINS: Platonism and the Argument from Causality . . . . .

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Tobias ROSEFELDT: Frege, Pünjer, and Kant on Existence . . . . . . .

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Robert SCHWARTZKOPFF: Numbers as Ontologically Dependent Objects. Hume’s Principle Revisited . . . . . . . . . . . . . . . . . . . . .

353

Mark TEXTOR: Sense-Only-Signs: Frege on Fictional Proper Names

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Grazer Philosophische Studien 82 (2011), vii–x.

FOREWORD In the year in which Wolfgang Künne turned sixty, a collection of essays appeared under the title Semantik und Ontologie (Semantics and Ontology).1 It was not by coincidence that this is also the subtitle of Künne’s first monograph:2 the papers in the collection were written by colleagues and former students of Wolfgang, and they were published in his honour. However, as the editors hastened to point out in the first sentence of the introduction, the book was not a Festschrift for Wolfgang—for, they argued, the purpose of a Festschrift is to look back at an academic career, its stages and outcomes. It was not the time, however, to look back but rather to look forward to what was yet to come in Künne’s productive career. The latter can still be said today. Fortunately, Künne has not stopped contributing to philosophy. He is currently working on a substantial monograph on Bolzano’s life and work. All Bolzano scholars are looking forward to reading the result. Nevertheless, this anthology is a Festschrift for Künne, one richly deserved. It celebrates the achievements he has made as a philosopher up until this day. Incidentally, it also celebrates his 65th birthday. *** Some years ago Wolfgang Künne introduced himself to a meeting of new philosophy students and told his audience that he had written his PhD thesis on the topic of Plato as a Reader of Hegel. Even though the students had little knowledge of philosophy, and no knowledge of Künne, a number of them had sufficient background knowledge to realize that this was a surprising topic. But even after Künne had corrected his mistake, the actual topic of his PhD thesis remained a surprising revelation to many who were familiar with his work. The main part of his philosophical work does not make his academic upbringing obvious: from 1964 onwards, he studied philosophy (and theology) at the Department of Philosophy in 1. Mark Siebel & Mark Textor (eds.), Semantik und Ontologie, Frankfurt a. M.: ontos, 2004. 2. Wolfgang Künne, Abstrakte Gegenstände – Semantik und Ontologie, Frankfurt a. M.: Suhrkamp, 1983. Revised edition with a postscript, Frankfurt a. M.: Klostermann, 2007.

Heidelberg, which had a focus on ancient philosophy, German idealism, and hermeneutics. Still in Heidelberg, Künne finished his dissertation in 1972 under the supervision of Hans-Georg Gadamer. The topic of his dissertation derives from this academic background. But Künne came to know and love analytic philosophy quite early when he spent the academic year of 1967/68 in London at King’s College. After his PhD, he devoted his research wholeheartedly to analytic philosophy. Künne’s qualities as a philosopher are manifold. His work lives up to the highest standards of clarity, rigour, and respect for the details of philosophical arguments and problems. But he is not only an excellent, precise, and elegant writer and lecturer in English and German, he is also an extremely careful and charitable interpreter of philosophical texts. He is, we may suspect, a reader of the kind that Wittgenstein desired to have, when he famously wrote ‘I should like to be read slowly. (As I read myself )’. Künne is moreover well aware that the long history of philosophy contains a wide range of ideas which deserve to be remembered, and that an investigation of how certain ideas have developed can itself be a fruitful and insightful philosophical exercise. His treatments on historical figures splendidly illustrate this important insight. All of Künne’s qualities are manifested in his critically acclaimed Conceptions of Truth,3 which made Sir Peter Strawson close his review of Künne’s book with the following words: ‘It would be folly to claim, on behalf of any work on a major work of philosophical contention, that it is a definitive treatment of its subject. But Conceptions of Truth seems to me to come as close to this merely regulative ideal as any work known to me.’4 But there are other qualities which make a great philosopher other than his written work. Künne is also a dedicated teacher of philosophy who strives to explain philosophical positions and problems with a maximum of clarity, thereby making them accessible to an untrained audience. The way he receives his students’ seminar papers reflects his general approach to philosophy: going through them in great detail, he gives an example of how to pursue philosophy with a sharp pencil rather than a broad brush. The care and seriousness with which he discusses students’ contributions is distinctive about Künne. In return, he has always been greatly admired by many students aware of his excellence as a teacher, and of the personal qualities which make someone a philosophical exemplar or model. Künne 3. Oxford: Clarendon Press, 2003. 4. “Usefully True”, Times Literary Supplement, May 2004.

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thus inspired many of his students to choose an academic career. We are therefore happy that a number of his students have contributed to the current volume: while Mark Siebel and Mark Textor studied with Künne more than a decade ago and are now established philosophers, the youngest generation of Künne’s students is represented here too (Nick Haverkamp, Stephan Kraemer, and Robert Schwartzkopff ). *** Although Künne’s philosophical interests are broad and this breadth is represented in his publications, there are certain core topics which dominate his writings. First and foremost, Künne has worked on issues in ontology— in particular on the ontology of abstract objects—and the philosophy of language and logic—in particular on the notions of reference and truth. Other topics he has published on include intentionality, the philosophy of action, and the philosophy of perception. Künne has, second, usually approached philosophical topics with an eye on their history, and he has written numerous insightful essays on the works of important early analytic philosophers—in particular on Bernard Bolzano and Gottlob Frege, but also on G. E. Moore, Edmund Husserl, Ludwig Wittgenstein, Adolf Reinach, and, as already mentioned, on Plato. The present collection covers all the topics belonging to Künne’s central research interests: the essays treat topics (most of them from ontology and the philosophy of language) which bothered and intrigued early analytic philosophers and which still intrigue analytic philosophers today. Moreover, a number of the essays approach their topic with a close eye on the position of a particular philosopher and thereby foster the understanding of early analytic philosophy. *** We thank the authors in this volume for their willingness to contribute to it, and for the efforts they made to ensure the appearance of this Festschrift. Unfortunately, there is a group of people who wanted, or would have liked to contribute to this volume but who actually did not. In fact, that group of merely potential contributors is larger than the group of actual contributors. For, firstly, there are several philosophers who intended to

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contribute something to the Festschrift but could not meet our demanding schedule. Then there are others who we would have liked to ask if we had not already received too many positive responses to our invitations— limitation of space just meant a limitation of authors. Moreover, there are those we have not asked since we did not want this volume to become a mere reprise of Siebel and Textor’s Semantik und Ontologie: we decided to invite only very few contributors (four out of seventeen) of that earlier collection, just because there were so many others to be asked who had so far lacked the opportunity to deliver an essay in honour of Künne. Finally, there are doubtless yet others who deserved to be asked to contribute, but whom we missed out inadvertently. We are sorry for not having asked those friends, colleagues, and students of Künne who would have liked to be on board. As you may imagine, it was hard to make the choices and we certainly did not want to offend anyone by not asking her or him. But it is also an indication of Künne’s standing, of the respect and admiration he has earned, that so many people would have had a genuine and rightful interest in being represented in this collection. *** Enough has been said. Praise is pointless—the work is there. It deserves to be read. This is why we decided to supplement this short laudatio with a bibliography of Künne’s writings. His writings so far, we should add. As we remarked earlier, although this is a Festschrift we are not looking back at a completed philosophical career. There is, we hope and trust, more to come, much and soon.5 Benjamin Schnieder and Moritz Schulz

5. The editors are currently members of the research group Phlox at the Humboldt-Universität zu Berlin. Hence, we would like to thank the DFG for the financial support of the group which made it possible to publish this volume. Moreover, we would like to thank the Thyssen-Stiftung for the financial support of the conference Truth and Abstract Objects – Issues from Bolzano and Frege (Berlin 2009), at which early versions of some of the papers in this volume were presented.

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Grazer Philosophische Studien 82 (2011), xi–xvii.

WOLFGANG KÜNNE: BIBLIOGRAPHY I. Monographs M.1 Abstrakte Gegenstände. Semantik und Ontologie. Frankfurt a. M.: Suhrkamp, 1983. 2nd edition with postscript, Frankfurt a. M.: Klostermann, 2007. M.2 Conceptions of Truth. Oxford: Oxford University Press, 2003. M.3 Versuche über Bolzano / Essays on Bolzano. Sankt Augustin: Academia, 2008. Contains revised versions of J.16, J.18, A.23, A.25, A.27–A.30, A.35, A.37. M.4 Die Philosophische Logik Gottlob Freges. Frankfurt a. M.: Klostermann, 2010. M.5 Bernard Bolzano: Ein Analytischer Philosoph im Schatten des Deutschen Idealismus. In preparation for Frankfurt a. M.: Klostermann.

II. Editorships E.1 E.2 E.3

Direct Reference, Indexicality, and Propositional Attitudes. Wolfgang Künne, Albert Newen & Martin Anduschus (eds.), Stanford: CSLI, 1997. Bolzano and Analytic Philosophy. Wolfgang Künne, Mark Siebel & Mark Textor (eds.), Amsterdam: Rodopi, 1998 (Grazer Philosophische Studien 53). Was ist Wahrheit? Eine Anthologie. In preparation for Paderborn: mentis.

III. Articles in Journals J.1 J.2 J.3 J.4

J.5 J.6

“Beschreiben und Benennen”. Neue Hefte für Philosophie 1 (1971), 33–50. “Hegel als Leser Platos”. Hegel-Studien 15 (1979), 109–146. “Verstehen und Sinn”. Allgemeine Zeitschrift für Philosophie 6 (1981), 1–16. Repr. in: Axel Bühler (ed.), Hermeneutik. Heidelberg: Synchron, 2003, 61–78. “Analytizität und Trivialität”. Grazer Philosophische Studien 18 (1982), 207–222. (This issue of GPS is also available as: Rudolf Haller (ed.), Schlick und Neurath, Ein Symposium. Amsterdam: Rodopi, 1982.) “Indexikalität, Sinn und propositionaler Gehalt”. Grazer Philosophische Studien 18 (1982), 41–74. “Megarische Aporien für Freges Semantik”. Zeitschrift für Semiotik 4 (1982), 267–290.

J.7 J.8 J.9 J.10

J.11 J.12 J.13 J.14 J.15 J.16

J.17 J.18 J.19 J.20

J.21 J.22 J.23 J.24 J.25

“Im übertragenen Sinne. Zur Theorie der Metapher”. Conceptus 17 (1983), 181–200. “Handlungs- und andere Ereignissätze. Davidsons Frage nach ihrer logischen Form”. Grazer Philosophische Studien 39 (1991), 27–49. “Hybrid Proper Names”. Mind 101 (1992), 721–731. “Fürsprecher der böhmischen Juden. Der Philosoph Bernard Bolzano”. Tribüne, Zeitschrift zum Verständnis d. Judentums 32 (1993), 107–117. (Part of A.20) “Truth, Rightness and Permanent Acceptability”. Synthese 95 (1993), 107– 117. “Sehen. Eine sprachanalytische Betrachtung”. Logos (N.F.) 2 (1995), 103– 121. “Some Varieties of Thinking. Reflections on Meinong and Fodor”. Grazer Philosophische Studien 50 (1995), 365–395. “Bolzanos Philosophie der Religion und der Moral”. Archiv für Geschichte der Philosophie 78 (1996), 309–328. “Paul Ernst und Ludwig Wittgenstein”. Scientia Poetica, Jahrbuch für Geschichte der Literatur und der Wissenschaften 2 (1998), 151–166. “Propositions in Bolzano and Frege”. Grazer Philosophische Studien 53 (1998), 203–240. [ibid., Michael Dummett, “Comments on Wolfgang Künne’s Paper”]. (Cp. M.3) “Substanzen und Adhärenzen. Zur Ontologie in Bolzanos Athanasia”. Philosophiegeschichte und logische Analyse 1 (1998), 233–250. “Are Questions Propositions?”. Revue internationale de philosophie 57 (2003), 157–168. (Cp. M.3) “Die ‘Gigantomachie’ in Platons Sophistes”. Archiv für Geschichte der Philosophie 86 (2004), 307–321. “The Modest Account of Truth Reconsidered. With a Postscript on Metaphysical Categories”. In: Book Symposium—Conceptions of Truth by Wolfgang Künne, Dialogue [Canada] 44 (2005), 563–596. “Der Universalienstreit in der neueren analytischen Philosophie”. Information Philosophie (2006), 22–33. “A Dilemma in Frege’s Philosophy of Thought and Language”. Rivista di estetica 34 (Saggi in onore di Diego Marconi) (2007), 95–120. “Frege on Truths, Truth and the True”. Studia Philososophica Estonica 1 (2008), 5–42. “Précis of Conceptions of Truth” and “Replies to Commentators [Göran Sundholm & Jan Wolenski]”. Dialectica 62 (2008), 355–357, 385–401. “The Modest, or Quantificational, Account of Truth”. Studia Philososophica Estonica 1 (2008), 122–168.

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J.26 “Sense, Reference and Hybridity: Reflections on Kripke’s Recent Reading of Frege”. To appear in Dialectica. J.27 “Circularity Worries. Reply to Paul Boghossian”. Forthcoming in Dialectica. J.28 “‘True’ without Truths? Reply to Kevin Mulligan”. Forthcoming in Dialectica.

IV. Articles in Anthologies A.1

A.2

A.3

A.4 A.5

A.6 A.7

A.8 A.9

A.10

A.11

“P. F. Strawson: Deskriptive Metaphysik”. In: Josef Speck (ed.), Grundprobleme der großen Philosophen. Philosophie der Gegenwart III. Göttingen: Vandenhoeck und Ruprecht, 1975, 168–207. “Criteria of Abstractness. The Ontologies of Husserl, Frege and Strawson”. In: Barry Smith (ed.), Parts and Moments. München-Wien: Philosophia, 1982, 401–437. “Sinn(losigkeit) in Über Gewißheit”. In: Brian F. McGuinness & Aldo Gargani (eds.), Wittgenstein and Contemporary Philosophy (=: Teoria 5), Pisa 1985, 113–133. “Wahrheit”. In: Ekkehard Martens & Herbert Schnädelbach (eds.), Philosophie—Ein Grundkurs. Hamburg: Rowohlt, 1985 (21991), 116–171. “Edmund Husserl: Intentionalität”. In: Josef Speck (ed.), Grundprobleme der großen Philosophen. Philosophie der Neuzeit IV. Göttingen: Vandenhoeck und Ruprecht, 1986, 165–215. “Vom Sinn der Eigennamen”. In: Eva-Maria Alves (ed.), Namenzauber. Frankfurt a. M.: Suhrkamp, 1986, 64–89. “The Intentionality of Thinking: The Difference between States of Affairs and Propositional Contents”. In: Kevin Mulligan (ed.), Speech Act and Sachverhalt: Reinach and the Foundations of Realist Phenomenology. Dordrecht: Martinus Nijhoff, 1987, 175–187. “Abstrakte Gegenstände via Abstraktion?”. In: Matthias Gatzemeier & Klaus Prätor (eds.), Aspekte der Abstraktionstheorie. Aachen: Rader, 1988, 19–24. “Kategorien—im Lichte Wittgensteins und Carnaps”. In: Regina Claussen & Roland Daube-Schackat (eds.), Gedankenzeichen, Tübingen: Stauffenburg, 1988, 71–81. “G. E. Moore: Was ist Begriffsanalyse?”. In: Margot Fleischer (ed.), Philosophen des 20. Jahrhunderts. Darmstadt: Wissenschaftliche Buchgesellschaft, 1990 (31995), 27–40. “On What One Thinks: Singular Propositions and Contents of Judgements”. In: Friedrich Rapp & Reiner Wiehl (eds.), Whitehead’s Metaphysics of Creativity. New York: State University of New York Press, 1990, 117–126.

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A.12 “Perception, Fiction, and Elliptical Speech”. In: Klaus Jacobi & Helmut Pape (eds.), Thinking and the Structure of the World. Berlin: De Gruyter, 1990, 259–267. [ibid., H.-N. Castañeda, “Reply to Wolfgang Künne”] A.13 “Prinzipien der wohlwollenden Interpretation”. In: Forum für Philosophie (ed.), Intentionalität und Verstehen. Frankfurt a. M.: Suhrkamp, 1990, 212–236. A.14 “The Nature of Acts—Moore on Husserl”. In: David Bell & Neil Cooper (eds.), The Analytic Tradition. Oxford: Blackwell, 1990, 104–116. A.15 “ ‘Was für eine höllische Idee!’ Wittgensteins Kritik an Sokrates und G. E. Moore”. In: Rudolf Haller et al. (eds.), Wittgenstein: eine Neubewertung II; Akten des 14. Internationalen Wittgenstein-Symposiums. Wien: HölderPichler-Tempsky, 1990, 217–227. A.16 “Bolzanos blühender Baum. Plädoyer für eine realistische Wahrheitsauffassung”. In: Forum für Philosophie (ed.), Realismus und Antirealismus. Frankfurt a. M.: Suhrkamp, 1992, 224–244. A.17 “Truth, Meaning and Logical Form”. In: Ralf Stoecker (ed.), Reflecting Davidson. Berlin: De Gruyter, 1993, 1–20. [ibid., Donald Davidson, “Reply to Wolfgang Künne”] A.18 “Das Vorkommen des Wortes ‘ich’ in einem Satze gibt noch zu einigen Fragen Veranlassung”. In: Ingolf Max & Werner Stelzner (eds.), Logik und Mathematik; Frege-Kolloquium Jena. Berlin: De Gruyter, 1995, 291–302. A.19 “Fiktionale Rede ohne fiktive Gegenstände”. In: Johannes Brandl, Alexander Hieke, Peter M. Simons (eds.), Metaphysik. Neue Zugänge zu alten Fragen. Sankt Augustin: Academia, 1995, 141–161. Repr. in: Maria E. Reicher (ed.), Fiktion. Wahrheit, Wirklichkeit. Philosophische Grundlagen der Literaturtheorie. Paderborn: mentis, 2007, 54–72. A.20 “Bernard Bolzano über Nationalismus und Rassismus in Böhmen”. In: Edgar Morscher & Otto Neumaier (eds.), Bolzanos Kampf gegen Nationalismus und Rassismus. Sankt Augustin: Academia, 1996, 97–139. A.21 “Gottlob Frege (1848–1925)”. In: Tilman Borsche (ed.), Klassiker der Sprachphilosophie. München: Beck, 1996, 325–345. A.22 “Thought, Speech, and the ‘Language of Thought’”. In: Christian Stein & Mark Textor (eds.), Intentional Phenomena in Context. Hamburg: Universität Hamburg, 1996, 53–90. A.23 “‘Die Ernte wird erscheinen …’: Die Geschichte der Bolzano-Rezeption (1849– 1939)”. In: Heinrich Ganthaler & Otto Neumaier (eds.), Bolzano und die österreichische Geistesgeschichte. Sankt Augustin: Academia, 1997. (Cp. M.3) A.24 “First Person Propositions”. In: Wolfgang Künne et al. (eds.), Direct Reference, Indexicality, and Propositional Attitudes. Stanford: CSLI Publications, 1997, 49–68.

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A.25 “Bolzanos oberstes Sittengesetz”. In: Edgar Morscher (ed.), Bolzanos Erbe für das 21. Jahrhundert. Sankt Augustin: Academia, 1999, 371–391. (Cp. M.3) A.26 “Truth and a Kind of Realism”. In: Julian Nida-Rümelin (ed.), Rationality, Realism, Revision. Berlin: De Gruyter, 1999, 17–41. A.27 “Über Lug und Trug”. In: Edgar Morscher (ed.), Bolzanos Erbe für das 21. Jahrhundert. Sankt Augustin: Academia, 1999, 29–58. Estonian translation: “Monest pettuse tüübist”. In: Akadeemia 20 (2008), 41–62. (Cp. M.3) A.28 “Die Geschichte der philosophischen Bolzano-Rezeption bis 1939 (II)”. In: Helmut Rumpler (ed.), Bernard Bolzano und die Politik. Wien: Böhlau, 2000, 311–352. (Cp. M.3) A.29 “Constituents of Concepts”. In: Albert Newen et al. (eds.), Building on Frege. Stanford: CLSI, 2001. (Cp. M.3) A.30 “Die theologischen Gutachten in den Verfahren gegen den Professor und Priester Bolzano”. In: Winfried Löffler (ed.), Bolzano als Religionsphilosoph und Theologe. Sankt Augustin: Academia, 2002. (Cp. M.3) A.31 “Disquotationalist Conceptions of Truth”. In: Richard Schantz (ed.), What Is Truth?. Berlin: De Gruyter, 2002, 176–193. A.32 “From Alethic Anti-Realism to Alethic Realism”. In: James Conant & Urszula M. Żegleń (eds.), Hilary Putnam—Pragmatism and Realism. London: Routledge, 2002, 144–165. A.33 “Ausdrücke und literarische Werke als Typen” (reprint of chap. 6.2 of M.1). In: Reinold Schmücker (ed.), Identität und Existenz. Studien zur Ontologie der Kunst. Paderborn: mentis, 2003, 141–148. A.34 “Bernard Bolzano’s Wissenschaftslehre and Polish Analytical Philosophy”. In: Jaakko Hintikka et al. (eds.) Philosophy and Logic. Dordrecht: Kluwer, 2003, 179–192. A.35 “Bolzanos frühe Jahre”. In: Alexander Hieke & Otto Neumaier (eds.), Philosophie im Geiste Bolzanos. Sankt Augustin: Academia, 2003, 5–47. (Cp. M.3) A.36 “Analyticity and Logical Truth: From Bolzano to Quine”. In: Maria E. Reicher & Johann C. Marek (eds.), Experience and Analysis. Wien: öbv & hpt, 2005, 81–100. (Short version of A.37) A.37 “Analyticity and Logical Truth: From Bolzano to Quine”. In: Mark Textor (ed.), The Austrian Contribution to Analytic Philosophy. London: Routledge, 2006, 184–249. (Cp. M.3) A.38 “Properties in Abundance”. In: Peter F. Strawson & Arindam Chakrabarti (eds.), Universals, Concepts, and Qualities. Aldershot: Ashgate, 2006, 249–300. A.39 “Wahrheit, Metonymie und Metapher”, “Propositionale Äußerungsgehalte, minimalistisch konzipiert” and “Das Prinzip der Austauschbarkeit”. In:

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A.40 A.41

A.42

A.43

A.44

A.45

A.46

Franz Josef Czernin & Thomas Eder (eds.), Zur Metapher. München: Fink, 2007, 57–74, 123–127, 129–132. “Eigenschaften und Begriffe, Postskriptum 2007”. In: M.1, 2nd edition (2007), 310–352. “Two Principles Concerning Truth”. In: Randall E. Auxier & Lewis E. Hahn (eds.), The Philosophy of Michael Dummett. The Library of Living Philosophers, Bd. XXXI, Carbondale: Open Court, 2007, 315–344. [ibid. M. Dummett, “Reply to Wolfgang Künne”] “Bolzano and (Early) Husserl on Intentionality”. In: Guiseppe Primiero & Shahid Rahman (eds.), Acts of Knowledge: History, Philosophy and Logic. Essays Dedicated to Göran Sundholm. London: College Publications, 2009, 95–140. “Wittgenstein and Frege’s ‘Logical Investigations’”. In: John Hyman & Hans-Johann Glock (eds.), Wittgenstein and Twentieth-Century Analytic Philosophy. Essays for P. M. S. Hacker. Oxford: OUP, 2009, 26–62. “Eadem sunt, quae sibi mutuo substitui possunt, salva veritate: Leibniz über Identität und Austauschbarkeit”. In: Jahrbuch der Akademie der Wissenschaften zu Göttingen 2009. Berlin: De Gruyter, 2010, 110–119. “Dubbi sulla Spiegazione Modesta della verità: risposta ad Andrea Bianchi”. In: Massimiliano Carrara & Vittorio Morato (eds.), Verità, Milano: Mimesis, 2010, 89–98. “Un conflitto interno alla teoria di Frege: risposta ad Andrea Sereni”. In: Massimiliano Carrara & Vittorio Morato (eds.), Verità, Milano: Mimesis, 2010, 98–109.

V. Varia: Book Reviews and Encyclopaedic Entries V.1 V.2 V.3 V.4 V.5

V.6

Review of: W. Mays & S. C. Brown (eds.), Linguistic Analysis and Phenomenology, London 1972. In: Foundations of Language 12 (1975), 439–440. Review of: Rainer W. Trapp, Analytische Ontologie, Frankfurt/M 1976. In: Philosophische Rundschau 25 (1978), 125–133. Entries “a priori / a posteriori”, “Negation”. In: Friedo Ricken (ed.), Lexikon der Erkenntnistheorie und Metaphysik. München: Beck, 1984. “Bob Hale on Abstract Objects” (book review). Ratio 2 (1989), 89–100. Entries “Frege”, “Neurath”, “Schlick”. In: Walther Killy (ed.), LiteraturLexikon: Autoren und Werke deutscher Sprache. Gütersloh: Bertelsmann, 1989–1991. Entry “Kritik und Rezeption der Metaphysik in der Analytischen Philosophie”. In: Theologische Realenzyklopädie, vol. 22. Berlin: De Gruyter, 1992.

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V.7 V.8 V.9 V.10 V.11

V.12 V.13

Entries „Wesen“, „Wissen“. In: Lexikon für Theologie und Kirche, vol. 10. Freiburg: Herder, 32001. Entry “Deixis”. In: Marcelo Dascal et al. (eds.), Philosophy of Language, Bd. 2. Berlin: De Gruyter, 1996, 1152–1161. “Edmund Husserl, Briefwechsel” (book review). Archiv für Geschichte der Philosophie 79 (1997), 106–115. “Ultraminimal Realism: Alston on Truth” (book review). Ratio 11 (1998), 193–199. Entries “Analytische Philosophie”, “Bedeutung”, “Denken”, “Extension / Intension”, “Frege”, “Gegenstand”, “Gewißheit”, “Semantik”, “Sinn”. In: Religion in Geschichte und Gegenwart, 4. Aufl. Tübingen: Mohr, 1998–2005. Entry “Bolzano”. In: Edward Craig (ed.), Routledge Encyclopedia of Philosophy. London: Routledge, 1999, 823–828. Entry “Wahrheit, [C.] Analytische Philosophie, Oxforder Neu-Hegelianismus, Pragmatismus”. In: Joachim Ritter et al. (eds.), Historisches Wörterbuch der Philosophie, vol. 12. Basel: Schwabe, 2004, 115–123.

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I. TRUTH AND ASSERTION

Grazer Philosophische Studien 82 (2011), 3–48.

TRUTH AND THE DETERMINATION OF CONTENT: VARIATIONS ON THEMES FROM FREGE’S LOGISCHE UNTERSUCHUNGEN * Ian RUMFITT Birkbeck College, University of London Summary In his late writings, Frege was tempted by a minimalist, or deflationary, account of truth. I elaborate a version of minimalism that is consistent with Frege’s key insights into the nature of truth. No form of minimalism, though, is consistent with the thesis that a statement’s truth-conditions determine its sense, so the present theory of truth needs to be supplemented with an alternative account of the determination of content. I argue that Frege was not committed to a truthconditional account of the determination of content; I then sketch a non-truthconditional theory—called evidentialism—that incorporates insights from his account of Sinn. On this theory, it is the evidence that would fully support an affirmative use of a statement that determines its content. As formulated, however, evidentialism collapses into an anti-realism that Frege would certainly have repudiated. So I conclude by elaborating and recommending a variant theory called bilateral evidentialism. On this view, a statement’s content is determined jointly by the evidence that would fully support its affirmation and the evidence that would fully support its rejection. If bilateral evidentialism is not to collapse into evidentialism simpliciter, one of Frege’s claims in “Die Verneinung” needs to be repudiated: rejecting a statement cannot be analysed as accepting its negation.

Among the many fruits of Wolfgang Künne’s long and distinguished philosophical career are some penetrating articles about Frege and a marvellously * This essay condenses some lectures that I have delivered on several occasions during the past ten years at the Universities of Oxford and London. It has benefited from the reactions of audiences at both those places, but especially, and most recently, from the responses of fellow participants in the conference held in August 2009 at the Humboldt University of Berlin to celebrate Wolfgang Künne’s 65th birthday: Hanjo Glock, Andreas Kemmerling, Kevin Mulligan, Tobias Rosefeldt, Mark Siebel, Peter Simons, Mark Textor, David Wiggins, and Wolfgang Künne himself. Thanks to one and all.

rich book about truth. So I hope he will accept in tribute a paper that takes as its point of departure some of Frege’s last thoughts on that topic. 1. Frege on truth Frege never fully resolved his puzzlement about truth. In “Der Gedanke”, part of the Logische Untersuchungen, his final but still incomplete attempt to paint the philosophical backdrop to his formal discoveries, he begins by telling us that ‘it falls to logic to discern the laws of truth’ (Frege 1918, 58) and that thoughts—Gedanken, propositional contents—are the primary bearers of truth (60).1 But against these confident pronouncements, doubts soon press in: All the same, it is something worth thinking about that we cannot recognize a property of a thing without at the same time finding the thought this thing has this property to be true. So with every property of a thing there is tied up a property of a thought, namely that of truth. It is also worth observing that the sentence ‘I smell the scent of violets’ has just the same content as the sentence ‘It is true that I smell the scent of violets’. So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth. And yet is it not a great result when the investigator, after much hesitation and laborious researches, can finally say ‘What I have conjectured is true’? The meaning of the word ‘true’ seems to be altogether sui generis. May we not be dealing here with something which cannot be called a property in the ordinary sense at all? (Frege 1918, 61)

Three years earlier, in a fragment that survives in his Nachlaß, he had pressed these doubts further, to the point where they cast doubt on his characterization of logic as comprising the laws of truth: If I assert ‘It is true that sea-water is salt’, I assert the same thing as if I assert ‘Sea-water is salt’. This enables us to recognize that the assertion is not to be found in the word ‘true’, but in the assertive force with which the sentence is uttered. This may lead us to think that the word ‘true’ has no sense at all. But in that case a sentence in which ‘true’ occurred as a predicate would have no sense either. All one can say is: the word ‘true’ has a sense that con1. Frege recognized that we ordinarily attribute truth to objects of many different kinds, but he always held that these other attributions are to be explained in terms of truth’s application to thoughts. See for example Frege 1897, 140 = Frege 1979, 129; Frege before 1906, 189 = Frege 1979, 174; Frege 1914, 251 = Frege 1979, 233; Frege 1918, 60.

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tributes nothing to the sense of the whole sentence in which it occurs as a predicate. But it is precisely for this reason that this word seems fitted to indicate the essence of logic. Any other adjective would be less suitable for this purpose by virtue of its particular sense. So the word ‘true’ seems to make the impossible possible: it allows what corresponds to the assertive force to assume the form of a contribution to the thought. And although this attempt miscarries, or rather through the very fact that it miscarries, it indicates what is characteristic of logic. And this, from what we have said, seems something essentially different from what is characteristic of aesthetics and ethics. For there is no doubt that the word ‘beautiful’ actually does indicate the essence of aesthetics, as does ‘good’ that of ethics, whereas ‘true’ only makes an abortive attempt to indicate the essence of logic, since what logic is really concerned with is not contained in the word ‘true’ at all but in the assertive force with which a sentence is uttered (Frege 1915, 271f. = Frege 1979, 251f.).

The last paragraph, especially, is Delphic. Quite uncharacteristically, Frege can tell us only what seems to be the case, not what is the case. There are, I shall eventually suggest, some important points for which he is groping, but in these late ruminations about truth there is much that needs clarifying and sorting out. In one respect, these late writings seem to mark a fresh approach to the topic. In Grundgesetze, and in the papers on philosophical logic that Frege had published in the early 1890s, the discussions of truth introduce us to the two truth-values—the True and the False—and seek to persuade us of the logico-philosophical advantages to be gained by recognizing these two objects (which is what Frege took them to be).2 We know from the notes he sent to Ludwig Darmstaedter in July 1919 that Frege continued to believe in the two truth-values even as he composed the Logische Untersuchungen (see Frege 1919b, 276 = Frege 1979, 255). However, they are not directly mentioned in that work. Because it bears on the relationship between his earlier and later discussions of truth, it will be worth making one or two remarks about the doctrine that truth-values are objects. According to Michael Dummett, this doctrine is a serious mistake. As Dummett reads Grundgesetze, Frege’s category of ‘name of a truth-value’ shows that he ‘assimilated’ complete declarative sentences to names; that is, he classified sentences as a species of complex singular term (see especially Dummett 1981, 183f., 196, 248–9, 643ff.). In doing so, Dummett thinks, 2. They make their debut on p. 13 of “Funktion und Begriff”.

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Frege robbed himself ‘of the insight that sentences play a unique role [in our speech], and that the role of almost every other linguistic expression […] consists in its part in forming sentences’ (Dummett 1981, 196). In a word, Frege lost sight of his own Context Principle, a principle which Dummett regards as one of the key philosophical advances made in Die Grundlagen. For this reason, Dummett’s assessment of the claim that truth-values are objects is severe. The doctrine is ‘a ludicrous deviation’, ‘a gratuitous blunder’, ‘an almost unmitigated disaster’ (op. cit., 184, 644). Frege often describes ordinary sentences as referring to their truthvalues. However, the crucial passages in which he sets out to explain his notion of a ‘name of a truth-value’ suggest that such descriptions are to be taken with several pinches of salt. Certainly, Dummett’s claim that Frege classified truth-values as objects because he lost sight of the distinction between expressing a thought and designating an object is hard to square with the text of Grundgesetze. In the very passage in which he introduces his concept of a truth-value, for example, Frege writes: The value of the function 2 = 4 is either the truth-value of what is true or that of what is false. It can be seen from this that I do not mean to assert anything if I only write down an equation, but that I only designate a truthvalue, just as I do not assert anything if I only write down ‘22’, but only designate a number. (Frege 1893, 7)

Here, Frege shows himself to be fully alert to the importance of the distinction between expressions which can be used to say things and expressions which can be used to refer to objects—that is, expressions which designate objects. He also appears to assume that an expression which designates an object cannot be used to say anything. So it is hard to read the passage as blurring the distinction between expressing a thought and designating an object, or between the speech acts of saying and referring. Rather, the passage is more naturally read as a warning that, in Frege’s symbolism, mathematical equations do not mean what one first expects them to mean. In ordinary mathematical usage, the sequence of signs ‘22 = 4’ is a complete formula which says that the square of two is four. Frege is warning us that this is not the right way to read the same sequence of signs in his formalized language: ‘I do not mean to assert anything if I only write down an equation’. In the language of Grundgesetze, the expression ‘22 = 4’ does not by itself say anything. Rather, it designates an object: it designates the truth-value of the square of two’s being four, which is the truth-value True.

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Frege, however, goes on to say that ‘the sense of a name of a truth-value I call a thought. I further say: a name expresses its sense’ (ibid.). And this may seem to reintroduce the problem. For surely only a complete sentence (or a complete mathematical formula) can express a thought, whereas ‘22 = 4’ is now supposed to be a complex singular term. But to this objection there is a reply. In a language in which every complete sentence has the form name of a truth-value + predicate, and in which there is only one predicate, one can speak in a transferred sense of the thought expressed by a name of a truth-value. For this can be understood to mean: the thought expressed by the complete sentence that is formed by combining the given name of a truth-value with the language’s single predicate. The moral of the passage we have been analysing is that the language of Grundgesetze is such a language. We know that Frege had the concept of such a language, for the formalized language of his earlier treatise, Begriffsschrift, is stipulated to be one: We can imagine a language in which the sentence ‘Archimedes perished at the conquest of Syracuse’ would be expressed in the following way: ‘The violent death of Archimedes at the conquest of Syracuse is a fact’. Even here, if one wishes, he can distinguish subject and predicate; but the subject contains the whole content, and the predicate serves only to present this as a judgement. Such a language would have only a single predicate for all judgements; namely, ‘is a fact’ […] Our Begriffsschrift is such a language, and the symbol — is its common predicate for all judgements (Frege 1879, 3f.).

Similarly, in the language of Grundgesetze, the content of each complete sentence is localized in a component complex singular term, although this time it is ‘is the truth-value True’, rather than ‘is a fact’, that is the common predicate.3 Frege, then, did not assimilate sentences to singular terms. Rather, he created two formalized languages in which the entire specific content of a sentence is localized within a component singular term—the ‘business part’ of the sentence, as we might call it. 3. In the later theory, the entire expression‘
’ is no longer taken to be the predicate that mates with a singular term to form a complete sentence. This change is part of Frege’s unsuccessful attempt to extirpate the confusion evident in the passage just quoted from Begriffsschrift, whereby ‘
’ is supposed to be at once a formal predicate and an indication of assertive force. But going into this properly would take me too far from my theme.

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Why, though, would anyone wish to construct a formalized language on this rather strange pattern? I think we can see why Frege might have done so when we reflect on his oft repeated claim that the key to his logical advances had been his extension of the mathematical notion of a function (see especially Frege 1891 and 1906a). If we read the language of Grundgesetze in the manner suggested, then symbols that one is initially tempted to read as sentential connectives emerge as functional expressions—things out of the same grammatical box as ‘the square of…’ or ‘the ratio of… and---’. Thus where A means ‘Archimedes’s having died at Syracuse’,
—— A means: ‘The negation of the truth-value of Archimedes’s having died at Syracuse is the True’. Whilst the whole formula is equivalent to ‘Archimedes did not die at Syracuse’, no part of it can be picked out as meaning precisely ‘it is not the case that’. Matters are similar with the quantifiers. –– x = x means: ‘The universal quantification of the function is identical with itself is the True’. Whilst the whole formula is equivalent to ‘Everything is identical with itself ’, no part of it can be picked out as meaning precisely ‘every’. The particular advantage of this comes out in the quantificational case. In the domain of natural numbers, ‘x y x  y’ is true whereas ‘y x x  y’ is false. The sentence in the language of Grundgesetze that corresponds to the first formula will say: ‘The universal quantification (into the place of the first relatum) of the existential quantification (into the place of the second relatum) of the relation of being less than is the True’. The sentence corresponding to the second formula will say: ‘The existential quantification (into the place of the second relatum) of the universal quantification (into the place of the first relatum) of the relation of being less than is the True’. Given Frege’s analysis, then, to explain how ‘x y x  y’ and ‘y x x  y’ can differ in respect of truth, it suffices to explain how the universal quantification of the existential quantification of a given function can differ from the existential quantification of the universal quantification of that very function. But that is explained by a more general, and more familiar, principle of the theory of functions: in applying two second-level functions (what a modern mathematician would call ‘functionals’) to the same first-level two-place function, the order of application matters. That different truth-values can be obtained by reversing the order of quantifiers in a doubly quantified sentence is explained, then, by the same basic principle that also explains, for example, why different numerical values can be obtained by reversing the definite integrals in a double integration.4 4. Frege himself makes the comparison between quantifiers and definite integrals: ‘Second-

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In saying this, I am not recommending that we revert to formalized languages cast from Frege’s mould. Frege’s perception of the analogies between quantifiers and functionals was perhaps his single most important insight: by his own account, it opened the door to many others (see again Frege 1906a). Today, we can be grateful for his having seen the analogy, whilst ourselves resisting the temptation to turn quantification into a special case of functional application. Frege, though, was writing at a time when multiple quantification was still found mystifying, so we can well see why he went further, and analysed quantification as a special case of something that was better understood. At any rate, it was this impulse that led him to the notion of a ‘name of a truth-value’ and to postulating truth-values as objects—not an inept attempt to assimilate sentences to names. Admittedly, a passage in “Über Sinn und Bedeutung” suggests a more ‘philosophical’ argument for the thesis that truth-values are objects, one that does not depend on the syntax of Frege’s preferred formalized language: These two objects [the True and the False] are recognized, if only implicitly, by everybody who makes a judgement, who takes something to be true—and so even by a sceptic. The designation of truth-values as objects may appear to be an arbitrary fancy or perhaps a mere play on words, from which no profound consequences may be drawn. What I am calling an object can be discussed more exactly only in connection with concept and relation. I will reserve this for another essay [viz., “Über Begriff und Gegenstand”]. But so much should already be clear, that in each judgement [sc., in each act of recognizing the truth of a thought]—however self-evident it may be—the step from the level of thoughts to the level of reference (the objective) has already been taken (Frege 1892, 34).

However, it is hard to see how this sketch could be elaborated so as to produce a cogent argument for the claim that truth-values are objects. As we shall see, it is far from clear that making a judgement is a matter of ascribing truth to a thought, let alone that it involves recognizing that a certain complex singular term stands for the truth-value True. At any rate, Frege never properly spells out the argument at which he gestures here, and the absence of any mention of it from the Logische Untersuchungen suggests that by that stage Frege himself had come to doubt whether it could be cogently elaborated. level functions have actually long been used in Analysis, e.g., definite integrals, insofar as we regard the function to be integrated as the argument’ (Frege 1891, 27).

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My suggestion, anyway, is that Frege’s doctrine that truth-values are objects never rested on the ‘gratuitous blunder’ of assimilating sentences to names. His chief ground for accepting the doctrine was always the logico-philosophical virtues of a formalized language in which all that is specific to a sentence’s content is localized within a component complex singular term. He continued to accept the doctrine into old age, and we may suppose that he did so because he saw no better way of formalizing the logic of quantification than that presented in Grundgesetze. That supposition explains why the doctrine is not expounded in the Logische Untersuchungen:5 in that ‘philosophical’ treatise, there is no discussion of formalization. But since Frege’s ground for the doctrine is weak, we can set it aside, and assess the arguments that he advances about truth in his late work on their own merits. 2. The Ramsey-Prior theory of truth Let us return to the two late passages about truth quoted at the start of § 1. In both of them, Frege starts from the claim that any instance of It is true that A  has the same content as the corresponding instance of A. Adopting some useful terminology of Simon Blackburn’s, we may describe Frege as starting from the claim that the expression ‘it is true that’ is transparent.6 In the first paragraph quoted from “Meine grundlegenden logischen Einsichten”, Frege observes that the transparency claim ‘may lead us to think that the word “true” has no sense at all’, and it is easy to spell out an argument which might lead one to think this. One way of formulating the transparency thesis is that any instance of It is true that A  has the same content as the corresponding instance of  A , where ‘’ is a ‘null’ operator without any semantic content. And then, it might be argued, ‘it is true that’ must have the same content as this null operator, so ‘it is true that’ will have no content at all. But this argument is a bad one. First, even if the operator ‘it is true that’ lacked content, it would not follow that the same went for genuinely predicative occurrences of the word ‘true’, as in 5. His decision to write ‘as though truth were a property, until some more appropriate way of speaking is found’ (Frege 1918, 61–2) may, though, be an allusion to the doctrine. 6. ‘It is as though you can always look through “it is true that” to identify the content judged, inquired after, and so on, as if the reference to truth was not there’ (Blackburn 1984, 227). Frege makes the transparency claims in earlier writings: see e.g. Frege 1892, 34 and Frege 1897, 153 = Frege 1979, 141.

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‘Pope Benedict’s most recent pronouncement is true’, so the argument fails to establish that ‘true’ lacks a sense. But in any case the argument does not even show that ‘it is true that’ lacks content: it is an egregious example of what P. T. Geach called the ‘cancelling-out fallacy’ (Geach 1980, 88). ‘Brutus killed Brutus’ says the same as ‘Brutus killed himself ’, but we cannot ‘cancel out’ the corresponding occurrences of ‘Brutus’ to conclude that ‘killed Brutus’ means the same as ‘killed himself ’. Again, ‘It is actually red’ says the same as ‘It is red’, but we cannot conclude that ‘actually’ lacks semantic content: ‘It is possible that everything that is actually red should have been shiny’ has quite different truth-conditions from ‘It is possible that everything that is red should have been shiny’ (Davies 1981, 220). Similarly, in the present case, we cannot cancel out the corresponding instances of A to conclude that ‘it is true that’ has the same meaning as our postulated null operator. It is consistent with the transparency thesis that ‘it is true that’ should possess substantial semantic content. It is, indeed, clear that the word ‘true’ does have a sense: it contributes systematically to the sense of a statement7 in which it occurs.8 In ‘Pope Benedict’s most recent pronouncement is true’, the word ‘true’ clearly contributes to the sense of that statement—that is, to the thought expressed by the statement. If we were simply to delete ‘true’, we would no longer have a complete statement. And if we were to replace it with a non-synonymous 7. By a ‘statement’, I understand an ordered pair whose first element is a declarative type sentence (identified as belonging to a language), and whose second element comprises all the contextual features that may be relevant to assessing the truth or falsity of an utterance of that type sentence. (Thus if a statement’s first element is the English type sentence ‘You are ill’, its second element will comprise the addressee and the time of utterance.) Because they belong to languages, my statements are not Fregean thoughts: a statement has, or expresses, a propositional content; it is not itself such a content. But it makes sense to predicate truth or falsity of statements simpliciter. It also makes sense to speak of a statement’s being asserted and denied: a statement will be asserted if its component sentence is uttered or inscribed with assertive force in the relevant context of utterance. 8. On the best elaboration of Frege’s theory of sense and reference, there is no room for the claim that a sub-sentential expression has a sense which makes no contribution to the thought expressed by a statement in which the expression occurs. (Certainly, no elaboration of the theory of sense and reference that respects Frege’s earlier Context Principle can allow such a claim.) It may be that, in the passage quoted from “Meine grundlegenden logischen Einsichten”, Frege is entertaining a view whereupon the word ‘true’ has an established meaning, but one which does not contribute to the thought expressed by a statement in which the word occurs. Frege leaves room for expressions of this kind: the examples he gives include interjections like ‘unfortunately’ and ‘Thank God’ (in German ‘gottlob’ (!)), which ‘act on the hearer’s feelings, his mood, or arouse his imagination’ (Frege 1918, 63) but lack cognitive content. But any account of the meaning of ‘true’ along these lines would be utterly implausible.

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predicate—as it might be, ‘false’—then the resulting statement would express a very different thought from the original. It is beyond doubt that ‘true’ makes a regular contribution to the thought that is expressed by a statement containing it. Frege, then, should not even have flirted with the idea that ‘true’ altogether lacks a sense. Rather, the interesting question raised by the passages we are considering is this: is it possible to specify the sense of ‘true’ in such a way as to validate the transparency claim? That is: can we specify the systematic contribution that ‘true’ makes to the statements in which it appears in such a way that any instance of It is true that A  has the very same content as the corresponding instance of A? In addressing this question, it helps to bring into consideration the work of F. P. Ramsey. Like the Frege of the Logische Untersuchungen, Ramsey starts from the transparency claim: ‘“It is true that Caesar was murdered” means no more than that Caesar was murdered, and “It is false that Caesar was murdered” means that Caesar was not murdered’ (Ramsey 1927, 38). He recognizes that an account of ‘true’ cannot confine itself to cases in which the word is wrapped up as part of the operator ‘it is true that’. But he seems to glimpse a way of extending a treatment of truth that respects the transparency claim so that it covers the genuinely predicative uses of ‘true’: In the […] case in which the proposition is described and not given explicitly [as in ‘The Pope’s most recent pronouncement is true’] we have perhaps more of a problem, for we get statements from which we cannot in ordinary language eliminate the words ‘true’ and ‘false’. Thus if I say ‘He is always right’, I mean that the propositions he asserts are always true, and there does not seem to be any way of expressing this without using the word ‘true’. But suppose we put it thus ‘For all p, if he asserts p, p is true’, then we see that the propositional function p is true is simply the same as p, as e.g. its value ‘Caesar was murdered is true’ is the same as ‘Caesar was murdered’. We have in English to add ‘is true’ to give the sentence a verb, forgetting that ‘p’ already contains a (variable) verb. This may perhaps be made clearer by supposing for a moment that only one form of proposition is in question, say the relational form aRb; then ‘He is always right’ could be expressed by ‘For all a, R, b, if he asserts aRb, then aRb’, to which ‘is true’ would be an obviously superfluous addition. When all forms of proposition are included the analysis is more complicated but not essentially different; and it is clear that the problem is not as to the nature of truth and falsehood, but as to the nature of judgement or assertion, for what is difficult to analyse in the above formulation is ‘He asserts aRb’. (Ramsey 1927, 38f.)

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Commenting on this passage, Davidson remarks that ‘if Ramsey had carried out the “more complicated” analysis [that he contemplates here], he might have ended up with something much like one of Tarski’s truth definitions’ (2005, 11). But this is surely wrong. For Tarski, the primary bearers of truth were declarative sentences, and while Ramsey is more casual about quotation marks than a modern reader might wish, it is tolerably clear that his variable ‘p’ is to be replaced by substituents such as ‘the proposition that Caesar was murdered’, not ‘the English sentence “Caesar was murdered”’.9 Ramsey faces a problem because an expression like ‘the proposition that Caesar was murdered’ is grammatically a complex singular term, and so needs to be attached to a predicate in order to fill the gap in ‘If he asserts that Caesar was murdered, then ---’. Since we shall only get the intended result if the predicate to which it is attached means ‘is true’, the hoped for analysis of ‘true’ is compromised. Thus what Ramsey is groping for in the ‘perhaps clearer’ proposal is not a Tarksian truth definition, but a form of quantification whose variables may be replaced by complete sentences, not singular terms.10 A substitutional reading of the quantifier will not serve here. The formula p (if he asserts that p, then p), where ‘p’ is a universal substitutional quantifier whose substitution class comprises complete sentences, is perfectly well formed. But it will be understood to mean that every substitution instance of the schema ‘if he 9. For this reason, among others, we should not confuse the redundancy theory espoused here by Ramsey, with the ‘disquotational’ account of truth espoused by Quine, whereby ‘the truth predicate is a device of disquotation’ or semantic descent (Quine 1986, 12). Both theories may be called ‘minimalist’ or deflationary, inasmuch as they deny that there is much for a philosopher to say in answering the question, what it is for a potential bearer of truth to be true. But they differ radically over what the primary bearers of truth are. For Quine these must be things that can be quoted; he duly takes them to be eternal type sentences or individual tokens of sentences. (Other sorts of thing may be deemed to be true only in a transferred sense, as when we call a belief true when a true sentence could express it.) For the Ramsey of “Facts and propositions”, by contrast, ‘truth and falsity are ascribed primarily to propositions’ (Ramsey 1927, 38)—although he went on argue that apparent reference to propositions should itself be eliminated, and later held that the primary bearers of truth were individual instances of belief. (See Ramey 1991 and, for discussion, Rumfitt forthcoming.) Each theory has very different problems and prospects. 10. This anti-Davidsonian reading is confirmed by the unfinished manuscript on truth that Ramsey wrote about a year after publishing “Facts and propositions”. See Ramsey 1991, 9 and 15, and Rumfitt forthcoming.

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asserts that p, then p’ is true, so it is of no use in showing how to eliminate all occurrences of ‘true’.11 Prior, though, found what Ramsey needed.12 English, he noticed, is replete with ‘non-nominal’ quantifier expressions, including words that function grammatically as adverbial phrases, as in ‘I met him somewhere’ and ‘However he threw it, the boomerang came back’. Wittgenstein, Prior further remarked, had noted that ‘this is how things are’ and ‘things are thus’ can play the role of ‘propositional variables’ in a formal language (see Wittgenstein 1953, Part I § 134). In ‘He explained his position to me, said that this was how things are, and that therefore he needed an advance’ (Wittgenstein’s example), ‘this is how things are’ gets its sense from an antecedent complete sentence, rather as some pronouns pick up their reference from an antecedent name. Putting these points together, Prior found a way of expressing ‘He is always right’ without using the word ‘true’: ‘“However he says things are, thus they are” is a very natural rendering of “For all p, if he says that p, then p”’ (Prior 1971, 38).13 The quantification into sentence position that is invoked here is not substitutional: we need not assume that, however things may be, there is a sentence in the relevant substitution class which says that they are thus. 11. Hartry Field once suggested reading a universally quantified formula (under the substitutional interpretation) as a conjunction (which will in general be infinite) of all the instances of the quantificational matrix (see Field 1986, 55f.). Thus ‘p (if he asserts that p, then p)’ will be understood to say ‘If he asserts that snow is white then snow is white, and if he asserts that coal is pink then coal is pink, and…’ But whatever its general merits as an account of the substitutional quantifier, on this reading of ‘p’, ‘p (if he asserts that p, then p)’ does not capture the content of ‘Whatever he says is true’. For surely the latter statement does not say ‘If he asserts that snow is white then snow is white, and if he asserts that coal is pink then coal is pink, and…’. One can, after all, understand ‘Whatever he says is true’ without understanding ‘snow’, ‘white’, ‘coal’, or ‘pink’. Compare Frege: ‘It should be clear that someone who utters the sentence “All men are mortal” does not mean to state something about a certain Chief Akpanya of whom he may never have heard’ (Frege 1894, 327). 12. In fact, Prior thought Ramsey had already found it: ‘Ramsey thought of this one too [sc., the problem of extending the redundancy theory to cases in which truth is ascribed to unspecified statements]; his answer to it—the right one, it seems to me—was to move to a slightly more stylized language than ordinary English, with quantifiers binding variables that stand for sentences’ (Prior 1971, 24). All the same, the ‘slightly more stylized language’ needs to be explained, and the explanation must not employ the concept of truth. Prior’s contribution was to provide such an explanation. 13. Prior also suggested rendering instances of quantification into sentence position using ‘anywhether’ and ‘somewhether’ as quantifiers and forms of ‘thether’ as the attendant variables (see Prior 1971, 37ff.). Thus ‘For all p, if he says that p, then p’ would be glossed: ‘Anywhether, if he says that thether, then thether’. But these neologisms have won few friends, and I prefer to revert to Wittgenstein’s original formula.

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There is, all the same, an issue about how sentential quantification is to be pressed into service in illuminating the topic of truth. In 1927, Ramsey was seeking a generally applicable method for eliminating (his term) the words ‘true’ and ‘false’; only this would clear up the ‘linguistic muddle’ that truth presents. But there is no good reason to deem the notion of truth to be muddled.14 Putting the semantic paradoxes aside (cfr. n. 25 below), ‘true’ is a perfectly intelligible, and coherently applicable, English predicate which many things (of many different kinds) satisfy, and which many other things do not. The word calls for explanation—that is, for a specification of its sense—not elimination. Prior saw things this way.15 He deploys his sentential quantifiers to elucidate—indeed, to define—the sense of ‘true’. Like Ramsey, he regards propositions (Fregean Gedanken) as ‘pseudo-entities’; apparent reference to them is to be eliminated by logical analysis. However, he proceeds to give an account of truth and falsehood […] as applied to particular believings and assertings. ‘X ’s belief (assertion) that there will be a nuclear war is true’ means no more and no less than ‘X believes (says) that there will be a nuclear war, and there will be one’, while ‘X ’s belief (assertion) that there will be a nuclear war is false’ means no more and no less than ‘X believes (says) that there will be a nuclear war, but there won’t be one’. Justified and unjustified hopes and fears can be similarly dealt with. (Prior 1971, 21)

Like Ramsey, Prior begins with the simple cases, in which the content of a belief or assertion is expressly reported. But truth-bearers of all kinds will have, or express, propositional contents: a belief (or assertion, or …) is always a belief (or …) that things are thus-and-so. So we may deploy Prior’s sentential quantifiers to make the requisite generalization, and say that a belief is true if and only if, for some p, it is a belief that p, and p; that an assertion is true if and only if, for some p, it is an assertion that p, and p;

14. As Ramsey himself saw by 1928, when he began his unfinished book on truth. See Ramsey 1991, 6ff. and Rumfitt forthcoming. 15. One of Wolfgang Künne’s contributions to the contemporary debate about truth has been to revive interest in the theory expounded in Prior’s posthumously published Objects of Thought. That theory made a deep impression on some philosophical logicians of the time (see notably Mackie 1973, chap. 2). But by 1999, when Künne came to Oxford to deliver the Jal Pavry Lectures, appreciation of its merits was confined to a dwindling band of philosophers, each of whom had been taught either by Prior himself or by one of his close associates. As a member of the band, I hope that Conceptions of Truth, the book that resulted from those Lectures, will inspire further work on Prior’s theory.

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and so forth.16 That is: a belief (or assertion, or …) is true if and only if it is a belief (or …) that things are somehow, and things are thus. There is a parallel explanation of ‘false’: a belief (or …) is false just in case, for some p, it is a belief (or …) that p, and it is not the case that p.17 Indeed, Prior presses this as far as to yield actual definitions of truth and falsity—or, at least, schemata that yield definitions of truth and falsity as these notions apply to various sorts of truth-bearer. The schema for truth is (T ) a is true if and only if for some p, a is a…that p, and p and that for falsity is (F ) a is false if and only if for some p, a is a…that p, and it is not the case that p. Let us call the theory of truth that comprises the various instances of the schemata (T ) and (F ) the Ramsey-Prior theory. In these schemata, the lacunae are to be replaced by a specification of the sort of thing (belief, assertion, …) that the truth-bearer is. But it is the schemata themselves that partly specify the established meanings or senses of the words ‘true’ and ‘false’—the meanings that are common to their various applications. I say ‘partly specify’, for a full specification must delineate the things to which these predicates can apply, and (T ) and (F ) permit an application that is wider than most competent users of ‘true’ and ‘false’ will accept. I desire that it does not rain while I am walking; and it does not rain while I am walking. So, for some p, my desire is a desire that p, and p. All the same, most English speakers are reluctant to predicate truth of desires. Some philosophers regard this reluctance as mere prejudice. However, I think we can respect it without departing from the deflationary view of truth and falsity that (T ) and (F ) encapsulate. For we can say that a mental state whose content is (the thought) that p is a candidate for truth only if it is defective unless p. Thus beliefs are candidates for truth because a belief 16. As Künne notes, Ramsey anticipated precisely this account of the truth of individual believings in his incomplete manuscript of 1928: see Künne 2003, 340, which quotes from Ramsey 1991, 15. 17. See Prior 1971, 98f. On Prior’s account, only something that has, or that expresses, a content can be false, so ‘false’ is not equivalent to ‘not true’. That is as it should be: my left leg, for example, is neither true nor false.

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that p is defective unless p. A belief that p is not well placed to fulfil the role that beliefs have—au fond, that of guiding actions so that they realize the believer’s desires—unless p. In this sense, a belief must ‘fit’ the world. By contrast, its not being the case that p does not imply that a desire that p is defective. A desire is not expected to fit the world. Rather, in attempting to fulfil our desires, we expect to have to change how things are. Admittedly, this account needs to be extended carefully in explaining why various sorts of linguistic item are candidates for truth. An assertion that p may also be said to be defective unless p. An assertion that p is not well placed to play the role that assertions play in our linguistic economy— the role, au fond, of being utterances on which hearers can rely in forming beliefs of their own—unless p.18 However, many declarative utterances and inscriptions which say that p (i.e., which express the thought that p) are non-defective even though not p. 2 is not a rational number, but there is nothing defective in the inscription ‘2 is rational (assumption)’ as it figures in a proof by reductio of 2’s irrationality. Among utterances and inscriptions, it would seem that only assertions are, centrally, candidates to be true, but that we extend the application of the truth-predicate by courtesy to other utterances of assertoric sentences (i.e., to other utterances of sentences that could be used in making assertions). From this perspective, the modern tendency to take truth to apply primarily to the entire class of assertoric utterances and inscriptions looks quite wrong-headed. For it is only by an extension of meaning that many items in this class qualify as candidates for truth. The dots in (T ) and (F ), then, must be filled with the name of a kind of thing that is a candidate to be true. All the same, even when this restriction is imposed, the schematic formulation of (T ) and (F ) brings with it a real benefit. We apply truth and falsity to things of many different kinds: we say that the witness’s testimony, which took up the whole of Tuesday afternoon, was true in every particular; that the rumour now sweeping Westminster that Peter Mandelson has resigned from the Cabinet is false; and so forth. Rumours and pieces of testimony are different sorts of thing, and each in turn is different from the theorems, conjectures, etc., to which we also ascribe truth and falsity. Of course we want an account of the senses of ‘true’ and ‘false’ which makes their application to things in diverse categories more than mere homonymy. But it is arbitrary to unify the senses 18. A false belief and a false assertion, then, are defective in different (although related) ways. Those differences reflect differences between the roles that beliefs play in an individual thinker’s mental economy and the roles that assertions play in our shared linguistic economy.

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by deeming one application of these predicates to be ‘primary’ and reducing the others to that one. The schematic specification of the senses of ‘true’ and ‘false’ avoids such arbitrariness. The common schema of definition, (T ), gives the condition for applying the word ‘true’ to a potential truthbearer, something that is common to its various determinations. This marks a point of difference with Wolfgang Künne’s own theory. According to Künne, ‘true’ applies primarily to propositions, and in that application it may be defined by the ‘modest’ principle (MOD)

x (x is true p ((x = the proposition that p)  p)).19

I agree with Künne that we often speak and reason as though propositions are objects. Pace Prior, belief in propositions is not a simple mistake, born of misconstruing ‘Fred believes that there is life on Venus’ as a relational sentence when it should properly be divided ‘Fred / believes that / there is life on Venus’ (cfr. Prior 1971, 19). Rather, the relational parsing is well nigh forced on us by our acceptance of such inferences as ‘Fred believes Einstein’s Law; Einstein’s Law is (the proposition) that E = mc 2; therefore Fred believes that E = mc 2. But, as I have argued elsewhere (Rumfitt 2011), we succeed in making singular reference to propositions (or Fregean Gedanken) only when certain conditions are met in the relevant context of discussion. By contrast, our ascriptions of truth and falsity to more readily identifiable objects, such as particular utterances or inscriptions of declarative sentences, do not depend on those conditions obtaining. So it is a mistake to regard propositions as the primary bearers of truth. If there are such objects as propositions, then (MOD) tells us what it is for any one of them to be true. But even if such objects exists, we should prefer the more general schema (T ) to Künne’s (MOD) as a specification of what it is for something to be true.20 19. Künne 2003, 337. The corresponding principle for falsity will say: x (x is false p ((x = the proposition that p)  p)). Contra Ramsey, these two principles together dispel any mystery over the relationship between truth and falsity as these notions apply to propositions. 20. Künne’s belief that propositions are the primary bearers of truth also leads him to propound a doctrine that will make the further development of the Ramsey-Prior theory far harder than it needs to be. According to Künne, the quantifier ‘p’ used in (MOD) is at once non-nominal quantification into sentence position and quantification over propositions (Künne 2003, 360, 365). The notion of what a species of quantifier ‘quantifies over’ properly belongs to a formal semantic theory—e.g., a theory of truth, or of truth under an interpretation—for a language containing that species of quantifier, and Künne does not propound theories of this

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3. On the definability of truth Prior took the various determinations of (T ) to define the sense of ‘true’, as it applies to various sorts of thing. However—in his later writings, as earlier—Frege insisted that truth is indefinable. Does this mean that a Fregean cannot accept the Ramsey-Prior theory? Before we can address the question, we need to resolve an equivocation on the term ‘indefinable’. The Ramsey-Prior theory yields a definition of truth in the sense that it specifies necessary and sufficient conditions for applying the predicate ‘true’ to various sorts of truth-bearer. It is consistent with its successfully doing so much that it should be ineffective in explaining the concept of truth to a thinker who does not already possess that concept. When Frege argues for the indefinability of truth, however, he is precisely arguing that it is impossible to explain the notion of truth to someone who does not already possess it. His conclusion might more happily be expressed as the thesis that truth cannot be analysed than as the thesis that truth is indefinable. For what exactly is Frege’s argument? In “Der Gedanke”, he presents it as follows: Any other attempt to define truth also breaks down. For in a definition one would have to specify certain characteristic marks (Merkmale). And in application to any particular case the question would always arise whether it was true that these characteristic marks were present. So we should be going round in a circle (Frege 1918, 60).21 kind. But it is far from clear how a semantic theory could assign to ‘p’ both of these roles. A true Priorean, in contrast, will not try. On Prior’s view, it is Quinean dogma to suppose that there must be a category of things over which a non-substitutional quantifier is understood to range. The sentential quantifiers may be explained, or glossed, just as Prior explained them, and once they are understood, they may be used (in the metalanguage in which the semantic theory is stated) to specify the conditions under which formulae containing them are true, or are true under a given interpretation. There can be no objection in principle to this sort of circularity, for objectual quantifiers are used in formulating semantic theories for languages containing objectual quantifiers. To be sure, the construction of such a theory faces some technical problems. Consideration of those must wait for another occasion. 21. The immediately preceding sentences in “Der Gedanke” suggest a rather different argument for the indefinability of truth. Namely: if the truth of a thought were defi ned as its possessing characteristics F, then in order to enquire whether it was true, we should have to enquire whether it was F. To enquire whether a thought is F, however, is to enquire whether it is true that it is F. This enquiry would involve enquiring whether the thought that the first thought is F is itself F. And so forth. The argument for indefinability is then that any definition of truth

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The argument rests on a perceived difficulty in applying a definition of truth and, given other Fregean theses, it is straightforward to say where Frege thought that the difficulty lay. Frege always posited a close connection between truth and assertion. He defines an assertion as the verbal expression of a judgement; and to judge is to recognize the truth of a thought. In asserting that p, then, a speaker presents the thought that p as true. But if this is right, then there is a patent difficulty in analysing truth, if an analysis is supposed to enable someone with no prior apprehension of that concept to grasp it. For in advancing such an analysis, its proponent will assert that something is true if and only if it has such-and-such a property, or stands in such-and-such a relation to other things. One requirement, if such an assertion is to constitute an analysis of ‘true’, is that the specified properties or relations should not presuppose the concept of truth. At least for the sake of argument, Frege is prepared to concede that this requirement can be met. Another requirement, though, cannot be met. If the recipient of the putative analysis of ‘true’ is to receive it in the way intended, he must apprehend it as an assertion. But in order so to apprehend it, he must know that the analysis is being presented as true. So, even if the particular analysans does not presuppose a grasp of the concept of truth, the total speech act of propounding the analysis does. This argument relies upon the fact that in applying any definition of truth, one will need to make an assertion or a judgement, and one will thereby presuppose an understanding of the notion of truth. So, if it works at all, the argument is effective against any candidate analysis of truth. This is why Frege concludes that it would be ‘futile to employ a definition in order to make it clearer what is to be underwould send us on an infinite regress. Dummett (1981, 442f.) reconstructs Frege’s argument for indefinability in this way. Dummett then objects that this argument ‘does not sustain the strong conclusion that [Frege] draws, namely that truth is absolutely indefinable’ (op. cit., 443). In order to do that, it would have to be shown that the regress is vicious. But there is no reason to suppose that it is vicious. As Dummett remarks, ‘it is true enough that, in determining that some statement A is true, I thereby also determine the truth of infinitely many other statements, namely ‘A is true’, ‘The statement “A is true” is true’, … But there is no harm in this, as long as we recognize that the truth of every statement in this series is determined simultaneously: the regress would be vicious only if it were supposed that, in order to determine the truth of any member of the series, I had first to determine that of the next term in the series’ (ibid.). I agree with Dummett that, on this reconstruction, Frege’s argument fails to yield its intended conclusion. I appear to differ from him, though, in holding that Frege had a simpler and better argument for his conclusion—one which does not depend on the viciousness of any infinite regress.

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stood by “true”’ (Frege 1897, 139 = Frege 1979, 128). Truth is incapable of analysis.22 Like Wolfgang Künne (2003, 449–52), I doubt the main premiss of this argument—viz., that one needs the concept of truth in order to make an assertion or to apprehend an assertion as such. In order to make an assertion, one must implicitly understand that there are norms regulating acts of assertion. And in apprehending an assertion, one must implicitly understand that the speaker at least presents himself as conforming to those norms. It is far from clear, though, that understanding those norms requires grasping the concept of truth. One might understand them as schemata such as ‘Assert that p only when you know that p’, or ‘Assert that p only when you are justified in believing that p’. Contrary to Frege’s view, indeed, Dummett has argued (in his 1990) that it is the concept of justified belief that is latent in the notion of assertion, and that we come by the concept of truth only when we master the rules for asserting certain complex sentences—notably indicative conditionals. For, as is clear from examples like ‘If Mrs Thatcher spied for the KGB, then she will have taken care to destroy all the evidence that she did so, so we shall never be justified in believing that she did’, what we conditionalize upon in asserting a conditional is the truth of the antecedent, not its justifiability. I cannot assess Dummett’s argument here, but if its conclusion is correct, then the premiss of Frege’s argument for the indefinability of truth is wrong. Moreover, Frege’s dictum that to judge is to recognize the truth of a thought will need to be amended. However we assess Frege’s argument, though, its conclusion does not gainsay the Priorean theory of truth. Even if truth cannot be explained in more primitive terms, every instance of the schema (T) may yet be correct, and collectively its instances may specify the conditions for things of various kinds to be true.23 22. James Levine (1996) rightly stresses the role played by Frege’s account of assertion in the argument for the indefinability of truth. But he complicates matters unnecessarily by claiming that the argument also rests on Frege’s principles of definition. Those principles concern the introduction into a language of a new expression, not hitherto understood. So they do not directly bear on the enterprise of analysing the notion of truth. (For Frege’s views on the difference between defining a new term and analysing the sense of an expression with an established use, see especially Frege 1914, 226–29 = Frege 1979, 209ff.) 23. There is also the question of whether (T) gainsays Tarski’s theorem that truth is indefinable and, if it does, which of Tarski’s premisses the Ramsey-Prior theorist should reject. The issue is delicate, because Tarski takes the basic application of truth to be to sentences; he then has to relativize the ascription of truth to languages. For relevant discussion, see Prior 1971, chap. 8 and the writings cited in n. 25 below.

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4. Merits of the Ramsey-Prior theory of truth The Ramsey-Prior theory of truth has a number of merits. First, as we have seen, it confirms that the word ‘true’ has a Fregean sense: it specifies the regular contribution that the word makes to the thought expressed by a statement that contains it. Second, pace the doubts Frege expresses in his late writings, that specification vindicates the commonsense view that ‘ is true’ is grammatically and semantically a predicate. So, if we understand a property as Frege understands it—namely, as the reference of an intelligible predicate—then we should overcome those doubts and admit that truth is a property. All the same, the Ramsey-Prior theory goes some distance towards vindicating Frege’s claim that any statement A is equivalent to the corresponding statement It is true that A , so that ‘with every property of a thing there is tied up a property of thoughts’. Exactly how it does so depends on how we construe statements of the form It is true that A . Künne adduces evidence for the view that these statements involve a truth-predicate. In ‘It is true that his paper is clever, but her objection is also true’, the ‘also’ would be out of place if there were no previous occurrence of a truth-predicate (Künne 2003, 351). One might add that our evaluation of certain inferences supports the same conclusion. ‘Alfred believes that sea-water is salt; it is true that sea-water is salt; therefore Alfred believes something true’ would seem to be logically valid as it stands, rather than an enthymeme. We can account for this if we construe ‘It is true that sea-water is salt’ as a cleft form of ‘That sea-water is salt is true’, i.e. ‘The thought that sea-water is salt is true’. Schema (T) then yields (1) It is true that sea-water is salt if and only if, for some p, (the thought) that sea-water is salt is a thought that p, and p. How does (1) vindicate the claim that a property of a thought is tied up with any property of a thing? Well, let us also assume that whenever the thought that q is a thought that p, then q if and only if p (where the biconditional is material). Applied to the present case, then, we have that (2) For any p, if the thought that sea-water is salt is a thought that p, then sea-water is salt if and only if p. Now suppose

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(3)

It is true that sea-water is salt.

From (1) and (3) we may then infer (4)

For some p, (the thought) that sea-water is salt is a thought that p, and p.

And from (2) and (4) we may infer (5)

For some p, sea-water is salt if and only if p, and p

which in turn yields (6)

Sea-water is salt.

Conversely, suppose (7)

Sea-water is salt.

(7) entails (8)

(The thought) that sea-water is salt is a thought that sea-water is salt, and sea-water is salt

which in turn yields (by existential generalization) (9)

For some p, (the thought) that sea-water is salt is a thought that p, and p.

Together with (1), (9) entails (10) It is true that sea-water is salt. Given the Ramsey-Prior theory of truth, then, we have a mutual entailment between ‘It is true that sea-water is salt’ and ‘Sea-water is salt’. The argument generalizes to establish a mutual entailment between any statement in the form It is true that A  and the corresponding instance of A. What about the stronger transparency claim from which Frege starts— the claim that any instance of It is true that A  expresses the same sense

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as the corresponding instance of A? The Ramsey-Prior theory of truth does not validate this claim; nor should it, for it is highly doubtful. If an instance of It is true that A  always means the same as the corresponding instance of A, then they must be false in precisely the same circumstances. However, some philosophers hold that ‘It is true that Zeus is bad-tempered’ (sc., ‘The thought that Zeus is bad-tempered is true’) is straightforwardly false—because the thought that Zeus is bad-tempered exists but is not true—whereas ‘Zeus is bad-tempered’ is neither true nor false—because there is no such thing as Zeus (cfr. Dummett 1959, 4f.). It is, in any case, notoriously hard to reconstruct from Frege’s texts a sufficient condition for two statements to share a sense;24 without such a condition, the transparency claim cannot be well founded. In his discussions of these matters, Frege sometimes writes as though the mark of two statements’ sharing a sense is that anyone who understands both of them will find it obvious that if one is true then so is the other. By itself, this cannot serve as the criterion of sameness of thought expressed, for the relation of obviously sharing a truth-value is not transitive. But it suggests a deflated transparency thesis which we can accept—namely, that corresponding instances of It is true that A  and A are obviously mutually entailing. Insofar as a thinker who grasps the notion of truth may be taken to possess implicit knowledge of (1), the simple derivation just presented may be regarded as spelling out explicitly the reasoning our implicit grasp of which makes this mutual entailment obvious.25 5. The need for a non-truth-conditional theory of content So far, so good, then. The Ramsey-Prior theory serves to separate sound from unsound elements in Frege’s late lucubrations about truth. There is, however, a problem. For the chief worry about the Ramsey-Prior theory— as about theories like it—has always been that it buys its elegance and 24. For discussion, see again Rumfitt 2011. 25. The Ramsey-Prior theory of truth also opens the way to a distinctive approach to the Liar paradox, whereby the paradox is taken to show that certain utterances and inscriptions of such sentences as ‘This statement is not true’ do not succeed in expressing a thought— even though the sentence is meaningful, and even though utterances or inscriptions of that sentence in other contexts would succeed in expressing thoughts. For versions of this approach see Prior 1971, chap. 6, Kneale 1972, Mackie 1973, chap. 6, Smiley 1993, and Williamson 1998. This approach to the Liar seems to me promising, but I cannot justify that assessment here.

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simplicity as a theory of truth at the price of incurring an unredeemable debt in the theory of content. The Ramsey-Prior theory makes free use of the notions of an assertion’s being an assertion that things are thus-and-so, of a belief ’s being a belief that things are thus-and-so, and so forth. But it precludes what many philosophers have taken to be the natural account of these notions. According to that account, part of what it is for an assertion to be an assertion that p is that the assertion is true if and only if p: this is the basic thought that underlies all truth-conditional theories of meaning. Indeed, many philosophers are attracted to a truth-conditional theory of content generally, not just of linguistic content. Thus, on a truth-conditional view of mental content, part of what it is for a belief to be a belief that p is that the belief will be true if and only if p. But the Ramsey-Prior theory precludes any of these theories of meaning or content from being accepted. If part of what it is for an assertion to be an assertion that p is that it is true if and only if p, then the formula ‘An assertion is true if and only if, for some p, the assertion is an assertion that p, and p’ cannot define ‘true’ as it applies to assertions. For such an application of ‘true’ will be implicit in the notion of something’s being an assertion that p, a notion which the definiens invokes. Similarly, if part of what it is for a belief to be a belief that p is that the belief is true if and only if p, then the formula ‘A belief is true if and only if, for some p, the belief is a belief that p, and p’ cannot define ‘true’ as it applies to beliefs. For such an application of ‘true’ will be implicit in the notion of a belief ’s being a belief that p. This is just to apply to the present case an observation that Dummett made long ago about the redundancy theory (see Dummett 1959). If, in saying what it is for an assertion or belief to be true, we take as understood such notions as being an assertion that p, and being a belief that p, then we cannot take the truth of an assertion or belief as understood in saying what it is for something to be an assertion, or belief, that p. If we did, we should have a single equation with two unknowns. Let us say that a theory of content answers such questions as what it is for something to be an assertion that p, and what it is for something to be a belief that p. Then what we have just seen is that the Ramsey-Prior theory of truth precludes any truth-conditional theory of content. Accordingly, some other theory of content must in the end be brought in to complement the Ramsey-Prior theory. In pressing Dummett’s point in the present connection, I am claiming only that the Ramsey-Prior theory of truth and the truth-conditional

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theory of content cannot combine to provide coherent answers to the two constitutive questions, ‘What is it for a truth-bearer to be true?’ and ‘What is it for a truth-apt utterance or a truth-apt mental state to have the content that it has?’ When they are so combined, the circle of explanation is so small that neither question can be said to have been answered. I do not deny that there are other philosophical projects to whose completion the theories can combine to contribute. In particular, it may be that anyone who grasps the concept of truth knows (implicitly) that a truth-bearer is true if and only if, for some p, it has the content that p, and p; and also that anyone who grasps the notion of having the content that p knows (implicitly) that if something has the content that p and is truth-apt then it is true just in case p. Whether true or false, these epistemological claims do not directly bear on the constitutive, or metaphysical, questions with which I am here concerned. The problem that Dummett’s point raises seems to be particularly acute for Frege. Many philosophers read § 32 of the first volume of Grundgesetze as the first clear statement of a truth-conditional account of content: ‘Not only a reference, but also a sense, appertains to all names correctly formed from our signs. Every such name of a truth-value expresses a sense, a thought. Namely, by our stipulations it is determined under what conditions the name refers to the True. The sense of this name—the thought—is the thought that these conditions are fulfilled’ (Frege 1893, 50). On this reading of § 32, there is a deep tension between Grundgesetze and Frege’s later minimalism about truth. Although he does not labour the point, the incompatibility between truth-conditional theories of content and his own redundancy theory of truth was clear to Ramsey. He concludes his discussion of truth by remarking that ‘the problem is not as to the nature of truth and falsehood, but as to the nature of judgement or assertion, for what is difficult to analyse in the above formulation is “He asserts aRb” […] what we have to explain is the meaning of saying that the judgement is a judgement that a has R to b, i.e. is true if aRb, false if not’ (1927, 39). His pragmatist theory of meaning is supposed to provide the needed account of the contents of judgements and assertions: ‘the meaning of a sentence is to be defined by reference to the actions to which asserting it would lead, or, more vaguely still, by its possible causes and effects’ (1927, 51). It would be worth investigating whether a pragmatist theory of content could be developed to the point where it could sustain the Ramsey-Prior theory of truth. This is not the place for that investigation, which would lead us far from 26

Frege.26 But where else—closer to home—might one look for a non-truthconditional theory of content? 6. Content as determined by the conditions for correct assertion At this stage, it helps to revert to another of the Delphic remarks quoted earlier from Frege’s Nachlaß. ‘What logic is really concerned with’, he says, ‘is not contained in the word “true” at all but in the assertive force with which a sentence is uttered’ (Frege 1915, 272 = Frege 1979, 252). As we have seen, Frege identifies assertions as the verbal expressions of judgements; he is clear that there are epistemic norms which regulate the making of judgements (see e.g. Frege 1897, 139 = Frege 1979, 128), and which consequently regulate the making of assertions. When those epistemic norms permit the assertion of a sentence (taken in a given context), we may call the corresponding statement ‘correctly assertible’. Part of Frege’s point in the sentence last quoted from him is that the laws of logic contribute to the epistemic norms of assertion: if a thinker is correct to assert some premisses, and deduces a conclusion from them in accordance with the laws of logic, then he is also correct to assert the conclusion. Now the Fregean sense of an expression is the contribution it makes to the logically relevant content of a sentence that contains it (see e.g. Frege 1906c, 213f. = Frege 1979, 197f.). The Delphic remark also suggests that a statement’s logically relevant content may be given by the conditions under which it is correctly assertible—its assertibility-conditions, for short. Could Frege accept such a theory of content—a theory whereby a statement’s sense is given by its assertibility-conditions—as what he needs to complement the Ramsey-Prior theory of truth? I do not think that the passage quoted from § 32 of Grundgesetze should be read as precluding his doing so. To be sure, the passage looks at first glance as though it might be an early piece of writing by Donald Davidson, 26. Recent attempts to develop a pragmatist theory of content along Ramseyan lines have rested on what has come to be called Ramsey’s Principle: ‘a belief ’s truth conditions are those that guarantee the success of an action based on that belief whatever the underlying motivating desires’ (Dokic and Engel 2005, 8; see also Whyte 1990; Dokic and Engel 2002). But even philosophers sympathetic to pragmatism have noted that a presupposition of Ramsey’s Principle is false: the truth of a belief almost never guarantees the success of an action based upon it; even the best laid plans are liable go awry. (For this point, see Brandom 1994 against Whyte, and Blackburn 2005 against Dokic and Engel.) I investigate whether a pragmatist can do better in Rumfitt forthcoming.

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whereby the sense of a statement is given by its truth-conditions, not its assertibility-conditions. But that cannot be the right reading. As Davidson well appreciated, if a statement’s sense is to be given by its truthconditions, then the notion of a statement’s truth cannot be explained as the truth of the thought it expresses. If a statement’s content is to be given by the conditions for it to be true, then truth for statement cannot be explained in terms of truth for contents (or Fregean thoughts). As we have seen, though, that is how Frege always insisted on explaining it: ‘For brevity, I have here called a sentence true or false although it would certainly be more correct to say that the thought expressed in the sentence is true or false’ (Frege 1914, 251 = Frege 1979, 233; see further Dummett 1986, 253). How, then, are we to read the passage quoted from Grundgesetze? I propose that we should read it in the context of Frege’s lifelong insistence that the truth—or the truth-value True—is what any serious inquiry aims to reach. The very first sentence of the early “Logik” tells us that truth is the goal of intellectual inquiry (‘das Ziel des wissenschaftlichen Strebens’) (Frege 1879–91, 2 = Frege 1979, 2). As many as forty years later, the second sentence of “Der Gedanke” says that all intellectual disciplines (‘alle Wissenschaften’) have truth as their goal (1918, 58), words that are taken almost verbatim from the “Logik” of 1897 (Frege 1897, 139 = Frege 1979, 128). But what does Frege mean by saying that truth is the aim of inquiry? The “Einleitung in die Logik” of 1906 contains a striking gloss, where Frege equates concerning ourselves with truth (wenn es uns um Wahrheit zu tun ist) with engaging in serious intellectual inquiry (wenn wir uns wissenschaftlich verhalten) (Frege 1906b, 210 = Frege 1979, 194). Now merely happening to hit upon the truth is different from successfully concluding an inquiry, just as merely happening to hit the bulls-eye is different from succeeding in one’s goal of throwing the dart at the bulls-eye. If someone succeeds in hitting the bulls-eye, then he will have hit it, but his having hit it will be the result of his having aimed the dart at the bulls-eye. Similarly, when a serious intellectual inquiry is brought to a successful conclusion, the report of the outcome will be true; but the statement in question will be more than one that merely happens to be true—or to have a business part which ‘refers to the True’. For the investigation will have been concluded successfully only when the inquirer has come to know the answer to the question that he set out to investigate, so the final report of a successfully concluded inquiry will not merely happen to hit the truth, but will express the knowledge that the investigator has gained.

28

Putting these elements together, we reach a position whereby a statement’s sense (its logically relevant content) is given by the conditions under which a thinker who conforms to the norms of wissenschaftliches Verhalten is entitled to assert it. In other words, we reach a position whereby a statement’s sense is given by the conditions under which it may be correctly be asserted. Despite his having for many years contrasted such an account of sense with Frege’s, Michael Dummett has lately attributed this position to Frege. In the course of replying to an essay by Eva Picardi, Dummett suggests that we need to distinguish two notions of truth in Frege. The first notion, commonly expressed by the predicate ‘ is true’, is ‘merely an identity operation at the level of sense rather than of reference, which maps any thought on to that very thought’ (Dummett 1994, 282f.). The second notion, which Frege usually signifies by ‘truth’ or ‘the True’, is ‘that to which assertoric force constitutes a claim’; we apprehend this second notion through our grasp of the difference between ‘the expression of a judgment [and] the mere expression of a thought’ (op. cit., 283). When Frege says that truth is the subject-matter of logic, or that logic comprises the laws of truth, it is this latter notion that he has in mind. Crucially for present purposes, the same goes for the claim in Grundgesetze that the thought a sentence expresses is determined by the conditions for it to refer to the True. For ‘what it is for any sentence to be true—considered, when necessary, as uttered in particular circumstances—is given by the significance an assertion of it would have’ (op. cit., 284). On this conception of the matter, it is the conditions for correct assertibility that are the fundamental determinants of sense. Dummett’s distinction between these two notions of truth responds to something important and insightful in Frege’s conception of the relationship between logic and truth.27 All the same, I do not think that Frege could accept any theory whereby a statement’s sense (its logically relevant content) is given by the conditions under which it may correctly be asserted. Any such a theory is committed to the following thesis:

27. The distinction opens the way to a rapprochement between Frege’s thesis that the laws of logic unfold the meaning of ‘true’ and his claim (quoted at the start of this section) that what logic is concerned with ‘is not contained in the word “true” but in the assertive force with which a sentence is uttered’ (Frege 1915, 272 = Frege 1979, 252). Logic does comprise the laws of truth—in the sense of that to which assertive force constitutes a claim—but it does not comprise the laws of the trivial identity operation on thoughts. A fuller exploration of the distinction must wait for another occasion.

29

( ) The conditions under which a statement may correctly be asserted determine its sense and ( ) has a consequence that is incompatible with a key Fregean claim. To see this, observe first that the goal of wissenschaftlicher Streben will have been reached only when the inquirer attains knowledge: the Fregean inquirer wants to find out—sc., to come to know—the answer to a question. Accordingly, the norms that regulate the making of those assertions that report the outcomes of Fregean inquiries will include ‘Assert that p only if you know that p’, and hence (since knowledge is factive) ‘Assert that p only if p’.28 This means that the relevant notion of being correctly assertible must itself be factive, so the theory of correct assertibility will include every instance of the schema If it is correctly assertible that A, then A . Or, using the symbol ‘
’ to mean ‘it is correctly assertible that’, it will include every instance of the schema
A A. We may also postulate that correct assertibility distributes over conjunction: the theory of correct assertibility will also include every instance of the schema
(A  B) (
A 
B). This is a simple application of a principle that Frege also accepts: namely, that the laws of logic—in this case, the rule of conjunction elimination—contribute to the norms of assertion. Given these two postulates, however, we can prove that truth and correct assertibility are equivalent: in addition to factivity, our theory must include every instance of the corresponding biconditional schema A
A. The proof is straightforward. Let A be any given statement, and consider the pair of statements A  
A (‘A and it is not assertible that A’) and A  A (‘A and not A’). By factivity, we have
(A  A) (A  A), so that it is a consequence of the theory of assertibility that 
(A 
A). The second of our pair of statements, then, is not assertible under any condition whatever. By distribution, however,
(A  
A) (
A 

A), and by factivity (
A 

A) (
A  
A), so that it is also a consequence of the theory of assertibility that (
A 

A). Thus the first of our pair of statements is also not assertible under any conditions whatever. The statements A  
A and A  A, then, may be correctly asserted under exactly the same conditions—namely: never. Accordingly, by thesis ( ), they must share their sense. Since the latter statement is invariably false, the same must go for the former, so we have (A 

A), 28. Timothy Williamson (e.g. in his 2000, chap. 11) and others have argued that these norms partly constitute the ordinary speech act of assertion, but my argument does not need so strong a claim.

30

i.e. A
A. This combines with factivity to yield A
A. On the assumptions, then, that assertibility is factive and that it distributes over conjunction, thesis ( ) entails that a statement’s correct assertibility is materially equivalent to its truth. While an anti-realist like Dummett may welcome this consequence of ( ), I do not think that Frege could have accepted it. In the “Logik” of 1897, he wrote that ‘in order to be true, thoughts—e.g. laws of nature— not only do not need to be recognized by us as true: they do not have to have been thought by us at all’ (Frege 1897, 144f. = Frege 1979, 133). Frege is committed, then, to the existence of true thoughts that are never known (indeed, which are never even entertained). He holds, in other words, that there are some true instances of the schema (*) A and it is never known that A. However, as Wolfgang Künne has stressed in the last chapter of Conceptions of Truth, very weak assumptions render this plausible claim inconsistent with the thesis that a statement’s correct assertibility is materially equivalent to its truth. Or at least, this is so given our principle that a statement may be correctly asserted only when it is known. For let A be some statement which makes (*) true. Since the relevant instance of (*) is true, the proposed equivalence would yield It is correctly assertible that (A and it is never known that A). Given the principle that a statement may be correctly asserted only when it is known, this in turn yields It is possible that someone knows that (A and it is never known that A). But it is surely necessary that when a thinker knows that (A and B), he knows that A and he knows that B. So we may further deduce that It is possible that (someone knows that A and someone knows that it is never known that A). It is certainly necessary that when a thinker knows that A then A, so we have that

31

It is possible that (someone knows that A and it is never known that A). However, it is clearly impossible that someone knows that A while it is never known that A. This reductio shows that the universal equivalence of truth and correct assertibility is inconsistent with the existence of unknown truths upon which Frege insists in the 1897 “Logik”. Since abandoning that insistence would be to abandon a large element of his realism, as well as being intrinsically implausible, it is surely the equivalence that has to go.29 But we have shown that that equivalence follows from thesis ( ). So thesis ( ) must be rejected too. 7. Bilateralism: content as determined jointly by the conditions for correct assertion and the conditions for correct denial If we want a theory of content, then, in which truth does not collapse into correct assertibility, we must reject theories according to which a statement’s content is determined by its conditions of correct assertibility. However, a closely related account avoids the collapse. In other writings, I have urged the merits of bilateral theories of content whose characteristic thesis is not ( ), but rather ( ) The conditions under which a statement may correctly be asserted, together with the conditions under which it may correctly be denied, jointly determine its content. Let us postulate a theory of correct assertibility whose axioms are all instances of the schema of factivity (
A A), all instances of the schema of normality (
(A B) (
A
B)), and in which all classical tautologies are correctly assertible. (By virtue of normality, assertibility will distribute over conjunction.) In this theory, A will not in general imply
A. If we further assume that a statement may be correctly denied in precisely those circumstances in which its negation may be correctly asserted, then a theorem of Williamson’s (1990) shows that ( ) is already implicit in this theory of assertibility. So a bilateral theory of content, which conforms to ( ), differs from unilateral theories, which conform 29. Anti-realist philosophers have explored ways of avoiding the inconsistency; see notably Dummett 2001. But their methods will not find favour with Frege and are in any case open to objections: see Künne 2003, 446–49.

32

to ( ), in making room for a distinction between truth and correct assertibility. Could Frege accept a bilateral theory? In his late writings, he set his face firmly against it. It is natural to suppose that a statement may be correctly denied just in case its negation may be correctly asserted, but in “Die Verneinung” (1919) Frege argued for a stronger thesis: denying a statement is to be analysed or defined as asserting its negation. If this thesis is accepted, the conditions under which a statement may be correctly denied will ipso facto be conditions under which a related statement may be correctly asserted, so ( ) will collapse into ( ), and we shall be no further forward. However, Frege’s argument for this stronger thesis is weak. It rests on the dubious principle that we should economize on primitive notions wherever possible: if we accept the thesis, then we need postulate only one primitive mode of judgement, namely acceptance, and ‘if we can make do with one way of judging, then we must’ (1919a, 154). Our discussion, though, brings out the high price of this ‘making do’. By ruling out the possibility that understanding a statement involves coordinated but distinct items of knowledge—when it may be asserted, and when it may be denied—Frege rules out a theory that is otherwise well placed to provide the non-truth-conditional theory of content that the Ramsey-Prior theory of truth requires. Indeed, once the strictures of “Die Verneinung” have been removed, we can find a more stable and satisfactory place for another element of Frege’s logical theory. A striking respect in which Frege’s stipulations in Grundgesetze differ from a modern truth-theoretic semantic theory is the role they accord to the truth-value False. Davidson would convey the sense of ‘not’ by saying: not A is true if and only if A is not true. Frege, by contrast, says: ‘the value of the function — shall be the False for every argument for which the value of the function — is the True; and shall be the True for all other arguments’ (Frege 1893, 10). If acceptance is the only mode of judgement, and assertion the only logically relevant speech act, then this second truth-value must strike one as intrusive and anomalous: it is quite unclear what, in our practices of making judgements and making assertions, is supposed to account for our ability to apprehend the truthvalue False. Certainly, Frege’s famous claim about the two truth-values in “Über Sinn und Bedeutung” limps at the crucial point. Both the True and the False, he says, ‘are recognized, if only implicitly, by everybody who judges something to be true—and so even by a sceptic’ (Frege 1892, 34). If we suppose for a moment that a judgment is made by accepting in foro

33

interno a sentence in a language constructed along the lines of Frege’s formalized language, then what he says here about the True has some internal plausibility: if judging is always taking something to be true, and if the business part of any true sentence refers to the True, then anyone who goes in for judgement at all does implicitly recognize the truth-value True. But this consideration signally fails to extend to the False. A thinker who judges falsely will have failed to reach the True, but the claim that there is some other object which he has thereby reached is no more plausible than the claim that there is some one place—anti-Rome?—which any unsuccessful pilgrim to the Holy City will reach. For just this reason, indeed, clear-headed adherents of the thesis of “Die Verneinung” have been led to deny that there is such a truth-value as the False. Thus Geach recommends that we should ‘avoid the logical Manichaeanism of Frege’s two objects, the True and the False, by holding that judgements and sentences purport to be oriented to just one object, the True, though they may be wrongly oriented’ (Geach 2001, 76). Once denial is in the frame, though, we can find a place for the False—if we also accept Frege’s basic syntactic contention that in a well-constructed formalized language the load-bearing parts of statements will be ‘names of truth-values’. For just as the maker of an assertion commits himself to the business part of the asserted statement’s referring to the True, so the maker of a denial commits himself to the business part of the denied statement’s referring to the False. Or, prescinding from the treatment of truth-values as objects, we can say this: just as a norm for assertion says ‘Assert a statement only if it is true’, so a norm for denial says ‘Deny a statement only if it is false’. Frege’s claim in “Über Sinn und Bedeutung” makes much more sense once it is amended as follows: the two truth-values are recognized, if only implicitly, by everybody who judges some things to be true and other things to be false. On the bilateralist picture, we exercise these two modes of judgement every day—whenever, for instance, we answer ‘yes’ or ‘no’ to a yes-no question.30

30. For this gloss on assertion and denial, and further discussion of relevant passages in Frege, see Rumfitt 2000.

34

8. An evidentialist theory of content Whilst this is progress, it does not take us all the way towards our goal of a non-truth-conditional account of the determination of content. It is good that truth is no longer equivalent to warranted assertibility, but there is nothing in the theory as it stands that distinguishes between the content of two statements whose conditions of correct assertibility and conditions of correct deniability are equivalent. Consider the statements ‘Phosphorus contains carbon dioxide’ and ‘Hesperus contains carbon dioxide’. Each of these statements is correctly assertible and neither is correctly deniable. Indeed, it is metaphysically necessary that each will be correctly assertible, and correctly deniable, just when the other is. But it does not follow that the statements share a content, that they say the same thing. At least, anyone impressed by the arguments that originally led Frege to propound his notion of sense will deny that they say the same thing. On the Ramsey-Prior theory, though, a statement’s truth is defined in terms of what it says. So we remain some distance from finding the account of the determination of content that we need to complement that theory of truth. How can we do better? In addressing this question, it helps to go back to Frege. His notion of sense is au fond epistemic: ‘Phosphorus contains carbon dioxide’ differs in sense from ‘Hesperus contains carbon dioxide’ because they differ in cognitive value. That difference in turn reflects the fact that the two statements are supported by different evidence. If someone were to turn an astronomical spectrometer to the morning sky, and observe appropriately located signs of carbon dioxide, the evidence thereby acquired would support the statement ‘Phosphorus contains carbon dioxide’; in and of itself, though, the evidence does not support ‘Hesperus contains carbon dioxide’. Evidential support comes in degrees, and in the end these will need to be brought into the story. But for now let us consider a theory whereby a statement’s content relates to the evidence that would fully support it—i.e., by the evidence, apprehension of which puts a thinker in a position to know the statement’s truth. Fully supportive evidence, then, need not render the statement in question subjectively certain. If a statement’s content is to be determined by any epistemic factors, then those factors need to stand some distance above the vagaries of what people actually know. The notion of what a thinker is in a position to know does part of the necessary work of idealization. Although the notion is now common currency in epistemology, it could do with much more

35

explanation than I can give it here, but one aspect of it is noteworthy for the arguments to come. I shall say that some premisses entail a conclusion when the conclusion follows from the premisses and it is in principle possible for someone to deduce the conclusion from the premisses. Then, as I shall use the notion, if someone is in a position to know that p, and p entails q, he is also in a position to know that q. Thus one role for the notion of being in a position to know is to abstract from deductive incompetence or deficiency. How might a statement’s content relate to the evidence that fully supports it? Let the theory postulate some background set of things (statements? propositions?) to serve as the relevant or available pieces of evidence. I shall not try to decide how these pieces of evidence are best individuated, but will construct a theory that ought to be applicable whatever account is eventually given of their nature. The theory of content will then associate with each statement the set of pieces of evidence that fully support it. When some evidence fully supports a statement, I call that evidence a ground of the statement: on the current approach, the set of possible grounds of a statement will be part of what determines its content (I shall come to the other part in the next section). Where A is a statement, I use the notation
A
+ to signify A’s possible grounds. We should not think of grounds as being determined compositionally from atoms to molecules: a complex statement can be fully supported by evidence that does not fully support any of its constituents. But the theory will comprise axioms that constrain the relations between the possible grounds of complex statements and those of their components. What are these axioms? That for conjunction is straightforward. Evidence fully supports a conjunction just in case it fully supports each conjunct, so we may lay down: (C +) For any piece of evidence x, x fully supports the conjunction A and B if and only if x fully supports A and x fully supports B. Thus the grounds of a conjunction are simply the intersection of the grounds of each conjunct: (C +)
A and B
+ =
A
+ 
B
+. However, the corresponding claim for disjunction would be wrong. The corresponding claim would say that evidence fully supports a disjunc-

36

tive statement if and only if it supports at least one disjunct. And while the ‘if ’ part is correct, the ‘only if ’ part is wrong. Inspector Morse might have conclusive evidence that the murderer was in the house at the time of the crime, and conclusive evidence that only Smith and Jones were then in the house. That evidence fully supports the disjunction ‘Either Smith or Jones committed the murder’, but it need not fully support either disjunct. So what can we say about the grounds of disjunctive statements? Where U is any set of possible grounds of statements, let us define the closure of U, Cl (U), by the condition x  Cl (U) if and only if x is a ground of every statement of which all the members of U are grounds. That is: x  Cl (U) if and only if, for every statement C, x is a ground of C if every member of U is. I shall argue that x is a ground of A or B if and only if x  Cl (
A
+ 
B
+). To establish the ‘only if ’ half of this bi-conditional, let us suppose that x is a ground of A or B . We need to show that x is a ground of every statement of which all the members of
A
+ 
B
+ are grounds. So let C be an arbitrary statement meeting this condition. We have, in particular, that absolutely any possible ground that belongs to
A
+ is a ground of C. That is: absolutely any possible ground, apprehension of which puts one in a position to know A, puts one in a position to know C. This will be so only if A entails C. Similarly, absolutely any possible ground that belongs to
B
+ is a ground of C, which implies that B entails C. We have, then, that A entails C and that B entails C. So, by the logical law of dilemma, the disjunctive statement A or B  also entails C. Now x is a ground of A or B, so apprehension of x puts one in a position to know A or B. And since A or B  entails C, apprehension of x also puts one in a position to know C. That is, x is a ground of C. But C was an arbitrarily chosen statement of which all the members of
A
+ 
B
+ are grounds. So our argument shows that when x is a ground of A or B, it is also a ground of every statement of which all the members of
A
+ 
B
+ are grounds. Hence, by the definition of closure, whenever x is a ground of A or B it belongs to Cl (
A
+ 
B
+). It may be noted that this argument requires only the weak form of the law of dilemma, the form without side premisses, so the logical principle on which it rests is acceptable to classical, intuitionist, and even quantum logicians.

37

To establish the ‘if ’ half of our bi-conditional, suppose that x 
Cl (
A
+ 
B
+). By the definition of closure, this implies that, for any statement C, if all the members of (
A
+ 
B
+) are grounds of C, x is a ground of C. Now A entails A or B , and B entails A or B , so all the members of (
A
+ 
B
+) are grounds of A and B . Hence x is a ground of  A or B . In this way, we reach the semantic principle for ‘or’ that I propose: (D +) x is a ground of A or B  if and only if x  Cl (
A
+ 
B
+), or, more briefly, (D +)
A or B
+ = Cl (
A
+ 
B
+). The argument just given for (D +) may seem to cheat. The definition of closure quantifies over statements, and the argument for the ‘if ’ half of (D +) presumes that the domain of quantification already contains the disjunctive statement A or B  (or a statement that shares its content). It might then be objected that the proposed semantic axiom for ‘or’ offers no insight into how our understanding of the connective ‘or’ combines with our antecedent understanding of A and B in such a way as to yield an understanding of the disjunctive statement of A or B . The axiom offers no insight, in other words, into how a competent speaker’s understanding of a disjunctive statement’s parts combines to yield an understanding of the whole. And yet—in the eyes of many philosophers of language—providing such insight is the semantical task par excellence. So (D +) is not really a starter as a semantic axiom for ‘or’. In reply, we need to distinguish between different tasks that a semantic theorist might undertake. One is indeed that of accounting for the productivity of understanding, and (D +) is of no help with that. But that is not the task that our discussion has led us to address. In § 5 above, I remarked that the Ramsey-Prior theory of truth cannot combine with the truth-conditional theory of content to provide coherent answers to the two constitutive questions, ‘What is it for a truth-bearer to be true?’ and ‘What is it for a truth-apt utterance or a truth-apt mental state to have the content that it has?’ Accordingly, our tentative adoption of the Ramsey-Prior theory has led us to seek non-truth-conditional answers to the latter, metaphysical, question. A satisfactory answer to that question can comprise axioms that specify the relations between the grounds of complex statements and those of their components, even when grounds

38

are not determined compositionally upwards from atoms to molecules (as they usually will not be for disjunctive statements). Of course, the problem of accounting for productivity remains, but there is a minimalist solution to that problem that is fully consistent with any answer to the metaphysical question. Any competent French speaker knows that ‘La neige est blanche’ says that snow is white. Any such speaker also knows that ‘La terre se déplace’ says that the earth moves. Suppose that such a speaker also knows that, whenever the French statements A and B say that P, and that Q, the disjunctive statement A or B  says that either P or Q. We can then account for the speaker’s knowing that ‘La neige est blanche ou la terre se déplace’ says that either snow is white or the earth moves by reference to his knowledge of what the parts say.31 This approach to the problem of productivity casts no light on what makes it the case that statements say what they say, but that might well be a merit. On this approach, we cleanly separate the epistemological problem of accounting for our knowledge of what statements say from the metaphysical problem of explaining in what their saying what they say consists. At any rate, because it takes no stand on what determines what statements say, the minimalist approach to the problem of productivity just sketched is available to any theorist who offers an answer to the metaphysical question so long as he does not try to parlay that answer into a theory of understanding. An entire theory of the determinants of linguistic content is latent in the proposed axiom for ‘or’. I call the theory that is so latent evidentialism. To see its shape, let us remark first that closure, in the present sense, is a closure operation in the sense favoured by lattice theorists. That is to say, the operation is INCREASING IDEMPOTENT

U  Cl (U) Cl Cl (U) = Cl (U)

and MONOTONE

If U  V then Cl (U)  Cl (V).32

31. For this approach to the problem of productivity, see Davies 1981, 42ff. Davies finds theories of meaning of this kind wanting, but his argument against them presupposes a nonminimal notion of truth. 32. Proofs. INCREASING: immediate from the definition of closure. IDEMPOTENT: since closure is INCREASING, it suffices to show that Cl Cl (U)  Cl (U). Suppose then x  Cl Cl (U).

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Let us call a set closed when it is identical with its own closure. By idempotence, the closure of any set is closed, and by monotonicity the closure of U is the smallest closed set containing U. We then have the following general axiom of evidentialism: (R +) The possible grounds of a statement form a closed set. The argument for (R +) is straightforward. Let U be the set of all possible grounds of the statement A, and consider an arbitrary member, x, of the closure of U. By the definition of closure, x is a ground of any statement of which all the members of U are grounds. Since every member of U is a ground of A, A is such a statement, so x is a ground of A. But then, since U comprises all the grounds of A, x must be a member of U. That is to say, any member of the closure of U must belong to U itself, so U is closed, as required. An evidentialist theory of content, then, will associate with each statement a closed set of possible grounds. The theory’s compositional principles will say how the grounds of a complex statement relate to the grounds of its components. The intersection of any two closed sets will be closed,33 so postulate (C +) respects our general principle that the grounds of any statement should form a closed set. So too does our postulate (D +) for disjunctions, since the closure of any set is closed. Although I cannot argue for the claim here, I believe that natural generalizations of these postulates can serve as semantic principles saying what the grounds are of universally and existentially quantified statements.34 Then x is a ground of every statement of which every member of Cl (U ) is a ground. Consider an arbitrary statement A of which every member of U is a ground. By definition, every member of Cl (U) will be a ground of A. Hence x is a ground of A. But that shows that x is a ground of every statement of which every member of U is a ground, so that x  Cl (U ), as required. MONOTONE: suppose that x  Cl (U ) and that U  V. Since x  Cl (U), x is a ground of every statement of which all the members of U are grounds. Since U  V, it follows that x is also a ground of every statement of which all the members of V are grounds. That is, x  Cl (V ), as required. 33. Proof. Suppose that U = Cl (U ) and that V = Cl (V ). We need to show that U  V = Cl (U  V ). Since INCREASING already yields U  V  Cl (U  V ), it suffices to show that Cl (U  V )  U  V. Now U  V  U, whence by MONOTONE Cl (U  V )  Cl (U) = U. Similarly, Cl (U  V )  Cl (V) = V. Together, these inclusions yield Cl (U  V)  U V, as required. 34. For the generalizations that I envisage, see Mares, forthcoming. Mares works with a notion of ‘objective information’ rather than grounds, but modulo differences consequential upon that, his treatment of disjunction is equivalent to that proposed here.

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Under evidentialism, the logic of disjunction need not be classical: because the possible grounds of a disjunctive statement may include evidence that does not ground either disjunct, our semantic principle for ‘or’ can accommodate logics (such as quantum logic) that invalidate distribution. But that, as it seems to me, is how things should be. The validity of the distributive law is not guaranteed by the meanings of ‘or’ and ‘and’ alone. Rather, it is sustained by those meanings in tandem with other principles concerning logical consequence. A plausible principle is that strictly logical consequence should be absolute in the sense that, whenever we have an instance of logical consequence, it should remain so even if we accept additional premisses, or make additional suppositions.35 In the present framework, this amounts to the following requirement of stability: whenever a possible ground x belongs to the closure of a set of possible grounds U, the combination of x with an arbitrary possible ground y (if such a combination exists) will belong to the closure of the set formed by combining each member of U with y. If the space of possible grounds is stable in this sense, then the natural definition of consequence will validate distribution (see Sambin 1995, especially the remarks on distribution on p. 864, lemma 2 on p. 865, and theorem 4 on p. 868). So distribution is validated by the meanings of ‘or’ and ‘and’ along with the stability of the space of possible grounds—i.e., along with the thesis that logical consequence is absolute. In this way, evidentialism can accommodate classical logic. 9. Bilateral evidentialism For a bilateralist, however, this can only be half of the evidentialist story. So far, in expounding the evidentialist theory of content, I have been drawing upon our common understanding of what it is for evidence fully to support a statement—that is, fully to support its truth. But we also understand what it is for evidence fully to rebut a statement—that is, fully to support its falsehood. Evidence fully rebuts a statement when apprehension of it puts a thinker in a position to know the statement’s falsehood. The problems latent in () give good reason to be bilateralist, and a bilateral evidentialist will insist on giving equal weight to the notion of fully rebut35. For elaboration and defence of this conception of specifically logical consequence, see McFetridge 1990 and Rumfitt 2010.

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ting a statement. Thus, a statement’s content will be determined jointly by the possible evidence that fully supports it and the possible evidence that fully rebuts it. When a piece of evidence fully rebuts a statement, let us call it an anti-ground of the statement. I use the notation
A
 to signify A’s possible anti-grounds. According to bilateral evidentialism, then, a statement’s content is determined jointly by its possible grounds and its possible anti-grounds. What are the axioms that relate a complex statement’s anti-grounds to the anti-grounds of its parts? Where U is a set of possible anti-grounds for statements, let us define the closure of U, Cl (U), by the condition x  Cl (U) if and only if x is an anti-ground of every statement of which all the members of U are anti-grounds. A proof parallel to that in n. 32 shows that the closure operation on antigrounds is again INCREASING, IDEMPOTENT and MONOTONE; as before we may call a set of anti-grounds closed when it is identical with its own closure. Then, parallel to the principle (R +) of the last section, we have a further general axiom of bilateral evidentialism: (R ) The possible anti-grounds of a statement form a closed set. The argument for (R ) runs parallel to the one given in § 8 for (R+). Let U be the set of all possible anti-grounds of the statement A, and consider an arbitrary member, x, of the closure of U. By the definition of closure, x is an anti-ground of any statement of which all the members of U are anti-grounds. Since every member of U is an anti-ground of A, A is such a statement, so x is an anti-ground of A. But then, since U comprises all the anti-grounds of A, x must be a member of U. That is to say, any member of the closure of U must belong to U itself, so U is closed, as required. We need to supplement the semantic axioms given in § 8 with further principles that say how the anti-grounds of statements built up using ‘and’ and ‘or’ relate to the anti-grounds of their parts. Adherents of classical logic will propose principles that are the duals of the axioms concerning grounds. We are in a position to know the falsehood of the disjunction  A or B  just when we are in a position to know both the falsehood of A and that of B, so we have (D )
A or B
 =
A
 
B
.

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When it comes to anti-grounds, conjunctions are more problematic than disjunctions. A thinker who is in a position to know a statement’s falsehood is in a position to know the falsehood of any conjunction of which the statement is a conjunct. However, the converse does not hold. If I know nothing about a ball’s colour, I am not in a position to know the falsehood of ‘The ball is red all over’, nor the falsehood of ‘The ball is green all over’, but I am in a position to know the falsehood of the conjunction ‘The ball is both red all over and green all over’. However, an argument parallel to that given in § 8 for (D +) yields the principle: (C )
A and B
 = Cl (
A
 
B
). As with their positive counterparts, both (C ) and (D ) ensure that, so long as the atomic statements respect the master principle (R ), so will all the molecular statements built up from them using ‘and’ and ‘or’. With this apparatus in place, we can characterize negation, very simply, as a logical switch that ‘toggles’ between grounds and anti-grounds, between being in a position to know a truth and being in a position to know a falsehood. For what are the grounds, apprehension of which puts us in a position to know the truth of Not A ? A plausible answer is that they are precisely the grounds, apprehension of which puts us in a position to know the falsehood of A. That is, we have: (N +) x is a ground of Not A  if and only if x is an anti-ground of A, i.e., (N +)
Not A
 =
A
. Similarly, we need to ask what are the grounds, apprehension of which puts us in a position to know the falsehood of Not A . A classical logician will answer that they are precisely the grounds, apprehension of which puts us in a position to know the truth of A. That is, we have: (N ) x is an anti-ground of Not A  if and only if x is a ground of A, i.e., (N )


Not A
 =
A
.

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Together, (N +) and (N ) ensure that Not not A  has the same grounds, and the same anti-grounds, as A itself. Given bilateral evidentialism, then, a statement and its double negation have the same content. The classical equivalence between A and
Not not A
is then assured. In tandem with the assumption of stability, indeed, our bilateral semantic axioms validate the full classical logic of ‘and’, ‘or’, and ‘not’. On classical assumptions, then, our bilateral axioms for these operators determine their content sufficiently to determine their logic. I do not imagine that this observation will persuade any non-classical logician to convert to classicism. The (C ) and (D) principles shamelessly build into the semantics the classical duality of ‘and’ and ‘or’; the (N ) principles similarly build in the validity of double negation elimination. Moreover, the meta-logical proofs that the classical rules for ‘and’, ‘or’, and ‘not’ are sound with respect to the proposed semantics employ distinctively classical principles at various points. All the same, the observation has significance. It shows that an adherent of bilateral evidentialism who uses a classical meta-logic has the resources to account for the soundness of (the propositional fragment of ) classical logic for the object language. So there need be no clashing of logical gears in moving between the object language and the meta-language. Our theorist is not left in the embarrassing position of being unable to account for the soundness of the logical rules that he employs—even if he allows himself to employ those very rules when attempting to provide that account. In this respect, classical logic is stable with respect to the proposed semantics. Frege never wavered from classical logic. Accordingly, the form of stability just delineated is a significant point in favour of the present semantic theory, considered as a non-truth-conditional theory of meaning that he could have accepted. Our bilateral evidentialist semantic axioms, then, determine which sequents involving ‘and’, ‘or’, and ‘not’ are valid. But there is more to the notion of a statement’s content than its strictly deductive behaviour. For one thing, evidence often provides some degree of support for a statement even though it falls short of putting someone in a position to know it. And a full specification of a statement’s content ought to include the principles that determine its place in a network of partial evidential support. In fact, our postulates about the conditions in which we are in a position to know a statement yield principles of this latter kind quite directly, once the postulates are supplemented by plausible axioms about the structure of evidential support. Following Williamson (2000, chap. 10), let us use the familiar dyadic or conditional probability operator P(A/B) as a measure

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of evidential probability. That is, let us understand P(A/B) as a measure of the degree to which B supports the truth of A. Thus, where B is evidence, apprehension of which enables us to know the truth of A, we take P(A/B) to be unity; and where B is evidence, apprehension of which enables us to know the falsehood of A, we take P(A/B) to be zero. In our terminology, then, B is a ground for A just in case P(A/B) = 1, and B is an anti-ground of A just in case P(A/B) = 0.36 On this way of understanding P(A/B), the following axioms are highly plausible: I

0  P(A/B)  P(A/A  B) = P(t/B) = 1 P(f/C) = 0 unless P(D/C) = 1 for all D

II

P(A  B/C) = P(B  A/C)

III

P(A  B/C) = P(A/C) P(B/A  C)

In these axioms, t is a known logical truth of the relevant logic, and f is a known logical falsehood. Where C cannot obtain, we take it to be a ground of any statement; thus the second clause of axiom I says that any evidence that can obtain is an anti-ground of a known logical falsehood. Given these axioms, a theorem of van Fraassen’s shows that our semantic postulates entail further plausible principles that specify the relationship between the degrees to which evidence supports atomic statements and the degrees to which it supports complex statements.37 There is a strong case, then, for saying that our semantic postulates specify the contribution that ‘and’, ‘or’ and ‘not’ make to the place that statements containing them occupy in a network of partial evidential support. Whilst the results reported in the previous paragraph are suggestive in showing how bilateral evidentialism can transcend the purely deductive elements of a statement’s content, much work remains to be done. I have shown how such a theorist can treat ‘and’, ‘or’, and ‘not’, but only after we have a bilateral evidentialist semantics for a reasonably large fragment of a natural language will we be in a position to compare the combination of that theory and the Ramsey-Prior theory of truth with the combination 36. So, on this way of understanding it, P(A/B) can be 1 even when apprehension of B does not render A subjectively certain. See Williamson 2000, 213ff., for elaboration of this point. 37. See propositions (2-7) and (3-1) of van Fraassen 1981b (503, 505). Van Fraassen has a rather different way of understanding P(A/B) (see his 1981a), but the difference in interpretation does not affect his formal proofs.

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(such as Davidson proposes in his 2005) of a theory which takes truth to apply primarily to individual utterances with a truth-conditional theory of those utterances’ contents. It would be foolish to anticipate the result of that comparison. But I hope to have identified a promising place in which a philosopher of Fregean sympathies may seek the non-truth-conditional theory of content which the Ramsey-Prior theory of truth demands, but which is not at all easy to find.

REFERENCES Blackburn, Simon W. 1984: Spreading the Word. Oxford: Clarendon Press. — 2005: “Success Semantics”. In: Lillehammer and Mellor (eds.) 2005, 22–36. Brandom, Robert B. 1994: “Unsuccessful Semantics”. Analysis 54, 175–8. Davidson, Donald H. 2005: Truth and Predication. Cambridge, Mass.: Harvard University Press. Davies, Martin K. 1981: Meaning, Quantification, and Necessity. London: Routledge. Dokic, Jérôme and Pascal Engel 2002: Frank Ramsey: Truth and Success. London: Routledge. — 2005: “Ramsey’s Principle Resituated”. In: Lillehammer and Mellor (eds.), 8–21. Dummett, Michael A. E. 1959: “Truth”. Proceedings of the Aristotelian Society 59, 141–62. — 1981: Frege: Philosophy of Language, 2nd edition. London: Duckworth. — 1986: “Frege’s Myth of the Third Realm”. Untersuchungen zur Logik und zur Methodologie 3, 24–38. Page references to the reprint in Dummett 1991, 249–62. — 1990: “The Source of the Concept of Truth”. In: George S. Boolos (ed.), Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge: Cambridge University Press. — 1991: Frege and Other Philosophers. Oxford: Oxford University Press. — 1994: “Reply to Picardi”. In: Brian McGuinness and Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Dordrecht: Kluwer, 282–91. — 2001: “Victor’s Error”. Analysis 61, 1–2. Field, Hartry H. 1986: “The Deflationary Conception of Truth”. In: Graham Macdonald and Crispin Wright (eds.), Fact, Science and Morality. Oxford: Blackwell, 55–117. Frege, F. L. Gottlob 1879: Begriffsschrift. Halle: Nebert. — 1879–91: “Logik”. In: Frege 1969, 1–8. English translation in Frege 1979, 1–8.

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— 1891: Funktion und Begriff. Jena: Hermann Pohle. — 1892: “Über Sinn und Bedeutung”. Zeitschrift für Philosophie und philosophische Kritik 100, 25–50. — 1893: Grundgesetze der Arithmetik, volume I. Jena: Hermann Pohle. — 1894: “Rezension von E. G. Husserl: Philosophie der Arithmetik I”. Zeitschrift für Philosophie und philosophische Kritik 103, 313–32. — 1897: “Logik”. In: Frege 1969, 137–63. English translation in Frege 1979, 126–51. — Before 1906: “Siebzehn Kernsätze zur Logik”. In: Frege 1969, 189–90. English translation in Frege 1979, 174–5. — 1906a: “Was kann ich als Ergebnis meiner Arbeit ansehen?”. In: Frege 1969, 200. English translation in Frege 1979, 184. — 1906b: “Einleitung in die Logik”. In: Frege 1969, 201–212. English translation in Frege 1979, 185–96. — 1906c: “Kurze Übersicht meiner logischen Lehren”. In: Frege 1969, 213–18. English translation in Frege 1979, 197–202. — 1914: “Logik in der Mathematik”. In: Frege 1969, 219–70. English translation in Frege 1979, 203–50. — 1915: “Meine grundlegenden logischen Einsichten”. In: Frege 1969, 271–2. English translation in Frege 1979, 251–2. — 1918: “Der Gedanke”. Beiträge zur Philosophie des deutschen Idealismus I, 58–77. — 1919a: “Die Verneinung”. Beiträge zur Philosophie des deutschen Idealismus I, 143–57. — 1919b: “Aufzeichnungen für Ludwig Darmstaedter”. In: Frege 1969, 273–7. English translation in Frege 1979, 253–57. — 1969: Nachgelassene Schriften. Ed. Hans Hermes et al. Hamburg: Felix Meiner. — 1979: Posthumous Writings. Trans. Peter Long and Roger White. Oxford: Blackwell. Geach, Peter T. 1980: Reference and Generality, 3rd edition. Ithaca, New York: Cornell University Press. — 2001: Truth and Hope. Notre Dame, Indiana: University of Notre Dame Press. Kneale, William C. 1972: “Propositions and Truth in Natural Languages”. Mind 81, 225–43. Künne, Wolfgang 2003: Conceptions of Truth. Oxford: Clarendon Press. Levine, James 1996: “Logic and Truth in Frege”. Proceedings of the Aristotelian Society, Supplementary Volumes 70, 41–75. Lillehammer, Hallvard and Mellor, D. H. (eds.) 2005: Ramsey’s Legacy. Oxford: Clarendon Press. McFetridge, Ian G. 1990: “Logical Necessity: Some Issues”. In: McFetridge, Logical Necessity and Other Essays. London: Aristotelian Society, 134–55.

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Mackie, John L. 1973: Truth, Probability, and Paradox: Studies in Philosophical Logic. Oxford: Clarendon Press. Mares, Edwin D. Forthcoming: “The Nature of Information: a Relevant Approach”. Prior, Arthur N. 1971: Objects of Thought. Oxford: Clarendon Press. Quine, Willard V. O. 1986: Philosophy of Logic, 2nd edition. Cambridge, Mass.: Harvard University Press. Ramsey, Frank P. 1927: “Facts and Propositions”. Proceedings of the Aristotelian Society Supplementary Volumes 7, 153–70. Page references are to the reprint in Ramsey (ed. by D. H. Mellor), Philosophical Papers. Cambridge: Cambridge University Press, 1990, 34–51. — 1991: On Truth. Dordrecht: Kluwer. Rumfitt, Ian 2000: “‘Yes’ and ‘No’”. Mind 109, 781–823. — 2010: “Logical Necessity”. In: Bob Hale and Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford: Clarendon Press, 35–64. — 2011: “Objects of Thought”. In: Gary Ostertag (ed.), Meanings and Other Things: Essays in Honor of Stephen Schiffer. Cambridge, Mass.: MIT Press. — Forthcoming: “Ramsey on Truth and Meaning”. Sambin, Giovanni 1995: “Pretopologies and Completeness Proofs”. The Journal of Symbolic Logic 60, 861–78. Smiley, Timothy J. 1993: “Can contradictions be true?”. Proceedings of the Aristotelian Society Supplementary Volumes 67, 17–33. Van Fraassen, Bas C. 1981a: “Probabilistic Semantics Objectified I: Postulates and Logics”. Journal of Philosophical Logic 10, 371–94. — 1981b: “Probabilistic Semantics Objectified II: Implication in Probabilistic Model Sets”. Journal of Philosophical Logic 10, 495–510. Whyte, Jamie T. 1990: “Success Semantics”. Analysis 50, 149–57. Williamson, Timothy 1990: “Verification, Falsification, and Cancellation in KT”. Notre Dame Journal of Formal Logic 31, 286–90. — 1998: “Indefinite Extensibility”. Grazer Philosophische Studien 55, 1–24. — 2000: Knowledge and Its Limits. Oxford: Clarendon Press. Wittgenstein, Ludwig 1953: Philosophische Untersuchungen. Oxford: Blackwell.

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Grazer Philosophische Studien 82 (2011), 49–75.

TRUTH-BEARERS AND MODESTY* Manuel GARCÍA-CARPINTERO LOGOS-Departament de Lògica, Història i Filosofia de la Ciència University of Barcelona Summary In this paper I discuss Künne’s Modest Theory of truth, and develop a variation on a worry that Field expresses with respect to Horwich’s related view. The worry is not that deflationary accounts are false, but rather that, because they take propositions as truth-bearers, they are not philosophically interesting. Compatibly with the intuitions of ordinary speakers, we can understand proposition so that the proposals do account for a property that such truth-bearers have. Nevertheless, we saliently apply the truth-concept also to entities such as utterances or assertions, and the deflationary accounts do not provide a similarly deflationary account for those applications. In fact, there are good reasons to suspect that no such account would be forthcoming; we need something more substantive or inflationary there.

1. Introduction Wolfgang Künne’s Conceptions of Truth is a wonderful book in many respects. It is written with clarity, precision, and wit. It is informed by the most significant contributions to its topic, not just from philosophers in the Analytic tradition and its Austrian predecessors, but from philosophers whose work spans the whole history of the subject. It judiciously selects from these riches, providing what is in my view the best up-to-date introduction to the subject. Last but not least, it provides a compelling critical * Financial support for my work was provided by the DGI, Spanish Government, research project HUM2006-08236 and Consolider-Ingenio project CSD2009-00056; through the award ICREA Academia for excellence in research, 2008, funded by the Generalitat de Catalunya; and
by the European Community’s Seventh Framework Programme FP7/2007-2013 under grant agreement no. 238128. Thanks to Teresa Marques, Sven Rosenkranz and, especially, the editors of this volume for very helpful discussion of some topics in this review, and to Michael Maudsley for the grammatical revision.

overview of the different approaches to truth, and an interesting proposal of its own which, even if—as the author acknowledges—it is close to others previously advanced, has sufficient novelties to count as original. The qualification ‘modest’ places Künne’s account in the vicinity of those proposals that have become popular in the past two decades, under epithets such as ‘deflationary’ or ‘minimal’. Künne (2005, 564; 2008, 130ff.) is understandably dissatisfied with the confusing multiplicity of senses that these labels have received in the literature; he (2008, 123) indicates that he would have preferred labels such as ‘Quantificational Account’ to ‘modest’ for his view. Yet, his proposal is encapsulated by this definition: (MOD)
x (x is true  p ((x = the proposition that p)  p)) On Künne’s proposal, propositions are the primary truth-bearers. This is a widespread view, which was vigorously defended by two of the earliest pioneers of analytic philosophy, Bernard Bolzano and Gottlob Frege, and which is also a component of Horwich’s account. (See Bolzano WL I, § 24; Frege 1918; Horwich 1998.) Also, and even though in a more indirect way, like Horwich’s account Künne’s proposal is “deflationary” or “minimalist” in a sufficiently precise sense (Patterson 2005, 528; Künne 2005, 564f.; 2008, 132ff.). Together with minimal resources, it implies all instances of a Denominalization Schema: (Den)

The proposition that p is true if and only if p

The proposition expressed in the right-hand side of instances of Den is designated in the left-hand side by a “revealing designator” (one such that anybody who understands it is thereby in a position to know which proposition is designated). As Künne (2005, 564f.) points out, though, the fact that an account of truth entails instances of Den is not enough to count it as deflationary, minimal or, indeed, modest. That crucially depends on what resources the account requires for such entailments—which, as Gupta (2002, 228) notes, will not depend only on pure formal validities. In the case of Horwich’s theory, they are indeed minimal: the account simply consists of all infinitely many instances of the schema. Künne’s own derivation is more indirect, because his MOD is intended as a generalization, which makes a general claim about truth. Because of this, it has the following advantages over Horwich’s account, with which Künne

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otherwise sympathizes: it is finitely stated; it tells us what all truths have in common; and it is conceptually slim, so that it escapes the “argument from conceptual overloading” advanced by Gupta (2002), according to which, in order to understand the concept of truth, one must possess all other concepts. For MOD to be the bona fide generalization that it purports to be, its glaringly salient existential quantification into sentence-position should be explained, in ways compatible with the goals of the account. The intelligibility of such quantification is suspect; if explained as substitutional in an intelligible way, we run the risk that the interpretation will turn MOD into a viciously circular account.1 Künne argues that the quantification is objectual, or ontic, not substitutional; to show that it is intelligible, he argues firstly that we do have in natural language the equivalent of variables corresponding to ‘p’ in MOD, “pro-sentences” (as we have for variables allowing for quantification into predicate position), and he then provides a semantics for it; Künne (2008, 137–152) has the most recent development. This is a satisfactory procedure in general, but I am not sure that, in its application to our case, it answers qualms such as those voiced by Gómez-Torrente (2005, 373) and David (2005, 187–190). Künne takes expressions such as ‘es verhält sich so’ in German, or ‘things are that way’, as pro-sentences;2 the concern is that, even if they are, it is not clear that we do have genuine quantification over such variables in natural language. Be that as it may, I am not going to press the point in what follows; I am happy to grant that Künne has done enough to allay such qualms. An issue to me much more pressing is whether such intuitions as we may have about these matters settle in any sufficiently determinate way which are the entities “expressed” or “connoted” by sentences that we quantify over in those cases, and the consequences that this may have for the correctness of Künne’s proposal as a full account of truth; I will have more to say about this later, following the lead of David (2005, 189f.). To sum up, (1) is the kind of thing we might say about truth in the vernacular jargon that Künne appeals to; (2) is an instantiation of the schema Den using that jargon, and MOD* a more vernacular presentation of MOD: 1. Cf., however, Hill (2002), who offers an account of truth very similar to Künne’s using substitutional quantification, and argues that no vicious circularity ensues by introducing the notions of the substitutional quantifiers through inferential rules. 2. Hill (2002, 24–27) invokes similar constructions to contend that his own account in terms of substitutional quantification has close counterparts in ordinary thought and talk.

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Anna thinks that it is almost dawn, and things are that way The proposition that it is almost dawn is true just in the case that things are that way (MOD*) For all x (x is true just in case x is the proposition that things are a certain way, and things are that way) (1) (Den)

We can thus conclude that, even if we duly grant Künne’s concerns about the imprecision of accusations of deflationism or minimalism, the resources MOD invokes to produce the relevant instances of Den (Künne 2008, 133f.) stay sufficiently close to the minimum set by Horwich’s account for his theory to count as deflationary, minimal or, indeed, modest. In what follows, I am going to develop, against Künne’s theory, a variation on a worry that Field (1992, 322) expresses with respect to Horwich: “on most conceptions of proposition, the question of what it is for a proposition to be true is of little interest, […] what is of interest are the issues of what it is for an utterance or a mental attitude to be true (or, to express a truth or represent a truth).” The worry, I will argue, is not that Künne’s Modest Account—granting its intelligibility—is false, but rather that it is not very interesting. From a theoretically illuminated perspective, we can interpret its main locutions—‘proposition’, in particular—in a way fully compatible with whatever the intuitions of ordinary speakers using them might settle, so that the proposal almost incontrovertibly (putting aside concerns with the sentential quantification) accounts for a property that the relevant subclass of truth-bearers, thus understood, do have. Nevertheless, we ordinarily apply the truth-concept to other entities (in a more salient way, I will argue), and the Modest Account does nothing to promote a similarly deflationary, minimal or modest account for those cases. On the contrary, we have good reason to suspect that no such account would be forthcoming; we need something more substantive or inflationary. Field makes this case by contrasting a deflationary account of the truth of propositions understood as classes of possible worlds or as structured Russellian propositions (true, but trivial) with a deflationary account of the truth of utterances, or mental attitudes (interesting, but possibly wrong). In the next section, I will be making a case for a related distinction between propositions understood in either of the ways that Field contemplates, and what I will call illocutionary types, including (on an interpretation differ-

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ent from his own) Field’s “utterances and mental attitudes”. In the third section, I will suggest that only a subclass of the latter (sayings) are the intuitively underwritten primary truth-bearers. In the final section I will provide some examples relevant for a philosophical discussion of truth (vagueness, vacuous and indeterminate singular terms), regarding which taking sayings as primary truth-bearers is philosophically fruitful, and then, in conclusion, I will rehearse the Field-inspired worries about the Modest Account I have just mentioned. 2. Illocutionary types vs. propositions Since Frege, it has been customary in contemporary philosophy to distinguish between locutionary content and illocutionary force. Two sentences might present different contents with the same force, and vice versa. To illustrate the latter possibility I offer (2)-(4), uttered in the suggested appropriate contexts: (2) (A to B) Return the book tomorrow! (3) (B to A) I will return the book tomorrow. (4) Will B return the book tomorrow? The difference in illocutionary type is indicated in (2)–(4) by means of a conventional device, mood; it might rather be indicated by what many would count as indirect means, for instance, by following an utterance of (3) with ‘I promise’ after a pause. This distinction is not important for the main point I want to make here, although it is taken into consideration in the first argument I will invoke. In his discussion of truth-bearers, Künne (2003, 250–251) makes a common move. He states that “we ascribe truth to a motley multitude of entities such as allegations, beliefs, conjectures, contentions, judgments, reports, statements, suppositions, thoughts, and so on”. He then notes that our talk of such entities manifests the usual type-token ambiguity; two so-called statements might be different tokens (have different causes and effects, say) of the same type. Then he moves on to identify the former with (speech, or mental) acts, states or events, and the latter with their contents. This move overlooks a third entity, as abstract as the content might be taken to be, but, unlike contents as ordinarily understood, endowed with force-like features.

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Pendlebury (1986), Segal (1990/1), and, more recently, Hanks (2007) argue for these entities.3 Hanks’s first argument for them is also the main argument previously provided by Pendlebury: some such entities, for the specific case of forces conventionally indicated in natural language by mood, are required for an adequate account of the semantics of some propositional attitude embeddings. Thus, for instance, as both Hanks (2007, 144–153) and Pendlebury (1986, 362–367) point out, (5) differs in meaning from (6), as (7) does from (8); however, the propositions signified by the embedded clauses might well be the same:4 (5) (6) (7) (8)

Jones knows that Smith is tall. Jones knows whether Smith is tall. Jones told Smith that he will go to the store. Jones told Smith to go to the store.5

Hanks and Pendlebury consider different alternatives to account for the differences, and plausibly conclude that the best option requires acknowledging different “types of representational states or acts”, as Hanks describes them, signified by the embedded clauses. Misleadingly, Hanks proposes 3. See also Moltmann (ms). A friend of the traditional approach might argue, I fear, that the evidence she provides for recognizing “attitudinal objects” (as she calls them) with force-like features, distinct both from speech and mental acts, on the one hand, and their contents, on the other, can be perfectly well accommodated by the traditional dichotomy of acts and content. The problem I think lies in her additional goal of classifying items in this third category as concrete tropes (but still not mental/speech events or acts). I do not think we need such an ontology; in any case, I assume that, for present purposes, whatever you say assuming an ontology of tropesplus-similarity relations can be said in one of types. 4. Künne (2003, 253) argues, following Frege, that ‘whether’-clauses in indirect discourse may introduce the same propositions as corresponding ‘that’-clauses, without apparently noticing the differences in meaning between, say, (5) and (6). 5. Although here I am just reproducing Hanks’s and Pendlebury’s argument, it will be helpful for me to consider a doubt that the editors raise and that other readers might share. It may seem initially a little less natural to assume that a ‘to’-clause, as used in (8), signifies a proposition, than to assume that a ‘that’-clause signifies one. One reason is that you can prefix a that-clause with ‘the proposition’ and also apply predicates such as ‘is a true/well-known/curious/ important proposition’ to a that-clause. The same isn’t true for ‘to’-clauses: ‘the proposition to go to the store’ seems illicit, as does ‘to go the store is a true proposition’. Now, perhaps this is a grammatical accident due to the fact that, in the relevant constructions, we have lost the mandatory antecedent for the PRO subject of the ‘to’-clause. To me, ‘the proposition (or, better, in view of the terminology suggested below, ‘the directive/command …’) for Smith to go to the store’ seems legitimate, and so does ‘the directive/command for Smith to go to the store was complied with/came to be true’.

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to call them ‘propositions’, but I will reserve that name for the forceless features of those types, which a compositional semantics needs anyway (for instance, to ascribe them to disjuncts, antecedents and consequents of conditionals,6 sentences embedded under modal operators, etc).7 I will call questions what is signified by ‘whether’-clauses when they are embedded in sentences such as (6), and directives what is signified by ‘to’-clauses when they are embedded in sentences such as (8). I will use ‘sayings’ for the equivalent entity corresponding to declaratives, for reasons I will explain in the next section. What is distinctive about them is that they are not individuated just by what is usually called a proposition, but also by some force-like component, distinguishing questions, directives and sayings with the same propositional content. On an accurate semantic treatment, only sayings have truth-conditions, not questions and directives; however, all of them have something of which the truth-conditions of sayings are just a particular case, fulfillment conditions.8 I will not be concerned here with ontological issues; whatever one thinks about propositions can also be said about these entities. Thus, for instance, if one has a pseudo-realist but ultimately fictionalist view about them, of the kind favored by Künne after Schiffer (2003),9 as far as I can tell one might have the same view about illocutionary types. A second argument by Hanks for illocutionary types that I like concerns the old problem of the unity of the proposition, to which Gaskin (2008) has recently devoted a long book. I am dissatisfied with Gaskin’s proposal, as I am with King’s (2007), who, like Gaskin, nonetheless has the merit of acknowledging the problem. It will help us to appreciate the issue to examine reasons for dissatisfaction with King’s proposal in some detail. 6. As Ludwig (1997) rightly points out, the consequents of some conditionals (those expressing conditional assertions, conditional command or conditional questions) also have force-like features. 7. It is not clear to me whether Hanks wants to get rid of propositions/contents, but I think this would be a mistake, for the reasons mentioned in the main text, and it is unsupported by his arguments. 8. Ludwig (1997) and Boisvert & Ludwig (2006) provide an initially plausible proposal, which should be refined at least on the basis of considerations about vagueness and vacuous terms outlined below, in section 4. This is an account in the Wittgensteinian tradition canonically stated in Stenius (1967)—no matter how much their proponents purport to distance themselves from it—which, in addition to its precise articulation, has the merit of applying to conditional directives, questions (which perhaps at first sight do not seem amenable to a treatment in terms of fulfillment conditions) and so on. 9. A view with which, under a different guise, I myself also sympathize, cf. García-Carpintero (2010a).

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Both King and Gaskin criticize Frege’s and Russell’s accounts of the unity of the proposition. The Tractarian Picture Theory, that the expressions signifying structured facts/states of affairs are themselves facts/states of affairs, inspires King’s account. The main idea is that the unity of the proposition—the glue putting together object and property in a simple atomic proposition such as that expressed by ‘Rebecca swims’—is ultimately the syntactic relation syntactically linking (at the proper syntactic level, call it Logical Form) ‘Rebecca’ and ‘swims’: “that proposition is the fact of there being a context c and there being lexical items a and b in some language L such that a has as its semantic value in c Rebecca and occurs at the left terminal node of the sentential relation R that in L encodes the instantiation function and b occurs at R’s right terminal node and has as its semantic value in c the property of swimming” (King 2007, 51). Now, let us focus on this notion that the relevant syntactic relation R between the lexical items encodes the instantiation function. In his initial presentation, King leaves this aspect out of the account, but he then feels compelled to include it, as a result of reflection on “the semantic significance of syntax” (34). The problem is that the very same concatenation relation between ‘Rebecca’ and ‘swims’ under R might signify different things in different languages. It could signify that the semantic value of ‘Rebecca’ does not instantiate the semantic value of ‘swims’; or it could even signify the sheer concatenation of the semantic value of ‘Rebecca’, the instantiation function, and the semantic value of ‘swims’ (i.e., a list without propositional unity). It is in order to amend the account to deal with this difficulty that King introduces in the characterization of the properly unified proposition the additional feature that the syntactic relation between the lexical items encodes the instantiation function. Now, as he notes, this encoding relation “is … different from the sorts of semantic relations that obtain between words and things like Rebecca and the property of swimming” (King, op. cit., 37); for that is the relation between the syntactic concatenation relation and the instantiation function which obtains in the imagined language in which the sentence is no sentence but a mere list, and its meaning lacks propositional unity. So, what does this difference consist in? What distinguishes this semantic relation between syntax and signified proposition that King calls ‘encoding’, from the relation between ‘Rebecca’ and ‘swims’ and their semantic values? Here is King’s proposal: “In effect, we can think of this bit of syntax as giving the instruction to map an object o and a property P to true (at a world) iff

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o instantiates P (at that world). This instruction has two crucial features. First, it involves a specific function f: the function that maps an object and a property to true (at a world) iff the object instantiates the property (at the world). Call this function f the instantiation function. Second, the instruction tells us that f is to be applied to the semantic values of the expressions at the left and right terminal nodes (and a world) to determine the truth value of the sentence (at a world)” (34). Now the worry should be manifest: this instruction that the syntactic relation encodes is, precisely, the instruction to take the constituents as being in whatever relation it is that characterizes propositional unity, whatever relation it is that makes constituents into propositions which say something, represent a state of affairs, have a truth condition. For, as Gaskin (2008, 352) puts it, “what distinguishes a declarative sentence from a mere list of words is that a sentence has the capacity to say something true or false, whereas a list does not”. King’s account helps itself without further ado to our understanding of this, which is precisely what we wanted to understand in the first place. King appeals for his account to a very small circle he surprisingly claims to be virtuous.10 The failure of these serious and thorough efforts may suggest that it is folly to look for an account of propositional unity: better to take it as a primitive fact to be regarded with Wordsworthian natural piety. Or, rather, as Lewis (1983, 352) puts it in a related context (he is discussing the related “Third Man”-like regresses): “Not every account is an analysis! A system that takes certain Moorean facts as primitive, as unanalyzed, cannot be accused of failing to make a place for them. It neither shirks the compulsory question nor answers it by denial. It does give an account.” However, although I think this is in the end what we will have to accept, non-reductive accounts might be more or less illuminating, depending on how wide they cast their nets. Illocutionary types such as sayings, questions and directives also include ancillary types to which they help themselves, including referring and, even more basically, predicating—predicating in particular, at the most basic level, feature-placing contents of a contextually given circumstance or situation. I suggest that, by casting its net wide in this way, an account that helps itself to illocutionary types in addition to their contents will help us to understand better what the unity of the proposition comes to. 10. Cf. King’s (2007, 50) discussion of the circle. García-Carpintero (forthcoming-a) discusses Gaskin’s more complex proposal.

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I will conclude this section with a third consideration of my own in favor of illocutionary types, which I will also have to leave here at a rather impressionistic level. Hornsby (2001) and Williamson (2009) provide an account of derogatory words such as ‘Boche’ by taking the specifically derogatory aspects to be a conventional implicature, rather than a contribution to the specifically asserted content. It is doubtful, however, that an ordinary proposition can adequately capture what, on such views, is conventionally implicated in these cases; intuitively, to capture its properly derogatory nature, something with force-like features—in Alston’s (2000) category of expressives—is required. Similarly, ancillary speech acts include not just referring and predicating, but also presupposing. On the well-known Stalnakerian (2002) picture, presuppositions are explained in terms of attitudes concerning a “common ground”, defined also in terms of attitudes of belief and acceptance about propositions. There are cases—pejoratives might be one, in an alternative account of derogatory words defended by Macià (2002)—which would require taking presuppositions to have force-like features. Thus, in summary, we have good reason to acknowledge illocutionary types—types of representational states—in addition to the concrete acts, states or events that instantiate them and to the traditional propositions which are their contents: we need them at least to account for the semantics of some embedded clauses, to provide an illuminating account of the unity of the proposition, and to account for the nature of some conventional implicatures and presuppositions.11 In the next section I will show that some illocutionary types, and not propositions, are intuitively primary truth-bearers; I will then illustrate in the final section what acknowledging illocutionary types can do for us in the theory of truth, by considering some relevant examples (vagueness, vacuous and indeterminate singular terms). 11. As the editors pointed out to me, there is a more general, less controversial consideration to conclude that there are illocutionary acts, in addition to individual acts. We may have, in general, no problems with talking about types and tokens of things, and with finding many differently individuated types for groups of individual things. Since there is no reason why individual acts should not be grouped according to their illocutionary forces and other speechact properties, there should be no reason for denying that there are illocutionary types. This consideration gives us a general reason to accept illocutionary types, to the extent that we assume an “abundant” ontology of types (to help myself to the famous distinction by Lewis between two conceptions of properties). The three reasons mentioned in the main text would then provide reasons for acknowledging illocutionary types even in a more sparse ontology of types and properties, as sufficiently “natural”—explanatorily significant—types.

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3. Truth-aptness and what is said Truth-aptness poses a well-known problem for forms of deflationism that take linguistic items, sentences-in-context or utterances to be the primary truth-bearers (such as Field’s, which adopts this view consistently with his criticism of propositional deflationism mentioned in the first section). Sentences in the imperative or interrogative mood, and utterances thereof, are intuitively not truth-apt; can an adequate notion of truth-aptness be captured on deflationary assumptions about truth? (See Bar-On & Simmons 2006, 625–628 for a discussion.) Künne (2003, 265, fn) acknowledges that we do not count utterances of a non-declarative sentence (‘Did Frege die in 1925?’) as true or false even when it “does express a proposition”. Deflationists might appeal to what Bar-On & Simmons (2006, 625) call “syntacticism”, “according to which a sentence is truth-apt if it displays the appropriate syntax”; something like this is what Künne (p.c.) appears to resort to: “why is it inappropriate to comment in this way [i.e., with ‘That’s true’] on an utterance of a nondeclarative sentence? It seems to me that this inappropriateness is (just) a matter of grammar. Roughly, ‘That’s true’ as a comment on an utterance of sentence S is just a laconic version of ‘It is true that’ followed by S, and this requires that S be a declarative sentence. I say ‘roughly’ because when you say to me, ‘You are F’, my ‘That’s true’ comes to the same thing as (my) ‘It is true that I am F’”. I think that syntacticism is inadequate: as Bar-On & Simmons point out, uttering a sentence in the declarative mood is neither sufficient nor necessary for truth-aptness. It is not sufficient, because we do not find it intuitively plausible to make the comment (seriously, of course), for instance, on a sentence (‘Fred has flat feet’) written on the board in the course of a logic class so as to illustrate the kind of thing that ‘Fa’ formalizes, manifestly without the assertoric and ancillary referential intentions usually associated with such sentences (so that, as we may put it, there is no Fred): the student’s question, ‘who are you talking about? Who is Fred?’ would receive the appropriate scolding answer. Künne (p.c.) mentioned as an example of a non-assertoric sentence we would without hesitation classify as true or false the famous first sentence of Anna Karenina, “Happy families are all alike; every unhappy family is unhappy in its own way”; but that is a notorious case of a sentence which, while being part of a fiction, can be taken to (also) make a claim: I doubt that we have the same intuitions, say, about

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utterances constituting that same fiction which include the name ‘Anna Karenina’.12 Or consider an utterance of (3) above, followed by ‘I promise’; I do not think we would find it appropriate to respond ‘That’s true’, or even ‘That was true’ the day afterwards, when the promise has been complied with, even though (3) is still, of course, in the declarative mood in such a case. The proposal is also inadequate because declarative grammar is not necessary for truth-aptness either. Bar-On & Simmons mention as counterexamples sentence-fragments, such as ‘no’ or ‘expensive car that’. Consider also an utterance of ‘Are we not at war with Islam?’, manifestly intended as an indirect assertion;13 we could easily react to that with ‘That is not true, we are not in any sort of war with Islam’. So far we have discussed how the problem of truth-aptness afflicts linguistic varieties of deflationism. Künne’s reason to qualify as “rough” his syntacticist proposal mentioned above brings up an interesting related problem for propositional varieties. The need for the qualification, intuitively, derives from the same basic facts about our practice of ascribing truth and falsity already suggested by the previous counterexamples to the sufficiency and necessity for truth-aptness of the use of a declarative sentence. As Künne puts it in a text I already quoted, we ascribe truth to entities such as allegations, beliefs, conjectures, contentions, judgements, reports, statements, suppositions, thoughts and so on. If we kept the same indexical type used by the person expressing the relevant truth-bearer, while using it in a different context, we would run the risk of not properly individuating the allegation, contention, statement, or whatever we are ascribing truth to. Now, Künne is right that it is not the particular acts or events that we intuitively ascribe truth to: “When we ascribe truth (or falsity) to beliefs and statements we do not ascribe it to believing or statings, 12. We may well have the intuition that some other sentences in Anna Karenina that are less clearly assertoric than Künne’s example (for instance, sentences about the pursuits of the character called ‘Napoleon’, as one of the editors pointed out to me) are true or false; but for my anti-syntacticist point it is enough that some of them, despite their declarative form, are intuitively not truth-apt. Note, by the way, that here I am just pointing out facts about our intuitions; there are theories of fictional discourse according to which those utterances count as straightforwardly true or false, and, of course, much more—serious theoretical work—is required to reject those views (as one ultimately should, I think, but that is a different issue). 13. Once more, I note that I am just describing intuitions—there are theories of assertion, such as Alston’s (2000), cf. fn. 16 below, and many others—that are incompatible with the existence of indirect assertions, because they have as a condition on asserting p that the assertion is made with a sentence that literally conveys the proposition p. Here too, I take this to be a reason to reject them, but that is not the point at stake here.

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but rather to what is believed and what is stated” (op. cit., 250); an act of making an allegation, or contending something, is intuitively not true or false. However, is it a proposition what we are counting as such? Given the way Künne proposes to introduce propositions and to individuate them, I take it that these identities are, according to him, all true when they concern the assertion that B made with (3), and the question asked by (4):14 (9) What B asserted = that B would return the book the day after. (10) What (4) asks = whether B would return the book the day after. As I already mentioned, Künne (2003, 253) thinks that the same proposition can be introduced both by a that- and a whether-clause: “a yes/no interrogative expresses the same proposition as the corresponding declarative sentence. So propositions can also be specified by whether-clauses, the oratio oblique counterparts of such interrogatives. Thus in ‘What A asked (herself or B) was whether p’, both clauses single out a proposition”. Thus, it appears that the right-hand side of these identities might well refer to the same entity. Now, if the assertion (in the object-sense, not the act-sense) mentioned in the left-hand side of (9) is true, on the basis of Leibniz’s Law we seem to be forced to conclude that the question is also true. In fact, even though Künne does not discuss promises, it seems that we can make the same point about the promise B might have made instead by adding ‘I promise’ to (3), having to conclude also that that promise is true: (11)

What B promised = that B would return the book the day after

To put it in a nutshell: if truth-bearers are things such as claims and contentions, and these are just propositions, then, assuming that speechacts in any non-assertive category might represent the same propositions, it seems difficult to understand why we do not intuitively count them also as true or false. This is significant, because Künne’s claims about the most fundamental truth-bearers are not intended as revisionary, but, on the contrary, based on straightforward intuitions. This is the problem of truth-aptness for the propositional version of deflationism: explain, using only modest resources, why some representational acts representing propositions that are allegedly identical to truth-bearers such as allegations, 14. Künne thinks that propositions should be individuated in a fine-grained Fregean way. I will come back to this below; for the moment, I am putting aside issues of individuation; I take it that this does not affect what I say in the main text.

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contentions and so on, are not truth-apt. On the proposal sketched in the previous section, this is not a problem; for it is not propositions that on that view are intuitively taken to be truth-bearers, it is rather propositions qua alleged, contended, claimed, asserted, stated, believed, and so on and so forth; i.e., entities individuated not just in terms of a traditional proposition, but also in terms of force-like features.15 Is there something in common to those forces we take to be truthevaluable? Several writers, including Salmon (1991) and Bach (1994), usefully distinguish two senses for the ordinary notion of saying. In one sense, saying is a speech act, or rather a genus of which speech acts such as assertions, predictions, claims, contentions, allegations, and so on are species—roughly, the one corresponding to Alston’s (2000) category of assertives; in the other, saying is something like conveying conventionally encoded contents, i.e., propositions. Putting aside thorny hermeneutical issues, in Austin’s terminology saying in the first sense is a (generic) illocutionary act; saying in the second sense is a locutionary act. Is there a feature characterizing saying (in the illocutionary sense, the one we are interested in here)? I guess it should be the word-to-world direction of fit distinctive of assertives—difficult as it has proved to be to define it in a clear-cut way. In the next section I will put the distinction to work, elaborating on the worry with Künne’s modest account I presented in the first section. In this section I have pointed out that we intuitively only count illocutionary acts of certain types, having a particular force, as true and false, and also that this is not just a point of grammar. This at the very least 15. For a minimalist who tries to deal this problem, cf. Alston (2007, 23–26). Alston crucially appeals to his own account of assertion; although I like its normative features, I consider it misguided. Alston wants to identify assertions as commitments to the truth of the asserted propositions. The obvious problem with this is that other speech acts involve commitments to the truth of represented propositions; for instance, presupposing that p also involves commitment to the truth of p. To deal with this, Alston adds to his account of assertion the condition that in assertion the asserted proposition is explicitly presented. I think this is a mistake. In the first place, the proposal is manifestly ad hoc. Why would it be possible to perform any other speech act but an assertion in an indirect way? In addition, it is manifestly counterintuitive; in asking ‘Where the heck are you going?’, I am asserting that (to put it mildly) you should not go anywhere. Aside from depending on an account of assertion subject to these objections, Alston’s proposal about the present issue is unsatisfactory. His proposal is that we feel like applying truth and falsity to assertions, but not to promises, requests, etc., because the propositions whose truth the agents of these acts commit themselves to “are hidden from public view. It takes analytical theorizing to dig them out” (op. cit., 26), while in the case of assertions “it stares one in the face” (ibid.). It should be clear that this does not work; in many cases it is just those propositions whose truth the speaker making a promise or a request commits himself to that “stare one in the face”.

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shows that it is not enough for a philosophical account of truth to work well for propositions; it should be shown in addition how the account is to be extended so as to capture the intuitively most salient notion of truth, while still respecting the account’s fundamental theoretical assumptions. Note, however, that for all I have said the following is still a viable position: (i) Theoretically if not intuitively, propositions are the primary truthbearers. (ii) Whether an illocutionary act (or type of such as acts) is truth-apt, depends on its force: only acts with the right direction of fit are truth-apt. (iii) Now if an illocutionary act is truth-apt, its truth/falsity is inherited from the primary truth-bearer expressed by it, i.e. from a proposition. In the following section we will examine this priority question: what are the primary truth-bearers? If Fs are primary truth-bearers, and Gs are non-primary or derivative truth-bearers, then true Gs are true because they are related in an appropriate way to Fs (e.g., they signify them). When it comes to illocutionary types and propositions, the outlined position would make such a claim: the assertion that p is true because (i) it has the right direction of fit and (ii) it expresses the true proposition that p. 4. Illocutionary truth and the point of assertion In previous work, I have invoked the distinction between sayings as illocutionary types and the propositions they represent in order to provide replies to several objections to the supervaluationist account of vagueness. I will summarize the main points here, for they provide a useful background to restate later the main objection I am raising here for Künne’s Modest Account. To fix the terminology, I will use ‘express’ for the relation between linguistic items and illocutionary types, including sayings, and ‘signify’ for the relation between both linguistic items and illocutionary types and the propositions encoding their fulfillment conditions. (i) Williamson’s argument for bivalence. Wright (2004, 88) expresses as follows a well-known worry with the supervaluationist rejection of bivalence: “The wide reception of supervaluational semantics for vague discourse is no doubt owing to its promise to conserve classical logic in

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territory that looks inhospitable to it. The downside, of course, rightly emphasized by Williamson and others, is the implicit surrender of the T-scheme. In my own view, that is already too high a cost”. The argument by Williamson (1994)—further developed in Andjelkovic & Williamson (2000)—that Wright alludes to here appeals to the following schemas: (T) If an utterance u says that P, then u is true iff P (F) If an utterance u says that P, then u is false iff not P (B) If an utterance u says that P, then either u is true or u is false The conditionalized truth-schema (T) differs from the standard disquotational one. Andjelkovic & Williamson (2000, 216) argue that “[a formalized variant of ] (T) is more basic than the disquotational biconditional; it explains both the successes and the failures of the latter.” Three kinds of cases are mentioned in support. Firstly, context dependence (‘we are Europeans’) constitutes a problem for the traditional version, but not for (T). Secondly, the liar paradox “merely falsifies the antecedent” (216). Finally, “[t]he principle [of Bivalence] should not imply that non-declarative sentences are true or false, for presumably they are not intended to say that something is the case. For the same reason, the principle does not imply that a declarative sentence is true or false if it does not say that something is the case” (217f.). Williamson (1994, 187–198) has similar considerations. Truth-bearers are here assumed to be linguistic items. Here is Williamson’s (1994) reason for it: “Bivalence is often formulated with respect to the object of the saying, a proposition (statement, …). The principle then reads: every proposition is either true or false. However, on this reading it does not bear very directly on problems of vagueness. A philosopher might endorse bivalence for propositions, while treating vagueness as the failure of an utterance to express a unique proposition. On this view, a vague utterance in a borderline case expresses some true propositions and some false ones (a form of supervaluationism might result). […] The problem of vagueness is a problem about the classification of utterances. To debate a form of bivalence in which the truth-bearers are propositions is to miss the point of the controversy” (Williamson 1994, 187). I would subscribe to all these points, very much related to Field’s objection against propositional deflationism mentioned in the first section that I am developing here against Künne’s Modest Account; I myself would take utterances not as linguistic items (as Williamson proposes and as Field had in mind), but

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as the types of illocutionary contents in the generic category of assertives I am calling sayings. This requires us to distinguish, as I am suggesting we should do, between the sense in which linguistic items “say” (expressing sayings), and the sense in which they, and saying themselves, “say” or signify Russellian propositions.16 Williamson’s (1994) argument for bivalence goes roughly as follows. Take any utterance that allegedly invalidates bivalence, like one of ‘TW is thin’, assuming TW to be a borderline case of thinness. Now, from the relevant instance of excluded middle, which the supervaluationist accepts, plus (T) and (F), we get (B), the relevant instance of the principle of bivalence. Thus, the supervaluationist must reject (T) or (F), or both. Williamson then challenges him to provide an acceptable motivation for that rejection: “The rationale for (T) and (F) is simple. Given that an utterance says that TW is thin, what it takes for it to be true is just for TW to be thin, and what it takes for it to be false is for TW not to be thin. No more and no less is required. To put the condition for truth and falsity any higher or lower would be to misconceive the nature of truth and falsity” (1994, 190). Williamson’s main point thus depends on intuitions about what utterances (or sentences in context) say, and the effect of this on their truth-conditions. It is this challenge—as developed in Andjelkovic & Williamson (2000)— that García-Carpintero (2007) confronts. In the original application of the supervaluationist techniques to empty names by van Fraassen (1966), the main goal was to account for an intuitively correct distribution of truthvalues for utterances (13)-(15), made under the reference-fixing stipulation (12). While (13) is neither true nor false, (14) and (15) are true: (12) Let us give the name ‘Vulcan’ to the only planet causing perturbations in Mercury’s orbit. (13) Vulcan is bigger than Mars. (14) Either Vulcan is bigger than Mars or Vulcan is not bigger than Mars. 16. Williamson (1999, first section) in fact suggests in his reply to Schiffer (1999, first section) that nothing important for his argument hangs on whether we take as truth-bearers linguistic items or rather contents—including I think the sayings I am positing here. If we take this option, the debate would then be about whether contents satisfy bivalence. If so, the argument I will sum up below purports to establish that, in the relevant cases, the expressed sayings do not allow a (determinate) truth-evaluation; for they collectively signify a plurality of precise propositions, which only individually satisfy bivalence.

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(15) Vulcan causes perturbations in Mercury’s orbit, if it exists. The following example presented by Sorensen (2000, 180) provides a second illustration of the use of the techniques. The stipulation (16) is made by explorers before traveling up the river Enigma; after they finally reach the first pair of river branches, they name one branch ‘Sumo’ and the other ‘Wilt’. Sumo is shorter but more voluminous than Wilt, which make them borderline cases of ‘tributary’. A supervaluationist diagnostic allows us then to count (17) as neither true nor false, while still counting (18) as true: (16) Let us give the name ‘Acme’ to the first tributary of the river Enigma. (17) Acme is Sumo. (18) Either Acme is Sumo or Acme is Wilt. Now, imagine the previous platitudinous quote from Williamson (“Given that an utterance says that TW is thin, what it takes for it to be true is just for TW to be thin, and what it takes for it to be false is for TW not to be thin. No more and no less is required”) uttered with either (13) or (17) replacing ‘TW is thin’. In the paper I mentioned before, I invoke the distinction between expressing sayings and signifying propositions in order to elaborate claims along the following lines about these cases. The first is one about their effect on intuitions: far from sounding platitudinous, now they just appear puzzling. The second claim is that a theoretical account of the cases along the previously sketched lines explains the puzzlement. Firstly, there are sayings that utterances (13)–(15), (17)–(18) express; on my proposal, moreover, these sayings are truth-evaluable, in fact those expressed by (14), (15) and (18) are true. But, secondly, on account of failure of reference the saying that (13) expresses only signifies a truncated or “gappy” proposition, while on account of underdetermination of reference the one that (17) expresses signifies a plurality of propositions with a distribution of truth-values that does not allow for a definite evaluation. On the view outlined, the puzzlement we feel when considering these versions of Williamson’s challenge is due to the fact that while, on the one hand, in its most natural sense the definiteness implicit in phrases such as ‘what it takes for u to be true’ is not adequately satisfied—due to the truncated character of the candidate in one case, and the existence

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of two candidates producing opposite evaluations in the other—on the other hand we feel that something specific is indeed “said”, and thus the antecedents are satisfied. These are theoretical matters, difficult to pinpoint without substantial theoretical mediation; hence the puzzlement. GarcíaCarpintero (2007) develops these and related points about the arguments elaborated in Andjelkovic & Williamson (2000). (ii) Schiffer on reports of vague contents. Schiffer (1998, 196ff.; 2000, 246ff.) advances an argument against supervaluationist accounts of vagueness, based on reports of vague contents. Suppose that Al tells Bob ‘Ben was there’, pointing to a certain place, and later Bob reports, ‘Al said that Ben was there’, pointing in the same direction. According to supervaluationist semantics, Schiffer contends, both Al’s and Bob’s utterances of ‘there’ indeterminately refer to myriad precise regions of space; Al’s utterance is true just in the case that Ben was in either of these precisely bounded regions of space, and Bob’s is true just in the case that Al said of each of them that it is where Ben was. However, while the supervaluationist truthconditions for Al’s utterance might be satisfied, those for Bob’s cannot; for Al didn’t say, of either of those precisely delimited regions of space, that it is where Ben was. From a perspective more congenial to supervaluationism than Schiffer’s, McGee & McLaughlin (2000, 139–147) pose a related problem about de re ascriptions of propositional attitudes and indirect discourse. The same difficulty is gestured at in this argument: “there are additional concerns about the ability of supervaluational proposals to track our intuitions concerning the extension of ‘true’ among statements involving vague vocabulary: ‘No one can knowledgeably identify a precise boundary between those who are tall and those who are not’ is plausibly a true claim which is not true under any admissible way of making ‘tall’ precise” (Wright 2004, 88). In reply, I (2010b) invoke the following theoretical model: “propositional attitude verbs … express relations between agents and interpreted logical forms (ILFs). ILFs are annotated constituency graphs or phrase-markers whose nodes pair terminal and nonterminal symbols with a semantic value” (Larson & Ludlow 1993, 305). Larson & Ludlow’s semantic values are classical semantic values: objects for terms, sets for predicates, truthvalues for sentences. On an alternative version (Pietroski, 1996), symbols are paired with Fregean senses in ILFs (which, in their turn, determine semantic values). Now, ILFs, under either of those proposals, are the sort of entity that can be vague, in the sense that they admit different precisifications, and admit thereby a supervaluationist treatment. Vague ILFs can

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be neither true nor false as a result of the fact that (ignoring higher-order vagueness) at least some terminal node (say, the one corresponding to ‘Ben’ in Schiffer’s example) is paired, not with an appropriate semantic value, but with a class of them (its admissible precisifications). On Pietroski’s version, this might obtain if the mode of presentation with which the symbol is paired does not determine a unique semantic value, but a class of admissible ones. Schiffer’s objection focuses on de re ascriptions, which pose specific problems on which I cannot elaborate here. But, to put it impressionistically, the fundamental assumption elaborated on the basis of the ILF model, as further applied to the case of de re ascriptions, goes as follows: Supervaluationism agrees in accepting, besides the precise Russellian propositions indeterminately signified in vague sentences, some “vague entities”: i.e., vague sayings, with contents modeled along the ILF accounts. Far from being incompatible with the philosophical account of vagueness that supports the use of supervaluationist techniques, this is taken to be a crucial aspect of it. What matters is that truth and falsity are ultimately determined relative to the class of precisifications.17 There are other applications of the distinction between sayings and propositions relevant for the theory of truth, but the ones I have just summarized should do for present purposes.18 The arguments in the two preceding sections support the distinction between sayings and propositions, both of which can be evaluated for truth, and the intuitive saliency of the truth of sayings; and the considerations we have briefly reviewed so far in this section show that we cannot mechanically move from the truth of propositions to the truth of sayings. Firstly, a saying might (indeterminately, we are discounting higher-order vagueness here) signify a plurality of propositions, and supervaluationist techniques might be required for its intuitively correct truth-evaluation; secondly, a term in the expression of the saying might fail of reference, which once again might call for 17. Keefe (2008)—a nice presentation of the main ideas defining supervaluationism— emphasizes the centrality of quantification over precisifications to the account, and its compatibility with “vague entities” of some such representational sort. 18. García-Carpintero (2008) invokes the distinction to reject the truth-relativist argument in Richard (2004), predicated on the vagueness-inducing features of gradable adjectives such as ‘rich’ or ‘tall’; García-Carpintero (forthcoming-b) invokes it to reply to the similar truth-relativist argument in MacFarlane (2003) based on the possibility of the Open Future; García-Carpintero & Pérez-Otero (2009) appeal to the distinction to dispose of anti-conventionalist arguments by Boghossian and others, arguing in fact that, while those arguments appeal to facts concerning the truth of propositions, conventionalist claims concern the truth of sayings.

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supervaluationist techniques. How does this affect our appraisal of Künne’s theory? As I mentioned above, in discussing worries about the quantification into sentence position in MOD in the first section, even if we grant that we do understand this quantification along the lines that Künne proposes, it is still an open question what sort of entity we are committed to in speaking of “ways for things to be”. If we just stay at the level of what intuitions underwrite, it is perfectly possible that it is just what I have been calling propositions—the Russellian propositions of contemporary theorists such as Kaplan, Salmon and Soames, which Künne (2003, 261) prefers to classify as states of affairs; and this intuitive diagnosis will be more substantively supported by the theoretical considerations I have merely touched on here. Now, when it comes to the truth of Russellian propositions (or the obtaining of states of affairs, if this is how we prefer to classify them following Künne), I think we should concur with Field (1992, 323): “Russell viewed atomic propositions as complexes consisting of an n-place relation and n objects, in some definite order. But an account of truth for such propositions is obvious: Such a proposition is true iff the objects taken in that order stand in the relation. It can hardly be a matter of philosophical controversy whether this definition of truth is correct, given the notion of proposition in question, so what is there for the minimalist and the full-blooded correspondence theorist to disagree about?” I do not want to sound stingy in my praise here; certainly, even when we consider the truth of propositions of this sort, philosophically it is not the same whether we adopt Horwich’s form of minimalism, say, or Künne’s; and putting aside the qualms I expressed above, I think Künne has done us an important philosophical service, allowing us to understand his proposal better, and giving us good reasons for it.19 But, as Field says, this is not the debate confronting minimalists with the defenders of more substantive conceptions of truth—such as some form of the correspondence view, which Künne (2003, 112–174) dismisses. At this point, a reader of Künne might point out that, structurally, there is not that much difference between what I am proposing and the views he actually advocates. For it is not Russellian propositions that, he argues, his account applies to, but entities individuated by Fregean require19. The same applies to Hill (2002), for the alternative account in terms of substitutional quantification.

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ments of cognitive significance. And, in fact, he (2003, 351ff.) ends up suggesting a way of rejecting bivalence for propositions thus understood, taking into consideration cases of reference-failure. Moreover, he (2003, 258–263) provides a role for Russellian propositions (states of affairs, in his ontology) as objects, not contents of intentional acts. So, where I posit sayings, he has Fregean propositions, which might equally be neither true nor false, and where I have Russellian propositions signified by sayings, he posits states of affairs as intentional objects. I am doubtful about Künne’s two moves. In the first place, to make truth-value gaps compatible with the Modest Account, he needs two negations, “choice” and “exclusion” or “internal” and “external”, and I am rather doubtful that such ambiguity exists, or, if we just stipulate it, that it might properly account for gaps. Secondly, it makes sense to me to count as “intentional objects” the actual world that is supposed to provide truth-makers for our sayings, or parts thereof (“situations”); but the Russellian propositions I think we need, signified by illocutionary types, need not of course be fulfilled. Thus, I still think that, while Künne might have provided an acceptably modest account of truth for the contents of “sentence-radicals” (and their mental counterparts)—in Stenius’s (1967) Wittgensteinian terminology—we should not thereby remain convinced that any deflationary account for the truth of the intuitively most salient truth-bearers is forthcoming. Indeed, once we make the sort of distinction I have been advocating, it seems that some form of the correspondence theory emerges as a genuine option for the truth of sayings. As I mentioned above, on a more general account the truth-conditions of sayings are a particular case of the fulfillment-conditions of intentional acts. In the case of those for mental states such as intentions and speech acts such as directives, there are good reasons for positing a dependence relation between the truth of the signified Russellian proposition (or the obtaining of the state of affairs) and the intentional act itself, for the latter to count as properly fulfilled (Ludwig 1997, 38f.). Similarly, in the case of the truth of sayings, it might well be that the (indeterminate, given higher-order vagueness) specification of the plurality of Russellian propositions signified by vague sayings, or of the conditions giving rise to gappiness, would amount to a dependence relation in the opposite direction between the intentional state and the truth-making Russellian propositions;20 so that, at the end 20. I think that these opposed dependence relations are what the asymmetry in “direction

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of the day, a correspondence account might be vindicated for the truth of sayings.21 The kind of correspondence theory I am thinking of is a truth-maker view, but for the limited purposes of this paper it is enough to think of it in the abstract terms suggested by Hill (2002, 145, fn 2). Hill provides a way of capturing the correspondence intuition compatible with his favored substitutional-quantification deflationary account; but he acknowledges that we might intuitively operate with, in fact, two notions of truth, a more robust one that we are deploying when we question that normative claims, or claims with vacuous or vague terms, are either true or false. On the view I have in mind, such an account is required for the intuitively most salient truth-bearers, sayings. How does this leave the priority issue raised at the end of last section? There would not be any suggestion on the view outlined, of course, that the obtaining/truth of state of affairs/Russellian proposition depends in any way on the truth of sayings signifying them; on the contrary, the obtaining/truth of the state of affairs/Russellian propositions signified by sayings provides part of the explanation for their truth. Thus, the fundamentality in the outlined sense of the notion of truth that Künne’s proposal might well account for is compatible with the view I have suggested. But that does not suffice to vindicate modest accounts of truth, for there is a notion of truth which plays a fundamental role in our thinking about these matters and does not appear to be explainable merely on modest terms. This, I take it, was the worry that Field was raising. I have just drawn the barest suggestions, in need of careful philosophical elaboration if they are to stand challenges such as the ones that Künne himself levels against correspondence accounts; but I think they are enough for the present purposes, which were just to substantiate the main charge I am raising against Künne’s theory. To sum it up: the notion of proposition is highly theoretical; depending on our choice, propositional truth might well be definable with modest recourses. This leaves unaccounted of fit” between sayings on the one hand, and directives, questions, promises and so on, on the other, ultimately comes to. 21. A dual account of the envisaged kind (minimalist for the truth of propositions, correspondentist for that of intentional states) is advanced as pinpointing the use of supervaluationist techniques in McGee & McLaughlin (1995); they, however, favor giving prominence to disquotational truth, invoking supervaluationism to account for the determination operator, unlike what I am suggesting here. This is what García-Carpintero (forthcoming-b) suggests for the Open Future, but only because in that case there is a unique signified truthmaking fact (true Russellian proposition, or obtaining state of affairs).

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for something that requires explanation, as Dummett (1959/1978) insisted a long time ago. A deflationary definition effects a division in the class of propositions, separating the true ones from others. Now, there are other propositional acts, in addition to assertions and judgments; promises and requests have contents, which are the contents of possible assertions and judgments. The deflationary definition also effects a division in the class of promises and requests, exactly as it does in the class of assertions. However, while we call the ones in the second division ‘true’, we do not do so with the ones in the first; we say that a promise in that group is “complied with”, or something of the sort. This suggests at least that, when it comes to characterizing the correctness conditions of propositional acts, something more is required than establishing whether or not “the” intended proposition (if there is just one) is (modestly) true; and the point applies to promises and requests, to assertions and judgments. As Dummett puts it, the deflationary characterization fails to countenance the point (the purpose, or normative force) of propositional acts. I have concluded suggesting that a proper characterization of truth as expressing the/a normative point of sayings should end up invoking the “correspondence” intuitions that, for instance, Wright (1999/2003) voices.

REFERENCES Alston, William 2000: Illocutionary Acts & Sentence Meaning. Ithaca: Cornell U.P. — 2007: “Illocutionary Acts and Truth”. In: Dirk Greimann & Geo Siegwart (eds.), Truth and Speech Acts. New York: Routledge, 9–30. Andjelkovic, Miroslava & Williamson, Timothy 2000: “Truth, Falsity and Borderline Cases”. Philosophical Topics 28, 211–244. Bach, Kent 1994: “Conversational Implicitures”. Mind and Language 9, 124–162. Bar-On, Dorit & Simmons, Keith 2006: “Deflationism”. In: Ernest Lepore & Barry Smith (eds.), The Oxford Handbook of Philosophy of Language. Oxford: Oxford University Press, 607–630. Boisvert, Daniel & Ludwig, Kirk 2006: “Semantics for Nondeclaratives”. In: Ernest Lepore & Barry Smith (eds.), The Oxford Handbook of Philosophy of Language. Oxford: Oxford University Press, 864–892. Bolzano, Bernard [WL] 1837: Wissenschaftslehre. 4 vols. Aalen: Scientia, 1981. David, Marian 2005: “Künne on Conceptions of Truth”. Grazer Philosophische Studien 70, 179–191.

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Dummett, Michael 1959/1978: “Truth”. In his Truth and Other Enigmas, Cambridge, Mass.: Harvard UP, 1–24. Field, Hartry 1992: “Critical Notice of Horwich’s Truth”. Philosophy of Science 59, 321–330. Frege, Gottlob 1918: “Der Gedanke”. Beiträge zur Philosophie des deutschen Idealismus I, 58–77. García-Carpintero, Manuel 2007: “Bivalence and What Is Said”. Dialectica 61, 167–190. — 2008: “Relativism, Vagueness and What Is Said”. In: Manual García-Carpintero & Max Kölbel (eds.), Relative Truth. Oxford: Oxford University Press, 129–154. — 2010a: “Fictional Entities, Theoretical Models and Figurative Truth”. In: Roman Frigg, & Matthew Hunter (eds.), Beyond Mimesis and Convention— Representation in Art and Science. New York and Berlin: Springer, 139–168. — 2010b: “Supervaluationism and the Report of Vague Contents”. In: Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds: Essays in the Nature and Logic of Vagueness. Oxford: Oxford University Press, 345–359. — forthcoming-a: “Gaskin’s Ideal Unity”. Dialectica. — forthcoming-b: “Relativism, the Open Future, and Propositional Truth”. In: Fabrice Correia & Andrea Iacona (eds.), Around the Tree. Synthese Library: Springer. García-Carpintero, Manuel and Pérez Otero, Manuel 2009: “The Conventional and the Analytic”. Philosophy and Phenomenological Research 78, 239–274. Gaskin, Richard 2008: The Unity of the Proposition. Oxford: Oxford University Press. Gómez-Torrente, Mario 2005: “Review of Künne’s Conceptions of Truth”. Philosophical Quarterly 55, 371–373. Gupta, Anil 2002: “An Argument Against Convention T”. In: Richard Schantz (ed.), What Is Truth?. Berlin: De Gruyter, 225–237. Hanks, Peter 2007: “The Content-Force Distinction”. Philosophical Studies 134, 141–164. Hill, Christopher 2002: Thought and World. Cambridge: Cambridge University Press. Hornsby, Jennifer 2001: “Meaning and Uselessness: How to Think about Derogatory Words”. In: A. Peter French & K. Howard Wettstein (eds.), Midwest Studies in Philosophy XXV. Oxford: Blackwell, 128–141. Horwich, Paul 1998: Truth (2nd rev. ed.). Oxford: Clarendon Press. King, Jeffrey 2007: The Nature and Structure of Content. Oxford, Oxford University Press. Künne, Wolfgang 2003: Conceptions of Truth. Oxford: Oxford University Press.

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— 2005: “The Modest Account of Truth Reconsidered: With a Postscript on Metaphysical Categories”. Dialogue XLIV, 563–596. — 2008: “The Modest, or Quantificational, Account of Truth”. Studia Philosophica Estonica 1.2, 122–168. Larson, Richard & Ludlow, Peter 1993: “Interpreted Logical Forms”. Synthese 95, 305–355. Ludwig, Kirk 1997: “The Truth about Moods”. Protosociology 10, 19–66. Macià, Josep 2002: “Presuposición y significado expresivo”. Theoria 17, 499–513. MacFarlane, John 2003: “Future Contingents and Relative Truth”. Philosophical Quarterly 53, 321–336. McGee, Vann & McLaughlin, Brian 1995: “Distinctions Without a Difference”. Southern Journal of Philosophy XXXIII, sup., 203–251. — (2000): “The Lessons of the Many”. Philosophical Topics 28, 129–151. Moltmann, Friederike October 2009: “Attitudinal Objects”. MS. Available online at http://semantics.univ-paris1.fr/index.php/visiteur/contenu/afficher/menu/24. Patterson, Douglas 2005: “Sentential Truth, Denominalization, and the Liar: Aspects of the Modest Account of Truth”. Dialogue XLIV, 527–537. Pendlebury, Michael 1986: “Against the Power of Force: Reflections on the Meaning of Mood”. Mind 95, 361–372. Richard, Mark 2004: “Contextualism and Relativism”. Philosophical Studies 119, 215–242. Salmon, Nathan 1991: “The Pragmatic Fallacy”. Philosophical Studies 63, 83–91. Schiffer, Stephen 1998: “Two Issues of Vagueness”. The Monist LXXXI, 193–214. — 1999: “The Epistemic Theory of Vagueness”. Philosophical Perspectives 13, Epistemology, James Tomberlin (ed.), Oxford: Blackwell, 481–503. — 2000: “Vagueness and Partial Belief ”. Philosophical Issues 10, Enrique Villanueva (ed.), Boston: Blackwell, 220–257. — 2003: The Things We Mean. Oxford: Clarendon Press. Segal, Gabriel 1990/1: “In the Mood for a Semantic Theory”. Proceedings of the Aristotelian Society XCI, 103–118. Sorensen, Roy 2000: “Direct Reference and Vague Identity”. Philosophical Topics 28, 177–194. Stalnaker, Robert 2002: “Common Ground”. Linguistics and Philosophy 25, 701– 721. Stenius, Erick 1967: “Mood and Language-Game”. Synthese 17, 254–274. Van Fraassen, Bas 1966: “Singular Terms, Truth-value Gaps, and Free Logic”. Journal of Philosophy LXIII, 136–152. Williamson, Timothy 1994: Vagueness. London: Routledge. — 1999: “Schiffer on the Epistemic Theory of Vagueness”. Philosophical Perspectives 13, Epistemology, James Tomberlin (ed.), Oxford: Blackwell, 505–517.

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— 2009: “Reference, Inference, and the Semantics of Pejoratives”. In: Joseph Almog & Paolo Leonardi (eds.), The Philosophy of David Kaplan. Oxford: Oxford University Press, 137–158. Wright, Crispin 2004: “Vagueness: A Fifth Column Approach”. In: J.C. Beall (ed.), Liars and Heaps. Oxford: Oxford University Press, 84–105. — 1999/2003: “Truth: A Traditional Debate Reviewed”. In: Simon Blackburn & Keith Simmons (eds.), Truth. Oxford: Oxford University Press, 203–238, 1999; also in his Saving the Differences. Cambridge, Mass.: Harvard UP, 241–287, 2003.

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Grazer Philosophische Studien 82 (2011), 77–90.

LOGICAL TRUTH AND LOGICAL FORM* Edgar MORSCHER University of Salzburg Summary According to a criterion of logical truth, presented by Quine (in “Carnap and Logical Truth”, and similarly also in “Truth by Convention” and in Mathematical Logic), every sentence which is purely logical (i.e., contains no other expressions or symbols but purely logical ones), such as xy™(x = y) or ™xy™(x = y), must be logically determinate (i.e., either logically true or logically false). This odd consequence was even canonized by Carnap as a theorem in his Logical Syntax of Language. The paper shows how to avoid it by shifting from the skeleton view to the mould view of logical form.

1. Quine’s criterion of logical truth In “Carnap and Logical Truth” (from now on: CLT) W. V. O. Quine attacks a view called the “linguistic doctrine of logical truth”. He concedes that this doctrine may be more epistemological than linguistic in nature (cf. CLT 388), and ventures to say that it might be better not to attribute it to Carnap, though he thinks that it corresponds to “Carnap’s own orientation and reasoning” (cf. CLT 385). Quine begins the discussion by presenting a pretheoretical “mark” of logical truth as the first step in the later development of the linguistic doctrine of logical truth. He introduces the criterion in the following passage: * In the bibliography of Wolfgang Künne’s book Versuche über Bolzano/Essays on Bolzano (Sankt Augustin: Academia, 2008) there is a reference to my unpublished paper “Quine on Carnap on Logical Truth”. This paper is still unpublished, although I had revised and expanded it some time ago due to an exchange of thoughts with Karel Lambert. (During this course of revision I gave the paper also a new title.) Since Wolfgang Künne found it worthy of being mentioned, I hope he will be kind enough to let me dedicate it to him on the occasion of his 65th birthday.

Without thought of any epistemological doctrine, either the linguistic doctrine or another, we may mark out the intended scope of the term ‘logical truth’, within that of the broader term ‘truth’, in the following way. First we suppose indicated, by enumeration if not otherwise, what words are to be called logical words; typical ones are ‘or’, ‘not’, ‘if ’, ‘then’, ‘and’, ‘all’, ‘every’, ‘only’, ‘some’. The logical truths, then, are those true sentences which involve only logical words essentially. What this means is that any other words, though they may also occur in a logical truth (as witness ‘Brutus’, ‘kill’ and ‘Caesar’ in ‘Brutus killed or did not kill Caesar’), can be varied at will without engendering falsity. (CLT 387)

Now this criterion is one with which Carnap is assumed to agree. Indeed, it is still adopted in textbooks, and even now influences and misleads quite a few people. But it is not adequate, even for elementary logic, i.e. first order predicate logic with identity, for which at least it is intended to work. This can be shown by means of simple examples. Consider the following sentence of everyday language: ‘There are at least two things’. Within the language of first order predicate logic with identity, this sentence from everyday language is paraphrased as follows: (1a) xy ™(x = y) Within the language of second order predicate logic, the sentence may be paraphrased as follows: (1b) xyF(Fx š ™Fy) Most people will take such a sentence to be true and its negation—(2a) or (2b), respectively—to be false: (2a) ™xy™(x = y) (2b) ™xyF(Fx š ™Fy) Similarly for sentences such as ‘There are at least three things’, ‘There are at least four things’ etc. and their negations, as well as for the paraphrases of these sentences and their negations in the language of first order predicate logic with identity or in the language of second order predicate logic. Hardly anybody, however, will take one of these sentences to be either logically true or logically false.1 It seems to be beyond doubt that which1. Carnap, as we will see at the end of this paragraph, is an exception in this regard. More

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ever truth-value they have, it is not a logical affair: we say they are logically indeterminate. But none of them contains any non-logical word or symbol. Therefore, they can involve no non-logical (but only logical) words or symbols essentially. Thus, according to the informal criterion presented above, the sentences under consideration that turn out to be true would have to be logically true and those that turn out to be false would have to be logically false. But none of these sentences is logically true or logically false. Should one then require that a logically true and a logically false sentence involve at least one non-logical word or symbol? No, because there are sentences containing only logical words and symbols, but which nevertheless are obviously logically true (or logically false), as for example: (3a) xy ™(x = y) › ™xy ™(x = y) (3b) xyF(Fx š ™Fy) › ™xyF(Fx š ™Fy) These sentences are logically true, and their negations (or the corresponding sentences with an ‘š’ instead of ‘›’ as their main connective) are logically false. This objection to Quine’s criterion of logical truth can be answered in different ways, either systematically (i) or historically (ii). (i) In attempting to answer the objection against Quine’s criterion systematically, the paraphrases in the language of second order predicate logic could, e.g., be refuted due to a general rejection of taking predicate variables to be bindable variables or due to the fact that we restrict our considerations to elementary logic. The paraphrases in the language of first order predicate logic with identity, however, could be rejected as counterexamples by taking ‘is identical with’ or ‘=’, respectively, not to be a logical but rather an extra-logical phrase or symbol. This, however, is no way out for Quine himself, since he includes identity theory explicitly within elementary logic and mentions ‘=’ as belonging to the logical vocabulary (cf. CLT 388). (ii) There is also a historical answer to the objection against Quine’s criterion of logical truth: The criterion is supposed to reflect Carnap’s view of logical truth, but the counter-examples we used against it—such as (1a) and (2a)—are, according to Carnap, in clear agreement with this recently, this view was defended by Timothy Williamson, 2000 (I am indebted for this reference to Benjamin Schnieder.)

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view, since for Carnap, (1a) is logically true and (2a) is logically false. More generally, according to Carnap every purely logical sentence (i.e. every sentence containing no extra-logical expression at all) is logically determinate.2 How can this be? The reason for Carnap’s adopting this strange view does not lie in his concept of logical truth and analyticity, but rather in his definition of a logical expression (cf. LSL 177f.); and this definition in turn is a consequence of his philosophical position as a leading figure of Logical Empiricism.3 How does Carnap see to it that his proof theory accommodates this strange view? He does so by using an axiomatic basis for his logic which includes an axiom of infinity or is so strong that we do not need it, since the corresponding sentence is derivable from the axioms.4 In accordance with his Principle of Tolerance (LSL 51), Carnap is tolerant enough to allow also other regulations.5 He takes it as useful, however, to have at least an axiom fixing the number of objects of the universe of discourse (cf. ESL 87f.). This, of course, is enough for making all purely logical formulas of first order predicate logic with identity, and in particular all numerical formulas among them, logically determinate. Be that as it may, whether or not our objection can be answered depends on whether or not we allow for sentences which contain only logical phrases or symbols, and no extra-logical ones. If there are such sentences, then Quine’s criterion is inadequate. And there seems to be no good reason for excluding such sentences from a language.

2. Carnap LSL 179: “Theorem 50.1. Every logical sentence is determinate; every indeterminate sentence is descriptive.” LSL 184: “Theorem 52.3. Every logical sentence is L-determinate; there are no synthetic logical sentences.” 3. Cf. LSL 177: “But if we reflect that all the connections between logico-mathematical terms are independent of extra-linguistic factors, such as, for instance, empirical observations, and that they must be solely and completely determined by the transformation rules of the language, we find the formally expressible distinguishing peculiarity of logical symbols and expressions to consist in the fact that each sentence constructed solely from them is determinate.” 4. Cf. LSL 97, 140f.; ESL 154f. For certain logical languages an axiom of infinity and all the numerical theorems following from it are no problem for the following reason: “The Axiom of Infinity (see § 33, 5a) and sentences like ‘(x)(x = x)’ are demonstrable in Language II, as are similar sentences in Language I. But the doubts previously mentioned are not relevant here. For here, those sentences only mean, respectively, that for every position there is an immediately succeeding one, and that at least one position exists. But whether or not there are objects to be found at these positions is not stated” (LSL 141). 5. They are carefully discussed by Carnap in § 38a (of the English edition of LSL) which had to be omitted, unfortunately, in the German edition due to the publisher’s demand for abridgement.

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2. Repairing Quine’s criterion of logical truth In order to repair Quine’s criterion of logical truth, I shall resurrect an old idea, the idea that logical properties—like the property of being logically true—are formal properties, that is, they are properties of logical forms. What we need is the old concept of a sentential form to which we primarily attribute a logical property (like the property of being universally valid); with respect to this attribute of a sentential form, the property of logical truth of a substitution instance of it—i.e. of a particular sentence—is merely derivative. In face of the arguments brought forward by John Etchemendy (1983; cf. also 1990) against the idea of logical form, resurrecting this idea seems to be a miracle comparable with the resurrection of Lazarus. There is more than one view of logical form, however, and for our purpose, it all depends on which view of logical form we adopt. Before I present my view of logical form, let me introduce the auxiliary notion of an expression’s being purely logical. First we have to fix the list of simple expressions or symbols which are purely logical. It comprises (i) logical particles like ‘not’, ‘and’, ‘all’, ‘some’, ‘identical’ or the corresponding symbols (‘™’, ‘š’, ‘’, ‘’, ‘=’),6 as well as (ii) variables of different types or corresponding phrases in a natural language, and (iii) auxiliary symbols like punctuation marks or parentheses. An expression (in particular a sentence, a sentence form, an argument or an argument form) is then purely logical iff it contains no simple expressions or symbols other than purely logical ones. The term ‘universal word’ will be used in what follows in accordance with Carnap (LSL 293f., ESL 36f.) for such words as ‘thing’, ‘object’, ‘human being’, ‘number’, etc. According to the view of logical form underlying the following considerations, a pure (or logical) sentence form is an expression which can be generated from a given sentence (or closed formula) that is not purely logical (i.e., it contains at least one non-logical expression or symbol) by replacing all of its simple non-logical expressions or symbols, including the universal words, by appropriate variables; this replacement need not necessarily be performed in a uniform way (i.e., an expression or symbol occurring at 6. Alfred Tarski (1936, 418f.) complained that no objective grounds are known to him which permit us to draw a sharp boundary between logical and extra-logical terms. (The same complaint was already expressed 100 years earlier by Bernard Bolzano in his Wissenschaftslehre, Vol. II, 84.) Tarski’s attempt of 1986 to define the concept of a logical notion was not really successful as he himself conceded; see Tarski 1986, 149f.

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different places in the sentence or formula in question need not necessarily be replaced everywhere by the same variable). By saying that all simple non-logical expressions (in the case of formulas: symbols) in a sentence (or formula) are to be replaced by appropriate variables, we mean that all simple predicates (predicate constants) and universal words are replaced by predicate variables (‘F ’, ‘G’,…), all simple singular names (individual constants) by individual variables (‘x’, ‘y’,…), all unanalysed simple sentences (sentential constants) by sentential variables (‘p’, ‘q’,…) etc., and that the occurrences of these variables are everywhere in the resulting expression free. A substitution instance of a pure sentence form X is a sentence (or formula) resulting from X by a simultaneous and uniform replacement of all free variables in X by corresponding expressions or constants, i.e., by uniformly replacing predicate variables by predicates (or predicate constants), individual variables by singular names (or individual constants), sentential variables by sentences (or closed formulas), etc. The set of expressions or constants which can be substituted for the variables includes logical expressions and constants such as ‘identical’ or ‘=’, and also universal words.7 A pure sentence form is universally valid iff all of its substitution instances are true, and it is universally invalid iff all of its substitution instances are false. A sentence (or a closed formula) is logically true iff there is at least one universally valid pure sentence form of which it is a substitution instance, and it is logically false iff there is at least one universally invalid pure sentence form of which it is a substitution instance, i.e., iff its negation is logically true. In these definitions we presuppose, of course, that the language in question is rich enough to have names for everything (i.e. for every individual) and predicates for every kind of individual and for every relation among individuals. This presupposition is required in order to make sure that a lack of a true or false substitution instance of a pure sentence form is not just due to our language failing to have the right word for the expression thereof. Such a requirement is well-known from the substitutional interpretation of quantifiers where we also have to postulate that every member 7. If the use of variables should not be welcomed in an everyday language context, instead of speaking of the replacement of non-logical expressions by corresponding variables we could also speak of their variation or their replacement by other expressions of the same category. A logical variant of a sentence then is the result of such a variation or replacement of all of its simple non-logical parts. We could then represent a pure (or logical) sentence form also by the set of all logical variants of a sentence that is not purely logical; a substitution instance of a pure sentence form then is a member of this set.

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of the domain is assigned to at least one individual constant under every interpretation. With these modifications, the definition of logical truth as presented parallels the standard definition given in logic books today where a logically true sentence is defined as a sentence that is true under every interpretation. Such an interpretation may be more or less complex depending on the complexity of the language of which it is an interpretation. Usually it contains at least a domain or universe of discourse and an assignment function (the so-called interpretation function). Because the domain may vary from interpretation to interpretation, we require in our approach, correspondingly, that we also replace the universal words by variables. Replacing the universal words (such as ‘thing’, ‘object’, ‘human being’, ‘number’, etc.) by variables reflects the alteration of domains in interpretations. This treatment of universal words has the same welcome result as varying the domain of interpretation and requiring a logically true sentence to be true under every interpretation and therefore also in every domain, including the empty one. This results in purely logical sentences (or formulas), such as (1a) and (2a) and similar numerical sentences (or formulas, respectively), being logically indeterminate, as they should be. This is true also, of course, of ‘There is at least one thing’ and of ‘There is nothing’, i.e.: (4a) x(x = x) (4b) xF(Fx › ™Fy) (5a) ™x(x = x) (5b) ™xF(Fx › ™Fy) By contrast, according to Quine’s criterion of logical truth, (4a) and (4b) are logically true—as are our introductory examples (1a) and (1b); and (5a) and (5b) are logically false—as are our introductory examples (2a) and (2b). Nevertheless, I have not used (4a) and (5a), or (4b) and (5b) respectively, for my attack on Quine’s criterion of logical truth for the following reason: In the standard systems of first order predicate logic with identity the formula (4a) is a theorem. Thus, in the corresponding semantics of first order predicate logic with identity it must be required of an interpretation that its domain be non-empty. Since people familiar with modern predicate logic are accustomed to this requirement, they do not find it shocking that (4a) is logically true and (5a) is logically false. Also to those “socialized” with standard predicate logic, however, it will come

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as a surprise that also all other purely logical formulas such as (1a) and (2a) turn out to be logically determinate according to Quine’s criterion. If we wanted to parallel within our approach the requirement of standard semantics for first order predicate logic that only non-empty domains are considered for its interpretations, we would just have to require that the universal words substituted for variables consist solely of non-empty expressions. 3. Logical form—skeleton or mould? In the preceding paragraph I have used a certain view of logical form. This view of logical form, however, is not the only one and—what is more important—it is not the one which is common today. It could be called the “mould view” of logical form, as opposed to the “skeleton view”. These two different views of logical form have always haunted and still haunt the minds of people, including those of logicians. I will now try to explain this distinction. In doing so, I will extend the concept of logical form in such a way that it applies both to sentences and to arguments. According to the skeleton view, the pure (or logical) form of a sentence or an argument (or of its symbolic representation in a formal language) is that which remains when we carve out its material or content, i.e. all of its non-logical parts. A logical form, on this view, is the skeleton which remains after a sentence or an argument is deprived of its flesh and blood. This is the skeleton view of logical form. The idea behind the mould view of logical form goes like this: A logical form of a sentence or argument (or of its symbolic representation in a formal language) is something which suits the sentence or argument in question so that the sentence or argument in question fits it. A logical form in this sense is like a mould in which a sentence or argument can be embedded or cast. This is the mould view of logical form. Is there a substantial difference between these two intuitions about logical form? Does it matter for logic in terms of results whether we apply the skeleton view or the mould view of logical form? In what follows I will try to show that the difference is substantial. Before this can be done, however, I have to define some concepts in a more precise form. X is a pure skeleton sentence form or a pure skeleton argument form, respectively, iff there is a sentence or an argument (or a symbolic representation of such a sentence or argument) Y, and X results from Y by replacing all

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of its simple non-logical expressions (in the case of formulas: symbols) by appropriate variables, whereby the replacement need not be performed necessarily in a uniform way. X is a pure mould sentence form or a pure mould argument form, respectively, iff there is a sentence or an argument Y, respectively, that is not purely logical (i.e., it contains at least one non-logical expression or symbol), and X results from Y by replacing all of its simple non-logical expressions or symbols (including universal words) by appropriate variables, not necessarily in a uniform way. In these definitions we presuppose, of course, that the language we are considering is rich enough to supply us with a name for every individual of the domain and with a predicate for every kind of individual and for every relation among individuals. Note that the definition of a pure mould form differs from the definition of a pure skeleton form only with respect to the phrase which was inserted in the definiens of the definition of a pure mould form and printed in italics, i.e., insofar as a mould form cannot whereas a skeleton form can be generated from a purely logical sentence or argument. The three following definitions are the same for pure skeleton forms and for pure mould forms. A substitution instance of a pure (skeleton or mould) form X is a sentence or an argument which results from X by uniformly replacing all of its free variables by appropriate expressions or constants (including logical predicates such as identity). A pure (mould or skeleton) form of a sentence or argument can then be understood as a pure (mould or skeleton) sentence or argument form of which the sentence or argument in question is a substitution instance, i.e.: Y is a pure (mould or skeleton) form of a sentence or argument X iff Y is a pure (mould or skeleton) sentence or argument form, respectively, and X is a substitution instance of Y. In this sense, a purely logical sentence or argument can have, of course, arbitrarily many mould and skeleton forms, but it can never be a mould form. Every purely logical sentence or argument, however, is necessarily a skeleton form whose own and only substitution instance is the sentence or argument itself. A pure (skeleton or mould) sentence form is universally valid iff all its substitution instances are true, and it is universally invalid iff all its substitution instances are false. A pure (skeleton or mould) argument form is formally valid iff there is no substitution instance of it with all its premises being true and its conclusion being false.

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At last, we come to the main difference between the two views: A sentence X is S(keleton)-logically true iff there is at least one pure skeleton sentence form Y such that Y is universally valid and X is a substitution instance of Y; and a sentence X is S(keleton)-logically false iff there is at least one pure skeleton sentence form Y such that Y is universally invalid and X is a substitution instance of Y, i.e., iff the negation of X is logically true; and a sentence X is S(keleton)-logically determinate iff X is S-logically true or S-logically false. An argument X is S(keleton)-valid iff there is at least one pure skeleton argument form Y such that Y is formally valid and X is a substitution instance of Y. A sentence X is M(ould)-logically true iff there is at least one pure mould sentence form Y such that Y is universally valid and X is a substitution instance of Y; and a sentence X is M(ould)-logically false iff there is at least one pure mould sentence form Y such that Y is universally invalid and X is a substitution instance of Y, i.e., iff the negation of X is logically true; and a sentence X is M(ould)-logically determinate iff X is M-logically true or M-logically false. An argument X is M(ould)-valid iff there is at least one pure mould argument form Y such that Y is formally valid and X is a substitution instance of Y. Now, if logicians speak of the logical form of a sentence or an argument they sometimes mean a skeleton form of it, and sometimes they mean a mould form of it. And if they speak of a sentence being logically true or of an argument being valid, they sometimes mean S-logical truth and S-validity and sometimes M-logical truth and M-validity. The substantial difference between the skeleton view and the mould view of logical form comes to light as soon as we consider purely logical sentences and arguments. For these, M-logical truth does not coincide with S-logical truth, and M-validity does not coincide with S-validity. Since a purely logical sentence or argument does not contain any non-logical expression or symbol, there is nothing in it which could be replaced by a variable; every purely logical sentence or argument is therefore automatically also a pure skeleton form, and, at the same time, it is also its own and only substitution instance. Thus, if a purely logical sentence is true, it is automatically S-logically true, and if false, it is automatically S-logically false; and if a purely logical argument has a false (and therefore S-logically false) premise or a true (and therefore S-logically true) conclusion, it will automatically be S-valid. The skeleton view of logical form therefore does not work in

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the case of purely logical sentences and arguments, since purely logical sentences can be logically indeterminate and purely logical arguments can be invalid even if they have a false premise or a true conclusion or both. If we take the attributes of logical truth, logical falsity, validity etc. to be formal, i.e., derived from attributes of pure sentence and argument forms, it cannot be a matter of skeleton forms, but only of mould forms: it depends on whether or not there is a mould form with appropriate properties of which the sentences and arguments in question are substitution instances. The following examples serve the purpose to explain what has been said. The examples in (6) are purely logical formulas which are M- and S-logically true (i.e. logically true according to the mould as well as to the skeleton view), those in (7) are M- and S-logically false (i.e. logically false according to the mould as well as to the skeleton view). Whereas the formulas in (8), however, are M-logically indeterminate, all of them are S-logically determinate (i.e. logically true or logically false according to the skeleton view): (6) purely logical sentences which are M- and S-logically true: x(x = x) o x(x = x), xy(x = y) o xy(x = y), x(x = x o x = x), x(y(y = x) o y(y = x)), xF(Fx o Fx), xF(Fx) › ™xF(Fx) (7) purely logical sentences which are M- and S-logically false: x(x = x) š ™x(x = x), ™(xy(x = y) o xy(x = y)), ™x(x = x o x = x), ™x(y(y = x) o y(y = x)), ™xF(Fx o Fx), xF(Fx) š ™xF(Fx) (8) purely logical sentences which are M-logically indeterminate, but S-logically determinate: x(x = x), ™x(x = x), xy(x = y), ™xy(x = y), xy™(x = y), ™xy™(x = y), xyF(Fx š ™Fy), ™xyF(Fx š ™Fy) Similarly for arguments. Under the skeleton view every purely logical argument with a false premise or a true conclusion (or both) turns out to be S-valid; they can be invalid, however under the mould view as the following examples illustrate:

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(9) a purely logical argument which is M-invalid even if its second premise is false: x(x = x) o xy™(x = y) ™x(x = x) ? ™xy™(x = y) (10) a purely logical argument which is M-invalid even if its conclusion is true: x(x = x) o xy™(x = y) xy™(x = y) ? x(x = x) (11) an M-invalid purely logical argument with a true premise and a true conclusion:   x(x = x) ? xy™(x = y) (12) an M-invalid purely logical argument with a false premise and a true conclusion:   ™x(x = x) ? x(x = x) The logical truth of a sentence is indeed a formal property of it as is the logical falsity of a sentence, i.e., it is derived from a property of a pure (or logical) form of which the sentence in question is a substitution instance. Similarly, the deductive correctness or validity of an argument is a formal property of it, i.e., it is derived from a property of a pure (or logical) form of which the argument in question is a substitution instance. The pure sentence or argument form in question, however, cannot be a skeleton form as our examples of purely logical sentences and arguments show each of which is a skeleton form which is its own and only substitution instance. It is nowadays much more common to use the concept of an interpretation instead of the concept of logical form in order to define logical properties and relations. So, e.g., a logically true sentence is usually defined in contemporary textbooks of logic as a sentence that is true under every interpretation. When we define the logical truth and the logical falsity of sentences or the validity and invalidity of arguments in terms of logical forms, however,

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it must be a mould form and not a skeleton form which we refer to in these definitions. The examples presented above make it clear that the logical truth and the logical falsity of a sentence and the validity of an argument do not depend on skeleton forms. They rather depend on whether or not there is a mould form with appropriate properties of which the sentence or argument in question is a substitution instance. This is the modest moral which can be drawn from this short story. It is quite clear, what kind of logic results from this proposal. It is a logic, whose logical truths are true under every interpretation in every domain, including the empty one; it is—in Quine’s term—an inclusive logic. What is less common: This kind of logic treats identity as an extra-logical notion requiring for identity an extra logical theory of its own. Whereas ‘x(x = x o x = x)’ is logically true in this framework, ‘x(x = x)’ and—due to the system being an inclusive logic—also ‘x(x = x o x = x)’ are not so.8 Postscript: When I wrote this paper and introduced the distinction between the skeleton and the mould views of logical form, I was not aware that Quine ever used the term ‘skeleton’ for the logical form of a sentence. Only after having finished this paper I came across this term in “Truth by Convention” (originally published in 1936, reprinted in The Ways of Paradox and Other Essays, Revised Edition, Cambridge MA: Harvard UP, 1976, 77–106; cf. 80 and 81), and in Mathematical Logic (originally published in 1940, Revised Edition, New York: Harper & Row, 1951, 28). I take this as confirmation ex post facto that in attributing the skeleton view of logical form to Quine I was not on the wrong track.

REFERENCES Bolzano, Bernard 1837: Wissenschaftslehre. Sulzbach: J. E. v. Seidel. Carnap, Rudolf LSL, 1937: The Logical Syntax of Language. London: Routledge & Kegan Paul (reprint with corrections 1964). — ESL, 1963: Einführung in die symbolische Logik mit besonderer Berücksichtigung ihrer Anwendungen, 3rd edition. Wien: Springer-Verlag. 8. I thank Robin Rollinger, Benjamin Schnieder, Moritz Schulz and Peter Simons for many valuable comments. For substantial improvements of the first two sections of the present paper I am very much indebted to Karel Lambert.

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Etchemendy, John 1983: “The Doctrine of Logic as Form”, Linguistics and Philosophy 6, 319–334. — 1990: The Concept of Logical Consequence. Cambridge, Mass., London: Harvard University Press. Quine, W. V. O. 1963: “Carnap and Logical Truth”. In: Paul Arthur Schilpp (ed.), The Library of Living Philosophers, Vol. XI: The Philosophy of Rudolf Carnap. La Salle, Illinois: Open Court; London: Cambridge University Press, 385–406. Tarski, Alfred 1936: “On the Concept of Logical Consequence”. Page numbers refer to the reprint in: John Corcoran (ed.), Logic, Semantics, Metamathematics. Papers from 1923 to 1938, 2nd edition, Indianapolis, Indiana: Hackett, 1983 (last reprint with corrections 2006). — 1986: “What Are Logical Notions?” (corrected version). History and Philosophy of Logic 7, 143–154. Williamson, Timothy 2000: “Existence and Contingency”. Proceedings of the Aristotelian Society 100, 321–343.

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Grazer Philosophische Studien 82 (2011), 91–127.

“IT FALLS SOMEWHAT SHORT OF LOGICAL PRECISION.” BOLZANO ON KANT’S DEFINITION OF ANALYTICITY Mark SIEBEL University of Oldenburg Summary Kant’s famous definition of analyticity states that a judgement is analytic if its subject contains its predicate. Bolzano objects that (i) Kant’s definiens permits an interpretation too wide, (ii) the definiens is too narrow, (iii) the definiendum is too limited, and (iv) the definition does not capture the proper essence of analyticity. Objections (i), (iii) and (iv) can be countered. Objection (ii) remains because, among other things, the Kantian definition has an eye only for an analysis of the subject within a judgement.

In a short manuscript titled “Zur Lebensbeschreibung”, Bolzano relates that he began to study Kant’s Kritik der reinen Vernunft when he was eighteen. Although he was immediately attracted by the distinction between analytic and synthetic judgements, as well as the one between judgements a priori and a posteriori, he could not accept Kant’s explanations of them.1 Bolzano’s quadripartite objection to Kant’s definition of analyticity can be found in the Wissenschaftslehre and in the Neuer Anti-Kant, a collection of Bolzano’s critical remarks on Kant which was put together by his pupil Franz Příhonský.2 Kant’s definition in the Introduction to the Kritik states, roughly, that a judgement is analytic if its predicate is contained in its subject. Bolzano demurs that (i) Kant’s definiens permits an interpretation too wide, (ii) the definiens is too narrow, (iii) the definiendum is too limited, and (iv) the definition does not capture the proper essence of analyticity. 1. See Bernard Bolzano-Gesamtausgabe 2 A 12/1, ed. by Jan Berg. Frommann und Holzboog: Stuttgart–Bad Canstatt 1977, 67f. Wolfgang Künne (2006, 184) preludes his “Analyticity and Logical Truth” with a citation of this passage. 2. I refer to the Wissenschaftslehre by ‘WL’ plus number of volume, paragraph, and (where applicable) page number(s) following a colon; to the Neuer Anti-Kant (Příhonský 1850) by ‘NAK ’; and to the Kritik der reinen Vernunft (Kant 1787) by ‘KrV ’. ‘AA’ abbreviates the Akademie-Ausgabe of Kant’s writings (Kant 1902ff.).

In section 1, I shall introduce Kant’s account of analytic judgements, while sections 2–5 deal with Bolzano’s four objections in the given order. Even though my general philosophical sympathies lie more with Bolzano than with Kant, I must acknowledge that Bolzano’s criticisms are often a bit hasty. Their significance primarily consists in the fact that, by expanding on them, one encounters serious problems every now and then. In other words, Bolzano sometimes focused on the right target even if his own arrows missed it. The volume at hand is devoted to Wolfgang Künne, teacher, friend and mentor. Without him, my philosophical life would have taken place in a possible world not philosophically accessible from the actual one. And even if it is accessible, I do not want to know what this world looks like. My contribution benefitted especially from two of Wolfgang Künne’s papers: “Constituents of Concepts: Bolzano vs. Frege” (2001) and “Analyticity and Logical Truth: From Bolzano to Quine” (2006). Many of the following considerations rest on the insights found in these papers. Moreover, I extracted a crucial methodological maxim from the latter: Unlike ‘true’ and ‘necessary’, the word ‘analytic’ is a philosopher’s term of art. Memories of doctrines associated with this term (be they Kantian, Fregean, Carnapian, or whatever) should not be mistaken for pre-theoretical ‘intuitions’ concerning analyticity. There simply are no such intuitions one could appeal to. (Künne 2006, 219)

In order not to get lost in fruitless discussions on what analyticity “really” or “truly” or “actually” is, I shall follow the maxim: Read Bolzano’s objections as inner-Kantian objections! For example, Bolzano’s second demur should not be understood as saying that Kant’s definiens is too narrow because there are judgements which do not satisfy the definiens but are analytic in some external, pre-theoretical or whatever, sense. The demur rather is that the definiens is too narrow from Kant’s perspective because some judgements do not satisfy it although Kant would take them to be analytic. 1. Kant’s definition of analyticity Kant’s famous definition of analyticity in terms of conceptual containment reads as follows:3 3. Hintikka (1973, 125) and Morscher (2006, 251) point out that Kant’s account is closely similar to Thomas Aquinas’ characterisation of “self-evidence” in Summa Theologica I, 2, 1.

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In all judgements in which the relation of a subject to the predicate is thought (if I consider only affirmative judgements, since the application to negative ones is easy) this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in it; or B lies entirely outside the concept A […]. In the first case I call the judgement analytic, in the second synthetic. (KrV, B 10)

Kant’s best-known example is ‘All bodies are extended’, but he could as well have offered ‘All drakes are male’. In both cases, the predicate(-concept) seems to be contained in the subject(-concept). But what does Kant mean by ‘judgement’, ‘subject(-concept)’ and ‘predicate(-concept)’? Firstly, even though Kant quite often talks about analytic and synthetic “sentences”, he cannot allude to linguistic expressions when using the terms ‘subject’ and ‘predicate’. Elsewise, ‘All bodies are extended’ would not be analytic because the letter combination ‘extended’ is patently not contained in the letter combination ‘bodies’. Secondly, Kant does not mean subjective mental representations, i.e., what immediately comes to the mind of a thinker when she imagines the given objects, or what she regularly associates with the given expressions. Otherwise, ‘Every bird can fly’ would be analytic for many people because their prototype of a bird includes the ability to fly. I assume (cum Bolzano) that Kantian “judgements” and “sentences” strongly resemble Bolzanian “sentences in themselves”, Fregean “thoughts” or, in today’s terminology, “propositions”. They are neither mental nor linguistic entities, but the contents of such things; and the same holds for what Kant refers to by “subject(-concept)” and “predicate(-concept)”. Thus, the sentence ‘All drakes are male’ expresses an analytic proposition because the subject-notion within this proposition, the concept of a drake, contains the predicate-notion, the concept of maleness. In other words, drakes are defined by being male (as well as by being ducks); maleness is part of the definition of drakes.4 I shall freely vacillate between ‘judgement’, ‘proposition’ and ‘statement’; and I shall use single quotation marks to refer to words and sentences as well as concepts and propositions. The initial sentence of the above-quoted passage points out that Kant’s definition is restricted to (a) affirmative judgements of (b) subject-predicate Compare also Locke’s “trifling propositions” in his Essay (1690, IV.VIII) and Leibniz’s “frivolous sentences”, including “identical” and “semi-identical sentences”, in the Nouveaux essais (1705, IV.VIII). 4. Cf. KrV, B 746: “what I actually think in my concept of a triangle […] is nothing further than its mere definition”; and Marc-Wogau 1951, 147.

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form. In short, it is restricted to judgements in which a property is assigned to some object(s). Because of (a), Kant’s characterisation applies to statements of the form ‘All A are B’ and, apparently, ‘Some A are B’ and ‘The A is B’, but not to ‘No A is B’, ‘Some A are not B’ and ‘The A is not B’. On account of (b), the characterisation is hardly applicable to ‘If all humans are mortal and Socrates is a human, then Socrates is mortal’ or ‘It is raining’. Including these constraints on the intended range of application, Kant’s definition reads as follows: (KA1) An affirmative subject-predicate proposition x is analytic =df. the predicate-concept of x is contained in its subject-concept. As to restriction (b), van Cleve (1999, 19) adds that Kant’s definition “does not apply to existential judgments (such as ‘there are lions’), which (if we accept the dictum that existence is not a predicate) are not of subjectpredicate form”. However, there is reason to think that Kant complies with Bolzano’s understanding of such statements, which anticipates the Fregean view. According to this understanding, they are of subject-predicate form, albeit the subject is a higher-order notion representing a concept and the predicate is not the notion of existence but the one of instantiation.5 Thus, ‘There are lions’ translates into ‘The concept of a lion is instantiated’. Since the notion of instantiation is not contained in the notion ‘concept of a lion’, such a judgement is synthetic. This conforms to Kant’s position that “every existential sentence is synthetic” (KrV, B 626; cf. Proops 2005, 592f.). Speaking of existence, it should be emphasised that Kant’s account of analyticity would be jeopardised if his reading of universal affirmative statements agreed with the one of Bolzano and Aristotle. The latter assume that ‘All A are B’ is true only if there exists at least one A. But then ‘All drakes are male’ would fail to be analytic. For while analytic judgements are a priori in Kant’s view (cf. KrV, B 9–12), ‘All drakes are male’ would entail the existence of drakes and thus could not be shown to be true without recourse to experience. However, unlike Bolzano and Aristotle, Kant does not take ‘All A are B’ to have existential import. In the section 5. Cf. Der einzig mögliche Beweisgrund zu einer Demonstration des Daseins Gottes, AA 2, 72f.; KrV, B 626f.; WL II, § 137; and Frege 1884, § 53. Bennett (1974, § 72) refers to the abovementioned account as “the Kant-Frege view” and Wiggins (1994) as “the Kant-Frege-Russell view”. Rosefeldt (2008, 2010) argues that Kant is rather a Meinongian because he takes existence to be a property some objects fail to have.

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of the Kritik in which he presents his animadversion on the ontological proof of God’s existence, we are told: Every sentence of geometry, e.g., ‘a triangle has three angles’, is absolutely necessary […]. The unconditioned necessity of judgements, however, is not an absolute necessity of things. For the absolute necessity of the judgement is only a conditioned necessity of the thing, or of the predicate in the judgement. The above sentence does not say that three angles are absolutely necessary, but rather that under the condition that a triangle exists (is given), three angles also exist (in it) necessarily. (KrV, B 621f.)

According to this passage, ‘All drakes are male’ would be true even if there was no drake, so that mere conceptual analysis suffices to recognise its truth.6 More generally, if statements of the form ‘All A are B’ do not imply the existence of an A, there is no longer any obstacle to describing them as analytic in case their subject contains the predicate. Hanna (2001, sect. 3.1.1) ignores Kant’s confinement to affirmative judgements and, in return, augments his definition with the stipulation that analytic judgements are necessary. Kant in fact assumes that analytic judgements are a priori and hence necessarily true (cf. KrV, B 3f., 9–12). But I see no reason to assume that this is part of his definition of analytic judgements; it is rather a corollary. Similarly, I follow de Jong (1995, 619) and Proops (2005, 603f.) in their interpretation of Kant’s reference to the principle of contradiction in a later passage of the Kritik: “if the judgment is analytic, whether it be negative or affirmative, its truth must always be able to be cognised sufficiently in accordance with the principle of contradiction” (B 190). This remark is not meant to offer a defining characteristic of analytic statements. Its point is rather an epistemological one: in the case of analytic statements the principle of contradiction provides an effectual basis for proving that they are true. I have not incorporated into (KA1) the bracketed addition in Kant’s formulation “the predicate B belongs to the subject A as something that is (covertly) contained in it” (KrV, B 10; my emph.). Furthermore, I have omitted Kant’s suggestion to call analytic judgements judgements of clarification and synthetic ones judgements of amplification (B 11). Whereas on (KA1) ‘All male ducks are male’ expresses an analytic proposition just as much as ‘All drakes are male’, this is not so obvious against the background of Kant’s reference to covertness and clarification. After all, the wording 6. Cf. also KrV, B 314. This undermines one of Bolzano’s objections to Kant’s view on the origin of analytic cognition (see WL III, § 305: 178).

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‘All male ducks are male’ does not conceal that the predicate-concept is part of the subject-concept; and the triviality of ‘All male ducks are male’ casts its clarificatory power into doubt. For several reasons, however, one should take the reference to covertness and clarification with a pinch of salt. Regarding covertness, firstly, one should bear in mind that Kant bracketed the word ‘covertly’, possibly suggesting thereby that these attributes are possessed only by a subclass of analytic judgements. Secondly, if these features were considered necessary for analyticity, one would run the risk of ending up with a subjectively relativised version of the analytic-synthetic distinction. Consider a person who immediately and clearly recognises the concept of extension within the concept of a body. For her, the predicate of ‘All bodies are extended’ is not covertly but openly contained in the subject. Does this mean that this proposition is not analytic for such a person, although it is analytic for the man on the street? Concerning clarification, the first reason for taking it with a grain of salt is that Kant uses the fairly tentative formulation that one could call judgements of the analytic ilk judgements of clarification. Secondly, he continues in the same sentence by explaining this proposal in terms of nothing other than the containment idea. Thirdly, later on in the Kritik Kant offers as an example of a negative analytic judgement ‘No unlearned person is learned’ (B 192). This suggests that, despite the triviality of the equivalent ‘Every learned person is learned’, as well as the triviality of ‘All male ducks are male’, he would consider the voiced judgements analytic. Finally, if one still wants to insist on the general clarificatory power of analytic statements, note that even ‘All male ducks are male’ provides an elucidation insofar as it makes clear that the function of the concept ‘male’ in ‘male duck’ differs from the one of ‘putative’ in ‘putative duck’. In the former but not in the latter compound, the constituent administered by the adjective serves as a conjunctive part: a male duck is a duck which is male, but it makes no sense to say that a putative duck is a duck which is putative. But what is to be done with cases where subject- and predicate-expression are identical? At first glance, Kant’s examples of analyticities encompass ‘Man is man’ (‘Der Mensch ist ein Mensch’), which is mentioned in the Jäsche-Logik (AA 9, 111), and ‘a = a’ (‘Every whole is equal to itself ’), on which he touches in the Kritik (B 16f.). In order to integrate these judgements, Kant’s containment definition must be read in such a way that the predicate-concept can also be an improper part of the subject-concept, that is, be identical with it. However, as will be discussed further in section 3,

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it is not clear that Kant is, and should be, serious about the analyticity of ‘a = a’. For if the concept of equality is part of the predicate, the predicate exceeds the subject. As to ‘Man is man’, some adepts have reservations about the authenticity of the Jäsche-Logik.7 The analyticity of this statement is thus open to question. But note also that denying its analyticity has a serious consequence. After all, if Kant does not want to call such propositions synthetic either—and why should he?—, he has to narrow down the scope of his analytic-synthetic distinction further. Then it does not apply to all affirmative subject-predicate propositions because it does not apply to ‘Man is man’ and the like. Whatever Kant’s position on such statements in the Kritik might be, he is quite explicit in the Preisschrift über die Fortschritte der Metaphysik, which he began around 1793: Judgements are analytic, we may say, if their predicate merely presents clearly (explicite) what was thought, albeit obscurely (implicite), in the concept of the subject; e.g., any body is extended. If we wanted to call such judgements identical, we should merely cause confusion; for judgements of that sort contribute nothing to the clarity of the concept which all judging must yet aim at, and are therefore called empty; e.g., any body is a bodily (or in other words material) entity. Analytic judgements are indeed founded upon identity, and can be resolved into it, but they are not identical, for they need to be dissected and thereby serve to elucidate the concept; whereas by identical judgements, on the other hand, idem per idem, nothing whatever would be elucidated. (AA 20, 322)

Proops (2005, 602) takes passages like this one to show that Kant revised his conception of analyticity by coming to draw the analytic-synthetic division only within the class of knowledge-advancing judgements. In this spirit, we read in Gotthilf Busolt’s notes of Kant’s lectures on logic, which are dated to 1788–90: “Propositions which explain idem per idem expand knowledge neither analytically nor synthetically. They are tautological propositions. By them I have neither an increase in distinctness nor a growth in cognition.” (AA 24, 667) Perhaps, the Kant who seems to speak here would even dispute that ‘All male ducks are male’ is analytic, thereby replacing definition (KA1) with something to the effect that a knowledge-advancing affirmative subject-predicate judgement is analytic if its predicate is covertly contained in its subject. 7. See Hinske 2000, 90f.; Boswell 1988 and 1991. Stuhlmann-Laeisz (1976) does nowhere allow for the Jäsche-Logik in his standard work Kants Logik.

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However, I shall concentrate on (KA1) as the characterisation which is most strongly suggested by the Introduction to the Kritik. It does not bear the risk of a subjectively relativised variant of the analytic-synthetic dichotomy because it does not mention covertness, clarification or anything similar; and it is the characterisation towards which Bolzano’s objections are directed. Incidentally, these objections are also applicable to a Kantian definition of analyticity which is restricted to knowledgeadvancing judgements. (KA1) tells us only under which conditions an affirmative subjectpredicate judgement is analytic since, as Kant avers, “the application to negative ones is easy” (KrV, B 10). In that case, how about Kant’s own example ‘No unlearned person is learned’ (B 192)? Why is it analytic? Kant’s answer may be found in the section “Analytik der Grundsätze”: In the analytic judgement I remain with the given concept in order to discern something about it. If it is an affirmative judgement, I only ascribe to this concept that which is already thought in it; if it is a negative judgement, I only exclude the opposite of the concept from it. (KrV, B 193; cf. Metaphysik Mrongovius, AA 29, 789)

In slightly improved words, ‘No unlearned person is learned’ excludes the property of being learned from unlearned persons. Since the predicateconcept ‘learned’ is the opposite of a part of the subject-concept ‘unlearned person’, the judgement is analytic. But what exactly does Kant mean by “the opposite”? Marc-Wogau (1951, 145) and Proops (2005, 598) use the formulation that the predicate contradicts (a part of ) the subject. Contradiction, however, admits of too broad an interpretation because one can also acknowledge it in case of the following synthetic proposition: (1) No triangle has an angular sum different from two right angles. In a later section of the Kritik (B 744f.), Kant outlines the corresponding Euclidean proof (Elements, prop. 32) in order to show that (2) Every triangle has the same angular sum as two right angles. is a synthetic truth a priori (cf. also WL III, § 305: 185f.). According to the official definition, a triangle is a three-sided polygon. Since this

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definition does not mention the sum of the angles, the concept of having the same angular sum as two right angles is not contained in the concept of a triangle. Nevertheless, the sum of the angles in a triangle necessarily coincides with two right angles. Hence, the predicate-notion of (1)—‘has an angular sum different from two right angles’—contradicts the subjectnotion—‘triangles’—insofar as nothing can fall under both notions. But then ‘No triangle has an angular sum different from two right angles’ would be analytic according to the proposal in question, which does not coincide with Kant’s perception that its equivalent ‘Every triangle has the same angular sum as two right angles’ is synthetic.8 To rule out that (1) is analytic, ‘contradiction’ must be understood in a more direct or, in other words, a more explicit or purely logical way. Proops (2005, 591) heads in the right direction when explaining that a negative judgement is analytic if the predicate is the negation of one of the subject’s constituents (cf. also Marc-Wogau 1951, 145). To be sure, ‘negation’ must be understood in a broad sense here. It is natural to treat ‘unlearned’ as the negation of ‘learned’, such that ‘No learned person is unlearned’ is analytic because the predicate is the negation of a part of the subject. However, Kant’s example was ‘No unlearned person is learned’, entailing that we must also regard ‘learned’ as being the negation of ‘unlearned’. Let us define that a notion negates another notion if and only if one of them is composed of the other and one of the prefixes expressed by ‘not’, ‘un-’ or the like. Then ‘No unlearned person is learned’ is analytic because ‘learned’ negates ‘unlearned’ (even though the former might not be the negation of the latter in a stricter sense). And ‘No event is without a cause’ is synthetic because ‘without a cause’ does not negate ‘event’ (even though the former contradicts the latter). Thus Kant’s definition of the analyticity of subject-predicate propositions in general, i.e. affirmative and negative ones, reads (cf. Proops 2005, 598): (KA2) A subject-predicate proposition x is analytic =df. either x is affirmative and its predicate-concept is contained in its subject-concept, or x is negative and its predicate-concept negates a constituent of its subject-concept. This could be called the containment-or-negation conception of analyticity. 8. Arguments of the same ilk can be carried out with ‘No event is without a cause’, ‘No straight line between two points is the longest’ (cf. KrV, B 13, 16) and ‘No object which is red all-over is green all-over’.

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If Kant allows for analyticities such as ‘No man is not a man’, ‘constituent’ must be read as meaning a proper or improper part. Before I move on to Bolzano’s four objections, it should be mentioned that he also praises Kant’s division between the analytic and the synthetic. Firstly, he acclaims that it “is one of the most felicitous and influential discoveries made in the field of philosophical research” (NAK, 34). “[E]ven if it is true that this distinction was mentioned before at times, nevertheless it was never properly pinned down and fruitfully applied. The merit of having been the first to have done that indisputably belongs to Kant” (WL II, § 148: 87). Secondly, although Bolzano wants to replace Kant’s conception of analyticity with his own, in some places he explicitly makes use of the Kantian conception (cf. Künne 2006, 235; de Jong 2001, 334). Among other things, he argues that, by allowing for synthetic judgements a priori, Kant embraces the fact “that there are properties possessed by an object, and necessarily possessed by it according to the concept we form of it, without being thought in this concept as constituents” (WL I, § 65: 288; cf. § 120; AA 8, 229f., 241f.; de Jong 1995, 632–638). This holds for Kant’s example: (2) Every triangle has the same angular sum as two right angles. Although triangles necessarily possess the property assigned to them by this judgement, it is not part of the definition of a triangle, entailing that the concept of having the same angular sum as two right angles is not contained in the concept of a triangle. Bolzano himself instances propositions quite close to (2) (cf. WL I, § 64: 271, 274): In every square the side is related to its diagonal as 1 : 2. Equilateral triangles are equiangular. In addition, as Morscher (2006) strongly emphasised, we must not overlook that Bolzano is far from being hostile to the synthetic a priori even when it comes to his own understanding of these terms. In concert with Kant, he offers (2) as an exemplar (cf. WL IV, § 447: 116), and he could as well have mentioned the last two examples.9 9. Cf. Frege (1884, § 89). I assume that Kant, Bolzano and Frege agree in taking some arithmetical and geometrical truths to be analytic, e.g., ‘Prime numbers are numbers’ and ‘Triangles are polygons’.

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The praise for Kant notwithstanding, Bolzano is dissatisfied with Kant’s explication of analyticity because it “fall[s] somewhat short of logical precision” (WL II, § 148: 87). The following four sections will expand on Bolzano’s discontent. 2. The definiens permits an interpretation too wide In “Two Dogmas of Empiricism” Quine criticised Kant’s definition by stating that “it appeals to a notion of containment which is left at a metaphorical level” (1951, 21). He does not hold forth about this issue, but there could be something at the back of his mind which is close to Bolzano’s much more precise plea: If it is said […] that in analytic judgements the predicate is contained in the subject (in a concealed manner), or does not lie outside of it or already occurs as a component of it; […] these are in part merely figurative forms of expression that do not analyse the concept to be explained, in part expressions that admit of too wide an interpretation. For everything that has been said here can also be said of propositions no one would take for analytic, e.g., The father of Alexander, King of Macedon, was King of Macedon; A triangle similar to an isosceles triangle is itself isosceles […].” (WL II, § 148: 87f.; cf. NAK, 34f.)

Bolzano does not bluntly criticise Kant’s characterisation for being wrong, but for being too unspecific because Kant’s talk of containment could be understood in such a way that synthetic propositions had to be counted among the analytic ones. Here is Bolzano’s first paradigm, supplemented by two further examples: (3) The father of Alexander, King of Macedon, was King of Macedon. (4) Every son of a bachelor is a bachelor. (5) No putative bachelor is married. The linguistic meaning of ‘King of Macedon’ is enclosed in the meaning of ‘father of Alexander, King of Macedon’. Similarly, it is not possible to know what a son of a bachelor is without knowing what a bachelor is. There is thus a sense of ‘contained’ according to which (3) and (4) satisfy the Kantian definition because their predicate-concepts are contained in their subject-concepts. Furthermore, since the subject-notion of (5), i.e. ‘putative bachelor’, includes the notion ‘bachelor’ and therefore ‘unmar-

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ried’ on this interpretation of containment, the predicate-notion ‘married’ negates one of the subject-notion’s constituents. It thus appears that (5) is analytic according to the Kantian containment-or-negation conception. But no one would classify these judgements as analytic (cf. de Jong 2001, 334f.; Künne 2001, 272f.; 2006, 213; Lapointe 2007, 229f.). Kant in particular would deny that they are analytic because he considers analyticities to be a priori and hence necessary, while (3) is a contingent truth and (4) and (5) are contingent falsities (cf. KrV, B 3f., 9–12). In § 65 of the Wissenschaftslehre, Bolzano emphasises that logicians might not associate the same meaning with the phrase that there are complex notions. He explains his own conception by saying that “everything which must necessarily be thought in order to really think a given notion is a constituent of it” (WL I, § 65: 282f.; my emph.). When talking about analyticity, Kant frequently makes use of similar formulations, e.g., “in the case of an analytic proposition the question is only whether I actually think the predicate in the presentation of the subject” (KrV, B 205; my emph.). In the light of the traditional distinctions between clear and opaque and between distinct and obscure ideas, such characterisations in terms of what people have in mind when they grasp a notion are delicate. Bolzano explicitly admits in § 56 of his Wissenschaftslehre that acts of thinking and their conceptual contents could differ with respect to their constituents. A subjective act of thinking might lack parts of the corresponding objective concept, and it might contain parts which are not contained in the latter (WL I, § 56: 246; cf. § 64: 273). No matter how Bolzano’s sense of ‘containment’ or ‘constituent’ is to be spelled out, he is surely justified in blaming Kant for using unclear formulations. But he overlooks that the theory behind these formulations resists his examples. When noting in § 65 of the Wissenschaftslehre that logicians conceive of complex notions in disparate ways, Bolzano refers to the notion ‘man who has no integrity’. Many logicians, so Bolzano observes, “say that the concept of integrity is not connected with the concept man in this notion, but is rather separated from it, and therefore must not be regarded as a constituent of the whole notion” (WL I, 282). Had he wondered what kind of account this denial is based on, he might have hit upon the so-called “traditional theory of concepts”. De Jong (1995) and Lanier Anderson (2004, 2005) called attention to this theory which is in the background of Kant’s definition of analyticity. Within this theory we do not only find the relational expression ‘is contained in’ but also ‘is contained under’ (see Friedman 1992, 67). A concept which is contained in a

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concept x is taken to be part of x’s intension or content; and if something is contained under a concept x, then it is part of x’s extension or sphere. From the perspective of modern logic, one can hardly resist the temptation to read ‘is contained under’ as meaning falls under. It would thus denote what Frege called subsumption, i.e., a relation usually holding between objects and concepts.10 In this sense, Donald Duck would be contained under the concept of a drake because he falls under, or is subsumed under, this concept. Kant himself makes use of this sense at some places (see, e.g., Wiener Logik, AA 24, 910f., 925). When Bolzano criticises “the canon that content and extension stand in an inverse relationship” in § 120 of the Wissenschaftslehre, he assumes this reading; and Künne (2001, 268f.) follows him. But a closer look reveals that containment-under in Kant’s primary use is not a relation between objects and concepts but solely between concepts. Here are two representative passages (see also KrV, B 94; Logik Pölitz, AA 24, 568; Wiener Logik, AA 24, 910): Now one must […] think of every concept as a representation that is contained in an infinite set of different possible representations (as their common mark), which thus contains these under itself […]. (KrV, B 39f.; my emph.) Let us consider a series of several concepts subordinated to each other, e.g. iron, metal, body, substance, entity […]. The lower concept is not contained in the higher, for it contains more in itself than does the higher; but it is contained under the latter […]. (Jäsche-Logik, AA 9, 97f.; my emph.)

The (higher) concept of metal is contained in the (lower) concept of iron. Since ‘iron’ includes further constituents besides ‘metal’, ‘iron’ is not contained in ‘metal’; but the former is contained under the latter. In this sense, it is not Donald who is contained under the concept of a drake but, say, the concept of a clumsy drake. Note that Kant talks about subordination when a concept is contained under another concept, thereby using the term Frege contrasts with ‘subsumption’. And note also that he calls a concept a mark (Merkmal) of another concept when the former is contained in the latter. Interestingly enough, there seem to be close similarities between Kant’s ‘is contained in’ and Frege’s ‘is a mark of ’; and the same might hold for Kant’s ‘is contained under’ and Frege’s ‘is subordinated to’. 10. Künne (2001, 274) stresses that there are some places where Frege, contrary to his official definition in “Funktion und Begriff” (1891), does not mean by ‘concept’ the reference of a predicate (a function whose arguments are truth-values) but its sense (a part of a thought).

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The key for the answer to Bolzano’s challenge is that, in the traditional theory of concepts, containment-in is the inverse of containment-under:11 The concept x is contained in the concept y  y is contained under x. For example, ‘metal’ is contained in ‘iron’, entailing that ‘iron’ is contained under ‘metal’. Now consider proposition (4), ‘Every son of a bachelor is a bachelor’. Bolzano is right in pointing out that there is a weak sense of ‘contained in’ on which the notion ‘bachelor’ is contained in the notion ‘son of a bachelor’. But the Kantian sense, according to which containment-in is the inverse of containment-under, appears to be stronger. It thus might introduce further restrictions to the effect that ‘son of a bachelor’ is not contained under ‘bachelor’, and hence ‘bachelor’ not contained in ‘son of a bachelor’, so that (4) would not be analytic on the proper understanding of Kant’s definition. In this spirit, I assume that Kantian containment-in coincides with Bolzanian containment-in plus an extra: x is contained in y in the strong sense (that is, y is contained under x) =df. x is contained in y in the weak sense & … The crucial question then is: what does this extra consist in which turns weak containment-in into strong containment-in and thus the inverse of containment-under? Kant’s reference to the series ‘iron’, ‘metal’, ‘body’, ‘substance’, ‘entity’ suggests as a minimal constraint for a concept y being contained under a concept x that everything represented by y is also represented by x. For example, ‘iron’ would not be contained under ‘metal’ if there were pieces of iron which are not pieces of metal. According to what may be called the extensional interpretation of the sought-after extra, it thus demands that the extension of y is a (proper or improper) subset of the extension of x: There is nothing falling under y without falling under x. Bell (1982, 458) and Wiggins (1998, 142) suggest to interpret Fregean ‘marks’ in this way. Prima facie, Hanna (2001, 127–141) reads Kant in the extensional manner when claiming that y is contained under x if the 11. Cf. de Jong 1995, 627; and Lanier Anderson 2004, 507; 2005, 27. The left-to-right half of this equivalence was brought forward by Kant in the above-quoted passage from the Kritik (B 39f.).

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comprehension of y is part of the comprehension of x. However, Hanna takes a Kantian comprehension to include not only the actual objects falling under the concept but also possible ones. He thereby subscribes to the modal conception to be discussed in a moment. Quite obviously, the extensional reading does not take us very far. It has the benefit of excluding (4) and (5) from the analytic realm. Since there are sons of a bachelor who are not themselves bachelors, ‘son of a bachelor’ is not contained under ‘bachelor’, and hence ‘bachelor’ is not contained in ‘son of a bachelor’. Furthermore, on this conception of containmentunder, ‘putative bachelor’ is not contained under ‘unmarried’, and thus does not include the latter, because some putative bachelors are married. However, the extensional reading does not filter out Bolzano’s example (3), ‘The father of Alexander, King of Macedon, was King of Macedon’. For the object represented by the subject-notion, i.e. Philip II, falls under the predicate-notion, i.e. was King of Macedon. More generally, subject and predicate already satisfy the extra condition at hand when the judgement is true. This extra is thus suited only for excluding false synthetic judgements. Kant’s definition of analyticity would still be too wide if we added that the predicate represents the objects falling under the subject because there would remain synthetic truths still satisfying the definiens. Next there is the modal reading of our key notion, stating that a concept is contained under another concept only if the extension of the former must be a part of the extension of the latter: Necessarily, there is nothing falling under y without falling under x. There are various places in Frege’s writings suggesting that he had something on these lines in mind when using the term ‘marks’. Künne (2001, 272f.; 2006, 213) coined the name ‘Port Royal Constraint’ for the given condition, and he supposes that Kant’s characterisation of analytic judgements includes it. Unfortunately, the modal reading does not take us far enough either because the given constraint is met by every necessary truth. Since it is not necessary that Alexander’s father was King of Macedon, the concept ‘father of Alexander, King of Macedon’ would not be contained under, and thus would not include, the concept ‘King of Macedon’. Consequently, we need no longer accept the corresponding judgement (3) as analytic. The following proposition, however, cannot be ruled out:

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(6) Every square of a number greater than 1 is greater than 1. The predicate-concept is contained in the subject-concept in Bolzano’s broad sense. Furthermore, (6) is a mathematical and hence a necessary truth: nothing can fall under ‘square of a number greater than 1’ without falling under ‘greater than 1’. But this means that (6) would be analytic because the predicate-notion ‘greater than 1’ was contained in the subjectnotion ‘square of a number greater than 1’ even according to the strong sense given by the modal conception of the sought-after extra. Frege would definitely embrace the outcome that (6) is an analyticity, but remember that Kant cannot approve of it because he regards such arithmetical truths as synthetic. How to conceive of the crucial extra if not even the modal variant comes to grips with all examples? Interestingly, Bolzano himself provides the essential clue for the proper reading of Kantian containment-in. Subsequent to his objection that Kant’s definiens admits of too wide an interpretation, we find the following idea for improvement: This unfortunate state of affairs could be avoided if […] one made use of the expression that in analytic judgements the predicate is one of the essential parts of the subject or (which comes to the same thing) constitutes one of its essential marks, understanding these to be constitutive marks, i.e. such as are present in the concept of the subject. (WL II, § 148: 88; cf. NAK, 35)

In an earlier passage of the Wissenschaftslehre the term ‘essential mark’ is explained in a bit more detail: “many logicians distinguish between essential or constitutive and inessential or derivative marks; [that is] between properties of an object which are thought as constituents in its concept and others where this is not the case” (WL I, § 65: 290f.). Like Kant and Frege, Bolzano uses the term ‘(essential) marks’ both for particular properties and concepts.12 If we apply it to concepts, the idea is that ‘bachelor’ is contained in ‘blonde bachelor’ as an essential mark because the former is not only a constituent of the latter in the weak sense but, in addition, represents one of the defining properties of the objects given by ‘blonde bachelor’. In contrast, ‘bachelor’ is neither an essential mark of ‘son of a bachelor’ nor of ‘putative bachelor’. For even though both notions contain ‘bachelor’ in the Bolzanian sense, its function within these notions is not to determine their extension by specifying properties 12. As for Frege, cf. the sentences cited by Künne (2001, 274f.); as for Kant, cf. the Handschriftlicher Nachlaß zur Logik, AA 16, 297f.

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of the objects falling under ‘son of a bachelor’ or ‘putative bachelor’ (cf. Frege 1893, xiv, 3, 150). Frege (1903, 271) also called such extensiondetermining constituents logical parts. And Kant, in the Handschriftlicher Nachlaß zur Logik, makes comments to the effect that marks are partial notions constituting a ground of the recognition (Erkenntnisgrund) of the corresponding objects (cf. AA 16, 297f.). In accordance with the aforementioned interpretation, this could mean that, by detecting the specified properties in an object, we have a sufficient reason for subsuming it under the notion composed of the marks. So, let us assume that Kant refers to marks in the given sense when talking about concepts being contained in other concepts: x is contained in y in the strong sense (that is, y is contained under x) =df. x is contained in y in the weak sense, where x specifies properties of the objects falling under y. On this account of containment the judgement voiced by (6), ‘Every square of a number greater than 1 is greater than 1’, is not analytic. It is true that being a number greater than 1 is a necessary property of the objects falling under the subject-concept of (6). But this does not entail that ‘greater than 1’ is contained in ‘square of a number greater than 1’ in the Kantian sense. After all, it does not belong to those properties which ‘square of a number greater than 1’ lists as properties of the objects in its extension. That is to say, in contrast to a number greater than 1, the square of a number greater than 1 is not defined by being greater than 1; it is rather defined by being the result of multiplying a number greater than 1 by itself.13 In this way, Bolzano himself inspires a solution to the difficulty that Kant’s specification of analyticity permits too wide a reading: since Kant reverts to the notion of essential marks, all of the seemingly problematic judgements emerge as synthetic. In Ayer’s view (1936, 77f.), this pro must be seen as a con because he considers geometrical and arithmetical truths, such as (2) and (6), to be analytic. But remember that we are interested in inner-Kantian objections. Nonetheless, when suspecting Kant’s characterisation of being too broad, Bolzano’s line of attack could have been proper even if the attack itself did not hit the mark. Consider particular affirmative statements, viz. statements of the form ‘Some A are B’. At first glance, many of them 13. Cf. De Jong 1995, 632–638 on propria and essentialia; and Marc-Wogau 1951, 146–154.

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conform to Kant’s definition because the given concept of an A contains the concept of a B as an essential mark. Just have a look at: (7) Some drakes are male. On the other hand, ‘Some A are B’ appears to be loaded with an existential supposition so that (7) entails that there is at least one drake. Since the existence of a drake cannot be proved without falling back on experience, ‘Some drakes are male’ seems to be a posteriori and therefore not analytic. Taken together, there is reason for assuming that Kant’s characterisation is too wide because it does not exclude a posteriori truths like (7).14 Bolzano provides a resort for Kant. In Bolzano’s view, particular affirmative judgements are to be treated in the same way as simple existential judgements: ‘Some A are B’ states that there is at least one A which is B and is thus synonymous with ‘The concept of an A which is B is instantiated’ (see WL II, § 137). If Kant agrees with this, as Morscher (2006, 252) relates, then his containment account of analyticity is put in a position to keep analyticity back from (7). For if the proposition expressed by ‘Some drakes are male’ is The concept of a (male) drake is instantiated. then subject and predicate are not ‘drake’ and ‘male’ anymore but ‘concept of a (male) drake’ and ‘instantiated’. Since the latter notion is not contained in the former, ‘Some drakes are male’ would be synthetic according to Kant’s definition. Propositions of this type could therefore not be used to show that Kant’s specification of analyticity in terms of containment is too broad. Note, however, that this could be a Pyrrhic victory. If Kant complies with Bolzano’s understanding of particular affirmative statements, one would expect him also to approve of Bolzano’s analogous interpretation of universal negative statements. In Bolzano’s view, we prevalently read ‘No A is B’ as claiming that the concept of an A which is B is uninstantiated (cf. WL II, §138). But then Kant’s paradigm of a negative analyticity would fail to be analytic on his own standards because ‘No unlearned person is learned’ translated into:

14. Singular affirmative judgements of the type ‘The A is B’ raise the same problem.

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The concept of an unlearned person who is learned is uninstantiated. If we conceive of this judgement as a negative judgement with the predicate ‘instantiated’, then it is not analytic because the subject ‘concept of an unlearned person who is learned’ does not contain a notion which negates ‘instantiated’. And the same holds if it is an affirmative statement with the predicate ‘uninstantiated’. Then it is not analytic either because the notion ‘uninstantiated’ is not included in ‘concept of an unlearned person who is learned’. Viewed from any angle, ‘No unlearned person is learned’ does not emerge as analytic in Kant’s sense if we assume the Bolzanian reading of ‘No A is B’. Moreover, no universal negative statement would be analytic. Curiously enough, Kant should thus be cautious of unanimously accepting this reading and the analogous one of particular affirmative statements. For although the latter promises help in allaying the suspicion that Kant’s conception of analyticity is too wide, the former has the equally unwelcome consequence that it is too narrow.15 3. The definiens is too narrow Bolzano’s first objection against Kant’s definition was that it permits an interpretation too wide. But Bolzano himself had an idea for improvement: a judgement is analytic if and only if its subject contains its predicate as an essential mark. Directly subsequent to this clarification, however, Bolzano proceeds by discrediting it for being too narrow: But this definition is applicable to only one kind of analytic judgements, only those of the form: A which is B is B. Should there not be others as well? Should we not count [(i)] the judgement: A which is B is A, and also [(ii)] the judgement: Every object is either B or not B, among analytic judgements? (WL II, §148: 88; cf. NAK, 35)

Part (i) of this objection seems to say that the improved definition is too restrictive because, say, (8a) would be an analytic statement according to it whereas (8b) would be synthetic: (8a) A ball which is red is red. (8b) A ball which is red is a ball. 15. For a potential loophole see Siebel in prep.

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I admit unashamedly that what Bolzano means in this remark is not clear to me. After all, in ‘ball which is red’ the concept ‘ball’ seems to represent an essential characteristic just as much as the concept ‘red’ does. It thus appears that the predicates of both propositions are contained in the right manner in their common subject. I might have misinterpreted Bolzano’s talk of essential marks, but I can conceive of no sustainable interpretation on which ‘red’ is a mark of ‘ball which is red’ whereas ‘ball’ is not. De Jong comments on this part of Bolzano’s objection as follows: “The first example makes clear in particular that Bolzano regards formal precision as important to a degree seldom previously encountered in traditional logic.” (2001, 335) But this mystifies me no less than Bolzano’s original claim. Part (ii) of the worry is that a logical truth like the following does not prove analytic: (9)

Every object is either red or not red.

Note that this example already threatens Kant’s definition as given by the weak interpretation against which Bolzano’s first attack was directed. The sense of ‘object’ contains neither the sense of ‘red’ nor the one of ‘either or’ nor the one of ‘not’. In other words, even though being red or not is a necessary feature of all objects, it is not part of the definition of an object. Hence, the predicate-notion is not even in the weak sense contained in the subject-notion. Should Kant take Bolzano’s concern to heart? Künne (2006, 214) answers in the affirmative, and he is surely right if Kant considers all truths of logic analytic, as some scholars assume (cf. Hanna 2001, 140; Morscher 2006, 250, 261; Pap 1958, 29; WL III, § 315: 240). There are then analytic judgements of subject-predicate form, such as (9), in which the subject does not contain the predicate. And there are analytic judgements which do not even have subject-predicate structure:16 (10) If all fans of Werder Bremen are relationally disturbed and Tom is a fan of Werder Bremen, then Tom is relationally disturbed. 16. (10) would have subject-predicate structure if it could be read as being composed of the subject ‘Tom’ and the predicate ‘is relationally disturbed if he is a fan of Werder Bremen and all fans of Werder Bremen are relationally disturbed’. But then the subject does not enclose the predicate.

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However, to my knowledge Kant nowhere explicitly says that all truths of logic are analytic. Hence, there remains a loophole, namely, simply clinging to the original definition. “Should we not count (9) among analytic judgements?”, Bolzano asks. “No, at least not in my sense of ‘analytic’”, Kant could answer, “because (9) and the like add to the subject a predicate that was not thought in it at all, and could not have been extracted from it through any analysis. (9) is thus a further synthetic truth a priori.”17 Thus the examples by which Bolzano tried to show that Kant’s explication is too close are weakened. They would have bite if Kant considered all truths of logic to be analytic, or if there was some inevitable sense of ‘analytic’ in which logical truths are of that type; but both of these claims are vulnerable. Nonetheless, by indicting Kant’s definition for being too narrow, Bolzano was on the right track even if he used the wrong examples. First of all, Bolzano’s worry seems to be applicable to two of Kant’s own examples. Shortly after his introduction of the syntheticity of geometry, Kant adds: To be sure, a few principles that the geometer presupposes are actually analytic and rest on the principle of contradiction; […] e.g., a = a, the whole is equal to itself, or (a + b) > a, i.e., the whole is greater than its part. (KrV, B 16f.)

According to this passage, Kant perceives the following propositions as analytic (cf. Marc-Wogau 1951, 142): (11) Every whole is equal to itself. (12) Every whole is greater than a proper part of it. Taken at face value, however, the predicate-concepts of these propositions are not even contained in their subject-concepts in Bolzano’s broad sense. For the sense of ‘whole’ neither includes the sense of the relational expression ‘equal to’ nor that of ‘greater than’. It thus seems that Kant’s definition of analyticity is too parsimonious even from his own perspective because it does not allow (11) and (12) to be analytic. Prima facie, there is an avenue, at least for (11). I have assumed that the predicate-concepts of the given propositions are expressed by the entire phrases following the copula ‘is’, so that the predicate-concept of (11) 17. Cf. KrV, B 11. Kant has to grant then that some synthetic judgements are not “judgements of amplification” because (9) can hardly be said to increase knowledge in any substantial sense.

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is ‘equal to itself ’. But Kant could reply that the purely relational part of this notion, viz. ‘equal to’, does not belong to the predicate. Rather, the predicate-notion is nothing more than ‘itself ’. This interpretation is confirmed by Kant’s rationale for the syntheticity of arithmetical equations, such as ‘7 + 5 = 12’: “The concept of twelve is by no means already thought merely by my thinking of that unification of seven and five; and no matter how long I analyse my concept of such a possible sum, I will still not find twelve in it.” (KrV, B 15; my emph.) Kant’s reason for deeming ‘7 + 5 = 12’ synthetic is not that the subject ‘7 + 5’ does not contain the concept ‘identical with 12’. His reason is rather that ‘7 + 5’ does not contain the concept ‘12’, which thus seems to be the constituent of the given proposition Kant treats as the predicate-notion. However, such a treatment of equations amounts to lumping together the ‘is’ of identity and the ‘is’ of predication. Whereas the ‘is’ in ‘7 + 5 is even’ might be thought of as providing a kind of glue sticking together the subject and the predicate, the ‘is’ in ‘7 + 5 is 12’ goes beyond that. It is an abbreviation for ‘is equal to’ (or ‘is identical with’), expressing not only the glue given by the predicative ‘is’ but also what is given by ‘equal to’ (or ‘identical with’). The ‘is’ of identity thus appears to make a contribution to the predicate in ‘7 + 5 is 12’, this predicate being not only ‘12’ but ‘is equal to 12’. In short, what Kant presents as examples of analytic judgements do not conform to his own definition. He is well advised to either rework his definition or exclude the recalcitrant judgements from the class of analyticities. De Jong (2010, 248) comes to the aid of Kant by recommending the second option. Judgements like (11) and (12), de Jong suggests, are relational and thus not of subject-predicate form, entailing that Kant’s definition is not applicable. However, if affirmative subject-predicate judgements are defined as judgements in which a property is assigned to some object(s), then every judgement which relates something to something is of subject-predicate form. For if a and b stand in relation R, then a has the (relational) property of standing in relation R to b. Nonetheless, de Jong is right in describing it as far from obvious that Kant accepts propositions like (11) and (12) as analytic. Although Kant opens the crucial paragraph by claiming that ‘a = a’ and ‘(a + b) > a’ are analytic, he continues in a surprising way: And yet even these, although they are valid in accordance with mere concepts, are admitted in mathematics only because they can be exhibited in intuition. What usually makes us believe here that the predicate of such apodictic judge-

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ments already lies in our concept, and that the judgement is therefore analytic, is merely the ambiguity of the expression. We should, namely, add a certain predicate to a given concept in thought, and this necessity already attaches to the concepts. But the question is not what we should think in addition to the given concept, but what we actually think in it, though only obscurely, and there it is manifest that the predicate certainly adheres to those concepts necessarily, though not as thought in the concept itself, but by means of an intuition that must be added to the concept. (KrV, B 17)

Kant appears to be asserting here that the judgements in question are not analytic because their predicates are not contained in their subjects. He could substantiate this claim with reference to the argument above: the concepts ‘equal to’ and ‘greater than’ are not included in ‘whole’; (11) and (12) are thus synthetic according to the containment-or-negation conception. This gives Kant the possibility of adhering to this characterisation of analyticity. But it has the serious drawback that it cannot be accommodated with the first sentence of the paragraph, where it is explicitly said that (11) and (12) are analytic. There is a way to solve this discrepancy. Have a further look at the first sentence and especially its mention of the principle of contradiction: To be sure, a few principles that the geometer presupposes are actually analytic and rest on the principle of contradiction, e.g., a = a, the whole is equal to itself, or (a + b) > a, i.e., the whole is greater than its part. (KrV, B 16f.; my emph.)

Perhaps, the ‘and’ in ‘and rest on the principle of contradiction’ is to be interpreted as prefacing a rationale for the analyticity of the propositions ‘a = a’ and ‘(a + b) > a’: they are analytic because they rest on the principle of contradiction. However, Kant would then claim in the paragraph in question that these propositions are analytic even though their predicates are not contained in their subjects. That is, he would straightforwardly concede that the containment definition, which he presented only six pages earlier, is too narrow. This kind of criticism can easily be extended to a wide range of examples. The problematic paragraph from the Introduction anticipates Kant’s famous reference to the law of contradiction in a later part of the Kritik: “if the judgment is analytic, whether it be negative or affirmative, its truth must always be able to be cognised sufficiently in accordance with the principle of contradiction” (KrV, B 190). As I said in section 1, this is presumably not meant to provide an alternative definition of analyticity, but is to be understood as an epistemological remark. Never-

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theless, it can be used to shed light on the extension of Kant’s concept of analyticity. Taken literally, Kant offers a necessary condition of analyticity. However, in the Prolegomena he says that synthetic judgements “can never originate according to the principle of analysis alone, namely the principle of contradiction” (AA 4, 267). Similarly, we read in the Kritik that in “the synthetic part of our cognition we will, to be sure, always be careful not to act contrary to this inviolable principle, but we cannot expect any advice from it in regard to the truth of this sort of cognition” (KrV, B 191). Kant thus maintains that, if a judgement is synthetic, then it is not cognisable solely on the basis of the rule of contradiction. By implication, this means that, if a judgement is cognisable in this way, it is not synthetic and thus, given that it is of subject-predicate form, analytic. Hence, Kant appears to take knowability on the basis of the law of contradiction to be a sufficient condition for the analyticity of subject-predicate judgements (cf. de Jong 1995, 619f.). But this provides grist to Bolzano’s mill: Kant’s definiens is then too parsimonious because there is a plethora of judgements which meet the principle-of-contradiction criterion and should therefore be accepted as analytic by Kant, even though their predicate-notion is neither contained in nor negates a constituent of the subject-notion. Among other things, this applies to the following judgement: (13) There is no married bachelor. The principle of contradiction, as conceived by Kant, says that no object both possesses and lacks a property at the same time (cf. KrV, B 190; Metaphysik Mrongovius, AA 29, 789). To prove the truth of a judgement by recourse to this principle means to derive from the opposite of the judgement an explicit contradiction to the effect that some object both has and lacks a certain attribute (cf. Metaphysik Arnoldt (K 3), AA 29, 964f.; Marc-Wogau 1951, 143). This can be done with (13). Its opposite ‘There is a married bachelor’ implies that there is a man who is both married and not married. Since this is incompatible with the principle of contradiction, we can, vice versa, infer from this principle that (13) must be true. Its truth can thus be recognised solely with the help of the principle of contradiction, so that it is analytic according to the corresponding criterion. But it is not analytic according to the containment-or-negation definition, given that (13) means ‘The concept of a married bachelor is uninstanti-

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ated’. After all, the corresponding subject ‘concept of a married bachelor’ neither contains ‘instantiated’ nor a notion which negates ‘instantiated’, and the same holds for ‘uninstantiated’. Hence, the definition seems to be too narrow.18 Or remember (9), ‘Every object is either red or not red’. If (9) expressed a falsehood, there would be an object for which it does not hold that it is red or non-red: (
x)(Rx  Rx). Due to a close relative of De Morgan’s laws, this entails that there exists an object which is non-red and not non-red: (
x)(Rx & Rx), implying straightforwardly that there is something which is both not red and red: (
x)(Rx & Rx). Since this is in conflict with the law of contradiction, this law entails that (9) is a truth, even though, again, the predicate-concept is not contained in the subject-concept.19 Thirdly, take ‘All A are A or B’. If its opposite ‘Some A are not (A or B)’ were true, there would be an A which is neither A nor B because ‘(
x) (Ax & (Ax  Bx))’ implies ‘(
x)(Ax & (Ax & Bx))’. Contrary to the rule of contradiction, there would thus be something which is A and not A. Nonetheless, the predicate ‘A or B’ is not contained in the subject ‘A’. To present a concrete example, the concept ‘red or green apple’ is not included in ‘red apple’. Hence, (14) All red apples are red or green apples. is analytic on the rule-of-contradiction criterion while it is synthetic on the containment-or-negation definition. Finally, consider judgements of the form ‘No non-A is a B which is A’, for example, a close relative of Kant’s ‘No unlearned person is learned’: (15) Nothing learned is a person who is unlearned. 18. There is a further reason for foisting the analyticity of (13) on Kant. In the next section, it will be pointed out that he seems to see no obstacle to incorporating analytic falsehoods, such as ‘All bachelors are married’. But it is quite natural to suggest that, if ‘All bachelors are married’ is an analytic falsehood, then ‘There are no married bachelors’ is an analytic truth. 19. Kant could reply that the derivation of (9) does not only assume the principle of contradiction but also the given De Morgan-like law, so that the truth of (9) is not cognisable solely on the basis of the principle of contradiction. But, firstly, we do not need anything like that law for most of the other examples. And, secondly, Kant would have a hard time explaining why the use of other purely logical principles does not have the same effect. Just think of the first step in such an indirect inference: the formation of the opposite proposition.

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If (15) were false, i.e., if something learned were an unlearned person, there would be an object which is both learned and unlearned. So, again, we arrive at a claim which is ruled out by the principle of contradiction. But (15) does not satisfy Kant’s official specification. Since the judgement is a negative truth, it would be awarded as analytic by (KA2) if the predicate ‘unlearned person’ negated the subject ‘learned (thing)’ or a constituent of it. But remember the associated conception of negation: a notion negates another notion if and only if one of them is composed of the other and one of the prefixes expressed by ‘not’, ‘un-’ or the like. According to this explanation, only a part of the predicate, namely ‘unlearned’, but not the predicate ‘unlearned person’ as a whole, negates the subject ‘learned’. (15) is therefore not analytic in the sense of the Kantian containment-ornegation regulations. More generally, those regulations embody the idea that a judgement is analytic only if an analysis of the subject unearths the predicate or something negating it. Judgements of the type ‘No non-A is a B which is A’ suggest that even Kant himself might condemn this idea as too narrowminded upon closer inspection. For it does not leave room for an analysis of the predicate leading to a similar result, such as in the case of (15) where decomposing the predicate results in a concept negating the subject. Moreover, propositions of the form ‘No A which is B is a C which is not B’ can also be recognised as true just on the basis of the rule of contradiction. As an example, consider (16) No German-speaking person who is blonde is an English-speaking person who is not blonde. Its opposite ‘Some German-speaking persons who are blonde are Englishspeaking persons who are not blonde’ entails the existence of someone who is blonde and not blonde. It thus appears that Kant should also provide for statements whose analyticity is based on the fact that an analysis of both subject and predicate reveals constituents negating each other. To be sure, opening Kant’s account for such statements is not too difficult. We just need a specification of the following type: A true negative subject-predicate proposition x is analytic =df. The predicate-concept of x or a constituent of it negates its subjectconcept or a constituent of it.

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However, this update merely results in judgements of the form ‘No non-A is a B which is A’ and ‘No A which is B is a C which is not B’ emerging as analytic. It does not yield a definition capturing (9), (13) and (14); and the same holds true for what Kant considers as analytic “principles that the geometer presupposes”, i.e. (11) and (12). Hence, even though the examples presented by Bolzano are debatable, his criticism goes in the right direction. It seems that Kant’s containment-or-negation definition of analyticity does not do justice to all of the propositions it should. 4. The definiendum is too limited It was, and still is, quite popular to accuse Kant’s definition of being too restricted because it has nothing to say about judgements which are not of subject-predicate form. Frege (1884, § 88) and Quine (1951, 20f.) are among those who addressed this problem; and Ayer (1936, 72) complained even more rigorously that Kant’s definition is based on “the unwarranted assumption that every judgement, as well as every German or English sentence, can be said to have a subject and a predicate”. Bolzano, however, never expressed his thoughts on this issue. He most likely does not make this point because, in his eyes, the confinement to subject-predicate propositions does not amount to any limitation at all (cf. Morscher 2006, 253). After all, like Leibniz, he thinks that each and every proposition has subject-predicate structure even though the corresponding sentences do not always exhibit it (see WL II, § 127). For example, Bolzano takes a disjunction ‘Either P or Q’ to express a statement of the form ‘The collection of the proposition that P and the proposition that Q contains exactly one true proposition’ (cf. WL II, § 160.3). Note, however, that this reading does not allow disjunctions to express analytic propositions in Kant’s sense. For even in the case of ‘Either it is raining or it is not raining’, the predicate-concept—‘contains exactly one true proposition’—is not included in the subject-concept—‘the collection of the proposition that it is raining and the proposition that it is not raining’. Bolzano’s reason for treating Kant’s definiendum as too limited is not that it is restricted to subject-predicate propositions but that it is meant to comprise only analytic truths and thus does not account for analytic falsehoods:

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I thought it useful to interpret both notions, of analytic as well as synthetic propositions, so broadly that not only true but also false propositions could be included under them. (WL II, § 148: 88)

Of all Bolzano’s attacks, this one can be parried most easily. Since Kant was primarily interested in knowledge, his division concerns only truths. That is why his definition of analyticity does not provide for the fact that there is a respect in which the truth ‘All bachelors are unmarried’ is more similar to the falsehood ‘All bachelors are married’ than to the truth ‘All bachelors are younger than 1000 years’. Nonetheless, as Proops (2005, 590f.) pointed out, Kant could be quite happy with extending the analytic-synthetic division. In his Reflexions on Metaphysics, he wrote: “If it is said: a resting body is moved, then this means: insofar as I conceive it as resting, it is moved, and the judgement would be analytic and false” (AA 18, 648). Elsewhere he suggests that ‘God is mortal’ expresses an analytic falsehood because the predicate-concept negates a constituent of the subject-concept.20 Moreover, it seems that Kant has the resources to capture analytic falsehoods with a close variant of his definition (KA2): (KA3) A subject-predicate proposition x is analytic =df. either the predicate-concept of x is contained in its subjectconcept (this holds for true affirmative and false negative analyticities), or the predicate-concept of x negates a constituent of its subject-concept (this holds for true negative and false affirmative analyticities). In light of this definition, the falsehoods ‘All bachelors are married’ and ‘No bachelor is unmarried’ are as much analytic as the truths ‘All bachelors are unmarried’ and ‘No bachelor is married’ are. For the predicate-notion of the affirmative judgement ‘All bachelors are married’ negates a constituent of the subject-notion, namely ‘unmarried’; and the predicate-notion of the negative judgement ‘No bachelor is unmarried’ is included in the subject-notion.

20. Cf. Versuch den Begriff der negativen Größen in die Weltweisheit einzuführen, AA 2, 203; and Metaphysik Mrongovius, AA 29, 810.

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5. The definiens does not capture the proper essence of analyticity Bolzano saved his most severe criticism for the conclusion. In the Wissenschaftslehre he demurs that the Kantian definitions “fail to place enough emphasis on what makes this sort of judgement really important” (WL II, § 148: 88), and in the Neuer Anti-Kant we are told in a sterner voice: Kant’s explication […] keeps entirely unaffected the proper essence, the difference philosophers should be most after when establishing this division, namely, that the truth or falsity of certain propositions (and these are only the analytic ones) in no way depends upon each of the notions of which these propositions are composed, but that they remain true or false whatever variation some of those notions are subjected to […]. (NAK, 35)

Unsurprisingly, the distinctive feature given here is the very same one that is highlighted by Bolzano’s own definition of analyticity (cf. WL II, § 148: 83): (BA) The proposition x is analytic =df. x contains at least one notion whose uniform substitution leads only to admissible variants of x with the same truth-value as x. As customary for Bolzano’s method of variation, variants of the original proposition whose subject-concepts are uninstantiated are not admissible (cf. WL II, § 147: 80). Bolzano takes propositions with uninstantiated subject-concepts to be false (cf. WL II, § 127: 16). Hence, if such propositions were permitted, the judgement ‘All drakes are male’ would not be analytic because, by replacing ‘male’ with ‘eight-legged’ or ‘duck’ with ‘lioness’, one would get a false variant of this judgement and thus a variant whose truth-value differs from the one of ‘All drakes are male’.21 However, given the above-mentioned constraint, both the true ‘All drakes are male’ and the false ‘No drake is male’ are analytic. For the uniform substitution of the concepts ‘male’ and ‘duck’ in the former invariably results in true admissible variants, such as ‘All green cars are green’; and substituting 21. Bolzano’s explanation of analyticity in §148 of the Wissenschaftslehre allows for a conception slightly differing from (BA): x contains at least one notion whose uniform substitution leads only to true or only to false admissible variants of x (cf. Siebel 1996, ch. 4.4; Künne 2006, 192–194 and fns. 21, 36, 39). De Jong (2001, 337; 2010, 252) and Lapointe (2007, 230; 2010, 265) just offer the latter as Bolzano’s definition without noting that Bolzano’s words suggest also (BA).

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‘male’ and ‘duck’ in the latter always leads to a false admissible variant, such as ‘No three-year-old girl is three years old’. In other words, these propositions contain elements which are insignificant to their truth-value. Back to Bolzano’s fourth objection, stating that Kant does not capture the proper essence of analyticity as it is given by Bolzano’s explication. In a similar way, Morscher (2006, 256) avers that Bolzano’s specification (i) “catches Kant’s concept of analyticity more appropriately than his own definition” and (ii) “blocks all the objections raised against Kant’s definition by Bolzano”. Part (ii) is true and does not pose a problem for Kant. Consider just one of the examples discussed. ‘Every son of a bachelor is a bachelor’ does not express an analytic falsity in Bolzano’s sense because neither ‘son’ nor ‘bachelor’ nor one of its other constituents is irrelevant for its falsity. For example, if you replace ‘bachelor’ with ‘son’, you end up with a truth; and the same holds for substituting ‘son’ with ‘unmarried father’. However, if part (i) of Morscher’s claim were true, this would be extremely embarrassing for Kant. Let us suppose that, when introducing his containment account of analyticity, there actually was analyticity in Bolzano’s sense at the back of his mind. As to the Kantian paradigms, such as ‘All bodies are extended’, this is unproblematic because they are also Bolzano-analytic. Since the notion in predicate-position is also contained in the subject as an essential mark, this notion is insignificant for their truth. Rather, part (i) of Morscher’s claim is embarrassing because, if Morscher were right, Kant would have accidentally centred on a special case of insignificance, thereby carelessly neglecting that there are other cases en masse. Just consider the following examples in which the irrelevant constituents are italicised: Every object is either red or not red. Every whole is greater than a proper part of it. There is no married bachelor (= unmarried man). No German-speaking person who is blonde is an English-speaking person who is not blonde. (17) 1 + 2 = 3, when read in Leibniz’s way: 1 + (1 + 1) = (1 + 1 + 1).22

(9) (11) (13) (16)

22. See Leibniz’s derivation of ‘2 + 2 = 4’ in the Nouveaux essais (1705, IV.VII.10). It is quoted by Frege in Die Grundlagen der Arithmetik (1884, § 6) and used by Bolzano in the Wissenschaftslehre (§ 305, 186). Note that ‘1 + 2 = 3’ is not analytic in Bolzano’s sense when interpreted à la Peano because in the proposition expressed by ‘1 + the successor of 1 = the successor of the successor of 1’ the concept ‘1’ is not irrelevant. Substituting ‘1’ with ‘2’ results in

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(18) Every equilateral triangle has the same angular sum as two right angles. (19) All green bodies are heavy. (20) Every bygone event has its cause. Kant could have been prepared to file the first half under ‘analytic’, but certainly not the second half. For Kant’s prime example of the syntheticity of arithmetic, viz. ‘7 + 5 = 12’, can be handled in the same way as (17) and would thus be analytic. Secondly, even if Kant tolerates some exceptions to the rule that geometrical truths are synthetic, e.g. ‘Triangles are polygons’, it is hardly conceivable that (18) is among them. After all, Kant illustrates the syntheticity of geometry by (2), ‘Every triangle has the same angular sum as two right angles’, and (18) is distinguished from the latter merely by virtue of being restricted to equilateral triangles.23 Likewise, (19) and (20) closely resemble Kantian paradigms of synthetic judgements a posteriori and a priori, namely ‘All bodies are heavy’ and ‘Every event has its cause’ (see KrV, B 11, 13). The sole difference is that the latter concern all bodies and all events whereas the subject-concepts of (19) and (20) contain further specifications and therefore only represent green bodies and bygone events, respectively. Again, I do not think Kant would react to the consideration that (19) and (20) contain an element which is insignificant for their truth by conceding analyticity to them. Additionally, Bolzano’s explication allows for a posteriori analyticities (cf. Textor 2001; Künne 2006, 195). For example, given that all fans of Werder Bremen are relationally disturbed, ‘All adult fans of Werder Bremen are relationally disturbed’ is Bolzano-analytic. But Kant would probably have no praise for analytic judgements of this type. Since they cannot be justified without recourse to experience, they violate a condition which seems to be central to Kant’s account. All in all, if Morscher’s diagnosis were true, Kant’s definition of analyticity and its surroundings would be lightyears removed from the conception they are meant to express. I therefore doubt that Bolzano’s regulations capture Kant’s ideas more appropriately than his own definition. a false variant because 2 + 3 (the successor of 2) ≠ 4 (the successor of the successor of 2). 23. See KrV, B 744f. Since (18) follows from (2), and (2) is synthetic on Bolzano’s standards, his account has the consequence that a synthetic proposition sometimes implies an analytic one (cf. WL IV, § 447: 115f.; Künne 2006, 194). Note, however, that Kant’s conception opens up the same possibility because (2) is Kant-synthetic and implies the Kant-analytic truth ‘Every triangle having the same angular sum as two right angles has the same angular sum as two right angles’.

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In section 3, it was argued that the definition in terms of containmentor-negation is too narrow because there are propositions which do not satisfy it even though they are analytic according to the principle-of-contradiction criterion. Hence, if Kant’s basic idea behind the introduction of the term ‘analytic’ is to capture the latter propositions, the containmentor-negation specification does not properly mirror his basic idea. However, this does not mean that Bolzano’s account gets to the heart of Kant’s actual intentions. It is then more probable that Kant had something like Frege’s or Ayer’s account in mind because the principle-of-contradiction criterion is much closer to them than to Bolzano’s regulations in terms of irrelevant elements. Frege (1884, § 3) says in Die Grundlagen der Arithmetik that propositions are analytic if and only if they can be proved to be true only with recourse to definitions and general logical laws. In Language, Truth and Logic, Ayer (1936, 73) considers sentences analytic if their truth depends solely on the definition of their constituents. The most striking common feature is that a judgement is perceived as analytic if its truth rests on nothing but fundamental logico-semantic principles, such as the law of contradiction (Kant), general logical laws and definitions (Frege) or just definitions (Ayer). Moreover, a proposition which is analytic in the sense of being indirectly derivable from the law of contradiction is clearly Frege-analytic; and I suppose that Ayer would also accept it as analytic. Hence, based on the assumption that Kant’s original intent is expressed in the principle-of-contradiction criterion, if there really is an explanation of analyticity which is closer to this intent than Kant’s own explanation, it is rather Frege’s or Ayer’s than Bolzano’s. In addition, unlike Frege, Bolzano does not contend that his account only articulates what Kant intended all along. When offering his definition of analyticity, Frege asserts his claim “only to state accurately what earlier writers, Kant in particular, have meant” (1884, § 3, fn.). Similarly, Ayer thinks that his account preserves “the logical import of Kant’s distinction […] while avoiding the confusions which mar his actual account of it” (1936, 73). Bolzano, however, does not maintain that his specification in terms of irrelevant elements catches the Kantian thoughts. For example, when he rebukes Kant for not having grasped the analytic-synthetic division with the required clarity (see NAK, 34), he does not find fault with Kant’s formulations, but rather with the idea they are meant to articulate. Accordingly, Bolzano’s fourth objection does not state that Kant’s definition misses Kant’s intent but rather that it misses “the proper essence, the

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difference philosophers should be most after when establishing this division” (NAK, 35; my emph.). Evaluating this objection with all due thoroughness would go beyond the scope of this paper. But remember Künne’s (2006, 219) remark that there are no pre-theoretical intuitions concerning analyticity because ‘analytic’ is a term of art. It is thus not possible to delineate “the proper essence” of analyticity by invoking such intuitions. But how to establish then what “the proper essence” is? There is something along these lines only if there is some external (pre-theoretical or whatever) sense of ‘analytic’, in other words, a standard applicable to any specification of analyticity whatsoever, whether it is Kant’s, Bolzano’s, Frege’s, Ayer’s, etc. That is to say, talk of “the proper essence” of analyticity makes sense only if questions like ‘What is analyticity actually?’ do. But do they? It appears to me that questions of this sort are rather a stumbling block to the substantial issues. Just consider the dispute about arithmetic and geometry. Frege (1884, §89) thought that Kant was mistaken about arithmetic because it is in fact analytic. Ayer (1936, 79f.) went one step further and accused Kant for being also wrong about geometry. Both overlook the possibility that there is no genuine conflict at all for the simple reason that they do not share a common topic and use the term ‘analytic’ in a different way than Kant does. For example, even if the following geometrical truths are analytic in some Ayerian sense, they are not analytic according to the Kantian definitions because their subjects do not contain their predicates (cf. the end of section 1): Every triangle has the same angular sum as two right angles. Equilateral triangles are equiangular. In every square the side is related to its diagonal as 1 : 2. In the introduction to the Kritik we find Kant’s famous formulation of the central task he sets out to perform: “The real problem of pure reason is now contained in the question: How are synthetic judgments a priori possible?” (KrV, B 19) This is a substantial question, no matter whether arithmetical or geometrical truths are synthetic in Bolzano’s, Frege’s, Ayer’s or in yet another sense. The examples mentioned above make it clear that there exist synthetic judgements a priori in Kant’s sense; and it is legitimate to ask how it is possible to recognise without recourse to experience that such a judgement is true, and even necessarily true. This question cannot be answered by alluding to conceptual analysis, or the principle of contradiction, because the subject-concepts of these propositions neither

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contain their predicate-concepts nor constituents negating the predicateconcepts or a part of them. Kant’s answer is, very briefly, that such truths are cognised through “pure intuition”, whereas Bolzano takes this to be the basic mistake within the Kritik: “What entitles the intellect to attribute to a subject A a predicate B which does not reside in the concept of A? Nothing else, I say, than the intellect’s having and knowing both concepts A and B.” (WL III, § 305: 180; cf. NAK, 40, 69) Whatever the correct answer might be, questions of the type ‘What, really, is analyticity?’ only interfere with the search for it. To be sure, further conceptions of analyticity become relevant when a Kant-synthetic truth is analytic in another sense. For example, if a truth is reducible to logic à la Frege, the question arises whether we need “pure intuition” in order to show that it is true. However, this does not mean that there is anything along the lines of a “proper essence” of analyticity. It just means to tell apart different conceptions which have equal right to be labelled ‘conceptions of analyticity’. To conclude, three of Bolzano’s four objections against Kant’s definition of analyticity can be countered or at least weakened. The accusation remains that the definition appears to be too narrow on Kant’s own standards because it takes into account only those cases where an analysis of the subject reveals a constituent identical with the predicate or negating it. It thus discounts judgements which are analytic insofar as an analysis of the predicate, or both subject and predicate, unearths conflicting constituents. Moreover, even if we clear the way for such analyticities by means of the modification proposed at the end of section 3, the resulting explanation is still not broad enough. There remain judgements which do not satisfy it although Kant would presumably call them analytic because they are derivable from the principle of contradiction. Whether this is a serious drawback is another question.24

24. I am grateful for criticism and suggestions from the audience of my talk on the conference Truth and Abstract Objects in Berlin (August 2009), the audience of my talk on the conference Philosophy and Mathematics in the Work of Bernard Bolzano in Prague (April 2010) and the participants in a seminar on analyticity and a colloquium for theses in Oldenburg. Special thanks go to Lisa Beesley, Andreas Hettler, Thomas Hilbig, Miguel Hoeltje, Joseph Hossfeld, Sandra Lapointe, Holger Leerhoff, Tobias Rosefeldt, Paul Rusnock, Benjamin Schnieder, Michael Schippers, Moritz Schulz and Jean Stünkel.

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REFERENCES Ayer, Alfred 1936: Language, Truth and Logic. London: Victor Gollancz Ltd. Repr. London: Penguin, 1990. Bell, David 1982: “Review of The Metaphysics of Gottlob Frege: An Essay in Ontological Reconstruction by Eike-Henner W. Kluge”. Mind 91, 457–459. Bennett, Jonathan 1974: Kant’s Dialectic. Cambridge: Cambridge University Press. Bolzano, Bernard 1837: Wissenschaftslehre, 4 vols. Sulzbach. Republ. by Wolfgang Schultz, Leipzig 1929–31. Partly transl. by Rolf George as Theory of Science. Berkeley & Los Angeles: University of California Press, 1972; and by Jan Berg as Theory of Science. Dordrecht: Reidel, 1973. Boswell, Terry 1988: “On the Textual Authenticity of Kant’s Logic”. History and Philosophy of Logic 9, 193–203. — 1991: Quellenkritische Untersuchungen zum Kantischen Logikhandbuch. Frankfurt a. M.: Peter Lang. De Jong, Willem R. 1995: “Kant’s Analytic Judgments and the Traditional Theory of Concepts”. Journal of the History of Philosophy 33, 613–641. — 2001: “Bernard Bolzano, Analyticity and the Aristotelian Model of Science”. Kant-Studien 92, 328–349. — 2010: “The Analytic-Synthetic Distinction and the Classical Model of Science: Kant, Bolzano and Frege”. Synthese 174, 237–261. Frege, Gottlob 1884: Die Grundlagen der Arithmetik. Ed. by Christian Thiel, Hamburg: Meiner, 1988. Transl. by John L. Austin as The Foundations of Arithmetic, 2nd, rev. ed. Oxford: Blackwell, 1953. — 1891: “Funktion und Begriff”. In: Mark Textor (ed.), Funktion—Begriff— Bedeutung, 2nd, rev. ed. Göttingen: Vandenhoeck & Ruprecht, 2007, 1–22. — 1893: Grundgesetze der Arithmetik. Repr. Hildesheim: Olms, 1998. — 1903: “Über die Grundlagen der Geometrie II”. In: Kleine Schriften, ed. by Ignacio Angelelli, Hildesheim: Olms, 1967, 267–272. Friedman, Michael 1992: Kant and the Exact Sciences. Cambridge, Mass.: Harvard UP. Hanna, Robert 2001: Kant and the Foundations of Analytic Philosophy. Oxford: Clarendon Press. Hinske, Norbert 2000: “Die Jäsche-Logik und ihr besonderes Schicksal im Rahmen der Akademie-Ausgabe”. Kant-Studien 91, 85–93. Hintikka, Jaakko 1973: “An Analysis of Analyticity”. In his: Logic, Language-Games and Information. Kantian Themes in the Philosophy of Logic, Oxford: Clarendon Press, 123–149.

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Kant, Immanuel 1787: Kritik der reinen Vernunft, 2nd ed. Riga: Johann Friedrich Hartknoch. Republ. by Jens Timmermann, Hamburg: Meiner, 1998. Transl. by Paul Guyer & Allen W. Wood as Critique of Pure Reason. Cambridge: Cambridge University Press, 2007. — 1902ff.: Gesammelte Schriften, 29 vols. Berlin: Königlich Preußische Akademie der Wissenschaften. Künne, Wolfgang 2001: “Constituents of Concepts: Bolzano vs. Frege”. In: Albert Newen, Ulrich Nortmann & Rainer Stuhlmann-Laeisz (eds.), Building on Frege. New Essays on Sense, Content, and Concept. Stanford: CLSI Publications, 267–285. — 2006: “Analyticity and Logical Truth: From Bolzano to Quine”. In: Mark Textor (ed.), The Austrian Contribution to Analytic Philosophy. London & New York: Routledge, 184–249. Lanier Anderson, R. 2004: “It Adds Up After All: Kant’s Philosophy of Arithmetic in Light of the Traditional Logic”. Philosophy and Phenomenological Research 69, 501–540. — 2005: “The Wolffian Paradigm and its Discontents: Kant’s Containment Definition of Analyticity in Historical Context”. Archiv für Geschichte der Philosophie 87, 22–74. Lapointe, Sandra 2007: “Bolzano’s Semantics and his Critique of the Decompositional Conception of Analysis”. In: Michael Beaney (ed.), The Analytic Turn. London & New York: Routledge, 219–234. — 2010: “Bolzano, A Priori Knowledge, and the Classical Model of Science”. Synthese 174, 263–281. Leibniz, Gottfried W. 1705: Nouveaux essais sur l’entendement humain. Transl. as New Essays on Human Understanding by Peter Remnant & Jonathan Bennett, Cambridge: Cambridge University Press, 1996. Locke, John 1690: An Essay Concerning Human Understanding. Ed. by Peter H. Nidditch, Oxford: Oxford University Press, 1975. Marc-Wogau, Konrad 1951: “Kants Lehre vom analytischen Urteil”. Theoria 17, 140–154. Morscher, Edgar 2006: “The Great Divide within Austrian Philosophy: The Synthetic A Priori”. In: Mark Textor (ed.), The Austrian Contribution to Analytic Philosophy. London & New York: Routledge: 250–263. Pap, Arthur 1958: Semantics and Necessary Truth. New Haven & London: Yale University Press. Příhonský, Franz 1850: Neuer Anti-Kant. Bautzen: A. Weller. Republ. by Edgar Morscher, St. Augustin: Academia, 2003. Proops, Ian 2005: “Kant’s Conception of Analytic Judgment”. Philosophy und Phenomenological Research 70, 588–612.

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Quine, Willard V. O. 1951: “Two Dogmas of Empiricism”. The Philosophical Review 60, 20–43. Rosefeldt, Tobias 2008: “Kants Begriff der Existenz”. In: Valerio Rohden et al. (eds.), Recht und Frieden in der Philosophie Kants. Akten des X. Internationalen Kant-Kongresses, Bd. 2: Sektionen I-II. Berlin & New York: de Gruyter, 657–668. — 2011: “Frege, Pünjer, and Kant on Existence”. Grazer Philosophische Studien 82 [this volume], 329–351. Siebel, Mark 1996: Der Begriff der Ableitbarkeit bei Bolzano (Beiträge zur BolzanoForschung 7). St. Augustin: Academia. — in prep.: “Das Fehlen von Existenzimplikationen in Kants Logik”. To be submitted to Kant-Studien. Stuhlmann-Laeisz, Rainer 1976: Kants Logik. Eine Interpretation auf der Grundlage von Vorlesungen, veröffentlichten Werken und Nachlaß. Berlin & New York: de Gruyter. Textor, Mark 2001: “Logically Analytic Propositions A Posteriori?”. History of Philosophy Quarterly 18, 91–113. Van Cleve, James 1999: Problems from Kant. Oxford: Oxford University Press. Wiggins, David 1994: “The Kant-Frege-Russell View of Existence: Toward the Rehabilitation of the Second-Level View”. In: Walter Sinnott-Armstrong (ed.), Modality, Morality, and Belief. Essays in Honor of Ruth Barcan Marcus. Cambridge: Cambridge University Press, 93–113. — 1998: Needs, Values, Truth. Oxford: Clarendon Press.

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II. CONCEPTS AND PROPOSITIONS

Grazer Philosophische Studien 82 (2011), 131–163.

A COGNITIVIST APPROACH TO CONCEPTS Hans-Johann GLOCK University of Zurich Summary This article explores a cognitivist approach to concepts. Such an approach steers a middle course between the Scylla of subjectivism and the Charybdis of objectivism. While concepts are not mental particulars, they have an ineliminable cognitive dimension. The article explores several versions of cognitivism, focusing in particular on Künne’s Neo-Fregean proposal that concepts are modes of presentation. It also tackles a challenge facing all cognitivist accounts, namely the ‘proposition problem’: how can the cognitive dimension of concepts be reconciled with the idea that concepts are components of propositions. My moral is that this challenge can be met only by combining Neo-Fregean ideas with certain Wittgensteinian insights.

1. Introduction Philosophers and logicians talk of comparative (x is heavier than y), quantitative (x weighs 20kg), individual (the author of Atemschaukel ), logical (negation, implication), spatial and temporal concepts. My focus here will be on predicative concepts, concepts that correspond to general terms of a particular kind, namely to the verbs, adjectives or count-nouns that feature in one-place predicates like ‘x runs’, ‘x is radioactive’ and ‘x is a tool’. It is relatively uncontroversial that such concepts are involved when rational creatures entertain thoughts like (1) Dogs bark. The nature of this involvement remains controversial, however. Even if we abstract from merely terminological variations, concepts have been assigned a multitude of different and potentially incompatible roles. In spite of this diversity, one can detect a pervasive contrast between two

fundamentally opposed approaches (e.g. Rey 1998). According to objectivist accounts, concepts exist independently of individual human minds, as self-subsistent abstract entities. According to subjectivist accounts, concepts are mental phenomena, entities or goings-on in the mind or in the head of individuals. In previous writings I have criticized both subjectivism and objectivism (Glock 2009; 2010b). This article is devoted to the positive task of exploring a third and, in some respects, intermediate approach. It agrees with objectivism in denying that concepts are mental particulars, while at the same time maintaining, with subjectivism, that they have an ineliminable mental or cognitive dimension. Hitherto I have labelled this approach ‘(concept) pragmatism’, reluctantly following the lead of Fodor (e.g. 2003, 9). But any pragmatism worthy of the name accords a central place to overt activity rather than to (potentially covert) mental operations. ‘Cognitivism’ avoids such specific connotations. It is also superior to talk of ‘epistemic conceptions’, since not all conceptual judgement amounts to knowledge. To put it differently, my account is inspired by both Frege and Wittgenstein. And while the former was certainly no pragmatist, the latter wasn’t much of an -ist. In a more direct and personal manner, I am indebted to Wolfgang Künne. He has not only developed the most attractive version of what has come to be known as ‘Neo-Fregeanism’, he has also enlightened and corrected my thinking for almost twenty years, both through his wonderful writings and in many memorable discussions. One version of cognitivism might be called intersubjectivism. It holds that concepts exist independently of individual rational subjects, while insisting that they are constituted by intersubjective linguistic practices. Another version brackets the question of existence, yet holds that what concepts are—their essence—can be explained only by reference to the operations and capacities of rational subjects. I shall explore this less committal idea. And I shall devote most attention to the Neo-Fregean variant of the cognitivist approach. In the course of this discussion, however, reasons will emerge for moving from the more objectivist end of the cognitivist spectrum towards the more pragmatist one. My perspective on concepts is also closer to Wittgenstein in another respect. Instead of investigating whether concepts need to be posited for the purposes of a formal semantic theory (whether it is Fregean, NeoFregean or other), I start out from the established uses of ‘concept’ and its cognates. This established use includes not just its employment in ordinary parlance but also in specialized forms of discourse, including history of

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ideas, psychology, logic and philosophy. Accordingly, I shall assess various definitions or conceptions of concepts against the role that the notion of a concept plays in these different forms of discourse (for a defence of this procedure see Glock 2010b). 2. Concepts and abilities The most natural version of cognitivism identifies concepts with mental abilities, dispositions or capacities. Thus, in response to the question ‘Are concepts entities or are they dispositions?’ Price states: ‘a concept is not an entity […] but a disposition or capacity’ (1953, 320, 348). In the same vein Geach pronounces that concepts ‘are capacities exercised in acts of judgement’ (1957, 7). And Kenny has recently followed the same line: ‘Concepts are best understood as a particular kind of human ability’ (2010; also Saporiti 2010). This proposal respects several features of established use. First, it pays heed to an important difference between concepts on the one hand, properties on the other (a difference ignored by authors like Carnap who identify the two, see Glock 2010b, 313ff.). Properties are possessed by things of all kinds. By contrast, concepts are possessed exclusively by rational subjects capable of classifying things according to their properties. This is simply part and parcel of the cognitive dimension of concepts. Secondly, the identification of concepts and capacities does not fall foul of the constraint that concepts must be shareable. As Geach points out, it does not entail that ‘it is improper to speak of two people as “having the same concept”’, since different individuals can possess the same mental capacities (1957, 14). Thirdly, concepts and abilities alike can be acquired, applied and lost, and some of them may be innate. Finally, to possess a concept is to possess a certain kind of mental ability, capacity or disposition. In this essay I refrain from deciding which of these notions is the most appropriate general category (see Glock 2010b, 319–22). Barring that issue, identifying concept-possession with an ability, capacity or disposition of some kind is inevitable. Concepts are involved not just in occurrent thoughts or beliefs, but also in long-standing or dispositional beliefs. Consequently, the possession of concepts must be at least as stable as the possession of dispositional beliefs. Put in Aristotelian terms, concept-possession must be a potentiality of some kind, since it combines two features. On the one hand, it is enduring rather than episodic. On

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the other hand, it is something which manifests itself in certain episodes, notably of overt or silent classification or inference. Nevertheless, the established use of ‘concept’ differs from that of ‘ability’ in other important respects. First, one thing we do with concepts is to define or explain them. But to define or explain a concept is not to define or explain a capacity. Normally, to explain an ability is to explain its causal preconditions (causal explanation), whereas to explain a concept is to explain the content of a predicate (semantic explanation). Furthermore, even when we define an ability, we specify what it is an ability to do. By contrast, to explain a concept is to specify the conditions that an object must satisfy to fall under it. Secondly, concepts can be instantiated or satisfied by things; conversely, things instantiate, satisfy or fall under concepts. These things cannot be said of abilities, or at least not in the same sense. Thirdly, concepts have an extension (the set of objects which fall under them); yet this cannot be said of abilities. Insofar as the ability linked to possessing the concept F has an extension, it is not the range of things that are F, but either the range of subjects that possess F, or the range of situations in which these possessors can apply or withhold F.1 3. Tools, techniques and rules Let us return to the strongest consideration in favour of the identification of concepts with mental abilities of a certain kind. It starts out from (I) to possess a concept is to possess a certain mental ability. Next, it glosses (I) as 1. It is tempting to add that a (predicative) concept also has an intension or linguistic meaning, something which cannot even be meaningfully said of abilities. Such a contrast indeed exists on a common everyday understanding of concepts as general terms with a meaning. But concepts as standardly conceived in philosophy and psychology are not general terms with a meaning, since they cut across languages. And even if one resists the suggestion that concepts in that sense simply are intensions qua meanings (as one should), it remains problematic to say that they have intensions. For the intension of a general term F is plausibly regarded as those features that determine whether objects belong to the extension of F, and these features also determine the concept expressed by F. Accordingly, ‘concept’ and ‘intension’ are too close for it to be the case that concepts possess intensions.

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(Ic) to possess a concept = to possess a certain mental ability. Finally, it invokes the general principle (II) to possess x = to possess y Ÿ x = y in order to reach the conclusion that (III) a concept = a certain mental ability. But this reasoning is problematic. First, it is unclear whether (I) is indeed an identity statement, as the paraphrase (Ic) assumes. Often statements of the form ‘to ) is to