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 . . . . . . . . . . . . . . . . . . . . .
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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.
15
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.
16
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.
27
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.
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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.
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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.
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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
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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.
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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
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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-
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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.
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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
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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 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 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 Fy) xyF(Fx Fy) These sentences are logically true, and their negations (or the corresponding sentences with an ‘’ 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 (‘’, ‘’, ‘’, ‘’, ‘=’),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) 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) (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 Fy), xyF(Fx 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 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 <’ merely express a generality statement of the form ‘For all x, if x is F then x is G)’. The latter need not even be reversible (as in ‘to be a Cretan is to be a liar’). And although (I) is reversible, this by itself does not establish an identity. It only means that everyone who possesses a concept also possesses a certain kind of mental ability, and vice versa.2 Furthermore, it remains an open question whether (I) should not instead be glossed as: (I*) S has the concept F S has the ability of operating with F. To be sure, someone who identifies concepts with abilities will resist that paraphrase and insist that the ability with which possessing the concept F is to be identified must be explained without mentioning the concept F, an entity with which the subject operates. But it is an alternative that her arguments do not rule out. That alternative is based on the following line of thought. If having a concept is an ability, it is an ability to operate with concepts. In that case, however, the concept itself cannot be identical with the ability. Rather, it is something employed in the exercise of that ability. A cognitivist conception which picks up this cue is the popular idea that concepts are a kind of cognitive or linguistic tool. Concepts are things employed in the exercise of conceptual abilities, just as tools are things employed in the exercise of manual (technical) abilities. Unfortunately, the idea that concepts are tools in the sense of being mental or abstract objects with which we operate in conceptual thought amounts to a reification. There is a difference between the possession of a 2. I owe this point to Benjamin Schnieder.
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tool and the possession of the ability to employ the tool—as I keep discovering to my cost when trying to operate with our electric drill. This distinction cannot be drawn in the case of concepts. To possess a concept is ipso facto to possess the ability to use the concept.3 A third cognitivist account promises to heed that point. It maintains that a concept is not an object, properly speaking, but a technique. Thus Wittgenstein maintained that ‘a concept is a technique of using a word’, or ‘the technique of our use of an expression: as it were, the railway network that we have built for it’ (1988, 50; 2000, MS 163: 56v). To master or possess a technique is to master or possess an ability. Yet techniques are not themselves abilities, but something which the possessor of an ability uses in exercising the ability. There is a difference, for instance, between the ability to skin a rabbit and the various techniques one might employ to this end. Wittgenstein regarded concepts as linguistic techniques. But his idea can be given a Kantian twist, in order to avoid the potentially problematic implication that concepts are the prerogative of linguistic creatures. One can tie concepts instead to thought or understanding rather than language. Concepts are techniques not just for using words, but for mental operations or mental acts which may or may not be expressed in language. The capacity for such mental operations may presuppose possession of language, yet it can be exercised by a subject that does not engage in either overt or silent speech at the time. But what kind of mental operation? A plausible answer is that conceptual thought revolves around classification and inference. Accordingly, the proposal currently under consideration is this: a concept is not identical with the capacity to classify or infer, but only with the technique employed by someone who exercises the ability to classify or infer. Next, the term ‘technique’ needs to be made more specific. What matters as far as concepts are concerned are the rules or principles that guide conceptual thought. Concepts, the proposal now runs, are rules or principles of classification and/or inference. Even this modified proposal is threatened by category mismatches. It does not seem that to define a concept is to define a principle or rule. Rather, the principle or rule features in the definition. On the other hand, perhaps this is just a vagary of the current use of ‘definition’ in English, 3. The point does not trade on an ambiguity of ‘to possess’, e.g. between having material possession and having operational control. For it is tantamount to insisting that the two latter notions can be distinguished in the case of tools, but not in the case of concepts.
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without further conceptual import. There is no linguistic infelicity in maintaining that to explain a concept is to explain a principle or rule for performing certain mental or linguistic operations. Another qualm would be that principles can be true or false, whereas concepts cannot. Prima facie, at least, rules escape this difficulty. Even if they are expressed by sentences in the indicative mood, it is arguable that their ‘truth’ amounts to nothing other than a particular prescription being actually in force. The question remains, however, what form these principles or rules should take. Here we seem to be facing a dilemma. One option is that these rules are standards for the employment of concepts. They might, for instance, take the form of the rules Bennett extracts from Kant (Bennett 1966, 145): (2) You may apply concept F to x iff x is … Accordingly, the concept F itself would not be identical with the rule. It would rather be a predicate the use of which is governed by the rule. A second option is that the rule specifies another activity, e.g. (3) You may treat x in way W iff x is … In that case the danger is that we are stuck with two unpalatable options. One is that W is a place-holder for practical activities which may presuppose concept-possession, but which someone who has mastered the concept need not engage in; the other is that W is a place-holder for conceptualization, which would render the account unexplanatory. 4. Modes of presentation I now turn to a version of cognitivism that prima facie avoids this dilemma, since it eschews mention of practical activities while nonetheless explaining concepts in cognitive terms. It is the Neo-Fregean proposal—epitomized by Peacocke and Künne—that concepts are ‘senses’ of general terms, and hence ‘modes of presentation’. Unfortunately, the latter is merely a catch-phrase, and one Frege himself never elaborated, least of all with respect to concepts, which he regarded as referents rather than senses of predicates.
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Following Evans (1982, ch. 1), Peacocke (1991, 525; 2008, 288) has brought into play the idea that a mode of presentation is a ‘way of thinking’. Obviously, in this context that phrase must not be understood in an adverbial sense, as in ‘She thought hard about the problem’ or ‘He thought longingly about home’. Rather, the mode of presentation of x depends on this: as what is x thought or conceived of? In that case, however, it is unclear what work the idea of a way of thinking can do in explaining that of a mode of presentation. According to Künne, concepts qua modes of presentation are ‘representational abstract entities’ (2007, 346f.). This proposal must not be confused with Fodor’s subjectivism, which has it that concepts are mental representations. For one thing, Fodor’s mental representations are concrete particulars in the skulls of individual subjects, rather than abstract entities. For another, they are linguistic symbols, words of a language of thought. In both respects, Fodor misses essential features of the established concept of a concept. The former cannot account for the fact that different individuals can share the same concept. The latter is incompatible with the fact that even if concepts are not identical with meanings, they are situated at the semantic level; they are things represented by linguistic signs rather than signs themselves (Glock 2009). Künne’s position is compatible with both points. Qua modes of presentation concepts are not predicates of a language of thought. Instead, they are at the same time representanda of the predicates of public languages and representantia of properties. And they are subjective not in the sense of being inside the minds or brains of individuals, but only in the sense of having an essential cognitive dimension. According to Künne, the general term ‘dog’ applies to all and only dogs, connotes the property of being a dog, and expresses the concept dog (2005, 254 and fn. 31, 263; 2007, 340–8; see also his 2003, 4). The concept expressed by a general term ‘F ’ is a ‘mode of presentation’ of the property of being F, and ‘determines’ that property (2007, 342ff.; 2005, 263). The point of this apparatus is revealed by looking at the different criteria of identity for extensions, properties and concepts, respectively, associated with a general term. (Extension-Identity) The extension of F is identical with the extension of G iff all and only Fs are Gs. (Property-Identity) The property of being F is identical with the property of being G iff necessarily all and only Fs are Gs.
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(Concept-Identity1) The concept F is identical with the concept G iff thinking of something (an object) as (falling under) F is thinking of it as (falling under) G. While ‘creature with a kidney’ and ‘creature with a heart’ apply to the same things—have the same extension—they connote different properties and express different concepts. And while ‘triangular’ and ‘trilateral’ apply necessarily to the same things and hence connote the same property, they express different concepts. By the same token, the concept triangular and the concept trilateral determine one and the same property, yet they are different modes of presenting that property (2007, 343–8; 2005, 263ff.). The next question is: what kind of thing is presented or conceived through a concept? For Frege, the sense of an expression is a mode of presentation of its referent (Bedeutung). In Künne’s semantic framework, that notion does not occur. However, he maintains that a concept is a mode of presentation of a property. Thus one may think or conceive of the property of being a triangular figure. At the same time, (Concept-Identity1) links concepts not so much with thinking about properties as with thinking about an object (or objects) as possessing a certain property. Thus one may think of a particular figure as being triangular. Literally speaking, there can be no way of presenting a referent unless there is a referent. If concepts were modes of presenting objects that actually possess certain properties (the objects that fall under the concept), this would rule out uninstantiated concepts, which is absurd.4 Ways of thinking about objects as having certain properties should be construed, therefore, as directed not just at those objects which actually possess the properties in question, but at all objects of which the relevant properties can be predicated either truly or falsely. To put it differently, a concept is a mode of presenting (way of thinking of ) objects from a suitable range as possessing or lacking certain properties. This reintroduces the idea of classification. Finally, we can operationalize ways of thinking as follows. The concept expressed by a predicate is determined by the features to which 4. Construing concepts as modes of presenting properties does not avoid this problem altogether, at least if Künne is to be trusted. For according to him there are bona fide concepts— e.g. property that does not exemplify itself—which do not determine a property, since they lead to paradox (2005, 281ff.). In my view, one should take the cognitive dimension of concepts one step further and deny that paradox engendering general terms like ‘property that does not exemplify itself ’ express concepts. The reason is that they do not allow of consistent classifications and inferences across the board, with the result that we lack the kind of semantic and epistemic control over them that a cognitivist approach should insist on.
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subjects who understand the predicate (aka competent speakers) refer in deciding whether a given object falls under the predicate, or would decide, if the question arose. What is it to think of something as possessing the property of being F ? Künne answers this question in the course of exploring various sufficient conditions for concept-possession. (Concept-Possession1) A subject S possesses the concept F if S is capable of thinking of an object (objects) as being an F. And he further suggests two sufficient conditions for this sufficient condition of concept-possession. (Concept-Possession2) A subject S is capable of thinking of an object as being F—and hence possesses the concept F—if S understands the term F or a synonym of it. Künne further explains that ‘one thinks of something as F if one judges, that it is F, when one hopes that it is F, when one wonders, whether it is F, etc.—for all propositional attitudes and acts’ (2007, 343). Alas, when I hope that or wonder whether Susan is well, I normally do not think of her as being well. Hence ‘thinking of something as F ’ cannot have its ordinary meaning here. Rather, it functions as a dummy for intentional verbs. In that case, the hope of giving substance to the Neo-Fregean approach by explaining the idea of a ‘way of thinking’ once more proves elusive. That content is provided instead by linking concept-possession to the applicability of intentional verbs. This yields (Concept-Possession3) A subject S is capable of thinking of an object as being F—and hence possesses the concept F—if S is capable of V-ing that/whether an object is F (where ‘V’ is a place-holder for an intentional verb). In a previous publication, however, Künne suggests that (Concept-Possession2) is too weak. He strengthens (Concept-Possession2) by insisting that in order to be capable thinking of an object as being F, S should fully understand the (univocal) term F. And he goes on to deny that S needs to satisfy that strengthened condition in order to be in an intentional state. This opens up the possibility of also denying that S needs to possess
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concepts in order to be in an intentional state—contrary to (ConceptPossession3). And Künne does just that: ‘take any general term “F” and any propositional attitude verb “V”; it may not be true that a person commands the concept F although it is true that she Vs that … F…’ (2005, 264). I am sympathetic to this separation of intentional states and conceptpossession, not least because it allows for the possibility of ascribing intentional states to creatures that lack concepts (see Glock 2010a). But the separation does foreclose the option of explaining concepts or modes of presentation simply by saying that the concept F, for instance, is just something that one must possess if one is to be capable of entertaining thoughts of the form ‘x is F ’. Instead, it would appear, concept-possession must be explained in terms of abilities—notably the abilities to classify and infer—which go beyond the mere capacity for having beliefs and desires. Once again the attempt to spell out the idea of modes of presentation (ways of thinking) leads us back to abilities or capacities, albeit those of a cognitive rather than practical kind. 5. The individuation of concepts In this section I consider objections to cognitivist approaches that concern the individuation of concepts. Fodor has alleged that concepts are more finely individuated than abilities. For instance, ‘creature with a kidney’ and ‘creature with a heart’ apply to all and only the same things, but they express different concepts. Furthermore, ‘equilateral triangle’ and ‘equiangular triangle’ apply necessarily to the same things, yet they still express different concepts. In current jargon, concepts are not just ‘intensional’ but ‘hyperintensional’. Now, an ability is individuated by reference to its exercise. But, Fodor maintains, the same sorting and inferential performances can manifest the possession of different concepts. Confining ourselves to the ability to sort or discriminate, sorting equilateral triangles from all other figures is also sorting equiangular triangles from all other figures (2003, 25f., 143–6). It seems to follow that concepts cannot be individuated by the exercise of an ability, and hence that they cannot be individuated by reference to abilities. In effect, Fodor’s objection runs as follows: P1: Abilities are individuated by their exercise (ability to ) = ability to < iff )ing =
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P2: One and the same sorting activity can manifest different concepts. C: Concepts cannot be individuated through the abilities which constitute their possession. The argument is valid. Yet P2 is arguably false. At any rate, the example that Fodor uses to establish P2 fails, because—contrary to what he supposes—it involves not merely one but two activities. Sorting triangles according to lengths is not the same activity as sorting triangles according to angles, even though the results are the same. The difference in the two activities can be displayed by linguistic creatures, who can justify their sorting along different lines. It can even be manifested in non-linguistic behaviour. A creature that sorts on account of measuring lengths applies equilateral triangle, a creature that sorts on account of measuring angles applies equiangular triangle. These are different activities, manifesting different abilities and thereby the possession of different concepts.5 And it is obvious that one can have one of these abilities or concepts without having the other. Indeed, most children actually learn how to measure lengths before learning how to measure angles. Individuation also poses another challenge to identifying concepts with abilities. Many cognitivists grant that there is no precise way of individuating abilities. Thus Travis (2000) concedes that linking concepts to abilities may not be much help in individuating concepts, since it is not clear how abilities are to be counted. That concession needs to be put in perspective, however. Like Travis, Geach (1957, 15) accepts that it is absurd to ask how many abilities are exercised in a judgement. Yet he also insists, rightly, that we can still distinguish between such abilities. More generally, one must distinguish between the possibility of enumerating and the possibility of individuating entities of a particular kind (see Strawson 1997, ch. 1; Glock 2003, 47–52). And this general lesson applies equally to abilities. Still a problem remains. It is prima facie plausible to hold that we are able not only to distinguish the concept of a dog from that of barking, but also to specify that precisely two concepts are involved in judging that (1) Dogs bark. 5. Benjamin Schnieder informs me that Sober (1982, 185f.) makes a similar point in a different context.
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So concepts and abilities seem to come apart on the issue of enumerability. This verdict can be contested, however, on the grounds that it does not compare like with like. The claim that the number of concepts involved in (1) is determinate is only even remotely plausible if we confine ourselves to predicative concepts (otherwise we have to add at least one quantitative concept that corresponds to the plural in English; alternatively, if we analyse (1) with the help of Fregean logic, we need to add the logical concepts of universal quantification and of material implication). But the very same consideration applies to abilities. It is just as plausible to insist that precisely two predicative abilities are involved in judging that (1)— namely that of thinking about dogs and that of thinking about things that bark—as it is to maintain that precisely two predicative concepts are involved in (1). Accordingly, individuation is no obstacle to the idea that concepts are a kind of ability. How does the Neo-Fregean association of concepts with the sense (Fregean terminology) or meaning (pre-theoretical terminology) of a general term fare here? While concepts cannot be identified with ‘meanings’ (Glock 2010b, 315), it is plausible to hold that the criterion for the identity of concepts coincides with the criterion for the identity of the meaning of expressions that express concepts: (Concept-Identity2) Two general terms ‘F’ and ‘G’ express the same concept iff ‘F’ and ‘G’ are synonymous. Alas, the criteria for synonymy are as contested as those for the identity of concepts. What is uncontroversial is a point enshrined in the contrast between (Property-Identity) and (Concept-Identity1). Both concepts and meanings are more finely individuated than properties. One way of capturing this is loosely inspired by Frege’s (1979, 197) idea of ‘equipollence’. (Equipollence) Two general terms ‘F’ and ‘G’ are synonymous iff they are ‘equipollent’ or cognitively equivalent: anyone who understands them both accepts that they can be substituted salva veritate, independently of contingent facts, in all declarative sentences (except for special cases, e.g. when ‘F’ or ‘G’ are mentioned rather than used). Wittgenstein can be interpreted as countenancing (Equipollence). Unlike current orthodoxy, however, he would deny that this principle individuates
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concepts as finely as the thesis of their hyperintensionality has it. According to him, mathematical proofs effect concept-formation. By accepting ‘All and only equilateral triangles are equiangular triangles’ as a geometrical theorem, we have modified the meaning of the terms ‘equilateral triangle’ and ‘equiangular triangle’ in such a way that a locution like ‘x is an equilateral triangle but x is not an equiangular triangle’ is not just false, but downright nonsensical. By the same token, once the theorem has been accepted, one cannot fully understand the two terms without recognizing that they are necessarily co-extensional. Accordingly, (Equipollence), would yield that ‘equilateral triangle’ and ‘equiangular triangle’ are synonymous and express the same concept. The moot question is: by what standards does someone who fails to recognize that all equilateral triangles are equiangular evince linguistic misunderstanding of the term ‘equilateral triangle’? Wittgenstein’s own criteria for understanding require only the ability to apply the term—notably by distinguishing equilateral triangles from other types—and the ability to explain it. They do not require knowledge of (all of ) its conceptual connections with other geometrical terms. Wittgenstein’s own emphasis on explanation points the way forward. The meaning of an expression is what the explanation of meaning explains (see 1953, § 560). And the proper explanation of the meaning of ‘equilateral triangle’ differs from the proper explanation of the meaning of ‘equiangular triangle’. A correct and canonical explanation of ‘equilateral triangle’ is ‘closed figure with three straight sides of equal length’, but not ‘closed figure with three identical internal angles’. This route is in line both with the individuation of abilities that I invoked against Fodor and with (Concept-Identity1). The concept of an equilateral triangle and that of an equiangular triangle are different concepts, since thinking of x as a figure with three sides of equal length is different from thinking of x as being a figure with three identical internal angles. At the same time, Wittgenstein’s stress on explanation helps to block unwanted subjective interferences that threaten the Neo-Fregean criterion and which are encouraged in particular by the idiom of ‘ways of thinking’. On pain of psychologism we must avoid conceding that whether or not thinking of something as F is thinking of something as G depends on contingent mental associations. To illustrate the problem, consider the question of whether the concept half-empty is the same as the concept halffull. Künne insists that they are not the same, since the contrast between
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optimists and pessimists shows that to think of something as half-empty differs from thinking of it as half-full (2005, 265). But the difference between positive and negative connotations of a term is merely one of colouring. For surely optimists and pessimists attach the same sense to phrases like ‘in the new year’, contrasting associations notwithstanding. The Wittgensteinian criterion of canonical explanation is more pertinent. From this perspective, it is plausible to hold that both terms have a single canonical explanation and hence express the same concept X is half-full/-empty (of Y):= 50% of X’s volume is taken up (by Y). Admittedly, one might insist that two canonical explanations are in play here: X is half-full (of Y):= 50% of X’s volume is taken up (by Y). X is half-empty (of Y):= 50% of X’s volume is not taken up (by Y). Yet the initial explanation can serve to introduce both ‘half-full’ and ‘halfempty’. And only someone committed to the non-equivalence of ‘halffull’ and ‘half-empty’ seems to have a reason for insisting that this initial explanation is ambiguous. At the same time, it must be conceded that composite adjectives like ‘at least half full’ and ‘at least half empty’ can be more straightforwardly explained by using the two distinct explanations, since we can simply add ‘at least’ in both explanandum and explanans. 6. The proposition problem Unsurprisingly, given their intellectual roots, the Neo-Fregeans emphasize the role of concepts in logic, or, more generally, in inferences, whether these be formal or material. Concepts are, among other things, components of propositions (e.g. Peacocke 1999, 335). Nonetheless they face a difficulty here, which they share with other cognitivist positions. I shall call it the proposition problem. At least prima facie, neither abilities, nor rules, nor principles nor modes of presentation occur in standard propositions or statements. Of course, abilities, for instance, can occur in propositions in the sense of being mentioned in them, as in
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(4) The ability to lie convincingly is a great asset in business. But it seems that concepts occur in propositions in yet another and more pervasive way, not just as topics or referents, something the proposition is about, but as components. The concept of being sweet occurs in the proposition that (5) Sugar is sweet even though no ability occurs in it. The same holds for modes of presentation. How can concepts be both modes of presentation and components of propositions? Orthodox Fregeans might dismiss the problem by insisting that propositions themselves are modes of presenting, namely of truth-values. But that dismissal seems to presuppose the dubious idea that sentences refer to truth-values. Furthermore, even if that idea were acceptable in the context of Fregean theories of meaning, the established notion of a proposition with which I am concerned here, is definitely not that of a mode of presentation. Leaving aside Fregean orthodoxy, there are two ways of responding to the proposition problem, which are associated, respectively, with the figureheads of Strawson and Wittgenstein. I shall argue that in combination, these responses promise to resolve the ‘proposition problem’, which would otherwise seem intractable. If Strawson is to be trusted, universals like properties can enter a proposition not just in the direct sense that the sentence expressing the proposition contains words or phrases referring to the property of being F, but also in the less direct sense that the sentence contains words or phrases signifying them (see Strawson 1959, Part II). Künne extends this idea to concepts. A sentence may contain a general term expressing the concept F, even though it does not refer to that concept. And, following the NeoFregean proposal, this means that the predicate in (5) expresses a mode of presentation (way of thinking), either of the property of being sweet or of substances as possessing the property of being sweet. Something like the distinction between referring and expressing is a prerequisite for capturing the different semantic properties or dimensions of general terms. Nonetheless the Strawson–Künne solution to the proposition problem immediately faces two challenges. First, why not extend the courtesy of being allowed to enter into a proposition indirectly from ways of thinking to all otherwise plausible
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candidates for being concepts, notably abilities or rules? Secondly, why should one accept that any of these candidates feature in all propositions, however indirectly? A partial response to the first challenge can be given by appeal to the relationship between concepts and general terms. It is perfectly commonplace to speak of words as expressing concepts. And there is no violent infelicity in speaking of general terms as expressing ways of thinking or even modes of presentation. The same goes for rules of classification and/ or inference. Perhaps one of these notions comes closer to capturing the ordinary meaning of ‘concept’, yet it is not on account of the possibility of being expressed by general terms. By contrast, general terms cannot be said to express an ability. Conceptual abilities are possessed by cognitive subjects, and they are manifested by the mental activities—notably the judgements and inferences—of such subjects. And we might say that those activities manifest concepts indirectly, keeping this relation apart from the expression of concepts by general terms. The notion of a conceptual ability points to the subject of conceptual thought and to the activity (in a suitably loose sense of the term) of conceptual thinking. It is out of place, however, when it comes to the content of conceptual thought, which is precisely what the idea of concepts as components of propositions points to. What we still need is a way of reconciling the mental or cognitive dimension of concepts with the objective dimension suggested by their occurrence in propositions. This takes us straight to the second challenge. So far we have at best removed an obstacle to claiming that concepts can be ways of thinking and yet appear in propositions. But what positive reasons do we have for accepting that ways of thinking appear in propositions, let alone as components of propositions? The answer, I submit, is that the idiom of concepts as ‘components’ of propositions is misleading. Ultimately, both propositions and their components are logical constructions out of the practices and abilities of concept-exercising creatures. What is the rationale for speaking about concepts and propositions and for parsing propositions into concepts? These notions are helpful in accounting for facts like the following: first, different people can think the same thing—that is, share the same thoughts; secondly, they can entertain thoughts which, though different, stand in logical relations to each other; thirdly, they can do both of these things without sharing a language. When a monoglot Anglophone A and a monoglot Germanophone B both believe that
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(6) Cats are animals then they share a thought. Similarly, if A believes that (7) Cats are mammals and B believes that (8) Cats are vertebrates then what B believes follows from what A believes. These facts are easily explained in terms of propositions and concepts. A and B can both believe that (7) because they have both mastered the concepts that occur in (7), irrespective of the fact that they express them through different words (e.g. ‘mammal’ vs. ‘Säugetier’). What A believes entails what B believes because of the relations that obtain between the concepts that occur in (7) and (8). The most straightforward explanation of these features appears to be ‘the building-block model’ of propositions and concepts.6 According to this model, what a subject believes (the content of A’s belief ) is a proposition or thought, a complex (abstract) object of which concepts are the components; thus the thought that dogs bark is a complex abstract object of which the concepts DOG and BARK are abstract parts. By a similar token, A’s state of believing is a mental process of accepting the whole proposition, and thinking one of the component concepts is a stage in this process; thus to believe that dogs bark, A must think DOG and think BARK. In summary, if A believes that p, then she stands in a relation of grasping and accepting an abstract entity, a proposition, of which concepts are (equally abstract) components. It follows that one cannot grasp or accept the whole proposition without having or grasping its constituent concepts. Its popularity notwithstanding, however, the building-block model is problematic. There are both empirical and conceptual qualms about the idea that entertaining a part of a thought correlates with a definite stage of a more protracted mental or neuro-physiological process—the entertaining or judging of the whole thought. As Künne has remarked, ‘the complexity of a judgment is not like that of a melody but rather like that of a chord. In judging that the moon is round you simultaneously exercise 6. As far as I can tell, the dismissive phrase ‘building-block theory’ goes back to Davidson. See his 1984, 4, 220.
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your ability to think of the moon and your ability to attribute roundness. In this respect episodic thinking is different from saying’ (1996, 75).7 Even if these points could be waved, we would only be dealing with stages of thinking a thought (of believing that p), not with stages of thoughts (of what is believed, namely that p). As regards the latter, the building-block model transposes the part/whole relation from the spatial and temporal sphere to a sphere—that of abstract entities—to which, ex hypothesis, neither spatial nor temporal notions apply. What seems to give sense to talk of parts and wholes in the case of propositions or thoughts is the fact that the linguistic expressions of thoughts—namely sentences—have components—namely words (see Kenny 1989, 126f.). What is said or thought has genuine components to the extent to which its linguistic expression has components. These ‘conceptual components’ are, for instance, what A explains when A is called upon to explain what she has asserted (queried, etc.) through the utterance of a sentence composed of words expressing the concepts concerned. Following Quine, many philosophers regard propositions as dubious entities. They are not just abstract objects, but intensional, and hence, allegedly, lack criteria of identity. Such philosophers often replace propositions by sentences as the objects of propositional arguments (cp. Glock 2003, chs. 4, 7f.). I am more inclined to challenge an assumption which the orthodox view shares with its nominalist-cum-extensionalist critics, namely that intentional verbs signify relations to either abstract or concrete objects. The idea of propositional attitudes is problematic not just, or even primarily, on account of ‘propositional’ but also on account of ‘attitudes’. For the idea that belief is a relation between a subject and an entity amounts to a reification. 7. Intentional verbs and that-clauses The most radical consideration in favour of this complaint was advanced by Prior. According to Prior, a sentence like (9) Sarah fears that there will be a nuclear war 7. There is an affinity with Wittgenstein’s remark: ‘Thought and intention are neither “articulated” nor “non-articulated”; to be compared neither with a single note which sounds during the acting or speaking, nor with a melody’ (1967, II ix 217). I owe both references to Kevin Mulligan.
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does not state a relation between two things (Sarah and the proposition that there will be a nuclear war). It is to be parsed not as (9c) Sarah / fears / that there will be a nuclear war but instead as: (9*) Sarah / fears that / there will be a nuclear war. In (9*), the apparent name, ‘that there will be a nuclear war’ is eliminated in favour of a sentence, ‘there will be a nuclear war’. And instead of the two-place predicate ‘—fears—’ it features ‘—fears that—’ as a predicateforming operator on sentences. Accordingly, ‘fears that there will be a nuclear war’ is a one-place predicate which is formed from the operation of ‘—fears that—’ on the sentence ‘there will be a nuclear war’ (Prior 1971, 16–21; see also Quine 1960, 215f.). As I shall indicate below, this analysis reveals something important about the linguistic practices which underlie the semantics of intentional verbs and that-clauses. Alas, as Künne among others has shown, it sits uneasily with English grammar (2003, 69). A less ambitious position dispenses with Prior’s questionable parsing of intentional statements, while nonetheless denying that that-clauses are referring expressions (Dolby 2007, ch. 3). This contradicts the orthodox view shared by Künne, according to which that-clauses are ‘singular terms which designate’ events, states of affairs or propositions (2003, 253f.). In my view, there is no need to give a straight Yes or No answer to the question of whether that-clauses refer. That-clauses are noun-phrases in that they can occupy the role of grammatical subjects. Yet not all grammatical subjects and not all noun-phrases refer to objects. This has long since been recognized in cases like ‘everything’ and ‘nothing’. And while the role of that-clauses may come closer to that of paradigmatic referring expressions, it also differs in crucial respects. To cut a long story short, what is said or believed is an object only in the emaciated logical sense of an object of discourse—an entity in philosophical lingo—rather than the strong sense of a material object or thing. Indeed, the analogy with the latter is even thinner than in the case of abstract objects like sets, numbers or virtues. Thus that-clauses are ungrammatical in contexts that appear to be emblematic of reference and which accept abstract singular terms, e.g. ‘The referent was …’, ‘We spoke about …’, ‘She ascribed something to
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…’, ‘It is a characteristic of …’, ‘The subject was …’ (Dolby 2007, 14f.). On the other hand, we can refer to what is said, stated or believed by that-clauses, and predicate certain things of it, e.g. that it is implausible, wonderful, unexpected, etc. In some cases we even have names for what is said (the Pythagorean theorem, Newton’s second law, Tractatus 3.5). But what is said is not like what is eaten (a cake). The word ‘what’ introduces a propositional clause, not the name of a thing. We say (believe/ judge) that such-and-such is the case. The that-clause does not have the function of introducing an object, but of specifying a sentence that can be used to say something. Contrast ‘Barack Obama is wonderful’ with ‘That the Republicans lost the election is wonderful’. In the former case, there is a thing or person which has the quality of being wonderful. In the latter case, there is no such thing or person: what is wonderful is not an object, but that the Republicans lost. It might be replied that what is wonderful here is a fact. But facts are just as clausal as what is said; indeed, the two concepts are intimately connected. If I say that p and what I say is true, then it is a fact that p. Nor can it be argued that that-clauses must refer to objects of some kind, since some of them are co-referential with names. While we can substitute co-referential expressions salva significatione even in intensional contexts, we cannot do so in the case of that-clauses and names of propositions: ‘that p is my belief ’ is well-formed, but ‘the theorem/proposition is my belief ’ is not; I can have heard of Newton’s second law, but not of that F = ma. It may seem, however, that that-clauses can occur to the left and right of the identity-sign, which is often taken to be a hallmark of referring expressions. But a statement like ‘Newton’s second law is that F = ma’ is less common and perspicuous than ‘Newton’s second law is: F = ma’. In these latter cases, the clause to the right of ‘is’ does not refer to Newton’s second law, it states or expresses it. This is part and parcel of the fact that in many contexts, that-clauses are eliminable without change of sense or truth-value: ‘A believes that F = ma’ { ‘A believes F to equal ma’; ‘A expects that B will come’ { ‘A expects B to come’; ‘A suspects that there is foul play’ { ‘A suspects foul play’, etc. In these cases, the only things referred to are B, A, and (at a pinch) what A said or believed. Admittedly, that-clauses such as ‘that the cat went up the oak tree’ or ‘what Carl said’ are grammatically speaking the objects of beliefs. But they are intentional rather than object-accusatives (White 1972). (10) Clare Short believes Tony Blair
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entails that there is an object x such that Short believes x. In (10) the psychological verb expresses a genuine relation, since here two relata must exist, one to believe, and one to be believed. By contrast, (11) Short believes that Saddam Hussein possesses weapons of mass destruction does not entail that there is an object x such that Short believes x. Nothing in reality need correspond to the noun-phrase of (11), since the relevant state of affairs need not exist or obtain. A defender of the building-block model will dig his heels in and insist that something must exist, namely a propositional content which is a real object, though an abstract one. But this ‘something’ is a grammatical projection from that-clauses rather than a genuine object.8 Brentano was right to insist that to believe is to believe something. (11) entails that there is something Short believes. Yet in the first instance this simply means that Short cannot believe anything unless there is an intelligible answer to the question ‘What does Short believe?’ Furthermore, the wh-clause ‘what Short believes’, like ‘what Short weighs’, normally incorporates an interrogative rather than a relative pronoun. Thus ‘Prescott knows the person Short believes’ and ‘The person Short believes is Blair’ together entail ‘Prescott knows Blair’. Yet ‘Prescott knows what Claire Short believes’ and ‘What Short believes is that Saddam Hussein possesses weapons of mass destruction’ do not entail ‘Prescott knows that Saddam Hussein possesses weapons of mass destruction’, if only because one cannot know a falsehood.9 Similarly, ‘Prescott knows what Short weighs’ and ‘Short weighs 70 kg’ do not entail ‘Prescott knows 70kg’, since that sentence is ungrammatical. Neither ‘what Short weighs’ nor ‘what Short believes’ signify an object to which Short is related. By the same token, believing that p is no more a genuine relation to an object than weighing n kilograms. It might be objected that there are pertinent contexts in which ‘what Short believes’ does incorporate a relative pronoun. In conjunction with (11)
8. Pace Quine, the term ‘something’ is syntactically transcategorial: it can quantify into the positions of singular term, general term, and sentence. Only in the first case is ‘There is something …’ equivalent to ‘There is an object …’. For the complex relations between these expressions, as well as ‘exists’, ‘there is’ and ‘real’, see Glock 2003, 52–63. 9. An analogous argument against regarding knowledge of meaning as acquaintance with an object goes back to Austin. See Glock 2003, 76.
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(12) Prescott believes what Short believes entails (13) Prescott believes that Iraq possesses weapons of mass destruction. But (12) is not underwritten by our knowledge that Short and Prescott are related in the same way to an entity beyond space and time, whatever that might mean. It is underwritten by the fact that both share certain properties regarding a particular question, namely the question of whether Iraq possesses weapons of mass destruction. Even in this context, ‘what Short believes’ ultimately derives its sense from the way in which Short would or could respond to a certain question, or react in certain situations, e.g. when it comes to approving the attack on Iraq in Parliament. That different people A and B can think the same thought or hold the same belief—that p—does not mean that there is an abstract object to which they severally stand in the relation of thinking, believing, saying, etc. It just means that both A and B believe that p; that is to say, what they believe can be expressed by the same declarative sentence—‘p’. If A and B are to disagree, what A says or asserts must be what B denies. But this does not commit one to the existence of self-subsistent entities beyond space and time, but only to the conceptual truism that if B denies what A asserts, and A asserts that p, then B denies that p. 8. Propositions and concepts as logical constructions The building-block model also goes astray in assuming that the alleged objects to which subjects of belief are related are propositions. Many intentional verbs cannot be characterised as expressing a relation either to a proposition or to a sentence. It makes no sense to expect, fear or hope a sentence or proposition, at least not the same sense as to expect, fear or hope that p. And given that what I can suspect is what you can believe, this difficulty may be contagious. That is to say, it may show that even though it makes sense to believe the proposition that p, believing that p is not the same as believing the proposition that p (see White 1972; Hacker 1992). One might respond that in its philosophical usage, ‘proposition’ is a term of art which is exempted from the vagaries of certain intentional verbs in English that rule out locutions like
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(14) A fears/expects/hopes the proposition that p.10 But this invites the challenge to explain what precisely that technical term means. Worse still, because of the illicitness of (14) that challenge cannot be met by stipulating that propositions are simply what we believe, expect, hope, etc. And this in turn threatens to undermine Künne’s proposal to define propositions simply as sayables or thinkables, things that we say or think, or could say or think (2003, 249–58). The denial that what we believe is always a proposition seems to imply, however, that in cases in which we do believe the proposition that p, we have two beliefs, the belief that p and the belief ‘in’ the proposition that p. But this objection can be fended off as follows. To say that A believes the proposition that p is not to ascribe to her a belief in addition to her belief that p. Rather, it is to place her belief that p in a certain context. Believing that p is simply a matter of believing something to be so, whereas believing the proposition that p is a matter of believing something to be true. In the case of simply believing, the focus is on how things are or might be, in the case of believing a proposition, on how they have or might be stated or believed to be. Prefixing ‘the proposition’ to a that-clause ‘that p’ is appropriate only if a proposition—a sentence or statement—is already in circulation or at least in the air (see Rundle 2001). Künne has developed an ingenious way of combining a referential conception of that-clauses with an acknowledgement of the difference between ‘A believes that p’ and ‘A believes the proposition that p’. The orthodox view according to which that-clauses always refer to propositions, the latter being what we believe, is bedevilled by substitutional problems, he acknowledges. Yet these difficulties can be avoided, he insists, by treating that-clauses as ‘systematically ambiguous’. They can ‘designate’ x propositions—which may be true x states of affairs—which may be the case or obtain x events—which may occur, take place or come to pass Propositions are ‘modes of presentation’ of states of affairs (2003, 9, 249– 58). Furthermore, Künne distinguishes between the objects and the contents of intentional acts and states. In special contexts, e.g. ‘They debated the 10. In the St. John’s College discussion group, which Wolfgang attended during his sojourns in Oxford, Peter Strawson once tried to assuage nominalist qualms by insisting: ‘“Proposition” is just a term of art.’ To which Bede Rundle replied: ‘Yes, one of the black arts!’.
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proposition that p’, the apposition ‘the proposition’ is not eliminable salva congruitate. Only in these cases is the proposition designated by the clause the intentional object of the act or state, i.e. what the latter is ‘directed at’. In standard contexts, the apposition cannot be introduced salva congruitate or salva veritate. In these cases the proposition that p is the intentional content of the act or state; its intentional object being the state of affairs (2003, 258–61). One problem with this manoeuvre is that regarding standard contexts, the apposition ‘the state of affairs’ creates substitution problems no less than ‘the proposition’. (15) A hopes the state of affairs/fact that p is just as ungrammatical as (14) (see King 2002, 353; Dolby 2007, 11). At the very least, we need an argument why failure of substitution should be less calamitous in the former case than in the latter. In some cases, the incongruity resulting from insertion of ‘the state of affairs’ can at least be mitigated by adding a preposition such as ‘of ’ or ‘in’. In my view, however, this is just one further indication that all appositions for that-clauses involve a degree of reification (here understood in the non-pejorative sense of an additional linguistic construction-cum-practice taking us in the direction of paradigms of reference) that goes beyond that involved in naked that-clauses. The latter require nothing more than our practices of ascribing beliefs and of transforming oratio recta into oratio obliqua. By contrast, the former turn what is said or thought into intentional objects of various kinds—things that can be discussed, named, etc. And we should not be surprised that these additional referential constructions can make for nonsense or for a change of sense when they are combined with intentional verbs. The original locus of all intentional verbs is the less committal practice of belief ascription or oratio obliqua, and in some cases this has remained the exclusive locus. At the same time, we can, of course, take the additional step with respect to everything people can say or think. In this regard, propositions can be explained as sayables and thinkables (see Künne 2003, 318). Künne is also right to maintain that one can speak of objects in a sense which lies somewhere between the supremely logical notion of a subject of predication or topic of discourse—aka entity or, as I would prefer, thingamabob—and the everyday, weighty notion of a material space-occupant. Furthermore, his denial that propositions are the intentional objects of intentional states
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promises a solution to the proposition problem. For it paves the way for a properly low-key understanding of how concepts are involved in propositions. The crucial point is that standard sentences, and by implication our common and garden thinking, are not about either propositions or concepts. Propositions are contents of thinking, i.e. simply what corresponds to the that-clauses we use in stating what people think. By the same token, concepts are not objects of conceptual thought, but something involved in conceptual thought. As Price put it: ‘The concept is not before the mind as an object of inspection. It is at work in the mind, but not as one inspectable content among others […] It shows itself not as a detectable item of mental furniture, but rather as a guiding force, determining the direction which the series of presented particulars [mental images or words] takes […]’ (1953, 342). Indeed, the basic insight goes back at least to Aquinas, as illuminated by Kenny (1980, 71). Ideas (species) are ‘not what is thought of (id quod intelligitur) but that by which thinking takes place (id quo intelligitur)’. 9. The measurement analogy The aforementioned analogy between saying that a subject thinks that p and that a subject weighs n kg does not just pinpoint a weakness in the building-block model, it also promises to furnish the basis for a cognitivist alternative. (On the measurement analogy see Beckermann 1996 and Matthews 2007.) When we ascribe a weight to a person, we do not ascribe to them a genuine relation to an abstract object. Rather, we ascribe to the person a relation to other material objects, for instance that it would be in balance with 60 litres of water. Mutatis mutandis for the case of belief. In ascribing a belief to a person, we ultimately describe and explain their actual or possible behaviour. We place the subject not in a relation to a genuine object, but in the context of a system of describing and explaining the subject’s behaviour and behavioural capacities. In the final analysis, talk about propositions and concepts is to be elucidated in terms of what subjects think or say, or, more accurately still, could think or say. Although propositions are not themselves linguistic entities, they are akin to what Prior called logical constructions from linguistic phenomena, namely from the that-clauses by which we report and refer to what people say or think (Prior 1971, ch. 2). The criteria of identity for propositions
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make essential reference to sentences. There are propositions no one has ever uttered or thought of. But what distinguishes two such propositions is evident from the declarative sentences which express them. Although our criteria of identity for propositions are not the same as our criteria of identity for sentences, we can only identify the former because we can identify the latter. Although there are different linguistic expressions for the most important truth discovered by Newton and the most important truth discovered by Einstein, what distinguishes these two truths is evident from their expressions—‘F = ma’ and ‘E = mc2’. At this juncture a satisfactory solution to the proposition problem requires a detailed logical construction of talk about both propositions and concepts out of talk about the abilities of rational subjects. Although I do not know of any entirely convincing execution of this programme, there are several noteworthy attempts.11 I also hope to have contributed to the project here by blocking some possible objections. Assuming the feasibility of the constructivist project, let us return to the proposition problem from the perspective of the measurement analogy. In what sense can abilities, modes of presentation or ways of thinking occur in propositions? The answer is, very roughly: in the sense that S can only think that a is F if S has the capacity to think about objects as being F. Propositions are what is or can be said or thought. Concepts are ways in which subjects do or could conceive of objects as having properties. Accordingly, it is more felicitous to think of concepts as involved in propositions, in that the capacity to entertain a propositional thought involves the possession of the concept. The idea that concepts occur in propositions, by contrast, derives its sense from propositions regarded as objects rather than mere contents of thought and speech, and hence from the occurrence of general terms in that-clauses. Talk of propositions and concepts is not just a façon de parler, on this view, and propositions and concepts are not just ‘make-believe entities’ (to use what is indeed a currently fashionable façon de parler). Rather, they are logical constructions in a non-reductive sense. It may prove impossible to paraphrase concepts away. We may need to refer to them in order to describe the practices of creatures with highly evolved cognitive and/ or linguistic abilities. At the same time, the existence and nature of concepts, as well as their individuation, becomes unmysterious once their role 11. In addition to the aforementioned measurement analogy and to Prior’s own account, see, e.g., Sellars 1963; von Savigny 1983; Brandom 1998; Dolby 2007.
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within that practice and its description is understood.12 It is only possible to state what propositions and concepts are in terms which implicitly refer to what people say or do; and we identify propositions and concepts by grouping or classifying actual or potential token-expressions according to what they say or mean. On this basis we may at least hope to reconcile two apparently incompatible features of the established use of ‘concept’, the cognitive dimension and the appearance in propositions. Human beings have highly evolved perceptual and cognitive capacities which allow them, among other things, to form complex beliefs. They are also capable of expressing and communicating these beliefs through assertoric utterances, roughly, the utterance of declarative sentences. Both their behaviour and their utterances allow them to ascribe beliefs to others through oratio obliqua, adding a ‘that’ to a declarative sentence. Furthermore, the move to oratio obliqua removes the restriction to a single language that oratio recta is generally presumed to suffer from. As a result of the apparatus of oratio obliqua we can speak not just about linguistic relations between the sayings of people, but also of logical relations between what they say. It is at this juncture that talk of concepts comes into play, as an expedient abstraction for describing and explaining our linguistic practices. To sum up, I have argued against identifying concepts with abilities, techniques or rules. I have also explored the Neo-Fregean option of regarding them as modes of presentation, but concluded that it takes us back to the connection between concept-possession and abilities. Throughout, I have considered the proposition problem, i.e. how these different cognitivist approaches can do justice to the idea that concepts are components of propositions. My verdict is that this problem can be overcome by realizing that both concepts and propositions are logical constructions. That is to say, they are expedient and perhaps indispensable abstractions for describing our linguistic practices and abilities, but not bona fide objects with the former being components of the latter. 10. Methodological epilogue In the spirit of conceptual analysis I have been relying on considerations of grammaticality and substitutability throughout. It has recently been urged, 12. Here I take myself to be in line with the conclusion, if not the arguments, of Künne (2003, 258).
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however, that such considerations are insufficient to support ontological or metaphysical conclusions about the nature of things. These methodological qualms, appropriately formulated, seem to cast doubt both on some of my arguments against identifying concepts with abilities and on my diagnosis of the proposition problem. For in both cases I objected to identifying concepts with things of a kind X on the grounds that something which can be said of concepts does not hold of things of kind X, or vice versa. These qualms also seem to count against my attempt to draw conclusions about the nature of what we believe and hence about the nature of intentional states from observations about the logico-grammatical behaviour of thatclauses, in particular the fact that such clauses cannot be substituted for singular terms, including propositional descriptions. Schnieder (2006) has developed a sophisticated scepticism about attempts to draw categorial distinctions on the basis of failures of substitutability. He maintains that we cannot rule out that such arguments rely on premises which are tacitly meta-linguistic in nature and hence cannot sustain conclusions about ontological or categorial identities or differences. Schnieder challenges us to specify a difference between substitutability arguments for categorial distinctions and clearly fallacious substitutability arguments that trade on matters of linguistic propriety. Schnieder uses examples of fictional linguistic practices. This is problematic in that the precise nature of the (im)propriety can easily remain unspecified. Let me therefore turn to actual cases instead (see Glock & Hyman 1994). There are co-referential personal names, titles, etc. whose use is fixed by rules of linguistic etiquette. The employment of the wrong term on a given occasion can produce statements which are so inappropriate, insulting or presumptuous that they are greeted with ‘laughter or consternation’ (to use Schnieder’s phrase). For instance, one cannot substitute ‘David’ for ‘The Prime Minister’ or ‘is telling a lie’ for ‘is economical with the truth’ in (16) The Prime Minister was economical with the truth when making a statement in the House of Commons. But of course this does not show that David is not the Prime Minister. Now, the substitutability arguments I invoked are also meta-linguistic in nature, this is one respect in which I agree with Schnieder. But there is a clear difference. My arguments appeal not to what it is appropriate to say,
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but to what it makes sense to say, and what sense it makes.13 Whether it is licit or illicit to combine ‘David’ or ‘The Prime Minister’ with a certain predicate depends upon the social context. But whether, for instance, it makes sense to use a naked that-clause or a propositional description depends on the linguistic context, on the intentional verb. Furthermore, as argued above, the differences go along with a more general difference, namely between believing something to be the case (our eyes being on the world or states of affairs), and believing something to be true (our eyes being on what is or might be said or thought). Next, people who fail to recognize the inappropriateness of (16) in the context of the debate in the House of Commons are ignorant of a rule of linguistic etiquette. By contrast, anyone who fails to recognize the difference between, e.g., expecting that p and expecting the proposition that p, or between the extension of a concept and the extension of an ability, is ignorant of what the relevant terms mean. By a similar token, in the fallacious cases, inappropriate locutions like (16) remain perfectly intelligible: No competent speaker will have difficulties relating what was said in oratio obliqua. And benighted philosophers excepted, nobody will suspect that David Cameron undergoes a substance change by moving from a debate in the Palace of Westminster to a family dinner at 10 Downing Street. What if we change the scenario slightly by envisaging a community in which the inapposite utterances evince genuine misunderstanding? People no longer understand what was said by an utterance like ‘David is telling a lie’ made in the House of Commons. In that case, terms like ‘David’ or ‘the Prime Minister’ will no longer be singular terms referring to a flesh-andblood person the identity of which is determined by continuity in space and time. And in that case there will be genuine conceptual differences both between the current practice and the new one, and between the relevant terms as used within the latter. The differences between expressions and constructions invoked in categorial arguments are of this abstract kind. Considerations of spatio-temporal continuity cannot settle, e.g., whether the event of Sarah’s falling ill at t is identical with the fact that Sarah falls ill at t. Instead, we rely precisely on what it makes sense to say about 13. Dolby 2007, ch. 1.3 rejects Schnieder’s scepticism without accepting the meta-linguistic nature of categorical arguments. But his response shares with mine the conviction that one can meet Schnieder’s challenge of specifying pertinent differences between substitution arguments that trade merely on socio-linguistic proprieties and the substitution arguments that feature in conceptual analysis. In Dolby 2009 he also gives a compelling response to Oliver’s attack on these substitution arguments.
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events and facts, respectively. For instance, unlike events, facts cannot be located within space and time; unlike facts, events cannot obtain but do take place, etc. Still, one might hold that like epistemic concepts, ‘it does not make sense to say …’ creates an intensional context, and is therefore no obstacle to a metaphysical thesis about identity. But it is not obvious that what it makes sense to say does create an intensional context. ‘It makes no sense to say that the central truth of the theory of relativity is 2 cm long’ and ‘That E = mc2 is the central truth of the theory of relativity’ entails ‘It makes no sense to say that that E = mc2 is 2 cm long’. Unless one follows Wittgenstein, that is. While it makes sense to say that the number of planets is greater than 9, it makes no sense to say that 8 is greater than 9. In any event, however, the appeal to intensional contexts concedes that, alleged ontological identities notwithstanding, there are conceptual differences between naked that-clauses and propositional descriptions (‘the proposition that p’). Unfortunately, I do not share the enviable capacity of many of my colleagues to divine the de re essence of reality from the armchair. My a priori reflections on categories are therefore by necessity confined to delineating differences and connections within our conceptual scheme, as in Strawson’s descriptive metaphysics. But as Clint Eastwood points out at the end of Dirty Harry: ‘A man’s got to know his limitations!’14
REFERENCES Beckermann, Ansgar 1996: “Is There a Problem about Intentionality?”. Erkenntnis 51, 1–23. Bennett, Jonathan 1966: Kant’s Analytic. Cambridge: Cambridge University Press. Brandom, Robert 1998: Making it Explicit. Cambridge, Mass.: Harvard UP. Crane, Tim 2004: “Something Else, Surely”. Times Literary Supplement 07.05.04, 4. Dolby, David 2007: Propositions, Substitution and Generality. PhD thesis (University of Reading). — 2009: “The Reference Principle: a Defence”. Analysis 69, 286–96. Evans, Gareth 1982: Varieties of Reference. Oxford: Clarendon. 14. I wish to thank David Dolby, Peter Hacker, Benjamin Schnieder and Moritz Schulz for comments and suggestions. This material has also profited from discussions in Bielefeld and Berlin, for which I am grateful.
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Fodor, Jerry 2003: Hume Variations. Oxford: Clarendon. Frege, Gottlob 1979: Posthumous Writings. Oxford: Blackwell. Geach, Peter T. 1957: Mental Acts. London: Routledge & Keegan Paul. Glock, Hans-Johann 2003: Quine and Davidson on Language, Thought and Reality. Cambridge: Cambridge University Press. — 2009: “Concepts: Where Subjectivism Goes Wrong”. Philosophy 84, 5–29. — 2010a: “Can Animals Judge?”. Dialectica, forthcoming. — 2010b: “Concepts; between the Subjective and the Objective”. In: John Cottingham & Peter M. S. Hacker (eds.), Mind, Method and Morality: Essays in Honour of Anthony Kenny. Oxford: Oxford University Press, 306–29. Glock, Hans-Johann and Hyman, John 1994: “Persons and their Bodies”. Philosophical Investigations 17, 365–79. Kenny, Anthony 1980: Aquinas. New York: Oxford University Press. — 1989: The Metaphysics of Mind. Oxford: Clarendon. — 2010: “Concepts, Brains and Behaviour”. Grazer Philosophische Studien 81, 105–13. Künne, Wolfgang 1996: “Thought, Speech, and the ‘Language of Thought’”. In: Christian Stein & Mark Textor (eds.), Intentional Phenomena in Context. Papers from the 14th Hamburg Colloquium on Cognitive Science. Bericht Nr. 55, 53–90. — 2003: Conceptions of Truth. Oxford: Oxford University Press. — 2005: “Properties in Abundance”. In: Peter F. Strawson & Arindam Chakrabarti (eds.), Universals, Concepts and Qualities. Aldershot: Ashgate, 249–300. — 2007: Abstrakte Gegenstände. Frankfurt: Klostermann (1st edn. 1983). Peacocke, Christopher 1991: “The Metaphysics of Concepts”. Mind 100, 525–46. — 1992: A Study of Concepts. Cambridge, Mass.: MIT Press. — 2008. Truly Understood. Oxford: Oxford University Press. Price, Henry H. 1953: Thinking and Experience. London: Hutchinson. Prior, Arthur 1971: Objects of Thought. Oxford: Clarendon Press. Rey, Georges 1998: “Concepts”. In: Edward Craig (ed.), The Routledge Encyclopedia of Philosophy. London: Routledge. Rundle, Bede 2001: “Objects and Attitudes”. Language and Communication 21, 185–98. Ryle, Gilbert 1971: Collected Papers. Vol. II. London: Hutchinson. Saporiti, Katia 2010: “In Search of Concepts”. Grazer Philosophische Studien 81, 152–72. von Savigny, Eike 1983: Zum Begriff der Sprache: Konvention, Bedeutung, Zeichen. Stuttgart: Reclam. Schnieder, Benjamin 2006: “By Leibniz’s Law: Remarks on a Fallacy”. Philosophical Quarterly 56, 39–54. Sellars, Wilfried 1963: “Abstract Entities”. Review of Metaphysics 16, 627–71.
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Sober, Elliot 1982: “Why Logically Equivalent Predicates May Pick out Different Properties”. American Philosophical Quarterly 19, 183–9. Strawson, Peter F. 1959: Individuals: an Essay in Descriptive Metaphysics. London: Methuen. Travis, Charles 2000: Unshadowed Thought: Representation in Thought and Language. Cambridge, Mass: Harvard UP. White, Alan 1972: “What We Believe”. In: Nicholas Rescher (ed.), Studies in the Philosophy of Mind: American Philosophical Quarterly Monograph Series 6. Oxford: Blackwell, 69–84. Wittgenstein, Ludwig 1988: Wittgenstein’s Lectures on Philosophical Psychology 1946-47. Edit. by Peter T. Geach. Hassocks: Harvester Press. — 2000: Wittgenstein’s Nachlass. In: The Bergen Electronic Edition. Oxford: Oxford University Press. References according to manuscript number and page number.
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Grazer Philosophische Studien 82 (2011), 165–188.
THOUGHTS WITHOUT PARTS: FREGE’S DOCTRINE Andreas KEMMERLING University of Heidelberg Summary Does a thought à la Frege consist of parts? There are several passages in his later works which suggest an affirmative answer. However, if these passages are balanced against many of Frege’s claims concerning thought-identity and thoughtdiversity, a negative answer is more credible. For Frege, a thought proper is an amorphous entity, but one which can be decomposed, in more than one way, into parts.
Für WK, in Freundschaft und Verehrung
In this paper I want to revisit a question concerning Frege’s concept of a thought.1 The question “A thought consists of (unsaturated and completing) parts.”—Should this claim be considered as a tenet of Frege’s mature doctrine (i.e., of his theory of thought from 1892 on)? * * * 1. For my previous attempt to answer it, see Kemmerling (1990). During the past twenty years, several authors have argued for answers which seem to faintly resemble the one I gave twenty years ago. See, for example, David Bell (1996), José Luis Bermúdez, Pieranna Garavaso, Wolfgang Künne (2009), James Levine, Mark Textor and Carlo Penco. I shall not discuss, nor draw on, their claims and arguments here. Although they arrive at answers which may appear somewhat similar, their accounts differ from the one presented here. It would take another paper to compare and evaluate them in detail.—The new version has profited from comments by Kit Fine, Andreas Graeser, Wolfgang Künne, Chris Peacocke, Tobias Rosefeldt, Stephen Schiffer, Benjamin Schnieder, Moritz Schulz, Mark Siebel and Julia Zakkou. Thanks to all of them. Special thanks to H.-P. Schütt for enriching my Latin vocabulary.
Many authors, including David Bell (1987), Dalia Drai, Michael Dummett, Paul Horwich, Jeffrey King, Christopher Peacocke, Ian Rumfitt, Stephen Schiffer, Robert Stalnaker, and Pavel Tichý have answered The Question affirmatively. It seems to be widely assumed that Frege held what sometimes is called a building-block theory of thoughts: a thought consists of parts, pretty much like a stone wall consists of stones. And there is a lot of textual evidence in Frege’s writings which may seem to suggest this. I have included some of the relevant quotations in the appendix. Nevertheless, I think that this answer is mistaken. What I shall try to do in this paper is to argue that Frege held thoughts to be intrinsically unstructured entities. Although they do not consist of parts, they can be decomposed or split up into parts, like a square can be divided into triangles. In a recent paper, Wolfgang Künne, after carefully displaying several thorny exegetical problems, prefers, and therein seems to recommend, to side-step the issue. Without going so far as to scold Frege for his “partwhole talk about thoughts”, he proposes to “shun [this kind of talk] entirely” and suggests a self-made “revision” in which he tries to “preserve as much of Frege’s theory as possible” (Künne 2007; for the quotations, see 109 and 96). Preserving as much as possible of an untenable theory is a very kind thing to do, especially if it is executed by a sympathetic admirer who knows better. But Frege’s position concerning The Question is tenable, I think. Maybe Künne indeed knows better what Frege rather should have said on this topic, from an otherwise strictly Fregean point of view. (I shall not discuss the merits or, God forbid, weaknesses of Künne’s revision of Frege.) My humble aim here is just to defend Frege against the accusation of incoherence, in the light of what he has said concerning The Question.2 He doesn’t need anybody’s help on this, however well-meant and nicely done—but merely a charitable reading of what he has written. A reading which grants him, here and there, an innocent equivocation in his use of the word “thought”. At least, this is what I shall argue in the following. So what I present in the following is presented in the spirit of: amicus Wolfgang, sed magis amica fregitas. 2. There is no explicit accusation of incoherence in Künne (2007). If I get his drift, he wants to help Frege out of an avoidable muddle in which he has brought himself by talking about thought-parts.—In his exegetical work on Frege’s Logische Untersuchungen, Künne (2009) attributes to Frege a view which appears to me as very similar to the one I argue for. For more on this, see the end of this paper.
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1. How “Something consists of this and that” is to be understood here Let A be some of those things which can be decomposed into things of type (like sentences can be decomposed into words or some walls into bricks). Let’s concentrate on the simplest case, in which A consist of just two -components.3 I shall say that: A consists of the -entities B and C iff (i) B and C, if taken together in a certain manner m, are identical with A; and (ii) for any X of type it holds: if X B und X C, then there is no Y of type , such that X and Y, taken together in whatever manner, are identical with A. That is to say: A consists of B and C, iff there is no decomposition of A into things of type which yields -components different from B or C. (That is not to say that there is only one way of decomposing A; for it is not excluded that there are two different manners in which A can be decomposed into B and C.)4 This characterization is not meant to capture each and every feasible sense of “consisting of ”. It is designed to capture a particular sense of this phrase, one which is apt for the purpose at hand. “Consisting of ”, as used in our question, must mean something more demanding than just “being decomposable into”, at least if we accept that a sheet of paper is decomposable into halves (upper/lower, front/back, left/right, etc.), although it does not consist of halves-tout-court (but only of sufficiently specified halves). It is completely uncontroversial that Frege held thoughts to be decomposable, in the weak sense just hinted at. What is contentious is whether he held them to consist of parts, in the stronger sense specified above.
3. “The simplest case is that of a thought which consists of a complete part and an unsaturated part.” (NS 262) 4. So a soccer team A (in a particular match) consists of the eleven players B and the substitutes C; but it may happen that B and C are also what results, if A is decomposed into those who played in the previous match and those who didn’t.
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2. Basics Thoughts, for Frege, are abstract entities which can be expressed by sentences but which are themselves nothing linguistic nor existentially dependent on language. They determine a truth value timelessly; they are intersubjectively accessible (in this point, Frege allows for exceptions); they are eternal and unchangeable as regards their intrinsic properties. The entities of which Fregean thoughts consist, if they consist of parts, are of two types: unsaturated and complete abstract entities. Unsaturated thought-parts are, in particular, senses of predicates; complete thoughtparts are senses of proper names. All entities divide into the unsaturated ones and the complete ones. Concrete particulars like a table or a dog, and abstract things like sets or thoughts are complete entities. All other entities are unsaturated, they are functions in Frege’s sense of this word. Examples of unsaturated entities are properties of any kind and mathematical functions. Concepts, for Frege, are functions which always assign a truth value to their arguments. Concepts are of various orders; first-order concepts have arguments which are complete entities; second-order concepts, like the one signified by the existential quantifier, have only arguments which are first-order concepts; and so on. It should be noticed here that the distinction between the unsaturated and the complete is ontologically fundamental for Frege; there is no deeper level in the order of things such that the elements of this level divide into the unsaturated and the complete. (By the way, this is why speaking, as I just did, of entities some of which are complete and some of which are unsaturated is, from a sternly Fregean point of view, at best a clumsy manner of speaking.) In particular, there is absolutely no sense in which something unsaturated could be identified with something complete. And there is no clear sense in which a function or concept could be viewed as the unsaturated version of a certain complete entity, or vice versa. What is important for us is how this distinction applies to the three realms which concern us here: language, sense and Bedeutung, i.e., the realm of what we talk about in using language. In the linguistic realm, proper names (among them sentences) are complete; predicates and other function-names are unsaturated. In the realm of sense, thoughts themselves are complete, and they can be decomposed into an unsaturated and a completing part. In the realm of Bedeutung, truth values and other objects are complete, concepts and other functions are unsaturated. Frege’s scheme is this: any proper name expresses a complete sense which in turn deter-
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mines an object; any other meaningful linguistic expression expresses an unsaturated sense which in turn determines a function. In the following I shall restrict my discussion to fairly simple sentences and the thoughts they express.5 3. Thought identity: two criteria There seem to be two candidates for a criterion of thought identity in Frege’s writings. One is mentioned in unpublished manuscripts and a letter; the other is nowhere to be found explicitly formulated, but it seems to suggest itself by many of his remarks concerning thought-parts.6 Let’s call the first the equipollence criterion: (EC)
At least for simple sentences it holds: They express the same thought iff they are equipollent (roughly: understanding the sentences involves recognizing that acceptance-as-true of any one of them commits one to acceptance-as-true of the others).
The second is the criterion in terms of thought-parts: (TPC) Two sentences express the same thought only if those components of the sentences which belong to the same category express the same sense (which is part of the thought expressed by the respective sentence). (Gloss: So if a thought consists of an unsaturated part U and a completing part C, then any sentence which expresses this thought must contain an unsaturated component which expresses U and a completing component which expresses C.) Frege expresses a slight uneasiness concerning his own use of the word “part” as applied to thoughts. Speaking this way, he says, is using a simile. But he clearly thinks that using this simile is harmless. It stands to reason, 5. There is even an exegetical excuse for concentrating on such trite sentences as the ones I shall present below. At one of the rare points at which Frege explicitly addresses our issue, he expressly restricts what he says to sentences of which “there is no difficulty in grasping their contents” (NS 213). See the appendix below. 6. For some pertinent quotations, see the appendix below. Sometimes I have changed the available English translations.
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he says, and it is, by and large, correct (or at least applicable, or appropriate; his word is zutreffend). Occasionally, the simile doesn’t quite work, but even then we hardly perceive that as troublesome (KS 378).—In brief, speaking of thought-parts is an O.K. metaphor for Frege which he accepts not only ungrudgingly but with a good grace. So I shall make no fuss about it. (The situation is crucially different, for Frege, when he feels himself driven into talking about ‘parts’ of a truth value. After explaining why this way of talking is crucially inappropriate, he hastens to add that a new expression, instead of “part”, ought to be created for what he has in mind. See KS 150f. and cf. Kemmerling 2003.) 4. A difficulty: The apparent incompatibility of the criteria That these two criteria may easily appear incompatible, can be seen by considering two simple sentences which are equipollent but express thoughts which, prima facie, consist of different parts.7 (1) Harvey is stupid. (2) Stupidity is one of Harvey’s properties.8 We can render the sense of these two sentences as
1: u2 (c1) 2: u4 (c3), 7. As instances of equipollent sentences, (1) and (2) may not seem beyond reasonable doubt. After all, Künne (2007, 117) bothered to mention in a footnote that every ‘nominalist’ will claim to be a living counter-example to my contention that the two are equipollent (or ‘cognitively equivalent’, as he prefers to put it).—I’m not convinced. I tend to doubt that anyone, even a scare-quoted nominalist, could consider himself a counter-example to a claim which is exclusively about the sense of sentences. Of course, someone may pride himself on not understanding (2), or on being able to consider it as false while considering (1) as true. But given that the vast majority of his fellow-speakers will disagree with him on his alleged feats, even he himself should have second thoughts about whether he quite understands both sentences—and not take it for granted that he does (or assume that the others don’t). My guess is that what really marks out a reflective nominalist, with or without scare-quotes, from us regular folks is not his sheer preference for (1), but his insistence on M* as the only ontologically acceptable method of decomposition among those which will be mentioned in the following. 8. This, of course, may be continued: “[Being one of Harvey’s properties] is a property of stupidity”, “[Being a property of stupidity] is a property of the property of being one of Harvey’s properties”, &c.
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if we, ‘naturally’, assume that c1 = the (complete) sense of “Harvey”; u2 = the (unsaturated) sense of “… is stupid”;9 c3 = the (complete) sense of “stupidity”; u4 = the (unsaturated) sense of “… is one of Harvey’s properties”. Given this, it clearly holds that neither the two unsaturated senses nor the two completing ones are identical, i.e. c 1 c 3 u 2 u4
1 is a natural way of representing the thought expressed by sentence (1), 2 of representing the thought expressed by (2). But the unsaturated components of the two sentences do not express the same sense, neither do the completing components. Hence in the light of (TPC) the thoughts expressed by (1) and (2) are different, although they are the same thought according to (EC). Let’s call the method of decomposition we applied in getting this undesirable result: method M:10 M-decomposition of (1): [Harvey] is stupid. M-decomposition of (2): [Stupidity] is one of Harvey’s properties. We can get rid of this difficulty by applying a different method of decomposition, namely M*: M*-decomposition of (1): [Harvey] is stupid. M*-decomposition of (2): Stupidity is one of [Harvey]’s properties. It assigns to the sentences (1) and (2) the thoughts 1 and *2, and these can be accepted as one and the same thought even according to (TPC). 9. Frege would not have appreciated this way of presenting the sameness of unsaturated senses, but let that go. 10. A method of decomposition, as I use this term here, is a way of systematically splitting up the sentences of a language into complete and incomplete constituents and assigning senses to them in such a manner that the semantical properties of, and relations obtaining among, the sentences are respected.
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The trick is this: to decompose sentence (2) not in what may seem the most natural way, but rather in a way which categorically imitates the M-decomposition of sentence (1). The upshot of all this, so far, is this. Our original way of dealing with (1) and (2) was M. This method proved to be unsatisfactory for a faithful Fregean who tries to adhere to both criteria, for it assigns to the sentences—which express the same thought, according to (EC)— senses which are different thoughts according to (TPC). To get rid of this difficulty, we introduced another way of dealing with our sentences, namely M*. According to M*, a new predicate, “Stupidity is one of ...’s properties” shows up; so, in the light of M*, the sense of (2) should be rendered as
*2: u5(c1)
[u5 = the sense of “Stupidity is one of …’s properties” = u 2]
So far, so good. M* looks satisfactory, because it assigns to both sentences the same thought, even in the light of (TPC). 5. A further difficulty Now what if we played this trick the other way round: decompose sentence (2) in the first way, i.e., according to M, and now decompose sentence (1) in a way which categorically imitates the M-decomposition of (2)?11 What we would be doing thereby, in effect, is applying a third method of decomposition which assigns to (1) and (2) the thoughts 1 and 2, and these again can be accepted as one and the same thought even according to (TPC). So, there seems to be another method of analyzing (1) and (2), in order to reach the desired result, namely M**-decomposition of (1): Harvey is [stupid]. M**-decomposition of (2): [Stupidity] is one of Harvey’s properties. 11. The point of the ensuing consideration is not to develop an objection to Frege’s position, but rather to bring to the fore a certain difficulty. In sections 6–9, I shall consider several solutions which are not in accord with Frege’s doctrines. Eventually, in section 10, I shall present a way of solving the difficulty which is faithful to the spirit and (most of ) the letter of Frege’s framework.
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M** introduces a new predicate, “Harvey is …”, and a new complete sentence-part, “stupid”.12 Accordingly, the sense of (1) should be represented as
**1: u6(c3)
[c6 = the sense of “Harvey is …” = u4]
and this is the same thought as 2. So there seem to be at least two ways of decomposing the two sentences to our satisfaction, i.e., in such a way that they express the same thought. This result gives rise to the next difficulty because each of the methods M* and M** assigns the same thought to the two sentences, but the thought assigned by the one method is, in the light of (TPC), a thought different from the one assigned to them by the other method. Assuming that (1) and (2) are univocal sentences and that (TPC) is true, not both M* and M** can be correct methods of decomposition. But Frege repeatedly claims that different methods of decomposition are equally correct. Herein lies the next difficulty. The source of this difficulty is this. It looks like Frege wanted to make all four of the following claims: (I) A univocal sentence expresses exactly one thought. (II) There are univocal sentences of the same language which express the same thought. (III) Thoughts consist of parts. (IV) There are different correct methods of decomposition. These four claims are incompatible, if we suppose that our examples are O.K., i.e., if we suppose that the following claims are acceptable instantiations of (I)–(IV): (a)
Sentences (1) und (2) are univocal, and hence each expresses exactly one thought.
12. Of course, at first sight it may look a bit surprising or even unnatural to decompose (1) in this way. But a devout Fregean should not care, as long as the application of M* at large leads to results which are as true to the semantical facts as the results one gets from applying M. After all, according to Frege’s own pet method of decomposition, in a sentence like “Everything flows”, the first word expresses an unsaturated sense which is completed by the sense of the second. Hence the prima facie artificiality of a decomposition ought not be considered as an objection against its correctness. (“If the logician wanted to pay attention to objections of unnaturalness, he would run the risk of getting tangled up in endless squabbles over what is natural—issues which […] do not belong to logic”. NS 158)
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(b) (c) (d)
Sentences (1) and (2) express the same thought. The thoughts expressed by (1) and (2) consist of parts. M* and M** are correct methods of decomposition.
In the rest of the paper, I shall discuss three ways of dealing with this difficulty. 6. Option #1: Giving up (a). The indeterminacy doctrine It says: 1 and 2 are different thoughts. (1) may express both of them, as may (2). Relative to M*, (1) expresses 1, relative to M** the same sentence expresses 2. The expressing-relation which obtains between sentences and thoughts is a three place relation: “Sentence … expresses thought --- relative to method of decomposition ~~~”. It is only relative to a method of decomposition that a sentence determinately expresses a thought. Because of (IV) the choice of a method of decomposition is not determined by objective features alone; for all objective properties of and relations between sentences and thoughts are preserved by all correct methods of decomposition: truth value, entailment, identity or diversity of the thought expressed. Two speakers who grasp the thoughts expressed by the sentences of their language relative to two correct but different methods of decomposition do not thereby disagree on any factual issue. They may hold true the same sentences under the same circumstances, they may accept the same sequences of sentences as valid inferences, and they may regard the same sentences as expressing one and the same thought. If one person, in understanding sentence (1), grasps the thought 1, whereas someone else grasps 2, this doesn’t have a bearing on any factual issue concerning Harvey’s cognitive abilities. Since the choice of a method of decomposition is not a matter of objective factors alone, and since a sentence expresses exactly one thought only relative to a method of decomposition, it is objectively indeterminate which thought is the sense of a given sentence. 7. Why the indeterminacy doctrine should not be ascribed to Frege There is no textual evidence whatsoever that Frege held such a view. He never mentions what would be a remarkable fact, namely that simple,
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seemingly univocal sentences like (1) are semantically indeterminate as long as they are not accompanied by a method of decomposition. Even when he speaks of different correct methods of decomposition, he never claims that the expressing-relation is a three place relation and that it therefore would never be strictly true that a sentence expresses a thought. According to the indeterminacy doctrine, almost any sentence would be like a structurally ambiguous sentence of the “Flying planes can be dangerous” kind; such sentences express the thoughts they express only relative to a certain way of decomposing them. But the semantical indeterminacy here envisaged is even more dramatic than structural ambiguity: since there may be indefinitely many correct methods of decomposition, there may be indefinitely many thoughts expressed by the most harmless univocal sentence. 8. Option #2: Giving up (b). The super-determinacy doctrine It says: 1 and 2 are different thoughts. The expressing-relation which obtains between sentences and thoughts is a two place relation: “Sentence … expresses thought ---”. Sentence (1) expresses only the first one, sentence (2) expresses only the other, or possibly—if somewhat perversely—vice versa. 9. Why the super-determinacy doctrine should not be ascribed to Frege According to this doctrine, hardly any two sentences of the same language, except strictly synonymous ones, could express the same thought. (That’s why I call it the super-determinacy doctrine: Very few exceptions aside, the expressing-relation is superlatively determinate in assigning exactly n thoughts to n sentences of the same language.13)—But Frege very often points out that non-synonymous sentences may express the same thought. Here are some examples he gives between 1884 and 1914: “M gave document A to N ” / “N received document A from N ” “Alfred has not yet come” / “Alfred has not come” 13. The exceptions concern cases of ambiguity, in which one sentence expresses more than one thought, and cases of glaringly strict synonymousness (or congruency, as Frege puts it in a letter to Husserl) in which different sentences of the same language express the same thought.
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“p, but q” / “p and q” “p” / “p or p” / “p and p” “If p, then q” / “If not-q, then not-p” “Some bodies are light” / “There are light bodies” “There are men” / “There are men identical with themselves” / “Something identical with itself is a man” “There is at least one square root of 4” / “The concept square root of 4 is satisfied” / “The number 4 has the property that there is something the square of which it is” “Frederick the Great won the battle of Rossbach” / “It is true that Frederick the Great won the battle of Rossbach” Frege often insists that common language is misleading as to the identity of the thoughts expressed by different sentences. Common language is misleading in this respect precisely because the differences in the lexical material and the grammatical constructions of the sentences lure us into assuming that the thoughts expressed are different. It is of the essence of the very concept of a thought à la Frege that it captures a common content aspect of sentences which differ in other aspects of their grammar and meaning. * * * As far as I can see there is no textual evidence that Frege ever held the indeterminacy doctrine or the super-determinacy doctrine. But apart from textual evidence, it is hard to make coherent sense of the very idea that 1 and 2 may be structures of different thoughts. How would such thoughts be related to each other? They are nothing but contents, contingent contents, and they entail one another. They seem to have something in common, as regards their content. But it is hard to see, within an otherwise Fregean framework, in what their content overlap might consist. To make things vivid, think of two languages, L1 and L2, such that there is a sentence in L1 which expresses the thought 1, but no sentence which expresses thought 2. Correspondingly, in L2, there is a sentence which expresses the thought 2, but no sentence which expresses 1. These languages would not be translatable into each other. (This is an illustration of the indeterminacy doctrine, because what we are trying to imagine, in effect, are two languages with built-in methods of decomposition; L1 is a language which has built in M*, L2 is a M**-language.) Frege would have abhorred the idea of such untranslatability.
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Or think instead of a language in which there are sentences, (1) and (2), such that (1) expresses only 1, and (2) expresses only 2. (This is what the super-determinacy doctrine says about English.) A competent speaker of such a language would have to grasp different thoughts when he thinks that the one sentence is true and when he thinks that the other sentence is true. But as a competent speaker he knows, if only implicitly, that “x is stupid” analytically entails and is entailed by “x has the property of being stupid”, and that the following is a conceptual truth: stupidity is the property anyone has who is stupid, and has not if he is not stupid. Given this, and his implicit grammatical knowledge, he can derive each sentence from the other. In a purely a priori manner he can switch, as it were, from judging one of these contingent thoughts to judging the other. For Frege, this kind of switchability is precisely the mark of thought identity, as long as we deal with contingent thoughts and deal with sufficiently simple sentences expressing them. But nevertheless, let’s try to assume that (1) and (2) do express different thoughts. Barring skepticism, it could not escape the competent speaker of such a language that these two thoughts have something in common which allows for this kind of switchability. But what could this common feature of the two thoughts be? Their unsaturated building blocks are different, and so are their completing building blocks. And if Fregean thoughts consisted of parts, the nature of the common feature of these two different thoughts would seem a mystery. It would have to be something which could transcend the boundary between the realms of the complete and the unsaturated entities. Impossible! There is nothing in Frege’s framework which is beyond this division. There can be no proper name, no concept word for any component these two thoughts have in common. Nevertheless, they obviously have something in common. We couldn’t possibly say what it is. (Maybe something which cannot be said but which shows itself? Frege wouldn’t accept such a way out.) * * * God made the thoughts proper, all other is the work of men. (Ancient saying)
There is a whole lot of textual evidence that Frege held a different doctrine concerning thought identity. A doctrine according to which thoughts do
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not consist of, but can be decomposed into, parts. I call it the amorphousness doctrine. In the following sketch of it, I try to capture the spirit of what I take to be Frege’s thinking on this point. As to its letter, I shall be cavalier. (Sometimes one must restrain the impulse to inundate the reader with quotations.) 10. Option #3: Giving up (c). The amorphousness doctrine
1 and 2 are the same thought as viewed in the light of different methods of decomposition. This one thought is expressed by all sentences which are equipollent with (1). The expressing-relation which obtains between sentences and thoughts is a two-place relation: “Sentence … expresses thought ---”. All correct methods of decomposition assign the same thought to a sentence. The thought expressed does not consist of thought-parts, yet it is decomposable into thought-parts. A thought has to be decomposable in order to become the object of human cognition and communication. For human cognition and communication require judging, and judging requires predication—which in the simplest case is the act of predicating of something that it falls under a concept. In judging, we accept a thought as true, and in order to do that we have to decompose it, in the simplest case into a concept-part and an object-part. We accept that a certain predication (“Aussage”) is the True. A predication consists of parts.14 The predication of Harvey that he is stupid is not the same as the predication of stupidity that it is exemplified by Harvey. Both predications are the True,15 but they are different predications. Because predications consist of parts, thoughts must be decomposed whenever we 14. This is, as Wolfgang Künne rightly remarked in discussion, not exactly the way Frege uses the word Aussage. By this term, he refers to what is being predicated of something in a statement; so with regard to, e.g., sentence (1), he may say that in using it a certain Aussage is being made about Harvey, presumably, that he is stupid. But he variously makes it clear that there can be no Aussage without an existing object which it is about; without such an object it is merely a virtual [mögliche] Aussage, one which lacks an object (cf. for example KS 231, 352). Hence I consider this use of the term, though admittedly not in total accord with the letter of Frege’s doctrine, as vindicable even for a staunch Fregean. (It is, of course, highly revealing that Frege carefully avoids using a special word for what I call an Aussage; as he remarked in this context: “a distinct expression ought to be created for this”, KS 151.) 15. Frege is quite explicit about this. Cf. for example his “Funktion und Begriff” (KS 137) or Grundgesetze der Arithmetik, §§ 4ff.—This has to do with his view that an assertion of a sentence like (1) is to be construed as a way of saying of the truth value of the thought that Harvey is stupid that it is (identical with) the True.
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grasp them and want to make a judgement. Sentences express thoughts; they consist of words but not of subject and predicate. What is to be considered as the subject of a sentence is dependent on which predication is made by asserting the sentence. The subject is that of the referent of which something is predicated by asserting the sentence. Which predication is being made is dependent on how the thought expressed is decomposed into a concept-determining thought-part and an object-determining thoughtpart. And the decomposition is ad lib, as long as a correct method is applied. According to the amorphousness doctrine, a crucial difference has to be recognized between two aspects of linguistic reference to the world. On the one hand, there is the objective, determinate and amorphous aspect (the A-aspect), which concerns sentences, thoughts and truth values as unstructured (but “structureable”) wholes. On the other, there is the aspect (the S-aspect) under which we consider them as they play their roles in our judgments: as having a certain structure. This aspect is subject to a certain amount of arbitrariness, or indeterminacy. Let’s get back to our examples. Considered under the A-aspect, sentence (1)-as-a-whole expresses the amorphous thought which determines, say, the True; sentence (2) expresses the same thought which, of course, again determines the True. If we consider things under the S-aspect, sentences are decomposed into logical subject and predicate, thoughts into a concept-determining thought part and an object-determining thought part, and truth values into a concept and an object. (Decomposing a truth value requires, as Frege remarks in “Über Sinn und Bedeutung”, going back to the thought at issue—see KS 150—and, according to the amorphousness doctrine, it involves a decomposition of it.) Decomposition requires a way of doing it; different ways may yield different structures. If method M* is applied to sentence (1), the resulting structures—of sentence (1) as a whole, of thought , and of the True—can be represented as <<“Harvey“, „is stupid“>, <c1, u2>,
>. Whereas the application of M** yields: <<”stupid”, “Harvey is”>, <c3, u4>, >.
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Decomposing a univocal sentence into logical subject (completing part) and logical predicate (unsaturated part), however it is done correctly, does not affect the identity of the sentence: The sentence as decomposed into the predicate “… is stupid” and the subject “Harvey” is the same sentence (“Harvey is stupid”, to wit) as the sentence which is decomposed into the subject “stupid” and the predicate “Harvey is …”. (Just to give it a name, let’s call a sentence-cum-parsing, i.e., as decomposed in a certain correct way, a formula.)—Correspondingly, according to the amorphousness doctrine, decomposing a thought into a completing and an unsaturated part, however it is done correctly, does not affect the identity of the thought. Hence <c1, u2> (i.e., 1) and <c3, c4> (i.e., 2) are the same thought, the one we called . (Let’s call thoughts-cum-structure, as an hommage to Stephen Schiffer, Fregean propositions. Cf. Schiffer 2003, 22.)—Moreover, the amorphousness doctrine says that decomposing a truth value in the light of a given decomposition of a given univocal sentence does not affect the identity of the truth value. and are the same truth value. The importance of distinguishing between the A-aspect and the S-aspect becomes obvious when we consider the different identity criteria involved. The two formulae we’ve just considered are different formulae but the same sentence. The two Fregean propositions we’ve considered are different Fregean propositions but they are the same thought. And the two predications we’ve considered are different predications, but they are the same truth value. One lesson of this doctrine is this: In addressing semantical issues, we should be careful about whether we are considering things under the A-aspect (and talk about sentences proper, thoughts proper, and truth values proper) or whether we are considering things under the S-aspect (and talk about formulae, Fregean propositions, and predications). Often we consider things under a certain S-aspect (by implicitly presupposing a certain method of decomposition), but are unmindful of doing so. This seems true of Frege himself occasionally, when he talks about thought-parts in his late and especially in his last writings, without explicitly mentioning the method of decomposition he has in mind. (But commonly, it is clear enough from the context which way of decomposing he is envisaging; in the default case, it is his preferred way which he has taught us.) Moreover, although almost always he should be understood as speaking of thoughts proper, there are passages, especially in his Logische Untersuchungen, in
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which he must be read as speaking about Fregean propositions (e.g., when he speaks of “the two thoughts: A and the negation of the negation of A”, KS 377). It is the equipollence criterion which applies to thoughts proper, to thoughts ‘as they are in themselves’, if you wish.16 Therefore it is, for Frege, the ultimate criterion for thought-identity. (Remember that he held thoughts to be eternal—not merely timeless in their relation to the True and unchanging in their intrinsic properties. Thoughts were always there, even before there were human beings who would grasp them and make judgements, therein assigning them a structure, or more than one.17) Künne seems not to concur. Thoughts à la Frege are not amorphous but rather, as he puts it, polymorphous (Künne 2009, 566). What he means by this, he explains as follows: “Hence the thought expressed by the sentence ‘¬¬A’ is, as it were, polymorphous: it has the one structure [roughly: ¬¬(A)] with regard to the one decomposition of this sentence, and it has the other structure [roughly: ¬(¬A)] with regard to the other decomposition.” (Künne 2009, 583; square brackets mine). Since this seems not to point to any substantial disagreement with what I have argued for, I assume that Künne takes his preferred term to be more apt. And maybe he is right, as usually. But finally and more importantly, Frege himself, at least at one point, may seem not to concur. In “Die Verneinung” he says that in grasping a (true) thought one neither creates it nor bestows on it the interconnection of its parts; and he carries on: denn der Gedanke war schon vorher wahr, bestand also schon in der Ordnung seiner Teile, bevor er gefaßt wurde (“for the thought was true before, and hence existed already in the arrangement of its parts before it was grasped”, KS 371). This dictum does not smell, at least not heavily, of the amorphousness doctrine. Is he not saying here, 16. “By the way, singularity does not, properly speaking, belong to a thought in itself [kommt einem Gedanken eigentlich nicht an sich zu], but only in respect of a way of possible decomposition”. (NS 203) 17. In “Der Gedanke”, Frege speaks of thoughts as timeless, as eternal and as strictly atemporal , and “timeless” seems to be his favourite word, when the thought’s relation to its truth value is concerned (KS 361). In his “Logik” from 1897 he says that true thoughts are always true, and, on the same page, that they are “im wesentlichen unzeitlich”, which may mean either: by and large atemporal, or (under a somewhat less natural reading of this phrase, but one which could be defended given the rest of the sentence): essentially atemporal (NS 160). Anyway, his speaking of thoughts as eternal seems not to be just an occasional carelessness, for in one of his last published writings, “Die Verneinung”, he says twice that the thought existed before it was grasped (KS 371).
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in effect: “Thoughts in themselves do have a structure independently of how they are grasped”? No, fortunately, this is not what he says. He speaks of temporal order, not of essential inherence; not of what thoughts are in themselves, but of what comes first. I recommend to understand the dictum as follows: Methods of thought-decomposition are entities as eternal or atemporal as thoughts themselves. A thinker who is grasping a thought therein neither creates the thought nor the method of decomposition by which he grasps it; both are abstract entities which are not created by human acts of thinking. What the thinker does, in grasping the thought—in this “most mysterious act of all” (NS 157)—, is to apply just one method of decomposition, among the many methods which in principle could be applied. All this, of course, is not to say that Frege considered thoughts proper as metaphysically, or even temporally, prior to Fregean propositions. Their priority rather has to do with the concerns of logic, as Frege envisages them. What the logician is after, according to Frege, are certain laws about the interrelations of thoughts proper—interrelations which obtain irrespectively of whatever structures they admit of, but which can be recognized and formulated, by us, only if we pay scrupulous attention to the structures in which we actually grasp and represent thoughts. * * * The Answer No.
APPENDIX: SOME TEXTUAL EVIDENCE Concerning the equipollence criterion Zwei Sätze A und B können nun in der Beziehung zu einander stehen, daß jeder, der den Inhalt von A als wahr anerkennt, auch den von B ohne weiteres als wahr anerkennen muß, und daß auch umgekehrt jeder, der den Inhalt von B anerkennt, auch den von A unmittelbar anerkennen muß (Äquipollenz), wobei vorausgesetzt wird, daß die Auffassung der Inhalte von A und B keine Schwierigkeiten macht. (“Kurze Übersicht meiner logischen Lehren”, 1906, NS 213)
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Now two sentences A and B can stand in such a relation that anyone who recognizes the content of A as true must thereby also recognize the content of B as true and, conversely, that anyone who accepts the content of B must straightway accept that of A. (Equipollence). It is here being assumed that there is no difficulty in grasping the contents of A and B.
— Um nun zu entscheiden, ob der Satz A denselben Gedanken ausdrücke wie der Satz B, scheint mir folgendes Mittel allein möglich zu sein, wobei ich annehme, dass keiner der beiden Sätze einen logisch evidenten Sinnbestandteil enthalte. Wenn nämlich sowohl die Annahme, dass der Inhalt von A falsch und der von B wahr sei, als auch die Annahme, dass der Inhalt von A wahr und der von B falsch sei, auf einen logischen Widerspruch führt, ohne dass man zu dessen Feststellung zu wissen braucht, ob der Inhalt von A oder von B wahr oder falsch sei, und ohne dass man dazu anderer als rein logischer Gesetze bedarf, so kann zum Inhalte von A, soweit er fähig ist, als wahr oder falsch beurteilt zu werden, nichts gehören, was nicht auch zum Inhalte von B gehörte; … (Letter to Husserl, December 12, 1906; WB 105f.) Now in order to decide whether sentence A expresses the same thought as sentence B it seems to me that the following means is the only possible one, and I assume here that neither of the two sentences contains a logically evident sensecomponent. For if both the assumption that the content of A is false and that of B true and the assumption that the content of A is true and that of B false lead to a logical contradiction, and if in order to note this contradiction one does not need to know whether the content of A or of B is true or false, and if one doesn’t, for this purpose, require any laws except purely logical ones, then nothing can belong to the content of A, insofar as it can be judged as true or false, which would not also belong to the content of B; …
— See also Frege’s manuscript “Logik” (1897, KS 155).
Concerning the criterion with thought-parts (nowhere formulated as a criterion by Frege) Wie der Eigenname Teil des Satzes ist, ist sein Sinn Teil des Gedankens. (“Einleitung in die Logik”, 1906, NS 208)
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As the proper name is part of the sentence, so its sense is part of the thought.
— Wie der Gedanke Sinn des ganzen Satzes ist, ist ein Teil des Gedankens Sinn eines Satzteils. (loc. cit., NS 209) As the thought is the sense of the whole sentence, so a part of the thought is the sense of a part of the sentence.
— Wenn wir den Satz zerlegen in einen Eigennamen und den übrigen Teil, so hat dieser übrige Teil als Sinn einen ungesättigten Gedankenteil. (loc. cit., NS 210) If we split up a sentence into a proper name and the remainder, then this remainder has as its sense an unsaturated part of a thought. — Wie der Satz im allgemeinen ein zusammengesetztes Zeichen ist, so ist auch der Gedanke, den er ausdrückt, zusammengesetzt; und zwar so, daß Teile des Gedankens Teilen des Satzes entsprechen. So wird im allgemeinen auch eine Gruppe von Zeichen, die in einem Satze vorkommt, einen Sinn haben, der Teil des Gedankens ist. (“Logik in der Mathematik”, 1914 NS 224) As a sentence is generally a complex sign, so the thought expressed by it is complex too: in such a way that parts of the thought correspond to parts of the sentence. So as a general rule when a group of signs occurs in a sentence it will have a sense which is part of the thought expressed. — Die Sprache hat die Fähigkeit, eine unübersehbare Fülle von Gedanken auszudrücken, mit verhältnismäßig wenigen Mitteln. Dies wird dadurch möglich, daß der Gedanke aus Gedankenteilen aufgebaut wird und daß diese Gedankenteile Satzteilen entsprechen, durch die sie ausgedrückt werden. (loc. cit., NS 262) Language has the power to express, with comparatively few means such a profusion of thoughts that no one could possibly command a view of them all. What makes this possible is that a thought has parts out of which it is con-
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structed and that these parts correspond to parts of sentences, by which they are expressed.
— Die Welt der Gedanken hat ihr Abbild in der Welt der Sätze, Ausdrücke, Wörter, Zeichen. Dem Aufbau des Gedankens entspricht die Zusammensetzung des Satzes aus Wörtern, wobei die Reihenfolge im allgemeinen nicht gleichgültig ist. (“Die Verneinung”, 1918/19, KS 367) The world of thoughts is pictured in the world of sentences, expressions, words, signs. To the structure of the thought there corresponds the compounding of words into a sentence; and here the order is in general not insignificant.
— Der Satz kann als Abbildung des Gedankens betrachtet werden, in der Weise, daß dem Verhältnisse vom Teil zum Ganzen bei den Gedanken und Gedankenteilen im großen und ganzen dasselbe Verhältnis bei den Sätzen und Satzteilen entspricht. (“Aufzeichnungen für Ludwig Darmstaedter”, 1919, NS 275) We can regard the sentence as an image of the thought: corresponding to the whole-part relation of thoughts and thought-parts we have, by and large, the same relation for sentences and sentence-parts.
Concerning the correctness of different methods of decomposition Ich glaube nicht, daß es für jeden beurteilbaren Inhalt nur eine Weise gebe, wie er zerfallen könne, oder daß eine der möglichen Weisen immer einen sachlichen Vorrang beanspruchen dürfe. (Brief an Marty, July 29, 1892, WB 164) I do not think that for each judgeable content [after 1891, Frege considered his concept of a “judgeable content” as a conflation of the two concepts of thought and truth value—A.K.] there is only one way in which it can decompose, or that one of the possible ways could always claim a factual priority.
— Dies ist nur wunderbar für einen, der verkennt, daß ein Gedanke mannigfach zerlegt werden kann und daß dadurch bald dies, bald jenes als Subjekt und Prä-
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dikat erscheint. Durch den Gedanken selbst ist noch nicht bestimmt, was als Subjekt aufzufassen ist. (“Über Begriff und Gegenstand”, 1892, KS 173) This will be miraculous only to somebody who fails to see that a thought can be split up in many ways, so that now one thing, now another, appears as subject or predicate. The thought itself does not yet determine what is to be regarded as the subject.
— Es ist daher nicht unmöglich, daß derselbe Gedanke bei einer Zerlegung als singulärer, bei einer andern als partikulärer, bei einer dritten als allgemeiner erscheint. Danach darf es nicht wundernehmen, daß derselbe Satz aufgefaßt werden kann als eine Aussage von einem Begriffe und auch als eine Aussage von einem Gegenstande, wenn nur beachtet wird, daß diese Aussagen verschieden sind. (loc. cit., KS 173) It is thus not impossible that one way of decomposing one and the same thought should make it appear as a singular judgment; another, as a particular judgment; and a third, as a universal judgment. It need not then surprise us that the same sentence may be conceived as a predication about a concept and also as a predication about an object; only we must observe that these predications are different.
— Es ist aber zu bemerken, dass ein und derselbe Gedanke oft in verschiedener Weise zerlegbar ist und demnach auch in verschiedener Weise aus Teilen zusammengesetzt erscheint. Das Wort “singulär” gilt nicht für den Gedanken schlechtweg, sondern nur hinsichtlich einer besonderen Weise der Teilung. (“Kurze Übersicht meiner logischen Lehren”, 1906, NS 218) But it has to be noticed that one and the same thought often is decomposable in different ways and therefore in different ways appears to be composed of parts. The word “singular” [as in “singular thought”, i.e., a thought expressed in making a judgement about one object which is referred to by a proper name—A.K.] does not apply to the thought tout court, but only with respect to a particular way of division.
— See also “Einleitung in die Logik” (August 1906, NS 203; partially quoted in footnote 17 above), where Frege makes the same point.
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REFERENCES Bell, David 1987: “Thoughts”. Notre Dame Journal of Formal Logic 28, 36–50. — 1996: “The Formation of Concepts and the Structure of Thoughts”. Philosophy and Phenomenological Research 56, 583–596. Bermúdez, José Luis 2001: “Frege on Thoughts and Their Structure”. Logical Analysis and History of Philosophy 4, 87–105. Drai, Dalia 2002: “The Slingshot Argument: An Improved Version”. Ratio 15, 194–204. Dummett, Michael 1981: The Interpretation of Frege’s Philosophy. London: Duckworth. Frege, Gottlob 1893: (GGA) Grundgesetze der Arithmetik, I. Band. Jena: Pohle. — 1967: (KS) Kleine Schriften. Ignacio Angelelli (ed.), Darmstadt: Wissenschaftliche Buchgesellschaft. (trans. as: Collected Papers on Mathematics, Logic, and Philosophy, 1984) — 1969: (NS) Nachgelassene Schriften. Hans Hermes et al. (eds.), Hamburg: Meiner. (trans. as: Posthumous Writings, 1979) — 1976: (WB) Wissenschaftlicher Briefwechsel. Gottfried Gabriel et al. (eds.), Hamburg: Meiner. (trans. as: Philosophical and Mathematical Correspondence, 1979) Garavaso, Pieranna 1991: “Frege and the Analysis of Thoughts”. History and Philosophy of Logic 12, 195–210. Horwich, Paul 1990: Truth. Oxford: Blackwell. Kemmerling, Andreas 1990: “Gedanken und ihre Teile”. Grazer Philosophische Studien 37, 1–30. — 2003: “Das Wahre und seine Teile”. In: Dirk Greimann (ed.), Das Wahre und das Falsche—Studien zu Freges Auffassung von Wahrheit. Hildesheim: Olms, 141–153 King, Jeffrey 2001: “Structured Propositions”. Stanford Encyclopedia of Philosophy (Fall 2001 Edition), Edward N. Zalta (ed.), URL = — 2007: The Nature and Structure of Content. Oxford: Oxford University Press. Künne, Wolfgang 2007: “A Dilemma in Frege’s Philosophy of Thought and Language”. Revista di estetica 34, 95–120. — 2009: Die Philosophische Logik Gottlob Freges—Ein Kommentar. Frankfurt a. M.: Klostermann. Levine, James 2002: “Analysis and Decomposition in Frege and Russell”. The Philosophical Quarterly 52, 195–216. Peacocke, Christopher 1986: Thoughts: An Essay on Content. Oxford: Blackwell.
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Penco, Carlo 2003: “Frege: Two Theses, Two Senses”. History and Philosophy of Logic 24, 87–109. Rumfitt, Ian 1994: “Frege’s Theory of Predication: An Elaboration and Defense, with Some New Applications”. Philosophical Review 103, 599–637. Schiffer, Stephen 1987: The Remnants of Meaning. Cambridge, Mass.: MIT Press. — 2003: The Things We Mean. Oxford: Oxford University Press. Stalnaker, Robert 1984: Inquiry. Cambridge, Mass.: MIT Press. Textor, Mark 2009: “A Repair of Frege’s Theory of Thoughts”. Synthese 167, 105–123. Tichý, Pavel 1988: The Foundations of Frege’s Logic. Berlin: de Gruyter.
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Grazer Philosophische Studien 82 (2011), 189–208.
BOLZANO ON THE INTRANSPARENCY OF CONTENT1 Stephan KRÄMER University of Leeds Summary Content, according to Bolzano, is intransparent: our knowledge of certain essential features of the contents of our contentful mental acts (such as their identity and composition) is often severely limited. In this paper, I identify various intransparency theses Bolzano is committed to, and present and evaluate the defence he offers for his view. I argue that while his intransparency theses may be correct, his defence is unsuccessful. Moreover, I argue that improving on his defence would require substantial modifications to his general epistemology of content.
1. Introduction One of the most well-researched components of Bernard Bolzano’s philosophy is his theory of the contents of certain of our mental acts and states, i.e. his theory of propositions (Sätze an sich) and objective Ideas (Vorstellungen an sich). This paper is concerned with an aspect of Bolzano’s theory of content which, as far as I am aware, has received comparatively little attention in the existing literature: the thesis that content is intransparent in the sense that our knowledge of the contents of our mental acts and states is often severely limited. While it is well-known that Bolzano held this view, I know of no detailed examination of the defence he offers for it. I shall here attempt to close this gap in the literature. The main source for my discussion is Bolzano’s Wissenschaftslehre (henceforth: WL), and in particular WL III, § 350 which contains Bolzano’s most explicit discussion of his intransparency thesis.2 1. Numerous people provided helpful feedback on the material on which this paper is based. I would like to thank in particular Peter Simons, Mark Textor, Benjamin Schnieder, Moritz Schulz, and Mirja Holst. Thanks are also due to the audience at the conference on Truth and Abstract Objects: Issues from Bolzano and Frege, where I presented an earlier version of the paper. 2. A note on citation. Titles of Bolzano’s works are abbreviated; a key is provided in the
The structure of the paper is as follows: After briefly explaining the key concepts of Bolzano’s theory of content in § 2, I distinguish a number of intransparency theses that Bolzano is explicitly or implicitly committed to (§ 3). § 4 analyses Bolzano’s attempt to provide a defence for one of his intransparency theses and shows how, and under what assumptions, it can be extended to the others as well. In § 5 I evaluate the defence of intransparency and argue that it fails. § 6 briefly summarizes the paper’s main conclusions. 2. Preliminaries The core elements of Bolzano’s theory of content are his concept of a proposition and his concept of an objective Idea. Before I explain these concepts, a brief remark on terminology: Bolzano often uses ‘Vorstellung’ (idea) without qualification and leaves it to context to disambiguate between the objective and the subjective variety. I will use ‘Idea’ (capital ‘I’) for objective Ideas, and ‘idea’ for subjective ones. In quotations, unqualified occurrences of ‘Vorstellung’ are translated by ‘idea’. A proposition is the kind of thing that is grasped in an act of thinking, that is judged to be true in a judgement, or presented as true in an assertion, where it is to be understood that a proposition need not be considered in thought or expressed in speech in order for it to exist (cf. WL I, § 19: 76ff.). So if someone judges that p, the content of his judgement is the proposition that p.3 (In what follows, I shall often abbreviate ‘the proposition that p’ by ‘[p]’.) Note that these remarks are intended by Bolzano merely as an informal elucidation of the concept of a proposition, not as a reductive analysis; Bolzano explicitly says that he does not know how to give such an analysis (cf. WL I, § 23: 91). Every proposition is either true or false, but not both, and it is true or false simpliciter. In contrast to utterances or acts of thinking, which are also true or false simpliciter, propositions are non-actual, i.e. they are incapable of acting upon something. Bolzano contends that by drawing on these characteristics, we can fix the extension, though not the content, of bibliography. References to WL are made by volume, paragraph, and (where applicable) page number following a colon. 3. Bolzano calls what is judged in a judgement the matter (Stoff) of the judgement; I will use the more common term ‘content’ instead.
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‘proposition’: something is a proposition iff it is non-actual and true or false simpliciter (cf. B/Exner, 62f.).4 Bolzano thinks that both propositions and the mental acts they are the contents of are mereologically structured. Every part of a proposition which is not itself a proposition is an objective Idea. Analogously, every part of a propositional act (such as an act of judging) which is not itself a propositional act is a subjective idea.5 According to Bolzano, we can turn these observations into analyses of the concepts objective Idea and subjective idea:6 (Objective Idea—OI) x is an objective Idea l x is not a proposition & y (y is a proposition & x < y). 4. On proposition’s being true or false simpliciter, see also WL II, § 125; on actuality, see AA, 85; on proposition’s being non-actual, see WL I, § 19: 78; WL II, § 122.—The bi-conditional invites questions: Could there not be, in addition to Bolzano’s propositions, which are individuated very finely, truth-bearers which are more coarsely individuated, such as intensions? If so, the bi-conditional might be false, since intensions are also non-actual. Bolzano might reply that intensions couldn’t be true or false in the same sense that his propositions are, so the bi-conditional comes out true on the intended reading of ‘true’ and ‘false’. (In the paragraph of the WL which is concerned with the notion of truth, Bolzano does distinguish numerous senses of the terms ‘true’ or ‘false’, differing in part in what kind of thing they apply to (cf. WL I, § 24).) However, if this reply is adequate, then the non-actuality condition appears redundant, since the sense in which judgements or utterances are true or false presumably also differs from the sense in which propositions are. (Note that Bolzano usually calls judgements ‘correct’ or ‘incorrect’ rather than ‘true’ or ‘false’, where a judgement’s correctness (incorrectness) is defined as the truth (falsity) of its content (cf. WL I, § 34).—Thanks to Moritz Schulz and Mark Textor for pressing me on these points. 5. According to Bolzano, judgings are the only acts of thinking which have propositions as their complete contents; an act of merely considering whether p is about the proposition that p, which is represented (denoted) by the complete content of the act of thinking. Künne argues convincingly that we do Bolzano a favour if we modify his account so as to allow that mere entertainings of a thought have propositions as complete contents (cf. Künne 1997, 218ff.). I shall here adopt this modification and use ‘propositional act’ for both kinds of acts of thinking. 6. ‘<’ means is a proper part of.—Naturally, in the case of subjective ideas, Bolzano’s explanation appeals only to judgements (cf. WL III, § 270). On objective Ideas, cp. WL I, § 48: 216; WL II, § 128; B/Exner, 67. Note that in WL I, § 52: 228 Bolzano denies that (a variant of ) (OI) is to be seen as a conceptual analysis; I am following Künne in taking the opinion expressed in the passages mentioned before to be his considered view (cf. Künne 1997, 211). Finally, in WL I, § 48: 216; § 49: 221 Bolzano explains an objective Idea as something which can be part of a proposition. The possibility operator is redundant unless there are objective Ideas which are not (but could have been) parts of propositions which seems implausible. The fact that in WL I, § 52: 228, Bolzano himself endorses the non-modal version of the claim indicates that he also thinks that the possibility operator is redundant.
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(Subjective Idea—SI) x is a subjective idea l x is not a propositional act & ◊y (y is a propositional act & x < y). Some, but not all, Ideas are themselves composite; their parts are either Ideas or propositions. Likewise, some, but not all, ideas are composite; their parts are either ideas or propositional acts. The relation between Ideas and ideas corresponds to that between propositions and judgements: every idea has an Idea as its content (cf. WL I, § 56, 58, 61; WL III, §§ 271, 277). Given that propositional acts, ideas, and their contents are structured, how are they structured? Firstly, the structures of propositions and Ideas correspond, though only roughly, to the structures of their linguistic expressions. Only roughly, because some simple expressions have composite contents, because some natural language sentences are syntactically ambiguous, and because not all structural differences between sentences affect the content of the sentences.7 Restricting attention to structurally perspicuous expressions, we can say that if c is the content of expression e, then every significant fragment of e expresses a part of c, and the significant parts of e are arranged in the same way as their respective contents are arranged in c. Secondly, there is an exact correspondence between the structures of acts of thinking and their contents: if c is the content of an act of thinking t, then every part of c is the content of a part of t, every part of t has a part of c as content, and the parts of t are arranged in the same way as the corresponding parts of c (cf. WL III, § 281: 39; § 291: 109). It is clear that in addition to having contents, many propositional acts and subjective ideas also stand in some special relation to an expression of their respective content. When we think in words, or read a sentence with understanding, we grasp the relevant propositions, in some sense, by means of linguistic vehicles that express them (or maybe which we take to express them). Correspondingly, some of the subjective ideas that make up 7. Bolzano takes it to be obvious that the structure of expressions is a guide to the structure of their contents, he does not argue for the claim (cf. e.g. WL I, § 50: 222, § 56: 244; WL II, § 123). As for syntactical ambiguity, see Bolzano’s remarks in WL I, § 59 on ‘a painted fish’, which may mean a fish, of which there is a painting but is usually used to mean painting of a fish, and on the ambiguity of phrases of the form ‘this A’. As for insignificant structural differences: Bolzano thinks that in Ideas of the form [something which has a, b, c] (I here extend the bracketnotation in the obvious way), the property-Ideas [a], [b] and [c] are not ordered, so ‘something which has a, b, c’ expresses the same Idea as ‘something which has b, c, a’ (cf. WL I, § 58: 256f.). See also Textor 1997, 190f.
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a propositional act are likewise associated with an expression that occurs in the expression corresponding to the propositional act and that expresses (or is taken to express) the content of the idea. I shall call the expression (if any) thus associated with a given contentful mental act or state its guise. Although Bolzano does not have an official term equivalent to my ‘guise’, there is a way of interpreting the term within Bolzano’s framework. In WL III, §§ 283f., Bolzano discusses the phenomenon that an idea may renew, create, or, as I shall say, trigger another idea. When one has frequently had an idea with content c and an idea with content d at (roughly) the same time, one may come to associate ideas of these kinds so that often when one has an idea with content c, one will also form an idea with content d, which is triggered by the former. For example, if a certain song keeps reminding you of a particular event at which it was played, your hearing the song may trigger an idea of that event. Now on seeing an expression which one understands, say ‘snow’, one will usually form an idea of snow, and when one thinks of snow, one will often form an idea of ‘snow’ (or of another term expressing [snow]). Bolzano conceives of these cases of reading with understanding and thinking in words as instances of the phenomenon just described: for thinkers who are familiar with the word ‘snow’, ideas of snow and ideas of ‘snow’ tend to trigger each other (cf. WL III, § 285). It does not appear very plausible to claim that the fact that an idea or propositional act has triggered, or was triggered by, an idea of an expression of its content guarantees that the expression in question is the guise of the idea.8 Perhaps, if one is attempting to translate ‘snow is white’ into German, one’s idea of snow that is guised by ‘snow’ could also trigger an idea of ‘Schnee’. Fortunately, as far as I can tell, Bolzano is not committed to this stronger and implausible thesis. Thus, we should ascribe to him only the weaker (if less specific) claim that the relationship between a guised idea or propositional act x and its guise consists in x’s having triggered or having been triggered by an idea of an expression of its content in the right kind of way (whatever it is). 3. The intransparency theses Discussions, and endorsements, of claims to the effect that our knowledge of the contents of our mental states is often very limited can be found in 8. Thanks here to Moritz Schulz.
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many passages throughout the WL (cf. e.g. I, §64; III, §§ 280f., 350ff.; IV, §§ 554ff.). These claims play a particularly important role in Bolzano’s theory of Explanations of Ideas. The demand for an Explanation of an Idea, in Bolzano’s use of the term, is […] the demand that we specify in a way conforming to the truth whether a certain idea which we presently find in our consciousness is atomic or complex, and in the latter case, out of which further ideas and in what combination of them it is composed. (WL III, § 350: 397)9
In his discussion of Explanations, Bolzano sometimes oscillates between talk of Ideas and talk of ideas. His notion of Explanation officially applies to both. Given the structural correspondence between ideas and their contents, one presumably straightforwardly obtains an Explanation of an idea from an Explanation of its content, et vice versa. As will become evident later on, Bolzano regards knowledge of the composition of an idea as prior to knowledge of the composition of its content; that is, one explains an Idea by explaining an act of grasping it. Bolzano’s notion of an Explanation clearly is a close relative to what is nowadays usually called ‘conceptual analysis’. The latter notion is notoriously troubled by the threat of paradox: it appears that if an analysis is to be correct, analysans and analysandum have to be synonymous, but that if they are, the analysis must be trivial.10 A version of this puzzle appears in Bolzano’s discussion of the epistemology of Explanations. Bolzano concedes that it may appear very easy to figure out the composition of an Idea one grasps, but insists that experience proves this appearance to be deceptive: At first glance, one is inclined to think that a question of this kind is very easy to answer; since it seems that everybody must know whether an idea which he possesses is atomic or composed out of parts and [if complex] out of which parts and in what 9. Translations from Bolzano’s works are my responsibility. I have usually consulted, but not always stuck to, the translations in ToS or those of other commentators, and am therefore to be blamed for mistakes but not to be praised for accuracy. In key quotations, I reproduce the German original in footnotes.—‘[…] die Forderung, daß wir auf eine der Wahrheit gemäße Art bestimmen, ob eine gewisse Vorstellung, die wir so eben in unserem Bewußtsein vorfinden, einfach oder zusammengesetzt, und in dem letzteren Falle, aus welchen andern Vorstellungen und in welcher Verbindung sie aus denselben zusammengesetzt sey.’ 10. Langford 1942 is the classical source for (this version of ) the paradox of analysis. Langford’s paper is explicitly concerned with Moore’s notion of analysis, Moore replies in Moore 1942, 660–7. See also Black 1944; 1945; 1946; White 1945a; 1945b; Church 1946; Carnap 1947, § 15.
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combination of them it is put together. But experience teaches us that just this is one of the most difficult tasks. (ibid.)11
Bolzano is therefore committed to the claim that specifying the composition of an idea one presently has is often very difficult. And the context in which he endorses this claim also makes it clear why it is important to him: it forms the basis of his answer to the paradox of analysis. A bit of conceptual machinery will be useful for finding a more precise reformulation of this intransparency claim as well as the ones we will discuss later on. I shall try to capture the intransparency theses in terms of what a thinker is or is not guaranteed to be in a position to know concerning the contents of his present mental acts or states. Roughly, a thinker is said to be in a position to know something iff were he to consider it, he would know it or come to know it. This is somewhat vague, but for our purposes it is good enough. The knowledge with which the various intransparency theses are concerned is supposed by Bolzano to be often very difficult to acquire. If it is very difficult to come to know something, then one is not, in the relevant sense, in a position to know it.12 The kind of knowledge the above intransparency claim is concerned with is knowledge of the composition of an idea one presently has (or equivalently, its content). I therefore propose to reformulate the claim thus: (I-ComS—Intransparency of Composition, Specification) It is not the case that necessarily, if one has an idea x, then one is in a position to know the composition of x. Note that in order to be interesting, this claim has to be construed as restricted to ‘cognitively well-functioning’ individuals, i.e. individuals capable of a normal degree of rational reflection in a standard epistemic situation. (This point applies to all the intransparency claims I discuss in what follows.) Even when so construed, (I-ComS) is a fairly weak intransparency thesis. Notably, it is consistent with the claim that as soon 11. ‘Auf den ersten Blick möchte man zwar glauben, daß eine Frage der Art sehr leicht zu beantworten wäre; indem es doch Jeder, wie es scheint, selbst wissen muß, ob eine Vorstellung, die er besitzt, einfach oder aus Theilen und aus welchen Theilen und in welcher Verbindung derselben sie zusammengesetzt sey. Die Erfahrung aber lehrt, daß gerade diese Aufgabe eine der schwierigsten sey.’ 12. On the notion of being in a position to know, see also Williamson 2000, 95, from where I have borrowed the terminology.
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as one is confronted with a correct specification of the composition of an idea one presently has, one must be in a position to recognize it as correct. That Bolzano also rejects this latter claim is clear from his discussion of the identity conditions of objective Ideas in WL I, §64: 269ff. Bolzano here considers the thought that an Idea x is identical with an Idea y if necessarily, all and only those objects stand under x as stand under y. He points out that this thesis commits one to numerous counter-intuitive claims concerning the composition of our ideas. For example, since necessarily, all and only equilateral triangles are equiangular, the thesis implies that [equilateral triangle] is identical to [equiangular triangle] and thus that [equiangular], which is a part of [equiangular triangle], is also a part of [equilateral triangle], which is counter-intuitive. Crucially, although Bolzano takes the proposed identity criterion to be inadequate, he does not take this particular argument to decisively refute it, on the grounds that we might simply be unaware of the alleged part of our idea (cf. WL I, § 64: 272f.). Bolzano thus allows for the possibility that one may take a correct (partial) specification of the composition of an idea one currently has to be incorrect: (I-ComR—Intransparency of Composition, Recognition) It is not the case that necessarily, if one has an idea x, and is presented with a correct specification S of x’s composition, one is in a position to know that S is correct. Note also that Bolzano has to allow for this possibility in order for his response to the paradox of analysis to be satisfactory, since it seems that even a correct conceptual analysis need not be instantly recognizable as correct. At any rate, many of the Explanations Bolzano himself puts forth, such as the Explanation of [Idea] as [non-propositional part of a proposition], are certainly not immediately obvious. A slight modification of the above example also makes clear that one may have two ideas with the same content without being in a position to know that they have the same content. If this was not the case the identity thesis could be refuted by pointing out that it implies the claim that [equilateral triangle] is identical with [equiangular triangle], although it certainly does not seem as though ideas which have these Ideas as contents are content-identical. Bolzano is therefore also committed to the following intransparency thesis:
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(I-ConI—Intransparency of Content-Identity) It is not the case that necessarily, if one has an idea x and an idea y, and x has the same content as y, one is in a position to know that x has the same content as y. In addition to these claims, there is a further, stronger intransparency thesis which I think Bolzano has to accept, even though his commitment to it is less direct and explicit than in the previous cases. Consider again the case of [equilateral triangle] and [equiangular triangle]. Not only may one (rightly) doubt that these are one and the same Idea, one may also fail to be in a position to know that they have same extension; more precisely, one may fail to be in a position to know the proposition expressed by ‘All and only equiangular triangles are equilateral triangles’ under the guise of that sentence.13 It is clear from Bolzano’s discussion in the mentioned passage that he does not regard even this as establishing the distinctness of the Ideas in question. But of course, even one who is not in a position to have this knowledge may at the same time be in a position to know the proposition expressed by ‘All and only equiangular triangles are equiangular triangles’ under the guise of that sentence. Bolzano is therefore also committed to the following intransparency claim: (I-Eqv—Intransparency of Equivalence) It is not the case that necessarily, if one attaches the same proposition x to sentences S and T, then if one is in a position to know x under the guise of S, one is in a position to know x under the guise of T. Note that again, the paradox of analysis would appear to force Bolzano to accept this claim: it is plausible that misleading evidence may prevent one from being in a position to know even the extensional adequacy of a correct analysis. (Some have argued that there are actual counter-examples to the claim that knowledge requires belief, but no one has ever taken the mere fact that some philosophers believe there to be such counter-examples to establish, by itself, the falsity of analyses of knowledge which entail that knowledge requires belief.)
13. Here and in what follows, ‘knowing a proposition x’ is to be understood not in the sense of acquaintance with a proposition, but as equivalent to knowing that p, where the proposition that p = x.
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4. The defence of intransparency We have seen that while Bolzano concedes that it is prima facie very plausible to think that the composition of one’s present ideas is the kind of thing one must be in a position to know, he thinks that experience shows otherwise. By itself, this does not constitute a satisfactory defence of intransparency. Firstly, even if Bolzano is right about what experience shows, it is still puzzling why it is hard to know the composition of one’s ideas. His view would thus be significantly strengthened by an account of why our pertinent intuitions are misleading. Secondly, I don’t think it is obvious that Bolzano is right about what experience shows. It is clear, perhaps, that we know from experience that conceptual analysis is hard; this is part of what makes the paradox of analysis a paradox. But from this it only follows that knowing the composition of one’s ideas is hard given that Bolzano’s account of conceptual analysis is correct. That Bolzano’s account is correct, however, cannot simply be taken for granted. It is certainly conceivable that what we do when we try to analyse certain concepts is not accurately described as an attempt to specify the composition of our acts of grasping these concepts. A satisfactory defence of intransparency must therefore tell us both why the transparency claims appear so plausible, and why this appearance is deceptive. Bolzano comes closest to providing an explicit answer to these questions in the following passage: Because most of our ideas do not achieve clarity, or, what means just the same, are not intuited by us; so the same often holds for those part-ideas (Theilvorstellungen) out of which some other [idea] is composed, even in the case where we intuit the latter, insofar as it is a whole. But if we do not intuit each of the parts of an idea individually, then it is no wonder that we also cannot make the judgement that those ideas occur as parts in [the complex idea]. (WL III, § 350: 397f.)14
The phrase ‘one cannot make the judgement that p’ is here most naturally understood in such a way that one’s being able to make the judgement that p implies that one is in a position to make the judgement and thereby 14. ‘Denn weil die meisten unserer Vorstellungen sich nicht zur Klarheit erheben, oder was eben so viel heißt, nicht von uns angeschaut werden: so geschieht dieß auch häufig mit jenen Theilvorstellungen, aus welchen irgend eine andere zusammengesetzt ist, selbst in dem Falle, wenn wir die letztere, sofern sie ein Ganzes ist, anschauen. Schauen wir aber die Theile, aus denen eine Vorstellung bestehet, nicht einzeln an: so ist es begreiflich, daß wir auch nicht das Urtheil, diese Vorstellungen seien in jener als Theile vorhanden, aussprechen können.’
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come to know that p. Bolzano’s suggestion then seems to be that as soon as one appreciates that in most cases, the parts of our complex ideas are not clear, one should no longer find it surprising that one is often not in a position to know how one’s ideas are composed.15 We can capture his proposal by the following theses: (T1) Most of one’s ideas are not clear. (T2) One can make the judgement that a complex idea one presently has is composed in such and such a way only if its parts are clear. (T3) (T1) and (T2) jointly make it unsurprising that one is often not in a position to know the composition of one’s ideas. If true, (T1)–(T3) would constitute an adequate defence of the first of Bolzano’s intransparency claims, (I-ComS). In § 4.1, I examine the notion of clarity Bolzano’s account invokes; § 4.2 uses the results of this discussion to further spell out (T1)–(T3) and then shows how the proposal might generalise to the other intransparency claims as well.16 4.1 The explication of clarity A subjective idea is clear (klar), according to Bolzano, iff its bearer has an intuition of it (cf. WL III, §280: 29):17,18 (Clear) If a person x has a subjective idea y then y is clear (at t) iff x has an intuition of y (at t).19 15. If (and when) a thinker knows how and of what parts an idea he presently has is composed, Bolzano calls the idea in question ‘distinct’ (cf. WL III, § 281: 40f.). 16. For more recent defences of the intransparency of content—often focussing on principles akin to (I-Eqv)—see e.g. Burge 1978, Burge 1986, and Williamson 2006. 17. ‘Intuition’ is a technical term of Bolzano’s. I trust that in what follows, context makes it clear whether the Bolzanian use of ‘intuition’ is intended, or the more common one that is in play when I speak of, for example, our intuitions contradicting the intransparency theses. 18. For a very thorough discussion of Bolzano’s notion of clarity, as well as his related notion of an idea’s distinctness, which goes into much more detail than I do here, see Centrone forthcoming. 19. The relativization to a time is not explicit in Bolzano. It is strictly speaking required, though, as Centrone points out, since no idea is ‘born’ clear, but becomes clear if and when its bearer forms an intuition of it (cf. Centrone forthcoming, § 2).
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A (subjective) intuition is a subjective idea which has an (objective) Intuition as content; an Intuition is an Idea which is both singular, i.e. exactly one object stands under it, and atomic.20 Paradigmatic examples of Intuitions are the Ideas expressed by the demonstrative ‘this’ in a context of utterance; Intuitions of one’s subjective ideas can also be expressed by ‘this’ (cf. WL I, § 72: 326f.; III, § 280: 38f.).21 (Clear) is not meant to be a mere stipulation, nor is it intended to capture precisely an ordinary use of ‘clear’, as applied to ideas. Bolzano suggests that in every-day life, ‘clear idea’ is used to express a variety of different concepts, and seeks a definition of the kind Carnap would later call ‘explication’, i.e. he tries to define the term in such a way as is most useful for scientific purposes (cf. WL III, § 280: 25).22 Bolzano approximates the intended sense of ‘clear’ by saying that an idea is to be called ‘clear’ iff its bearer is aware of it. The awareness in question, he argues, ought not to be construed as requiring that the thinker judges that she has this idea, since whether or not such a judgement is made depends in part on accidental aspects of the situation. It ought to be both necessary and sufficient for a thinker’s being aware of an idea, Bolzano suggests, that she would make such a judgement if she had any cause to do so (cf. WL III, § 280: 27). In my terminology, this means that a thinker’s idea is to be called ‘clear’ iff she is in a position to judge that she has it. Bolzano’s argument that (Clear) underwrites this bi-conditional is as follows:23 Any judgement to the effect that I have a certain idea x must have a component under which x and only x stands. So, Bolzano contends, I am, in the relevant sense, in a position to judge that I have x only if I have a singular idea of x. But not any idea which represents x exclusively makes one aware of x. Suppose that of all my present ideas, x is the one whose content I have grasped most often. It is plausible that merely forming an idea with the content [the present idea of mine whose content I 20. In Bolzano’s terminology, objects stand, rather than fall, under Ideas representing them. 21. For more on ‘this’, see WL I, §§ 59, 68 and the detailed discussion of Bolzano’s notion of Intuitions in Textor 1996, ch. 2. 22. In a long first note to § 280, Bolzano also discusses in detail how his explication of ‘clear’ relates to those of previous authors, stressing in particular its similarities to Descartes’ acceptation of the term as well as its strong dissimilarities to Leibniz’s. For a detailed examination of Bolzano’s and Leibniz’s notions of clarity, see Centrone forthcoming. 23. Bolzano does not accept the bi-conditional as an Explanation of [clear] because such an Explanation would present as a part of [clear] the idea of a judgement to the effect that one has the respective idea. This is in tension, he claims, with the fact that such a judgement need not actually be made in order for an idea to be clear (cf. WL III, § 280: 27).
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have grasped most often] does not make me aware of x; as Bolzano points out, I may form such an idea without so much as knowing the idea it represents (ohne [die Vorstellung] zu kennen; WL III, § 285: 28f.). What makes the idea unfit to ‘clarify’ x, Bolzano claims, is that it is in virtue of the idea’s specific composition that it represents x and only x. This leads him to demand of clarifiers not just that they are singular, but also that they are atomic, i.e. intuitions (cf. ibid). It is not clear that the restriction of the title ‘clarifier’ to atomic ideas of ideas is well-motivated. If the awareness of an idea Bolzano wants to capture is supposed to be a kind of direct awareness, then it does seem plausible that only atomic ideas can serve as clarifiers. But if Bolzano merely wants to rule out ideas of ideas which one can have without knowing the idea they represent, then the exclusion of all complex ideas may be unwarranted. For if knowing the represented idea is knowing which idea is represented, and if one knows that if one knows that the represented idea is, say, my present idea of a pen, then ideas whose content can be expressed by ‘my present idea of F ’ are also suitable as clarifiers.24 For the moment, we can set this issue aside, but we shall later encounter more reasons to think that ideas representing ideas in terms of their contents are perhaps more pertinent to the relevant kind of reflection on one’s present thinking than Bolzanian intuitions. 4.2 Explaining away the counter-intuitions We can now return to Bolzano’s defence of intransparency. We saw that in order for his position to be satisfactory, it needs to explain why transparency, if it is false, nevertheless seems intuitively plausible. Bolzano’s answer, recall, consists of the following claims: (T1) Most of one’s ideas are not clear. 24. On these issues, see also Dähnhardt 1992, 61ff. and Textor 1996, 114.—Note that one might even wonder whether and how intuitions of ideas make one aware of their objects. Suppose I have an idea of a ball and I make a judgement to the effect that I have this idea, in which the idea is represented by an intuition. What is the content of such a judgement? Intuitions of ideas can be expressed by ‘this’, so the proposition in question can be expressed by ‘I have this (idea)’ (cf. WL III, § 280: 38f.). Intuitively, if I am to be said to be aware of my idea of a ball, I should also be able to say something more informative, for example: I have this/an idea of a ball. That is, I should be able to characterize the idea I am aware of in terms of its content. Intuitions thus can only be clarifiers if my intuiting the idea somehow guarantees that I know a way to express the content of the idea. How this might work is not obvious to me.
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(T2) One can make the judgement that a complex idea one presently has is composed in such and such a way only if its parts are clear. (T3) (T1) and (T2) jointly make it unsurprising that one is often not in a position to know the composition of one’s ideas. An idea’s being clear consists in its bearer having a kind of introspective awareness of the idea. (T1) then says that we often lack this kind of introspective awareness of our ideas, and (T2) says that this kind of introspective awareness is required if one is to be able to judge the composition of one’s ideas.25 According to (T3), (T1) and (T2) jointly make (I-ComS) unsurprising; that is, recognizing the truth of (T1) and (T2) undermines the intuitive support for the negation of (I-ComS). Whether (T1)–(T3) are plausible will be discussed in the next section. In the remainder of this section, I want to ask whether if they are correct, the defence of (I-ComS) generalises to the other intransparency claims Bolzano is committed to. The most obvious strategy for arguing that it does is to try and show that these intransparency claims follow from (I-ComS). So let us see how one could defend this idea. (I-ComR) says that even when confronted with an adequate Explanation of an idea one presently has, one need not be in a position to recognize it as true. This follows from (I-ComS) just in case recognizing an Explanation as correct requires that one first comes to know how one’s idea is composed in order to then judge the proposed Explanation against this knowledge. This suggestion has at least some plausibility; the only way I see in which it could be false is if one could come to know that two of one’s ideas are content-identical without first ascertaining the composition of each. If this is not a possibility, the defence of (I-ComS) will apparently generalise to (I-ComR), and equally to (I-ConI), which says that one is not always in a position to know that two of one’s ideas have the same content even if they are in fact content-identical.26 25. On a strong reading, (T2) has obvious counter-examples. Suppose I am aware of my present idea of an F and I know that every idea of an F is an idea of a G which is H. I can then infer how my idea of an F is composed independently of any kind of introspective awareness of its parts. On Bolzano’s view though, this way of coming to know how an idea of mine is composed is parasitic: it depends on knowledge which one standardly acquires by figuring out the composition of just such an idea. The objection therefore misfires if, as is plausible, Bolzano is talking about the canonical way of coming to know the composition of an idea. 26. There are some passages in WL which suggest that Bolzano does hold that knowledge of the composition of ideas is prior to knowledge of content-identity between ideas. For example, when discussing the thesis that necessarily co-extensive ideas are identical, Bolzano considers whether ‘perhaps the difference we make between so-called equivalent ideas consists merely
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Finally, let us consider (I-Eqv), which says that one may fail to be in a position to know some proposition under the guise of some sentence even if one is in a position to know it under the guise of some other sentence. This claim does not follow in any straightforward way from any of the previous intransparency claims: coming to know a proposition which one already knows under some guise under an additional guise does not require prior knowledge that the guises (or one’s propositional acts guised by them) are content-identical. Nevertheless, it is not absurd to think that our intuitions against (I-Eqv) are based on the thought that one must be in a position to know the relevant content-identities: if one can fail to be in a position to recognize the content-identity, what intuitive reason is there to deny (I-Eqv)? If there is no such reason, the defence of (I-ComS) extends to (I-Eqv) as well. 5. Objections Bolzano’s defence of intransparency rests on the claims (T1) Most of one’s ideas are not clear. (T2) One can make the judgement that a complex idea one presently has is composed in such and such a way only if its parts are clear. (T3) (T1) and (T2) jointly make it unsurprising that one is often not in a position to know the composition of one’s ideas. Given that the clarity of an idea requires the existence of a further idea exclusively representing the former, (T1) seems plausible to me. It certainly doesn’t seem as though we more or less constantly introspectively in the fact that in the one [idea] we think these, in the other we think those parts distinctly, while thinking the others only indistinctly’ (WL I, § 64: 273, emphasis added). This remark suggests that the fallibility of our judgements concerning content-identity between ideas would be explained by differences with respect to which parts of an idea we tend to be aware of. This, however, would be implausible unless knowledge of content-identity between ideas is standardly based on knowledge of the ideas’ composition. Unfortunately though, in other places Bolzano presupposes the contrary view. In particular, Bolzano recommends, roughly, that one can test a proposed Explanation of an idea by checking whether substituting the Explanans-expression for the Explanandum-expression in an arbitrary sentence results in an expression of a different content (cf. WL III, § 350: 399). This advice would be singularly unhelpful if checking whether the propositional acts guised by the sentences have the same content required first ascertaining their respective composition.
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reflect on our present acts of thinking. Moreover, it is not clear that any significant benefit would be gained from doing so, so it would be a surprise if we found that we do constantly introspect our ideas. However, this is consistent with saying that in situations in which we have reason to attend to our present thinking, we invariably succeed in making our pertinent ideas clear—roughly speaking, that most of our ideas are not clear does not imply that they are hard to clarify.27 I think that this observation spells trouble for Bolzano’s defence of intransparency. Recall that according to Bolzano, if an idea one presently has is not clear, then one is not in a position to judge—and thereby come to know—of the idea that one has it, because such a judgement would have to include a clarifier of the idea in question. We may grant that one cannot make a judgement of the pertinent sort without first clarifying the idea in question. Nevertheless, if clarifying the idea presents no obstacle—if one succeeds in clarifying one’s ideas whenever one has reason to—then one may be said to be in a position to judge (know) of the idea in question that one has it even if one has not (yet) clarified it. (I cannot leave my flat without first unlocking the door, but if unlocking the door presents no obstacle, I am in a position to leave my flat even when the door is locked.) A similar point then applies to (T2). According to (T2), one cannot make the judgement that a complex idea one presently has is composed in such and such a way unless one has clarified its parts. The reasoning, as before, is that such a judgement would have to include clarifiers of the parts of the complex idea (cf. WL III, § 281: 41f.). But while it may be true that one cannot make a judgement of the pertinent sort until one has clarified the parts of the respective idea, one may nevertheless be in a position to make such a judgement even before that, provided that clarifying the parts, and recognizing that and how the complex idea is composed of them, presents no obstacle. (At least, this is so unless one construes the phrase ‘in a position to’ in such a demanding fashion that the claim that one isn’t always in a position to know the composition of one’s ideas loses interest.) According to (T3), the claims (T1) and (T2) jointly undermine the intuitions against the view that one need not be in a position to know the composition of one’s ideas. The preceding considerations show that, on the reading of ‘in a position to know’ which is relevant in our context, (T1) and (T2) do not imply that one need not be in a position to know the 27. Of course, we cannot at any time clarify all of our ideas, as this would require having an infinite number of ideas. (Bolzano uses this argument to show that at least some ideas are unclear; cf. WL III, § 280: 30.)
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composition of one’s ideas. While this does perhaps not entail that (T1) and (T2) do not undermine the transparency-intuitions, I see no reason to think that they do. When presented with (T1) and (T2), someone who is attracted to the view that content is transparent can sensibly stick to her view and reply that she’s been given no reason to think that the composition of one’s ideas can be hard to figure out. I conclude that in the absence of an argument to show that introspective awareness of our ideas is not just not automatic, but often hard to achieve, Bolzano’s defence of intransparency is unsuccessful.28 Moreover, I think the prospects for supplementing his defence by trying to provide such an argument are dim. Insofar as it is difficult to find out whether two ideas, or their guises, have the same content, or what the composition of some Idea is, the difficulty surely is not one of achieving introspective awareness of the relevant ideas and their parts. Rather, it seems to me, the difficulty is to come up with the relevant hypothetical scenarios against which to test the alleged identity of the content, or to recognize potential differences in their respective inferential connections, etc. Closer attention to what is and what is not difficult in trying to determine the composition of certain Ideas reveals a further, more fundamental problem with Bolzano’s view. Any account of how we come to know the composition of Ideas, or acts of grasping them, must make the following datum intelligible: parts of a complex idea which correspond to a part of the guise of the idea are easier to recognize than parts of a complex idea whose guise has no significant parts. For example, if one grasps [Idea] under the guise of ‘Idea’, the part of one’s idea whose content is [proposition] must be harder to become aware of than when one grasps [Idea] under the guise of ‘non-propositional part of a proposition’.29 Bolzano’s 28. There is no doubt that Bolzano believes that it is often very hard to become aware of one’s ideas, and in particular to recognize the parts of a complex idea one presently has. For instance, he explicitly says that even when we have focussed our attention on a given idea we have, and made a determined attempt to discern parts in it, failure to recognize such parts ought to make us at best moderately confident that the idea in question is atomic (cf. WL III, § 350: 398). 29. When discussing the example of [equilateral triangle] and [equiangular triangle] I mentioned above, Bolzano suggests that the intuitive difference between necessarily equivalent ideas may consist merely in the fact that ‘in the one [idea] we think these, in the other we think those parts distinctly, while thinking the others only indistinctly’ (WL I, § 64: 273). Presumably, what he means is that while in ideas guised by ‘equilateral triangle’, the part with content [equilateral], but not the (hypothesized) part with content [equiangular] tends to be clear, while in ideas guised by ‘equiangular triangle’, it tends to be the other way round. Why would that be, if not because of which parts correspond to parts of the respective guise?
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account makes this datum appear mysterious, for it is hard to see how an idea’s being guised could affect the difficulty or otherwise of forming an intuition of it. An intuition is an atomic idea which directly represents whatever object it is an idea of. The connection between an idea and its guise, according to Bolzano, consists in the idea’s triggering, or having been triggered by, an idea of the guise (in the right kind of way). It is unclear to me how a certain expression’s being associated in this way with a given idea could facilitate one’s forming a direct representation of this idea. One way of getting around this problem might be to say that clarifiers, rather than being intuitions, are ideas that represent the ideas they clarify in terms of their guise. Earlier I suggested that certain ideas whose content can be expressed by instances of ‘my present idea of F’ might play the role of clarifiers. Thus, one might think that an idea x clarifies an idea y iff: x represents y and only y, and x is guised by (a translation of ) ‘my present idea of F’, where ‘F’ is the guise of y. However, on this view, guiseless parts of a complex idea cannot be clarified at all. Accordingly, it can no longer be maintained that coming to know the composition of an idea guised by a simple expression involves the clarification of its parts. Rather, one might suggest, knowledge of the composition of a complex idea standardly depends on prior knowledge of the content-identity of two of one’s ideas, one of which has a complex guise. Whether or not such a modification is promising, it substantially deviates from the view Bolzano presents, and it still faces the challenge of explaining away the intuitions to the effect that one must always be in a position to know whether two of one’s ideas have the same content. 6. Conclusion In numerous places throughout his writings, Bolzano claims or implies that content is intransparent, i.e. that our knowledge of the contents of our own current mental acts or states is often severely limited. One of the main uses to which he puts this thesis is his attempt at a solution to the paradox of analysis—the puzzle of how a conceptual analysis can be both correct and informative. In this paper, I identified four different intransparency theses that Bolzano is explicitly or implicitly committed to and examined Bolzano’s defence of one of them—that one need not be in a position to know the composition of an idea one presently has (or that of its content)—as well as his notion of a clear idea on which it draws. I
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then presented what I take to be the most plausible assumptions on which the defence can be generalised to Bolzano’s other intransparency claims. Finally, I argued that as it stands, Bolzano’s defence of his intransparency theses is unsuccessful because it shows at best why we often lack knowledge of certain features of the contents of our mental acts and states, but not why such knowledge is often hard to acquire. Moreover, I suggested that Bolzano’s defence is hard to improve on without substantially modifying his overall epistemology of content as the latter appears ill-equipped to explain the relevance of the linguistic guises of our mental acts to the acquisition of knowledge of their—or their contents’—composition.
REFERENCES Black, Max 1944: “The ‘Paradox of Analysis’”. Mind 53, 263–7. — 1945: “The ‘Paradox of Analysis’ Again: A Reply”. Mind 54, 272–3. — 1946: “How Can Analysis Be Informative?”. Philosophy and Phenomenological Research 6, 628–31. Bolzano, Bernard [WL] 1837: Wissenschaftslehre. 4 vols. Aalen: Scientia, 1981. Partial translation as Theory of Science. — [AA] 1838: Athanasia oder Gründe für die Unsterblichkeit der Seele. Sulzbach: J. E. v. Seidel. — [B/Exner] 1935: Der Briefwechsel B. Bolzano’s mit F. Exner. Prag: Königlich böhmische Gesellschaft der Wissenschaften. — [ToS] 1972: Theory of Science (ed., transl. by Rolf George). Oxford: Basil Blackwell. Burge, Tyler 1978: “Belief and Synonymy”. Journal of Philosophy 75, 119–38. — 1986: “Intellectual Norms and the Foundations of Mind”. Journal of Philosophy 83, 697–720. Carnap, Rudolf 1947: Meaning and Necessity. Chicago: The University of Chicago Press. Centrone, Stefania forthcoming: “Bolzano und Leibniz über Klarheit und Deutlichkeit”. To appear in Archiv für Geschichte der Philosophie. Church, Alonzo 1946: “A Note on the ‘Paradox of Analysis’; The ‘Paradox of Analysis’ Again: A Reply; Analysis and Identity: A Rejoinder; How Can Analysis Be Informative?”. The Journal of Symbolic Logic 11, 132–3. Dähnhardt, Simon 1992: Wahrheit und Satz an sich. Pfaffenweiler: Centaurus. Künne, Wolfgang 1997: “Propositions in Bolzano and Frege”. In: Künne et. al. 1997, 203–40.
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Künne, Wolfgang; Siebel, Mark; Textor, Mark (eds.) 1997: Bolzano and Analytic Philosophy. Amsterdam: Rodopi. Langford, Cooper H. 1942: “The Notion of Analysis in Moore’s Philosophy”. In: P. Schilpp (ed.), The Philosophy of G. E. Moore, 321–42. Moore, George E. 1942: “A Reply to My Critics”. In: Paul Schilpp (ed.), The Philosophy of G. E. Moore, 535–677. Textor, Mark 1996: Bolzanos Propositionalismus. Berlin: Walter de Gruyter. — 1997: “Bolzano’s Sententialism”. In: Künne et. al. 1997, 181–202. White, Morton G. 1945a: “A Note on the ‘Paradox of Analysis’”. Mind 54, 71–2. — 1945b: “Analysis and Identity: A Rejoinder”. Mind 54, 357–61. Williamson, Timothy 2000: Knowledge and its Limits. Oxford: Oxford University Press. — 2006: “Conceptual Truth”. The Aristotelian Society, Supplementary Volume 80, 1–41.
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Grazer Philosophische Studien 82 (2011), 209–237.
NOTHING BUT OBJECTS Nick HAVERKAMP Humboldt University of Berlin Summary This paper is a defence of objectualism, the thesis that everything is an object. The most fully worked out alternative, the Fregean ontology, will be reviewed and rejected. It will be shown that the notorious paradox of the concept horse is a symptom of a disease non-objectualist theories generally suffer from: drawing erroneous ontological conclusions from syntactic and semantic insights. Objectualism turns out to be a triviality that is compatible with any such insights.
What is an object?1 Following Frege, one can give metalinguistic criteria: something is an object if (i) an object term signifies it,2 if (ii) a first-level concept term applies to it, or, if (iii) a second-level function term quantifies over it. More on these criteria below. Objectualists claim that everything is an object. Frege, on the other hand, held certain semantic views which led him to deny that there are only objects. According to Frege, there are also concepts and (other) functions of various types arranged in an infinite hierarchy. In his early period, including the time he wrote his book Die Grundlagen der Arithmetik, Frege tried to express his non-objectualist views, which were centered around his prominent thesis that objects and concepts form exclusive categories, in a seemingly straightforward way. But from 1891 onwards he gradually became aware of difficulties in his presentation. Ini1. This paper is based on parts of my master thesis which I have written under the supervision of Wolfgang Künne in 2005/6. Wolfgang Künne was virtually the only person who taught me philosophy, and I am greatly thankful for everything I learned from him and for all his support. (That my philosophical education took place under such excellent circumstances has one serious disadvantage: I have to assume responsibility for all my philosophical flaws myself.) I would like to thank Robert Schwartzkopff and the members of the Phlox group Miguel Hoeltje, Benjamin Schnieder, Moritz Schulz, and Alex Steinberg for their comments on an earlier draft of this paper. 2. I follow Künne’s advice (Künne 2010, 203f.) to use ‘signification’ as the translation of ‘Bedeutung’.
tially, in his article “Über Begriff und Gegenstand”, he only acknowledged the impossibility to refer to concepts by using expressions like ‘the concept horse’. This alleged insight led to his famous exclamation that the concept horse is not a concept. About 20 years later, after Russell had proved the formal axiomatic system of Frege’s Grundgesetze der Arithmetik I/II to be inconsistent, Frege took a far more radical stance towards his semantic and ontological views: he then claimed that they cannot be literally expressed at all. To communicate them one has to use what Frege now took to be defective expressions like ‘concept’ or ‘function’. Although Frege found some followers in his belief in fundamental but inexpressible insights, the majority of Fregeans has attempted to develop strategies to express what Frege deemed to be inexpressible. I will identify the crucial shortcomings of these and any other possible such strategy. Furthermore, I will demonstrate that these deficiencies do not speak in favour of the existence of inexpressible truths but rather in favour of the thesis that there are only objects. The truth of objectualism will be shown to be an utter triviality. This explains why any attempt to express Frege’s non-objectualist ontology and semantics must fail, and it forestalls the approach to take refuge in inexpressible ontological and semantic insights. In section 1 Frege’s pertinent ontological and linguistic views will be sketched. In section 2 the development of Frege’s perspective on the challenge that his views seem to be inexpressible will be reviewed. In sections 3 and 4 the different strategies for expressing Frege’s views will be discussed, and in section 5 insurmountable limitations of any such strategy will be highlighted. In section 6 the triviality of objectualism will be demonstrated. In section 7 some concluding remarks will be made. 1. Frege’s Theory In this section an exposition is given of what I will call Frege’s Theory, i.e. his most general ontological and linguistic views.3 3. Frege’s ontological and linguistic views underwent two major changes. Since 1891 Frege distinguished the notions of sense and signification and claimed concepts to be functions, and since 1906 he considered his attempt to demonstrate logicism to have failed; cf. Dummett 1981, 21f. By the use of the phrase ‘Frege’s Theory’ I refer to the most general ontological and linguistic views which Frege held between 1891 and 1906. For his own presentation of his theory see especially Frege 1891 and the summary in the first four paragraphs of Frege 1893.
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Frege claims that everything is either an object or a function and that nothing is both. Functions are arranged in an infinite hierarchy of types. Applied to arguments, i.e. appropriate tuples of objects and functions of lower types, they yield objects as values. Let me introduce the following four types of functions: unary first-level functions are applicable to objects; binary first-level functions are applicable to pairs of objects; unary second-level functions are applicable to unary first-level functions; unary third-level functions are applicable to unary second-level functions. These types of functions are of importance for what follows. There are two special objects, the two truth values T and F. Functions that yield only those two objects as values are called concepts or relations depending on whether they are unary or not. Apart from this ontological hierarchy, there is also a syntactic one, a hierarchy of terms: every term is either an object term or a function term, and nothing is both. Function terms form a hierarchy which is isomorphic to the hierarchy of functions. The correspondence of the two hierarchies is witnessed by the relation of signification: object terms signify objects and function terms signify functions of corresponding types. What is signified by a term is also called the significatum of the term.4 Function terms that signify concepts (relations) are called concept terms (relation terms). Up to this point I have presented the skeleton of Frege’s Theory. It describes isomorphic ontological and syntactic hierarchies. If WO is the ontological type corresponding to a syntactic type W, the core of Frege’s Theory can be formulated thus: (FT) A term of type W signifies something of type WO. To develop this skeleton into a full-blown theory more needs to be said about its basic notions: what are objects and functions of the various types, what are object terms and function terms of the various types, and what is the relation of signification, linking the latter to the former? Frege takes the ontological notions of an object and of the various types of functions to be basic and indefinable. (Cf. Frege 1891, 134 [18]; Frege 4. As I use this word, every term signifies something. Empty expressions like ‘Santa Claus’ are not terms.
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1892, 167f. [193].)5 He tries to elucidate them by two different strategies. On the one hand, he says that functions are unsaturated (incomplete, in need of supplementation) while objects are saturated (complete, not in need of supplementation). On the other hand, he gives metalinguistic criteria along the lines of FT: something is a function (of a certain type) if it is the significatum of a function term (of the corresponding type), and something is an object if it is the significatum of an object term. On closer inspection, however, it turns out that the non-linguistic elucidations are mere by-products of the linguistic ones. Fundamentally, terms differ in whether they are saturated or unsaturated. This characterization is only transferred to the significata of the terms. (Cf. Frege 1892–5, 129; Frege 1903, 269f. [371f.]; Frege 1904, 279 [665].)6 In his later writings Frege claims that primarily the senses of terms are saturated or unsaturated while a term inherits its status from the sense it expresses. No more than four years after Frege first used the word ‘unsaturated’ to characterise functions he expressed dissatisfaction with this characterization. (Cf. Frege 1892-5, 129.) One aspect of the problem seems to be that Frege describes senses and terms as saturated or unsaturated depending on what kinds of parts they are in senses and terms containing them (cf. Frege 1891, 128f. [7–8]; Frege 1892, 178 [205]), while analogous mereological characterizations are not applicable to the significata of complex terms.7 There is another aspect of the problem: if function terms and their senses are unsaturated while objects are not, then they have to be functions; a consequence that Frege apparently did not accept.8 To sum up, the only feasible Fregean criteria for belonging to this or that ontological category are the metalinguistic ones encapsulated in FT. To apply the metalinguistic criteria one has to know about the various categories of terms and about the relation of signification. The fundamental 5. Whenever possible, I mention the page numbers of the original publications of Frege’s articles in square brackets. 6. In (Frege 1891), he applies the word ‘unsaturated’ initially to functions (128 [6]) and only later to function terms (134 [17]). But the surrounding discussion of the initial application supports the thesis that here too Frege is transferring a property from the function terms to their significata. 7. Frege 1919, 275 gives the following example: although the term ‘Sweden’ is a part of the term ‘the capital of Sweden’, the significatum of the latter is part of the significatum of the former. Dummett (1997, 244) notes that Frege knows about this disanalogy between terms and their senses on the one hand and the significata of terms on the other hand already in 1913. 8. See Dummett 1973, 291–4 for a defence of the interpretative thesis that Frege took senses of function terms to be objects.
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idea of Frege’s syntactic categorization is already present in his first book Begriffsschrift. (See Frege 1879, 15–9.) I will illustrate this categorization with respect to the language L, a horizontal version of a fragment of the interpreted formal language invented by Frege. The easiest way to define the class of object terms of L uses a modern trick. First one defines the larger class Q of quasi object terms, and then one declares something to be an object term iff it is a quasi object term without free variables and without vacuous quantifiers. Given infinite supplies of object variables ‘x1’, ‘x2’, ‘x3’, … and unary first-level function variables ‘f1’, ‘f2’, ‘f3’, …, Q is to be the smallest class of expressions which contains the object variables such that the following is true: if x is an object variable, f is a unary first-level function variable, and Q contains t and t*, then Q also contains x ‘ft’, ‘−t’, ‘¬t’, ‘(t o t*)’, ‘(t = t*)’, ‘x t’, ‘2f t’.9 What then is a function term of L? One can think of function terms as perforated object terms like ‘x1 (x1 = )’ together with rules which determine how the gaps of the perforated expressions can be filled by terms of lower types.10 To visualise a function term one can take some object term t and systematically replace terms which are contained in t by new symbols. The following list illustrates this visualization with respect to what might be called the basic function terms of L: x «−[», «¬[», «([ o ])», «([ = ])», «x )x», «2f µyfy». These are two unary and two binary first-level function terms, a unary second level function term, and a unary third-level function term.11 Apart from the basic function terms there are infinitely many further function terms which can be thought of as being obtained from object terms by deleting terms contained in them; for example the first-level function terms «([ = ])», «¬([ o ¬])» and «(¬[ o ])», the second-level function term «¬x ¬)x», and the third-level function term «¬2f ¬µy fy». 9. The Fregean language L contains only one basic category: the category of object terms. A modern formal language of (higher-order) predicate logic contains two basic categories: the category of singular terms and the category of formulae. 10. Peter Simons (1981; 1983) develops the idea that function terms are best thought of as patterns. 11. See Frege 1893, 34–42 for a concise description of higher-level function terms.
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Before I say something about the application of this syntactic analysis to natural languages, let me present the significata of the basic function terms from which the significata of all terms of L can be obtained: (−) the significatum of «−[» maps T to T and every other object to F; (¬) the significatum of «¬[» maps T to F and every other object to T; (o) the significatum of «([ o ])» maps the pair ¢T,F² to F and every other pair of objects to T; (=) the significatum of «([ = ])» maps the pairs of identical objects to T and every other pair of objects to F; () the significatum of «x )x» maps to T every first-level concept which maps every object to T and to F every other first-level concept; (2) the significatum of «2f µyfy» maps to T every second-level concept which maps every first-level concept to T and to F every other second-level concept. With respect to a natural language like English, there are at least two syntactic categories of object terms (and possibly empty expressions of the same form): sentence terms and singular terms. Sentence terms are object terms which combine with a grammatical mood to form, for example, declarative or interrogative sentences.12 Singular terms are certain singular noun/determiner phrases. Proper names are prototypical examples of singular terms; non-adverbial indexicals like ‘you’ and demonstrative phrases like ‘this book’ are also fairly uncontentious examples. Definite descriptions and nominalizations like ‘being wise’ or ‘that Socrates is wise’ are more controversial. As will be seen in section 2, syntactic units beginning with the definite article are normally classified as singular terms by Frege.13 Note that a singular term and a sentence term may have the same significatum; e.g. the singular term ‘the True’ and the sentence term ‘Socrates is wise’ both signify the truth value T. Finally, there is the notion of signification. As Michael Dummett has argued (cf. Dummett 1973, 198–203), it is a basic fact about the relation of signification that a proper name signifies its bearer. Many 12. Two English sentences like ‘Snow is white.’ and ‘Is snow white?’ differ only in their grammatical mood; I will use the expression ‘snow is white’ to signify their shared sentence term. See Frege 1891, 137 [22], fn. 7 for his conviction that the difference between sentence terms and sentences is semantically relevant. 13. For more on singular terms see Dummett 1973, ch. 4; Hale 1996; Hale 1994.
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semantic theories have a notion corresponding to Frege’s notion of signification restricted to singular terms. I will use the verb ‘to denote’ to express this notion. It suffices for formulating a useful criterion for being an object: (Ob1) ‘everything denoted by a singular term is an object’. Characteristically, Frege extends the relation of denoting to cover all other categories of terms. The principles guiding him in this process are not easily identified. (Cp. Dummett 1973, ch. 7; Burge 1986, 104.) What is most important for present purposes is that Frege was led to the conviction that although function terms signify something, they do not signify objects. As a consequence of the central claim FT of his theory, there is nothing that is signified by terms of different types; in particular, what a function term signifies is not also signified by a singular term. As is now well known, this component makes it difficult to coherently present Frege’s Theory. In the next section I will describe how Frege’s views on these difficulties developed. 2. Frege on the presentation of his theory Before Frege distinguished between sense and signification and claimed concepts to be functions, he had already drawn a categorical distinction between objects and first-level concepts. Originally, he put less emphasis on the metalinguistic criteria for distinguishing them; rather, he took it to be a distinguishing characteristic of first-level concepts that only with respect to them it makes sense to ask whether something falls under them. (See Frege 1881, 20.) By this time, Frege did not see any problems in speaking about first-level concepts; in particular, he meant to refer to them by using expressions like ‘the concept square root of 4’. Metalinguistic criteria for drawing the distinction between objects and first-level concepts enter the picture by the time Frege wrote his book Die Grundlagen der Arithmetik. He stuck to the idea that it is characteristic of first-level concepts that it makes sense to ask whether something falls under them. But, primarily, he based the ontological distinction on the syntactic distinction between object terms and first-level concept terms. (Cf. Frege 1884, § 51 [63f.].) It is not entirely clear whether Frege still believed at this time that expressions like ‘the concept horse’ signify concepts. (See
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ibid., § 68 (footnote) [80].) At the latest when he wrote the article “Über Begriff und Gegenstand” he had given up this belief. There he famously reasoned as follows (cf. Frege 1892, 195ff. [169ff.]): P1 P2 P3 C1 P4 C2
The expression ‘the concept horse’ is an object term. An object term signifies an object. The expression ‘the concept horse’ signifies the concept horse. Therefore, the concept horse is an object. No object is a concept. Therefore, the concept horse is not a concept.
Frege based his judgement that the expression ‘the concept horse’ is an object term on the fact that it is a singular (noun/determiner) phrase which begins with the definite article.14 Frege did not conclude that there is something wrong with his theory, or with his way of presenting it.15 He merely acknowledged that concepts are not signified by expressions like ‘the concept horse’ but only by firstlevel concept terms like «[ is a horse». Shortly after his first engagement with the notorious paradox of the concept horse, Frege became more careful in his verdict on phrases like ‘the concept horse’. In Frege 1892–5 he said that such phrases signify objects, if they signify anything at all, leaving it open that they might be defective expressions without significata. Here again (cf. Frege 1892–5, 130) Frege saw the source of the troubles in the fact that phrases which were meant to denote concepts begin with the definite article. In line with that he recognised that an expression like ‘the significatum of the term «[ is a horse»’ is just as unsuited to signify a concept as an expression like ‘the concept horse’. (Cf. ibid., 133; cp. Wright 1998, 242.) Additionally, he noticed that one cannot apply the first-level relation term «[ is identical to ]» to concept terms, and he drew the conclusion that the relation of identity cannot obtain between concepts. (Cf. Frege 1892–5, 130.) But still, it seems, Frege had not grasped the full depth of 14. See ibid., 169f. [195]. The only exceptions to this criterion that Frege acknowledges are uses like ‘the horse’ in ‘the horse is a four-legged animal’ in which they are, according to Frege, mere stylistic variants of the corresponding plural noun/determiner phrases ‘the horses’ in ‘the horses are four-legged animals’; cf. ibid., 170 [196]. 15. In section 3 I will argue that this is compatible with Frege’s claims in “Über Begriff und Gegenstand” to the effect that natural languages face certain limitations for speaking about first-level concepts and other functions.
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the problem. I will give two examples. Not only the relation of identity cannot obtain between concepts, the relation of signification cannot relate something to a concept either: P1 The expression «some term signifies [» is a first-level concept term. P2 A first-level concept term applies only to objects. P3 The expression «some term signifies [» applies to everything that is signified by some term. C Therefore, everything signified by some term is an object. An analogous argument yields the conclusion that every concept is an object: P1 The expression «[ is a concept» is a first-level concept term. P2 A first-level concept term applies only to objects. P3 The expression «[ is a concept» applies to everything that is a concept. C Therefore, every concept is an object. At the latest three years after Russell demonstrated that Frege’s proposed logical axioms in Grundgesetze der Arithmetik I/II are inconsistent, Frege saw the full extent of the difficulties. He came to the conclusion that the whole trouble begins with an expression like ‘concept’ which belongs to the first-level concept term «[ is a concept». (Cf. Frege 1906, 192.) Frege apparently reached the radical conclusion that the word ‘concept’ is, strictly speaking, senseless. And since being senseless is a contagious disease, this would have the consequence that every expression containing such a word is senseless as well. In particular, the sentence terms which were meant to express his ontological and semantic views are senseless. Now, the important thing to note is that Frege did not give up his theory as a consequence; in the very same article in which he conceded the senselessness of words like ‘concept’, he put great emphasis on his view that there are concepts, i.e. significata of concept terms, and that concepts are not objects. (Cf. ibid., 191f.) Frege did not give up this esoteric attitude. He stuck to his theory although he conceded it to be inexpressible. (Cf. Frege 1906a, 209f; Frege 1914, 257f.; Frege 1919, 275.) In a short fragment, dated by the editors of Frege’s posthumous writings to the last year of his life, Frege claimed that he still understood the word ‘concept’ the way he had understood
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it at the time he had written Die Grundlagen der Arithmetik. (Cf. Frege 1924/5, 295.) What could have been downplayed as mere tendencies in earlier writings became Frege’s ultimate view on his theory. He embraced the esoteric attitude of sticking to it although he admitted it to be inexpressible. Although he classified expressions containing words like ‘concept’ or ‘function’ as defective, he went on to use them, and he did not give any hints on how his theory might be presented without them. Some philosophers, most notably Ludwig Wittgenstein (cf. Wittgenstein 1921, 6.54), followed Frege in postulating fundamental but inexpressible ontological and semantic insights. But the majority of Fregeans has attempted to develop strategies to express Frege’s non-objectualist theory. In the following three sections I will investigate such strategies. 3. Reference to first-level concepts In this part I will take a detailed look at sentence terms which have subject phrases that seem to signify first-level concepts and predicate phrases which seem to describe these. I will consider the following examples: (1a) ‘the first-level concept horse subsumes Fury’, (2a) ‘the first-level concept horse is not empty’, (3a) ‘the first-level concept horse is a first-level concept’. What could a defender of a Fregean ontology say about such sentence terms? Frege himself took some time to arrive at his ultimate position according to which all such sentence terms are defective. There are two alternative approaches in his writings which I will call the confused and the opaque approach. Both of them involve the assumption that the subject phrase of the above sentence terms is an object term which, consequently, signifies an object. According to the confused strategy all such sentence terms are false. It was shown in the preceding section that Frege applied the confused strategy to 3a in his article “Über Begriff und Gegenstand”. From the assumption that no object is a first-level concept he inferred that the object signified by the subject phrase ‘the first-level concept horse’ cannot fall under the firstlevel concept signified by the predicate phrase «[ is a first-level concept». He could have reasoned similarly in the other cases. For example, from
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the assumption that no object subsumes anything he could have inferred that the object signified by the subject phrase ‘the first-level concept horse’ cannot fall under the first-level concept signified by the predicate phrase «[ subsumes Fury». This approach is confused because it applies different standards to the subject phrase on the one hand and the various predicate phrases on the other hand. If Frege says that the subject phrase is an object term which, consequently, signifies an object, he should also say that the predicate phrase is a first-level concept term which, consequently, signifies a firstlevel concept. But then there is no reason for Frege to deny that the object signified by the subject phrase falls under the first-level concept signified by the predicate phrase.16 Frege’s other strategy, i.e. the opaque one, declares all three sentence terms to be true: the object signified by the subject phrase is said to fall under the first-level concept signified by the predicate phrases. The basic idea is that certain objects represent first-level concepts while certain first-level concepts represent second-level concepts. Consider the sentence term 2a. The object signified by ‘the first-level concept horse’ represents the first-level concept signified by «[ is a horse», and the first-level concept signified by «[ is not empty» represents the second-level concept signified by the existential quantifier. Furthermore, a sentence term in which the subject phrase signifies a representing object while the predicate phrase signifies a representing first-level concept is said to express a true thought if the represented first-level concept falls under the represented second-level concept. Frege applied this strategy to sentence terms like 2a. (Cf. Frege 1892, 171 [197].) Parsons notes that Frege could have applied it uniformly. (See Parsons 1986, 452ff.) Had Frege applied it to 3a, he could have claimed that the first-level concept horse is a first-level concept. The opaque strategy not only suffers from the drawback that it is unclear how to understand the verb ‘to represent’ in this context. It fails for the Cantorian reason that there are not enough objects to do all the representing. Surely, the representing objects signified by ‘the first-level concept F ’ and ‘the first-level concept G’ should be different if it is not the case that something is F iff it is G; i.e. if the first-level concept F is identical to the first-level concept G, then something is F iff it is G. But this principle is 16. This point is due to Terence Parsons: ‘[…] I think that the most plausible way to understand what Frege was saying here is to speculate that when he said “The concept horse is not a concept” he was speaking “strictly in the subject,” and “informally in the predicate” (Parsons 1986, 454).’
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syntactically of the same form as Frege’s Basic Law Vb, and like the latter it leads to inconsistency. (Cp. Parsons 1986, 454f.) In the end Frege adopts an esoteric attitude towards his theory: its central ontological and semantic claims cannot be expressed, and one has to use defective sentence terms to convey them. In section 5 I will present those sentence terms for which it is most plausible to claim that they are defective but indispensable for the presentation of Frege’s Theory. With respect to sentence terms like 1a−3a, on the other hand, it is quite unlikely that Frege takes them to convey inexpressible insights. To begin with, let me present what seem to be adequate replacements for 1a−3a in a language like L. In order to do so L has to be enriched by a suitable object term ‘a’ which signifies Fury and by a suitable first-level concept term «h[» which signifies the first-level concept that maps every horse to T and every other object to F . But then it seems to be easy to find sentence terms which express what Frege wanted to say by using 1a−3a: (1b ) ‘ha’, (2b ) ‘¬x ¬hx’, (3b ) ‘x (hx = −hx)’.17 In addition Frege would quite likely accept that there are also English sentence terms which express what 1a−3a were meant to express: (1c ) ‘Fury is a horse’, (2c ) ‘something is a horse’, (3c ) ‘every horse is a horse’. There is, of course, a crucial difference between the original sentence terms and these proposed alternatives: only in the original ones the subject phrase seems to signify a first-level concept. I conjecture that Frege, when he says that we are forced to use inappropriate expressions like 1a−3a (see Frege 1892, 177 [204]; ibid., 178 [205]), simply meant that it is impossible to express the thoughts expressed by 1c−3c by using sentence terms whose subject phrases signify first-level concepts. From this perspective the original sentence terms seem to be the result of misapplying a syntactic transformation that is quite useful and unproblematic in other cases. One 17. That 3b is a suitable replacement for 3a may not be obvious. The idea is simply to use a second-level concept term like «x ()x = −)x)» which yields a true sentence term iff the unary first-level function term it is applied to is a first-level concept term.
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can express that Plato admires Socrates in a way that makes Socrates the subject by using the sentence term ‘Socrates is admired by Plato’. Similarly, one can express that Ann believes that it is raining in a way that makes the content of Ann’s belief the subject by using the sentence term ‘that it is raining is something which Ann believes’. What Frege came to believe to be impossible is, I think, that one can express what 1c−3c express in a way that makes a first-level concept the subject. It is surely true that it is not possible to use a first-level concept term as the subject phrase of a sentence term. But does this imply that it is impossible to express what 1c−3c express by using sentence terms whose subject phrase signifies a first-level concept? There are at least two accounts according to which this consequence is denied; I will call them the most promising accounts for the presentation of Frege’s Theory. One of them is due to Terence Parsons. (See Parsons 1986, 459–63.) It can be seen as a way of freeing Frege’s opaque strategy from its reliance on the notion of representing; it combines the thesis that 1a−3a express what 1c−3c express with the claim that the subject and predicate phrases of the original sentence terms signify first-level concepts and second-level concepts respectively. The key idea is to see English as a CODED version of a logically proper language. Since codes typically alter syntactic form we should not expect predicative expressions in the logically respectable language to be encoded as predicative expressions of English […] (Parsons 1986, 459)
Parsons claims that ‘the first-level concept horse’ is a code for the first-level concept term «h[» and that the three predicate phrases are codes for the second-level concept terms «)a », «¬x ¬)x», and «x ()x = −)x)». Consequently, he claims that 1a−3a are codes for 1b−3b. It is not necessary to present Parsons recursive clauses for coding and decoding here. What should be recognised is that, according to Parsons, the original sentence terms and their simpler counterparts 1c−3c express the same thoughts. The second of the two most promising accounts is based on the notion of a general term. Paradigmatic examples of general terms are adjectives and syntactic units beginning with the indefinite article when these are not used as quantifier phrases.18 According to Künne verb stems should also be counted as general terms, and the same should be said about the “stems” of complex verb phrases like ‘swims faster than anyone I know’. (See Künne 2006, 250f.) 18. The phrase ‘a tiny man’ plays the role of a general term in the sentence term ‘he is a tiny man’, and it plays the role of a quantifier phrase in the sentence term ‘a tiny man has hit me’.
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The central ingredient of this other account is the assumption that firstlevel concepts are signified by general terms. According to one version, upheld by Dummett, this is a consequence of the fact that the syntactic difference between a first-level concept term like «[ is a horse» and the corresponding general term ‘a horse’ has no semantic significance. (Cf. Dummett 1973, 214.) According to another version, upheld by David Wiggins, this involves a departure from Fregean orthodoxy; attributing a semantic significance to the difference between first-level concept terms and general terms, Wiggins claims that only general terms signify first-level concepts. (See Wiggins 1984, 318f.) Whichever variant one subscribes to, once general terms are said to signify concepts, it is possible to formulate sentence terms which express the desired thoughts while having a subject phrase that signifies a first-level concept:19 (1d ) ‘a horse is something which Fury is’, (2d ) ‘a horse is something which something is’, (3d ) ‘a horse is something which every horse is’.20 Someone who follows this approach chooses 1d−3d as replacements for the original sentence terms 1a−3a and claims that the replacements express the same thoughts as 1c−3c. Let me stress that the different Fregean strategies for dealing with sentences like 1a−3a are not apt to present a part of Frege’s Theory that an objectualist has to reject. First of all, there are strategies like Frege’s confused and opaque strategies according to which the expression ‘the first-level concept horse’ is a non-defective singular term which signifies an object; according to such approaches, the sentence terms 1a−3a express thoughts which can be expressed in an extension of L containing some unary first-level function term, say «πx )x», to the effect that ‘the firstlevel concept horse’ corresponds to the singular term ‘πx hx’. More work 19. In the next section I will present what is arguably a more important application of this approach: sentence terms that seem to express quantification over first-level concepts. 20. Followers of this account claim that these sentence terms express what the sentence terms 1c−3c also express; cf. Dummett 1973, 217. This might be questioned because 1d−3d contain material which 1c−3c do not contain, namely the words ‘is something which’. Alternatively, one could propose to use the following sentence terms instead of 1d−3d: (1e) ‘a horse Fury is’, (2e) ‘a horse something is’, (3e) ‘a horse every horse is’. These expressions do not introduce new material but it is questionable whether they are syntactically well-formed.
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needs to be done if such an account is meant to challenge the objectualist. It is, to say the least, not obvious that referring to an object by means of a singular term containing a first-level concept term and describing this object by means of another first-level concept term could constitute an essential part of a successful attack on objectualism. Then, there are strategies like those of Dummett, Wiggins and Parsons according to which the original sentence terms 1a−3a are meant to express thoughts that can (also) be expressed by 1c−3c. Here it is even more apparent that the original sentence terms do not express or convey anything that an objectualist does not accept. That every horse is a horse, for example, does not have any non-objectualist flavour. Finally, there are also two kinds of strategies which I did not discuss in this section. On the one hand it might be claimed that the original sentence terms are meant to express thoughts which can only be expressed by sentence terms containing higher-level quantifiers. In the next section I will consider sentence terms for which it is less controversial that they are meant to express thoughts which can only be expressed by sentence terms containing such higher-level quantifiers. Its consequences for objectualism will be discussed then. On the other hand it might be claimed that there are true thoughts which the original sentence terms are meant to convey but that these thoughts cannot be literally expressed by any sentence term in any language. This is Frege’s ultimate position. Whether such esoteric manoeuvres might cause trouble for objectualism will be discussed in section 6. 4. Quantification over concepts In this part, I will take a closer look at sentence terms which seem to express quantification over unary first-level functions. I will consider the following examples: (4a ) ‘something is a first-level concept’, (5a ) ‘something is a unary first-level function’, (6a ) ‘every first-level concept is a unary first-level function’. What can defenders of Frege’s Theory say about such sentence terms? I will set aside the Fregean trinity: the confused Frege who, for example, rejects that something is a first-level concept because 4a is quantification 223
into object term position and would therefore only be true if some object were a first-level concept; the opaque Frege who claims that the predicate phrases signify first-level concepts which represent second-level concepts while the subject phrases signify second-level concepts which represent third-level concepts; the esoteric Frege who rejects all such sentence terms as defective but indispensable. So what other strategies for dealing with such sentence terms can a Fregean adopt? In the last section, we saw sentence terms (1a−3a) which, according to most followers of Frege, are meant to express thoughts which can clearly be expressed otherwise. Is this true here as well? Can we find sentence terms which express what one tries to express when one utters sentence terms like 4a−6a? As these sentence terms are meant to be quantifications over unary first-level functions, the appropriate approach would be to ask for sentence terms containing quantifiers which bind variables in the position of unary first-level function terms. In L there are such quantifiers, and it turns out to be rather easy to find appropriate replacements for 4a−6a: (4b ) ‘¬2f ¬x (fx = −fx)’, (5b ) ‘¬2f ¬x (fx = fx)’, (6b ) ‘2f (x (fx = −fx) o x (fx = fx))’. Consider, for example, the sentence term 4a. It was said in the last section that most followers of Frege claim that the sentence term ‘the first-level concept horse is a first-level concept’, i.e. 3a, should be replaced in L by the sentence term ‘x (hx = −hx)’, i.e. 3b. The idea was to replace the predicate phrase by a unary second-level function term like «x ()x = −)x)» which yields a true sentence term iff the unary first-level function term it is applied to is a first-level concept term. Now, the sentence term 4a can be obtained from 3a by replacing the phrase ‘the first-level concept horse’ by the existential quantifier expression ‘something’. Similarly, the sentence term 4b can be obtained from 4a by replacing the first-level concept term «h[» by an appropriate existential quantifier expression, a unary third-level function term. In the previous section I argued that Frege considered 1a−3a to be the result of the attempt to express certain thoughts by sentence terms whose subject phrase signifies a first-level concept. With respect to sentence terms like 4a−6a I conjecture that Frege saw them as the result of the attempt to express in English what 4b−6b express. This leads to the question of whether the thoughts expressed by 4b−6b can be expressed by English sentence 224
terms. The two most promising accounts for the presentation of Frege’s Theory (partially) affirm this question. It is obvious how Parsons treats these cases. Applying his idea that English is a coded version of a logically proper language, he claims that the original sentence terms 4a−6a already express what 4b−6b express as the former are codes for the latter. Dummett and Wiggins on the other hand claim that English contains quantifications into general term position, and they try to use this device to construct replacements for sentence terms which seem to express quantification over unary first-level concepts. As an example, consider the sentence term ‘Fury is a horse’. Here are three stylistic variants obtained from that sentence term by “replacing” the general term ‘a horse’ by an existential quantifier expression. x ‘there is something which Fury is’, x ‘something is such that Fury is it’, x ‘Fury is something’. So English has the resources to express existential quantification into the position of general terms. Is it plausible to assume that by such means we can express quantification over all unary first-level functions? It seems to be more likely that by such means we can express at most quantification over all first-level concepts since general terms are only supposed to take up the role of first-level concept terms and not of arbitrary unary first-level function terms. As a consequence, it is impossible to express in English by such means what 5b and 6b express. What is a suitable replacement of 4a? The idea is simply to consider the existential generalization into general term position of a sentence term like ‘every horse is a horse’ whose truth is independent of the particular choice of the general term: (4c ) ‘there is something such that everything that is it is it’. As desired, this replacement of 4a is trivially true. Do the two most promising accounts, applied to sentence terms like 4a which seem to express quantification over first-level concepts, come up with anything that poses a threat to objectualism? Both accounts share the assumption that, for example, existential quantification over first-level concepts is to be expressed by sentence terms containing quan-
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tifiers which correspond to «¬2f ¬µyfy» in L. The important question therefore is whether the use of such quantifiers conflicts with objectualism. The following argument seems to support an affirmative answer to this question: P1 ‘there is something Socrates and Plato both are’, P2 ‘there is no object Socrates and Plato both are’, C ‘there is something that is not an object’. On closer inspection, though, it becomes apparent that the two premises do not conflict with objectualism. The appearance to the contrary is a consequence of an erroneous argument by analogy. To see this, consider the following argument against nominalism: P3 ‘there is something that is a prime number’, P4 ‘there is no concrete object that is a prime number’, C* ‘there is something that is not a concrete object’. Why do the two premises imply the conclusion? Putting it metalinguistically, by P3, there is first-level concept term, «[ a prime number», which is satisfied by something, but, by P4, it is not satisfied by any concrete object. The impression that P1 and P2 jointly refute objectualism is the consequence of treating them as analogous to P3 and P4. That this is to misconstrue P1 and P2 becomes apparent once their logical form has been revealed. Premise P1 is a quantification into the position of a general term. In semi-formal notation, it could be expressed thus: P1F ‘there is something F such that Socrates is F and Plato is F’. Premise P2 is an ordinary quantification into the position of a singular term which can be expressed as follows: P2F ‘there is no object x such that Socrates is identical to x and Plato is identical to x’. By now the disanalogy to the argument against nominalism should have become obvious. By the second premise of the argument against objectualism, there is a first-level concept term, i.e. «Socrates is identical to [ and Plato is identical to [», which is satisfied by no object. But the first
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premise of the argument does not imply that this first-level concept term is satisfied by something; in its second and third occurrence in P1F, the word ‘is’ functions as a copula and not as a short version of ‘is identical to’. Consequently, the two premises cannot undermine objectualism; it is consistent to assume that everything is an object while there is something that two distinct objects both are. What does the previous discussion show? It shows that the application of the two most promising accounts to sentence terms like 4a do not presuppose anything that poses a threat to objectualism. Objectualism is compatible with the existence of true existential quantifications which are not quantifications into the position of an object term. 5. Insurmountable limitations The two most promising accounts for the presentation of Frege’s Theory shared the assumption that by using sentence terms like 1a−6a which seem to involve reference to and quantification over first-level concepts one tries to express thoughts (successfully according to Parsons, unsuccessfully according to Dummett and Wiggins) which can be expressed by sentence terms of L. In this section I will point out some severe restrictions of both accounts: the core of Frege’s Theory is not expressible in languages like Frege’s Concept Script. The central theses of Frege’s Theory blur type distinctions and are therefore beyond the reach of a language one of whose fundamental merits lies in the unexceptional adherence to type distinctions.21 Consider at first the problems associated with a verb like ‘to signify’ or common nouns like ‘function’ and ‘concept’ which are frequently used in the presentation of Frege’s Theory. Consider the following two sentence terms: (7a) ‘“Fury” signifies Fury’, (8a) ‘ «[ is a horse» signifies the first-level concept horse’. In a sentence term like 7a the word ‘signify’ is used to state the signification of an object term. In an extension of L it would correspond to a binary 21. Parsons acknowledges these limitations; cf. Parsons 1986, 451. Dummett’s position is, as we will see, less clear.
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first-level function term, say «([ d ])». In a sentence term like 8a, on the other hand, it is used to state the signification of a first-level concept term. For such a use, an extension of L would have to contain a binary function term applicable to pairs of object terms and unary first-level function terms, say «([ dx )x)». If the language is further expanded by two suitable object terms, say ‘s’ and ‘t’, which signify the terms ‘a’ and «h[» respectively, we can express in the expanded language what we tried to express by the use of 7a and 8a: (7b ) ‘(s d a)’, (8b ) ‘(t dx hx)’. In general, if we want to be able to state the signification of terms of a type W, we need a binary function term applicable to pairs of object terms and terms of type W. Applying his idea that English is a coded version of a logically proper language, Parsons would have to say that ‘signify’ is ambiguous in a rather extreme way: it is a code for terms of all the different types. In particular, the central thesis FT of Frege’s Theory would have to be treated as an ambiguous expression with infinitely many readings. As far as I can see, Parsons did not embrace this view. Someone who follows the approach of Dummett and Wiggins is forced to say that it is impossible to express in English what 8b expresses.22 Surprisingly, Dummett disagrees. Following a suggestion of Frege’s, he claims that the following sentence term expresses what 8a was meant to express (cf. Dummett 1973, 217): (8?) ‘a horse is what «[ is a horse» signifies’.23 Here Dummett errs. This sentence term is ambiguous. Under one reading, it is equivalent to the sentence term ‘«[ is a horse» signifies a horse’. In this case the phrase ‘a horse’ functions as a quantifier phrase in which 22. One might propose to replace 8a by something like (8a*) ‘«[ is a horse» applies to something iff it is a horse’. But while such a claim might well be part of a convincing semantic theory, it is clearly a departure from Frege’s approach. 23. Someone who departs from Frege in claiming that only general terms signify first-level concepts would prefer ‘a horse is what “a horse” signifies’ if he wanted to adapt Dummett’s proposal.
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the general noun ‘horse’ is combined with a quantifier expression, an expression belonging to the same syntactic category as ‘every’ and ‘some’. Under this reading, 8? is not an appropriate replacement of 8a. For Dummett’s strategy it is important that the subject phrase ‘a horse’ of 8? does not function as a quantifier phrase but as a general term, i.e. something which can be combined with the copula ‘is’ to form a verb phrase. To facilitate the discussion of Dummett’s proposal I will change the example by using the adjective ‘wise’ instead of the phrase ‘a horse’: (8a*) ‘«[ is wise» signifies the first-level concept wise’. (8?*) ‘wise is what «[ is wise» signifies’. This has the advantage of forestalling an unwanted reading analogous to the one above since adjectives cannot be used as quantifier phrases. But does 8?* have a reading under which it is an appropriate replacement of 8a*? It has a reading under which it is equivalent to the sentence term ‘«[ is wise» signifies something which is wise’. But this cannot be the reading which Dummett has in mind. After all, his idea is not that 8a* should be replaced by a sentence term which says that «[ is wise» signifies some wise object. Has 8?* a second reading? Dummett claims that it has, and he bases his claim on the principle that for any general term F the following principle is true (cf. Dummett 1973, 213f.): (D) F is completely interchangeable with ‘what «[ is F» signifies’ . But if one applies this principle to the sentence term 8?*, one obtains the ungrammatical expression ‘wise is wise’.24 Applying D to 8? would yield ‘a horse is a horse’ which is true, of course, but only because the initial occurrence of ‘a horse’ functions as a quantifier expression and not as a general term. It is important to see why there cannot be an appropriate replacement of 8a or 8a*. The reason is that transitive verbs like ‘to signify’ cannot be combined with general terms like, for example, adjectives. Such verbs can 24. Strictly speaking it might be incorrect to call this expression ‘ungrammatical’. After all, people frequently say such things as ‘Enough is enough!’. What is essential here is that applying D to 8?* results in an expression in which two occurrences of an adjective flank the copula. And even if there are acceptable uses of such expressions, these are not uses that Dummett has in mind here.
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be combined with phrases like ‘a horse’, but then these phrases function as quantifier phrases and not as general terms. I will now turn to a kind of problem that neither of the two most promising accounts can deal with: typeless quantification. (See Parsons 1986, 462f.) Consider the following sentence terms: (9) ‘everything is either an object or a function’,25 (10) ‘nothing is both, an object and a unary first-level function’, (11) ‘there is something that is not an object’. Although such sentence terms are meant to express essential parts of Frege’s Theory, their quantifiers are unintelligible by Frege’s lights. The quantifier of 10, for example, would have to bind a variable that occupies simultaneously the position of an object term and the position of a unary first-level function term, and there cannot be such a quantifier in a language like Frege’s Concept Script which strictly respects type distinctions. How should a Fregean react to these difficulties? By claiming that 9−11 express truths which cannot be expressed in a language like the Concept Script? By claiming that they convey truths which cannot be expressed in any language? Or by claiming that they do not even convey truths but that despite appearances Frege’s Theory is independent of those alleged truths? Although the unpleasantness of all three alternatives already makes a strong case for objectualism, we will see in the next section that objectualists do not have to worry about such proposals. 6. Objectualism wins As we have seen, the prospects of adequately presenting the essential ingredients of Frege’s Theory appear to be rather bleak. It seems as if one has to face the following choice: either one gives up Frege’s Theory and joins the objectualists, or one turns to esotericism. In this part I will dispel the illusion of any choice by showing that there is no alternative to objectualism; not even an esoteric one. To see that even the friends of inexpressible ontological and semantic insights should accept objectualism, consider a sentence term expressing 25. Note that the problem not only lies in the fact that there are functions of different types. Even an infinitary sentence term like ‘everything is either an object, or a unary first-level function, or …’ suffers from the shortcomings I am concerned with here.
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it: ‘everything is an object’. Its subject phrase is a universal quantifier, and its predicate phrase is the first-level concept term «[ is an object». What kind of a quantifier is the subject phrase? For syntactic reasons, it can only be a quantifier that binds the position of a singular term; in Fregean terminology, it can only be a second-level concept term. But since everyone accepts that by the use of such quantifiers one makes general claims about objects, everyone has to agree that this sentence term is true. One can bring the point home by asking oneself how to express the thesis of objectualism in the Fregean language L. To do so, one has to enrich L by some first-level concept term corresponding to «[ is an object», say by the term «O[». Now, the only universal quantifier applicable to such a first-level concept term is «x )x». That is, objectualism is expressible in L by the following sentence term: ‘x )x’. And again, even esotericism offers us no reason to reject this sentence term. How could one miss this line of reasoning? Suppose one concentrates on Frege’s metalinguistic criterion: if something is signified by an object term it is an object. We can rephrase it thus: (Ob1) ‘everything denoted by a singular term is an object’.26 This criterion could only be part of an argument in favour of objectualism if there was reason to think that everything is denoted by a singular term. But this is quite implausible. It is not even clear that for every object there is a singular term in the extension of some language which denotes it.27 Therefore, it is questionable whether it is possible to argue for objectualism from this metalinguistic criterion. But this is not the only Fregean metalinguistic criterion for being an object: (Ob2) ‘everything to which a first-level concept term applies is an object’. 26. We do not have to consider sentence terms separately as their significata are also signified by singular terms. And as was stated in section 1, the relation of signification is meant to extend the relation of denoting which only links singular terms to objects. 27. Assuming Zermelo-Fraenkel set theory to be true, it is doubtful whether for every set there is a way to extend some language to contain a singular term which denotes this set. Note that this doubt is not solely based on fact that there are uncountably many sets. There are also uncountably many positive real numbers smaller than 1 but, arguably, for every such real number there is a possible context in which the demonstrative phrase ‘the length of this stick’ denotes it.
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Frege would define application thus: a concept term t applies to something if t maps it to the True. But here we should take it to be a primitive on equal footing with denoting. In fact, it suffices to concentrate on one specific first-level concept term: ‘everything to which «[ = [» applies is an object’. But now note that we can free the criterion from its metalinguistic character: (Ob2*) ‘everything which is identical to itself is an object’. Using this criterion it is possible to argue for objectualism. On the one hand, it is a logical truth that everything is identical to itself. If one translates the sentence term ‘everything is identical to itself ’ into L one will arrive at ‘x (x = x)’, a formula that Frege of course accepts. On the other hand, Frege himself acknowledges that identity is a relation that only holds between objects, i.e., everything identical to itself is an object. But surely if everything is identical to itself and everything identical to itself is an object, then everything is an object. This argument has the desirable feature that it results from freeing a Fregean criterion for being an object from its metalinguistic character. But despite its brevity it appears to be cumbersome. Instead of tackling the sentence term ‘everything is an object’ directly, it makes an unnecessary detour involving the sentence term ‘everything is identical to itself ’. Fortunately there are not only such cumbersome arguments which result from freeing a Fregean criterion for being an object from its metalinguistic character. Here is a third Fregean metalinguistic criterion for being an object: (Ob3 ) ‘everything a quantification into the position of an object term quantifies over is an object’. One can simplify this criterion as one simplified Ob2 above. One only has to concentrate on one specific quantification into the position of an object term. Then, one arrives at the following “criterion” for being an object which does not have a metalinguistic character: (Ob3*) ‘everything is an object’. Establishing objectualism with the help of this criterion turns out to be rather straightforward.
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To be sure, I do not claim to have proved objectualism in a demanding sense of that word. To do so, one would have to present truths more fundamental than the one that everything is an object, and then one would have to show that objectualism is based on these more fundamental truths. I did not do that, and I doubt that it is possible. That there are only objects is as fundamental as a truth can be. What I have done is to show that there are metalinguistic considerations which are Fregean in spirit and which imply objectualism. A more modest approach along this or similar lines is all that can be done and all that needs to be done to dispel the illusion that Fregean foes of objectualism might have had any insights, expressible or not, which undermine the assumption that everything is an object. 7. Concluding remarks Objectualism is a triviality. As such it does not put any substantive constraints on linguistic or other theories. In this section I will mention two alternatives to Frege’s Theory which capture some of its central ingredients. Frege’s Theory can be seen as the inconsistent mixture of these alternatives. Followers of the maximalist alternative agree with Frege in accepting the following claims: (I1) ‘a function term signifies something’, (I2 ) ‘a second-level concept term like «x )x» applies to something’, (I3 ) ‘a third-level function term quantifies over something’. But, in contrast to Frege, they do so because they accept the following theses: (I1*) ‘a function term signifies an object’, (I2 *) ‘a second-level concept term like «x )x» applies to an object’, (I3 *) ‘a third-level function term quantifies over objects’. Maximalists claim that objects play the role attributed to functions in Frege’s Theory. Adherents of the minimalist alternative follow Frege in accepting the following claims:
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(J1) ‘function terms do not signify objects’, (J2 ) ‘second-level concept terms do not apply to objects’, (J3 ) ‘third-level function terms do not quantify over objects’. Unlike Frege, however, they do so because they accept the following theses: (J1*) ‘function terms do not signify anything’, (J2*) ‘second-level concept terms do not apply to anything’, (J3*) ‘third-level function terms do not quantify over anything’. Minimalists claim that nothing plays the role attributed to functions in Frege’s Theory. Frege wanted to have it both ways, and this led him to adopt an inconsistent theory. Having these two alternatives in mind, I would like to conclude by addressing two complementary interpretative worries. Trying to be charitable to Frege, one might reason as follows: ‘The thesis that there is nothing but objects is indeed trivial. And therefore it is absurd to claim that Frege denies it.’ And then one might continue in either of the following two ways. First Version: ‘Obviously, Frege believed that there are concepts and functions. Furthermore, he clearly held that they are signified by concept terms and function terms. But Frege’s claim that concepts and functions are not objects should not be taken literally. All he wanted to emphasise is that object and function terms play quite different semantic roles. But this is consistent with the fact that both signify objects.’ Second Version: ‘Clearly, Frege believed that only object terms denote objects and that only quantification into the position of an object term is quantification over objects. His claim that a function term denotes something and that a quantifier binding its position quantifies over something should not be taken literally. All he wanted to emphasise is that function terms are semantically significant and that there are true existential quantifications besides those into the position of an object term.’ In effect, someone following the first version attributes to Frege the belief in the maximalist alternative theory while someone following the second version attributes to Frege the belief in the minimalist alternative theory. I can understand the desire not to ascribe to someone beliefs which are trivially false. But the temptation to deny that Frege rejected objectualism should be resisted. Frege combined two separately plausible but jointly inconsistent theories. Initially, he failed to see that the resulting theory is confronted with special problems. Then, when he noticed that
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following his theory he has to ascribe counter-intuitive semantic properties to phrases like ‘the first-level concept horse’, he considered different ways to cope with these difficulties. Only very gradually he became aware of how deep the problem is. And even when he finally came to the conclusion that his theory can only be presented by the use of expressions he admitted to be defective, he still sticked to it. The sad truth is that Frege simply held an inconsistent position. From start to finish he denied that everything is an object. There is another interpretative objection which should be mentioned here.28 I have claimed that Frege believed that not everything is an object. But is it clear that Frege really had this belief? Let us assume that Frege assertively uttered the sentence ‘Not everything is an object.’, and let us assume that this utterance was of a “standard kind”: he intended to use this sentence with its literal meaning, he was sincere, reflective, neither ironic nor sarcastic, and he did not conversationally implicate anything by uttering it.29 May I legitimately infer that Frege believed that not everything is an object? One may question the legitimacy of this inference because one may doubt that Frege used the sentence term ‘not everything is an object’ with the same sense as I do. In particular, one may suspect that Frege used the word ‘object’ with a sense that is different from the sense that I attach to this word. To deal with this objection one has to answer the question of which sense Frege attached to the word ‘object’. This question is not easily answered since Frege took the notion of an object to be basic and indefinable.30 Consequently, Frege did not believe that the elucidation of the notion of an object he gave are definitions. This is too large an issue to be exhaustively dealt with here. Let me just mention two points which seem to undermine a defence of Frege’s views along these lines. First, I think that Frege’s as well as my understanding of the words ‘object’ and ‘identical’ is such that the sentence term ‘something 28. Thanks to Benjamin Schnieder for pressing me on this objection. 29. Probably, there are further ways in which an utterance can be “non-standard”; these should be excluded here as well. 30. See section 1. This way of expressing the point may appear to be problematic in the present context. It might be objected that I should not use the word ‘object’ when I speak about Frege’s commitments. After all, according to the present objection, my uses of this word do not correspond in sense to Frege’s uses of it. The worried reader is advised to replace my formulation by a more cautious one: ‘When asked (and in the right mood), Frege would have made a standard assertive utterance of the sentence term “the notion of an object is basic and indefinable”.’ The same applies mutatis mutandis to the following formulations.
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is an object if and only if it is identical to itself ’ expresses something which is trivially true. But then, no matter whether Frege understood the word ‘object’ exactly as I understand it, he used the sentence term ‘not everything is an object’ to express something which is trivially equivalent to the thought that is expressed by the sentence term ‘not everything is identical to itself ’; i.e. he used the sentence term ‘not everything is an object’ to express something which is trivially equivalent to something which is trivially false. Second, even if I am wrong and Frege did not understand the words ‘object’ and ‘identical’ in the proposed way, this does not seem to constitute a significant advantage for his position. Since he believed that not everything is identical to itself, he believed something trivially false no matter how he understood the word ‘object’. One may, of course, now question whether Frege understood the words ‘not’, ‘everything’, or ‘identical’ as I understand them, but I do not see any reason to doubt that he did. Once you have seen the triviality of objectualism it is hard to put yourself into the position of someone who disbelieves it. But sometimes there are theoretical considerations that prevent you from recognizing something no matter how obvious it is. In this case, the theory has to be adjusted to be compatible with the missed triviality, and one may take some comfort in the fact that it should not be too difficult to make something compatible with a triviality.
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— 1892: “Über Begriff und Gegenstand”. In: KS, 167–78. — 1892–5: “Ausführungen über Sinn und Bedeutung”. In: NGS, 128–36. — 1893: Grundgesetze der Arithmetik. Begriffsschriftlich abgeleitet. Bk. I. Jena: Pohle. Repr.: Hildesheim: Olms, 1962. — 1903: “Über die Grundlagen der Geometrie. II”. In: KS, 267–72. — 1904: “Was ist eine Funktion?”. In: KS, 273–80. — 1906: “Über Schoenflies: Die logischen Paradoxien der Mengenlehre”. In: NGS, 191–9. — 1906a: “Einleitung in die Logik”. In: NGS, 201–12. — 1914: “Logik in der Mathematik”. In: NGS, 219–70. — 1919: “Aufzeichnungen für Ludwig Darmstaedter”. In: NGS, 273–7. — 1924/5: “Zahlen und Arithmetik”. In: NGS, 295–7. [KS]: Gottlob Frege. Kleine Schriften. Ed. by Ignacio Angelelli. Hildesheim: Olms, 1990. [NGS]: Gottlob Frege. Nachgelassene Schriften. Ed. by Hans Hermes; Friedrich Kambartel; Friedrich Kaulbach. Hamburg: Meiner, 1983. Hale, Bob 1994: “Singular Terms (2)”. In: Bob Hale & Crispin Wright (eds.), The Reason’s Proper Study. Oxford: Clarendon Press, 2001, 48–71. — 1996: “Singular Terms (1)”. In: Bob Hale & Crispin Wright (eds.), The Reason’s Proper Study. Oxford: Clarendon Press, 2001, 31–47. Künne, Wolfgang 2006: “Properties in Abundance”. In: Peter F. Strawson & Arindam Chakrabarti (eds.), Universals, Concepts and Qualities. Aldershot: Ashgate, 249–300. — 2010: Die Philosophische Logik Gottlob Freges. Frankfurt: Klostermann. Parsons, Terence 1986: “Why Frege Should not Have Said ‘The Concept Horse Is not a Concept’”. History of Philosophy Quarterly 3, 449–66. Simons, Peter 1981: “Unsaturatedness”. Grazer Philosophische Studien 14, 73–97. — 1983: “Function and Predicate”. Conceptus 17, 75–90. Wiggins, David 1984: “The Sense and Reference of Predicates: A Running Repair to Frege’s Doctrine and a Plea for the Copula”. The Philosophical Quarterly 34, 311–28. Wittgenstein, Ludwig 1921: Tractatus logico-philosophicus. In: Ludwig Wittgenstein. Werkausgabe Band 1. Frankfurt a. M.: Suhrkamp, 7–85. Wright, Crispin 1998: “Why Frege Did not Deserve His Granum Salis. A Note on the Paradox of ‘The Concept Horse’ and the Ascription of Bedeutung to Predicates”. Grazer Philosophische Studien 55, 239–63.
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III. COGNITION AND VOLITION
Grazer Philosophische Studien 82 (2011), 241–254.
COGNITIVE OPERATIONS AND THE MULTIFARIOUS REIFICATIONS OF THE UNREAL Peter SIMONS Trinity College Dublin Summary Object Platonism treats some singular terms as denoting abstract objects. Meaning Platonism treats sentences, predicates and other expressions as having abstract meanings. Nominalists reject both, and so have to give an alternative account of the work done by both sorts of Platonism. We make a start by classifying the variety of cognitive operations lending credence to such Platonic entities. Distinguishing between ontic categories, which divide reality, and auxiliary categories, which do not, but assist our cognition, we focus on those auxiliary categories which correspond to common ways of coping with reality using cognitive operations. These and the language that expresses and carries them seem to call for Platonic objects and meanings. Names which appear to denote abstract entities, but do not, reify. Species of reification distinguished here are hypostatization, abstraction, and complexification. Sentences, predicates and other propositive expressions appear to correspond to propositions, abstract properties, and other items implicated in expressing truths and falsehoods. Seeing these as embodying cognitive operations of proponing, predicating, conjoining, quantifying and modalizing rather than denoting various species of abstract entity begins to explain how they are cognitively useful, helping to carry the nominalist’s burden.
1. The joys of Platonism, the miseries of Nominalism Platonists have life easy, at least in some ways. Their ontology of nonconcrete (abstract) entities, some or all of which exist non-contingently, makes it relatively straightforward to interpret forms of discourse which seem to make reference to abstract entities. It gives them a straightforward way to interpret at face value statements of mathematics, as being about abstract entities designated by the singular terms inherent in this discourse. For example the equation ‘7 + 5 = 12’ is about three objects,
the three natural numbers 7, 5, and 12, and says of them that the sum of the first two is the third. Call this Object Platonism. It embodies the first Platonist advantage. Secondly, Platonists are able, via the acceptance of such abstract semantic entities as propositions, concepts, and truth-values, to account for the objective and absolute truth of certain statements and the objective and absolute validity of certain inferences (and the degree of validity of others) by giving an explication of such truth and validity in terms of abstract propositions and their parts. This is the most important common plank of the logical objectivist platform shared by Bolzano, Frege, Husserl, and Künne. Call it Meaning Platonism. The independence of Platonic meanings is a mighty bulwark against all logical relativism and this is generally (though not quite universally) reckoned to be a Good Thing. Nominalists who share the Platonist wish to make good sense of mathematics and logic have a different and prima facie much more daunting task: to account for the objectivity of mathematical and logical results without a timeless anchorage in the abstract, while yet not sliding into relativism.1 They lack the ontological resources to do so in the same straightforward way—by definition, since they deny the existence of the abstract entities the Platonist affirms. There are well known difficulties facing Platonism as well, which is the main reason why some people are prepared to take on the pain of being a nominalist, at any rate a nominalist who is prepared to offer some philosophical justification and account of her position.2 I shall not be considering the problems of Platonism, nor shall I attempt to fully justify nominalism, which is a long and ultimately perhaps hopeless task—hopeless not because nominalism is false but because it may be rhetorically impossible to enlighten a convinced Platonist. 2. Two kinds of categories Following Jonathan Bennett (Bennett 1966, 88ff.), I understand categories as concepts which are indispensable to cognition.3 But do categories, so understood, yield highest classes of things, as Aristotle believed, or do they 1. I am not addressing relativism here, simply assuming it is undesirable and indeed false. 2. Unlike so-called ostrich nominalists, who simply refuse to face the issue. 3. I gratefully resist the temptation here to pause and reflect what indeterminacies may lurk in the concepts of indispensability, concept and cognition.
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constitute the cognitive apparatus we bring to bear on the manifold of appearances, as Kant thought? My answer is that some do the one, others do the other. Categories which, to quote Plato’s striking phrase, cut nature at the joints, I call ontic. Categories which assist us to make sense of our experience of the world but do not themselves divide the things of the world I call auxiliary (Hilfskategorien). That there are auxiliary categories is easily shown: the logical categories of existence, universality, identity, negation, disjunction and so on do not divide things. As Wittgenstein (1922, 4.0312) said, they do not stand for (vertreten) anything. Such logical categories figure among Kant’s twelve, as do others which would appear to be ontic, such as the substance/accident distinction. I am not primarily concerned here to motivate or justify the ontic/auxiliary distinction (for this see Simons 2005), but to engage in some taxonomy on the auxiliary side of the divide. 3. Two kinds of auxiliary categories Auxiliary categories are concepts indispensable to thinking which do not represent their own kinds of items in the world. So far, so definitional. But to put flesh on this bone is to hazard an ontological thesis, since what one philosopher takes to divide things another doesn’t, because she doesn’t think the things are there to be divided. So the rest of this essay throws ontological neutrality to the winds and proceeds on a nominalist assumption. Among auxiliary categories, some employ terms, nouns or noun-phrases. Some noun phrases really are about objects, but nominalists contend that terms expressing auxiliary concepts purport to be about objects but in fact aren’t. They are as if about objects. Such terms reify, treat as things what are not things, or even are as if there are things when there are no such things. I call all terms which either themselves name or purport to name, or else contribute towards a naming or purported naming, nominative. Other parts of speech, according to a systematic (categorial) grammar include sentences, verbs, and many more. These can be nominalized, which constitute reifications of distinctive kinds. But the forms of speech involved also do not necessarily divide things in the world, yet are essential to cognition. They correspond to a variety of cognitive functions, such as judging, predicating, quantifying and the like. Being all in the service of
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putting forward propositions for consideration, or proponing, I call them all propositive. 4. Reifying and nominative categories The grass-roots form of cognition is representing something, and this emerges linguistically as naming, with its attendant semantic function of denoting. Some names denote unproblematically, and when they do their denotata fall under ontic categories. But terms that seem to denote, but do not do so, reify. There are several species of reification. Nominalizing which puts something forward as if a thing, but there is no such thing, is hypostatization. This is perhaps the most widely discussed form of reification since the time of Plato. There appears to be a very strong tendency for human beings to express themselves in the subject-predicate mode of speech. This is one of our most basic forms of proponing, and the ease, brevity and familiarity of the form render it a favourite way to say things that are by no means grass-roots in their meaning. We have nominalization whenever a sentence containing some part of speech that is not a noun is transformed so that the non-nominal part of speech is replaced by a noun. For example, instead of saying ‘More people saw the eclipse than did not’ we may say ‘The majority of people saw the eclipse’ where the NP ‘the majority of people’ replaces the compound quantifier expression ‘More people … than not’, the gap being filled by a predicate. Likewise in ‘Sean’s love for Máire is passionate’ we have the nominalized subject where in another equivalent sentence we have a verb phrase ‘Sean loves Máire passionately’. Much ink has been spilt about the possibilities and limits of sensepreserving paraphrase and its ontological commitments and I do not intend here to spill more; I am merely drawing attention to the fact that we nominalize readily, enthusiastically, and often almost unconsciously. The tendency is witness to a cognitive drive to think and express ourselves briefly and clearly about progressively more complex matters. Some nominalizations seem indeed to render ontological commitments more, rather than less apparent, at least to those who warm to the entities so denominated: ‘The truck’s collision with the bridge caused it to collapse’ is metaphysically at least as transparent as ‘The truck collided with the bridge and as a result it collapsed’. Nominals serving to refer to events are in my view not reifying but revealing of ontology, and the same goes
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for a number of other derived nominals, those referring to tropes being another case. Some NPs trade the plural for a singular, in a number of ways, most frequently using collective modifier nouns: so ‘Several boys together stole apples from Farmer O’Brien’s orchard’ is replaced by ‘A group of boys stole apples from Farmer O’Brien’s orchard’. This is, like nominalization, a generic grammatical shift, and we call it (obviously) singularization. It has been with us at least since Plato. Some usages such as ‘Bravery is a virtue’ prove extremely difficult if not impossible to paraphrase into forms without the abstract singular NP. The general subject of collective expressions and what they may or may not denote is an extremely involved one and I cannot go into detail here. I will say just two things. Firstly, while some singularized NPs appear straightforwardly to denote collective entities The flock of sheep were driven over the cliff by Gabriel Oak’s dog The swarm of bees settled on the elm tree (and many others using the delightfully so-named terms of venery) others equally obviously denote nothing at all The average Englishman has 1.8 children The average throw of a single die is 3.5 points while yet others give rise to doubt whether they denote or not The whale is a mammal, not a fish. Secondly, spare a thought for philosophy carried out in such not unimportant languages as Chinese and Japanese where there is no singular/plural distinction. Singularization in such languages makes no more sense than a theory of the definite article in Polish or Russian, yet group terms are available in those languages. One of the most important and common sources of derived singular terms is the cognitive operation of abstraction. This and more particularly its correlated objects formed the topic of Wolfgang Künne’s first book Abstrakte Gegenstände (Künne 1983). He and I have long known that we stand on opposite sides of the divide over whether there are abstract objects. From my point of view abstraction is typically reification. We know a lot more about how abstraction works linguistically than we did three decades
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ago, not least because of debates in the philosophy of mathematics. Given an equivalence relation E with its field of (relative) concreta, abstraction lets us introduce a term-forming functor §E enabling us to form terms purporting to denote new abstract(ed) objects or abstracta, according to the synonymous equivalence §E(a) = §E(b) l aEb for example the age of a = the age of b l a is as old as b the shape of a = the shape of b la is geometrically similar to b the number of As = the number of Bs l there are as many As as Bs In addition, we are able to derive predicates true of the abstracta from predicates true of the concreta and invariant under the abstraction, with a suitable sense-adjustment, by a scheme *E(P)(§E(a)) lP(a) where the functors *E and §E effectively cancel one another out. As Künne has taught us, this minor adjustment (which is often overlooked linguistically) is ignored at our peril. The importance of abstraction as a cognitive operation was perhaps first realised by Locke, and it has been in one form or another an important tool in much empiricist philosophy as well as in philosophy of mathematics and science. It can teach us much about the applicability of straightforward mathematics, though as a foundation for pure mathematics, it has its limitations, as Fine (2002) has argued. Some abstract singular terms are clearly reifying. For example The total fertility rate of Germany in 2006 was 1.36 according to UN statistics TFR is a so-called synthetic rate, not derived by actually counting. Others are disputed, for example The blue of the Netherlands flag is darker than the blue of the Luxembourg flag
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(realists about universals take it at face value, nominalists do not). Finally there are cases where I consider abstraction should be considered to reveal the relationship between abstracta so-called and their underlying ontological bases, even though the abstracta in question are far from abstract in the common acceptation: The organism sustained by these vital processes = the organism sustained by those vital processes l these processes are genidentical to those processes. The latter is a kind of abstraction I label (for want of a better word) empirical, because the equivalence obtaining is an empirical (and sometimes messy) matter. In this it contrasts with what we might call logical or mathematical abstraction, which is the rather neat and hygienic sort of abstraction beloved of logicians and philosophers of mathematics. Abstraction warrants a whole book to itself and these remarks don’t even scratch the surface: it is probably the most important cognitive operation. The final kind of nominative cognitive operation I want to mention is one—or rather a family of ones—I call complexification. This kind of operation combines features of singularization and abstraction but is not itself of either kind. It is relatively less recognized in its generality than the others. Suppose we have a system of objects a1, a2, … and they stand in a bunch of relations (which may include properties) so that, say, a1R1a2, a5R2a3, … R6a8, … Letting m be the multitude of objects and r the multitude of relations connecting members of m, we call K(m;r) the complex of m as connected by r. Complexes are identical if they consist of the same objects standing in the same relations. If r has but a single member connecting some objects, e.g. such that aRb, then the complex K(a,b; R) is the kind of object that Meinong spoke about in his 1899 essay on objects of higher order, and Russell and Whitehead considered in the Introduction to Principia Mathematica (Whitehead & Russell 1910, 43). Russell calls it the complex a-in-the-relation-R-to-b (ibid). Complexes in this case either are or correspond closely to what Husserl, Wittgenstein and others call states of affairs, and Russell called facts. They are objects with a complexity derived from their terms and relations. If this is right then we are familiar with one linguistic functor forming complex-denoting terms, which is the nominalizer ‘that’ prefaced to whole sentences:
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that Sean loves Máire that Socrates drank hemlock and so on. Denoting the complex that aRb by ‘[aRb]’ we may express the existence conditions of this complex by the equivalence E![aRb] l E!a E!b aRb which is a formula long pondered over by Meinong, Russell and Wittgenstein, if ultimately rejected by the last because he rejected complexes (Wittgenstein 1922, 2.0201, 3.24).4 If there is but a single monadic relation Q then K(a;Q) may be considered the object a qua Q. Where there are several objects and relations the complex in question might be called a situation. By varying the cases we get other sorts of complex. Where the relations part is empty, we have that complexes are identical iff they consist of the same objects. This we might notate as K(m;–) but equally well we might follow a German writer and notate it as {m}. The writer in question is Cantor, and the complex in question is what Cantor, following Bolzano, called the Menge of the several objects m. Thus on this view, sets are a special case of complexes. By adding relations we get more interesting complexes with more structure; for example with four objects a, b, c, d and a relation R that holds of all and only the following triples: aaa abb acc add bab bba bcd bdc cac cbd cca cdb dad dbc dcb dda, we get a complex which itself, or whose type, is known to mathematicians as the Klein four-group, where the element a is the neutral or so-called identity element. Another example would be the rotations of 3D space as objects and the functional relation of combination (one rotation followed by another) which can be represented by the unit quaternions. This shows that complexes can be infinitely complex. Actually listing the elements and relations is only possible for very small complexes. I admit that complexification is the most artificial and correlatively least “natural” of the cognitive operations I have considered. Nevertheless it is I think the general form of what is behind the mathematical drive to consider ever newer, more complex and more interesting structures. The limits of what complexification allows are not something on which a 4. For a commentary on Wittgenstein and the background in Meinong and Russell see Simons 1985a.
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philosopher can or should pronounce a priori. As the history of set theory illustrates, they are to be discerned quasi-experimentally, by boldly postulating and then seeing whether the postulates lead to a contradiction or not. In this regard David Hilbert’s infamous view that, in mathematics, existence is consistency, strikes me as not unreasonable. What ontological conclusions one draws from this is another matter: my own anti-realism about mathematical objects entails that I reject the word ‘existence’ taken at face value. Incidentally, on this account, category theory in mathematics is itself about a certain very broad kind of complexes, those where the relations are functional (“arrows”), incorporating an identity function and functional composition (Mac Lane 1998, 7). 5. Proponing and propositive categories In cognition, simply naming things, whether simply or derivatively, is only part of the exercise. At least as important, since cognition is about knowing, is proponing, or putting things forward as true. It is indeed Wolfgang Künne’s (2003, 337, 347) contention that we can analyse the notion of truth as it applies to linguistic and psychological entities in terms of truth as it applies to propositions x x is true lp(x = the proposition that p p)) x(x is a sentence o. x is true l p(x means that p p)) and one might add Bolzano’s x(x is a thought o. x is true l p(x has the content that p p)) Propositions as items named or quantified over nominally (quantified over by the variable ‘x’ above, not the variable ‘p’) are themselves on my view reifications, and so fall under the previous section. But let’s consider the linguistic and mental activities, or operations, of stating, asserting, suggesting etc. on the one hand, of judging, assuming, considering etc. on the other. All of these correspond not (according to Wittgenstein, and pace Frege) to naming but to a wholly different kind of operation, of which judging etc. are various subspecies, and which for want of a better term I co-opt the old English word proponing. They are what make thoughts thoughts and not mere presentations, sentences sentences and not mere
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names. Let us accept for now (I think we should for once and all) Wittgenstein’s view that proponing is not naming, either generally or a subkind. Wittgenstein’s insight is expressed most clearly perhaps not in the Tractatus but in his Notes on Logic, where he talks about the true/false bipolarity of proponing (or sentences) as distinct from the mere pointing of naming. A name either names something or it doesn’t. But a sentence (etc.) is true or false.5 Since proponing is not naming, any entities (“items”) corresponding to proponing, propositions expressed, not named, are not objects as nameables. They are something like Bolzano’s Sätze an sich or Wittgenstein’s Sätze, and, echoes of complexes aside, Moore and Russell’s propositions. They are essentially expressible only by a sentence and thinkable only by a thought. The question arises whether there is anything in the world that is categorically at all like them. My own view, since I reject not only propositions but also states of affairs or facts, is that there is not, and that therefore to treat such items as corresponding to anything real is to fictionalize, though not to reify. There is no res, but neither is there what Abelard called a dictum as something objective: only thinkings and statings as concrete events. The simplest form of proposition is not the subject-predicate proposition but the particular existential proposition. In this view I follow Brentano, who spoke here of thetic judgements, to be contrasted with judgements involving more than one term, synthetic judgements. Linguistically, thetic (existential) judgements are expressed using ‘exists’, ‘there is’, ‘es gibt’, ‘il y a’, ‘est’, and a host of other expressions (Simons 1992). A particular existential proposition such as Socrates exists The Beatles exist The water in this glass exists states that it exists (they exist): it accepts the item(s) in question. The vast majority of our mental judgings are thetic, and very few of them come to linguistic expression. This is because they flow constantly as we take in the world. Perception is primitive thetic acceptance, and the flow of nameable phenomena in our experience presents us with a stream of subjects for 5. It is incidentally astounding how little Wittgenstein’s insight has been adequately appreciated and respected by subsequent logicians and philosophers of language, from Carnap and Tarski to Montague. As honourable exceptions I would mention Prior and Geach.
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the common “predicate” ‘exists’, which we hardly ever articulate expressly to ourselves because the default value is set to acceptance. I hear a noise and turning to the left see two cyclists crash into one another. The noise, the location to my left, the collision, the cycles, the cyclists, the way one falls while the other stays upright, the colours and other visual characters of the bicycles are taken in within a split second and all fit the blanket acceptance assumption. Only when doubts arise or when we seek to inform others do we need to use (or withhold) the ‘e’ word. When expectations are confounded or opinions rejected we venture to deny existence, we reject a (purported) object, we execute a negative existential judgement, as in Batman does not exist The Norns do not exist General existential judgements are different again. I may accept chihuahuas (in general) and reject dragons (in general), and we get general existential judgements There are chihuahuas Chihuahuas exist There are no dragons Dragons do not exist Helium exists Kryptonite does not exist The more familiar subject-predicate type of atomic proposition is one in which we predicate something of one or more things: that Máire is beautiful, that Sean loves Máire and so on. Extracting away the nominal terms from these sentences we have a remaining pattern (not part!) which we may call the predicate. This is all very familiar, post-Frege. But what, if anything, do predicates stand for, denote, or have as semantic values? We are all familiar with various ways to consider predicates: as names of properties and relations, as denoting sets of ordered tuples, and so on. I personally consider that no predicate stands for anything. That does not mean that predicates do not contribute to determining the sentences in which they occur as true or false: quite obviously they do. How they do this varies considerably from case to case, and the uniform treatment of predicates as denoting attributes or sets of tuples is nothing other than a logician’s device for dealing with them all by one method thereby
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avoiding the pain and (logically irrelevant) hard work of seeing how different kinds of predicate work. Someone who was a logician but did not shirk this work, at least as he understood it to be necessary at the time— around 1324—was William of Ockham, whose theory of connotation deals with the different ways in which predicates contribute to the truth of simple sentences in which they occur. That the ontology behind the truth of simple predications may be various is argued somewhat later in by Mulligan, Simons and Smith (1984). To those accustomed to thinking of their metaphysics through the spectacles of natural language or predicate logic, the view that propositions and predication do not correspond to anything in reality may be shocking. Of course true predications and propositions are always true for a reason, and for some atomic predications we can point to that reason in the form of entities making the propositions true. But in general predication is far from being a simple reading-off of something from reality. In his intriguing and generally excellent book Experience and Judgment Edmund Husserl, for once free of his usual methodological hangups, contributes an insightful account of how predication arises out of prepredicative experience. In the thetic or acceptance attitude, we accept an object with complexity: the tomato on the table in front of us as we enter the kitchen. The tomato’s obvious redness and roundness catch our attention and our accumulated comparative and linguistic experience allows us to crystallize out the type of these inherent characters (tropes) as red, round, which we maintain mentally attached to the tomato as experienced, the subject of these attributes and bearer of these tropes. Expressing both the bearer and the types linguistically requires us to reattach the detachable type words (predicates) to the bearer word (subject) and presto! we have a predication. Thus predication is a highly complex mental achievement, with a much less direct relationship to the things themselves than the ontology of instantiation or set-membership would have us believe. When we consider how various sentential functors and operators contribute to the truth and falsity of increasingly complex sentences it is clear that the cognitive operations they express or indeed embody fall into a number of different classes. I shall finish simply by listing some of these and declaring their investigation as in need of more work. Much work has been done on them from a linguistic and logical point of view, but the psychological side has been rather neglected. Firstly, there is modalization. This has been a hot topic in philosophy of logic and language for half a century now, and through Kripke, Lewis
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and others it has strongly infiltrated metaphysics. Very many of our sentences and thoughts are modal in some way or another, yet an uncontested view on the status of these modalities is not to be found. There are clearly many different kinds or strengths of modality, from epistemic and practical through nomological to metaphysical and logical. They are surely to be treated differently: some may have greater ontological toehold in the world than others. This is, despite the plethora of writings, more unfinished business. Predication is just one way of building up a sentence or thought, one component of proponing. More complex ones include the use of quantifier phrases like ‘several tall sailors’, and logical connectives like negation, conjunction, implication, and other so-called expressions of higher type, which include quantifiers but also perhaps some adverbs, and maybe even more. For example in The percentage of voters in the US who voted in the 1860 presidential election is nearly two-thirds higher than that of those who voted in the 1996 election we may be dealing with a third or even fourth-level predicate. There is no obvious limit to how complicated, sneaky and indirect we may get in proponing: this is the cue for a simple theory of types (types in potentia, not in actuality). Nevertheless, to make such sneaky proponing accessible and palatable to the average thinker, we are led, and perhaps psychologically compelled, to rely on something like those modes of reification mentioned in the previous section. 6. Concluding remarks: Truth and abstract objects on a tight budget There are perhaps ways to give denotative semantics for these kinds of propositive functor which do not entail commitment to abstract objects of any sort. Doing this properly is part of the nominalist’s pain and misery (cf. Simons 1985b, 2005). Nominalists may fortunately be able to steal some of the work already done by Platonists, but as to how it is to be done, that is yet more unfinished business. But for the moment I am content simply to draw attention to the wide variety of modes of cognition which do not self-evidently get their semantic values by virtue of denoting items in the world, and yet which appear to be indispensable to said thought.
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REFERENCES Bennett, Jonathan 1966: Kant’s Analytic. Cambridge: Cambridge University Press. Fine, Kit 2002: The Limits of Abstraction. Oxford: Clarendon Press. Künne, Wolfgang 1983: Abstrakte Gegenstände: Semantik und Ontologie. Frankfurt am Main: Suhrkamp. — 2003: Conceptions of Truth. Oxford: Clarendon Press. Mac Lane, Saunders 1998: Categories for the Working Mathematician. 2nd ed. Berlin: Springer. Mulligan, Kevin, Simons, Peter M. & Smith, Barry 1984: “Truth-Makers”. Philosophy and Phenomenological Research 44, 287–322. Repr. in Jean-Maurice Monnoyer (ed.) 2007, Metaphysics and Truthmakers. Frankfurt am Main: Ontos, 9–50. Simons, Peter M. 1985a: “The Old Problem of Complex and Fact”. Teoria 5, 205–225. — 1985b: “A Semantics for Ontology”. Dialectica 39, 193–216. — 1992: “Existential Propositions”. In: Joachim Schulte & Göran Sundholm (eds.), Criss-Crossing a Philosophical Landscape. Essays on Wittgensteinian Themes. Dedicated to Brian McGuinness. Grazer Philosophische Studien 42. Amsterdam: Rodopi, 229–259. — 2005: “The Reach of Correspondence: Two Kinds of Categories”. Dialogue: Canadian Philosophical Review 44, 551–562. Whitehead, Alfred N. & Russell, Bertrand 1910: Principia Mathematica. Vol. 1. Cambridge: Cambridge University Press. Wittgenstein, Ludwig 1922: Tractatus Logico-Philosophicus. London: Routledge.
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Grazer Philosophische Studien 82 (2011), 255–284.
MEANING SOMETHING AND MEANINGS Kevin MULLIGAN University of Geneva Summary Meaning something (meinen) with a word or expression is one thing. The meanings (Bedeutungen) words and expressions have quite another thing. What, if any, is the relation between the two? I explore, compare and evaluate elements of the very different accounts of the relation between meaning something and meanings given by two Austrian philosophers, Husserl and Wittgenstein.
1. Meaning something: 1900–1951 Meaning something (meinen) with a word or expression is one thing. The meanings (Bedeutungen) words and expressions have quite another thing. What, if any, is the relation between the two? Many twentieth century philosophies of language and mind have put forward views about the nature of meaning something with a word. Many more twentieth century philosophies of language have advanced accounts of meanings and their ilk. A handful of philosophies of the relation between meaning something with an expression and meanings exist. Two such philosophies are given by the two most influential twentieth century philosophers, the Austrian philosophers Husserl and Wittgenstein. In what follows I explore, compare and evaluate elements of their very different accounts of the relations between meaning something and meanings. Meaning something with an expression plays a certain role in both the Tractatus and the Notebooks: what we, on the basis of arbitrary agreement (Übereinkunft) mean (meinen) with parts of that proposition (Wittgenstein TLP, 3.315) and if we mean by “p” (meinen) ~p and things stand as we mean, then “p” in the new conception is true and not false (Wittgenstein TLP, 4.062)
Peter Hacker, in his discussion of Wittgenstein’s extensive account of meaning something in the Philosophical Investigations (in particular, Wittgenstein PI, §§ 661–93) notes that discussion of the nature of meaning something is a philosophical newcomer: [W]hy should such prominence be given to a topic [meaning something] which has no obvious claim to pre-eminence in the history of philosophy? (Hacker 1995, 679)
Just how new is the newcomer? Meinong and Marty note the novelty of the topic in 1910 and 1908 respectively and finger the culprit, another pupil of Brentano–Husserl: It did not escape the attention of pre-scientific psychology […] daily life has an expression for it […] but theory has omitted to reflect on it for a remarkably long time. Of a word which has not been understood […] one can have reason to clarify what is “meant” by it […].[I]f one addresses A and gets an answer from B, one may have reason to note that one “meant” A.[…] The moment of deliberate intention (Absichtlichkeit) which certainly attaches to many cases in which the expression “means” is used […] only obtains in some cases. For the same reason we need not let ourselves be influenced by another essentially different sense of the expression in which Meinen and Meinung are compared with judging and believing and the like as something less perfect than these.[…] [W]e find ourselves faced with a question that can be quite simply formulated: What kind of experience do we have before us under the name Meinen? […] Meinen might simply amount to a sui generis mental experience […] (Meinong GA IV, 238; cf. tr. 173) In the intellectual domain it has recently been thought necessary to assume a large number of elementary Beziehungsweisen or “act-qualities”. According to Husserl these include: comparing and distinguishing, combining and colligating, disjoining, “meaning” (das “Meinen”). But it is not always clear whether these are supposed to be modes of judging or presenting or basic classes coordinated with judging and presenting.1 (Marty 1908, 242)
In his Logical Investigations (1900–1901) Husserl frequently says that “[…] we mean (meinen) this or that with our spoken or written signs” (Husserl Hua XIX/1, I, § 21, 71, tr. 306) and the phenomenon plays a central role 1. As we shall see, “Meinen” is not, according to Husserl, an act quality or mental mode. Karelitzki (1914, 33) also attributes the paternity of the discovery of meaning something to Husserl.
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in his philosophy of meanings (Bedeutung), sense (Sinn) and language. Thus he says: Naturally the expressions ‘A tone is faint’ and ‘A tone belongs to the set of objects which resemble one another with respect to faintness’ are semantically equivalent. But equivalence is not identity. If someone says that talk about faintness of tones could only arise if we had noticed similarities amongst faint tones […] he may be right. But what has all this to do with [the] sense [of our words], with what we mean by our words? (Husserl Hua XIX/1, App. to II, § 39, 212)
Marty and Meinong do not, however, think that Husserl has made an important discovery. This is par for the course in the brentanian tradition: the heirs of Brentano often announce major philosophical discoveries—of states of affairs or objectives, of suppositions or assumptions, of conjectural self-evidence, of Gestalt qualities etc.—only to find that other students of Brentano are deeply unconvinced. Meaning something, as Husserl conceives it, has no place in the taxonomies of the mind of Marty and Meinong and so it is, they think, a philosophical fiction. “Meinen” they argue means either opine or believe or intend or to have a presentation (Vorstellung) or assume. This is not, however, Husserl’s opinion or the opinion of his earliest followers such as Reinach and Scheler. As far as I can see, neither Bolzano nor Frege attach any importance to meaning something with an expression. And so, discovery or fiction, meaning something à la Husserl is a philosophical newcomer (at least within modern philosophy). Invocation of the phenomenon is also everywhere present in early Cambridge analytic philosophy. Stebbing tells the following story: At the outset of the discussion, not Russell but a man whom I had never seen and took to be quite young, began to ask me questions with a vehement insistence that considerably alarmed me. “What ON EARTH do you mean by that?” he exclaimed again and again, thumping the table as he said “on earth” in a manner that clearly shewed he believed there was no earthly meaning in what I had said. (Stebbing 1968, 530)
Meaning something seems first to have puzzled Wittgenstein in the context of the question: can or must what we mean be perfectly clear, sharp, determinate? When I say, “The book is lying on the table”, does this really have a completely clear sense? (An EXTREMELY important question.)
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But the sense must be clear, for after all we mean (meinen) something by the proposition, and as much as we certainly mean must surely be clear […]. There could, however, very well occur cases in which I should not be able to say straight off whether the book is still to be called “lying on the table”. Then—? Then is the case here one of my knowing exactly what I want to say, but then making mistakes in expressing it? Or can this uncertainty TOO be included in the proposition? But it may also be that the proposition “The book is lying on the table” represents my sense completely, but that I am using the words, e.g., “lying on”, with a special reference (Bedeutung) here, and that elsewhere they have another reference. What I mean (meinen) by the verb is perhaps a quite special relation which the book now actually has to the table […] It seems clear that what we MEAN (meinen) must always be “sharp”[…]. When I say, e.g., that the table is a yard long, it is extremely questionable what I mean by this. But I presumably mean that the distance between THESE two points is a yard, and that the points belong to the table. (Wittgenstein NB, 20.6.15, 67f.) It is clear that I know what I mean by the vague proposition. […] I tell someone “The watch is lying on the table” and now he says: “Yes, but if the watch were in such-and-such a position would you still say it was lying on the table?” And I should become uncertain. This shews that I did not know what I meant by “lying” in general. If someone were to drive me into a corner in this way in order to shew that I did not know what I meant, I should say: “I know what I mean; I mean just THIS”, pointing to the appropriate complex with my finger. (Wittgenstein NB, 22.6.15, 70)
Hacker comments: “Hence it is, inter alia, acts of meaning that render apparently vague propositions sharp” ( Hacker 1996, 684). Hacker suggests that at one crucial point in the Tractatus “thinking” and “meaning” are interchangeable: [The phrase—“the method of projection is to think (das Denken) the sense of the proposition” (TLP 3.11)] could with some plausibility be interpreted to signify much the same as “to mean that state of affairs” […] So when we use a propositional sign as a projection of a possible situation, i.e. use it ´thinkingly`, mean it, then it is a proposition, a sinnvoller Satz. It is acts of meaning, thinking, that links names to their meanings (Bedeutungen), infuse sentences with life, and endow them with intentionality. (Hacker 1996, 684)
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For Husserl, too, meaning something with an expression introduces a special sort of determinacy: The matter therefore must be that in an act which first gives it a relation to an object, and a relation so completely determinate that it firmly determines not merely the object which the act means but also the way in which it is meant. (Husserl Hua XIX/1, V, § 20, 429; cf. tr. 589)
“Matter”, in Husserl’s jargon, refers to a token or “subjective” content. Husserl often uses “means” and “signifies” (bedeutet) (and the nominalisations, “meaning” (das Meinen) and “signifying” (das Bedeuten)), as synonyms or explains signifying in terms of meaning something: […] signifying or meaning something […] which makes names and other expressions meaningful […] (Husserl Hua XIX/1, II, § 22; cf. tr. 381) the determinate way of meaning the relevant object (die bestimmte Weise des den jeweiligen Gegenstand Meinens) = the act of signifying (der Akt des Bedeutens) (Husserl 1984 Hua XIX/1 I § 13, 54–5) = meaning intention (Bedeutungsintention) = thinking = meaning-lending acts (bedeutungsverleihende Akte) (Husserl Hua XIX/1, I, § 9).
And a central claim of his philosophy of logic, language and mind—to which we shall return—is that meaning something with an expression instantiates an ideal or abstract meaning (Bedeutung). He therefore wonders what the relation is between “variations (Schwanken, fluctuation) in meanings [and] variations in signifyings [meaning]” (Husserl Hua XIX/1, I, § 28). He argues that change in meanings is really change in signifying (Bedeutens). In other words, the subjective acts which confer meaning on expressions are variable, and that not merely as individuals, but, more particularly, in respect of the specific characters in which their meaning consists. But the meanings themselves do not alter […]. (Husserl Hua XIX/1, I, § 28, 96; cf. tr. 322)
Perceptual content, he thinks, is, in the simplest cases non-conceptual, and determinately indeterminate: When, e.g., a familiar melody begins, it stirs up definite intentions which find their fulfilment in the melody’s gradual unfolding […] The regularities governing melody as such, determine intentions, which may be lacking in complete objective determinacy but which find or can find their fulfilments. As concrete experiences, these intentions are of course fully determinate; the “indeterminacy” of what they intend is plainly a descriptive peculiarity pertaining
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to their character. We may say, in fact, with correct paradox […] that “indeterminacy” (i.e the peculiarity of demanding an incompletely determined completion, which lies in a “sphere” circumscribed by a law) is a determinate feature of such an intention. (Husserl Hua XIX/1, VI, § 10, 572–3; cf. tr. 700; italics KM)
As he puts it later, it belongs to the essence of the indeterminacy peculiar to perception that it is determinable (Husserl Hua XVI, § 18, 59). Husserl’s account of the relation between the determinacy and indeterminacy of what is meant is to be found in his account of the relation between meaning something and non-conceptual perceptual content in demonstrative reference. A demonstrative expression, he thinks, has a meaning (Bedeutung) which is simple (non-descriptive) and incomplete. Meaning something with the help of a demonstrative expression—an “act of thismeaning” ( Husserl Hua XIX/1, LU, VI, § 5)—instantiates such a simple, incomplete meaning and is completed by perceptual experience or perception. It thus inherits the determinate indeterminacy of the object of the latter. Meaning something with a demonstrative requires perception if the relation of reference is to come about. For from the fact that someone means something with an expression it does not follow that there is something which he means.2 Wittgenstein invariably rejects as creatures of darkness the sort of thing Bolzano referred to as Sätze an sich, Frege as Gedanken, Husserl as ideal, propositional Bedeutungen and some philosophers as propositions. The thoughts of the Tractatus, for example, unlike Fregean thoughts, are pictures and so subjective items. Wittgenstein’s meditations on meaning something may be considered as a series of attempts to understand the determinacy and indeterminacy of meaning something with an expression without appealing to ideal meanings. As we shall see, Wittgenstein comes to reject the identification of meaning something and thinking and Husserl’s pupils, too, were to reject the form of this identification often endorsed by Husserl. 2. Meaning something—what it is and is not: 1911 & 1951 As Husserl and Wittgenstein use the verb in the sense or use which interests them “meinen” takes either a nominal (singular or plural) or a sentential 2. Cf. Husserl Hua XIX/1, LU, V, § 11, 386; Reinach SW I, 419. For the details of Husserl’s account of demonstrative reference, cf. Mulligan & Smith 1986, Mulligan 1997a.
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complement. One may mean with an expression Mary, Mary and Sam or that it is raining. Husserl distinguishes—as does Bühler following Husserl—meaning temporal (individuelle) objects—things, colour tropes, shape tropes and sound tropes—which he calls “individual” meaning, and the “general” (spezialisierende, allgemeine) meaning of idealia. In the first case “we mean […] this red moment in the house”, in the second “we mean red (das Rot)” (Husserl Hua XIX/1, LU, II, § 1, 114; cf. LU, II, § 19, § 21). In his discussions of the sort of example introduced by Husserl Wittgenstein says that “characteristic experiences” may occur when we mean a shape, […]—But this does not happen in all cases in which I ‘mean the shape’, […]
and the same is true when we “mean the colour” (Wittgenstein PI, § 35; cf. §§ 33–6). His further claim, that meaning something is not any sort of process or activity entails a number of largely descriptive claims about meaning something. Each of these claims had been put forward by Husserl’s pupil, Reinach, in 1911 in a remarkable description of meaning something which corrects some aspects of Husserl’s earlier account. On Reinach’s account these claims follow from a thesis which entails Wittgenstein’s claim that meaning is no process. Meaning, Reinach, says, is punctual in nature: R1 A spontaneous direction and a temporally punctual nature (eine zeitliche punktuelle Natur) are essential to meaning something. (Reinach TNU, 102; cf. 105) The same, he says, is true of apprehending or coming to know that p (Erkennen), making a resolution (das Fassen eines Vorsatzes), deciding (Sichentschliessen) and judging or asserting.3 Thus the category to which meaning something, apprehending and forming a resolution belong differs from the category of states—his examples are conviction, belief (Reinach TNU, 99), joy and sadness (Reinach SW I, 295) and being resolved, and from the category of processes—his example is deliberation. A process, unlike a punctual event, has temporal parts. Ingarden later suggested reserving the term “event” for what is temporally punctual. In what follows I shall use the term “episode” for processes, punctual events and states. 3. Apprehending or coming to know that p (Reinach TNU, 120), making a resolution (Reinach TNU, 158), deciding (Reinach SW I, 158), judging or asserting (Reinach TNU, 100; Reinach SW I, 549).
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Kripke mentions the view that meaning something might be a state: “Perhaps we may try to recoup, by arguing that meaning addition by “plus” is a state […]” (Kripke 1993, 51), a suggestion we shall return to. Reinach’s second claim is that R2 Meaning something is always linguistically clothed. (Reinach TNU, 102) Meaning something is by its very nature bound to linguistic expressions. (Reinach TNU, 108) These two claims amount to an implicit correction of Husserl. For although the inventor or discoverer of the philosophy of meaning something typically refers to meaning or signifying something with an expression, he does not think that meaning something is essentially connected to linguistic expressions. Although Reinach says that the punctual event of meaning something with an expression depends on an expression and the occurrence of an expression is presumably a process, he does not tell us what the temporal relation between the event and the process is. Like Husserl and Wittgenstein Reinach distinguishes meaning an object and meaning that p: R3 Meaning something vs Meaning that p Reinach introduces simply meaning an object as follows: Suppose I am counting off, say, the mountains of Germany, either by calling out their names to someone else or by reciting them to myself […] in uttering the words I mean something by them, i.e. precisely the mountains they designate (bezeichnen). Anyone wholly ignorant of language would be limited to the utterance of the words without understanding them; that is without meaning by the words the objects correlated (zugeordneten) with them. In contrast, whoever utters the words understandingly thereby aims (zielt)—with them or through them—through and onto something else […]. (Reinach TNU, 102, tr. 323)
He distinguishes between this case and the following cases: If I say e.g.: “Is a P?” and then: “a is P”, then in both cases something is meant, indeed what is meant is identically the same state of affairs; but in the first case it is put into question, in the second case assertingly posited. We could distinguish within the total complex which we designate as the assertion of a state of affairs, the specific moment of assertion on the one
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hand from the constituent of meaning something (Meinensbestandteil) […] on the other. The assertion is constituted from them both. (Reinach TNU, 107, tr. 329–330)
This is a very clear formulation of a view, one version of which is attributed by Wittgenstein to Frege and criticised by Wittgenstein at Investigations § 22, the view that there is a sharp difference between the mode, the content and the object or correlate of judging or asserting that p (and of asking whether p). Reinach’s claim that there is such a three-way difference and the further claim that modes and token contents are components of judging and asking are both made by Husserl and by many other phenomenologists. Wittgenstein’s view that W1 Meaning is no activity, process or state. I remember having meant him. Am I remembering a process or state?—When did it begin, what was its course; etc.? (Wittgenstein PI, § 661) And nothing is more wrong-headed than calling meaning a mental activity! Unless that is, one is setting out to produce confusion. (Wittgenstein PI, § 693)
is, as we have seen entailed by Reinach’s first claim (R1). Curiously, Wittgenstein does not entertain the possibility that meaning something is a punctual event, although he allows, like many phenomenologists, for punctual understanding, remembering and, like Reinach, deciding: One can remember a situation or occurrence at a moment.—To that extent, then, the concept of memory is like that of instantaneous understanding or decision. (Wittgenstein RPP I, § 837)
The view rejected explicitly by Wittgenstein and implicitly by Reinach, that meaning is a process, may be that advanced by Karelitzki in 1914. Karelitzki simply dismisses without any argument Reinach’s claim that meaning something is punctual (Karelitzki 1914, 34).4 After describing some examples of meaning he says In all these cases one can ascertain (konstatieren) a sui generis mental process (geistiger Vorgang) in oneself […]. (Karelitzki 1914, 44; cf. 34) 4. Since Karelitzki, like Scheler, thinks that to understand someone who means something is to co-mean (mitmeinen) and that co-meaning is a type of meaning his objection to Reinach may be that understanding is not normally punctual.
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Of one type of meaning he says that it is a “mental action” (geistige Handlung) (Karelitzki 1914, 45). It is however possible that in the passages referred to Karelitzki does not intend to call episodes of meaning something processes and actions but rather episodes involving both meaning something and cognizing or verification. Just what he means is not entirely clear. Like Reinach, Wittgenstein thinks that W2 Only in a language can I mean something with something. (Wittgenstein PI, 38) and allows for both meaning something and meaning that p (cf. the quotations from the Tractatus above): W3 Meaning something vs Meaning that p Reinach and Wittgenstein use related metaphors (or similes) in talking about meaning something: to mean is to aim—“abzielen”, “auf-zielen” (Reinach TNU, 103; Wittgenstein PI, § 691). Reinach and Wittgenstein put forward half a dozen plausible negative claims about meaning each of which follows from (R1–R3) and from (W1–W3): to mean is not sich etwas vorstellen (to have a presentation), not to see, hear…, not to think, to attend to, to be interested in. Their position contrasts with that of Husserl in 1900–1901 who is not above identifying meaning with sich etwas vorstellen, with experiences which have the property of intentionality and with thinking, and even with attending to something. Meaning something vs sich etwas vorstellen One of the first philosophers to describe meaning something is Pfänder who argues that to mean something is to be presented with it and to think of it (Pfänder 1900, 23). Reinach disagrees: “[…] meaning differs from presenting (Vorstellen)” (Reinach TNU, 102). And so does Wittgenstein:
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It is only in a language that I can mean something by something. This shows clearly that the grammar of “to mean” is not like that of “sich etwas vorstellen”. (Wittgenstein PI, 38; cf. PI, § 680)
As we have seen, Reinach also thinks that meaning something, unlike presenting, is language-bound. One reason given by Reinach for his claim that meaning differs from presenting is that seeing, hearing, thinking of numbers and feeling values are presentings and there are as many kinds of presenting as there are distinct kinds of presented objects or correlates. But there is, he says, no difference between meaning colours and meaning numbers other than the difference in their objects: The acts in which objects are presented differ fundamentally according to the class of objects towards which they are directed. Colours are seen, sounds heard, things of the external world are perceived by the senses, numbers are thought, values are felt […]. There is no difference between meaning a colour and meaning a number which would correspond to the difference between seeing and thinking which we meet in the case of presentings (Vorstellen) of colours and numbers.5 (Reinach TNU, 104; cf. tr. 325)
But even if one cannot see without seeing colours, cannot hear without hearing sounds, one can certainly think without thinking of numbers. A better argument is that whereas meaning is punctual, presenting is extended in time: the punctual act of meaning [is not any] stretched out act of presenting. (Reinach TNU, 103, tr. 324) A Vorstellung […] is a simple receptive “having” of an object, which may have a greater or lesser duration. (Reinach TNU, 102, tr. 323)
Thinking takes time. (As does imagining seeing something). But is the same true of seeing? “See” has a punctual time-schema. Wittgenstein calls seeing a state and Reinach implies that it can last or endure. Their view may be connected with the fact that “zusehen”, which may last or endure, may be considered by German speakers to be a type of seeing. 5. Reinach’s use of “sich etwas vorstellen” is not consistent. In 1914 he distinguishes between perceptual seeing and hearing, on the one hand, and imagining seeing and imagining hearing (vorstellungsmäßiges Sehen oder Hören), on the other hand. He also says that presenting is a modification of sensory functions, that it is an “inner” hearing or “inner” seeing (Reinach SW I, 320). On this (Husserlian) view sich etwas vorstellen is an exercise of the imagination and not a determinable of which seeing and hearing are determinates.
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Reinach notes that it is easy to confuse non-intuitive meaning and non-intuitive Vorstellen (Reinach TNU, 102). But “non-intuitive meaning something is not non-intuitive Vorstellen” (Reinach TNU, 104): Recently the question whether there are absolutely intuition-free acts of consciousness has been frequently discussed. It has been overlooked that there are really two questions here: the question about intuitionless presenting and the question about intuition-free meaning. (Reinach TNU, 106)
The reference is to the discussions between the Würzburg school psychologists and philosophers (Külpe, Bühler, Messer) and their opponents (Wundt). Looking back on the results of the Würzburg psychologists of thought, Bühler writes: That meaning should be […] described as separate from (intuitive) presentings was one of the general results [of the psychologists of thought]. (Bühler 1934, 220)
Reinach’s own view is that There is both fullness of intuition and absence of intuition in the case of presenting and in the case of meaning. (Reinach TNU, 104)
Seeing, he would presumably say, like Husserl, is an example of presenting which displays great intuitive fullness whereas thinking of a number may be free of intuitive content. Similarly, meaning an object may coexist with seeing it or not. Meaning vs thinking As we have seen, according to Reinach, “to think is sich etwas vorstellen” (Reinach TNU, 104, tr. 325). But: The objective correlate of meaning something is not in any sense present (vor-stellig). (Reinach TNU, 102)
Reinach’s two claims imply that to think is not to mean, a conclusion he does not draw. But is something always present when we think? Surely Husserl is right to say that there is “empty” thinking of something without any confirmation or intuitive illustrations. A better argument for the claim that to think is not to mean is that thinking is not punctual. Wittgenstein agrees that to think is not to mean:
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For “to mean it” did not mean: to think of it. (Wittgenstein PI, § 692) This shows you how different the grammar of the verb “to mean” is from that of “to think”. (Wittgenstein PI, § 693)
Wittgenstein’s argument for this claim, to which we will return below, is very different from either of the two arguments just mentioned.6 One of the few recent philosophers to have considered the role of the category of punctual events in the philosophy of mind is Wolfgang Künne, who argues against Geach’s view that judgings are “loosely tied to time”: Thus Geach has not shown that judgings cannot occupy single instants. I’ve argued that they actually are durationless. Is that incompatible with my earlier claim in section 8 that judgments have an internal structure? By no means. A comparison might help: The complexity of a judgment is not like that of a melody but rather like that of a chord. In judging that the moon is round you simultaneously exercise your ability to think of the moon and your ability to attribute roundness. In this respect episodic thinking is different from saying. (Künne 1996, 75)
If Reinach is right, judging is indeed a punctual event and has an internal structure. But to judge that the moon is round is not to think of the moon and think that it is round. It is rather to mean the moon and mean that the moon is round—in a judgmental way. There may be, as Wittgenstein and others like to affirm, a number of interesting analogies between sentences and melodies. But, as Künne says, the temporal profile of judging has more in common with that of a chord than with that of a melody. Reinach is unfortunately not consistent. At one point he explicitly compares the way in which an assertion, my saying “positingly” that the rose is red, is “built up” from “successive” acts of meaning of the different elements of the state of affairs that the rose is red to the way in which a melody is “built up” from its elements (Reinach TNU, 126).7 The later Wittgenstein, on the other hand, rejects the very idea of articulated thought: 6. Reinach is not consistent. In a text from 1914 he writes: “[…] and to “mean” them, i.e. to aim thinkingly at them (denkmässig auf sie hinzielen)” (Reinach SW I, 320; cf. 339). Wittgenstein, too, may be guilty of inconsistency in the following parenthesis: “Reading the written sentence loud or soft is indeed comparable with singing from a musical score, but ‘meaning’ (thinking) the sentence that is read is not” (Wittgenstein PI, § 22). 7. Reinach does not tell us how this squares with his view that asserting and judging are the same thing and are punctual.
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Thought and intention are neither ‘articulated’ nor ‘non-articulated’; to be compared neither with a single note which sounds during the acting or speaking, nor with a melody. (Wittgenstein PI, II, ix, 217)
Had the question been put to him he would presumably also have rejected a comparison between thoughts or judgments and chords. For Wittgenstein is consistently sceptical of the sort of things the descriptive psychologists called the dependent moments or features of mental and psychological acts or experiences. Meaning something vs interest and attention Husserl notes the importance of asking “what the relation between attending and signifying or meaning [is]” (Husserl Hua XIX/1, LU, II, § 22, tr. 381). Reinach suggests that To mean an object […], that can also signify an involved turning towards the object or whatever other expressions of pointing interest are available. (Reinach TNU, 103; cf. tr. 324)
But this is not the type of “meinen” Reinach has described hitherto: The kind of meaning an object which involves an interested concern essentially presupposes the presence of the object which is “meant” in this fashion, and here we are concerned with that type of meaning something whose distinguishing peculiarity is precisely this: that it neither presents the object to us, nor in any way presupposes its being presented. (Reinach TNU, 103; cf. tr 324)
Reinach suggests that Husserl does not always clearly distinguish the two kinds of meaning something. Wittgenstein does not say that “meinen” may signify attending to something but he gives two effective illustrations of the difference between meaning something and attention: Imagine someone simulating pain, and then saying “It’ll get better soon”. Can’t one say he means the pain? and yet he is not concentrating his attention on any pain […]. (Wittgenstein PI, § 667)
Differences in attention may correlate with differences in what is meant but they are not the same thing: Imagine that you were in pain and were simultaneously hearing a nearby piano being tuned. You say: “It’ll soon stop”. It certainly makes a difference
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whether you mean the pain or the piano-tuning!—Of course; but what does this difference consist in? I admit, in many cases some direction of the attention (Aufmerksamkeit) will correspond to your meaning (Meinung) one thing or another, […]. (Wittgenstein PI, § 666)
Reinach describes the relation between meaning something and attending to something in the following terms: Anything that is presented is such that we can turn toward it with a specific interest, raise it up out of its surroundings, concern ourselves with its specific traits. In the sphere of meaning in our sense however there is no possibility of such modifications. Consider for example the situation in which in the course of speaking we direct ourselves, in succession, towards a series of objects. In such a case there can be no talk of a turning towards the objects, a raising of them into prominence. For of course whilst it is possible to turn one’s attention towards objects which are at first merely meant, this can never occur within the act of meaning itself; it requires its own new act, one which will bring these meant objects to presentation, and only what is thus brought to presentation can then be the subject of an attentive turning towards. We can only advert to that which is thus presented. (Reinach TNU, 103, tr. 325)
We may add, on behalf of Reinach and Wittgenstein, that interest and attention take time, unlike meaning something. 3. Meaning something as an instantiation of a meaning: 1900. Meanings wear the trousers What, if anything, constrains what one can mean with an expression? According to Reinach and Wittgenstein, language sets limits to what one can mean. According to Husserl, Reinach and Wittgenstein meanings (Bedeutungen) constrain what one can mean. Wittgenstein, of course, has an account of Bedeutungen which is not that given by Husserl and Reinach. Wittgenstein famously says: Can I with the word “bubu” mean: “If it doesn’t rain, I shall go for a walk?”—It is only in a language that I can mean something by something. (Wittgenstein PI, 18; cf. § 508, § 557)
Similarly, Bühler writes in 1934:
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[…] thus a determined subjectivist can […] say: “In the end I can mean everything with everything. Against this there is nothing more to be said than that such a maxim, once it becomes a principle, is the best way to make verbal intercourse impossible […]”. (Bühler 1934, 230f.; cf. tr. 258)
The formulations Wittgenstein puts in the mouth of the sort of philosopher Bühler calls a determined subjectivist, for example, But isn’t it our meaning something that gives sense to the sentence? (Wittgenstein PI, § 358)
are just the formulations introduced by Husserl: […] signifying or meaning something […] which makes names and other expressions meaningful (sinnvoll) […] acts which lend meaning (bedeutungsverleihende) (Husserl Hua XIX/1, LU, II, § 22)
Bühler seems to have thought Husserl was a determined subjectivist. Who did Wittgenstein have in mind when talking of someone who thinks that our meaning something gives or lends sense or life to dead marks? Did he merely mean the author of the Tractatus? Husserl was certainly no determined subjectivist. He argues repeatedly: To names there correspond certain meanings and through these we relate to (wir beziehen uns auf ) the objects. (Husserl Hua XIX/1. LU, II, § 14, tr. 365f.)
His view is: meaning something makes marks meaningful because meaning something is determined at least in part by meaning (Bedeutung). A corollary of this is that Object and meaning (Bedeutung) never coincide. (Niemals fällt aber der Gegenstand mit der Bedeutung zusammen.) (Husserl Hua XIX/1, LU, I, § 12, 52; cf. tr 287)
The later Wittgenstein agrees: It is important to note that the word “meaning” (Bedeutung) is being used illicitly if it is used to signify the thing that “corresponds” to the word. That is to confound the meaning of a name with the bearer of the name. (Wittgenstein PI, § 40)
The view that the object of a name is its Bedeutung, rejected by Husserl in 1900 and by the later Wittgenstein, is to be found not only in the Tractatus (3.203) but also much earlier in Meinong and before that in Frege.
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It is the view denounced in very similar terms by Wittgenstein in the first section of the Investigations and by Bühler in 1909 (cf. Mulligan 2009). It is because meanings determine or contribute to determining what can be meant that one cannot mean (anything with?) senseless series of words: But isn’t it our meaning something that gives sense to the sentence? (And here, of course, belongs the fact that one cannot mean a senseless series of words.) (Wittgenstein PI, § 358)
Husserl agrees. He points out that [a]n expression which has no meaning […] like Abracadabra […] is, properly speaking, no expression. (Husserl Hua XIX/1, LU, I, § 15, 59) [I]f […] we say a round or; a man and is etc., there are no meanings (Bedeutungen) which would correspond to such verbal combinations as their expressed sense. (Husserl Hua XIX/1, LU, IV, § 12; cf. tr. 517)
Categorial grammar rules out certain combinations of meanings: the other combinatorial possibilities are excluded by law; they result only in a heap of meanings (Bedeutungshaufen) instead of One meaning.8 (Husserl Hua XIX/1, LU, IV, § 10, 326)
(Wittgenstein, too, thinks that (his) categorial grammar rules out certain possibilities: “The proposition is no heap of words (Wörtergemisch)” (TLP, 3.141)). We should, Husserl argues, be resolute about nonsense. Our relation to nonsense is this: The word nonsense (Unsinn) […] is to be taken in its literal and strict sense; a heap of words, such as king but or similar and cannot be understood as a unit […]. (Husserl Hua XIX/1, LU, IV, § 14; cf. tr. 522)
Since Husserl thinks that my understanding the words I use and my signifying (Bedeuten) with these words are the very same thing (Husserl Hua XIX/1, LU, I, § 23), and that signifying and meaning (Meinen) are the very same thing, it follows that, on his view, I cannot mean (something with) nonsense.9 The view that we cannot mean nonsense also follows directly from Husserl’s first account of the relation between meanings and meaning, the instantiation theory. 8. Cf. “provided we do not conglomerate (konglomerieren) meanings meaninglessly” (Husserl Hua XIX/1, LU, VI, § 63, 723). 9. If Reinach is right, Husserl’s identification of a speaker’s understanding and meaning is only plausible for momentary understanding.
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Instantiation We have seen that, according to Husserl, Meaning something makes marks meaningful because meaning something is determined at least in part by meaning (Bedeutung). What does “determine” mean? Husserl’s answer is: For meaning something to be determined by meaning (Bedeutung) is just for meaning something to instantiate a meaning. Husserl’s fullest formulations of this view run as follows: The manifold singulars for the ideal unity meaning are naturally the corresponding act-moments of signifying something, the meaning-intentions. Meaning is related to varied acts of signifying (Logical Presentation to presentative acts, Logical Judgment to acts of judging, Logical Inference to acts of inferring) just as Redness in specie is to the slips of paper which lie here, and which all “have” the same redness. Each slip has […] its own individual redness, i.e its instance (Einzelfall) of this colour-species. (Husserl Hua XIX/1, LU, I, § 31, 106; cf. tr. 330) In the actual experience of signifying there is an individual feature, an instance of the species […], which corresponds to the unitary meaning (Bedeutung), just as to the specific difference Redness the moment of red in the object corresponds. If we perform the act and live in it, as it were, we naturally mean (meinen) its object and not its meaning. (Husserl Hua XIX/1, LU, I, § 34, 108; cf tr. 332)
What exactly is a Bedeutung? What are the main types of Bedeutungen? What is it to instantiate such a thing? What exactly instantiates Bedeutungen? On Husserl’s early view Bedeutungen are “ideal (and so rigid (starre)) unities” (Husserl Hua XIX/1, LU, I, § 28, 94), outside space and time, up there with Frege’s thoughts and sense and Bolzano’s Sätze an sich and Vorstellungen an sich. Around 1907 he rejected this view: Bedeutungen, unlike numbers, are now earth-bound—he mentions also the possibility of Mars-bound meanings. They are “bound idealities”, unlike “pure idealities” such as numbers. The main types of meaning distinguished by Husserl are:
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(1) Subject-Meanings, (2) predicate-Meanings, (3) relational Meanings and (4) combinatory Meanings […] (5) [The Meanings of the predicates] true and false, possible and impossible, general and singular, determinate and indeterminate etc. [which correspond to the] ideal determinations which hold primarily of meanings. (Husserl Hua XIX/1, LU, I, § 31, 100, tr. 330)
and (6) Propositional Meanings (statement-Meanings, Aussagebedeutungen). Of these (6) is the fundamental kind: […] a concept so fundamental as that of an (ideal) propositional Meaning (Aussagebedeutung), the ultimate point of unity to which all things logical must be referred back. (Husserl Hua XIX/1, LU, V, § 40, 513; cf. tr. 647)
Husserl, then, could have said with Wittgenstein that his “whole task consists in explaining the nature of the proposition” (Wittgenstein NB, 22.1.15). What sort of thing instantiates a Bedeutung? Only meaning (Meinen), that is to say, a person’s signifying (bedeuten), can instantiate a Bedeutung. The multiplicity of meaning something is determined by the multiplicity of Bedeutungen: there is meaning an object and meaning that p. An act of judging contains “subject-acts, predicate acts etc.” as “components” (Husserl Hua XIX/1, LU, V, § 20). “Concrete signifying”, that is, concrete meaning, may be simple or complex (Husserl Hua XIX/1, LU, IV, § 3): To a Bedeutung corresponds in the concrete act of signifying a moment which makes up the essential character of this act, i.e necessarily belongs to each concrete act in which the same Bedeutung is ‘realized’. In regard to the division of acts into simple and complex, a concrete act can contain several partial acts and these can belong to the whole either as independent or as non-independent parts. (Husserl LU, IV, § 7, 320; cf. tr. 506)
When one uses a word or sign which has what Husserl calls a “combinatory or connective meaning” (Verknüpfungsbedeutung), for example, one of the logical constants or “+”, does one typically mean something thereby? Reinach’s answer to this question is clearer and has been (deservedly) more influential than Husserl’s answer (cf. Mulligan 2009a). It is negative: To “and” there corresponds no meaning something but rather a function, the function of connecting (Verbinden). (Reinach TNU, 129)
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But although one does not mean anything when one uses “not” or “and” the functions of negating and connecting or conjoining can only occur, Reinach claims, together with meaning something or meaning that: Functions [“and”, “not”] occur only in the sphere of meaning something.10 (Reinach TNU, 136)
Thus if Reinach is right, the thought formulated by Kripke and quoted above is doubly wrong: meaning something is no state and nothing can be meant by “+”. I said above that, according to Husserl, only meaning (Meinen) instantiates Bedeutungen. That is a slight simplification. In every “act” or intentional experience Husserl distinguishes two components: In each act’s descriptive content we have distinguished quality and matter as two mutually dependent moments. (Husserl Hua XIX/1, LU, V, § 21, 417; cf. tr. 590)
“Quality” is what is sometimes called a “mode”: seeing, seeing that, judging that, desiring that are mental modes or qualities. By “matter”, as already noted, Husserl means a token content: “Content in the sense of matter is a component of the concrete act-experience” (Husserl Hua XIX/1, LI, V, § 20). With the help of these stipulations Husserl formulates his first considered view of the relation between mental acts and Bedeutungen: To the extent that we are dealing with acts which function or can function as meaning-giving acts for expressions … we should speak [of the unity of quality and matter as] the semantic essence of the act. Ideational abstraction of (from) this essence [a so called “individual essence” —KM] yields a meaning in our ideal sense. (Husserl Hua XIX/1, LU, V, § 21, 417; cf. tr. 590)
The quality-matter couples which make up the individual essences of meaning-giving acts include (judging + meaning that) and (imagining judging + meaning that). Thus Husserl thinks that it is not only meaning something or meaning that which instantiates Bedeutungen but these as qualified by certain mental modes: The identity of “the” judgment or of “the” statement (Aussage) lies in the identical Bedeutung repeated as the same in the many individual acts, and represented in them by their semantic essence. (Husserl Hua XIX/1, LU, V, § 21, 421; tr. 593) 10. Reinach also thinks that negation occurs in negative states of affairs.
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A more plausible view is that only meaning instantiates Bedeutungen and token mental modes instantiate such kinds or types as Judging and Imagining, and that no episode of meaning something can occur unless qualified by some mode. What is it to instantiate a meaning? Not anything like the relations Bolzano and Frege called grasping (erfassen, fassen) a thought or Satz an sich. Indeed it is not any sort of mental or psychological relation. It is rather the purely formal relation between tokens, on the one hand, and a type, where the latter is understood in some suitably robust fashion, as a “species” (cf. Mulligan 2004). It is not the equally formal relation of exemplification which relates an object and a property (although many philosophers now use “instantiation” and “exemplification” as synonyms). As Husserl puts it: “meaning (meinen) is a Vereinzelung of a Bedeutung” (Husserl Hua Mat, II, 68). One objection to Husserl’s claim that my meaning that p instantiates a meaning, the proposition that p, is that my meaning that p is an episode, if Reinach is right, a punctual event. But the type instantiated by an episode is a type of episode. Different particular collisions instantiate the type: Collision. One reply to the objection appeals to the intuition that one and same word type can be instantiated by a process (the occurrence of a word) and by a substance (a particular printed word). 4. Related views In order to better understand Husserl’s instantiation theory it is useful to consider some related views. We may distinguish four families of such views. There is (A) the view that there are structured episodes of meaning that p or other mental particulars which instantiate meanings. There is (B) the view, already mentioned, that there are unstructured mental graspings of abstracta such as sense, thoughts, meanings, propositions, Sätze an sich or Vorstellungen an sich. There is (C) the view that there are structured episodes of meaning that p or other mental particulars which instantiate no abstracta because there are no such abstracta. Finally, there is (D) the view that there are structured meanings that p or other mental particulars and abstracta such as propositions but the former do not instantiate the latter. One variant of the last view—(D)—was in fact adopted by Husserl around 1907: meaning that p does not instantiate but corresponds to a
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Bedeutung. Philosophers who have understood his earlier view have often found Husserl’s arguments against it and his alternative unconvincing (cf. Künne 2009; Mulligan & Smith 1984). In one of the many passages where he returns to and rehearses his—“important”—change of mind he writes: Two acts of judging, which mean (meinen) the same proposition (Satz), mean identically the same thing, and it is not the case that each means by itself an individual proposition as a moment, that each means a similar proposition, so that the one ideal proposition 2 < 3 would merely be a general genus for all such particularisations (Vereinzelungen). (Husserl 2004, 266)
But according to his earlier view two acts of judging that p contain two episodes of meaning that p. They mean or rather the judgers mean the very same thing, the very same state of affairs. Each of the episodes instantiates the Satzbedeutung or ideal proposition that p. The two judgers do not mean either the same or different Bedeutungen. Husserl’s later view is a reversion to the type of view to be found in Bolzano, Lotze and Frege. Husserl is about as reliable a guide to his earlier views as is Wittgenstein. Husserl, however, takes less time than Wittgenstein to become unreliable. Another variant of view (D) is the influential account put forward by Crimmins and Perry: beliefs are concrete, structured particulars: (i) Beliefs are concrete cognitive structures: they are particulars that belong to an agent, come into existence, endure, and go out of existence. (ii) Beliefs are related to the world and to other cognitive structures and abilities in a way that allows us to classify them by propositional content […] The propositions believed are the objects of belief. An agent believes some proposition in virtue of having a belief with that content […] Beliefs are neither public nor abstract; they are concrete particulars that belong to agents just like arms, headaches, and bouts of the flu. A belief comes into existence when an agent forms it; it is not the sort of thing that is around for the agent to adopt. To countenance beliefs as particulars is not to deny that there are interesting systems of abstract objects which might be used to classify them, such as meanings, Fregean senses, intensions, characters, or the like. (Crimmins & Perry 1989, 688)
Classification by e.g. senses, on this view, is not, it seems, instantiation. Propositions play the same sorts of roles as Husserl’s states of affairs and Russell’s singular propositions. Ideas and notions have the same ontological status as beliefs:
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Beliefs are structured entities that contain ideas and notions as constituents. Ideas and notions, like beliefs, are on our view concrete cognitive particulars. So there is no such thing as agents having the same idea or notion, but only similar ones. Admittedly, the technical use we make of these terms involves a departure from what we ordinarily say about ‘ideas’ and ‘notions’, or at least represents a choice among the many different ordinary uses of these terms. On our use of the terms, there are no notions and ideas that agents do not have, any more than there are headaches that no one has. The difference between notions and ideas is the difference between an agent’s “ways of thinking” about individuals versus properties. (Crimmins & Perry 1989, 690)
A variant of view (A) occurs as an interpretation of the Tractatus given by Ramsey in 1923. Ramsey says: A propositional sign is a sentence; but this statement must be qualified, for by ‘sentence’ may be meant something of the same nature as the words of which it is composed. But a propositional sign differs essentially from a word because it is not an object or class of objects, but a fact, “the fact that its elements, the words, are combined in it in a definite way” (3.14). Thus ‘propositional sign’ has type-token ambiguity; the tokens (like those of any sign) are grouped into types by physical similarity (and by conventions associating certain noises with certain shapes) just as are the instances of a word. But a proposition is a type whose instances consist of all propositional sign tokens which have in common, not a certain appearance, but a certain sense. As to the relation between a proposition and a thought Mr W. is rather obscure; but I think his meaning is that a thought is a type whose tokens have in common a certain sense, and include the token of the corresponding proposition, but include also other non-verbal tokens; […].11 (Ramsey 1931, 274)
Variants of view (C) were defended by some of Brentano’s heirs, in particular Anton Marty: judgings and presentations are structured concrete episodes which stand to one another in relations of greater or lesser similarity but do not instantiate Bedeutungen as Husserl conceived of these for there are no such things.12 Wittgenstein’s later account of the Bedeutung of a word as being, in many cases, its use is very different from Husserl’s account. But a formal 11. The view that propositions are types is later discussed by Moore, who attributes it to Ramsey; cf. Moore 1992, 39–47. 12. On this view in the Brentanian tradition, cf. Mulligan 1989, Mulligan (ed.) 1990. For a defence of the view, cf. Simons 2003.
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relation of instantiation does arguably play an important rôle in Wittgenstein’s account. The temporally extended use of a word is made up of many particular applications of the word in different sorts of context.13 Each such application involves following or breaking various rules. What is the relation between the episodes of breaking and following a rule and the rule itself? It has often been plausibly maintained that this relation is the internal, formal relation of instantiation. As H.-J. Heringer puts it: “meaning (Bedeutung) und meaning (Meinung) stand to one another as rule and rule-following” (Heringer 1974, 128). 5. Meaning something—an Austrian myth? We noted in § 1 that, according to Marty and Meinong, meaning something à la Husserl is a philosophical fiction. If they are right, then meaning something à la Husserl/Reinach/Scheler/Bühler/Wittgenstein is a myth. It is a striking fact that in the enormous literature defending one or another version of the Marty-Grice account of meaning14, the verb “mean” is standardly taken to ascribe a type of intention for the purposes of the account. It is also worth noting that, as we saw in § 1, Husserl uses “Intention” as a synonym of or gloss on “meinen”. He also thinks that willing, remembering and judging can each be described as an “Intention”, as can an “Absicht”—or intention! Is this not a symptom of the confusion Marty and Meinong thought they detected at the heart of Husserl’s phenomenology? What are the properties of the kind of thing Husserl, Reinach and Wittgenstein have in mind in their discussions of meaning something and meaning that p? As we have seen, Husserl seems to know that the verb is not factive. Sam may mean that Mary is generous although she is not generous. One cannot order someone to mean something.15 Nor can one ask “Why did you mean that p?” Meaning something is not the sort of thing which can succeed or fail. It therefore differs from referring, where this is taken to be an activity of a speaker (speaker’s reference). One may fail to understand a sentence but one may also fail to understand the person who uses the sentence, fail to understand what he means.16 13. On the relation between what Bühler and Wittgenstein have to say about the variety of such uses and contexts, cf. Mulligan 1997. 14. On Marty’s contribution to this account, cf. Mulligan (ed.) 1990. 15. It is not clear to me whether Reinach could accept this claim. 16. On all these claims, cf. Heringer 1974, 124–130. Cf. also Stampe 1968.
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Clearly “meinen” and “mean” sometimes mean something like intend (cf. Geyser 1913, 369). The French translation of “meinen” is “vouloir dire”. (French translations of “meinen” as used by Husserl sometimes employ the verb “viser” (to aim at). But this verb cannot take a sentential complement). “I meant you to F” does seem to mean something like: I intended you to F. Must “mean” in locutions of the form x meant y with w x meant that p with s ascribe an intention? The two most important cases which need to be considered are ascriptions of meaning something in the context of linguistic interactions and ascriptions of meaning something in the context of solitary intentionality. Suppose Sam forms the intention to help Maria. Suppose, too, that this is a momentary occurrence, like the momentary decidings allowed for by both Reinach and Wittgenstein. Sam’s intention to help Maria involves or contains his meaning Maria perhaps with the word “Marie”, perhaps with some mental equivalent thereof. If he didn’t mean Maria he could not intend to help her. How could Sam’s meaning Maria in the context of his intention to help her be a type of intention? If it were an intention, immediately a regress would arise, a regress which is vicious because it is psychological or mental.17 Suppose Sam tells Hans that Maria is sad intending to induce a belief or judgment to this effect in Hans. Is Sam’s meaning Maria with “Marie” not an essential part of the content of his intention? At one important point Wittgenstein uses “meinen” in a context where it may have the force of “intend”. His argument for the claim we have already introduced, that to mean something is not to think, goes as follows: Is it correct for someone to say: “When I gave you this rule, I meant that you ought to . . . . . in this case”? Even if he did not think of this case at all as he gave the rule? Of course it is correct. For “to mean it” did not mean: to think of it. (Wittgenstein PI, § 692, transl. modified ) 17. Ian Rumfitt has pointed out to me that this point has some similarities with the criticisms levelled by Dummett against the Grice-Strawson-McDowell account of linguistic meaning: that “they purport to explain what it is to make an assertion with a given content, given that we already grasp the notion of something’s having that content […] [B]eing informed that such-andsuch is so and believing that such-and-such is so both obviously involve having the thought that such-and-such is so: and thus this strategy of explanation takes as already given the conception of the thought expressed by a sentence […]” (Dummett 1993, 172).
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“When I teach someone the formation of the series . . . . I surely mean that he ought to write . . . . at the hundredth place.”—Quite right; you mean it. And evidently without necessarily even thinking of it. This shews you how different the grammar of the verb “to mean” is from that of “to think”. And nothing is more wrong-headed than calling meaning a mental activity! Unless, that is, one is setting out to produce confusion. (Wittgenstein PI, § 693, transl. modified )
Does “I mean(t) that you ought to …” mean: “I meant you to …”, that is, “I intended you to …”? This reading is perhaps suggested by Hacker’s exegesis: Meaning the pupil to continue past “1000” by writing “1002, 1004, 1006 …” does not imply that the teacher thought of this segment of the series, when he gave the order. Meaning someone to do something thus-and-so is not the same as thinking of it. (Hacker 1996, 729)
If so, then Wittgenstein’s conclusion should be that to mean, where this is to intend, is not to think.18 This is, in any case, Marty’s view in 1908: We say: our mind merely “means” the number 1000 but does not really think it.19 (Marty 1908, 466)
And Wittgenstein’s remark about the grammar of the verb “to mean” is a good example of the message tirelessly repeated by Marty: […] the thought of a doing or acting, which is awakened by a verb, belongs only in a minority of cases to the meaning of the relevant word; in the majority of cases it is merely a picture (Bild), […]. (Marty 1950, 56)
—a misleading picture. Adolf Reinach’s pioneering account of meaning something is a forerunner of the account given between 1911 and 1916 by Scheler of remembering, recalling, expecting, meaning something, meaning that p, willing and intending, all of which he calls “mental” (geistige) “acts” and sharp18. On Reinach’s behalf we may add that whoever intends or orders at a time must mean something, and to mean something is not to think. 19. For Husserl’s account of meaning the number 1000, cf. Husserl Hua XIX/2, LU, VI, § 20, 604. Marty’s 1908 distinction between meaning and thinking of a number is part of his account of “improper” thinking, presenting and naming, an account which differs in some respects from Husserl’s 1901 account of improper or purely descriptive thinking, presenting and referring; cf. Husserl Hua XIX/2, LU, VI, § 16ff. For Husserl, as for Wittgenstein (PI, § 353), there is an internal relation between meaning that p and the verifiability of the proposition that p.
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ly distinguishes from psychological (psychisch, seelisch) phenomena or experiences such as emotions and feelings. At the heart of Scheler’s analysis is a three-way distinction between the categories of private objects, public objects and non-objects. The category of private psychological objects is, he argues contra Husserl (1911), empty, indeed essentially empty. All psychological phenomena and experiences are public, reidentifiable objects, and this, too, is supposed to be an essential truth. Remembering, recalling, expecting, meaning something, meaning that p, willing and intending, on the other hand, are non-objects: they are not possible objects of knowledge by acquaintance, although they can of course be described and ascribed. They are not experiences, processes or states. The most direct form of knowledge I can have of your remembering, recalling, meaning etc. is the knowledge that results from understanding, from shared intentionality, from co-meaning (Mitmeinen). The philosophies of Scheler and Wittgenstein are about as different as philosophies can be. But in his descriptions of remembering, recalling, expecting, meaning something, willing and intending and of such public objects as the emotions of other people and in his views about public, reidentifiable objects Wittgenstein’s account turns out to have more in common with Scheler’s descriptive phenomenology than with any other account of these matters.20
Work on this paper was supported by the “Seventh Framework Programme FP7/2007-2013” of the European Commission (“grant agreement” No. FP7-238128) and by the Sinergia project of the Swiss FNS, “Perspectival Thoughts and Facts”, sub-project: “Intentionality as a Mark of the Mental. Metaphysical Perspectives on ContemporaryPhilosophy of Mind”. Thanks go to Benjamin Schnieder, Moritz Schulz and Laurent Cesalli for their critical remarks.
20. On the origins of these similarities between the views of Scheler and Wittgenstein, cf. Mulligan 2009.
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WITTGENSTEIN ON ACTION AND THE WILL John HYMAN University of Oxford, Queen’s College Summary In this article, I examine Wittgenstein’s views about action and the will in the Philosophical Investigations and some other texts, and explore its strengths and weaknesses.
§ 611 to § 632 and Part II, section 8 of Wittgenstein’s Philosophical Investigations are concerned with action and the will.1 In Peter Strawson’s review of the Investigations, which appeared in Mind in 1954, he says of these remarks, ‘rarely has a subject been treated so powerfully and suggestively in so few pages’ (95). In some respects, I share Strawson’s high opinion of this material, but I also believe that it is flawed, because Wittgenstein failed to challenge certain assumptions that shaped the philosophical tradition from which he was trying to break loose. I shall begin by describing the intellectual background to Wittgenstein’s remarks; then I shall set out his arguments and conclusions; then I shall discuss the flaws. 1. The intellectual background The main ideas we need to be acquainted with in order to understand Wittgenstein’s remarks on this topic are, first, Schopenhauer’s neo-Kantian theory of the will, which Wittgenstein seems to have fully accepted in 1916, and which still influenced his thinking in 1947, and second, the theory advanced in William James’s The Principles of Psychology, which 1. The other main places where remarks on this topic can be found are the 1914–1916 notebooks, where he is still under the spell of Schopenhauer’s idealist theory of the will, the Brown Book, where there are five pages on ‘volition, deliberate and involuntary action’ (150), and the 1947 typescript published as Remarks on the Philosophy of Psychology, volume 1 (some of these remarks also found their way into Zettel).
Wittgenstein encountered in the 1930s, and rejected root and branch. Schopenhauer and James were in turn reacting, in very different ways, to the empiricist theory of the will, which received its classic exposition in Locke’s Essay Concerning Human Understanding, with which we should therefore begin. Locke writes as follows: All our voluntary Motions […] are produced in us only by the free Action or Thought of our own Minds […]. For example: My right Hand writes, whilst my left Hand is still: What causes rest in one, and motion in the other? Nothing but my Will, a Thought of my Mind.2 (Essay, 4.10.19)
Willing, Locke explains, is ‘an act of the Mind, directing its thought to the production of any action, and thereby exerting its power to produce it’ (Essay 2.21.28). Willing is its proper name; but Locke concedes that it is hard to find the right words to describe it. At one point, he describes it as ‘a thought or preference of the mind ordering, or, as it were, commanding the doing or not doing such or such a particular action’ (ibid. 2.21.5). But he admits that the words preferring, ordering and commanding do not capture the phenomenon precisely. He concludes that since willing is ‘a very simple act, whosoever desires to understand what it is, will better find it by reflecting on his own mind, and observing what it does, when it wills, than by any variety of articulate sounds whatever’ (ibid. 2.21.30). In other words, one should not try to define the act of will: one should simply discover it by introspection. Schopenhauer has two objections to the empiricist theory of the will. First, he argues that an act of will cannot be ‘something different from the action of the body, and the two connected by the bond of causality’ (Schopenhauer 1966, 36)—like an internal order or command—for then we could choose whether or not to execute it or obey it, and the executive function would not belong to the will itself, but to whatever acted on this choice. Second, he claims that an act of will cannot be a Thought of my Mind—or, in Hume’s phrase, an ‘internal impression’ (Hume 2000, 2.3.1)—because thoughts and impressions are mere phenomena. They are occurrences we can experience or be conscious of—for example, we can be conscious of a sensation or a wish. But in themselves they are quite passive and inert. Whereas the will is an active principle, if it is anything at all. Schopenhauer’s own view was therefore that the 2. Was Wittgenstein aware of this passage? Z, § 586 includes the sentence: ‘One’s hand writes; it does not write because one wills, but one wills what it writes.’ It is striking that he attributes writing to the hand.
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act of will and the act willed—the action of the body, as he puts it—are identical: They are one and the same thing perceived and apprehended in a twofold manner. Thus what makes itself known to inner apprehension or perception (self-consciousness) as real act of will, exhibits itself at once in outer perception, in which the body stands out objectively, as the action of the body. (loc. cit.)
In Wittgenstein’s Notebooks, the same thoughts are repeated: ‘The act of will is not the cause of the action but is the action itself ’ (NB, 87); ‘Wishing is not acting. But willing is acting’ (NB, 88); ‘The act of will is not an experience’ (NB, 89). William James was equally sceptical about the ‘free Action or Thought of our own Minds’ postulated by Locke. Instead, in The Principles of Psychology, he explains voluntary action by postulating sensations corresponding to each of the physical movements we are able to perform. According to James, we are aware of the movements of our limbs and of various other parts of our bodies, without looking to see whether they occur, because these movements produce distinctive kinaesthetic feelings in our minds: Not only are our muscles supplied with afferent as well as efferent nerves, but the tendons, the ligaments, the articular surfaces, and the skin about the joints are all sensitive, and, being stretched and squeezed in ways characteristic of each particular movement, give us as many distinct feelings as there are movements possible to perform. (James 1950, 488)
James holds that while we are still infants involuntary movements produce these kinaesthetic feelings, and images of the feelings are stored in the memory. This process eventually equips us with ‘a supply of ideas of the various movements that are possible’; and these ideas are the only mental antecedents of the voluntary movements they enable us to perform: We do not have a sensation or a thought and then have to add something dynamic to it to get a movement. Every pulse of feeling which we have is the correlate of some neural activity that is already on its way to instigate a movement. … The popular notion that [action] must result from some superadded ‘will-force’, is a very natural inference from those special cases in which we think of an act for an indefinite length of time without the action taking place.3 (ibid., 526) 3. Russell agreed: ‘Sensations and images,’ he wrote, ‘with their relations and causal laws, yield all that seems to be wanted for the analysis of the will, together with the fact that kinaesthetic images tend to cause the movements with which they are connected’ (Russell 1921, 285).
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The difference between willing and wishing, according to James, is simply that willing is desire accompanied by the knowledge that what is desired is within one’s power, whereas wishing is desire unaccompanied by this knowledge. 2. Philosophical Investigations, Part I §§ 611–632 & Part II section 8 Wittgenstein’s treatment of these theories in the Philosophical Investigations is more probing and less polemical than Ryle’s famous attack on the Cartesian theory of the will in The Concept of Mind. But his conclusions are as radical as Ryle’s, as we shall see. He begins with the following antiSchopenhauerian remark: “Willing too is merely an experience,” one would like to say (the ‘will’ too only ‘idea’). It comes when it comes, and I cannot bring it about. (§ 611)
Wittgenstein replies to this remark by challenging the idea that I cannot bring willing about. For on the one hand, we can use the phrases ‘I can/ cannot bring it about’ to distinguish between the kinds of change in my body that occur when I act, such as the motion of my arm when I raise it, and the kinds of change that simply happen to me, such as when the violent thudding of my heart subsides. But in this sense of the phrase, it is a mistake to think of willing as something that I either can or cannot bring about, because it is not an instance of either of these kinds of change. On the other hand, we can use the phrase ‘bringing about’ to mean exploiting a mechanism or a known causal connection to produce an effect. But in this sense, Wittgenstein cleverly points out, I can bring about willing. For example, I can bring about willing to swim by jumping in the water. It is true that I cannot will willing, ‘that is, it makes no sense to speak of willing willing’, simply because willing is not ‘the name of an action; and so not the name of any voluntary action either’ (§ 613). But the remark ‘I cannot bring it about’, which suggests that I am at the mercy of events, is a misleading way of making this grammatical point. Why are we tempted to use this misleading form of words, that is, to say that we cannot bring about willing? Wittgenstein’s puzzling answer is that it is because we want to think of willing itself as ‘an immediate noncausal bringing-about’ (§ 613; cf. Z, § 580). This is a baffling phrase, and probably a contradiction. (What is bringing about, if not causing?) But Wittgenstein probably meant it to capture the way Schopenhauer and his own earlier self had thought of willing: ‘immediate’ and ‘non-causal’
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because there is supposed to be no gap between the ‘real, immediate act of will’ and the ‘action of the body’ for the ‘bond of causality’ to connect.4 According to this way of thinking, Wittgenstein explains in a related manuscript remark, the causal nexus is constituted through a series of cog-wheels … whereas the nexus of the will corresponds, perhaps, to that between the inner and the outer or to that between the movement of a physical body and the movement of its appearance … (MS 11, 167)5
In any event, it is not difficult to see how, from the premise that I cannot will willing, one might infer that willing ‘comes when it comes, and I cannot bring it about’. One only needs to add the premises that I can only bring something about if I can will it; and that whatever I cannot bring about comes when it comes. But what really interests Wittgenstein is that this train of thought seems to transmute the base metal of grammar—the simple grammatical truth that willing is not the name of an action; and so not the name of any voluntary action either—into the pure gold of metaphysics, viz. the doctrine that ‘willing too is merely an experience’, that is, a phenomenon I am powerless to control. His aim is not to defend the remark in the Notebooks: ‘The act of will is not an experience’ (NB, 89). It is to demystify the concept of voluntary action; and the result of this demystification, as we shall see, is that the act of willing as such vanishes altogether. So far I have commented on §§ 611–613. §§ 614–616 are concerned with the two other remarks from the Notebooks I quoted earlier: ‘The act of will is not the cause of the action but is the action itself ’ (NB, 87). ‘Wishing is not acting. But willing is acting’ (NB, 88). §§ 614–616 do not challenge these remarks. Indeed they support the claim, which is implicit in them, that willing cannot be wishing, or presumably wanting either. For if it were, we would in effect make use of a kind of mental lever—the wish or the want—to make the motion of our limbs occur. But, Wittgenstein insists, When I raise my arm ‘voluntarily’ I do not use any instrument to bring the movement about. My wish is not such an instrument. (§ 614)
This train of thought leads to the self-consciously Schopenhauerian conclusion, placed in quotes: 4. These are all Schopenhauer’s phrases. See above, n.8. 5. The MS number follows the catalogue in von Wright 1982, 35ff.
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Willing, if it is not to be a sort of wishing, must be the action itself. It cannot be allowed to stop anywhere short of the action. (§ 615)
And to this Wittgenstein replies that if it is the action, then it is so in the ordinary sense of the word. So willing is just speaking, writing, walking, etc., and imagining too, since this is also something we can do ‘at will’; and also trying to speak, write, walk, imagine, etc. As I put it earlier, the act of willing as such vanishes, and we are left with the action it was postulated to explain. Wittgenstein’s own answer to his famous question in § 621—what is left over if I subtract the fact that my arm goes up from the fact that I raise my arm?—therefore seems to be: nothing. What is left over is not wishing or wanting; and, he will now argue, it is not trying to move my arm; it is not the kinaesthetic feelings James postulated; and it is not deciding to move my arm either. Voluntary action occurs in a characteristic context, as we shall see. But, as he puts it in The Brown Book, ‘there is not one common difference between so-called voluntary acts and involuntary ones, viz, the presence or absence of one element, the “act of volition”’ (BB, 151f ).6 Wittgenstein gives short shrift to the idea that willing should be equated with trying: ‘When I raise my arm’, he writes, ‘I do not usually try to raise it.’ (§ 622; cf. RPP I, § 51) He takes James’s theory more seriously and writes about it at greater length. As we have seen, James held that I am aware of the movements of my limbs when I walk and of my lips when I speak because these movements produce characteristic kinaesthetic feelings in my mind; and he held that my voluntary movements are caused by the images or ideas of kinaesthetic feelings stored in my memory. For example, when I raise my arm, the motion of my arm is caused by an idea of the feeling associated with this movement. No ‘will-force’ over and above the idea needs to occur. Hence, according to James’s view, the occurrence of the idea, pure and simple, is what is left over, if I subtract the fact that my arm goes up from the fact that I raise my arm. Wittgenstein has much less sympathy for James than for his own earlier self, and his attack is radical and astute. He does not merely deny that voluntary movements are caused by memory images of kinaesthetic feelings, he rejects the very idea that kinaesthetic feelings ‘advise me’ 6. One could also say that Wittgenstein meant the reader to understand that the question posed in § 621 is misleading, to the extent that it makes us expect ‘one element’ to be left over when the subtraction is performed. I do not see a substantial difference between these ways of interpreting the remark.
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(belehren mich) of the movement and position of my limbs. It is true, of course, that I can normally feel—i.e. I am normally aware of—how my limbs are disposed and how they are moving. But it does not follow that I am normally aware of feelings—‘certain queer feelings in my muscles and joints’, as Wittgenstein puts it in § 624—which advise me of these things. And as a matter of fact, I am not normally aware of such feelings: I let my index finger make an easy pendulum movement of small amplitude. I either hardly feel it, or don’t feel it at all. Perhaps a little in the tip of the finger, as a slight tension. (185)
But if the idea that kinaesthetic feelings advise me of the movement and position of my limbs is not confirmed by experience, why does it seem plausible at all? Perhaps, as Witttenstein writes in § 598, ‘When we do philosophy, we should like to hypostatize feelings where there are none. They explain our thoughts to us.’ But he also suggests two reasons which bear more directly on the specific case. First, philosophers have tended to confuse being aware of something and being aware of sensations or sense-impressions caused by something. This confusion, which sometimes trades under the name indirect realism, should be easier to expose in the case of a distance sense, because in this case there is a spatial (and sometimes a temporal) gap between the thing one is aware of and the sensation postulated by the philosopher, which should make it easier to see that being aware of the thing cannot be identified with being aware of the sensation. So Wittgenstein introduces an ingenious example, in which touch is a distance sense. If I press the end of a stick against a stone, he points out, it may be tempting to imagine that sensations of pressure in my fingers tell me that the stone is hard. But in fact what I feel is ‘something hard and round there’; and not ‘a pressure against the tips of my thumb, middle finger, and index finger …’ (§ 626).7 So one reason why we imagine that kinaesthetic feelings advise me of the movement and position of my limbs may be that we are confusing being aware of something and being aware of sensations or sense-impressions caused by something. The other reason is that we may postulate these feelings because there seems to be no other way of explaining how I know what my limbs are doing: “But after all,” Wittgenstein imagines his interlocutor 7. The analogy between seeing something and feeling it with a stick was invented by the Stoics and used by Descartes, in his Optics, in both cases for very different purposes from Wittgenstein’s. But it is unlikely that Wittgenstein knew this.
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saying, “you must feel it, otherwise you wouldn’t know (without looking) how your finger was moving” (185). To this he replies: But “knowing” it only means: being able to describe it.—I may be able to tell the direction from which a sound comes only because it affects one ear more strongly than the other, but I don’t feel this in my ears; yet it has its effect: I know the direction from which the sound comes; for instance, I look in that direction. (185)
This remark is not convincing in detail. Knowing it does not just mean being able to describe it; and I can tell where a sound is coming from because of the phase difference between my ears, in other words, because the sound reaches one ear slightly before it reaches the other one. But the substance of the remark is true: whatever physiological mechanism enables me to know where a sound is coming from, there is no need to postulate a sensation corresponding to the direction. Similarly whatever mechanism enables me to know how my finger is moving, there is no need to postulate a kineasthetic sensation corresponding to the movement of my finger either. Pain, Wittgenstein points out, provides another analogy. I know that the itch is in my toe, but not because the itch has a toeish quality about it. And memory, he adds, provides yet another. I know I had toast for breakfast, but not because a feeling of pastness is associated with my thought of eating toast. Finally, Wittgenstein considers the idea that willing to raise my arm is deciding to raise it: Examine the following description of a voluntary action: “I form the decision to pull the bell at 5 o’clock, and when it strikes 5, my arm makes this movement.”—Is that the correct description, and not this one: “… and when it strikes 5, I raise my arm”?—One would like to supplement the first description: “and see! my arm goes up when it strikes 5.” And this “and see!” is precisely what doesn’t belong here. I do not say “See, my arm is going up!” when I raise it. (§ 627)
Wittgenstein’s thought here is influenced by Schopenhauer again. It is, in effect, that if willing is deciding, the so-called act it is supposed to cause cannot be an act at all: it can only be a phenomenon I observe. Another gap—a temporal one this time—helps to underline the point; but the point is independent of the gap. If willing were ‘something different from the action of the body, and the two connected by the bond of causality’, then whether it was wishing, wanting or deciding, a kinaesthetic feeling or a
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memory image of a kinaesthetic feeling, it could not make the motion of my arm qualify as my act. At this point it seems fair to ask whether Wittgenstein has anything positive to say about how voluntary action should be defined. The answer is that he does, and what he says is bold and interesting; but it is not adequately developed or explored. First, he returns to an idea mentioned some half a dozen pages earlier where the topic is what he calls ‘a false picture of the processes called “recognizing”’—a picture according to which one recognizes an object by comparing the impression of it with a memory image, and identifying the object in this way. There he writes: Asked “Did you recognize your desk when you entered your room this morning?”—I should no doubt say “Certainly!” And yet it would be misleading to say that an act of recognition had taken place. Of course the desk was not strange to me; I was not surprised to see it, as I should have been if another one had been standing there, or some unfamiliar kind of object. (§ 602)
Thus recognizing something need not involve an ‘act of recognition’ or a memory image of the object: it may involve no more than seeing the things in a familiar place, without feeling surprised. (It may also involve being able to confirm that this is the desk one would have expected to see had one thought about it, and similar things.) Equally, Wittgenstein now suggests, voluntary action need not involve an ‘act of volition’ (to use his phrase from The Brown Book again) or a memory image of a kinaesthetic feeling: it too may involve no more than behaving in a familiar sort of way, without feeling surprised. Following on from the last sentence of § 627—‘I do not say “See, my arm is going up!” when I raise it.’—he makes the following suggestion: So one might say: voluntary movement is marked by the absence of surprise.8 (§ 628)
Then, pursuing this thought further, he suggests that I can anticipate or ‘predict’ my own voluntary movements without doing so ‘on the grounds of observations of my behaviour’ (§ 631).9 For example, having decided 8. Aristotle’s definition of pleasure (Nicomachean Ethics, 1153a14) as the unimpeded activity of a natural disposition discards the idea that pleasure is anything over and above the activity itself, and defines pleasure in terms of the absence of an impediment. Ryle’s view, which is roughly that an activity enjoyed is one to which one gives one full attention without any reluctance, is similar. See Ryle 1949, 108. 9. § 631 also implicitly contradicts TLP 5.1362: ‘we could know them [sc. actions that still lie in the future] only if causality were an inner necessity like that of logical inference.’
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to pull the bell at 5 o’clock, I can anticipate that I shall do so without depending on the kind of evidence that enables me to anticipate, say, the effect of taking an emetic drug. It is doubtful whether either of these suggestions could be worked up into a definition of voluntary action (although Elizabeth Anscombe develops them fruitfully in her book Intention). Concerning the first, it is unclear whether Wittgenstein means that voluntary movement is invariably or normally marked by the absence of surprise, and whether he means to imply that involuntary movements are invariably or normally not marked in this way. Be that as it may, voluntary movement is not invariably marked by the absence of surprise. For example, a high-jumper may be surprised when she clears an exceptionally high bar, and I may be surprised when I succeed in wiggling my ears for the first time. Furthermore, we are not normally surprised by our involuntary movements and reactions. For example, I would not normally be surprised to find myself panting at the end of a strenuous run, and I am not surprised by the beating of my heart, or surprised when I blink or sneeze. Concerning the second idea, it is true that I can often anticipate my own voluntary movements without doing so ‘on the grounds of observations of my behaviour’, but the same is often true of involuntary reactions. For example, I may be able to predict that I will feel sad when my ailing friend or parent dies without relying on evidence of this kind. It is therefore doubtful whether an analysis of voluntary action could be devised on the basis of these ideas. But what is significant about them is that Wittgenstein makes a complete break with the doctrine that voluntary action is action with a particular kind of cause, without embracing the mysterious idea that ‘the nexus of the will corresponds … to that between the inner and the outer’, or anything similar. Perhaps the most telling remark is § 615. I quoted the first sentence above. Here is the remark in full: “Willing, if it is not to be a sort of wishing, must be the action itself. It cannot be allowed to stop anywhere short of the action.” If it is the action, then it is so in the ordinary sense of the word; so it is speaking, writing, walking, lifting a thing, imagining something. But it is also trying, attempting, making an effort,—to speak, to write, to lift a thing, to imagine something etc. (§ 615)
The interlocutor here is surely Wittgenstein’s earlier self, the author of the remarks in the Notebooks quoted above: ‘The act of will is not the cause of the action but is the action itself ’ (NB, 87). ‘Wishing is not acting.
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But willing is acting’ (NB, 88). Wittgenstein does not deny that what the interlocuter says is true. He merely points out what we are bound to acknowledge it implies, if we refuse to mystify the will. Wittgenstein’s conclusions flow naturally from this point. For if willing must be the action itself, then it cannot be what caused the action to occur, or an aspect of the action that is revealed to ‘inner apprehension’, whatever exactly this could mean. So perhaps it is the context of an act that makes it voluntary—‘its character and its surroundings’, as Wittgenstein puts it in a later remark (Z, § 587)—including, in most cases, the absence of surprise: ‘Voluntary movements’, he writes, ‘are certain movements with their normal surroundings of intention, learning, trying, acting’ (RPP I, § 776; cf. Z, § 577). For example, we regard the movements of a child playing with a doll as voluntary, not because we postulate invisible acts of will or images of kinaesthetic feelings preceding them and making them occur, but because we know that the child has learned how to make these movements, because the movements are coordinated and purposeful, because the child attends to what it is doing, is not alarmed or surprised or distressed by its own movements, and so on. If we feel the need to postulate a hidden cause, it is because we ignore these features of a movement and its context, which are for the most part in plain view. Wittgenstein’s critique of the theories he opposed is original and astute. But even if we set aside his failure to develop his ideas adequately and the obscurity of many of his remarks, there are also serious weaknesses in his treatment of this subject, because he fails to make a sufficiently radical break with the past. In particular, he makes three closely related mistakes, which have dominated philosophical thought about action and the will throughout the modern period. First, he confuses the voluntary/not voluntary distinction and the active/passive distinction. Second, he fails to distinguish between action and motion, for example, between raising something and the motion of the thing one raises. Finally, lying behind these two mistakes is—to use one of Wittgenstein’s own phrases—a onesided diet of examples, which in this case means that all of the actions he examines are movements of parts of the agent’s body. Arms are raised and fingers are moved, but few other actions are mentioned, and then only in passing. I shall comment on the first two points in turn. What I have to say about the third will emerge as I go along.
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3. The voluntary/not voluntary distinction and the active/passive distinction First, a terminological preliminary. The word ‘involuntary’ is normally defined in dictionaries as the contradictory of ‘voluntary’, but the actual use of the word is commonly confined to thoughts or changes in the body which a person is unable to control, such as ‘an involuntary concurrence of ideas’, ‘the inuoluntarie running of vrine’ or ‘the involuntary closing of the eyelids when the surface of the eye is touched’. (All of these examples are taken from the OED’s entry for ‘involuntary’.10) Thus, in the actual use of these words, ‘involuntary’ and ‘not voluntary’ are not equivalent, and if something is not voluntary, we cannot assume that it must therefore be involuntary. For example, a man who is conscripted into the army is not a volunteer, but he does not join the army involuntarily, in this limited sense. We are now principally concerned with what is and what is not voluntary. In reality, the voluntary/not voluntary distinction and the active/passive distinction cut across each other, since activity can be either voluntary or not voluntary, and the same is true of passivity. But philosophers have commonly ignored or failed to notice two of these possibilities. On the one hand, they have tended to think about the will exclusively in relation to action. They have not thought about it in relation to the feelings we experience or the conditions in which we place or find ourselves, or in relation to the occasions when we are acted upon. They have thought about voluntary activity, but they have ignored voluntary passivity, or even denied that it exists. On the other hand, activity and voluntary activity have commonly been equated, as if activity were always voluntary. So they have ignored activity that is not voluntary. The result is that the active/passive distinction and the voluntary/not voluntary distinction have appeared to coincide, and have commonly been confused. I shall discuss voluntary passivity and non-voluntary activity (sc. activity that is not voluntary) in turn. It is a mistake to suppose that only activity can be voluntary. As it happens, the OED’s entry for ‘voluntary’ begins with voluntary feeling and then proceeds to voluntary action; and if we turn to the entry for ‘voluntarily’, we find several quotations in which the word qualifies something passive, including the very first. Here are the first and the eighth: 10. The distinction between ‘involuntary’ and ‘not voluntary’ derives from Aristotle’s distinction between actions that are performed unknowingly which we do not regret (ouk hekousia) and ones which we do regret (akousia), but this is not the way in which philosophers now use these terms. (Nicomachean Ethics III.1, 1110b18–12; see Broadie 1991, 126.)
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c1374 CHAUCER Boeth. III. pr. xii. (1868) 103 Ther may no man douten, that thei ne ben gouerned uoluntariely. […] 1663 BP. PATRICK Parab. Pilgr. xiii. (1687) 87 At last he voluntarily, and without any compulsion but that of his Love, died upon a Cross.
The truth is that the distinction between what is and what is not voluntary applies to passivity and to inactivity in exactly the same way as it applies to activity. Children are sometimes picked up and carried voluntarily, they are sometimes kissed and tucked up in bed voluntarily, and they sometimes eat their green vegetables voluntarily. For their part, adults are sometimes voluntarily unemployed, sometimes undergo surgical procedures voluntarily, and sometimes die voluntarily, as Bishop Patrick says Christ did, and as the Italian poet and advocate of euthanasia Piergiorgio Welby did in 2006. There is no reason to deny that voluntariness can be attributed equally to all of these things; and there is no reason to think that it is a different attribute, depending on which of them we have in mind. The idea that only actions can be voluntary—or only the things we do, as opposed to the things that happen to us or are done to us—is an unsupported dogma. In fact, conditions such as exile and poverty can be voluntary, despite not being things we do, because they may be the result of a choice and not of force or compulsion, or undue influence by others, and the same is true of the kisses we give and also of the kisses we receive. Roughly, voluntariness is about choice versus compulsion, and a child can sometimes choose whether to be kissed or carried, just as it can sometimes choose what to eat. Equally, a man may allow himself to fall in love with a woman, in the knowledge that he could avoid falling in love with her if he chose to, or allow himself to fall asleep in the knowledge that he could avoid falling asleep if he chose to; or he may fall in love willy nilly, or fall asleep despite trying to remain awake. In the first case, he falls in love or falls asleep voluntarily, in the second case not. But falling in love and falling asleep are not actions, any more than falling down the stairs. Why has voluntary passivity been ignored? The most important reason is that the distinction between what is and what is not voluntary was regarded for three centuries as part of a story about the interaction between mind and body. The questions that exercised philosophers were not: what can the concept of voluntariness be applied to?, and how should it be defined? They were: what causes the kind of motion in our bodies that we regard as subject to our own direction and control?, and how 297
does this kind of motion differ from blinking, sneezing, or the beating of the heart? Furthermore, the empiricist theory of the will reinforced the tendency to neglect voluntary passivity. For if a man falls asleep voluntarily or dies voluntarily on a cross, the cause is unlikely to be an ‘internal impression’ or a ‘Thought of his Mind’. In fact it will probably be the same—tiredness in one case and asphyxiation in the other—whether he falls asleep or dies voluntarily or not. It was therefore hard to see that activity and passivity are equally capable of being voluntary, as long as the empiricist theory prevailed. However, it must be acknowledged that not only Wittgenstein, but also other trenchant critics of the theory ignored voluntary passivity, or actually denied that it exists (Ryle, op. cit., 74; cf. Anscombe 2000, § 49). Finally, many philosophers today are interested in the concept of voluntariness because of its importance in ethics and the philosophy of law. In fact, the concept of voluntary passivity plays an important role in moral and legal reasoning, notably where consent is involved, e.g. in connection with the law of rape. Nevertheless, voluntary passivity has proved to be less salient than voluntary activity in this context, perhaps in the case of law because of what is called the ‘act requirement’, the doctrine that criminal liability requires an act.11 The other mistake that has encouraged philosophers to confuse the active/passive distinction and the voluntary/not voluntary distinction is the thought or assumption that action is always voluntary. This assumption was made by Hobbes, Locke, Hume and Mill, and it remained dominant in philosophy during the first half of the twentieth century. It was also made by many nineteenth- and twentieth-century jurists.12 By the nineteenth century, it commonly took the form of a definition. For example, Mill defines action as follows: ‘What is an action? Not one thing, but a series of two things; the state of mind called a volition, followed by an effect’ (Mill 1973, 1.3.5). And Austin (the nineteenth-century jurist, not the twentieth-century philosopher) offers the following definition: ‘A voluntary movement of my body, or a movement which follows a volition, is an act’ (quoted in White 1968, 5). If we accept—as we certainly should—that action is not limited to animals capable of acting voluntarily, it is obvious that these definitions cannot be right (see Kenny 1975, 46; Alvarez & Hyman 1998, 243ff.). But 11. On this topic, see Duff 2004. 12. Cp. Williams 1978 and Dias 1970, 252. See White 1985, 28ff. for examples and references.
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even if we confine ourselves to human action they remain unconvincing. For some human actions are voluntary and some are not. It is debatable how much choice voluntariness requires. But if we are compelled to do something, and cannot choose whether to do it or not, then we do not do it voluntarily—whether the compulsion is physical, moral, psychological, or of some other kind. Do we pay our taxes voluntarily? Does a man who hands over his wallet do so voluntarily, if he is threatened with a gun? Does a prisoner reveal the names of his associates voluntarily, if he does so under torture? Perhaps we cannot answer these questions in general terms, and need to know more about each particular case. But it should be beyond dispute that some actions are not voluntary. Again, we are bound to ask why philosophers failed to understand this for so long. And again the tendency of philosophers to regard the distinction between voluntary and not voluntary as part of a story about the interaction between mind and body played an important role. For it meant that when philosophers thought about action, they thought exclusively about human action and almost always about actions that consist in a human being moving part of his own body. This one-sided diet of examples reinforced the idea that all action is voluntary, because most of our actions that consist in moving parts of our own bodies are voluntary. For example, when we raise our arms or move our legs these actions are mostly voluntary. (Sleep is the main exception to this rule.13) The reason for this is that one of the principal factors that cancels voluntariness is ignorance, as Aristotle pointed out; and it is unusual for us to be unaware of the motion of our own limbs. (Again, sleep is the main exception.) Other kinds of action are quite different. For example, when I have a salad for lunch I may occasionally consume a bug. I choose to have the salad, but I do not consume the bug voluntarily, because I am unaware of consuming it, and would avoid doing so if I could. Since my arm-raisings are mostly voluntary, whereas my bug-consumings are not, it is much easier to equate action and volun13. Wittgenstein comments on speaking in one’s sleep in The Brown Book, and also on ‘involuntary exclamations’, such as ‘Oh!’ and ‘Help!’ His aim is to show that ‘there is not one common difference between so-called voluntary acts and involuntary ones’ (151). About speaking in one’s sleep, he says, ‘this is characterized by our doing it without being aware of it and not remembering having done it’ (155). About the ‘involuntary exclamations’, he writes as follows: ‘I agree that an act of volition preparatory to or accompanying these words is absent,—if by “act of volition” you refer to certain acts of intention, premeditation or effort. But then in many cases of voluntary speech I don’t feel an effort, much that I say voluntarily is not premeditated, and I don’t know of any acts of intention preceding it’ (155).
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tary action if our attention is exclusively directed towards actions of this kind.14 This is an important part of the reason why philosophers have believed or assumed that all action is voluntary. But an equally important part of the reason is that the doctrine that matter is inert was accepted by several influential philosophers in the seventeenth century—including Descartes, Malebranche and Hobbes—and exerted an important influence on the way in which the relationship between action and voluntariness was understood. This comes out especially clearly in Locke’s discussion about the origin of our idea of active power, as I shall briefly explain now. According to Locke, the idea of power is indispensible in science, because it is, he says, ‘a principal ingredient in our complex ideas of substances’ (Essay, 2.21.3). For example, the liability of gold to be melted in a fire and to be dissolved in aqua regia are no less essential to our idea of gold than its colour and weight. And even colour and weight, Locke claims, will also turn out to be powers, if we consider their nature carefully. But if all the materials of reasoning and knowledge—all of our ideas—are ultimately derived from experience, as Locke insists they are, what are the sources in experience of the idea of power? Locke’s answer depends on distinguishing between two complementary kinds of power: active powers are abilities to produce various kinds of change, whereas passive powers are liabilities to undergo various kinds of change. Action, which is the exercise of an active power, is the production of some kind of change; passion, which is the exercise of a passive power, is the undergoing of some kind of change. The origin of our idea of passive power is, Locke thinks, quite clear. The idea is produced in us by bodies, because we cannot avoid perceiving the changes that they undergo: ‘and therefore with reason we look on them as liable to the same change’. But Locke claims that we cannot observe the production of a change in the same way. For example, when we see one ball strike another ball, and set it in motion, Locke says, [the first ball] only communicates the motion it had received from another, and loses in itself so much, as the other received; which gives us but a very 14. I ignore the doctrine, defended by Elizabeth Anscombe and Donald Davidson, that if someone performs one action by performing another action, for example, crushes an ant by taking a step, these are one and the same action. This doctrine is criticized in Alvarez & Hyman, op.cit., 234f.
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obscure idea of an active power of moving in body, whilst we observe it only to transfer, but not produce any motion. (Essay, 2.21.4)
Observing interactions between bodies cannot therefore be the source of our idea of active power. Rather, Locke claims, we have [this idea] only from reflection on what passes in ourselves, where we find by experience, that barely by willing it, barely by a thought of the mind, we can move the parts of our bodies, which were before at rest. (ibid.)
Thus, according to Locke, our idea of active power is drawn from the experience of producing motion voluntarily ourselves. Moreover, although Locke wanted to retain the idea that natural kinds of substance have characteristic active powers, it follows from these considerations that strictly speaking voluntary action is the only action there is. For when bodies interact, motion is communicated, but it is not produced; and action, Locke insists, is the production of motion, or some other kind of change. The mere transfer of motion does not amount to action. All real action must therefore be voluntary action, consciously effected by the mind. Locke’s argument is unconvincing, because the distinction between transferring and producing motion is specious. There is certainly a difference between producing and transferring people or goods. For example, manufacturers produce goods whereas exporters transport goods from one place to another; and parents produce children whereas bus-drivers transfer them from one place to another. Now if a bus-driver transfers children from a school to a playing-field, the same children who embark at the school disembark at the playing-field. Not just the same number of children, but the very same children. (That generally matters quite a lot to their parents.) But suppose one ball strikes another similar ball, sets it in motion, and decelerates appreciably itself. Has motion been transferred or produced? How are we to decide? We cannot ask whether the second ball acquires the very same motion—not merely the same quantity of motion but, as it were, the very same package of motion—that the first ball loses, because motion is not a substance that can be packaged and then either handed over or withheld. But if, as Locke says, the first ball loses the same quantity of motion as the second ball gains, is this not a reason for denying that motion has been produced? It is not; but we need to be clear about why not. It is tempting to point out that when a cannon is fired, motion is not transferred from
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the powder to the ball. But it would be easy to reply on Locke’s behalf that although he should have based his argument on the conservation of energy instead of motion, his basic point is sound. So this objection would not take us far. The real reason why the fact that the first ball loses approximately the same quantity of motion as the second ball gains should not encourage us to say that motion has been transferred rather than produced is that there is no reason why the production of motion—i.e. action—should be in breach of whatever conservation laws are enshrined in physics.15 This is the crux of the matter. Locke denies that the first ball produces motion in the second ball because it ‘loses in itself so much, as the other received’, in other words, because the interaction between the balls conserves the total quantity of motion. But it follows that he can only acknowledge that the production of motion—in other words, action—has occurred if the total quantity of motion is not conserved, but increased. An action must therefore be a breach of or an exception to the laws of nature. In other words, it must be a miracle, an interference in the natural course of events by a being with the strictly supernatural ability to inject motion into the natural world, rather than merely transferring it to something else. Locke’s conclusion, that we are acquainted with action by ‘reflection on what passes in ourselves’, is therefore unsustainable, since human beings do not have supernatural powers. If his argument were sound, it would really establish that miracles aside, action does not exist at all. Reflecting on Locke’s argument from our present vantage-point, it is not difficult for us to see this, in particular, because we understand that the conversation of energy—one of the great discoveries of nineteenth century physics—applies to our voluntary behaviour no less than to the behaviour of billiard balls. Since we understand this, we can see that Locke’s argument is really eliminativist in tendency. It does not confine action to the mind: it excludes it from the natural world altogether. Thus in Locke’s thought, and in the empiricist tradition stemming from Locke, the idea that all action is voluntary did not arise out of a theory 15. Interestingly, we distinguish between producing and transferring wealth in the way Locke wants to distinguish between producing and transferring motion. The rich man who leaves his money to his son merely transfers wealth from one person to another, but the entrepreneur (we say) actually creates wealth. The reason why we are able to think about wealth in this way is that there are no conservation laws in economics—something we all have reason to be grateful for most of the time.
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of the will. It appears to have arisen from a combination of two things: first, the idea that matter is inert, never a source of motion or change in its own right; and second, a not yet fully naturalized conception of human beings. But as so often in philosophy, the idea long outlived the intellectual context in which it first arose, in this case because it was reinforced by the one-sided diet of examples I referred to earlier. It is therefore not surprising that we find the same focus of attention in Wittgenstein’s writings on action and the will, from 1916 to 1947, with the same unfortunate results. Like his predecessors, Wittgenstein is exclusively interested in the will in relation to action. Voluntary activity is the topic: voluntary inactivity and voluntary passivity are ignored in all of his writings, with the exception of the following remark from 1947 (RPP I, § 845): Can’t rest be just as voluntary as motion? Can’t abstention from movement be voluntary? What better argument against a feeling of innervation?
This remark, which is unique in Witgenstein’s writings, is specifically about Wilhelm Wundt’s theory that voluntary actions are caused by feelings of innervation, which Wittgenstein was aware of because James opposed it in The Principles of Psychology. When one considers that the thought expressed here is just as good an argument against James and Russell, or indeed against Locke, as it is against Wundt, it is tantalizing to see Wittgenstein failing to develop it, or to consider how broad its implications are. It is also disappointing to see Wittgenstein noticing voluntary inactivity, but failing to notice, or at least to mention, voluntary passivity. Also like his predecessors, Wittgenstein focuses on the distinction between the movements of parts of our bodies which we direct and control, such as the movements of our legs when we walk or our lips when we speak, and the ones which we do not control, such as coughing and sneezing (RPP I, § 806; cf. Z, § 579) or the beating of the heart (PI, § 612). He ignores the difference between taking a step or extending one’s arm, which is normally voluntary, and crushing an ant underfoot or handing over one’s wallet, which may not be. And he ignores the difference between a child eating ice-cream, which is normally voluntary, and a child eating green vegetables, which is often not. Thus a remark composed in 1947 (RPP I, § 763) reads as follows:
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How do I know whether the child eats, drinks, walks, etc. voluntarily or not [willkürlich oder nicht willkürlich]? Do I ask the child what it feels? No; eating, as anyone does eat, is voluntary.16
It would not be quite right to say that Wittgenstein assumes that action is always voluntary. Indeed a sentence in § 613 implies the contrary: ‘“Willing” is not the name of an action; and so not the name of any voluntary action either.’17 But he frequently confuses questions about voluntariness and questions about activity. That is surely why he says that ‘eating, as anyone does it, is voluntary’. This is far from being true, particularly in the case of children. But even when it is not voluntary, eating is active as opposed to passive, and therefore something that one does and not something that one undergoes. So, once again like his predecessors, Wittgenstein confuses the voluntary/not voluntary distinction and the active/passive distinction. Some of the remarks in the Investigations are ostensibly about voluntariness—in particular, those which are directed against the theory that what makes an action voluntary is a special kind of mental cause, such as a kinaesthetic feeling. Others are clearly about action—for example, the famous question ‘what is left over if I subtract the fact that my arm goes up from the fact that I raise my arm?’ (§ 621), which has exactly the same meaning (and exactly the same answer) whether I raise my arm voluntarily or not. But there is no sign that Wittgenstein is aware of the difference between these topics. Only in 1947 does he begin to think about voluntariness as such. Now the focus of his attention broadens, he considers actions that do not merely consist in someone raising an arm or moving a finger (RPP I, §§ 762ff., 902), he notices that inactivity as well as activity can be voluntary (§ 845) and he makes the connection between voluntariness and awareness (§§ 761, 844, 902). It is as if he has settled accounts with his ealier self in the Investigations and is now able to take a fresh look at the nature of action and the will. 16. The published translation (by Anscombe) reads, ‘How do I know whether the child eats, drinks, walks, etc. voluntarily or involuntarily’. This is clearly not the correct translation of the German ‘willkürlich oder nicht willkürlich’, and it disguises the error. For of course the child who is made to eat his green vegetables, and does not do so voluntarily, does not eat them involuntarily either, in the sense explained above (p. 295)—that is, the movements of the child’s mouth are under its physical control. It should also be noted that Wittgenstein’s use of the word ‘willkürlich’ to mean ‘voluntarily’ (as opposed to ‘willingly’) is unidiomatic. He follows Schopenhauer’s use of the word in Die Welt als Wille und Vorstellung. 17. See also Z, § 577and RPP I, § 902. In PI, § 614, the word ‘voluntary’ is in scare-quotes, suggesting perhaps that the very concept may be tainted or unclear.
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4. Action and motion Wittgenstein’s second major mistake was his failure to distinguish between action and motion, or to consider how they are related. For example, suppose I raise my arm. How are my action, my raising of my arm, and the motion of my arm related? Some philosophers have claimed explicitly that they are identical. For example, when Donald Davidson considers the question of how actions should be located in space and time, he writes: ‘if a man’s arm goes up, the event takes place in the space-time zone occupied by the arm; but if a man raises his arm, doesn’t the event fill the zone occupied by the whole man? Yet the events may be identical’ (Davidson 1980, 124). Wittgenstein does not make this claim explicitly; but like many of his predecessors, including Schopenhauer, he confuses action and motion. This comes out clearly in the well-known passage in which he links voluntary action with the absence of surprise. I quoted this passage earlier, but it will be useful to have it before us again. 627. Examine the following description of a voluntary action [einer willkürlichen Handlung]: “I form the decision to pull the bell at 5 o’clock, and when it strikes 5, my arm makes this movement.”—Is that the correct description, and not this one: “… and when it strikes 5, I raise my arm”?— One would like to supplement the first description: “and see! my arm goes up when it strikes 5.” And this “and see!” is precisely what doesn’t belong here. I do not say “See, my arm is going up!” when I raise it. 628. So one might say: voluntary movement [die willkürliche Bewegung] is marked by the absence of surprise.
In § 627, Wittgenstein points out that we might describe a voluntary action (eine willkürliche Handlung) by saying ‘I raise my arm’, but not by saying ‘My arm makes this movement’ or ‘See, my arm is going up!’ (§ 627). And from this he infers, in § 628: ‘So one might say: voluntary movement [die willkürliche Bewegung] is marked by the absence of surprise.’ Thus he appears to believe that the reason why I do not describe my action by saying ‘See, my arm is going up!’ is that I am not surprised, and that what is wrong with the description ‘See, my arm is going up!’, what prevents it from being a satisfactory description of a voluntary action, is the word ‘See …!’, the expression of surprise, rather than the phrase ‘my arm is going up’. It does not occur to him that ‘my arm is going up’ describes the motion
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of my arm, and that the action and the motion—the Handlung and the Bewegung—are different things. In the remarks that date from 1947, Wittgenstein still shifts back and forth between Handlung and Bewegung, without considering whether there is a difference between them (e.g., §§ 840, 901f.); and, as we might expect, he also misses the distinction between the action of moving a limb and the motion of the limb in the passage in The Brown Book which lies behind PI §§ 627f. In this passage, he describes how one can press the back of one’s hand against the wall, then step away from the wall and let one’s arm rise ‘of its own accord’, commenting: There is a difference between the voluntary act of getting out of bed and the involuntary rising of my arm. But there is not one common difference between so-called voluntary acts and involuntary ones. (BB, 151f.)
The difference Wittgenstein fails to notice is that getting out of bed is a case of action whereas ‘the involuntary rising of my arm’ is a case of motion. He may be right in saying that there is not one common difference between so-called voluntary acts and involuntary ones; but the difference between getting out of bed and the rising of my arm is the difference between action and motion, and not the difference between two kinds of act. Commentators have uniformly failed to notice the switch from Handlung to Bewegung in PI, §§ 627f.18 But it is absolutely vital to see that these are different things, because if something is raised or lowered (or moved or affected in some other way) the raising or lowering of the thing is a case of action, whereas the motion of the thing raised or lowered is a case of passion. So if we fail to notice the difference between my raising of my arm (the Handlung) and my arm’s going up (the Bewegung), we’ve missed the very distinction between activity and passivity that we were trying to explain. It is just the same if someone is killed: the killing is a case of action, whereas the dying is a case of passion. And it makes no difference what is raised or lowered or killed. If I raise my hand, my glass and the nail on my little finger in a single gesture, my raising of my hand and of the nail are no less certainly distinct from the motion of the hand and the nail than my raising of my glass is distinct from the motion of the glass, despite the fact that the hand and the nail are parts of my body 18. For example, Hacker comments on § 628, ‘This concludes the discussion by citing one mark of voluntary action, which was intimated in the previous section. It is characteristic of voluntary actions that the agent is not surprised’ (Hacker, op. cit., 610f.). In Anscombe’s translation of RPP I, ‘Handlung’ is sometimes translated as ‘action’ and sometimes as ‘movement’ (e.g. § 840).
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whereas the glass is not. And if I commit suicide, this act is no less certainly distinct from my death than the killing is distinct from the death when one person kills another. So, if I raise my arm how is this action related to the upward motion of my arm? How is the Handlung related to the Bewegung? The answer is that the action, my raising of my arm, is as Locke put it, the production of the motion, in other words, the causing of it, by the agent, namely me. Von Wright calls the Handlung an ‘act’ and the Bewegung its ‘result’.19 So, if we adopt this terminology, we can say that my act of raising my arm is my causing of the result of this action. (This is von Wright’s own view, as we shall see.) Acting is not causing an action, as some philosophers in the 1950s and 60s believed; it is causing an event—the event von Wright calls the action’s result (see Taylor 1966, 115; Chisholm 1976). Hence, the answer to Wittgenstein’s question in § 621—what is left over if I subtract the fact that my arm goes up from the fact that I raise my arm?—is not willing or wishing or wanting or trying; but it is not nothing either, or the absence of surprise. What is left over is the fact that I made it happen, the fact that I caused the motion of my arm to occur. The other cases I mentioned are no different from raising my arm, in this respect. If I raise my glass, this action is my causing of the upward motion of my glass; and if A kills B, this action is A’s causing of B’s death. But notice that a causing is not the same thing as a cause. For example, we can trace our way back along a chain of causally connected events that led up to B’s death—events occurring in B’s body, in the space between A and B, and in A’s body; but we shall not find A’s killing of B anywhere along this chain of events. A’s killing of B is (roughly speaking) the causal relation between A and one of these events, namely, B’s death; A’s pulling of the trigger is the causal relation between A and an earlier event in the chain, namely, the motion of the trigger; and so on.20 During the last three centuries, philosophers have generally failed to distinguish between my raising of my arm, which is an action, and the motion of my arm, which is a mere event. And when the action and the motion are not simply identified—as they are by most philosophers, 19. This is a quasi-technical use of the term ‘result’, but it is useful to mark the distinction in this way. See von Wright 1963, ch. 2. 20. The reason for the parenthetical qualification is that there are more and less restrictive concepts of a relation. For example, if a relation is a way in which one thing can stand to another thing, or several things can stand to one another, then an action is not a relation, because acts are dynamic and not static. See Hyman 2001.
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including Wittgenstein—the action is held to be a combination of the motion and its cause (as we have seen it is by Mill) or else to be identifiable with the cause alone.21 The most important exception is G.H. von Wright, who writes as follows: The notion of a human act is related to the notion of an event, i.e. a change in the world. What is the nature of this relationship? // It would not be right, I think, to call acts a kind or species of events. An act is not a change in the world. But many acts may quite appropriately be described as the bringing about or effecting (‘at will’) of a change. To act is, in a sense, to interfere with ‘the course of nature’. (von Wright 1963, 35f.)
There was no need for von Wright to confine this observation to human acts alone, and the parenthetical phrase ‘at will’ is out of place, because while it is true that many acts are voluntary, it is equally true, as we have seen, that many are not. However, the principal idea expressed here is exactly right. An action is the bringing about or effecting—in other words, the causing—of an event. As I have already indicated, action cannot be described as interference in the course of nature, because it is part of the course of nature—unless it is miraculous, of course. But it can be described as interference in the course of events. Returning to Wittgenstein, we can again ask how he could have missed this. How could he have confused the Handlung and the Bewegung, the act and its result, when the relation between these things is the key to understanding what action itself is? The answer is the same as it was last time. First, the distinction between act and result was missed in the philosophy Wittgenstein had read. Second, Wittgenstein’s exclusive interest in actions that consist in human beings moving parts of their own bodies made the distinction between act and result less salient than it would otherwise have been. The reason for this is that the distinction is more obvious when the result is more remote from the agent. (This is another case where distance is an intellectual aid.) For example, it is harder to confuse my raising of a flag and the motion of the flag than it is to confuse my raising of my arm and the motion of my arm, because in the first case we can imagine the result without the action. We can cut the agent out of the picture, so to speak. But if the result is the motion of parts of the agent’s own body, we cannot do this; and if we imagine ourselves pointing to the action and pointing to its result, we are pointing towards roughly the same place. 21. The latter view is defended in Hornsby 1980.
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5. Concluding remarks
What conclusions should we draw about the treatment of action and the will in the Philosophical Investigations? On the one hand, it is seriously flawed. Wittgenstein fails to disentangle the active/passive distinction and the voluntary/not voluntary distinction; he fails to see that voluntariness is not only an attribute of activity, but of passivity as well; and he confuses action and motion. On the other hand, he discards the idealist mythology he had once accepted, although he retains Schopenhauer’s claim that willing (unlike hoping, wanting or deliberating) is not distinct from the act willed; and his criticism of James and Russell in Part II is radical and utterly convincing, in my view. Furthermore, there are signs in the remarks composed in 1947 that he is beginning to break fresh ground, although only glimpses of parts of a new picture can be found here: nothing is developed or sustained. Finally, although the remarks in the Investigations are unsatisfactory, they are framed (so to speak) by the following remarks, which express a constant theme of Wittgenstein’s writings about action and will, from The Brown Book onwards: There is not one common difference between so-called voluntary acts and involuntary ones, viz, the the presence or absence of one element, the “act of volition”. (BB, 151f.) Voluntary movements are certain movements with their normal surroundings of intention, learning, trying, acting. (RPP I, § 776)
Wittgenstein evidently agreed with Ryle’s view, expressed in The Concept of Mind, that the theory of volitions is ‘a causal hypothesis, adopted because it was wrongly supposed that the question, “What makes a bodily movement voluntary?” was a causal question’ (Ryle 1949, 67). It is largely because of his subtle and resourceful defence of this idea that the destructive work in the Investigations and the positive ideas in the later writings, fragmentary as they are, together with Ryle’s chapter on the will in The Concept of Mind, paved the way for the extraordinary renewal of the philosophy of action in the second half of the twentieth century.
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REFERENCES Alvarez, Maria & Hyman, John 1998: “Agents and their Actions”. Philosophy 73, 219–245. Anscombe, G[ertrude] E[lizabeth] M[argaret] 2000: Intention. 2nd edition (repr.). Cambridge, Mass.: Harvard UP. Broadie, Sarah 1991: Ethics with Aristotle. Oxford: Oxford University Press. Chisholm, Roderick M. 1976: “The Agent as Cause”. In: Myles Brand & Douglas Walton (eds.), Action Theory. Dordrecht: Reidel, 199–211. Davidson, Donald 1980: Essays on Actions and Events. Oxford: Oxford University Press. Dias, Reginald W. M. 1970: Jurisprudence. London: Butterworths. Duff, Antony 2004: “Action, the Act Requirement and Criminal Liability”. In: John Hyman & Helen Steward (eds.), Agency and Action. Cambridge: Cambridge University Press, 69–103. Hacker, Peter M. S. 1996: Wittgenstein: Mind and Will. Oxford: Basil Blackwell. Hornsby, Jennifer 1980: Actions. London: Routledge & Kegan Paul. Hyman, John 2001: “–ings and –ers”. Ratio 14 (new series), 298–317. Hume, David 2000: A Treatise of Human Nature. David F. Norton & Mary J. Norton (eds.). Oxford: Oxford University Press. James, William 1950: The Principles of Psychology. Vol. 2. New York: Dover. Kenny, Anthony J. P. 1975: Will, Freedom and Power. Oxford: Basil Blackwell. Locke, John [Essay] 1979: An Essay Concerning Human Understanding. Peter H. Nidditch (ed.). Oxford: Clarendon Press. Mill, John S. 1973: A System of Logic, Ratiocinative and Deductive. John M. Robson (ed.). Toronto: University of Toronto Press. Russell, Bertrand 1921: The Analysis of Mind. London: George Allen & Unwin. Ryle, Gilbert 1949: The Concept of Mind. London: Hutchinson. Schopenhauer, Arthur 1966: The World as Will and Representation. Vol. 2. Trans. Eric F. J. Payne, New York: Dover. Strawson, Peter F. 1954: “Review of Wittgenstein’s Philosophical Investigations”. Mind 63, 70–99. Taylor, Richard 1966: Action and Purpose. Englewood Cliffs, N.J.: Prentice-Hall. Von Wright, Georg H. 1963: Norm and Action. London: Routledge & Kegan Paul. — 1982: Wittgenstein. Oxford: Basil Blackwell. White, Alan R. (ed.) 1968: The Philosophy of Action. Oxford: Oxford University Press.. — 1985: Grounds of Liability. Oxford: Clarendon Press. Williams, Glanville 1978: Text Book of Criminal Law. London: Stevens & Sons.
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Wittgenstein, Ludwig [PI ] 1958: Philosophical Investigations. G[ertrude] E[lizabeth] M[argaret] Anscombe & Rush Rhees (eds.), trans. G. E. M. Anscombe. 2nd edition. Oxford: Basil Blackwell. — [NB ] 1961: Notebooks 1914–16. Georg Henrik von Wright & G[ertrude] E[lizabeth] M[argaret] Anscombe (eds.), trans. G. E. M. Anscombe. Oxford: Basil Blackwell. — [TLP] 1961: Tractatus Logico-Philosophicus. Tr. David Pears & Brian F. McGuinness. London: Routledge & Kegan Paul. — [BB] 1969: The Blue and Brown Books. 2nd edition. Oxford: Basil Blackwell. — [Z] 1967: Zettel. G[ertrude] E[lizabeth] M[argaret] Anscombe & Georg Henrik von Wright (eds.), trans. G. E. M. Anscombe. Oxford: Basil Blackwell. — [RPP I ] 1980: Remarks on the Philosophy of Psychology. Vol. 1. G[ertrude] E[lizabeth] M[argaret] Anscombe & Georg Henrik von Wright (eds.), trans. G. E. M. Anscombe. Oxford: Basil Blackwell.
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IV. REFERENCE AND EXISTENCE
Grazer Philosophische Studien 82 (2011), 315–328.
PLATONISM AND THE ARGUMENT FROM CAUSALITY David WIGGINS University of Oxford, New College Summary The paper argues that the causal argument urged by Benacerraf and others against mathematical Platonism misuses the truth that lurks behind the causal theory of knowing—a theory which the paper traces back to Charles Sanders Peirce’s account of the fixation of belief. Once we see (as Peirce himself came to see) that the essential insight of that theory relates not to causation but to the determination of belief and to rational vindication—of which mathematical proof is a special case—it becomes plain that the proper place to interrogate and refine Platonism lies not within general metaphysics but within mathematical philosophy. There is no sensible separation to be made between (1) the train of thought which at once explains and vindicates our collective belief in a given mathematical proposition; (2) the sense that we attach to the proposition which commands our collective assent; and (3) the account that is to be given of what the proposition with that sense is about—the objects which Quine’s ontological criterion suggests we commit ourselves to in embracing the proof of the proposition thus understood.
1. A Platonist says that there are or exist non-concrete things, and distinguishes between existence as such and material existence. It is no less integral to the Platonist outlook that human beings can attain to ordinary knowledge of that which is non-concrete. But there, it has appeared, lies a signal weakness of the position: if a person knows that such and such, then it ought to be possible to account for his or her state of mind with respect to whether or not such and such by tracing the ancestry of the state back along some causally explanatory route to the very fact that such and such. But, on such terms, how could anything be known about numbers or anything else that falls short of being concrete? How can that which is not concrete enter into any causal relation with persons or thoughts?
For Hermione to know that the black object she is holding is a truffle is for her […] to be in a certain state […] the black object she is holding must figure in a suitable way in a causal explanation of her belief that the black object she is holding is a truffle […]. (Benacerraf 1973, 671) [But] if numbers are the kinds of entities they are normally taken to be, then the connection between the truth conditions for the statements of number theory and any relevant events connected with the people who are supposed to have mathematical knowledge cannot be made out (op. cit. 673).
In order to arrive at a just assessment of Benacerraf ’s argument, one must seek out the originary insight which has made a causal theory of knowledge seem so irresistible. In that cause, I shall hark back not to recent or later 20th century attempts to arrive at such a theory, but to their unrecognized ancestor, namely C.S. Peirce’s account of four methods for the fixation of belief. The fourth method represents Peirce’s account of the way in which scientific knowledge and other genuine knowledge is to be arrived at. In advance of doing any of this, I remark that, if Benacerraf ’s argument is any good, then the consequences must perhaps be even worse than he says they are. If the argument holds for the relation between minds and numbers, how can it help but apply to the relation between minds and formal structures not rooted in the concrete? (What happens to logic itself?) 2. In “On the Fixation of Belief ”, the essay of 1877 to which Peirce himself so often returned and from which there radiate so many of his most characteristic claims about enquiry, hypothesis, perception, meaning, truth and reality, Peirce says that, with respect to any question that concerns us, belief or opinion is the state we seek (collectively and singly) to attain and doubt (by which is meant not knowing what to think about this or that) is the disquieted, irritable, dissatisfied state that we seek to end. Peirce reviews four different ways of escaping this vexation: the method of dogmatism or tenacity, the method of authority, the a priori method, and the method of experience. The method of experience embraces logic as understood in the broad nineteenth century sense of the term. “Logic is the doctrine of truth, its nature and the manner in which it is to be discovered” (Collected Papers 7.320–21).
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3. Concerning the method of tenacity or dogmatism, Peirce says that the social impulse and the inner compulsion to pay anxious heed wherever others think differently from oneself practically guarantees the method’s total ineffectiveness to implant or maintain conviction or to stave off the disquiet of not knowing what to think about this or that (whatever it may be). The second method, the method of authority, which proposes dogmatism further supported by the repression of social impulses that unsettle prescribed opinion, holds better promise than that of tenacity and dogmatism. Its past triumphs are manifest. But Peirce declares that in the end such a policy will be powerless to counter the irritation of doubt or to stabilize opinion. For No institution can undertake to regulate opinions upon every subject. Only the most important ones can be attended to, and on the rest men’s minds must be left to the action of natural causes. (Writings of Charles Sanders Peirce, 251)
And then (the argument continues) once unregulated convictions lead some of us to reject anything that is officially prescribed for general belief, the contagion can only spread and more and more others among us will come to think that their own adherence to this or that approved opinion may be owed to “the mere accident of [our] having been taught as [we] have”. The very idea that a belief of ours might come to us in that way destroys conviction. (Pausing from exposition to fill out what is, I think, Peirce’s line of thought, I remark how it seems that even the lowliest belief will never free itself altogether or entirely from some however faint aspiration to the status of knowledge.) Evidently then a third method of settling opinions must be adopted, which shall not only produce an impulse to believe, but shall also decide what proposition it is which is to be believed. Let the action of natural preferences be unimpeded, then, and under their influence let men, conversing together and regarding matters in different lights, gradually develop beliefs in harmony with natural causes. (Writings of Charles Sanders Peirce, 252)
Peirce calls this the a priori method, declaring that it “ought to be applied so long as no better method can be found”, because “it is the expression of instinct, which must be the ultimate cause of belief in all cases”. But even when dignified as a method for “the fermentation of ideas”, the a priori method will only restore the dissatisfied state we were in at the outset. It is hardly surprising then if (as Peirce claims)
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its failure has been the most manifest. [The a priori method] makes of inquiry something similar to the development of taste; but taste, unfortunately, is always more or less a matter of fashion […] [And] I cannot help seeing that […] sentiments in their development will be very greatly determined by accidental causes. Now, there are some people, among whom I must suppose that my reader is to be found, who, when they see that any belief of theirs is determined by any circumstance extraneous to the facts, will from that moment not merely admit in words that that belief is doubtful, but will experience a real doubt of it, so that it ceases to be a belief (Writings of Charles Sanders Peirce, 253, italics added).
In this last sentence we find both a true insight and the germ of the theory of knowledge which is commonly supposed to threaten Platonism. The sentence marks also the point of transition to Peirce’s fourth method of countering the disquiet of not knowing: To satisfy our doubts, therefore, it is necessary that a method should be found by which our beliefs may be caused by nothing human, but by some external permanency—by something upon which our thinking has no effect […].[That external permanency] must be something which affects, or might affect, every man. And, though these affections are necessarily as various as are individual conditions, yet the method must be such that the ultimate conclusion of every man shall be the same. Such is the method of science. Its fundamental hypothesis, restated in more familiar language, is this: There are real things, whose characters are entirely independent of our opinions about them; those realities affect our senses according to regular laws, and, though our sensations are as different as are our relations to the objects, yet, by taking advantage of the laws of perception, we can ascertain by reasoning how things really and truly are, and any man, if he have sufficient experience and [he] reason enough about it, will be led to the one true conclusion. The new conception here involved is that of reality. (Writings of Charles Sanders Peirce, 243f.)
So, if we are to escape the vexation of not having the answer to whatever question it is that disquiets us, and if our aim is that any opinion or belief we arrive at to the effect that p should be determined by circumstances that are not extraneous to the fact that p, we must cultivate or create and maintain in ourselves a state of being where we shall submit ourselves to some ‘external permanency’ or Real upon which ‘our thinking has no effect’. Here we catch our first glimpse of Peirce’s key notion of secondness. Secondness is the forcible element in our experience of perceiving or thinking and comes with the first intimation of that ‘external permanency’.
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4. ‘It may be asked’, Peirce then says, ‘how I know that there are any realities (Reals)’. To this question he has four replies. One of them is this: Nobody […] can really doubt that there are realities (Reals), for, if he did, doubt would not be a source of dissatisfaction. The hypothesis therefore is one which every mind admits […] the social impulse does not cause men to doubt it.
That simple answer would cohere well enough with the ordinary or everyday idea that there is no reason at all to doubt the reality of the world to which we are exposed in sense perception. On the basis of the anti-sceptical attitude that it expresses, it might seem that it is this ordinary idea which lends force and defeasible authority to sense-perception. But, presented in just that way, exactly thus, the ordinary idea seems both unsupported and insupportable – indeed perilously close to philosophical dogmatism. And everything looks back to front. Would it not be better—and perfectly consistent with Peirce’s reply to his questioner—to say first that senseperception and that to which one is exposed by the explorations that ensue upon sense-perception, has a force all of its own? If so, then it seems that the aggregated irresistibility of that force must enter into the justification (such as it is) of the everyday idea of the reality of the world to which sense perception exposes us. But, supposing that that is right about sense perception and the thinking that it supports, then what should one say of the however different but no less exigent and forcible compulsions that are part and parcel with (say) arithmetical or geometrical thinking? Shouldn’t we allow these to impart to us a no less ordinary or commonplace conviction of the reality of that which impinges upon us in that kind of thinking? This, I shall suggest, is the proper light in which to contemplate some reconstrual of a handful of notable utterances: Despite their remoteness from sense experience, we do have a perception also of the objects of say set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don’t see why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception. (Gödel 1947, 483f.) Classes and concepts may, however, also be conceived as real objects […] existing independently of our definitions and constructions. It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence. (Gödel 1944, 220)
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Whenever I am occupied even with the tiniest logistical problem […], I have the impression that I am confronted with a mighty construction, of indescribable complexity and immeasurable rigidity. This construction has the effect on me of a concrete tangible object, fashioned from the hardest materials a hundred times stronger than concrete and steel. I cannot change anything in it; by intense labour I merely find in it ever new details, and attain unshakeable and eternal truths. (Lukasiewicz 1970) I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’ are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards […]. (Hardy 1940, 123f.)1
There has been a tendency to read the authors of such utterances as seeking to ground their Platonism in a bare metaphor of perception.2 But maybe this is a misreading. On a less disobliging interpretation, one might say that the perceptual metaphor is intended to derive its meaning and import from the independently evident inescapability of a certain kind of thinking and the force with which its more incontrovertible findings enter into the experience of that thinking. For philosophers schooled in an all-embracing or dogmatic physicalism, it will be pointless to propose such a rereading of Gödel’s or Lukasiewicz’s remarks, because they will think they know already that there is no question of allowing any of the kinds of thing that these authors are concerned with to count as a ‘Real’ or ‘an external permanency’. But one might ask what enforces that exclusion. How does the exclusion flow from the original insight that moved us along from Peirce’s second and third to his fourth method? Did Peirce himself recognize any such restriction upon the ideas of experience and the forcible element in experience? There is nothing surely to that effect in the simple and uncontentious idea, the idea which was his starting point, that we have to discard beliefs that are determined by circumstances extraneous to the facts. There is nothing to that effect in the idea that if we know that p then it must be no mere accident that we are right. 1. Perhaps this is the least tractable of our candidates for reconstrual. Moreover, as we shall see, Peirce would deprecate the author’s needlessly spectatorial mode of expression. See section 7 below. 2. Compare serious misinterpretations of the moral philosophy of W.D. Ross which have read him as seeking to ground the judgments of morality in a specialized capacity for moral intuition. On Ross, see my 2006, 234, with note 14.
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5. At this point, we should take note of a manuscript of 1893–95 that Cheryl Misak (1991, 83) draws to our attention: As for the experience under the influence of which beliefs are formed, what is it? It is nothing but the forceful element in the course of life. Whatever it is […] in our history that wears out our attempts to resist it, that is experience […] The maxim that we ought to be ‘guided’ by experience means that we had better submit at once to that to which we must submit at last. ‘Guided’ is not the word; ‘governed’ should be said.3
If this is anything to go by, then it appears that Peirce’s general idea of experience is simply the idea of that by which we can and do expose our minds to realities/Reals and make our beliefs answerable to realities/ Reals. This trend in Peirce’s thinking is further confirmed by the extra words that he inserted in 1903 at the end of the first sentence of our last but one citation from “Fixation”. After the words ‘[…] something upon which our thinking has no effect’ he added ‘but which, on the other hand, unceasingly tends to influence thought; or in other words, by something Real’ (my italics). At this point there is a temptation to say that, if secondness is the forcible element in experience conceived in the very general way in which Peirce came to conceive it, then one of the things that Gödel is describing in our first citation is precisely such secondness. It is the very same secondness as that which Peirce himself is concerned with when he describes the process of experimenting by pencil and paper with a ‘representative diagram’, of running through all possible cases and of finding suddenly, or as one hoped, that some apparent plurality of alternatives reduces to one case. See, for instance, Collected Papers 4.530, 3.516. Experimentation of this sort creates the conditions under which ‘secondness jabs you perpetually in the ribs’ (Collected Papers 6.95) and enquiry makes advance.
3. Compare also Peirce’s own summation (1906) of “Fixation”: ‘My paper of 1877, setting out from the proposition that the agitation of a question ceases when satisfaction is attained with the settlement of belief […] goes on to consider how the conception of truth gradually develops from that principle under the action of experience, beginning with willful belief or selfmendacity, the most degraded of all mental conditions; thence arising to the imposition of beliefs by the authority of organized society; then to the idea of settlement of opinion as the result of fermentation of ideas; and finally reaching the idea of truth as overwhelmingly forced upon the mind in experiences as the effect of an independent reality’ (Collected Papers 5.564, italics added).
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6. So far so good, but if this interpretation has Peirce right, then how well does it cohere with the words by which he introduces the fourth method? The words are: “To satisfy our doubts, it is necessary that a method be found by which our beliefs may be caused by nothing human, but […]. by something upon which our thinking has no effect”. Experimentation in thought and with diagrams does indeed cause beliefs or affect belief, but it is scarcely ‘nothing human’. Better candidates to be Peircean realities and ‘nothing human’ would be the necessities themselves which are uncovered by experimentation with diagrams. These are nothing human. The only trouble is that, as we have seen, such things can hardly cause the beliefs that give voice to them.4 That is where we began – with Benacerraf. We are not the first to be troubled by the phrasing of this sentence. Peirce himself was troubled. In 1907, in the course of yet another rereading of “Fixation”, he deleted the word ‘caused’ as it occurs in this sentence and replaced it by ‘determined’ (see Short 2000, note 9). Why did he do that? Well, why else but because he wanted the reader to construe “[beliefs or opinions] determined by circumstances not extraneous to the facts” in a way that allows a narrative that explains a belief to turn upon (or turn in part upon) causation but equally leaves room for it to turn upon the contribution of other forms of determination?5 Suppose that the Cathedral at Chartres impinges on the conscious subject S, and thereafter, as a result of this event, S believes justifiably and correctly that the Chartres Cathedral has two spires. In this narrative, S is subjected to one particular kind of secondness, the secondness of senseperception. But, so far as knowledge itself is concerned, this need not be our only paradigm. For knowledge as such, the general thing that matters is simply this: that, where the conscious subject S has the belief that _ _ _, S’s belief counts as knowledge only if there is an explanation why S should have the belief that _ _ _ and the explanation for S’s having that belief 4. Nor is it quite right to say that they produce them, even if that would be slightly less bad. In the French version of “Fixation” published in Revue Philosophique de la France et de L’étranger: December 1878, Peirce wrote for ‘may be caused by nothing human’ ‘ne soient produits par rien d’humain’. 5. In these matters, it is important to remember that to speak of causation is usually to speak of a relation between occurrences, whereas to explain is something different. To explain is to answer a how- or why-question. It will not be at all straightforward to represent ‘explains why’ as standing for a relation. Issues of referential opacity loom here. This is not the place to explore the logic of ‘determine’ or to look out all the further senses of ‘cause’ that fall under the same shadow as ‘explain how’. On opacity, see Quine 1953, 28, 142–159.
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either turns upon the very fact that _ _ _ or else turns upon the subject’s awareness of that which shows forth why it must be that _ _ _. Where an explanation conforms to the second pattern and its working as an explanation involves the explainer’s readiness to enlarge at need upon that which shows forth why it must be that _ _ _, one may say that the explanation works by the rational vindication of S in S’s belief. (Compare here my Ethics, 366.) Here too, no less than in the empirical case, it will be otherwise than by accident that the subject has a true belief. Everything is still in line with the philosophical insight that moves Peirce from the second and third methods of fixation of belief to the fourth method. 7. How is this proposal to be brought to life within a Peircean context? Peirce says, ‘the truth of the pure mathematical proposition is constituted by the impossibility of ever finding a case in which it fails’. (Collected Papers 5.567.) How is that established, and how can the mathematician’s own conviction of this impossibility be explained by tracing it to the source of the impossibility itself? [to attain the necessity that is proprietary to the theorems of Mathematics] it is necessary to set down or to imagine some individual and definite schema, or diagram – in geometry, a figure composed of lines with letters attached; in algebra an array of letters of which some are repeated. This scheme is constructed so as to conform to a hypothesis set forth in general terms in the thesis of the theorem. Pains are taken so to construct it that there will be something closely similar in every possible state of things to which the hypothetical description in the thesis would be applicable, and furthermore construct it so that it shall have no other characters which could influence the reasoning. How it can be that, although the reasoning is based upon the study of an individual scheme, it is never the less necessary, that is, applicable, to all possible cases, is one of the questions we shall have to consider. Just now, I wish to point out that after the schema has been constructed according to the precept virtually contained in the thesis, the assertion of the theorem is not evidently true, even for the individual schema; nor will any amount of hard thinking of the philosophers’ corollarial kind ever render it evident. Thinking in general terms is not enough. It is necessary that something should be DONE. In geometry, subsidiary lines are drawn. In algebra permissible transformations are made. Thereupon, the faculty of observation is called into play. Some relation between the parts of the schema is remarked. But would this relation subsist in every possible case? Mere corollarial reasoning
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will sometimes assure us of this. But, generally speaking, it may be necessary to draw distinct schemata to represent alternative possibilities. Theorematic reasoning invariably depends upon experimentation within individual schemata. (“The Essence of Mathematics”, Collected Papers IV. 233)
In the acts of setting down the hypothesis, constructing its ‘diagram’, and bringing various transformations to bear upon the result, the mathematician explores more and more closely the possibility of finding a case where the proposition to be proved will fail. By the ‘elaboration of thought’, s/ he strengthens the forcible element in his/her experience. And then, if s/ he has found a way to take account of all possible cases, s/he can come to see how and why there is no case in which the thesis fails or an hypothesis holds and the consequent fails. In following out in this way the general idea that in explaining a belief one must trace its ancestry, and applying it to the geometrical and algebraic cases that Peirce is describing, we do not need to depart from his general observation that ‘if we mount the stream of thought instead of descending it, we see each thought caused by a previous thought’ (Writings of Charles S. Peirce 1872–1878, 32). When we move further upstream, however, it is bound to appear to a reader of Peirce’s text—if it be not yet corrected as Peirce corrected it in 1907—that one thing is still missing. In the Chartres case, the two spires themselves enter into the perceptual genesis of the belief that the Cathedral at Chartres has two spires. By the same token, the spires will enter into any explanation of the belief that purports to be vindicatory of it. Of course, nothing very like two spires is in prospect for Peirce’s explanation of the mathematician’s arriving at a conviction to the effect that p. But, if this is a deficit and it cannot be supplied by inserting the objects of mathematical thought into the role that is occupied in the empirical case by a thing perceived (compare Benacerraf ), this is not to say that nothing else can supply it. Once we remember that both the mathematical proposition that p, however we interpret it, and the proof of that proposition are common property between Platonist and non-Platonist, what we need is not far to seek. My suggestion is this. Let the one who explains the mathematician’s state of mind with respect to this or that true proposition embed some correct proof of the proposition within the attempted explanation itself. Lodged there, the proof itself will show what stands in the way of all attempts to find a case where the thesis in question fails. Once that is set forth, it will become apparent what forced the subject to a conclusion that coincides
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with the proposition proved. In so far as the subject understood the forms of words that were in question and was party to the considerations that make up the proof, there was no other possible destination! No wonder then that the subject reached the subject’s own conclusion. Where the explainer has access to more details of the subject’s thoughts or his ‘diagram’, further particulars may be supplied. But, even without details of the back and forth of the subject’s exploration, an explanation that incorporates the proof itself can engage in a general way with the ‘forcible element’ in the enquirer’s experience. Where a ‘diagram’ corresponding to the proof reveals how and why there is simply no room to think otherwise than that p, it is no wonder that, in so far as S was party to considerations all of a piece with that line of reasoning, S was forced to the conclusion that p. If a flock of sheep seeks to escape from a field in search of new pasture and there is only one gate and the gate is open, it is no wonder that they pass through that gate. In order to have a rough and ready analogy between this explanation and explanation by rational vindication, let us think of the passion that drives the sheep to find new pasture as corresponding to the passion (the passion, say, to end the irritation of not knowing) which drives the mathematician to seek to prove or disprove the hypothesis. Let such passions count (if you will) as causes.6 Then let us compare the way in which the openness of that single gate channels the passion of the sheep with the way in which the diagram and the truth that it sets forth—as recapitulated within a plenary version of the explanation of the mathematician’s belief—shape and configure the course of the mathematician’s efforts to end the disquiet of not knowing. Let the openness of the gate in the one case and that which the diagram shows forth in the other case count, not as a cause, but as a condition under which the cause operates. 8. So much for the response to Benacerraf ’s argument. Does such a defence lend any positive support to Platonism? Well, look at the explanation itself, as expanded to furnish the rational vindication of the mathematicians’ belief. One part of it is a piece of mathematics, and this will 6. Some will prefer to speak of events or processes such as the onset or persistence of the passion, and to modify accordingly the understanding of the cause/conditions distinction that takes up the rest of the present paragraph. It would be an understatement to say that there is still work for philosophy to do concerning the relation between the ordinary notion of cause, which requires the distinction appealed to in the text, and Humean accounts of causation (or J.S. Millian accounts).
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come with all the ontological commitments7—whatever they may be—of the language of mathematics. The truly substantial question that remains is what those commitments are. The thing that I hope to have made plausible is that the nature and extent of those commitments is a logical, mathematical or metamathematical question. This is not to say that this question is easy. Indeed it opens out into a host of problems about what exactly those commitments can amount to. Can the natural numbers as Platonists conceive them have the logical properties of particular objects? If it is objects we think mathematics needs, can we find objects which obey the principle of the determinacy of identity?8 Again, can this or that piece of mathematics—can mathematics as a whole—make do with a potential infinity of objects or must it have an actual infinity? If so, how large an infinity? What is the ontological significance of the fact (Skolem’s paradox) that, regardless of its apparent content, any first order theory which has a model has a denumerable model? And so on […]. Such questions are highly non-trivial, but they do not belong to run-of-the-mill epistemology, metaphysics or philosophy of mind. They are internal to logic and mathematical philosophy. If it will, let mathematical philosophy claim to have its own metaphysic. But in building that metaphysic, it should not compromise with physicalism or the metaphysics of material substance, or temporize with other encroachments from without. There is no reason for it to do so and reason for it not to do so. It is enough for mathematical philosophy to attend simply to the constraints that it generates for itself (as we saw it do in the first sentences of the present paragraph) from within its own subject matter. 9. In sum, my conclusion is that the causal argument is mistaken because it misuses the truth that lurks behind the causal theory of knowing. Once we see that that truth relates to explanation and we make the link between explanation and the possibility of rational vindication, it becomes plain that the proper place to interrogate and refine mathematical Platonism 7. Let me show my hand here. I accept the account of ontological commitment which was put forward by Quine (1953)—but only in the form in which Cartwright (1954) clarified and corrected Quine’s doctrine. 8. For the claim that, concerning any genuine object x, it must be determinate which object x is, see Frege, 1884, § 62; also see Wiggins 2001, 160, 162f., 167. In this connection, see also Benacerraf, 1965.
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lies outside general epistemology and metaphysics. No reason remains for us to confuse the incontrovertible denial of the materiality of mathematical things with the outright denial of their existence. The latter denial is rendered prima facie absurd by the inescapable force and exigence of settheoretical, arithmetical, geometrical […] thinking. Another way of recapitulating my contentions is this: there is no simple separation to be made between (1) that which at once explains and vindicates our inescapable collective belief in a given mathematical proposition; (2) the sense that we attach to the proposition which commands our collective assent; and (3) the account that is to be given of what that proposition has to be about—the objects that it is concerned with. 9
REFERENCES Benacerraf, Paul 1965: “What Numbers Could Not Be”. Philosophical Review 75, 47–73. — 1973: “Mathematical Truth”. Journal of Philosophy 70, 661–679. Cartwright, Richard 1954: “Ontology and the Theory of Meaning”. Philosophy of Science 21, 316–325. Frege, Gottlob 1884: Die Grundlagen der Arithmetik. Transl. by John L. Austin as The Foundations of Arithmetic, 2nd, rev. ed., Oxford: Blackwell, 1953. Gödel, Kurt 1944: “Russell’s Mathematical Logic”. In: Paul Arthur Schilpp (ed.), The Philosophy of Bertrand Russell. New York: Tudor Publishing Company, 123–153. — 1947: “What Is Cantor’s Continuum Problem?”. References to the revised version in: Paul Benacerraf & Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings (2nd ed.). Cambridge: Cambridge University Press, 1983, 470–485. Hardy, Godfrey H. 1940: A Mathematician’s Apology. Cambridge: Cambridge University Press. Lukasiewicz, Jan 1970: “In Defence of Logistic”. In his Selected Works, ed. by Ludwik Borkowski, Amsterdam: North-Holland. Misak, Cheryl 1991: Truth and the End of Inquiry. Oxford: Oxford University Press. 9. I am grateful for comments and suggestions made to me by Ian Rumfitt, Daniel Isaacson, Cheryl Misak, Peter Simons (who furnished the citation from Lukasiewicz) and Elliott Sober. In sections 2–5 of this article I seek to apply, to rehearse and to improve upon the interpretation of Peirce which I have set out in my contribution to Misak 2004.
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Misak, Cheryl (ed.) 2004: The Cambridge Companion to Peirce. Cambridge: Cambridge University Press. Peirce, Charles. S. 1931–1935: Collected Papers of Charles Sanders Peirce. Vols. 1–6, Charles Hartshorne & Paul Weiss (eds.), Cambridge, Mass.: Harvard University Press. — 1958: Collected Papers of Charles Sanders Peirce. Vols. 7–8, Arthur W. Burks (ed.). — 1981: Writings of Charles S. Peirce, A Chronological Edition. Peirce Edition Project (eds.), Bloomington and Indianapolis: Indiana University Press. Quine, Willard V. O. 1953: From a Logical Point of View. Cambridge, Mass.: Harvard University Press. Short, Thomas L. 2000: “Peirce on the Aim of Enquiry: another Reading of ‘Fixation’”. Transactions of the Charles S. Peirce Society 36, 1–23. Wiggins, David 2001: Sameness and Substance Renewed. Cambridge: Cambridge University Press. — 2006: Ethics: Twelve Lectures on the Philosophy of Morality. London: Penguin & Cambridge, Mass.: Harvard University Press.
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Grazer Philosophische Studien 82 (2011), 329–351.
FREGE, PÜNJER, AND KANT ON EXISTENCE Tobias ROSEFELDT Humboldt University of Berlin Summary The paper tries to shed new exegetical light on Frege’s “Dialogue with Pünjer on Existence” by showing that Pünjer’s position in the dialogue is strongly inspired by Kantian claims about existence. It is argued that Pünjer’s wavering between a broadly Meinongian and a broadly Fregean view on existence can be explained by the fact that there are Kantian remarks which seem to speak in favour of each of these views. A suggestion is then made how Kant’s claims can be interpreted in such a way that the tension which they seem to entail disappears.
At some time in the early eighties of the 19th century, Gottlob Frege and the Protestant theologian Bernhard Pünjer, both professors of the University of Jena at this time, met for a discussion about the nature of existence and the logical form of existential statements. Their dialogue is documented in an incomplete transcript as well as in a subsequent summary by Frege in which he tries to elucidate the structure of the development of their discussion and explains his own position in more detail.1 While both documents make it very clear for which account of existence Frege argued in the conversation—namely that of treating the concept of existence as a second level concept—, they leave the reader somehow puzzled as to what exactly Pünjer’s position was. In the dialogue, Pünjer seems to have made several claims which were then shown by Frege to be inconsistent with each other. He also seems to have refused several suggestions made by Frege how to arrive at a coherent position. All in all, Pünjer’s remarks give the impression of originating from rather substantial philosophical confusion. A charitable reader of Pünjer’s remarks will therefore raise two questions: First, is there a coherent account of existence which covers the motivation by which Pünjer apparently has been driven? Second, why is 1. Cf. Frege (1990); I will use the translation in Frege (1979) and make slight modifications if I find them appropriate. Page numbers refer to the English edition.
Pünjer so reluctant to accept one of Frege’s suggested amendments which would make his account coherent? In this paper, I want to argue that both of these questions can be answered if one realises that, in the dialogue, Pünjer tries to defend a basically Kantian account of existence. I will show how Pünjer’s remarks originate from certain things Kant writes about existence and existential statements. The main aim of my paper will be to show that Pünjer’s hesitation to accept Frege’s amendments can be explained by a certain exegetical puzzle which arises from Kant’s claims about existence: Kant’s writings contain passages which seem to speak in favour of a broadly Fregean, and hence anti-Meinongian, account of existence as well as passages which seem to support a broadly Meinongian, and hence anti-Fregean, account of existence. I will argue that this puzzle explains Pünjer’s confusion and I will also make a suggestion how it should be solved. The methodological lesson to be learned from Frege’s dialogue with Pünjer is that it is always very instructive for a Kantian to be confronted with the conceptual rigour and insistence on clarity of a Fregean. This gives me a very personal reason to contribute a paper on this dialogue to the present volume. When I first read Wolfgang Künne’s Abstrakte Gegenstände, it was shortly after I had finished my dissertation on Kant’s theory of self-consciousness. The book made a deep impression on me and left me with two wishes. The first was to do systematic ontology myself. The second was to write about Kant in a way that does not fall short of the standards of conceptual clarity that someone like Wolfgang Künne would find acceptable. Although I have doubts that the second wish will ever become true, I am grateful to Wolfgang for keeping it alive in me. 1. Pünjer’s predicament On the basis of Frege’s summary of his conversation with Pünjer, it is reasonable to assume that their dispute took its starting point from questions about the logical form of existential statements. Pünjer seems to have held the view that existence can be expressed in general statements such as ‘There are tables’ as well as in singular statements such as ‘This table exists’. More precisely, this view could be characterised (and is so characterised by Frege) in the following way (cf. Frege 1979, 61):
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(P1) The expression ‘there are’, in sentences of the form ‘There are Fs’, and the expression ‘exists’, in sentences of the form ‘a exists’, express essentially the same content. (P1) implies that existence is something which is predicable of individual objects, or—to put a non-Fregean claim in Fregean terms—that the concept of existence is a first-level concept and existence a property of objects. A second assumption that Pünjer seems to have held concerns the analysis of the general existence statements mentioned in (P1). It can be viewed as an explanation of how what is said in (P1) can be the case. For, it gives an analysis of statements of the form ‘There are Fs’ that implies that these statements somehow implicitly contain the first-order existence predicate. The assumption reads as follows (ibid. 61): (P2) Sentences of the form ‘There are Fs’ mean the same as the respective sentences of the form ‘Some existing things are F’. The upshot of this claim is that it is not the particular quantifier ‘some things’ as such that carries the existential commitment implied by a use of the expression ‘there are’ but rather the particular quantifier restricted by the existence predicate, i.e. the expression ‘some existing things’.2 A third claim that is distinctive for Pünjer’s view of existence has to do with an attempt to specify further what we mean when we say that a certain thing exists or fails to exist. According to Pünjer, the exclusive function that existence statements have for us consists in making it possible for us to deny of certain things that they are objects of mere hallucination and claim that the representations we have of them count as experience (53, §§ 3, 12; 54, §18). Pünjer furthermore believes that experience can be distinguished from hallucination on the grounds that it originates from an ‘affection of the subject’ (54, § 20). The idea behind this claim is probably that representations which constitute hallucination are somehow fully created by the subject herself whereas representations that constitute experience originate in a source outside the subject through some causal impact. Driven by these considerations, Pünjer makes the following claim (53, § 12): 2. In the dialogue, Pünjer insists that the inference from ‘Sachse is a man’ to ‘There are men’ is not logically valid but needs the additional premise ‘Sachse exists’ (cf. 60).
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(P3) For us, to say of an object that it exists means to say of it that it is an object of experience, i.e. something the representation of which originates from an affection of us. Hence, for us, ‘There are Fs’ means the same as ‘Some objects of experience are F ’, and ‘a exists’ means the same as ‘a is an object of experience’. For everyone familiar with Frege’s view of existence it should be clear that he would accept none of Pünjer’s three claims. From a Fregean perspective, (P1) and (P2) suffer from the defect of treating the concept of existence as a first-level concept, i.e. a concept under which objects can fall. (P3) moreover is prone to the confusion of matters of epistemology with matters of thought and meaning, a confusion Frege is always very eager to dissolve.3 Frege’s strategy for refuting Pünjer’s view of existence is to show that there is no plausible reading of (P1)–(P3) on which these three claims can consistently all be held together. His main focus lies on a discussion of (P2). According to Frege, it would only be correct to assume that ‘There are tables’ means the same as ‘Some existing things are tables’ if the predicate ‘exist’ expressed something pleonastic and trivial (‘etwas Selbstverständliches’) and had no real content, i.e. would be true of everything, such as the predicate ‘is self-identical’ (cf. 62 and 59, § 88). The reason for this is simple: Assume that the existence-predicate is not true of everything. Because of the equivalence of ‘Not all Fs are G’ and ‘There are Fs that are not G’, that would mean that there are existing as well as non-existing things. However, if this were the case, then to say that there are tables would not be equivalent to saying that some of the existing things are tables, for only the falsity of the first not that of the second statement would imply that there are no tables at all. The falsity of ‘Some of the existing things are tables’ would leave open the possibility that there are non-existing things which are tables. Hence, (P2) is true only if ‘exists’ expresses a property that applies to everything and if it is trivial to say of something that it exists. Let us call this consequence of Pünjer’s view ‘the triviality implication’. The triviality implication has several consequences. One consequence Frege draws is that even if (P2) is true the real content of a claim such as ‘Some of the existing things are tables’ or ‘Some tables exist’ cannot lie in 3. Since (P3) is rather implausible when formulated as a claim about sameness of meaning, a more charitable way of interpreting what Pünjer says might be to put the connection asserted by (P3) in terms of sameness of conditions of justified assertion. However, the possible criticism which could thus be avoided shall not concern us here.
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the predicate ‘exist’. Instead, it must lie in the ‘form of the particular judgment’. The reason is that when we claim that there are tables, what we say is not trivial. A further consequence of this is that (P2) cannot serve as an explanation of how (P1) can be true. The reason is that even if ‘there are Fs’ is equivalent to ‘some existing things are F’, what carries the existential commitment of ‘there are’ is the form of the particular judgement, rather than the existence predicate; and it is still hard to understand how something that is expressed by the form of the particular judgement can also be expressed by a first-order predicate. The most important consequence for Frege’s criticism is that the triviality implication shows that (P1) and (P2) are incompatible with Pünjer’s thesis (P3). If the existence predicate does not have any substantial content and is true of everything its function for us cannot consist in distinguishing between objects of experience and objects of mere hallucination, or between representations that originate from an affection of the subject and those which do not. For it is certainly not trivial to say of an object that it is not only an object of hallucination, or of a representation that it originates from an affection of the subject by some outer object. From a systematic point of view, there seem to be two possible strategies to answer Frege’s criticism. I will call them the ‘Meinongian’ and the ‘Fregean’ strategy. The first strategy owes its name to the fact that it consists in accepting a consequence of (P3) which is distinctive for the Meinongian conception of existence. The consequence is that, according to (P3), existence is a discriminating property of objects, a property that, as Meinongians assume, some objects have (e.g. objects of experience) and others lack (e.g. objects of mere imagination). Since this implies that there are existing as well as non-existing things, Pünjer would have to give up or at least modify claims (P1) and (P2). He would have to admit that there is at least one meaning of the expression ‘there are’ in which sentences of the form ‘There are Fs’ are not equivalent to the requisite sentences of the form ‘Some existing things are F’ and do not carry existential commitment. He might furthermore explain the prima facie plausibility of (P1) and (P2) by the fact that in most philosophical as well as ordinary contexts we are prone to what Meinongians call the ‘prejudice towards the actual’ and implicitly restrict our quantifiers to existing objects. At one point of the conversation, Frege explicitly confronts Pünjer with the Meinongian consequence of his claim (P3):
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Then it follows that there are objects of representations […] which do not exist. Now if you are using the word ‘exists’ in the same sense as the expression ‘there is’, then you have at the same time both asserted and denied the same predicate of the same subject. […] Do you grant this? Pünjer: Yes. But the word ‘there is’ is wrongly used in this context. Frege: Then put in its place another expression that will express the matter better. (59, §§ 79ff.)4 Frege:
The Meinongian response to this demand would be to distinguish between two senses of the expression ‘there is’—one in which it is equivalent with ‘there exists’ and another in which it is existentially neutral. This would make it possible to claim—to use Meinong’s own words—that ‘there are things of which it is true to say (in some other sense) that there are no such things’ (cf. Meinong 1904, 9). However, Pünjer is not willing to bite this Meinongian bullet. He answers to Frege’s challenge: Pünjer: We can’t: any other expression would again fail to say what is meant to be expressed. […] Before we deny the existence of anything whatever, we have to represent it as existing in order to go on to deny existence of it. But I don’t think that we shall get any further along these lines. (59, §§ 82, 84) Here, Pünjer seems to follow many contemporary Anti-Meinongians in finding it impossible to understand the expression ‘there is’ in a nonexistence entailing way. He seems to interpret the claim that there are things that do not exist as an unavoidable paradox of our talk about nonexistence the inconsistency of which cannot be avoided by use of some weaker reading of the expression ‘there is’ but rather only by reference to the temporal dimension of our utterances: In saying that there are things that do not exist, we first represent something as existing and later we deny the existence of what was presented as existing. However, the last remark of the quote makes clear that he did not himself believe that reference to the non-simultaneity of the utterance of the sentence-parts ‘there are things’ and ‘that do not exist’ really solves the problem Frege’s criticism had made apparent. 4. I departed from the quoted edition by translating the German word ‘Vorstellung’ by ‘representation’ rather than by ‘idea’ here. The reason is that, as I will argue below, Pünjer holds a Kantian position and for Kant, ideas are just one very special kind of representations.
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The Fregean strategy, on the other hand, is built on the idea that we can take seriously the motivation behind Pünjer’s claim (P3) without having to assume that existence is a discriminating property of objects. This assumption can be traced back to the indeed plausible claim that not all our representations represent objects in the world. In Pünjer’s own words: Pünjer: Yes; there are two kinds of representations: those that originate from the ego alone, and those that are formed through something affecting the ego. In order to distinguish these I say: the objects of representations of the latter kind can be experienced; to representations of the former kind there do not correspond any objects that can be experienced. (54, §335, 20) Interestingly, Pünjer does not say here that representations originating from the ego refer to objects that cannot be experienced but confines himself to denying that they refer to objects that can be experienced. This would offer him the possibility to give up the distinction between existing and non-existing objects and replace (P3) by a claim that assigns to existence claims the purpose of classifying representations as to whether they represent something or fail to do so. Frege confronts Pünjer with this modification of his original position: Frege: It seems to me then as if the real subject on your way of thinking is the representation. […] When you say ‘There are men’ and ‘There are no centaurs’ you are also making a classification. But you are not classifying things […], but you are classifying the concepts ‘man’ and ‘centaur’ by assigning one to the class of concepts under which something falls, and excluding the other from this class. This is why I hold that in these sentences the concepts are the real subjects. If you say ‘This can be experienced’, where this has the sense ‘This representation of mine is not something originating from myself alone’, then you are classifying the representation. […] This is why I maintain that it is here the representation that is the real subject. Another way of putting the same thing is to say: The representation has the property that something corresponds to it. (54, §§ 21, 23) What Frege suggests to Pünjer here is a view on existence which obviously has some similarity to his own. General existence statements such as ‘There
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are human beings’ or ‘There are no centaurs’ are analyzed as statements about the concepts of a human being and that of a centaur, saying of the first, and denying of the second, that at least one object falls under them. A singular existential statement such as ‘This exists’ or—in Pünjer’s reformulation—‘This can be experienced’ is interpreted as a statement about a particular representation, saying about that representation that at least one object corresponds to it. If Pünjer wanted to adhere to (P1) and assume that the expression ‘there are’ in general existence statements and the expression ‘exists’ in singular existence statements express the same content, he could assume that in both kinds of statements we ascribe to the property of being represented by such-and-such representations the second-order property of being instantiated by at least one object. (In the case of a general existence statement, the representation at issue would be a concept, in the case of a singular existence statement it would probably be some perceptual representation.) Although Frege certainly would not approve of the meta-representational touch of it, the resulting analysis would deserve to be called Fregean in that it sees a strong connection between existence and the second-order property of being instantiated by at least one object. (This connection would in turn leave no room for Pünjer’s claim (P2) any more.) As in the case of the Meinongian strategy, Pünjer explicitly refuses to accept the Fregean strategy as a way to deal with Frege’s objection and is not willing to interpret existential statements as implicitly meta-representational. He answers to Frege’s suggestion: Pünjer: […] Negation is possible only when something has already been posited. Hence if we say ‘Centaurs do not exist’, this is possible only because we first think of them as being outside ourselves. We have a twofold ground for denying existence: 1. a logical contradiction, 2. outside the concept or representation in experience. So properly speaking the real subject is neither the concept nor the representation. (55, § 24) Pünjer notices that, in the case of true negative a posteriori existential statements, it is not the concepts alone which make it the case that nothing falls under them but also the state of the world, of which we therefore need experience in order to find out whether the statement is true. From this he seems to conclude that such existential statements cannot be about our concepts. Now, a proponent of the Fregean strategy could agree that such
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statements are not made true by the concepts alone but also by the world as a whole which is responsible for the fact that none of its parts falls under the respective concept, and hence that the statements are not solely about concepts but also about the world as a whole. However, Pünjer seems to think that his argument moreover shows that a true negative a posteriori existential statement such as ‘Centaurs do not exist’ is somehow about centaurs, objects which we ‘posit’ by using the concept of a centaur and of which we then find out that they do not exist. Hence he is explicitly not willing to abstain from the assumption that there are non-existing objects. Pünjer’s refusal of the Meinongian as well as of the Fregean strategy leaves him in the uncomfortable situation of not being able to present any convincing answer to Frege’s challenge whatsoever. He seems to have been forced into the predicament of having to accept a Meinongian or a Fregean view about existence and at the same time not being willing to accept either of these views. This is the situation in which we find him until the end of the conversation, or at least until the end of that part of the conversation which is reported by the transcript. The pressing question at this point is why Pünjer is so reluctant to accept one of the two proposals Frege makes to him. In the next section, I try to answer this question by showing that Pünjer’s views are heavily inspired by Kantian claims about existence and that his unwillingness to accept either the Meinongian or the Fregean strategy is due to the fact that the Kantian claims themselves seem to waver between these two approaches. 2. Pünjer’s Kantian roots According to the editors, Frege’s conversation with Pünjer took place at some time between 1880 and 1884 (cf. Frege 1990, 172). Some years before, namely in 1874, Pünjer had published a small volume called Die Religionslehre Kants (Kant’s doctrine of religion, cf. Pünjer 1874). Although this book does not contain any detailed discussion of Kant’s claims about existence, we can take it for granted that its author was well familiar with these claims because most of them appear in the context of Kant’s refutation of the ontological proof in his early writing The only possible argument in support of a demonstration of the existence of God (1763) and in the Critique of Pure Reason (1781/21787). Moreover, it seems likely that a theologian whose primary contact with philosophy was an investigation
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of Kantian writings would try to bring in the Kantian position into a discussion like the one with Frege about existence. This suspicion is confirmed by the fact that much of what Pünjer says in the conversation can be traced back to Kantian remarks in either The only possible argument or the Critique of Pure Reason. The idea behind (P2)—namely that claims of the form ‘Fs exist’ or ‘There are Fs’ are not equivalent to the respective claim of the form ‘Something is an F’ but rather only with ‘Some existing thing is an F’—is probably inspired by passages from The only possible argument in which Kant speaks about the logical form of existential statements, such as the following: The expression “A sea-unicorn is an existing animal” is not […] entirely correct. The expression ought to be formulated the other way round to read “Some existing sea-animal has the predicates which I collectively ascribe to a unicorn”. (The only possible argument, AA II 72f., cf. also 745)6
(P3), which asserts a strong connection between existence—or at least existence we can make sense of—and the property of being an object of experience (and hence of representations which originate from an affection of the subject), obviously mirrors Kant’s remarks in the chapter on the “Postulates of Empirical Thinking” in the Critique of Pure Reason about empirical useful application conditions of the categories of modality, among them the category of existence. Kant writes there: In the mere concept of a thing no characteristic of its existence can be encountered at all. […] that the concept precedes the perception signifies its mere possibility; but perception, which yields the material for the concept, is the sole characteristic of actuality. (Critique of Pure Reason A 225 f./B 272 f.)
For Kant, perception entails an affection of the subjects by some outer object. Moreover, already in The only possible argument, Kant had claimed 5. In this paper, I follow, by and large, the translations in Kant (1998) and (2002). The page numbers refer to the Academy Edition of Kant’s writings (Gesammelte Schriften, hg. von der Preußischen [später: Deutschen] Akademie der Wissenschaften, Berlin 1900 ff.) and, in the case of the Critique of Pure Reason, to the pagination of the first (A) and second (B) edition. 6. Kant would also agree with Pünjer’s assumption that a singular statement such as ‘Sachse is a man’ does not have existential import and hence its truth does not imply the existence of men (cf. fn. 4). This is obvious from two passages. Firstly, Kant claims that judgements about impossible objects, such as ‘The God of Spinoza is subject to continuous change’, can be true, but he would certainly deny that there exists some Spinozean God (cf. AA II 74). Secondly, he writes: ‘The proposition “God is omnipotent” must remain true even for someone who does not acknowledge the existence of God […]’ (ibid.).
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that to say that sea-unicorns exist ‘simply means: the representation of a sea-unicorn is an empirical concept’ (AA II 74), i.e. a concept that is derived from sensible experience. Now, if Kant shares the core of Pünjer’s views on existence (or rather the other way round), he would be confronted with the same problems that Frege’s objections had made apparent. Hence, one might wonder whether there are any hints in the Kantian text that he has chosen either the Meinongian or the Fregean strategy to make his views coherent. As I will show next, the answer is that for both of these strategies we can find passages in Kant which seem to imply that he would have disapproved of them. This is the reason, I think, why Pünjer, trying to be a good Kantian, is so reluctant to accept any of the amendments of his conception which Frege offered to him. Let us start with the Meinongian strategy according to which we should accept that there are existing as well as non-existing objects. It is noteworthy that, when Pünjer and Frege speak critically about the view that there are non-existing things of which we can find out that they are not objects of experience, they use an expression which is characteristic for Kant’s talk about existence, namely the term ‘determine’ (‘bestimmen’): Pünjer: The statement ‘A cannot be experienced’ is not possible. […] Neither does it make sense to deny that a thing can be experienced. […] Frege: To say of a thing that it can be experienced is not to determine it in any way. (Durch die Aussage der Erfahrbarkeit wird dasjenige, von dem sie ausgesagt wird, nicht irgendwie bestimmt.) Pünjer: No. That is the difference between this statement and the others. (53, § 10; 54, §§ 15, 16) The claim that by saying that a certain thing exists or—which according to (P3) amounts to the same—that it can be experienced, we do not determine it in any way, is reminiscent of Kant’s most famous dictum about existence: […] the illusion [on which the ontological proof rests] consists in the confusion of a logical predicate with a real one (i.e. the determination of a thing [der Bestimmung eines Dinges]) […]. Being is obviously not a real predicate, i.e. a concept of something that could add up to the concept of a thing. (Critique of Pure Reason, A 598/B 626)
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Kant claims here that the concept of existence is only a logical predicate, i.e. a concept that can be used at the predicate position of a categorical judgement such as ‘God exists’, but not a real predicate, i.e. a concept by which objects are ‘determined’. This claim could be understood as a disclaimer of the Meinongian strategy if it was interpreted in the following way: Real predicates are predicates that express discriminating properties of objects, i.e. properties that divide the class of all objects in those which have it and those which fail to have it. To deny that the concept of existence is a real predicate would then mean that existence is not a discriminating property of objects and that it is not the case that, as the Meinongian strategy assumes, there are existing as well as non-existing objects. I think it is very likely that Pünjer interpreted Kant’s dictum in this way and for that reason was not willing to accept the Meinongian answer to Frege’s challenge. Would Pünjer have found support in Kant for subscribing to the Fregean strategy? At first sight it looks as if there are passages in which Kant sympathises with a Fregean account of existence.7 As I have characterised the Fregean strategy, its distinctive features are (i) that it interprets existence not as a first-order property of objects but rather as a second-order property of properties, namely the property of being instantiated by at least one object, and (ii) that it reconstructs existence-claims as implicit meta-representational in the sense that, in these claims, the property of being instantiated by at least one object is ascribed to the property of corresponding to such-and-such representations. Of the following three quotations from Kant, the first two seem to support the first, and the third the second of these two aspects of the Fregean strategy: [When I say] “God is”, or “There is a God”, then I add no new predicate to the concept of God, but only […] posit the object in relation to my concept. (Critique of Pure Reason, A 599/B 627) Existence cannot, therefore, itself be a predicate. If I say: “God is an existent thing” it looks as if I am expressing the relation of a predicate to a subject. But there is an impropriety in this expression. Strictly speaking, the matter ought to be formulated like this: “Something existent is God”. In other words, there belongs to an existent thing those predicates which, taken together, we designate by means of the expression “God”. (The only possible argument, AA II 74) 7. Many interpreters read Kant as a proto-Fregean with regard to existence. (E.g. Bennett 1974, 228 ff.; Forgie 2000; Reed 2007, 169f.)
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When existence occurs as a predicate in common speech, it is a predicate not so much of the thing itself as of the thought which one has of the thing. For example: existence belongs to the sea-unicorn but not to the land-unicorn. This simply means: the representation of a sea-unicorn is an empirical concept; in other words it is the representation of an existent thing. (The only possible argument, AA II 72)
A closer look at these passages, however, shows that they are far less Fregean as they may appear at first sight. According to the Fregean strategy described above, the statement ‘God exists’ should be analyzed as equivalent to the statement ‘There is at least one object that corresponds to the concept of God’. Hence, existence would be expressed by the quantifier ‘there is at least one object’, which Frege would interpret as a second-order predicate expressing a property of properties. What Kant suggests as an analysis of ‘God exists’ in the second quotation, however, is different from this approach. His analysis of ‘God exists’ is ‘There is at least one existing object that corresponds to the concept of God’, and it seems as if the existential import of the analysans is not carried by the quantifier alone. For God to exist it is not sufficient that there is some object corresponding to the concept of God, but that object has to be an existing object. In this analysis, however, the verb ‘exist’ is used as a first-order predicate expressing a property of objects. This difference between the Kantian and the Fregean account of existence is also apparent in the fact that for Frege existence is a quantity and existential statements are concerned with the number of objects falling under a certain concept. (To say that Fs exist is to deny that the number of Fs is zero. Cf. Frege 1988, § 53, 64; 2002, 18 f.) For Kant, however, the concept of existence does not appear among the categories of quantity but is a category of modality. For him, to exist seems to amount to being an actual not just a possible object (cf. Critique of Pure Reason, A 80/B 105). The most striking textual evidence for the assumption that Kant would not approve of the Fregean strategy are passages in which he explicitly says that there are existing as well as non-existing objects. Here is one from the The only possible argument: Take any subject you please, for example, Julius Caesar. Draw up a list of all the predicates which may be thought to belong to him […]. You will quickly see that he can either exist with all these determinations, or not exist at all. The being who gave existence to the world and to our hero within that world could know every single one of these predicates without exception and yet
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still be able to regard him as a merely possible thing which, in the absence of that Being’s decision to create him, would not exist. Who can deny that millions of things which do not actually exist are merely possible […]. Or who can deny that in the representation which the Supreme Being has of them there is not a single determination missing, although existence is not among them, for the Supreme Being cognises them only as possible things. (AA II 72, my emphasis)
I will return to the question of what the point about Julius Caesar and God’s complete representation of him is later. At the moment we simply have to acknowledge the fact that Kant not only seems to find it consistent to speak about non-existing merely possible objects—a way of talking that a Fregean would have to dismiss as being ill-formed—, but also claims that there are millions of such objects. If Pünjer was influenced by these claims, which I think he was, he must have thought that centaurs, for example, are such non-existing possible objects. And hence he must have found it plausible that, when we say that centaurs do not exist, we speak about these non-existing objects—objects of which we think as ‘being outside of ourselves’ (55, § 24), and not only about our concept of them. Now, you might think that it is one thing to assume that Pünjer was inspired by Kant’s critical philosophy and another thing to hold that he was convinced by every thing Kant claimed in one of his early pre-critical writings. It is important to note, however, that the distinction between existing and non-existing objects has not disappeared from his critical philosophy at all. Beside Kant’s remarks about the ‘1000 possible thalers’ which do not improve my financial situation in the context of Kant’s refutation of the ontological proof in the Critique of Pure Reason (cf. A 599/B 627) there is a highly instructive passage at the very end of the “Transcendental Analytic” in which Kant’s commitment to non-existing objects becomes apparent. Kant claims there that it is important to note that the real objects—i.e. those objects he was concerned with throughout the Critique so far—can be distinguished from objects of another kind, so that the class of ‘objects in general’ must be divided into the class of ‘objects that are something’ and the class of ‘objects that are nothing’. He then distinguishes different kinds of objects that are nothing, among them so called ‘objects of mere thought’ (‘Gedankendinge’ or ‘entia rationis’). An ‘object of mere thought’ is an ‘object of a concept to which no intuition corresponds’ (A 290/B 347). Objects of mere thought are distinguished from so-called ‘Undingen’ (impossible objects, another kind of ‘objects 342
that are nothing’) in that they are objects of non-contradictory concepts. And they are distinguished from real existing objects in that there is no intuition of them. According to this view, the concept of a centaur would represent an object of mere thought. Hence it would not be empty at all, but just fail to represent an existing object. One might not like what Kant is writing in the passages about nonexisting objects but it is undeniably something Kant himself seems to have found unproblematic. And this is the reason, I think, why someone like Pünjer, who tries to be a good Kantian, gets into a predicament if he is confronted with the alternative Frege offers to him: He cannot accept the Meinongian strategy because it seems to conflict with Kant’s dictum that existence is not a determination; and he cannot accept the Fregean strategy because it seems to run counter to Kant’s view that all representations, even those not constituting experience, represent objects, albeit some of them only represent non-existing objects. In the next section I will briefly sketch which of the two alternatives Pünjer should have chosen if his intention had been to adhere, as closely as possible, to the original Kantian view about existence. That is, I will try to solve the exegetical riddle that Kant’s remarks about existence and non-existing objects pose to his readers. 3. Kant’s view of existence 8 Although many people read Kant’s remarks about existence as protoFregean, I think there is no way of interpreting away the fact that he speaks of existence as a discriminating property of objects, a property that some objects have (e.g. objects of sensible experience) and others, such as merely possible objects, lack. It may be that such non-existing objects are objects in some other, weaker sense than the ones Kant usually talks about when he considers the question of how our representations refer to objects. But it is undeniable that he also makes use of a concept of an ‘object in general’ (‘Gegenstand überhaupt’) which allows him to distinguish between existing and non-existing objects. This makes his view of existence Meinongian avant la lettre.9 8. I presented an early version of the following on the 10th International Kant-Congress in Sao Paolo in 2005 (cf. Rosefeldt 2008). 9. This is far less surprising than it may first seem if we take into account the fact that many philosophers of the pre-Kantian philosophical tradition were Meinongians in this sense. Descartes—just to mention one famous example—found it completely unproblematic to speak
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This diagnosis leaves us with two pending exegetical questions: (i) If, for Kant, existence is a discriminating property of objects, what is meant by his claim that the existence-predicate is not a ‘real predicate’ and existence not a ‘determination of a thing’? (ii) If, for Kant, existence is a discriminating property of objects, what is meant by those of his remarks that seem to speak in favour of a meta-representational analysis of existential statements like the one in which he writes that existence ‘is not a predicate of the thing itself but rather of the thought one has of this thing’ (cf. AA II 72)? In the remainder of this paper, I will try to present the sketch of an answer to both of these questions. Let me quote again the passage from The only possible argument in which Kant speaks about non-existing possible objects: Take any subject you please, for example, Julius Caesar. Draw up a list of all the predicates which may be thought to belong to him […]. You will quickly see that he can either exist with all these determinations, or not exist at all. The being who gave existence to the world and to our hero within that world could know every single one of these predicates without exception and yet still be able to regard him as a merely possible thing which, in the absence of that Being’s decision to create him, would not exist. Who can deny that millions of things which do not actually exist are merely possible […]. Or who can deny that in the representation which the Supreme Being has of them there is not a single determination missing, although existence is not among them, for the Supreme Being cognises them only as possible things. (AA II 72)
Kant speaks here about the scenario of God’s creation of the world, and his description of this scenario is obviously Leibnizian in spirit. The general idea is that God chooses the actual world among different possible worlds and the actual individuals among different possible individuals. God can think of possible individuals—of those which he then decides to make actual and of those which he leaves uncreated—by means of Leibnizian complete individual concepts. Once we have accepted that those complete individual concepts represent objects, albeit maybe merely possible ones, it seems plausible to accept the following principle which I will call the ‘comprehension principle for possible objects’:
of objects that only have objective being but lack formal existence, a view that also seems to have been motivated by the fact that ideas which do not represent objects in the world can nevertheless be ideas of something and hence represent some intentional objects that do not really exist.
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(CP) For every complete individual concept, there is a possible object falling under it.10 Now, in the quoted passage, Kant apparently wants to stress that a concept can be a complete individual concept although it neither contains the concept of existence nor that of non-existence: God’s representation of a possible object misses ‘not a single determination’, although this representation neither represents the thing as existing nor as non-existing. The question is, then, what the point of this claim is and why Kant thinks that nobody would deny it. The answer, it seems to me, lies in a problem that, rather obviously, arises from (CP) together with the assumption that concepts have to contain either the concept of existence or its negation in order to be complete. Let us suppose that someone proposed the following ‘simple’ definition of complete individual concepts: (SD) A concept C is a complete individual concept iff, for every predicate P, C has either P or its contradictory counterpart P as a part (and does not contain predicates which are incompatible with each other).11 Now, let C be a concept which is almost complete and just indeterminate with respect to the predicate of existence. Let C + be the concept which we get if we add to C the predicate of existence, and C – the concept which we get if we add to C the predicate of non-existence. According to (CP), there would then be an object falling under C + (an existing C), and an object falling under C – (a non-existing C). This would have two unacceptable consequences: Firstly, God would have no choice as to whether to bring a C into existence or not, for solely on the ground that there is a concept of an existing C would there be an existing C. Secondly, and much more disastrously, there would be an existing and a non-existing variant of any 10. Regarding the fact that, in his critical philosophy, Kant distinguishes between real possibility and merely logical possibility, we have to read ‘possible object’ in the sense of ‘logically possible object’ here because, for Kant, real possibility is never established by the noncontradictoriness of a concept. 11. Kant does not use the term ‘predicate’ to refer to linguistic expressions. He wavers between speaking of predicates as of concepts (e.g. when he says that predicates can be parts of other concepts) and as of properties (e.g. when he says that predicates can be ‘determinations’ of things). I will use the term ‘predicate’ to refer to (non-individual, i.e. general) concepts and call what is expressed by them ‘property’ or ‘determination’.
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object one could think of. Using a Quinean slogan, one could say that (SD) together with (CP) would imply that everything exists, meaning, in a completely un-Quinean spirit, that for any kind of object there really exists an object of that kind. This is obviously absurd. It is the insight in this absurdity, I think, that motivated Kant’s claim that the predicate of existence is a merely logical, not a real predicate and does not express what he calls a determination of a thing. Any theory of possible objects which allows that there are contingently existing possible objects and entails a comprehension principle such as (CP) has to restrict the definition of complete individual concepts to a certain class of predicates of which existence is excluded. Kant calls those predicates ‘real predicates’ and claims that only real predicates are—or rather express— determinations of objects. This claim is not identical to the claim that a merely logical predicate such as the existence-predicate expresses no property of objects altogether, for we have seen that Kant does conceive of existence as a property of objects. Determinations rather form a subset of the set of properties. They are the properties which determine what an object is independently of whether it is an existing object or not. In more traditional terms, we could say that determinations make up the ‘realitas’ of a thing, and this, I conjecture, is the reason why Kant calls predicates that express those determinations ‘real predicates’. Building on the distinction between real predicates and merely logical predicates, we can formulate the following refined definition of complete individual concepts: (RD) A concept C is a complete individual concept iff for every real predicate P, C has either P or its contradictory counterpart P as a part and C does not have any non-real predicate as a part (and also does not contain predicates which are incompatible with each other). On the assumption that the concept of existence is not a real predicate we can avoid the absurd consequences that the simple definition of complete individual concepts together with the comprehension principle for possible objects have created. It is interesting to note that Kant’s distinction between real and non-real predicates and between determinations and properties that are not determinations is very similar to a distinction by which Meinong and contemporary Meinongians try to avoid certain unacceptable consequences of their
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theory of objects (for the following cf. Meinong 1904; Parsons 1980). As is well known, Meinongians do not only accept that for every consistent set of properties which form the content of a complete individual concept there is an object that has all these properties, but moreover want to assume that for every set of properties whatsoever—no matter whether it is complete or not, consistent or not—there is an object having exactly the properties in the set. That has the consequence that besides existing objects there are not only possible objects but also such things as incomplete objects and impossible objects. One might try to spell out this assumption in form of the following ‘naive’ comprehension principle for Meinongian objects: (NCP) For every set S of properties, there is an object that has exactly those properties which are elements of S. However, (NCP) leads to a problem very similar to the one which was caused by the conjunction of (CP) and (SD) above. If we allowed the property of existence to enter into the sets of properties (NCP) speaks about, we would end up with lots of false existence claims which follow from (NCP). For example, if you take the set of properties definitory for centaurs and add existence to this set, (NCP) would tell you that there is an object that has all this properties, i.e. an object that is a centaur and exists. In order to avoid this absurd consequence, Meinongians introduce the distinction between so-called ‘nuclear’ and ‘extra-nuclear’ properties (or ‘konstitutorische’ and ‘außerkonstitutorische Eigenschaften’ as Meinong himself called them). The general idea behind this distinction is that nuclear properties have a certain discriminatory potential while extranuclear properties lack it. Only nuclear properties P are such that we can distinguish by them, for any given set of further properties, two non-empty sets of objects which have these further properties, namely those that, in addition, have P and those that do not have P. Existence is an extra-nuclear property because we cannot distinguish by it centaurs that exist from those that do not exist, simply because there are no centaurs that exist. (In contrast, humility is a nuclear property, and among the non-existing centaurs there are humble ones and non-humble ones.) The distinction between nuclear and extra-nuclear properties allows Meinongians to restrict their comprehension principle in such a way that the absurd consequence of (NCP) are avoided, namely in the following way (cf. Parsons 1980, 19):
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(RCP) For every set S of nuclear properties, there is an object that has exactly all those properties which are elements of S. Since existence is not a nuclear property, we cannot use (RCP) in order to define all kinds of things into existence any longer. Although neither Kant nor the Meinongians give a precise definition of ‘real predicates’ or ‘determinations’ on the one hand and ‘nuclear properties’ on the other, it is clear that these two notions play a very similar functional role in their accounts. As soon as a theory assumes that objects in general can be divided into existing and non-existing objects, and claims that for objects in general it is true that there are certain kinds of such objects just because there are such-and-such individual concepts or such-and-such sets of properties, the theory has to mark certain properties as inappropriate for forming the content of these concepts, or for being elements of these sets, in order to avoid inconsistencies. The claim that existence is not a real predicate or that it is not a nuclear property is the claim that it is a property that suffers from this shortcoming. The second open exegetical question was this: If, for Kant, existence is a discriminating property of objects, what is meant by those of his remarks that seem to speak in favour of a meta-representational analysis of existential statements? One of these remarks occurs in the following passage: When existence occurs as a predicate in common speech, it is a predicate not so much of the thing itself as of the thought which one has of the thing. For example: existence belongs to the sea-unicorn but not to the land-unicorn. This simply means: the representation of a sea-unicorn is an empirical concept; in other words it is the representation of an existent thing. (The only possible argument, AA II 72)
How can Kant conceive of existence as a property of objects, and, at the same time, treat existential claims as claims about our own representations? The answer to this question lies in the fact, I think, that, in the case of merely possible objects, there is a very close ontological connection between these objects and the concepts we have of them. In the Critique of Pure Reason, Kant explains the difference between merely possible thalers and actual thalers in the following way: In the case of actuality the object is not merely included in my concept analytically (der Gegenstand ist bei der Wirklichkeit nicht bloß in meinem Begriffe analytisch enthalten), but is added synthetically to my concept […]. (A 599/B 627)
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This passage implies that a merely possible object has being only ‘within’ the concept by which it is represented, while actually existing objects have being ‘beyond’ the concepts we have of them. In my opinion, the best way to spell out the spatial metaphor in this characterization is the following: In the case of merely possible objects, there is a very strong ontological connection between these objects and the individual concepts by which they are represented. As we have already seen, Kant’s comprehension principle (CP) assures that all it takes for such objects to have being is that there is a certain individual concept, hence individual concepts could not exist without representing possible objects. The quoted passage suggests that the dependence also holds the other way round: A possible object could not have being unless there was a concept by which it was represented. In the context of The only possible argument, this claim is confirmed by the fact that all possible worlds and all the possible objects which inhabit them are represented in God’s intellect before he chooses which world to make actual (cf. AA II 74). In the Critique of Pure Reason, the strong ontological connection between non-existing possible objects and the representations we have of them is documented by the fact that Kant calls these objects ‘objects of mere thoughts’ (‘Gedankendinge’). All this is evidence, I think, that for Kant, non-existing possible objects are essentially intentional objects. They are the internal representata of concepts and have being only insofar as someone represents them. In contrast, existing objects have being independently of the concepts we have of them. (They are ‘added synthetically to my concept’, as Kant puts it.) This means two things: On the one hand, it is not enough to investigate our own concepts in order to find out whether there are such objects, but we need some other source of knowledge, namely intuition, by which they are given to us. On the other hand, existing objects are not merely intentional objects because they would not cease to exist if nobody had thought about them.12 If non-existing and existing objects can be distinguished by being more or less ontologically dependent on the concepts by which they are represented, it is clear in what sense the existence-predicate ‘is not a predicate of the thing in itself but rather of the thought one has of this thing’. To say that sea-unicorns exist does not simply mean to say that there are sea-unicorns, but rather to say that there are sea-unicorns which have a certain relation to the concepts we have of them, namely that of 12. This is the case if we allow for a somehow ‘realistic’ reading of Kant’s transcendental idealism. I argue for such an interpretation in Rosefeldt (2007).
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being ‘outside of ’ or independent of these concepts. As a consequence, we can reformulate the statement ‘Sea-unicorns exist’ by one about the concept of a sea-unicorn, namely the statement that this concept represents something ontologically independent of the concept itself. For Kant, the only justification for a statement like this would be that the objects which are claimed to be independent of our concepts are given to us by some other form of representation, namely intuition. This, in turn, would make the concepts applicable to objects of intuition and hence empirical concepts. It is for this reason, I think, that Kant writes that to say that sea-unicorns exist ‘simply means: the representation of a sea-unicorn is an empirical concept; in other words it is the representation of an existent thing’.
REFERENCES Bennett, Jonathan 1974: Kant’s Dialectic. Cambridge: Cambridge University Press. Forgie, J. William 2000: “Kant and Frege: Existence as a Second-Level Property”. Kant-Studien 91, 165–177. Frege, Gottlob 1979: “Dialogue with Pünjer on Existence”. In: G. Frege, Posthumous Writings, trans. Peter Long and Roger White, ed. Hans Hermes, Friedrich Kambartel, & Friedrich Kaulbach, Oxford: Blackwell, 53–67. — 1988: Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl. Ed. by Christian Thiel, Hamburg: Meiner. — 1990: “Dialog mit Pünjer über Existenz”. In: Schriften zur Logik und Sprachphilosophie. Aus dem Nachlaß. Edited by Gottfried Gabriel, 3rd edition. Hamburg: Meiner, 1–22. — 2002: “Funktion und Begriff”. In: Funktion, Begriff, Bedeutung. Edited by Mark Textor, Göttingen: Vandenhoeck & Ruprecht. Kant, Immanuel 1998: Critique of Pure Reason. Translated and edited by Paul Guyer & Allen W. Wood, Cambridge: Cambridge University Press. — 2002: Theoretical Philosophy 1755–1770. Translated and edited by David Walford, Cambridge: Cambridge University Press. Meinong, Alexius 1904: “Über Gegenstandstheorie”. In: Untersuchungen zur Gegenstandstheorie und Psychologie. Leipzig: Barth, 1–50. Parsons, Terence 1980: Nonexistent Objects. New Haven: Yale University Press. Pünjer, Bernhard 1874: Die Religionslehre Kants. Jena: Maucke’s Verlag. Reed, Delbert 2007: The Origins of Analytic Philosophy: Kant and Frege. London: Continuum.
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Rosefeldt, Tobias 2007: “Dinge an sich und sekundäre Qualitäten”. In: Jürgen Stolzenberg (ed.), Kant in der Gegenwart. Berlin, New York: de Gruyter, 161–203. — 2008: “Kants Begriff der Existenz”. In: Recht und Frieden in der Philosophie Kants. Akten des 10. Internationalen Kant-Kongresses. Edited by Valerio Rohden et al., 5 vol., Berlin: de Gruyter, vol. 2, 669–678.
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Grazer Philosophische Studien 82 (2011), 353–373.
NUMBERS AS ONTOLOGICALLY DEPENDENT OBJECTS HUME’S PRINCIPLE REVISITED Robert SCHWARTZKOPFF University of Oxford, New College Summary Adherents of Ockham’s fundamental razor contend that considerations of ontological parsimony pertain primarily to fundamental objects. Derivative objects, on the other hand, are thought to be quite unobjectionable. One way to understand the fundamental vs. derivative distinction is in terms of the Aristotelian distinction between ontologically independent and dependent objects. In this paper I will defend the thesis that every natural number greater than 0 is an ontologically dependent object thereby exempting the natural numbers from Ockham’s fundamental razor.
Not so long ago, foes of abstract objects like numbers rallied behind a principle oftentimes called Ockham’s razor. According to this principle, we should welcome as few kinds of objects as possible in our ontology. Since numbers were deemed especially unwelcome, they were usually among the first to suffer the razor’s ruthless stroke. However, in recent times it has been proposed to rather adhere to a principle one could call Ockham’s fundamental razor: entia fundamentalia non sunt multiplicanda praeter necessitatem (e.g. Schaffer 2009). So inclined philosophers find no difficulty in extending a welcoming hand to all kinds of things. The only caveat is that (i) such objects be non-fundamental or derivative, and (ii) that they ultimately derive from something such philosophers regard as unproblematic. One such sense of the fundamental vs. derivative distinction can be found in the Aristotelian tradition, a tradition in which substances are characterized as ontologically independent (fundamental) objects whereas the properties that inhere in them are said to be ontologically dependent (derivative) objects. It is the aim of this paper to make some headway towards showing that numbers are dependent objects and, thus, are not subject to Ockham’s
fundamental razor. To this end I will argue that a broadly Fregean way of conceiving of the natural numbers vindicates the following thesis: Dependence Thesis Every natural number greater than the number 0 is an ontologically dependent object. The procedure will be as follows. In the first section, I will argue for a version of Hume’s Principle—Frege’s contextual definition of the cardinality operator ‘the number of ’ (1884, §§ 62f.)—on which it is a 1st-level rather than a 2nd-level abstraction principle. This understanding of Hume’s Principle will be motivated by drawing attention to a hitherto unobserved flaw in Frege’s analyses of statements of (equi)numerousity, i.e. that they cannot handle collective predicates. In the second section, I will draw attention to the fact that Hume’s principle has an explanatory dimension in that the principle’s right-hand-side explains its left-hand side. In the third section, I will introduce a notion of ontological dependence that is just as serviceable when applied to the Aristotelian conception of substances as independent objects as it is when applied to the case of numbers. In the fourth and final section the Dependence Thesis will be vindicated. 1. Two levels for Hume’s Principle In this section I will motivate and develop an understanding of Hume’s Principle on which it is a 1st-level (rather than a 2nd-level) abstraction principle. This understanding will serve as the first headstone of my argument for the Dependence Thesis. (i) HP as a 2nd-level Abstraction Principle: What is the difference between abstraction principles of different levels? To answer this question it is helpful to first take a look at the general form of abstraction principles: AP 6[Di] = 6[Dj] l Di H Dj. Abstraction principles are intended to contextually define the term-forming operator 6[ ] by stipulating that sentences obtained by flanking ‘=’ with terms formed by combining 6[ ] with expressions Di and Dj are to be true just in case the equivalence relation signified by the relational
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expression H holds between the semantic values of Di and Dj (see, e.g., MacBride 2003, 111). Fregean Semantics: Abstraction principles can differ because of differences between the levels of the kind of expressions D that 6[ ] and H accept as inputs. To render this characterization more precise let us distinguish, with Frege, between sentences and referring expressions, and predicates and nominal functors of level 1 and 2.1 An n-ary 1st-level predicate is whatever remains of a sentence containing n referring expressions, after deleting n occurrences of referring expressions. Deleting ‘Socrates’ from the sentence ‘Socrates is snub-nosed’ yields the unary 1st-level predicate ‘[ is snub-nosed’.2,3 Thus, n-ary 1st-level predicates are sentence-forming operators on n referring expressions. Correspondingly, unary 1st-level nominal functors (schematically, 6[[]) are referring-expression-forming operators on one referring expression. In contrast, an n-ary 2nd-level predicate is a sentence-forming operator on n 1st-level predicates. For Frege, the sentence ‘There is at least one horse’ (in symbols: xh(x)), for instance, decomposes into the 1st-level predicate ‘[ is a horse’ (in symbols: h([)) and the 2nd-level predicate ‘There is at least one object such that it )’ (in symbols: x)x).4 Accordingly, unary 2nd-level nominal functors (schematically, 6x[)x]) are referring-expression-forming operators on one 1st-level predicate. Given these distinctions, 1st- and 2nd-level abstraction principles can be distinguished as follows: In 1st-level abstraction principles 6 and H are unary 1st-level nominal functors and binary 1st-level predicates, respectively. Hence, both operate on referring expressions. In 2nd-level abstraction principles, on the other hand, 6[ ] and H are unary 2nd-level nominal 1. Obviously, ‘referring expression’ has to be understood in the nowadays common, yet un-Fregean, sense in which at least some expressions are not referring expressions. From a Fregean perspective, it can be understood as meaning name which is not a sentence, where ‘name’ covers, as intended by Frege, both (singular) proper names and (singular) definite descriptions. 2. ‘[’ and ‘]’ are used to mark the gaps left behind by the deletion of a referring expression as having to be filled with (potentially) different referring expressions (see Künne 2009, 184). 3. Henceforth, I will distinguish between predicates and general terms. A general term is a (1st-level) predicate minus its copula (and ‘minus’ its gap). In the case of ‘[ is snub-nosed’ the copula is ‘is’ and the general term is the adjective ‘snub-nosed’ (see Künne 2006, 249–253). In the following, expressions like ‘A’ will be used as meta-variables for general terms, and expressions like < A([)> will stand for unary (1st-level) predicates. Similarly, for binary (1st-level) predicates that do not possess their own symbol. 4. Like ‘[’ and ‘]’, ‘)’ and ‘<’ are gap-markers. Unlike ‘[’ and ‘]’, however, ‘)’ and ‘<’ reserve gaps for (potentially different) 1st-level predicates.
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functors and binary 2nd-level predicates, respectively. Thus, they operate on unary 1st-level predicates. 1st- and 2nd-level abstraction principles are, therefore, of the following forms: AP-L1 6[[] = 6[]] l [ H ],5 AP-2L 6x[)x] = 6x[<x] l )x Hx <x.6 Why Level 2? To see why Frege construed Hume’s Principle as being of level 2, consider the following statement of numerousity: (1) There are exactly four horses. For Frege, (1) decomposes into the unary 1st-level predicate ‘[ is a horse’ and the unary 2nd-level predicate ‘There are exactly four objects x such that )x’ (in symbols: 4x()x)). This analysis of statements of numerousity carries over to an analogous analysis of statements of equinumerousity, i.e. to sentences like: (2) There are just as many horses as there are grooms. For Frege, (2) decomposes into two unary 1st-level predicates—in our case: ‘[ is a horse’ and ‘[ is a groom’—and the binary 2nd-level predicate ‘There are just as many objectsi such that iti ) as there are objectsii such that itii <’ for which Frege introduced ‘) is equinumerous with <’ (in symbols: )x ≈x <x) as a shorthand. As Frege (1884, 83–86) has shown, ‘)x ≈x <x’ can be given a purely logical definition in terms of one-to-one correspondence. In modern notation this definition is: Def. ≈x A(x) ≈x B(x) {def R (x (A (x) o y (B(y) z (R(xz) l z = y))) x (B(x) o y (A(y) z (R(zx) l z = y)))). In §§ 62f. of Grundlagen Frege uses Hume’s Principle to contextually define the cardinality operator by stipulating that sentences obtained by flank5. Frege’s Direction Principle (1884, 76): The direction of line a is identical with the direction of line b iff line a is parallel to line b, for instance, is a 1st-level abstraction principle. 6. Note that in 2nd-level abstraction principles the functors and relational predicates are variable binders and thus combine with (1st-level) open sentences—i.e. 1st-level predicates whose gap has been filled with a free variable—to form closed terms or sentences.
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ing ‘=’ with terms formed by combining it with certain expressions are to be true just in case corresponding statements of equinumerousity are. Thus, the relational expression on Hume’s Principle’s right-hand side is the 2nd-level binary predicate ‘)x ≈x <x’ whose inputs are 1st-level predicates. Now, the general form of abstraction principles requires that the introduced operator 6[ ] take as input expressions of the same kind as does the relational expression H on a principle’s right-hand side. Consequently, the cardinality operator has to be construed as a 2nd-level nominal functor. Using ‘Nx[)x]’ to symbolise the cardinality operator, the 2nd-level variant of Hume’s Principle can then be formulated as follows:7 HP-2L
, F
G (Nx[F(x)] = Nx[G(x)] l F(x) ≈x G(x)).
(ii) HP as a 1st-level Abstraction Principle: The 1st-level variant of Hume’s Principle can be arrived at by taking HP-2L and replacing the two 2nd-level functors on its left-hand side with suited functors of level 1 and, accordingly, replacing the binary 2nd-level predicate on its right-hand side with a suited binary predicate of level 1. But what are the suited replacements and, maybe more importantly, why would one want to stray from Frege’s path? The reason is, I contend, that there is a flaw in Frege’s analyses of statements of (equi)numerousity. Overcoming this flaw requires bringing in the resources of plural reference and plural logic. This in turn opens up the possibility to conceive of Hume’s Principle as an abstraction principle of level 1. The Collectivity Problem: The Fregean analyses are flawed because they cannot handle statements of (equi)numerousity when the involved predicates are collective. A predicate P is collective if it is not distributive; and P is distributive if (P applies to some objects only if P applies to each of them) (Sainsbury 2005, 171). Thus, the predicate in ‘Bucephalus and Incitatus are horses’ is distributive, since it applies to some objects (i.e. to Bucephalus and Incitatus), but also to each of them (i.e. to Bucephalus, 7. V (V) is not a nominal quantifier as it binds variables that occupy general-termposition. How is it to be understood, then? This is a tricky question, an exhaustive answer to which is beyond the scope of this paper. Today we can afford to remain neutral as to how exactly such quantifiers might be understood. What matters is that we seem to understand them. After all, there are natural language locutions that we seem to understand and for which such formulas appear to provide formal renderings: ‘F (F (Socrates) o F(Plato))’ (‘F F(Socrates)’) is the formal rendering of ‘Everything Socrates is (or does), Plato is (or does) as well’ (‘Socrates is (or does) something’). It is this understanding I will subsequently rely on. For more on quantification into general term position see Künne 2003, 356–365; Rayo & Yablo 2001; Wright 2007.
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and to Incitatus).8 The predicate in ‘The Greeks surround Troy’, on the other hand, is collective, since despite the fact that it applies to all the Greeks that surround Troy, it does not apply to any individual Greek be he at the shores of Troy or elsewhere. We can count how many objects satisfy a given collective predicate and the result can be expressed by a statement of numerousity. Let us assume that it took at least 1000 Greeks to surround Troy and that no more than that embarked on the perilous crossing. Thus, the following sentence is true: ‘There were exactly 1000 Greeks who surrounded Troy’. On the Fregean analysis, this sentence decomposes into ‘1000x)x’ and ‘gr([) st([)’, and gets formally represented as ‘1000x(g(x) st(x))’. However, whilst the original sentence is true, its formal rendering is false. This is because ‘st([)’ is a collective predicate. Hence, although it applies to some objects—the Greeks G1 … G1000 that besiege Troy—it neither applies to G1, nor to Gn, nor to G1000. On the standard analysis 1000x(g(x) st(x)) is true iff there are exactly 1000 variable assignments to ‘x’ that satisfy both ‘gr(x)’ and ‘st(x)’. But given that ‘x’ is a standard—i.e. singular—variable and that ‘st([)’ is a collective predicate, there are no (let alone 1000) variable assignments to ‘x’ that satisfy ‘st(x)’. This divergence in truth-value between ‘There were exactly 1000 Greeks who surround Troy’ and its formal representation shows Frege’s analysis of statements of numerousity to be inadequate. Frege’s analysis of statements of equinumerousity fails for analogous reasons: Take any two collective predicates ‘C1([)’ and ‘C2([)’ that apply to a different number of objects. Thus, ‘C1(x) ≈x C2(x)’ should be false. On Def. ≈x it comes out as true, however. This is because its definiens will be vacuously true, if the conjunction in the scope of R is true. This is precisely what happens in cases such as the above. The two universally quantified conditionals that constitute the conjunction come out true, since their antecedences are false—again owing their falsity to the presence of the singular variable ‘x’. In order to overcome these difficulties we have to avail ourselves of the resources of plural reference and logic. Thus, let me give a brief outline of the relevant ideas. Going Plural: Champions of plural reference hold that the class of referring expressions is not exhausted by singular referring expressions but 8. I here assume that the grammatical number of a predicate’s copula is inessential to its identity so that ‘[ is a horse’ and ‘[ are horses’ count as the same predicate.
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contains plural referring expressions as well.9 The difference between plural and singular referring expressions is this: a singular referring expression is only capable of referring to at most one object, while a plural referring expression is capable of referring to one or more objects (both kinds may be empty). Examples of such plural referring expressions are plural proper names (‘the Balears’), plural definite descriptions (‘the Spanish islands in the Mediterranean), and lists (‘Formentera, Ibiza, Majorca, and Minorca’). Analogously, there is a difference between singular and plural variables. While a singular variable is only capable of being assigned at most one object by some variable assignment, a plural variable is capable of being assigned one or more objects. For reasons soon to become apparent, special attention will be paid to plural definite descriptions. However, we first need some understanding of plural logic. Let us use ‘xx, yy, zz, …’ as plural variables. Such variables are bound by plural quantifiers.10 The use of and as plural quantifiers will be indicated by a suffixed plural variable. Modifying the notion of a variable assignment so as to allow for the assignment of multiple objects to plural variables, we can stick with the standard semantic clauses for the quantifiers. <vvI> (<vvI>) is true iff I is satisfied by some (every) variable assignment of one or more objects.11 The rules for the existential and universal quantifiers remain essentially the same. In addition to plural variables and quantifiers, plural logic contains a new logical predicate—‘[ d ]’—that is read as ‘is/are or is/are among’ which expresses the relation of inclusion. In the intended sense, Minorca is among the Balears, as are Majorca and Formentera. Thus, the relation of inclusion can hold between one object (Minorca) and some objects (the Balears), as well as between several objects (Majorca and Formentera) and several objects (the Balears). Identity (both singular and plural) is a limiting case of inclusion. Thus, is true iff each of the objects referred to by a is identical to one of the objects referred to by b. Plural identity—which we express as — obtains iff the objects referred to by b include the ones referred to by a, et vice versa. 9. Of course, countenancing plural referring expressions marks a departure from Frege’s views as he only allowed for singular ones. 10. The following borrows extensively from Oliver & Smiley 2006. 11. Note that plural referring expressions (variables) must only be capable of referring to more than one object (being assigned more than one value). Thus, plural referring expressions (variables) can well have only a single referent (value).
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We can now introduce plural definite descriptions. In the following, descriptions (both singular and plural) will be treated as genuine referring expressions.12 A singular description ‘the A’ is a complex referring expression that refers to some objecti iff (i) iti is A, and (ii) any objectii that is A is such that itii is identical to iti. Semi-formally, we could represent singular descriptions as . In principle, plural descriptions can be handled in an analogous fashion. A plural description ‘the As’ refers to some objectsi iff (i) theyi are A and (ii) all objectsii that are A are such that theyii are identical to themi. Using plural variables we could indiscriminately represent plural descriptions as . However, depending on whether the involved predicate is distributive or collective we can represent more structure. For every distributive predicate we can construct a corresponding collective predicate <y(A(y) l y d [)> that collectively applies to all and only those things to which applies individually. Consequently, we can represent plural descriptions that contain a distributive predicate as (, for short) and reserve for descriptions containing collective predicates. We can now move on to use this equipment to solve the collectivity problem that beset the Fregean analysis of statements of (equi)numerousity. Solving the Collectivity Problem: When ‘A([)’ is a distributive predicate, the existence of some As ensures the existence of the As. This thought can be captured by a principle we could call Definite Plural Comprehension: DPC x(A(x)) o xx (xx =P the xx: A(x)).13 This result enables us to construe plural paraphrases of statements of (equi) numerousity. The idea is as follows. If (1) is true, then there exist just four objects such that each of them is a horse. Moreover, if (1) is true, then there is at least one horse. By DPC, this entails that the horses exist. However, we can infer something even stronger than that, for if the horses exist and there are just four horses, then the following is true: ‘There are exactly four objects that are among the horses’. From the perspective of 12. Genuine referring expressions are capable of being generalised upon using (1st-order) and and, conversely, can instantiate variables bound by (1st-order) and . 13. DPC follows from the plural logic axiom of Plural Comprehension (x(A(x)) o xx y(A(y) l y d xx) together with the observation that for any given structure S in which ‘x(A(x))’ is true, there is exactly one variable assignment D over S to the plural variable ‘xx’ that would satisfy <y(A(y) l y d xx>.
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a broadly Fregean semantics that admits plural descriptions as genuine referring expressions, (1)’s plural paraphrase decomposes into the unary 1st-level predicate ‘There are exactly four objects such that it is among [’ (in symbols: 4x(x d [)) and the plural referring expression ‘the horses’ (in symbols: the yy: h(y)). Formally, we can represent (1)’s plural paraphrase as ‘4x(x d [the yy: h(y)])’.14 By replacing Frege’s original analyses with their plural paraphrases it becomes possible to overcome the collectivity problem. Where ‘C([)’ is a collective predicate satisfied by, say, exactly three objects, ‘3xC(x)’ comes out false, since there is no variable assignment to ‘x’ that satisfies ‘C(x)’. The corresponding plural paraphrase ‘3x(x d the Cs))’, on the other hand, comes out true, since there are exactly three variable assignments that satisfy ‘x d the Cs’. Just as we can give plural paraphrases of statements of numerousity we can, in an analogous fashion, state plural paraphrases of statements of equinumerousity. In the case of (2), doing so yields: ‘There are just as many objects that are among the horses as there are objects that are among the grooms’. (2)’s plural paraphrase decomposes into the binary 1st-level predicate ‘There are just as many objectsi such that iti is among [as there are objectsii such that itii is among ]’ (in symbols: [ | ]) and the two plural descriptions ‘the horses’ and ‘the grooms’.15 Thus, (2)’s plural paraphrase can be represented as ‘the yy: h(y) | the yy: g(y)’. It is also possible to define ‘[ | ]’ as the first 1st-level pendant of Frege’s 2nd-level predicate ‘)(x) |x <(x)’ in a way that solves the collectivity problem for statements of equinumerousity: Def. | a | b {def xx (xx a a l xx a b),16 where ‘[a]’ is—echoing Frege’s own definition—defined as: Def. a a a b {def x y (x d a y d b R (z (z d a o w (w d b s (R (zw) l s = w))) (z d b o w (w d a s (R(wz) l s = w))))).17 14. With slight modifications, it is also possible to define plural versions of the numerically definite quantifiers in the usual recursive method. 15. The binary 1st-level predicate ‘[ | ]’ is not to be confused with its binary 2nd-level cousin ‘)(x) ≈x <(x)’. 16. This formulation takes care of cases in which both a and b are empty such as, for instance, ‘the xx: x ≠ x | the xx: x ≠ x’. Such sentences have to come out true for otherwise a 1st-level version of a Frege-style argument for the infinity of the natural numbers will not get off the ground. 17. Note that by the definitions given above entails .
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Stepping Down: As previously argued, Frege’s 2nd-level construal of Hume’s Principle was informed by his analyses of statements of (equi)numerousity. We still want Hume’s Principle to contextually define the cardinality operator in terms of statements of equinumerousity. But on the plural construal of statements of equinumerousity presented above, the relational expression involved in such statements has become a binary 1st-level predicate whose inputs are (plural) referring expressions. In virtue of the general form of abstraction principles displayed by AP, the term-forming operators 6[ ] such principles are used to contextually define operate on the same kind of expressions as the binary predicates H on such principles right-hand sides. Consequently, the cardinality operator has to be re-construed as a 1st-level nominal functor, i.e. as ‘N[[]’ (see Bostock 2009, 119 for a similar treatment of the cardinality operator). Thus, we arrive at the 1st-level formulation of Hume’s Principle: HP-1L
,F G (N[the Fs] = N [the Gs] l the Fs | the Gs).
The 1st-level version of Hume’s Principle is the first headstone of my argument for the Dependence Thesis. This is because, unlike HP-2L, HP-1L contains expressions—the (plural) descriptions ‘the Fs’ and ‘the Gs’— whose positions are quantifiable using the first-order existential quantifier. As we will see, this feature is crucial when it comes to establishing the Dependence Thesis. 2. Explanatory Hume’s Principle 1st-level Explanatory Hume’s Principle is the thesis that to HP-1L there corresponds a true explanation in which the principle’s right-hand explains its left-hand side. For instance, the principle would have it that if the number of the horses is the number of the grooms, the former is identical to the latter because the horses are equinumerous with the grooms.18 Formally, this principle can be rendered as follows (‘W’ represents ‘because’): EHP-1L , F G (N[the Fs] = N[the Gs] o (N[the Fs] = N[the Gs] W the Fs | the Gs)). 18. The conditional formulation is due to the factivity of ‘because’: ‘p because q’ entails ‘p’ and ‘q’. Without it, acceptance of Explanatory Hume’s Principle would prejudge the existence of numbers.
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I will not give a detailed argument for EHP-1L but defer to Dummett as my warrantor instead. Dummett expresses the view that Frege’s thoughts on these matters align with the view expressed above: [A] The […] question is whether […], ‘The number of Fs is the same as the number of Gs’ [should be] explained as meaning ‘There are as many Fs as there are Gs’ [or the other way around]. Frege decides in favour of the [former] direction of explanation […]. [B] […] the argument for the conceptual priority of the notion of parallelism over that of a direction cannot be adopted, without being greatly modified, to a proof of the conceptual priority of the notion expressed by ‘just as many’ over that of a number. (Dummett 1991, [A] 114 [B] 116, emphasis added)
In [A] Dummett asks a question as to which direction of explanation between the two sides of Hume’s Principle is the correct one. In so asking, Dummett presupposes that, for Frege, there is an explanatory relation connecting the principle’s two sides. Furthermore, in [A] Dummett also depicts Frege as holding the view that the direction of explanation runs from the principle’s right-hand to its left-hand side. In [B] Dummett reports, albeit disapprovingly, on Frege’s reason to think of the explanation as so directed: it is because the notion expressed by ‘just as many’ is conceptually prior to the notion of a number. In the following, I will take Dummett’s word for it (for a similar sentiment see Hale 1987, 197). EHP1L is the second headstone for my argument in favour of the Dependence Thesis. We move on to consider the third, i.e. the notion of dependence that we will subsequently rely on. 3. Dependence The third headstone of my argument in favour of the Dependence Thesis will rest upon is a suited notion of ontological dependence. There are many ways in which something can depend on something else (Simons 1987, 293f.). I depend for my financial support on the Royal Institute of Philosophy. A roof depends for its support on the beams it rests upon. And what it is like to be engaged depends on whom you are engaged to.19 Ontological dependence is that sense of dependence in which some object 19. “What is it really like to be engaged?” asked Anne curiously. “Well, that all depends on who you’re engaged to”, answered Diana […] (Montgomery 1909, 352, emphasis added).
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depends for its existence on some other object or objects. Ontological dependence can be either generic or individual. Some object is generically dependent if it depends on there being some object or other of a certain kind but does not require there to be any specific object of that kind. A forest is generically dependent on trees, since any forest depends for its existence on there being some trees or other, yet no forest requires the existence of any specific tree. Individual dependence, on the other hand, is dependence (not on some objects or other of a certain kind but) on some specific individual object(s). The most prominent account of (individual) ontological dependence proceeds in purely modal terms: one object depends on another object if the object itself could not exist if the other did not. Unfortunately, understanding ‘dependence’ in purely modal terms is hopeless in the current setting. A somewhat naive modal account of dependence would have it that Dep-1 x depends1 on y {def. , (x exists o y exists) x ≠ y. However, Dep-1 trivializes ontological dependence as it renders the existence of every object x as being dependent on every necessary existent y. Commonly, Dep-1 is de-trivialized by requiring that which an object depends on to not exist necessarily:20 Dep-2 x depends2 on y {def , (x exists o y exists) x ≠ y ¬ , y exists. But there is a rub. According to Dep-2, no object can depend on a necessary existing object. But if numbers exist necessarily (as it is plausible to assume), then the Dependence Thesis has already been shown to be false by definition. One might think so much the worse for the Dependence Thesis, and that thinking about the dependence or independence of necessary existents was a bad idea to begin with. That would be a mistake, however. One use the notion of ontological dependence is prominently put to is to characterize substances, in the wake of Aristotle, as independent objects. But for this particular use Dep-2 is ill-suited. If substances (as they arguably do) have some of their particularized properties essentially (e.g. Socrates and his humanity), they will depend on these particularized properties in 20. For instance, all dependence definitions given by Simons (1987, 295–310) contain a clause to this effect.
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this sense (see Schnieder 2006, 400). In light of this difficulty, Schnieder (2006)proposes to analyze ontological dependence in terms of the connective ‘because’. Schnieder goes through some lengths to elucidate ‘because’ so as to be able to employ it in his analysis. Let me briefly summarize those of Schnieder’s results that are most relevant for the use he puts ‘because’ to. Explanations are expressed by sentences of a certain kind. This kind is exemplified but not exhausted by sentences of the form ‘p because q’. In such sentences we can call ‘p’ the explanandum and ‘q’ the explanans. Furthermore, ‘because’ is arguably asymmetric as well as factive.21 Explanations come in different types: (3) The roof collapsed because the supporting beams were torn down, (4) 3 is a prime number because its only divisible by 1 and 3, (5) (Assuming that my car green) My car is coloured because it is green. Whereas the explanation in (3) is causal, the explanations in (4) and (5) are conceptual. Just as causal explanations are grounded in the obtaining of the causal relation between a cause and its effect, conceptual explanations are grounded in relations obtaining between concepts. That a conceptual explanation obtains is grounded in certain conceptual truths, i.e. that every prime number is only divisible by 1 and itself, and that every green object is coloured. What the direction of a conceptual explanation is, is determined by a relation we can call conceptual priority. Generally, that which is conceptually prior explains that which is conceptually posterior. Conceptual priority can obtain in at least two ways that we, too, could call individual or generic. Individual priority obtains if one cannot possess a certain concept without possessing a specific other concept (or some specific other concepts). (4) is a case of individual priority, since one cannot possess the concept of a prime number without possessing specific other concepts such as, for instance, divisibility by 1. This is because the latter concepts constitute the former, i.e. because the former are analyzable in terms of the latter. Generic priority obtains if one cannot possess a certain concept without possessing some concepts of some specific kind, albeit not some specific concepts of that kind. (5) is a case of generic priority, since one cannot possess the concept expressed by ‘coloured’ without possessing 21. Asymmetry: ‘p because q’ entails ‘¬(q because p)’. See, e.g., Schnieder 2010, 11.
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at least some colour concepts, i.e. concepts of the same kind as the one expressed by ‘green’, albeit possession of the specific concept expressed by ‘green’ is not required. These results concerning (conceptual) explanation and ‘because’ enable Schnieder to tackle the troublesome case of Socrates and his humanity as follows: Dep-2 is problematic because it equates ontological dependence with necessary co-existence. The troublesome case of Socrates and his humanity arose because, on the assumption that they necessarily co-exist, the former depends on the latter in the sense of Dep-3, while the latter also depends on the former in this sense. However, it seems at least plausible that there should be a sense of ‘dependence’ that does not collapse into necessary companionship. Bringing in an explanatory component helps to articulate this. Although Socrates and his humanity necessarily co-exist, only one of the following explanations will—‘because’ being asymmetric—be true: (6a) Socrates’ humanity exists because Socrates is human, (6b) Socrates is human because Socrates’ humanity exists. But which one? In light of the above considerations concerning conceptual priority, the answer is (6a) and it is conceptual priority that sees to it. The expression ‘Socrates’ humanity’ is what Schnieder calls a canonical designator of a particularized property that is obtained by combining an expression ‘F-ness’ (‘humanity’) that refers to a property with an expression ‘a’ (‘Socrates’) referring to one of this property’s bearers. Schnieder argues that, generally, grasp of what is expressed by a designator of the form ‘a’s F-ness’ requires one to understand that it refers to a particular instance of F-ness’ that exists as a feature of a just in case a is F. Thus, grasp of what is expressed by ‘Socrates’ humanity’ requires one to understand that ‘Socrates’ humanity’ refers to a particular instance of humanity that exists as a feature of Socrates iff Socrates is human. That, however, one can only grasp if one grasps what is expressed by ‘Socrates is human’, i.e. the explanans of (6a). Using the quantifier F to generalize from the above example and then excluding cases of explanations that either obtain only contingently or else only at certain times, Schnieder finally arrives at a notion of individual, permanent, necessary, explanatory dependence that he sees fit to serve the Aristotelian idea of substances as independent objects. Schnieder (2006, 412) defines this notion as follows:
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Dep-3 x depends3 on y {def F , t (x exists at t o (x exists at t W F(y))). Numbers are arguably abstract objects and, hence, do not exist at times at all. Thus, the notion of dependence I will rely on will be a de-temporalized version of Dep-3. Furthermore, we will need to allow for the possibility that an object depends not only on a single object but also on one or more objects. Thus, we replace the singular variable ‘y’ with the plural variable ‘yy’. Finally, I will assume that the predicate ‘[ exists’ is adequately captured by ‘x (x = [)’. Thus, the notion of dependence that will serve as the third headstone for my argument in favour of the Dependence Thesis is: Dep-4 x depends4 on yy ldf. F , (z (z = x) o (z (z = x) W F(yy))). With all three headstones now in place, we are finally in the position to vindicate the Dependence Thesis. 4. The dependence thesis vindicated In order to establish the Dependence Thesis we will now put together the three, as of yet still quite unconnected, headstones that we have assembled in the previous sections. Although the argument itself is quite simple, we will first need to set the stage. Bringing in the above analysis of ontological dependence we can rephrase the Dependence Thesis as: For every natural number n greater than 0 there are some objectsi which are somethingii such that if n exists, it exists because theyi are itii. In symbols: Dependence Thesis n ((N(n) n > 0) o yy F , (x (x = n) o (x(x = n) W F(yy))). Next we (schematically) define—echoing Frege’s own definitions given in §§ 74f.— that (Def. n): for every natural number n greater than 0: x = n {def x = N[the xx: x = 0 … x = n–1]. Furthermore, let us call N-terms that can be introduced in this fashion canonical N-terms, and let us call the general term A that features in the descriptions contained in such a terms canonical general terms. The first thing to notice is that for all canonical general terms A, (HP-1L + Def. ≈) entail as theorems sentences of the 367
form via a suitably modified version of Frege’s argument for the infinity of the natural numbers.22 Once we add two plausible inference rules concerning the connective ‘because’ to our logic, (HP-1L + EHP-1L + Def. ≈) entail as theorems sentences like the following, for all canonical general terms A: Necessarily, If the number of the As exists, it exists because the As are equinumerous with themselves. In symbols:23 HP-1L , (x (x = N[the As]) o (x (x = N[the As]) W the As | the As)). My argument for the Dependence Thesis will be based on theorems of this kind. Finally, let us call a sentence that we have obtained from Dep-4’s right-hand side by replacing ‘x’ with a referring expression ‘a’ and binding ‘yy’ using an existential quantifier—i.e. a sentence of the form ‘yy F , (z (z = a) o (z (z = a) W F(yy)))’—a’s Dependence-Sentence. Now that the stage is set, we can move on to establish the Dependence Thesis by showing how we can prove of every individual natural number greater than the number 0 that it is an ontologically dependent object in the sense of Dep-4. Take, for instance, the number 1. To show that it is an ontologically dependent object, we will have to show that its dependence 22. The details are somewhat complicated. Firstly, the derivations require two special rules governing plural descriptions. Secondly, and more importantly, they require the use of a negative free logic in the spirit of Hale & Wright 2009, 446. This is because the special case of the number 0—i.e. N[the xx: x ≠ x]—requires our logic to countenance empty referring expressions like ‘the xx: x ≠ x’. Technically, however, those issues pose no major obstacles. I will, thus, leave it at that. 23. The needed rules are Transitivity of ‘because’ (TransW) and Existential Generalisation for ‘because’ (EGW). Schnieder (2010, 11/26), for instance, explicitly and sympathetically discusses TransW p W q EGW v must not occur in both TransW and EGW. qWr B(a) pWr v B(v) W B(a) Proof Sketch: Infer from (HP-1L + Def. ≈). By EGW, infer <x (x = N[the As]) W N[the As] = N [the As]>. De-modalize EHP-1L and instantiate both universal quantifiers on A. By MPP, infer . By TransW, infer <x (x = N[the As]) W the As ≈ the As>. Use paradox of material implication to infer <x (x = N [the As]) o (x (x = N[the As]) W the As ≈ the As)>. Re-modalize. q.e.d. Especially TransW is not beyond doubt, though. However, the proposed counter-examples employ comparatively longs chains of explanation and exploit cases of causal explanations. Thus, such counter-examples do not seem to affect TransW if it were restricted to short chains and non-causal explanations. Such a restricted version of TransW would still suffice to carry out the above derivation.
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sentence, i.e. DS-1, holds. Given the way I have set things up, this only requires the following four-line argument: (1) , (x (x = N [the xx: x = 0]) o from HP-1L & (x (x = N [the xx: x = 0]) W the xx: x = 0 | the xx: x = 0)) EHP-1L (2) , (x (x = 1) o (x(x = 1) W the xx: x = 0 | the xx: x = 0)) by Def. n (3) F , (x (x = 1) o (x (x = 1) W F(the xx: x = 0)))
2 I
(4) yy F , (x (x = 1) o (x (x = 1) W F(yy)))
3 I
In line 1, we introduce as a theorem that instance of 1st-level Existential Explanatory Hume’s Principle (HP-1L) that pertains to the number 1. In line 2, the canonical N-terms for the number 1 are, by appeal to Def. n, replaced with the appropriate numeral ‘1’. In line 3, we existentially generalize into the position of the general term ‘| the xx: x = 0’ (read: equinumerous with the things identical to 0) contained in the explanans of line 2. Finally, we existentially generalize into the position of the description ‘the xx: x = 0’ to arrive at line 4. Line 4, however, is nothing other than DS-1, the dependence sentence of the number 1. Thus, we have shown that the number 1 is an ontologically dependent object in the sense of Dep-4. In more colloquial language we can express this result as: DS-1 For some objectsi, namely the ones identical to the number 0, there is somethingii such that necessarily, if the number 1 exists, the number 1 exists because theyi are itii, namely equinumerous with the things identical to the number 0. In similar fashion we could show of each natural number n greater than the number 0 that for some objectsi, namely the ones identical to n’s predecessors, there is somethingii such that necessarily, if n exists, n exists because theyi are itii, namely equinumerous with the predecessors of n.24 Of course, 24. Thus, every natural number greater than 0 is an ontological dependent object because it depends for its existence on its predecessors. Interestingly, Schopenhauer defends a thesis the letter of which coincided with this result: “Each number pre-supposes its predecessors as the reason for its being: we can only reach the number ten by passing through all the preceding numbers, and it is only in virtue of this insight that I know, that where ten are there are also eight, six, four.” (1847, § 38, emphasis added) Whether our theses also converge in spirit, is an open question. At
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the above is but a sketch of a complete argument for the Dependence Thesis but it should suffice to show how the Dependence Thesis could be established in all generality. Let me bring this paper to a close with two comments. The first comment concerns the importance of using the 1st-level version of Hume’s Principle (HP-1L). To see why, notice that the step from line 3 to line 4 in the above argument is only possible if we use HP-1L. As I have already remarked towards the end of section 1, HP-1L contains expressions—the (plural) descriptions ‘the Fs’ and ‘the Gs’—whose positions are quantifiable using the (plural) first-order existential quantifier. This feature was then carried over to the formulation of 1st-level Explanatory Hume’s Principle (EHP-1L) outlined in section 2. This, in turn, led to a corresponding construal of the theorems we have called 1st-level Existential Explanatory Hume’s Principle (HP-1L). If it had not been for the fact that instances of HP-1L contain expressions whose positions are 1st-order quantifiable, the derivation of dependence sentences pertaining to numbers would have been blocked at the step from line 3 to line 4, since this step depends on the availability of 1st-order quantifiable positions. Consequently, the 2nd-level construal of Hume’s Principle (HP-2L) and the corresponding 2nd-level construals of Explanatory- and Existential Explanatory Hume’s Principle would not support an argument in favour of the Dependence Thesis. The second comment concerns the number 0. One may wonder whether it is not also possible to show that the number 0 is a dependent object so as to be able to generalize the Dependence Thesis to all natural numbers. This is not possible, however. Above I have already hinted towards the fact that our logic needs to be a version of free logic. If it were not, it would not allow for empty terms such as ‘the xx: x ≠ x’. As a consequence, such a logic would not support a Frege-style argument for the infinity of the natural numbers that employs HP-1L rather than HP-2L. In order to handle empty terms, free logics contain modified versions of I (E) that prohibit existential generalization (universal instantiation) on a term a unless a has been assumed to be non-empty. For the cases of descriptions contained in canonical N-terms for numbers larger than 0, such assumptions are quite unproblematic. Not so for the number 0. Running the first step of the above argument for the number 0 would yield: the very least, Schopenhauer’s argument—which strikes me as somewhat obscure—differs vastly from the one given above. Thanks to Benjamin Schnieder for alerting me to the Schopenhaueresque ring of my central claim.
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(20) , (x (x = 0) o (x (x = 0) W the xx: x ≠ x ≈ the xx: x ≠ x)). If we then tried to derive 0’s dependence sentence in the above fashion, the last step would be an application of I to ‘the xx: x ≠ x’. Given the assumed freedom of the required logic, this step would have to be legitimized by making the contradictory assumption that ‘the xx: x ≠ x’ is non-empty. Thus, we are not in a position to show that 0 is a dependent object in the required sense. Therefore, the Dependence Thesis cannot be generalized to all natural numbers. Should that not give me pause? After all, since 0 precedes all other natural numbers, every such number will, in part, depend on the number 0. Thus, the project of endearing numbers to the adherents of Ockham’s fundamental razor can only be successful if the existence of the number 0 can be accounted for in a way such philosophers deem unproblematic. Such an account, however, has not been offered so far. Let me, therefore, give you at least an impression of how I envision such a treatment to look like. Recalling our dependence definition Dep-4, we notice that what accounts for the dependence of some object x is the fact that (assuming x did exist) x’s existence would be explained by something. The existence of Socrates’ humanity was explained by some object, i.e. Socrates, being something, i.e. human. And the existence of the number 2, say, was explained by some objects, i.e. 2’s predecessors 0 and 1, being something, i.e. equinumerous with themselves. In both these cases the existence-explanation involved some object (or objects), namely Socrates and the numbers 0 and 1, respectively. This is how it should be. After all, ‘ontological dependence’ was supposed to express that sense of dependence in which some object depends for its existence on some other object or objects. Let us call existence-explanations with an object-involving explanans ‘objectual existence-explanations’. By extension, let us call the ontological dependence such explanations give rise to objectual ontological dependence.25 Now, as witnessed by (20), even the existence of the number 0 does not go unexplained. However, as we have seen above the explanans of the existence-explanation in question cannot, on pain of contradiction, be construed as being object-involving. But the existence of the number 0 would still be explained by something, although the pertinent explanans would not involve some thing (or things). Rather, the explan25. This is somewhat misleading because ontological dependence always involves some object, i.e. the putative dependent object. But humour me for a moment.
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ans of (20) only expresses the ontologically innocent fact that the xx: x ≠ x are equinumerous with themselves. For want of a better phrase, let us call existence-explanations with an explanans that is not object-involving ‘(merely) factual existence-explanations’, and let us call the dependence such explanations give rise to factual ontological dependence. My proposal regarding the number 0 would then be as follows. Like objectual ontological dependence, factual ontological dependence exempts an object from Ockham’s fundamental razor. But then, no natural number is subject to Ockham’s fundamental razor. After all, every natural number greater than 0 displays objectual ontological dependence, whereas 0 itself displays (mere) factual ontological dependence. Thus, the existence of all the natural numbers would have been accounted for in a satisfactory way. 5. Conclusion In this paper I have argued for a thesis concerning the ontological status of the natural numbers. To this end I motivated and argued for an understanding of Hume’s Principle on which it is a 1st-level abstraction principle (section 1). Furthermore, I have pointed out that, according to Frege, Hume’s Principle has an explanatory dimension in that its righthand-side explains its left-hand-side (section 2). Finally, I introduced a notion of ontologically dependence germane to the Aristotelian discussion about the independence and dependence of substances and their particularized properties (section 3). Pulling these strings together I have argued in favour of the thesis that every natural number greater than the number 0 is an ontologically dependent object in that sense (section 4). The endgame of these considerations was to endear the natural numbers to friends of Ockham’s fundamental razor. Thus minded philosophers are content to welcome all kinds of objects in their ontology provided they can be shown to be non-fundamental or derivative objects. Since one sense in which some object can be said to be derivative is the notion of dependence employed in the Aristotelian discussion alluded to above, I take to have the natural numbers thus endeared.
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REFERENCES Bostock, David 2009: Philosophy of Mathematics. Oxford: Oxford University Press. Dummett, Michael 1991: Frege: Philosophy of Mathematics. London: Duckworth. Frege, Gottlob 1884: Die Grundlagen der Arithmetik. Reprinted in 1934. Page references are to the reprint. — 1934: Die Grundlagen der Arithmetik. Breslau: Verlag von M. & H. Marcus. Hale, Bob & Wright, Crispin 2001: The Reasons Proper Study. Oxford: Oxford University Press. — 2009: “Focus Restored: Comments on John MacFarlane”. Synthese 170, 457–482. Hale, Bob 1987: Abstract Objects. Basil Blackwell: Oxford. Künne, Wolfgang 2003: Conceptions of Truth. Oxford: Oxford University Press. — 2006 “Properties in Abundance”. In: Peter F. Strawson & Arindam Chakrabarti (eds.), Universals, Concepts, and Qualities. Burlington: Ashgate, 249–301. — 2009: Die Philosophische Logik Gottlob Freges. Frankfurt a. M.: Klostermann. MacBride, Fraser 2003: “Speaking with Shadows: A Study of Neo-Logicism”. British Journal for the Philosophy of Science 54, 103–163. Montgomery, Lucy M. 1909: Anne of Avonlea. Boston: L. C. Page. Oliver, Alex & Smiley, Timothy 2006: “A Modest Logic for Plurals”. Journal of Philosophical Logic 35, 317–348. Rayo, Agustín & Yablo, Stephen 2001: “Nominalism through De-Nominalization”. Noûs 35, 74–92. Sainsbury, Mark R. 2005: Reference without Referents. Oxford: Clarendon Press. Schaffer, Jonathan 2009: “On What Grounds What”. In: David J. Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics. Oxford: Oxford University Press, 347–383. Simons, Peter 1987: Parts: A Study in Ontology. Oxford: Oxford University Press. Schnieder, Benjamin S. 2006: “A Certain Kind of Trinity: Dependence, Substance, Explanation”. Philosophical Studies 129, 393–419. — 2010: “A Logic for ‘because’”. Unpublished Manuscript (April 2010). Schopenhauer, Arthur 1847: Über die vierfache Wurzel des Satzes vom zureichenden Grunde. Translation follows: Hillebrand, Karl 1907: On the Fourfold Root of the Principle of Sufficient Reason, and on the Will in Nature; Two Essays. London: George Bell. Wright, Crispin 2007: “On Quantifying into Predicate Position”. In: Mary Leng, Alexander Paseau & Michael Potter (eds.), Mathematical Knowledge. Oxford: Oxford University Press, 150–174.
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Grazer Philosophische Studien 82 (2011), 375–400.
SENSE-ONLY-SIGNS: FREGE ON FICTIONAL PROPER NAMES1 Mark TEXTOR King’s College London Summary It seems obvious that fictional proper names like ‘Sherlock Holmes’ are empty. However, if one also accepts that fictional proper names express a sense that determines at most one referent, it turns out to be surprisingly difficult to ensure that they do not refer to real objects. In this paper I will draw on Frege’s remarks on fiction to solve this problem. The main point of the paper is that the reference of a singular term depends on its sense and the way in which the sense should be entertained.
1. Introduction: The sense of fictional proper names Works of fiction contain proper names of real people and things – Conan Doyle frequently refers to London and Baker Street in his work by those very names—and so-called ‘fictional names’ like ‘Sherlock Holmes’. ‘Sherlock Holmes’ purports to refer to a Victorian detective, but, if we trust common sense, Sherlock Holmes does not exist; the name is empty.2 The common sense view that fictional proper names are empty may be wrong, but it should be preserved if possible. If proper names, in general, express a sense, fictional proper names should also express one. Sense or mode of presentation is supposed to 1. I have presented material related to this paper at the conference ‘Truth and Abstract Objects’ in honour of Wolfgang Künne. I received my basic philosophical training in Wolfgang’s seminars and he supervised my PhD thesis. For this, and the many discussions we had over the years, I am immensely grateful and I am very happy that I can contribute this paper to his Festschrift. I want to thank the audience for criticism and helpful suggestions. Special thanks go to Karl Georg Niebergall, and Mark Siebel for (partly late night) discussions during the conference. Thanks go also to Tom Crowther, Mike Gabbay, Martin Holt, Malte Jahning, Christele Machut and Rory Madden for discussion. Thanks go also to Stacie Friend and Jessica Leech for comments and discussion of a previous version. Finally I want to thank Benjamin Schnieder and Moritz Schulz who provided detailed written comments that have led to significant changes. 2. For an elaboration of this intuition see Walton 2003.
explain differences in cognitive value. For instance, ‘Hesperus is Hesperus’ differs from ‘Hesperus is Phosphorus’ in cognitive value. What the first sentence says is, while what the second says is not, a direct consequence of the law of identity. (See Frege 1902, 152, 234f. The first number refers to the English translation, the second to the German text.) Since Hesperus is the same planet as Phosphorus, the difference in cognitive value cannot consist in a difference in reference. Frege argued that it consists in a difference in mode of presentation. The same referent can be presented in different ways. The way in which something is presented by a singular term determines, at least in part, the cognitive value of sentences containing it. In this paper I will rely on an intuitive understanding of what a mode or way of presentation is. Now ‘Sherlock Holmes is Sherlock Holmes’ and ‘Sherlock Holmes is Watson’s partner’ differ in something like cognitive value, although neither ‘Sherlock Holmes’ nor ‘Watson’s partner’ refers. One can bring out the difference between these sentences without supposing that they say something true (false) tout court. Although ‘Sherlock Holmes is Sherlock Holmes’ and ‘Sherlock Holmes is Watson’s partner’ are not true tout court, they are both true according to Conan Doyle’s fiction. However, one can only justifiably take the second sentence to be true according to Conan Doyle’s story if one has understood and properly appreciated parts of the story, while one can justifiably take the first sentence to be true according to the story without such backing. The cognitive difference between ‘Sherlock Holmes’ and ‘Watson’s partner’ just outlined is explained by saying that they express different modes of presentation. Hence, we should ascribe modes of presentation to fictional as well as to non-fictional proper names. The ascription of sense to empty proper names raises a problem. (See Evans 1982, 22.) If empty singular terms can express a sense, a sense cannot be a mode of presentation of a referent How can there be a mode of presentation that does not present something? Now every proper name purports to refer to something. As one can purport to do something in different ways, a singular term can purport to refer in different ways. Hence, a singular term that purports to refer will purport to refer in a particular way. Purporting to refer is sufficient to present something in a particular way, so a mode of presentation is a mode of purporting to refer. The term expresses a sense, a mode in which it purports to refer to an object. I take it that Frege has this point in mind when he argues that a proper name needs only to behave as if it names something to be assured a sense. (See
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Frege 1893–5, 122, 133.) All proper names, whether satisfied by an object (‘Berlin’), empty for empirical reasons (‘Vulcan’ as introduced by LeVerrier) or fictional (‘Sherlock Holmes’ as introduced by Conan Doyle) purport to refer and are thereby secured a sense. The conclusion that names purport to refer and are thereby secured a sense is strengthened further if we accept the corollary that one understands an expression ‘a’ if one grasps the mode of presentation it expresses. Both theses together explain how we manage to say something with the utterance of a sentence containing an empty proper name and how such an utterance can be understood. What does one’s knowledge of the sense of a fictional name consist in? Consider ‘Sherlock Holmes’. It is, like many non-fictional names, introduced ‘in use’. In A Study in Scarlet the fictional character Young Stamford simply starts to use the name and Dr. Watson plays along: Young Stamford looked rather strangely at me over his wineglass. “You don’t know Sherlock Holmes yet,” he said; “perhaps you would not care for him as a constant companion.” [Watson] Why, what is there against him? [Young Stamford] Oh, I didn’t say there was anything against him. He is a little queer in his ideas—an enthusiast in some branches of science. As far as I know he is a decent fellow enough. [Watson] A medical student, I suppose?
One can argue that one’s mastery of the name consists in knowledge of a definite description extracted from the introductory discourse plus further information: ‘Sherlock Holmes’ refers, if it refers at all, to the amateur detective and enthusiast in some branches of science who lives in Baker Street 221b. Since there is no such person, the proper name is empty, and atomic sentences containing it are either false or neither true nor false. Alternatively, one may take the introduction in use to bring about that the audience opens a dossier in which ‘information’ is filed under ‘Sherlock Holmes’. The sense of ‘Sherlock Holmes’ is not the sense of a definite description; it is primitive. (See Sainsbury 2005, ch. 1.6.) But the use of the proper name is guided by the information in the dossier and the reference of the proper name is the object that is the dominant source of information collected in the dossier. These ideas need sharpening, but they will suffice to set up the problem I will be concerned with in this paper. The next section will introduce this problem.
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2. The Fregean view of fictional proper names Frege does not only hold that a fictional proper name expresses a sense; it expresses a sense that might just as well be had by a non-fictional name. To see his point, imagine that you have read the Odyssey as a piece of fiction. After reading it you come across Schliemann’s Troy and its Ruins (1875) in which he argues that he has found the site of Troy in Hissarlek. (Frege could hardly have failed to know Schliemann’s work.) Now you believe that the Odyssey was told as fact and that ‘Troy’ and ‘Odysseus’ refer. Frege describes cases like this as ones in which one and the same thought ‘crosses over’ from the realm of fiction to the realm of fact: Let us just imagine that we have convinced ourselves, contrary to our former opinion, that the name “Odysseus”, as it occurs in the Odyssey, does designate a man after all. Would this mean that the sentences containing the name “Odysseus” expressed different thoughts? I think not. The thoughts would strictly remain the same; they would only be transposed from the realm of fiction to that of truth. (Frege 1906, 191, 208)
What does the ‘cross-over’ from the realm of fiction to the realm of fact consist in? Frege does not say. A first stab characterisation is that it is now appropriate to evaluate the thoughts expressed in the Odyssey for truth and criticise them if they get the facts wrong. More generally: the same thoughts are now open for evaluation with respect to different standards. Frege’s description of the ‘cross-over’ case assumes that one can grasp the sense of a proper name completely and correctly, although one is mistaken about the question whether the name is fictional or not. If ‘Troy’ was used in full knowledge of its sense first as a fictional name and is now used in full knowledge of its sense as a non-fictional name, the distinction between fictional and non-fictional proper names is not a distinction that concerns the sense of proper names. This assumption seems plausible enough. For example, one might read a piece of fiction that contains fictional and non-fictional proper names without being able to tell which name is fictional and which is not (see Sainsbury 2005, 205). Although you miss out on a fact that distinguishes the names, your grasp of their sense is not deficient. If one can be neutral with respect to the question whether a name is fictional or not and yet grasp its sense correctly and completely, the sense of a proper name cannot determine whether the name is fictional or non-fictional.
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But does ‘Troy’ really express the same sense before and after Schliemann’s discovery? Frege’s assumption that it does cannot be justified by appealing to his criterion of sense-identity: Given that the thought P and the thought Q are not self-evident, P is the same thought as Q if, and only if, everyone who grasps P and Q and acknowledges the truth of P must immediately acknowledge the truth of Q and vice versa. (See PW, 197; NS, 213.) This criterion can only be applied to one thinker who simultaneously entertains P and Q.3 But in the case Frege is concerned with either the same person entertains the thought expressed by, for instance, ‘Troy is a city’ before and after the discovery that ‘Troy’ refers to Hissarlek, or a thought is entertained by different people who have different views about the Odyssey. Although Frege’s criterion of sense-identity cannot be used to argue the case, we can bring further considerations to bear to make it plausible that ‘Troy’ has the same sense before and after Schliemann’s discovery. For instance, one may come to identify Hissarlek as the referent of ‘Troy’, the name introduced in the Odyssey, because it fits the sense given to the name in this book.4 One entertains the sense of ‘Troy’ and now finds out that Hissarlek is Troy. This discovery makes one revise one’s view about what kind of text the Odyssey is, but the thoughts expressed remain the same. Someone who is sceptical about Frege’s description will argue that a failure to appreciate the kind of text the Odyssey is will bear on one’s grasp of the sense of names like ‘Troy’. I will discuss this view in detail in the next section. The idea is, roughly, that one realises after the discovery that the sense of ‘Troy’ does not contain the sense of expressions like ‘is a fictional city’ etc. However, while it is prima facie possible to give this description (more in the next section), it is implausible and hard to motivate. What goes wrong when I mistake ‘Troy’ for a fictional name when reading the Odyssey is that I misconstrue the genre to which the Odyssey or better the crucial part of it belongs. We might spell this out further by saying that the sentences in the Odyssey are put forth with a distinctive kind of force; Frege will say that the thoughts that these sentences express should not be taken seriously. What I get wrong is the force of the utterances made by Homer. 3. See Evans 1982, 21 on this and other limits of the application of what he calls ‘the Intuitive Criterion of Difference’ for thoughts. The same limits hold for Frege’s criterion of thought identity. 4. Sainsbury 2002, 170 discusses the reverse case in which someone takes a fictional text to be a historical report.
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Now we usually take such a mistake not to be a mistake about the sense of the sentences uttered. If you asked a question by uttering ‘Paris is a city’ and I take you to have asserted something, I make a mistake, although I fully and correctly grasp the sense of every word you have uttered. Why should, then, my mistake about the kind of text the Odyssey is be treated differently? An independent reason is needed and, as far as I can see, has not been given so far. 3. Why we need ‘sense-only-signs’ Frege’s ‘cross-over’ example makes it plausible that the distinction between fictional and non-fictional proper names is not a distinction in sense. If this is right, a fictional and a non-fictional proper name can have the same sense. However, this consequence seems to refute Frege’s view. Consider the following thought-experiment: Let us assume that Conan Doyle indeed wrote the stories as pure fiction. He just made them up. He had no knowledge of anyone who did the deeds he ascribed to Holmes, nor had he picked up any garbled information originating in any such person. It may nevertheless be, purely by coincidence, that our own world is one of the worlds where the plot of the stories is enacted. Maybe there was a man whom Conan Doyle never heard of whose actual adventures chanced to fit the stories in every detail. Maybe he even was named “Sherlock Holmes.” Improbable, incredible, but surely possible. Now consider the name “Sherlock Holmes,” as used in the stories. Does the name, so used, refer to the man Conan Doyle never heard of? Surely not! It is irrelevant that a homonymous name is used by some people, not including Conan Doyle, to refer to this man. (Lewis 1978, 265)5
Although the fictional proper name ‘Sherlock Holmes’ and the co-spelled non-fictional proper name express both the same sense that is satisfied by the real-life Holmes, the fictional name does not refer to this person. Frege seems to have this distinctive feature of fictional proper names in mind when he makes a suggestive remark in “On Sense and Reference”: 5. Castañeda 1989, 176; Jubien 1997, 178; Moore 1959, 112; Kripke 1972, 157; Baldwin 1990, 190; Walton 1990, 427 construct similar thought-experiments. They all agree that the fictional name does not refer to the real person. The odd man out is Ryle 1933, 39 who argues that ‘we should say that while previously we had thought that Pickwick Papers was only a pretence autobiography, we now find that, by coincidence, it is a real one.’
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It would be desirable to have a special term for signs that are intended to have only a sense [die nur einen Sinn haben sollen]. If we name them say, pictures, the words of the actors on the stage would be pictures; indeed the actor himself would be a picture. (Frege 1892, 163, 33)
Lewis’s thought-experiment brings out that fictional proper names fit Frege’s description of ‘signs intended to have only sense’. ‘Sherlock Holmes’, the fictional proper name introduced by Conan Doyle, is intended to have only sense, no reference. If one takes the purpose for which a sign is introduced to determine its sense and reference ‘Sherlock Holmes’ can only have sense and no reference. The term ‘sense-only-signs’ describes in Frege’s terminology the intuition elicited by the thought-experiment. However, the given description raises an interesting problem for Frege. How can he hold that (i) a fictional proper name is intended to express only a sense and (ii) that the sense of a proper name determines its reference? If the sense of a proper name determines a reference, one cannot be in a position to intend that it only expresses a sense. The thought-experiment makes this vivid. There is one and only one person that satisfies the complex definite description one needs to extract from Doyle’s story in order to master the name ‘Sherlock Holmes’. Yet ‘Sherlock Holmes’ does not refer to this person, the real-life Sherlock Holmes. But if the sense of a name determines its reference, why doesn’t ‘Sherlock Holmes’ refer to the real-life Sherlock Holmes for short? Before pressing on, I want to set a tempting proposal aside. Lewis has set up the example in such a way that Doyle has never heard of the real-life Holmes. Doyle has ‘not picked up any garbled information originating in any such person’. It is independently plausible that a person can only bear a name if she plays the right causal role in the introduction of the name. (See Kripke 1972, 83f. and Walton 1990, 427.) In the fictional case, the real object was not causally responsible for the information in the file of the person introducing the name (the producer) or the framing of the associated description. Hence, the fictional name does not refer to the real object. However, whether or not the ‘right’ causal relation obtains or not seems irrelevant for our problem. Writers of fiction often pick up information originating in a person and introduce a fictional proper name on the basis of this information. For example, Victor Mann says that his brother Thomas has turned the story of his family into a ‘thick book’, Die Buddenbrooks (see V. Mann 1949, 86).
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4. Do sense-only-signs have special senses? The tension between (i) and (ii) would be resolved if fictional proper names had special senses that made it impossible for them to refer to any real object. In this section I will discuss and, finally, reject three representative elaborations of the idea that fictional proper names have such distinctive senses. 1. Lewis: fictional names have flexible senses, non-fictional names rigid senses. David Lewis proposed that a sentence like ‘According to A Study in Scarlett, Sherlock Holmes lives in Baker Street 221b’ is true, roughly, if in all possible worlds in which A Study in Scarlett is told as known fact, the sentence is true. In developing this proposal Lewis says: Suppose that a fiction employs such names as “Sherlock Holmes”. At those worlds where the same story is told as known fact rather than fiction, those names are really what they purport to be: ordinary proper names of existing characters known to the storyteller. Here at our world, the storyteller only pretends that “Sherlock Holmes” has the semantic character of an ordinary proper name. We have no reason at all to suppose that the name, as used here at our world, really does have that character. As we use it, it may be very unlike an ordinary proper name. Indeed, it may have a highly non-rigid sense, governed largely by descriptions of Holmes and his deeds that are found in the stories. That is what I suggest … (Lewis 1978, 267)
‘Sherlock Holmes’ does not have the semantic character of an ordinary proper name; it only pretends to have it. The difference between the semantic character of ordinary and fictional proper names seems to consist mainly in a difference in sense: ‘Sherlock Holmes’ pretends to name rigidly a person in the actual world, but it refers flexibly to different non-actual people in different possible worlds. Lewis’s special-sense theory undermines his own account of truth in fiction that assumes that the same story can be told as fiction and as fact. But how can I tell, for example, A Study in Scarlett as fiction and as fact if ‘Sherlock Holmes’ has one sense in the worlds where the story is told as fact and another where the story is told as fiction? How can it be the same story, if the sentences uttered in storytelling express different thoughts? Independently of this internal problem, Lewis’s proposal seems unmotivated and indeed hard to motivate. Which sense ‘Sherlock Holmes’ has depends according to Lewis on how the story is told, namely whether one only pretends to tell known facts or whether one really tells known
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facts. But how can this difference constitute a difference in the sense of a name? If we trust the appearances outlined in section 2 a name can be given the same sense in fictional and non-fictional utterances. The type of utterance does, in general, not bear on the sense of the words uttered. So why should fictional utterances of ‘Sherlock Holmes …’ bear on the sense of the name? 2. Dummett: fictional proper names have partial senses, non-fictional names complete ones. According to Dummett, the distinction between fictional and non-fictional proper names is, at least, in part, founded in a distinction between different types of senses. The sense of non-fictional names is complete; the sense of fictional proper names is incomplete: We should not, as Frege does, cite as examples of names having sense but no reference personal names used in fiction, for these have in fact only a partial sense, since there is no saying what would warrant identifying actual people as their bearers; while the use of a name in literary criticism to refer to a fictional character differs again from its use in fiction, for here, while the sense is quite specific, the reference does not fail. (Dummett 1980, 160, my emphasis. See also 1983a, 300.)
Let us assume that the sense of ‘Sherlock Holmes’ is given by a complex definite description like ‘the amateur detective and enthusiast in some branches of science who lives in Baker Street 221b’. While it is true that there is no saying what would warrant the identification of a real person as Sherlock Holmes, this is not due to the fact that ‘Sherlock Holmes’ has a partial sense. If the sense of ‘Aristotle’ is given by, say, the definite description ‘the inventor of formal logic’ and this sense is complete, we have no independent reason to say that the sense of ‘Sherlock Holmes’ is incomplete. ‘Incomplete’ seems only to label the feature of fictional proper names that they do not refer to real objects. However, we need to know why one should say ‘Sherlock Holmes’ does not refer to the reallife Sherlock Holmes although he fits the sense of the name. Dummett has not answered this question, he has merely named the problem under consideration. 3. Moore on speech act-reflexive senses. In his “Imaginary Objects” Moore proposes a different, more substantial version of the special sense view. He argues: I think what he [Dickens] meant [in his introduction of the name “Mr. Pickwick” in his book The Pickwick Papers] and what we all understand is: “There was only one man of whom it’s true both that I’m going to tell you about him
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and that he was called ‘Pickwick’ and that, etc. etc.” In other words, he is saying, from the beginning that he has one and only one real man in his mind’s eye, about whom he is going to tell you a story. That he has, is, of course, false, it is part of the fiction. [...] Dickens’s propositions are all of the form “There was only one man of whom it’s true both that I’m telling you of him and that, etc. etc.” And ex hypothesi no proposition would be true about the man in question [the real man of whom everything related of Mr. Pickwick in the novel was true], since Dickens was not telling us of him: that is what is meant by saying that it is only “by coincidence” that there happened to be such a man. (Moore 1933, 113)
The sense of the fictional proper name ‘Sherlock Holmes’ is given by a definite description like ‘the smartest detective in London whose hobby is playing the violin who takes drugs for recreation and I am telling you this about him’. By contrast, the sense of a non-fictional proper name does not include a reference to acts of telling: The historian writing about Napoleon is not always referring to him as the man, having such and such characters, about whom I’m telling this story, but as the man, having such and such characters, who was in such and such a place at such and such a time. (Moore 1933, 114)
Moore takes the ‘I’ in the relevant descriptions to refer to the author of the story (Dickens). But the storyteller need not be identical with the author: while Conan Doyle is the author of A Study in Scarlet, Watson is the storyteller in that story. The ‘I’ under consideration refers to the storyteller. The storyteller purports ‘—normally, if not invariably—to be telling the truth about matters whereof he has knowledge.’ (Lewis 1978, postscript A, 276) Assume now that the sense of ‘Sherlock Holmes’ is given by a description like the one above. According to the thought experiment there is in the real world exactly one person who is the smartest detective in London and whose hobby is playing the violin and who takes drugs for recreation. But the fictional storyteller is not telling us these things about him. Perhaps the story-teller might tell us truths verified by the real-life Holmes, but these truths are not known to the storyteller and imparted to us: he only pretends that they are. Since there is no one about whom the storyteller tells the truth, the definite description that fixes the sense of ‘Sherlock Holmes’ is empty. (See Lewis 1978, 266.) According to Moore’s view, the sense of a proper name includes a mode of presentation of acts in which the name has been introduced or is used. (See also Currie 1990, 163 and Künne 1995, 152ff. who sides with
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Moore.) Prima facie, this assumption is ad hoc. However, Lewis takes the specifications of the sense of proper names along the following lines to be independently plausible: The descriptive sense associated with a name might for instance be “the place I have heard of under the name ‘Tarameo’” or maybe “the causal source of this token: Tarameo”, and for an account of the relation being invoked here, just consult the writings of the causal theorists of reference. (Lewis 1997, 353, fn. 22)
The first proposal about the sense of proper names supports Moore’s view: the sense of a proper name contains a mode of presentation of acts of hearing about, that is, informational uptake, in which this very name is used. But there is a strong, independent objection to the proposal. I have heard of many people under the name ‘Randy Smith’, so there is not a unique person of which I have heard under this name. Hence, most names come out as empty and utterances containing them as not true. While some philosophers find this acceptable, I think it is a result better to be avoided. (See Bach 1981.) Can one defend the idea by switching from type-names to tokennames, that is, is the sense of a particular token of ‘Randy Smith’ the following sense the person I am just hearing of under this very token: Randy Smith? It should be possible that the sense of a proper name ‘NN’ remains constant from one occasion of use to another. Lewis’s modified proposal does not allow us to accept this. It can always be an interesting discovery that the object of which I have just heard under this token-(name): ‘NN’ is the same as the object about which I am now hearing of under this token-(name): ‘NN’. So how does one account for trivial identity sentences and the fact that sometimes we can take identity of an object for granted? Moore’s view is, then, not supported by a general view of proper names. It is also independently implausible to assume that our understanding of a proper name, whether fictional or not, draws on its introduction in acts of telling. Perhaps I start out thinking of a bearer of ‘NN’ as the NN about whom you have told me all these interesting things. But if I gather more information, this way of thinking loses any special importance. The same goes for fictional proper names. After I have read most of the story my understanding of ‘Sherlock Holmes’ can draw on various parts of the story; the idea that these propositions are imparted by a storyteller will no longer play a role in my understanding of the name.
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Moore can argue that in a controversial case we can always fall back on the author/story-teller-mentioning definite description. However, in general, one can forget most of the information associated with a name and still use it competently. Why should this be different for fictional proper names like ‘Sherlock Holmes’? I may even forget that I learned the name by reading a work of fiction. Forgetting this does not impair my knowledge of the sense of the name. There are further objections to hand. Imagine that a story contains the sentence “No one will ever write a story about Pedro Ruiz or tell something about him. His life will remain completely unnoticed.” The author introduces the fictional name ‘Pedro Ruiz’ in this act of story telling. The act of inscribing the sentence falsifies the thought it expresses, but the thought itself is non-contradictory, it might well be true. However, Moore’s view makes the thought itself contradictory! This seems plainly false. A similar objection can be levelled against the idea that the sense of a fictional name represents something as fictional. Assume that there is a Pynchonesque story in which the characters are not sure whether V is a fictional person or not. At some stage one of the fictional characters might say ‘V is not a fictional character, she is real’. If the sense of ‘V’ were given by anything like ‘the fictional person called ‘V’’, the inscription would express a manifest contradiction. But, again, it is implausible that the sentence expresses such a contradiction. Lewis, Dummett, and Moore give up too easily the idea that a fictional and a non-fictional name could have the same sense.6 However, Lewis’s thought-experiment saddles Fregeans with the formidable task to answer the question ‘Why does a fictional name not refer, even if there is a real object that satisfies its sense?’ that does not help itself to the assumption that fictional proper names have special senses. The main work in the answer cannot be done by the assumption that fictional proper names have a special sense, but by the purpose or intention with which the fictional proper name is introduced. In the next section I will flesh out this idea.
6. See Thomasson 2003, 213. Sainsbury 2005, chapt. 3 provides a semantic theory that underwrites the assumption that fictional and non-fictional names can be alike in sense.
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4. Sense-only-signs without special senses Again Dummett will start us off. While he originally argued that fictional proper names cannot refer to real objects because they have an incomplete sense, he makes in later work a different proposal: What concerns us are cases in which the name will have had no bearer when it was first introduced. […] The first [case] is that of a proper name, say “Guy Pringle” in Olivia Manning’s novels, introduced as that of a fictional character. Having been introduced in this way, it remains the name of a fictional character. No one you could ever meet, however similar in his characteristics and life history to that of the character in the novels could be Guy Pringle; and therefore it is not true that there might have been such a person as Guy Pringle. (Dummett 1983b, 333)
Hence, we should see Conan Doyle as introducing a name for a fictional object, a fictional character. If you want to use ‘Sherlock Holmes’, the name introduced by Doyle, you must use it in conformity with Doyle’s intention when he introduced the name to refer to a fictional character. Since the real-life Sherlock Holmes is not and cannot be a fictional character, a use of ‘Sherlock Holmes’ (the name Doyle introduced) cannot refer to the real-life Holmes. Prima facie, we sometimes refer with ‘Sherlock Holmes’ to a fictional character (‘Sherlock Holmes is Conan Doyle’s most famous character’). More about this in section 5. However, the idea that Conan Doyle himself intended to name a fictional character when he introduced ‘Sherlock Holmes’ is deeply implausible. For example, Conan Doyle may have no view about the existence of fictional characters at all or disbelieve that there are such things. For this reason he cannot intend to introduce names for such characters. Yet, he can successfully introduce fictional names. So far the appeal to the intention of the author has not helped us to answer our question. Rather we have now framed our question in a new way. We need a description of the author’s manifest intention which govern his introduction and use of a fictional name that makes it clear why the name does not refer, neither to a fictional character nor to a real object. Let’s turn to Frege for help. In his “Logic”, he provides a positive characterisation of what the author wants to do when writing fiction: The writer, in common with, for example, the painter, wants to create a fancy [‘den schönen Schein’]. Assertions in fiction are not to be taken seriously:
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they are only mock assertions. [‘Scheinbehauptungen’] Even the thoughts are not to be taken seriously: they are only mock thoughts. [‘Scheingedanken’] If Schiller’s Don Carlos were to be regarded as a piece of history, then to a large extent the drama would be false. But a work of fiction is not meant to be taken seriously in this way at all: it’s all play. Even the proper names in the drama are here [in fiction] mock proper names, although they match the names of historical personages, they ought not to be taken seriously. (Frege 1897, 130, 142. In part my translation.)
Let us first get clear about the main ingredients of Frege’s view. When Conan Doyle inscribes the sentence ‘Holmes was certainly not a difficult man to live with,’ (A Study in Scarlet) he wants, to use Frege’s own words, to create a fancy. What is a fancy? The fancy Frege has in mind consists, at least in part, of some thoughts that are make believed by an audience. How does one create a fancy? The writer creates a fancy by making utterances. An utterance that should be taken seriously—for example, an assertion—is made with the intention to transmit a belief (knowledge) to a potential audience. An utterance that says that p is made to create a fancy (or: made with fictive intent) if it is made with the communicative intention that a potential audience makes believe that p. (See Currie 1990, ch. 1.8; Sainsbury 2009, 27ff.). Such an utterance expresses a thought, but the question whether this thought is true is misplaced. (See also Frege 1906, 191.) What is to make believe? I know of no plausible reductive definition of make believe. Typically, make believe involves imagining that something is the case; sometimes it involves pretending that something is the case. For our purposes it is only important that there is such an attitude like make believe and that one can correctly make believe that something is the case, although one knows that it is not the case. Therefore the utterances and the thoughts expressed in fiction are not to be taken seriously, that is, truth is not the norm for their success. According to Frege, a thought is a sense for which the question of truth can arise. (Frege 1918, 353, 60) If what a fictional utterance says is not to be taken seriously, how can the question whether it is true arise for it? If you have yet to assess whether a story is fictional or not, you might ask yourself whether what is said in the story is true. Hence, the question whether the senses expressed are true can arise. If it is highly implausible that they are true, this is a defeasible reason to construe the author’s inscriptions as made with fictive intent. However, if I know that the story is fictional, I can no longer rationally ask whether it is true or false. 388
With this in mind, we can tackle now our main question ‘How can a fictional proper name be intended to have only sense?’ Answer: In writing fiction the author intends to ‘create a fancy’. In creating a fancy, one makes utterances with fictive intent. The fact that the name is introduced in utterances made with fictive intent (and not the fact that it has a special sense) prevents that the name acquires a referent. How? My answer to this question will draw on Chastain’s view that [t]he referential purport of a singular expression can be cancelled in a variety of ways, corresponding to the variety of purposes for which discourse can be produced. (Chastain 1975, 219)
Although our ultimate interest is not the cancellation of previously established reference, but rather the fact that sometimes reference is not established in the first place, we can build on Chastain’s work. The reference-resistance of fictional proper names will turn out to be a special case of prevention of referential purport. How can the purpose for which a discourse is produced cancel the referential purport of a singular term? Consider supposition as an independent case. (See Chastain 1975, 220ff.) One can, of course, suppose that a real object has certain properties. But let us set such suppositions aside and focus on suppositions that are made to illustrate or, more broadly, consider a general principle. Consider the following request: Suppose a man opened an account in your bank today. Let us call him “John Smith”. If John Smith were to deposit 5000 £ in his account at 5,25 % interest, compounded seminanually, after three years he would have 5.4210 £ in his account. (See Chastain 1975, 220.)
Now we often introduce proper names on the back of indefinite noun phrases. If I say ‘A man with black hair came to my office today. Let us call him “John Smith”’, ‘John Smith’ will be the name of the unique satisfier of the predicate ‘is a man with black hair who came to my office today’. However, even if one and only one man with the name ‘John Smith’ opened an account in your bank today, he would not be the bearer of the name ‘John Smith’ that I introduced. In the scope of a supposition one can introduce a name such that it does not refer to a real person, even if the descriptive content of the supposition is uniquely satisfied. If someone asked ‘Who is that man?’ or ‘Is this man John Smith?’, he would give us a reason to suppose that he has not understood ‘what is going on’. A name introduced in the scope of suppositions as one con-
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sidered here has no referential purport. (I will qualify this statement in section 5.) Why is that? The answer must have to do with the nature of supposition. A first stab explanation is that the supposition was only made to illustrate a general principle. Pointing out that there is no person who opens a bank account etc. or that I did not know of the existence of such a person are no reasons to criticise the act of supposing under consideration. Here is some theoretical background that will help us to systematise this and similar examples. I will assume with many other authors that there are constitutive rules for speech and mental acts. (See, for example, Williamson 1996, 489–92.) An example of a constitutive rule for assertion is: One ought to assert that p only if p. There is, of course, scope for discussion whether this is the right constitutive rule for assertion. Alternative proposals involve knowledge or justified belief. For the purposes of this paper I don’t need to decide which proposed constitutive rule is the right one. However, we need to assume that there are such rules. If one breaks a constitutive rule for a speech or mental act, one still performs the act under consideration, but one is now criticisable. A speech or mental act is identified by its constitutive rule and the specific form of criticism one incurs when one fails to conform to the constitutive rule. Of course there are different forms of criticism of such acts. But one form of such criticism is distinctive for the kind of act at which it is directed. According to any plausible constitutive rule for asserting that the F is G, the correctness of this speech act depends on how things are with the object that is the F. This is obvious for the constitutive rules for assertion that involve truth and knowledge. In the weaker version of the rule where only justified belief is required for assertion one incurs criticism if one asserts that the F is G without believing that there is a unique F. Hence, Frege says: Someone who does not acknowledge a reference, can neither ascribe nor withhold a predicate of it. (Frege 1892, 162, 33. My translation.)
However, there is family of speech-acts whose constitutive rules are different. I have already used a test to identify members of this family. If one can conform to the rules of I-ing that the F is G, although one knows that there is no F, I-ing that the F is G does not commit one to the existence 390
of an object. I propose to generalise this to the following principle: Correctness-Principle: If one can conform to the constitutive rule for a speech- or mental act, independently of the existence of an object a (the belief that there is such an object), the act is not about a. The Correctness-Principle covers suppositions. The supposition is not about the real John Smith, although he fits the supposed descriptive condition, because the correctness condition for this supposition does not require its existence or knowledge of its existence. The sense of ‘about’ under consideration can be illuminated by the widespread intuition that even if there was a real-life Sherlock Holmes the story would only be true by accident. The speech acts that sets up the story are not about the reallife Sherlock Holmes, although he may fit the descriptive content of the speech-acts perfectly. The real-life Sherlock Holmes plays no role in the assessment of whether the relevant speech act conforms to the rule constitutive of it. He plays only a role in the assessment of the act according to a rule that is not constitutive of it. Hence, the ‘by accident’ character. The reference-resistance of fictional names can also be explained on the basis of the Correctness-Principle. As the correctness of some suppositions does not depend on how things are with an object satisfying the supposition’s descriptive content, the correctness of an utterance made with fictional intent does not depend on how things are with an object satisfying the descriptive content of an act of make believe. In both cases, it would be a mistake to appeal to how things are with the satisfier of a definite description or, more generally, with an object fitting the sense of a singular term used, in an assessment whether the mental or speech-act conforms to the relevant constitutive rule. The object that satisfies the descriptions given in the story is not involved in the correctness conditions of the speech- and mental acts in which creation and consumption of the story consists. Let us apply this to our problem. If a name is introduced in speech acts made with fictive intent, the mental acts required to understand the speech act do not allow a reference for the name to become established even if there is an object fitting its sense. Why? The author’s utterances are made with fictive intent, they aim to create a fancy; their readers should make believe something. One can conform to the constitutive rule for an act of make believe that there is a unique F that is named ‘NN’, although there is no unique F and one knows that this is so. You can’t criticise my act of
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make believe that there is a unique F that is named ‘NN’ by pointing out that there is no F. You will ask ‘What is the constitutive rule for such acts?’ I have to leave the development of a positive answer for another occasion. For the purposes of this paper the negative answer that the constitutive rule neither involves truth, nor knowledge or belief is sufficient. Hence, these acts are not about the unique F and cannot make the proper name ‘NN’ a name of the unique F. However, they give ‘NN’ a sense. If I understand the utterances introducing the name, I will now be in a position to understand subsequent ‘NN’ utterances. To make this plausible, consider the following example. I can start a joint fantasy by saying: “Imagine there is a golden mountain. Let us call it ‘Goldie’. Imagine further that Goldie is in Mexico …” Even if there is one and only one golden mountain in Mexico, it is not Goldie; nothing is or can be Goldie. In setting up this joint fantasy I have assumed something like the role of the author of a work of fiction. The Correctness-Principle covers the joint fantasy and the more complex work of fiction. The reason why ‘Sherlock Holmes’ does not refer to the real life Sherlock Holmes is that the name has been introduced in a particular kind of speech act, not that it has a special sense. The given explanation allows for ‘Sherlock Holmes’ as used in the stories and ‘Sherlock Holmes’ as used for the real-life Holmes to have the same sense: competent users can associate with them exactly the same reference conditions. The intention of the producer of the fictional name is specified without bringing in fictional objects. For this reason the account need not assume, as Moore did, that fictional proper names have special senses that distinguish them from the names of real things. The view that some proper names have only sense and no reference has an interesting consequence if combined with the thesis that sense determines reference. The latter thesis can be expressed as follows: (x) (‘a’ has the same sense as ‘b’ o (‘a’ refers to x l ‘b’ refers to x)) If a fictional and non-fictional name can have the same sense, sense does not determine reference. While the fictional name can only have sense, the non-fictional can have sense and reference. Conclusion: sense does not determine reference; sense plus mode of thinking (force) determines reference. In the light of the general phenomenon of cancellation of referential purport, this complication of the theory of sense and reference has independent plausibility.
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5. Objections answered Let us consider five objections to the proposal that the fact that a fictional proper name is introduced in an utterance with fictive intent makes it non-referential. First, imagine that I read a fictional story in which an incredibly beautiful garden named ‘Paradise Found’ is described in painstaking detail. I am so taken by the story that I create a garden exactly like Paradise Found and start referring to it by the name ‘Paradise Found’. Is the garden I have created Paradise Found? The syntactically individuated name ‘Paradise Found’, we may assume, has the same sense in the story and my idiolect. However, my use of the name is not in conformity with the author’s intention to invite his readers to make believe that there is such a garden. Hence, the same syntactically individuated name with the same sense can be used as a fictional and as a non-fictional name. One uses ‘Paradise Found’ only as a fictional name if one uses it in conformity with the author’s intention. Compare: ‘Sherlock Holmes’ can become the nick-name of a brilliant Victorian because of his likeness to Conan Doyle’s Sherlock Holmes. In this case, the same syntactically individuated name with the same sense is used as a fictional and non-fictional name. Alternatively, one may hold that we have here two homonyms. However, we don’t need to decide which description is correct. Both descriptions offered are compatible with the proposal under consideration, since neither requires us to say that the fictional name refers to something.7 Second, what holds for fictional should also hold for ‘suppositional’ proper names, since neither the correctness conditions for supposing that the F is G nor the correctness conditions for making believe that the F is G seem to require the existence of a unique F.8 But things are different for ‘suppositional’ names. In a mathematical discussion, someone says ‘Let’s suppose there is a number solving this equation; let us call that number T. Now, T must have the following properties: etc.’ Later, the mathematicians prove that there is a number solving the said equation, and they go on referring to it by ‘T’. Here a name was introduced in the scope of a supposition, but it later turns out to refer 7. Things get more complicated if real things serve as props in games of make-belief. Since the puzzle discussed here arises independently of this phenomenon I ignore this possible complication here. For discussion see Evans 1982, 362. 8. Thanks to Benjamin Schnieder for drawing me out on this point.
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to something. This counter-example shows that the given explanation is incomplete. Reply: Here is an outline of how the explanation can be completed. If one wants to use the name ‘Sherlock Holmes’ that has been introduced by Conan Doyle (and not, say, the name ‘Sherlock Holmes’ that names my neighbour), one has to use the sign ‘Sherlock Holmes’ in conformity with Conan Doyle’s manifest intention when he introduced the name. This manifest intention prevents the name from referring to the real Sherlock Holmes. Any use of the sign ‘Sherlock Holmes’ that does refer to something is therefore not the use of the name introduced by Sherlock Holmes. (See Dummett 1983a, 300.) This is different for a name introduced in the scope of a supposition because one can use this name in conformity with the manifest intention of the person introducing it and yet refer to something. Why? Some suppositions are in the service of truth, fiction is not. (The suppositions discussed in the previous section are different. They had no heuristic function, they did not enable us to give proofs etc.) If we make a supposition to find out whether something is the case, the supposition was merely a means to an end. With respect to the suppositional name ‘T’, the name introducer has made the supposition in order to find out whether something is the case. If the supposition leads to a proof, the name introduced in the scope of the supposition will refer to the object that satisfies the equation because our fundamental intention was to find out the truth and to refer to something. Third, the explanation in terms of the intentions concerns only speaker reference, not semantic reference. The semantic referent of ‘Sherlock Holmes’ is the real life Sherlock Holmes, but when making utterances with fictive intent neither Conan Doyle nor his readers intend to speak about him. They intend to speak about nothing and hence speaker and semantic referent come apart in fictional discourse.9 Reply: We are concerned with cases where the name has no semantic referent to begin with. The semantic referent of a proper name is determined in the act of introduction, and the introduction under consideration prevents the name from acquiring a semantic referent. Hence, we will have cases where the speaker referent of ‘Sherlock Holmes’ is the real life Holmes, but the name cannot have this person as its semantic referent. Fourth, there seem to be literally true atomic sentences in which ‘Sherlock Holmes’ occurs in subject position: 9. Thanks to Moritz Schulz for this question.
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(a) Sherlock Holmes is admired by Fred. (b) Sherlock Holmes is a fictional character. If these sentences are true, ‘Sherlock Holmes’ must refer, most likely to a fictional character. Hence, ‘Sherlock Holmes’ is not a sense-only-sign. Anti-realists about fictional characters have argued that the problematic sentences are not straightforwardly true or can be paraphrased away. (a) is true relative to the presupposed proposition that there is such a person as Sherlock Holmes while (b) should be replaced by ‘There are works of fiction according to which Sherlock Holmes is a character’.10 I agree with these proposals and I don’t have anything to add to them. Frege’s view of fictional names even gives us a further reason to accept such proposals. We have provided an answer to the question why ‘Sherlock Holmes’ is not a name of the real-life Sherlock Holmes. The same answer underwrites also the view that ‘Sherlock Holmes’ does not name a character, an abstract object or artefact. The success of utterances introducing ‘Sherlock Holmes’ made with fictive intent does not depend on the existence of a fictional character.11 If the fictional name ‘Sherlock Holmes’ occupies subject position in an atomic sentence it can only refer to a fictional character if it changes the sense it has received in the story. However, such changes of sense and reference are implausible. In Conan Doyle’s story I might read ‘Sherlock Holmes concluded in a flash that Moriarty was the culprit’. The reader might respond by asserting (in his heart) ‘Therefore Sherlock Homes has a brilliant mind’. This seems like an intelligible and good inferential step. If it is an intelligible and good inferential step, ‘Sherlock Holmes’ should not shift its sense from premise to conclusion. Hence, we should prefer accounts that allow ‘Sherlock Holmes’ to have the same sense in and outside fictional discourse. Seeing the reader as reasoning relative to the presupposed proposition that there is such a person as Sherlock Holmes respects this constraint and is therefore preferable to a view that takes the utterance to be literally true. 10. See Friend 2007 and Sainsbury 2009 ch. 6. Künne 1995 provides paraphrases of inter- and intra-fictional sentences. 11. According to artefact theorists, fictional ‘Sherlock Holmes …’ utterances bring about the existence of a fictional character. Now my ‘Sherlock Holmes …’ utterances brings about the existence of many things: sound waves, feelings of joy etc. Yet ‘Sherlock Holmes’ seems not to refer to any of them. The artefact view needs to close this gap between ‘creation’ and reference in a plausible way.
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Fifth, some works of fiction introduce new proper names in fictional utterances and yet it is plausible to suppose that these proper names refer. Ed McBain’s 87th precinct stories take place on the island Isola. ‘Isola’ is introduced in utterances intended to create a fancy, but ‘Isola’ refers to Manhattan. How can this be on the proposed account? ‘Isola’ is a code name, a stand-in for ‘Manhattan’. (See Künne 1995, 149.) The reader can uncover this fact by making educated guesses. As real names retain their reference in utterances made with fictive intent, their stand-ins retain their reference. 6. Non-fictional names in fictive utterances We have now extracted from Frege’s work an explanation of the referenceresistance of fictional names that is compatible with the assumption that these names have a sense like any other name. According to this explanation, fictional proper names are introduced in a way that ensures that they have only sense. The purpose of such names is only to have sense and to contribute it to the propositional content of acts of make believe. This purpose prevents them from referring to any object. However, the explanation seems also to make non-fictional proper names used in fictional discourse empty. The first sentence of A Study in Scarlet is “In the year 1878 I took my degree of Doctor of Medicine of the University of London.” This is not an assertion, but an utterance made with fictive intent. Prima facie, the success of utterances made with fictive intent does not seem to require the existence of the referents of the singular terms involved, hence, in uttering ‘In the year 1878 I took my degree of Doctor of Medicine of the University of London’ with fictive intent, one does not refer to London. I think this difficulty motivates Frege’s surprising remark quoted before: [T]he proper names are here [in fiction] mock proper names, although they match the names of historical personages, they ought not to be taken seriously.
Green’s remark chimes with this idea: [B]ecause [Frege] took it that mock assertions must also have mock thoughts as their contents, he would have held that in the very act of simulating assertion the actor has brought it about that, there tokened, those words have no reference. By Frege’s lights it would follow that in such a case the actor was merely using expressions homonymous with those of a Begriffsschrift. (Green 1997, 226; my emphasis.)
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There is the genuine proper name ‘London’ that is used in factive discourse to name, well, London. There is also the co-spelled mock-proper name ‘London’ used in fiction that does not refer to anything. In some extreme cases this view is plausible. According to Schiller’s Don Carlos, Don Carlos is an enthusiastic young prince attempting to free Flanders from the grip of his father Philip. But Don Carlos was a mentally retarded, violent hunchback known among historians as ‘the crown prince who liked to beat up girls’. His father put him into solitary confinement not to quell his enthusiasm for republicanism; he simply tried to protect other people from Don Carlos’ violent attacks. People appraised of these facts might find it difficult to make believe concerning Don Carlos that he was a dashing champion of liberty etc. (Don Carlos is an unsuitable prop in the game of make believe that Schiller sets up for us.) The best construal of Schiller’s intention is therefore as introducing a fictional name that derives from the nonfictional name ‘Don Carlos’. The following abstract of Don Carlos is telling: Very loosely based on the events surrounding the real Don Carlos of Spain, Schiller’s Don Carlos is another republican figure—he attempts to free Flanders from the despotic grip of his father, King Philip (Wikipedia).
But while Schiller’s Don Carlos is indeed not Don Carlos, we have no reason to say that, for example, Sherlock Holmes’ London is not London. Readers of A Study in Scarlet are entitled to presume that ‘London’ refers to London; nothing in the story undermines this entitlement. They can easily imagine with respect to London that Sherlock Holmes lives in this city. For example, Doyle might have started his story with an assertion and only then, pretending to be Watson, shifted into fictive mode: “London is the biggest city in the UK. In the year 1878 I took my degree of Doctor of Medicine of the University of this city.” How should we understand the anaphoric expression ‘this city’ in fictional discourse if not as tied to a grammatical antecedent in non-fictional discourse from which it inherits its reference? Contrary to what Frege assumes, non-fictional proper names retain in general their normal reference in utterances made with fictive intent. This point raises a new question: How can one accept the CorrectnessPrinciple on the one hand, while, on the other hand, allowing non-fictional names used in utterances made with fictive intent to retain their ordinary reference?
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For a start, we must distinguish in an assertion (or any other utterance) sub-utterances.12 In an assertion of an atomic sentence one can distinguish the speech-acts of identifying reference and predication.13 Some constituents of your utterance single out an object, other constituents characterise it further. This is a rough characterisation, but the necessary refinements need not interest us here. Now you might combine a genuine reference with make believe predication. I might single out London for my audience in order to go on and invite you to make-believe that it is the city in which Watson and Holmes live. Hence, the Correctness-Principle does not force us to deny that non-fictional proper names retain their normal referents in fictional discourse. 7. Conclusion Frege’s theory of sense and reference has room for names that have only sense but no reference. They are not the only kind of sense-only-names. It seems plausible that other kinds include hoax names or names used in deceptive speech acts. A unified account is wanted, but has to wait for another occasion.
REFERENCES Bach, Kent 1981: “What’s in a Name”. Australasian Journal of Philosophy 59, 371–386. Baldwin, Thomas 1990: G. E. Moore. London: Routledge. Braun, David 2005: “Empty Names, Fictional Names, Mythical Names”. Nous 39, 596–631. Castañeda, Hector-Neri 1989: Thinking, Language & Experience. Minneapolis: University of Minnesota Press. Chastain, Charles 1975: “Reference and Context”. In: Keith Gunderson (ed.), Language, Mind and Knowledge. Minneapolis: University of Minnesota Press, 194–269. Currie, Gregory 1988: “Fictional Names”. Australasian Journal of Philosophy 66, 471–88. 12. Here I am indebted to discussion with Mark Siebel and Benjamin Schnieder. 13. For further discussion see Searle 1995, ch. 4 and 5. Predication is a distinguishable,
but no separable act.
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— 1990: The Nature of Fiction. Cambridge: Cambridge University Press. Dummett, Michael 1973: Frege: Philosophy of Language. 2nd edition, London: Duckworth, 1980. — 1983a: “Existence”. Reprinted in his 1993, 277–308. — 1983b: “Could there Be Unicorns?”. Extended version reprinted in his 1993, 328–49. — 1993: The Seas of Language. Oxford: Clarendon Press. Evans, Gareth 1982: Varieties of Reference. Oxford: Oxford University Press. Frege, Gottlob 1892: “Über Sinn und Bedeutung”. Zeitschrift für Philosophie und philosophische Kritik 100, 25–50. Translated as “On Sense and Meaning” in Brian McGuinness (ed.), Gottlob Frege: Collected Papers on Mathematics, Logic and Philosophy. Oxford: Basil Blackwell, 1984, 157–77. — 1892–5: “Ausführungen über Sinn und Bedeutung”. In: NS, 128–36. Trans. as “Comments on Sense and Meaning” in PW, 118–25. — 1897: “Logik”. In NS, 137–63. Trans. as “Logic” in PW, 126–51. — 1902: “Brief an Russell (28.12.1902)”. In: WB, 234–7. Trans. in PMC, 152–4. — 1906: “Einleitung in die Logik”. In: NS, 201–12. Trans. as “Introduction to Logic” in PW, 185–96. — 1918: “Der Gedanke”. Beiträge zur Philosophie des deutschen Idealismus, I, 58–77. Trans. as “Thoughts” in: McGuinness 1984, 351–73. — NS: Gottlob Freges Nachgelassene Schriften. Hamburg: Meiner 21983, ed. by Hans Hermes et al. — PW: Posthumous Writings. Transl. of NS, Oxford: Blackwell, 1979. — WB: Wissenschaftlicher Briefwechsel. Hamburg: Meiner, 1976, ed. by Gottfried Gabriel et al. — PMC: Philosophical and Mathematical Correspondence. Oxford: Basil Blackwell 1979. WB abridged by Brian McGuinness and transl. by Hans Kaal. Friend, Stacie 2007: “Fictional Characters”. Philosophy Compass 2, 141–56. Green, Mitchell 1997: “On the Autonomy of Linguistic Meaning”. Mind 106, 217–43. Jubien, Michael 1997: Contemporary Metaphysics. Oxford: Blackwells. Kripke, Saul 1972: Naming and Necessity. Cambridge, Mass.: Harvard University Press. 21980. Künne, Wolfgang 1983: Abstrakte Gegenstände. Frankfurt a. M.: Suhrkamp. — 1995: “Fiktion ohne fiktive Gegenstände: Prolegomenon zu einer Fregeanischen Theorie der Fiktion”. In: Johannes L. Brandl, Alexander Hieke & Peter M. Simons (eds.), Metaphysik. Neue Zugänge zu alten Fragen. Bonn: Akademia Verlag, 141–61. Lewis, David 1978: “Truth in Fiction”. In his Collected Papers I, Oxford: Oxford University Press 1983, 261–81.
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— 1997: “Naming the Colours”. In his Collected Papers III, Cambridge: Cambridge University Press, 1999, 332–59. Mann, Thomas 1961: Briefe (1889–1955) und Nachlese I. Edited by Erika Mann, Frankfurt: Fischer. Mann, Viktor 1949: Wir waren Fünf: Bildnis der Familie Mann. Konstanz: Südverlag. Moore, George E. 1933: “Imaginary Objects”. Aristotelian Society Supplementary Volume XII. Reprinted in his Philosophical Papers, London: Allen and Unwin 1959, 102–15. Ryle, Gilbert 1933: “Imaginary Objects”. Aristotelian Society Supplementary Volume XII, 18–43. Sainsbury, Mark 1999: “Names, Fictional Names, and ‘Really’”. Reprinted in his Departing from Frege. London: Routledge, 159–81. — 2005: Reference without Referents. Oxford: Oxford University Pres. — 2009: Fiction and Fictionalism. London: Routledge. Searle, John 1969: Speech Acts. Cambridge: Cambridge University Press. Thomasson, Amie L. 2003: “Speaking of Fictional Characters”. Dialectica 57, 205–23. Walton, Kendall 1990: Mimesis as Make-Believe. Cambridge; Mass.: Harvard University Press. — 2003: “Restricted Quantification, Negative Existentials, and Fiction”. Dialectica 57, 239–42. Williamson, Timothy 1996: “Knowing and Asserting”. The Philosophical Review 105, 489–523.
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