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Dummett : Philosophy of Language.
 9780745666723, 0745666728

Table of contents :
Cover
Title page
Copyright page
Key Contemporary Thinkers
Preface
Introduction
1 Fregean Foundations
Sense and Reference in Frege and Dummett
Truth, Assertion and the Central Argument against Bivalence
Frege's Platonism
Frege's Kantian Connections
The Context Principle
2 Wittgenstein and Quine
The Manifestability Constraint and Rejection of Mentalism
Dummett and Quine
Two Challenges: Holism and Strict Finitism
The Manifestability Constraint and the Priority of Language
How do Anti-Mentalism and Anti-Psychologism Stand to Each Other?
3 The Influence of Intuitionism. Brouwer's IntuitionismThe Intuitionist's Case against Bivalence
Metaphysical Debates and the Theory of Meaning
The Traditional Case for Nominalism and Subjective Idealism
Moderate Idealism and the Denial of Bivalence
The Case against Strict Finitism
Pure vs Mediated Constructivism, Truth Theories and Semantics
A Common-Sense Realist Appropriation of the Argument against Bivalence
4 The Reality of the Past
Anti-Realism with Respect to the Past
Anti-Realism with Respect to the Future
5 What do we Know when we Know a Language?
Languages and Idiolects. Davidson on Malapropism and the Social Character of Meaning6 Psychologism, Phenomenology and Philosophy of Mind
On the Relationship of Phenomenology to Analytic Philosophy
How Close are Frege and Husserl on Sense and Reference?
Wittgenstein and Intentionality
Conclusion
References and Bibliography
Index.

Citation preview

Dummett

Dummett Philosophy of Language

Karen Green

Polity

Copyright © Karen Green 2001 The right of Karen Green to be identified as author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. First published in 2001 by Polity Press in association with Blackwell Publishers Ltd. Editorial office: Polity Press 65 Bridge Street Cambridge CB2 1UR, UK Marketing and production: Blackwell Publishers Ltd 108 Cowley Road Oxford OX4 1JF, UK All rights reserved. Except for the quotation of short passages for the purposes of criticism and review, no part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Except in the United States of America, this book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher’s prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data Green, Karen, 1951– Dummett: philosophy of language/Karen Green. p. cm. Includes bibliographical references and index. ISBN 0–7456–2294–1 — ISBN 0–7456–2295–X (pbk.) 1. Dummett, Michael A. E.—Contributions in philosophy of language. 2. Language and languages—Philosophy. I. Title. B1626.D854 G74 2001 121¢.68¢092—dc21 2001021061 Typeset in 10 –12 on 12 pt Palatino by Best-set Typesetter Ltd., Hong Kong Printed in Great Britain by MPG Books Ltd, Bodmin, Cornwall This book is printed on acid-free paper.

Key Contemporary Thinkers Published Jeremy Ahearne, Michel de Certeau: Interpretation and its Other Peter Burke, The French Historical Revolution: The Annales School 1929–1989 Michael Caesar, Umberto Eco: Philosophy, Semiotics and the Work of Fiction Colin Davis, Levinas: An Introduction Simon Evnine, Donald Davidson Edward Fullbrook and Kate Fullbrook, Simone de Beauvoir: A Critical Introduction Andrew Gamble, Hayek: The Iron Cage of Liberty Karen Green, Dummett: Philosophy of Language Phillip Hansen, Hannah Arendt: Politics, History and Citizenship Sean Homer, Fredric Jameson: Marxism, Hermeneutics, Postmodernism Christopher Hookway, Quine: Language, Experience and Reality Christina Howells, Derrida: Deconstruction from Phenomenology to Ethics Fred Inglis, Clifford Geertz: Culture, Custom and Ethics Simon Jarvis, Adorno: A Critical Introduction Douglas Kellner, Jean Baudrillard: From Marxism to Post-Modernism and Beyond Valerie Kennedy, Edward Said: A Critical Introduction Chandran Kukathas and Philip Pettit, Rawls: A Theory of Justice and its Critics James McGilvray, Chomsky: Language, Mind, and Politics Lois McNay, Foucault: A Critical Introduction Philip Manning, Erving Goffman and Modern Sociology Michael Moriarty, Roland Barthes Harold W. Noonan, Frege: A Critical Introduction William Outhwaite, Habermas: A Critical Introduction John Preston, Feyerabend: Philosophy, Science and Society Susan Sellers, Hélène Cixous: Authorship, Autobiography and Love David Silverman, Harvey Sacks: Social Science and Conversation Analysis Dennis Smith, Zygmunt Bauman: Prophet of Postmodernity Geoffrey Stokes, Popper: Philosophy, Politics and Scientific Method Georgia Warnke, Gadamer: Hermeneutics, Tradition and Reason James Williams, Lyotard: Towards a Postmodern Philosophy

Jonathan Wolff, Robert Nozick: Property, Justice and the Minimal State Forthcoming Maria Baghramian, Hilary Putnam Sara Beardsworth, Kristeva Mark Cain, Fodor: Language, Mind and Philosophy James Carey, Innis and McLuhan Rosemary Cowan, Cornell West: The Politics of Redemption George Crowder, Isaiah Berlin: Liberty, Pluralism and Liberalism Thomas D’Andrea, Alasdair MacIntyre Eric Dunning, Norbert Elias Jocelyn Dunphy, Paul Ricoeur Matthew Elton, Daniel Dennett Nigel Gibson, Frantz Fanon Graeme Gilloch, Walter Benjamin Espen Hammer, Stanley Cavell Keith Hart, C. L. R. James Sarah Kay, Zˇizˇ ek: A Critical Introduction Paul Kelly, Ronald Dworkin Carl Levy, Antonio Gramsci Moya Lloyd, Judith Butler Dermot Moran, Edmund Husserl Steve Redhead, Paul Virilio: Theorist for an Accelerated Culture Chris Rojek, Stuart Hall and Cultural Studies Wes Sharrock and Rupert Read, Kuhn Nick Smith, Charles Taylor Nicholas Walker, Heidegger

Contents

Preface Introduction 1

2

1

Fregean Foundations

12

Sense and Reference in Frege and Dummett Truth, Assertion and the Central Argument against Bivalence Frege’s Platonism Frege’s Kantian Connections The Context Principle

13

Wittgenstein and Quine

53

The Manifestability Constraint and Rejection of Mentalism Dummett and Quine Two Challenges: Holism and Strict Finitism The Manifestability Constraint and the Priority of Language How do Anti-Mentalism and Anti-Psychologism Stand to Each Other? 3

ix

24 30 36 40

56 63 65 69 73

The Influence of Intuitionism

87

Brouwer’s Intuitionism The Intuitionist’s Case against Bivalence

89 95

viii

Contents Metaphysical Debates and the Theory of Meaning The Traditional Case for Nominalism and Subjective Idealism Moderate Idealism and the Denial of Bivalence The Case against Strict Finitism Pure vs Mediated Constructivism, Truth Theories and Semantics A Common-Sense Realist Appropriation of the Argument against Bivalence

4

5

6

105 108 117 124 128 130

The Reality of the Past

133

Anti-Realism with Respect to the Past Anti-Realism with Respect to the Future

134 145

What do we Know when we Know a Language?

149

Languages and Idiolects Davidson on Malapropism and the Social Character of Meaning

150 163

Psychologism, Phenomenology and Philosophy of Mind

176

On the Relationship of Phenomenology to Analytic Philosophy How Close are Frege and Husserl on Sense and Reference? Wittgenstein and Intentionality

179 183 194

Conclusion

201

Notes References and Bibliography Index

206 217 231

Preface

In the latter part of the twentieth century Michael Dummett’s name has epitomized the debate between realists and anti-realists, and his formulation of this issue has exerted a profound influence within the analytic tradition. This has been particularly true in Oxford, where he taught for much of the period, and from this centre his influence has spread to both the United States and Europe. Many of the foremost contemporary British analytic philosophers have been influenced by him, including Simon Blackburn, John McDowell, Christopher Peacocke, Timothy Williamson, Crispin Wright and the late Gareth Evans.1 Yet none of these thinkers could be classed as his disciples. It is difficult to exactly define the scope of Dummett’s influence. He is often, slightly inaccurately, thought of as a determined advocate of an original brand of anti-realism which involves the rejection of classical bivalent logic and the adoption of intuitionist styles of reasoning. When his philosophy is characterized in this fashion, it has seemed to some that, despite a prolific output, he has been rather ineffectual in stating his case.2 Moreover, the sheer bulk of this output and the complexity of many of the issues addressed mean that it is difficult for younger philosophers to come to grips with his work, with the result that it is in danger of being read less than it deserves. In a philosophical climate in which a high priority is placed on quick publication, it is more profitable for young philosophers to concentrate on more manageable authors, whose positions can easily be stated and criticized. Those of us who have always been impressed by

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the integrity and seriousness of Dummett’s philosophy find this unfortunate. Dummett’s project involves an attempt to understand what understanding a language consists in. Our capacity to reason, communicate and represent reality through language remains difficult to comprehend. Perhaps this is inevitable, for at some level the precondition of the possibility of understanding a language may resist capture within language. Those influenced by Wittgenstein and by various forms of holism will be inclined to say that at some point the explanation of understanding must stop. We can do no more than say that that is how we go on. Dummett, by contrast, believes that we should aim to do more than this. But the account of what understanding consists in that he provides comes at a price; for it suggests that we will have to acknowledge that there are some features of our current linguistic practice which cannot be justified or made genuinely comprehensible. In particular, the general acceptance of the principle of bivalence (which says that every meaningful sentence is either true or false) is difficult to justify from the perspective of this account. Dummett equates acceptance of this principle with realism, and the denial of bivalence with antirealism. For the time being I will follow this usage, though later in the book I will argue that the denial of bivalence brings with it only a very attenuated form of anti-realism. The aim of this book is to make Dummett’s thought more accessible, by providing an overview to orientate senior students of philosophy and a resource for those interested in following the implications of his thought further. Inevitably, the overview reflects my own preoccupations, but I have attempted to make the exposition as faithful to Dummett’s own position as possible, and I am grateful to him for having generously read and commented on some of the draft material for the book. Barry Taylor, Greg Currie, Sam Butchart, Helen Prosser, Mark English and Stephen Barker also deserve thanks for having read and commented on drafts of various stages of the book. Obviously they are not responsible for any flaws which remain. I would like to thank Denis Robinson who has been a generous source of encouragement for my philosophical efforts over many years. Michael Devitt should be credited with having provided the immediate stimulus which led me to write this book. Many years ago he supervised my Ph.D. thesis on Dummett and Frege, even though he did not share my enthusiasm for Dummett’s thought. The naturalistic slant which I have brought to my reading of Dummett is no doubt

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due to him, and many of the arguments in this work implicitly respond to his challenges. Even earlier in my philosophical career, Christopher Peacocke, Crispin Wright, David Bostock and Simon Blackburn pulled apart my first efforts at dealing with some of the issues addressed here, when they were my tutors at Oxford in the mid-1970s. It was Michael Woods who was responsible for sending me to such an interesting selection of tutors to read for the various papers in the B.Phil. It is, perhaps most importantly, thanks to Aubrey Townsend that, as a fourth-year student, at Monash, in 1973, I acquired a copy of Michael Dummett’s Frege: Philosophy of Language and began a lifetime’s fascination with Dummett, Frege and the philosophy of language.

Introduction

During the late nineteenth and early twentieth century philosophy took a linguistic turn. The linguistic tradition of analytic philosophy owes much to Frege, and Dummett’s thought belongs firmly within it. As characterized by Dummett, two beliefs distinguish the analytical school of philosophy: ‘that a philosophical account of thought can be obtained through a philosophical account of language, and, . . . that a comprehensive account can only be so obtained’ (Dummett 1975a/78c, p. 442; 1993b, p. 4).1 We will call this the ‘linguistic priority thesis’. It is, Dummett says, with the introduction of the context principle that Frege shows his commitment to the first of these beliefs. This principle, which states that it is only in the context of a sentence that a word has meaning, encapsulates Frege’s insight that an adequate account of the meaning of words depends on the proper analysis of the syntactic structure of sentences. It makes sentences primary in the account of meaning, and, as we will see, it turns out to be central to Dummett’s initial characterization of the dispute between realists and anti-realists. Indeed, for Dummett the context principle is the pivot around which philosophy made its linguistic turn; so the analytic approach to language depends ultimately on the plausibility and interpretation of this principle. When Frege recognized that a way to give an account of our understanding of number words was available if we begin with sentences, he was able to avoid the twin perils of mentalism, which makes meanings ideas in the mind, and of unsatisfactory forms of Platonism, which take the meanings of number words to be obscure denizens of an ideal realm, which are unrelated

2

Introduction

to our actual practice. Ultimately Frege’s account appeared inadequate, because it allowed the construction of the paradoxical set of all sets which are not members of themselves, as Bertrand Russell showed. Nevertheless, Frege’s approach constituted a significant breakthrough, and Dummett argues for its lasting significance. As well as formulating the context principle, Frege influenced the analytic tradition in other ways. His success in analysing the logic of generality influenced Russell, who thought of the method of descriptions, outlined in ‘On Denoting’, as improving on Frege’s insights. Russell’s successes in analysing the logic of definite descriptions resulted in a profound optimism regarding the benefits of logical analysis. The most influential expression of this optimism is found in Ayer’s Language, Truth and Logic, which popularized the project of the logical positivists for English-speaking audiences, and introduced them to the verification principle, which asserted that only verifiable sentences are meaningful. In Ayer’s hands, Russell’s theory of descriptions provides a paradigm of a philosophical method devoted to showing how apparent reference to metaphysically puzzling entities can be paraphrased away (Ayer 1946, pp. 59–71). For the logical positivists the verification principle provided a criterion for sorting meaningless metaphysical statements from those with a scientific and verifiable content. Understanding a sentence consists in knowing what sensory evidence would verify it. Since the ultimate evidence for scientific truth was taken to be sensory evidence, verificationism was also assumed to imply phenomenalism: the view that the world we know is constructed out of percepts, sense data or qualia, which are the sensory atoms on which knowledge is founded. As we will see, although Dummett also believes that understanding a sentence consists in knowing what would verify it, he rejects phenomenalism, and thinks that the positivists’ attempt to avoid metaphysics was futile. Wittgenstein’s Tractatus was also deeply indebted to Frege. And even Wittgenstein’s later philosophy of language bears the marks of the Fregean view of language against which he was reacting. As a result of the turn towards language, two attitudes to philosophy have dominated the twentieth-century Anglo-American philosophical scene. The first, ordinary language philosophy, took from the later Wittgenstein the attitude that most philosophical problems are pseudo-questions, which would be dissolved by removing puzzles engendered by language. The second, epitomized by Davidson’s development of the Fregean idea that meaning is given by truth conditions, assumed, rather, that all the fundamental problems con-

Introduction

3

cerning meaning and understanding could be illuminated through the analysis of the logical structure of language. Dummett is not an ordinary language philosopher. Indeed, he is dismissive of the piecemeal approach to language adopted by them. Yet in his work there is a strand of thought which derives from Wittgenstein which is entwined with central threads of the Fregean tradition. He uses Wittgenstein’s dictum that ‘meaning is use’ to question the adequacy, as it stands, of Davidson’s truth-conditional semantics, while at the same time rejecting the later Wittgenstein’s pessimism concerning the possibility of a systematic account of meaning. He explores the possibility that intuitionistic logic provides a way between these two options.2 But, as we will see, he is not an out-andout advocate of intuitionism. Different areas of language need to be considered on their own merits. In some areas of language, for instance in mathematics, the denial of bivalence appears much more plausible than in others, as when we are speaking of material objects. Global anti-realism would deny bivalence for all areas of discourse. There is little to suggest that Dummett is a global antirealist. Indeed, in chapter 4, I will argue that Dummett is not committed to anti-realism with regard to the past, although he has argued a case on behalf of such a view. At the end of the twentieth century, philosophy in the Englishspeaking world has taken another turn. Research into the theory of meaning has now been absorbed into the philosophy of mind, or cognitive science, and is being pursued as an aspect of research into the psychology of understanding, which includes causation, perception, memory and forms of prelinguistic thought. Rather than offering what Dummett calls a ‘philosophical account of language’, many researchers are now interested in giving a naturalistic and descriptive account of the psychology of language use which attempts to explain how we recognize properties, sound patterns and grammatical sentences (Chomsky 1995).3 Often the direction of explanation involves first explaining what it is for there to be a nonlinguistic grasp of concepts, so that the understanding of language can be explained in terms of non-linguistic thought. Dummett mentions Gareth Evans as one writer who has left behind the analytic tradition, as Dummett characterizes it, and who attempts to ground an account of linguistic understanding in prelinguistic ways of thinking of an object (Evans 1982; Dummett 1993b). Some have thought the exclusion of Evans from the analytic fold strange (Monk 1997, p. 37). Yet there are others associated with cognitive science who are, by their own lights, returning to a project initiated by

4

Introduction

Husserl in the Logical Investigations (Husserl 1900/70; Dreyfus 1982). Since analysis and phenomenology understood each other, in the mid-twentieth century, as opposed traditions, this rapprochement suggests a changing self-understanding within the Anglo-American philosophical scene. Once one becomes interested in the psychology of linguistic understanding, it begins to appear implausible that an account of thought can be attained through an account of language, for the capacity to understand language appears to be grounded in forms of non-linguistic thought. From this perspective one might well wonder whether the analytic tradition has anything to offer. If analytic philosophy is committed to the priority of language, as Dummett suggests it is, and if research into thinking shows that language cannot be prior to thought, then the linguistic turn seems to have taken us up a blind alley. This study of Dummett’s thought will seek to demonstrate that, on at least one interpretation, the linguistic priority thesis is both true and important. However, the issues are complex, for the priority thesis is ambiguous, as is the notion of thought. In the last two chapters we will look directly at the relationship between language and thought, through a discussion of Dummett’s criticisms of Chomsky, Davidson and Husserl. The last, in particular, defends a version of the linguistic priority thesis which is sympathetic to Dummett’s claims, though it goes beyond anything explicitly stated by Dummett. The first four chapters are more expository and set out the basic contours of Dummett’s philosophy. Much of Dummett’s writing has taken the form of commentary on other philosophers or philosophies: Frege, Wittgenstein, Quine, the intuitionists and, more recently, phenomenology and Husserl. This has meant that commentators rarely discuss Dummett’s contribution to philosophy directly. In order to do so, one needs considerable knowledge of the philosophers with whom he engages, but once one becomes immersed in the original texts, debate with Dummett is inclined to get sidetracked into issues concerning the interpretation of the original thinker. Dummett’s writing on Frege, for instance, has spawned a veritable industry of Frege scholarship, but much less commentary on Dummett’s own philosophy. At the same time, it is impossible to provide an introduction to Dummett’s thought without considering it in relation to the thinkers who have been major influences on him. For this reason I have adopted the following plan in this book. In the first part I investigate the origins of Dummett’s philosophy by looking at the three great pillars on which it is built: Frege, Wittgenstein and intuitionism. This also

Introduction

5

serves to introduce the strengths and weaknesses of the theories of meaning of the realist, the holist and the constructivist. With the completion of this overview the outline of Dummett’s contribution to the theory of meaning will be in place. I will then turn to a more detailed account of the two central issues which characterize Dummett’s own contribution to twentieth-century philosophy: the realism/anti-realism debate and the question of the shape of a theory of meaning. Last I will return to the issue of psychologism, as it emerges in Dummett’s discussion of phenomenology and, by implication, recent philosophy of mind. Isaiah Berlin (1979) has contrasted those thinkers, whom he calls ‘hedgehogs’, whose work is guided by one basic idea worked over in depth, from others, ‘foxes’ who explore many ideas along various avenues of thought.4 Dummett, taking up this metaphor, has been happy to describe himself as a fox, ‘who goes snuffling around among many things about each of which he knows a little’ (1994a, p. 318). And it is this fox-like tendency to follow many trails wherever they lead, sometimes to an impasse or round in a circle, that is one of the features that makes his work so difficult. This is particularly the case for those whose attitude to philosophy is, rather than that of either a hedgehog or a fox, that of the gull who surveys the territory and, finding an unoccupied position, defends it with whatever noise and posturing are effective. It is important, however, to recognize that Dummett’s philosophy is not intended to provide a monumental defence of a single position. Instead, it has the form of a life’s dialogue in which a line of thought is taken up and developed until an objection from some countervailing direction throws out an irresistible scent. So, rather than seeing Dummett as an ineffectual defender of anti-realism, for instance, we should accept his own words: I personally have no unshakeable commitment to anti-realism in any of these cases, even the mathematical one. . . . I have urged the claims of the anti-realist position only because it seemed to me that, in most cases, philosophers unthinkingly adopted a realist view without noticing that it required substantiation: to say that it is natural to take such a view or that it is ‘part of our theory of the world’ is merely the equivalent of Dr. Johnson’s kicking the stone. (Dummett 1978c, p. xxxix)

More recently he has emphasized that we should see him as having been engaged in a research programme which attempts to uncover

6

Introduction

the general structure of disputes between realists and anti-realists (Dummett 1993c). Dummett is as aware as others of the realist presuppositions of most of our talk, but he is also impressed by the apparent cogency of a certain kind of anti-realist argument. If we are to be justified in settling into a realist stance for a certain area of discourse, we must be able to do more than say that the stance is comfortable or natural. We should be able to show why the apparent cogency of the anti-realist’s argument is an illusion. In the preface to one of his later books Dummett suggests that he once hoped to resolve the issue concerning realism in its various manifestations, but now doubts whether he will ever do so. He leaves us a strategy for tackling the issue, and it is as a strategy, or set of strategies, that we should consider his writings on anti-realism (Dummett 1991e, p. x). In fact, it seems that while Dummett at one time thought that the case for anti-realism was very strong, he has come to emphasize to a much greater extent the inevitability of a gap between truth and the recognition of truth, and to accept that the notion of truth has a bias towards realism built into it (1991e, p. 182). He has also acknowledged that, since classical logic is standard, were it possible to give a theory of meaning which justified that logic, this would be far more satisfying than being forced to revise our practice (1991e, pp. 339–40). So far, however, classical logicians have not met the challenge of providing a justification for their preferred logic. The intuitionists have made greater progress towards giving a non-circular justification for their logic; but this does not imply an absolute vindication of anti-realism, since, as I will argue later, some interpretations of intuitionist truth are quite realist in character. Indeed, although Dummett argues a detailed case on behalf of the anti-realist, in his later works there is a certain reorientation towards realism. Because Dummett has always been interested in pursuing each issue with open-minded honesty to the conclusion that appears compelling at the time, we should not expect to find a monolithic doctrine in his writings. Nor is this where his importance lies. Rather, he has raised challenging questions about the relationship between logical truth and understanding, the justification of deduction, the foundations of our bias towards realism, and the notion of truth. He has developed these questions with care, insight and integrity. And his work provides a model of what philosophy ought to be: an open-minded, careful engagement with those philosophical ideas which strike one as important, no matter what school or tradition they derive from. One of his lasting con-

Introduction

7

tributions is to have offered a map of the possible positions within the theory of meaning and to have illuminated the strengths and weaknesses of each. According to the map that Dummett has provided, three positions dominate the landscape: realism, characterized by Frege; holism, which Dummett finds in Wittgenstein and Quine; and the constructivism that he develops out of Brouwer’s intuitionism. Because intuitionism ties truth to potential proof, and because it appears that some sentences are undecidable, intuitionism implies a refusal to assert the principle of bivalence.5 This refusal has been associated, by Dummett, with anti-realism. Indeed, Dummett is now committed to the view that the denial of bivalence always brings with it some form of anti-realism. This goes against an earlier view, which he spent many pages defending, according to which some denials of bivalence, for instance those that arise with regard to sentences that contain non-denoting terms or vague predicates, do not involve anti-realism. Dummett now suggests that accepting truth-value gaps for sentences containing non-denoting terms involves anti-realism with regard to non-existent entities; the denizens of Meinong’s jungle. Similarly, accepting ineliminable vagueness involves anti-realism with regard to a determinate fact that would make an attribution of a vague predicate determinately either true or false. It is not clear, however, that Dummett’s equation of the denial of bivalence with anti-realism should be accepted. As mentioned in the last paragraph, one can be an intuitionist, yet make significant concessions to realism, so the connection between the denial of bivalence and anti-realism is rather more complex than this equation implies. In the light of this, it may be preferable to categorize views as more or less realist, rather than assuming a single sharp dichotomy. Moreover, since realism is usually taken to be the ‘common-sense’ position, Dummett’s new emphasis on the connection between the rejection of bivalence and anti-realism looks as though it does the denial of bivalence a disservice. What most realists care about is realism with regard to common-sense material objects: that is, realism with regard to the objects and properties that causally impinge upon us. Bivalence can be denied for sentences which refer to fantastic other-worldly entities without offending the sensitivities of this kind of ordinary common-sense realist. It therefore seems counter-intuitive to deem such a position anti-realist. In chapter 3 these issues will be discussed in detail. There it will be argued that robust realism with regard to the things of this world is quite compatible with a measure of anti-realism with regard to

8

Introduction

postulated denizens of other worlds. It will be further argued that the common-sense realist, who wants to incorporate into her scientific account of the world a satisfactory explanation of our capacity to communicate truths about that world, should take seriously the arguments that Dummett offers on behalf of the adoption of intuitionist logic. Before engaging with the details of Dummett’s map, certain misapprehensions may be avoided, and a general orientation provided, by a brief account of the relationship between Dummett’s interest in a generalized verificationism and the earlier verificationism of the logical positivists, in particular that of A. J. Ayer. Ayer and Dummett both spent their working lives at Oxford. Dummett was appointed to the Wykeham Chair at New College, which Ayer had held for many years, and it is natural to suppose that Dummett’s defence of verificationism involves the continuation of the views made famous by the logical positivists. This is, as we will see, only partly correct, and in some ways creates a misleading impression. Dummett is certainly impressed by one element of the earlier verificationist way of thinking. He agrees that an account of what would verify or falsify an assertion must be central to an account of meaning. But whereas the positivists used the verification principle as a tool in a quest to eliminate metaphysics, Dummett has argued (and Ayer came to agree) that the verification principle has to be interpreted as providing the skeleton for a theory of meaning, and so itself embodies a particular metaphysical outlook (Ayer 1992, pp. 149–50; Dummett 1992, pp. 132–4). It embodies a certain conception of the kind of thing the existence of which may render our utterances true. Logical positivism involved various reductionist theses: the phenomenalist claim that the meaning of a material object statement could be given in terms of statements about sense data, the instrumentalist thesis that the meanings of theoretical statements could be given in terms of statements about material objects, and, in Ayer’s case, the claim that statements about the past are rules for predicting the discovery of present evidence for past events (Ayer 1946, pp. 101–2). Each of these assumes that some things, sense data, material objects or present events exist unproblematically, and attempts to show how more problematic entities can be constructed on this unproblematic basis. Early on, verificationists adopted strong reductionist theses involving translation. By the time Ayer wrote Language, Truth and Logic it no longer seemed plausible to claim that material object statements could be translated into equivalent statements about

Introduction

9

sense data; all the same, Ayer was prepared to assert that, ‘whether one realises it or not, to say that [a certain material] thing exists is equivalent to saying that [certain] sensations are obtainable’ (Ayer 1946, p. 50). In general, all meaningful statements were thought to be equivalent to statements about the obtainability of sensory evidence. Dummett has little sympathy with the reductionist elements in early verificationism. As will be spelled out in chapter 3, he has argued that the phenomenalists’ analysis of statements involving unobserved material objects ought to have led them to deny bivalence, although it did not do so (Dummett 1978b, pp. 158–60; 1982c/93d, pp. 248–53). Phenomenalists analysed statements about unobserved objects as counterfactual conditionals about what would be experienced by a suitably placed observer; but, since there is no reason to assume that a counterfactual conditional is always either definitely true or definitely false, their reductionism had the potential to lead to the denial of bivalence. Had they recognized this, the extreme character of their anti-realism would have been manifest (Dummett 1993b, pp. 189–90). Nevertheless, reductionism does not necessarily lead to anti-realism. It is compatible with a sophisticated realism. At least four positions are possible: 1 2 3 4

A realist view of some class of statements plus a reductive thesis = sophisticated realism. A realist view of some class of statements which are barely true (no-reductive class) = naive realism.6 Anti-realism that is the result of some reductive thesis = reductive anti-realism. Anti-realism which is non-reductive = outright anti-realism.

Dummett suggests that the most interesting forms of anti-realism (neutralism with regard to the future and intuitionism) are not reductionist in character (1982c/93d, pp. 254–9). Reductionist theses tend to presume that it is possible to provide an atomistic account of meaning. Some classes of simple sentences are barely true, and more complex sentences are logical compounds of simple sentences. But atomistic accounts of meaning are undermined by the underdetermination of theory by sensory evidence, as has been argued in detail by Quine. Although Dummett takes issue with Quine’s holism, he is sufficiently influenced by Quine’s critique of atomist accounts of meaning to be sensitive to the fact that our actual means for verifying a sentence may rely on a significant amount of back-

10

Introduction

ground information and theory. Outright anti-realism takes seriously the actual means used for verifying and falsifying statements; these may involve theoretical presuppositions. The distance which this introduces between Dummett and Ayer on the question of what justification there is for asserting sentences of a particular class emerges most strikingly in Dummett’s discussion of instrumentalism in the paper ‘Common Sense and Physics’. In The Central Questions of Philosophy Ayer considered the relationship between ordinary common-sense statements about macroscopic material objects and the statements of physical science. In his discussion he offers three possibilities for the relationship between common-sense physical objects and the entities that science tells us exist. 1 2 3

Common-sense perceptible objects really exist – scientific objects are merely explanatory. Things in themselves are the imperceptible entities that physics describes – common-sense objects are mere appearances. Physical particles are tiny parts of perceptible objects.

Ayer adopts the third position, but he takes seriously the choice posed between the instrumentalism expressed in the first and the denial of the reality of coloured macroscopic objects expressed in the second. Dummett, by contrast, rejects the cogency of the choice. He suggests that the distinction between what really exists and what only appears involves two different contrasts which have become confused. On the one hand, there is the contrast between truth and illusion: an illusion is not true but appears to be so. On the other hand, there is the distinction between an absolute and a relative form of description. An absolute description, like that offered by science, attempts to explain things as they are in themselves, rather than as they are relative to an observer, or frame of reference, but the relative description is not thereby shown to be incorrect. Rather, a good absolute description will explain why some relative description is true. The common-sense view of the world gives us a merely relative, rather than an illusory, description of the world. Dummett also suggests that this is a place where the tendency to confuse reductionism with anti-realism is operative. Those who think that by adopting a reductionist account they are adopting an anti-realist view are forced into one or other of two unpalatable alternatives. Either scientific entities are reduced to the perceptible

Introduction

11

objects of common sense, or vice versa, and this is taken to imply that the entities that can be so reduced do not really exist. This overlooks the possibility of a sophisticated realism that involves reductionism (Dummett 1979a/93d, pp. 389–90). Dummett goes further, and denies that we have, in the case of colour predicates, two clearly distinguishable classes of statement. Our ordinary use of colour vocabulary is inextricably bound up with a proto-theory of the behaviour of light and of the propensities of surfaces to look differently under different light conditions. We understand that there are different kinds of surface which react differently to light, and that much of this has to do with the reflection and absorption of light (Dummett 1979a/93d, p. 400). This means that the scientific conception of colour as a complex disposition of a surface is only a precisification of the ordinary notion. Science merely extends our common-sense view of the world, and the idea that perception is the result of the causal action of an object is part of common sense. So Dummett adopts a form of realism about colours, but wants to insist that this kind of debate rests on confusing reductionism with anti-realism. The arguments for anti-realism that Dummett finds impressive, and which he believes the realist must respond to, are not the reductionist arguments of the phenomenalists or the instrumentalists. They tend, rather, to be the views of outright anti-realists. He is particularly interested in the possibility of non-reductive anti-realisms which accept that our understanding of what verifies or falsifies a statement may itself involve considerable theory. One should not, therefore, assume that the verificationism that he explores is the outdated, discredited philosophy of the logical positivists. It is not. Nor does it involve a distrust of metaphysics. Rather, the questions which Dummett raises about the correct semantics for our language are questions about what exists, which are equivalent to questions about that to which we take ourselves to be referring. They are fundamental metaphysical questions.

1 Fregean Foundations

Dummett’s first published book was an extended discussion of Frege, in which he set out his understanding of Frege’s realist semantics and developed his central criticisms of semantic theories which are grounded in realist truth.1 When Dummett published Frege: Philosophy of Language in 1973, not much attention was being paid to Frege’s writing. Since that time, and directly stimulated by Dummett’s work, there has been a proliferation of books devoted to Frege, many of them taking issue with some aspect of Dummett’s interpretation, but virtually all of them profoundly influenced by it. If Dummett’s achievement had been only to stimulate research on Frege, it would have been significant, but this book, ostensibly on Frege, actually spans a great deal of the philosophy of language, and has done much to shape the contemporary discussion of truth, assertion, the theory of meaning, sense and reference, proper names, abstract objects and, most importantly, realism. Dummett treats Frege via a series of topics, and in this chapter I will do the same, albeit not following the same series as Dummett, but dealing with issues that have become central in subsequent years. In the first section we will look at Dummett’s account of Frege’s distinction between sense and reference. We will then turn to the morals, relating to the shape of a theory of meaning, that he draws from this distinction. This will allow us to introduce the revisionist argument, for which he is most famous, to the effect that we should follow the intuitionists in refusing to give unqualified endorsement to the principle of bivalence. In the last sections a fundamental assumption of this argument, the primacy of sentences in an

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account of meaning, will be illuminated via a discussion of Frege’s Platonism and the role of the context principle in both Frege’s and Dummett’s thought. Dummett’s book on Frege’s philosophy of language was to have been immediately followed by a work on Frege’s philosophy of mathematics. As matters turned out, this second volume did not appear until 1991. This was in many ways unfortunate. It is impossible to treat of Frege’s philosophy of language without taking into account his philosophy of mathematics; for much of Frege’s thought about meaning, truth and reference arose out of his attempt to place mathematics on a sure epistemological foundation. It appears that in the early seventies Dummett had an integrated view of Frege’s philosophy of language and philosophy of mathematics. There are hints in Frege: Philosophy of Language and in some of Dummett’s earlier writings of an argument leading from Frege’s thought to the conclusion that the only way to achieve Frege’s general logicist aims is to adopt intuitionist logic.2 However, because Frege: Philosophy of Mathematics took so long to appear, it is only recently that Dummett’s interpreters have had the most direct version of this argument before them, and in the meantime they have had to work with only part of the picture in place. It is clear that the book on the philosophy of mathematics which ultimately appeared is not the same book as that which would have existed had it been published in 1974. It nevertheless provides some important missing pieces of Dummett’s overall understanding of Frege, and of the importance of Frege’s work for the project which Dummett calls the theory of meaning: that of making the workings of our language clear to our view.

Sense and Reference in Frege and Dummett Frege’s logicist project was to contribute to the epistemological foundations of mathematics by showing how arithmetical truths were in fact truths of logic, or, as he said, analytic. In order to do this, he had first to develop a more adequate logic than those of Aristotle or Boole which were then available. It was Frege’s great achievement in his Begriffsschrift to develop a formal language using quantifiers which enabled him to formalize sentences that involve multiple generality, such as ‘Everybody loves somebody’, and to show how sentences involving relations could be dealt with as easily as those involving one-place predicates.3 Aristotelian logic

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was based on a syntax of subject and predicate. So the logical form of the sentence ‘Dido loved Aeneas’ was obscure. Frege replaced the syntactical categories of subject and predicate with those of singular term and functional expression. In ‘Dido loved Aeneas’ there are two singular terms, either of which can be thought of as occupying a position into which other singular terms can be substituted. Deleting these terms gives the functional expression ‘. . . loves ——’. By introducing variables, to stand in the place of the gaps, and quantifiers binding these variables, Frege achieved the syntactic analysis of language familiar to anyone who has learned modern predicate logic. Frege’s understanding of the semantics of this logic was not quite the modern one, however. Most students of logic are taught that the semantic value of a singular term is an object, the semantic value of a predicate is a set, and the semantic value of an n-place relation is an ordered n-tuple of objects. Frege also thought of the reference of a singular term as an object. But the reference of a one- or many-place functional expression which results in a sentence when it is completed is, according to him, a concept, or a relation, by which he means a function from objects to the referents of sentences. Concepts are, he says, ‘unsaturated’, or ‘not selfsubsistent’, unlike objects, which are ‘self-subsistent’, or ‘saturated’ entities. The referent of a sentence was initially thought of by Frege as a ‘possible content of judgement’ (sometimes translated as ‘judgeable content’). But between 1884, when he published Die Grundlagen der Arithmetik, and 1893, when his Grundgesetze der Arithmetik appeared, he had distinguished between what he called the thought expressed by a sentence and its truth value. The referent of a sentence is thereafter taken by him to be a truth value, and he is led to distinguish between the sense and the reference of most expressions (Frege 1893/1964, pp. 6–7). The relationship which Frege took to hold between the sense and the reference of expressions is rather neatly set out in a letter which he sent to Husserl in 1891 (Frege 1980, p. 63): proposition sense of proposition (thought) reference of proposition (truth value)

proper name sense of proper name

concept word sense of concept word

reference of proper name (object)

reference of concept word Æ object(s) falling (function) under concept

{

}

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15

We will not now discuss all that might be drawn out of this schema. It is enough to note that the sense of an expression is connected by Frege with what we know when we understand that expression, while the reference is something objective, which we know through the senses of the expressions which refer to it.4 The distinction between objects and concepts is important, and later I will suggest that it has not been taken sufficiently seriously; but for the time being we will follow Dummett’s central concerns, and concentrate on the distinction between sense and reference, which is developed in greatest detail by Frege in his 1892 paper ‘On Sense and Reference’.5 Early on in chapter 5 of Frege: Philosophy of Language, a chapter devoted to sense and reference, Dummett has this to say about Frege’s project: ‘he wanted to give a general account of the workings of language . . . An account of the working of language is a theory of meaning, for to know how an expression functions, taken as part of the language, is just to know its meaning’ (Dummett 1973a, p. 83). It is open to question whether this is an accurate account of Frege’s motivation. Frege’s interest in language was stimulated by the need to construct a precise, rigorous language in which to express the fundamental principles of arithmetic, so as to be able to establish his claim that arithmetic is analytic. In developing his logic he was content if the ‘meaning we fix on is not altogether in line with the everyday use of the word’. He is concerned with a narrower region than the whole of language, for he asserts that ‘the task of logic being what it is, it follows that we must turn our backs on anything that is not necessary for setting up the laws of inference’. Indeed, he goes so far as to claim that the business of the logician is ‘to conduct an unceasing struggle against . . . those parts of language and grammar which fail to give untrammelled expression to what is logical’. What Frege wanted was to get at the ‘logical kernel’ of language, in order ‘to become aware of the logical justification for what we think’ (Frege 1979, pp. 5–7).6 Since a general account of the workings of language ought to explain the failure of language as well as its successes, not to mention complex features like metaphor, malapropism, irony and puns, Frege’s interest in language is thus narrower than Dummett’s characterization of it. On the other hand, the passage cited gives an excellent summary of Dummett’s own project. And a proper understanding of that project reveals that it is not as distant from Frege’s preoccupations as may appear at first glance. Rather than giving a general account of the workings of language, both are concerned to give an

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account of the central cognitive aspect of language which enables us to grasp, communicate and infer truths. Frege distinguished, within the meaning of expressions of ordinary language, three ingredients: sense, tone and force. It is to the first of these that Dummett pays most attention. An account of force will explain the various acts we can perform, such as asserting, asking questions and making commands. Frege was aware of the need for such an account, but did not provide a well-worked-out theory of force.7 Dummett points out that Frege’s account of tone, which he also called ‘colouring’, and which involves the literary aspects of language, is even more inadequate (Dummett 1973a, pp. 84–9). This reinforces the impression that Frege was not interested in everything that can be done with language, but only with those elements of language which are fundamental for conveying and deriving truths. Central to Frege’s mature theory of this cognitive aspect of language is the notion of sense.8 According to Dummett, ‘The sense of an expression is . . . that part of its meaning which is relevant to the determination of the truth value of sentences in which the expression occurs’ (1973a, p. 89). Frege introduced senses in order to account for the informativeness of identity statements. If we identify the meaning of a singular term with the object it picks out, then the meaning of any true identity statement will be represented as a = a, and the difference in informativeness between, for instance, ‘Cicero is Tully’ and ‘Cicero is Cicero’, will be lost. The moral of Frege’s thoughts concerning the informativeness of identity statements is, according to Dummett, that reference cannot be ‘an ingredient of meaning’ (Dummett 1973a, p. 91; Frege 1984, pp. 157–8). If to know the meaning of an expression were to know its reference, then an identity statement could not be informative. Nor, for that matter, could we understand a sentence without knowing its truth value. So we need the notion of sense as that which is grasped when someone understands an expression and that which determines its reference. The heart of an account of the way language functions will therefore be an account of what is known by someone who understands a language: ‘An account of understanding language, i.e. of what it is to know the meanings of words and expressions in the language, is thus at the same time an account of how language functions, that is, not only of how it does what it does, but of what it is that it does’ (Dummett 1973a, p. 92). As was observed above, this project which Dummett finds in Frege is one that he makes his own. Yet, despite the superficial clarity of this statement, it soon runs

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into difficulties, and is easily subject to an interpretation which Dummett comes to reject. We should note in passing that it might well be objected that Dummett skews the interpretation of the relationship between sense and reference by insisting that Frege’s arguments show that reference is not an ingredient of meaning. ‘Meaning’ is a rather confused, non-technical term which, when analysed, yields various elements.9 There is what one knows when one understands a word, but we also speak of an object being meant when it is indicated by a gesture. There is also what Grice calls ‘natural meaning’, which we attribute to spots and clouds, which can mean measles or rain (Grice 1957). Frege’s arguments could be taken to show that there are various aspects, or elements, of meaning: force, tone, and, most importantly, sense and reference. Sense is known by competent speakers and is a way of being given a reference. Reference is not fully known, but is known only via a sense. In claiming that reference is not an ingredient of meaning, Dummett seems to be assuming that ‘meaning’ is to be understood as what is known when we understand a word. Since Frege’s arguments show that reference need not be (fully) known, reference cannot be an element of meaning. It would be equally possible to read Frege as attempting to disambiguate the vague term ‘meaning’ by pointing out that there are at least two elements to linguistic meaning: what is known, which is the sense of an expression, and what is standardly indicated, which is its reference, and will not in general be fully known. While I prefer this reading of the relationship between sense and reference in Frege, and will allude to it later, Dummett’s way of thinking of the relationship does not, so far as I can see, make a material difference to his argument. According to Frege, the sense of a complex expression is, as Dummett puts it, ‘compounded out of the senses of its constituents’. In providing his analysis of the syntactic structure of language, and paving the way for the later development of the standard truthconditional semantics, Frege’s work was important for the development of model theory and for Tarski’s recursive definition of truth.10 In a seminal paper of 1967, Donald Davidson argued that a truth theory for a language, of the kind Tarski showed us how to construct, can serve as a theory of meaning (Davidson 1967/85). Davidson described his project as that of showing that we do not need to use intensional vocabulary such as ‘sense’ or ‘meaning’ in order to construct a theory of meaning; all we need is a theory of reference.11 But Dummett argues that, in fact, a meaning-theory which states the

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truth conditions of all the sentences of a language, by providing a finitely axiomatized recursive method for deriving those truth conditions, can serve to show what it is that is known by a speaker of that language. In showing what is known by a speaker, it can, under certain conditions, play a central role in the theory of meaning, and will then effectively provide a theory of sense. The extra conditions must include, at a minimum, an account of the connection between the concepts of truth and falsity which occur in the meaning-theory and the use that is made by speakers of utterances of those sentences. In this way, Dummett manages to marry the truth-conditional account of meaning found in Frege to Wittgenstein’s claim that (for a large class of cases) ‘the meaning of a word is its use in the language’ (Wittgenstein 1967a, p. 20e). Wittgenstein’s identification of meaning with use is linked to his rejection of the view that meanings are private mental items. The consequent demand that meanings are publicly manifestable uses of words has been called ‘the manifestability constraint’. In the next chapter we will examine its justification. For the time being it is enough to state it. It should be noted that the usage that Dummett has come to adopt is one according to which a theory of meaning is a general account of the workings of language, while a meaning-theory is a Tarski truth theory which delivers biconditionals of the form S is true if and only if p

where S is a place-holder for a name, in the meta-language, of a sentence of the object language, and p is a sentence of the metalanguage, the language in which the truth theory is formulated. Despite the considerable differences which, as we will later see, exist between Dummett and Davidson over the role of the construction of a meaning-theory in a theory of meaning, Dummett continues to find Davidson’s ideas fruitful. Summarizing them in 1991 he says: The task of a theory of meaning is to give an account of how language functions, in other words to explain what, in general, is effected by the utterance of a sentence in the presence of hearers who know the language to which it belongs. . . . The notion of meaning need not, therefore, play any important role in a theory of meaning; if it does, this will be only because a connection is set up between the meaning of a sentence and our employment of it . . . I use the phrase ‘the theory of meaning’ as coordinate with ‘the theory of knowledge’ to designate a branch of philosophy . . . To distinguish this from what

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Davidson and others speak of as ‘a theory of meaning’ . . . I shall use for the latter the expression ‘a meaning-theory’. I am in agreement with Davidson that the correct methodology for the theory of meaning is to enquire into the general principles upon which a meaning-theory is to be constructed. (Dummett 1991e, pp. 21–2)

A meaning-theory is therefore only part of the theory of meaning. It needs to be enriched with a theory of sense, which explains what a knowledge of a meaning-theory consists in; a theory of force, which explains the capacity to use the language to ask questions and deliver commands, etc.; and, ultimately, a theory of tone, to account for metaphor and other literary devices. Important differences over the role of a meaning-theory in the theory of meaning divide Dummett and Davidson. They will be the subject of chapter 5, but they are rooted in an ambiguity in the Fregean notion of sense. Sense is both what is known by someone who understands an expression and something objective, but, since each speaker has a partial and idiosyncratic grasp of the language, these two features of sense pull in opposite directions. The observation that individual speakers differ with regard to their understanding of a language is taken up by Dummett immediately after his introduction of the notion of sense. Different people who understand proper names or general terms may determine their referents in different ways. Dummett uses the example of the river Thames. One person may think of the Thames as the river that flows out to sea east of London, another may understand the name as that of the river that flows through Oxford. Although anyone who understands the name must know something which is sufficient (perhaps only with the aid of further information) to identify the referent, there is no one piece of uniquely identifying information that anyone who understands the name ‘the Thames’ must know (Dummett 1973a, pp. 96–104).12 We might take this as evidence that sense is, after all, a subjective notion. But Dummett points out that, as soon as we are asked to justify the statements that we accept as true, we will attempt a reconstruction and systematization of the relevant part of language. We will try to fix the sense of the expressions involved so as to be able to determine precisely the conditions under which sentences containing them are true and our justification for believing them (Dummett 1973a, pp. 104–5). He then says: ‘The notion of sense is thus of importance, not so much in giving an account of our linguistic practice, but as a means of systematizing it.’ Eighteen years later he makes a similar

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point by considering the possibility that someone might claim to understand a logical law without being able to provide any justification for it. Simply knowing how to apply a rule, without any grasp of the point and justification of that rule, is not understanding. Although the ordinary speaker does not know the meanings of the logical constants ‘and’, ‘if then’, etc., in the sense of being able to provide the sort of precise account that it is the task of a meaningtheory to provide, still, in so far as we understand what we say, we must have some conscious grasp of those meanings: ‘Fully to know what one says is to command a completely clear view of the working of the language. . . . to achieve the level of understanding that we ordinarily have of our own utterances, some inchoate conception of what gives them significance and determines their content is needed’ (Dummett 1991e, p. 208). So sense is something of which we have only an inchoate grasp, and the project of making this inchoate understanding precise is very much the project on which Frege was engaged when he attempted to clarify our ordinary use of expressions like ‘There are nine apples in the basket’ or ‘Nine is greater than five’, in order to show what their content is and what kind of justification we can have for making them. It is important to keep this in mind, in order to head off a misunderstanding of the project which Dummett takes to be his own, and which he finds in Frege’s work. When he speaks of ‘a general account of the workings of language’, it is easy to hear him as speaking of an empirical, descriptive account of the way language functions, which would explain how we do what we do when we speak, by constructing a model of the psychological mechanism responsible for speaking and understanding. It then becomes deeply puzzling how such an account can lead to the sort of normative conclusions which he draws. But this is to misconstrue his project. Or, perhaps one should say, it is, according to Dummett, to misconstrue at a fundamental level what is involved in the project of making the workings of a language clear to view. In the 1970s Dummett often used to speak of implicit knowledge of a theory of meaning (by which he meant what he would now call ‘a meaning-theory’). Indeed, he claimed that a meaning-theory can be ‘thought of as an object of knowledge on the part of the speakers’ (Dummett 1978d/93d, p. 100). These phrases can be extremely misleading, and when interpreting them, it is important to keep in mind that Dummett does not believe that by speaking of knowledge, implicit or otherwise, he is providing a causal explanation of the workings of a language:

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The theory of meaning has, as its task, to explain what language is: that is, to describe, without making any presuppositions, what it is that we learn when we learn to speak. The fact that the use of language is a conscious rational activity – we might say the rational activity – of intelligent agents must be incorporated into any such description, because it is integral to the phenomenon of the use of human language. But it also affects the phenomenon itself . . . A meaning-theory should not, therefore, aspire to be a theory giving a causal account of linguistic utterances, in which human beings figure as natural objects, making and reacting to vocal sounds and marks on paper in accordance with certain natural laws. We have no need of such a theory. We can, in general, make some unfamiliar human activity – say a social function or ceremony – intelligible without either circularity or anything resembling a causal theory. (Dummett 1991e, pp. 91–2)13

Because speaking and understanding a language is a conscious rational activity, ‘It is . . . unreal to maintain a sharp distinction between the practice of speaking a language and the construction of a theory of its working’ (Dummett 1973a, p. 106; see also pp. 458 and 463). We already have an inchoate grasp of the notions of truth, and of meaning, as well as of the senses of ordinary words, and we make use of this grasp in the practice of speaking. It is important to remember, in reading Dummett, his deep commitment to the fundamental dictum of analytic philosophy as he understands it. This is the dictum that the way to an account of thought is through an account of language. The connection between this dictum and Dummett’s use of the notion of implicit knowledge is made particularly clear in the following passage: We communicate thoughts by means of language because we have an implicit understanding of the working of language, that is of the principles governing the use of language; it is these principles which relate to what is open to view in the employment of language, unaided by any supposed contact between mind and mind other than by the medium of language, which endow our sentences with the senses they carry. In order to analyse thought, therefore, it is necessary to make explicit those principles, regulating our use of language, which we already implicitly grasp. (Dummett 1975a/78c, p. 442)

The task, therefore, is to attempt to clarify principles that are already implicit in language, and which we use in interpreting, criticizing and making sense of the speech of others.

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Because Dummett speaks of speakers’ knowledge of language, it may appear that his way of thinking about meaning conflicts with Putnam’s arguments to the effect that meanings are not in individuals’ heads, and that there is a linguistic division of labour. Putnam has argued convincingly that an individual can use a general term – for instance, ‘alder’ – to refer to alders even if they have no way of distinguishing alders from poplars. Each of us can rely on the existence of experts who can make the necessary distinctions when we use technical vocabulary (Putnam 1975, pp. 245–9). But one need not read Dummett in a way that conflicts with Putnam. The principles to which Dummett is referring are implicit in our use of language, thought of as a social phenomenon, rather than implicit in the minds of speakers. He accepts Putnam’s contention that there is a linguistic division of labour, and so the existence of such a division is among the principles governing the functioning of language that we implicitly recognize (Dummett 1991e, pp. 83–6, 105–6). Nevertheless, Dummett’s talk of implicit knowledge of a meaning-theory, even when it is carefully expressed by others as implicit knowledge of the truths that a meaning-theory states, tends to suggest a view such as Chomsky’s, according to which we have implicit knowledge of a universal grammar.14 For Chomsky, knowledge of grammar is already unconsciously in each of us, and this knowledge accounts for the mechanism of learning a language. It has turned out, however, even in the case of grammar, to be extremely difficult to explain what justifies the attribution of implicit knowledge of a set of rules, and how having such knowledge differs from simply behaving in accordance with that set. Chomsky is happy to give up metaphorical attributions of ‘knowledge of language’ and to begin with the study of the individual, internal cognitive systems of speakers, using ordinary scientific methods to discover generalizations relating to such systems (Chomsky 1995, pp. 13–18). But Dummett, as we have seen, resists such a move. If one is interested in giving a description of the process of thought, the introduction of internal systems, or idiolects, along Chomsky’s lines seems almost unavoidable. It is simply implausible to claim that in the linguistic behaviour of each of us there is already a definite systematization of the language which irons out our idiosyncratic inconsistencies and partial understandings of words so as to delimit a single precise linguistic sense. There is substantial empirical evidence that most people are very bad reasoners. Many people (perhaps all) hold contradictory beliefs, and the knowledge which individuals have concerning the referents of

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the terms they use is often not uniquely identifying (Kripke 1980; Stich 1985). Even if there were a coherent systematization of one speaker’s usage, it is highly improbable that it would correspond to the systematization implicit in any other speaker’s usage. So Chomsky’s project naturally leads back to a mentalistic account of meaning, which both Frege and Dummett want to resist. Dummett’s view, by contrast, is that we should be interested not in the psychological processes of understanding, but rather in what is grasped. It is only by looking at language as a social phenomenon that we can start to characterize this and to fix definite senses for words. Yet even at the social level, the use of the expression ‘implicit knowledge’, when conjoined with the view that sense systematizes language, seems to imply commitment to a view which has been shown empirically to be false. This is that the ordinary use that we make of words is already implicitly coherent. What Dummett is saying, however, is not that coherent sense is already implicit in the language, but that it is implicit in the way we use language that one important aim of language is to make coherent sense of the world. At the same time, in order to bear this aim in mind, we need to be able to represent to ourselves what would count as coherent sense. It is the task of a semantic theory which justifies our logical practice to develop such a representation (Dummett 1976e/93d, pp. 64–5). If we understand him in this way, then Dummett’s theory of meaning is partly a theory of what we mean in the sense that is captured by one’s being prepared to say, ‘That is not what I meant’, when an interlocutor shows one that what one actually said was incoherent. Given that this is the right way to represent the relationship of our ordinary usage to a theory of sense, Dummett’s revisionist argument for the adoption of intuitionistic logic would come out as the claim that we have misrepresented to ourselves what counts as a coherent representation. We think that a representation which is constrained by classical logic will be coherent; but, among other things, Russell’s discovery of the set-theoretic paradoxes shows that, once we move to a language which involves quantification over essentially infinite domains, this is not the case. In order, then, to better represent to ourselves the implicit aim of our practice, we ought to revise our logic. But emphasizing this aspect of Dummett’s position reveals a certain tension within it. For, on the view sketched, it would make no sense to claim that ordinary speakers already knew the systematized language that their confused practice was implicitly aiming towards. Yet Dummett does seem to

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assume that speakers must know the meanings of the words they use, and be able to manifest this knowledge in the use that they make of them. The questions just broached will be a major preoccupation of this book and we will return to a direct discussion of the social character of meaning in chapter 5. For now it is enough to recognize that Dummett believes that we can go some way towards displaying the senses of the expressions of a language by constructing a meaningtheory for it. Such a meaning-theory will be more than a theoretical representation of the practical ability we call knowing a language. It will represent the knowledge that is essential to the special kind of activity that is knowing a language.15 It will not by itself be a theory of meaning, since we have not only to say what it is that a speaker must know in order to know a language, we must also say how such knowledge can be manifested. This requirement, that a knowledge of truth conditions can be manifested, is one which Dummett believes leads to a plausible argument for revisionism (Dummett 1979c/93d, pp. 115–16). In order to lead into this argument, we need to discuss briefly the connected notions of truth and assertion.

Truth, Assertion and the Central Argument against Bivalence To some readers who are superficially acquainted with Dummett’s views, the foregoing description of Dummett’s enterprise may be surprising. For it often seems as though he is proposing that we adopt a verificationist theory of meaning as an alternative to a truthconditional account.16 In part, this characterization is just, for this is a question on which Dummett has changed his views – or, perhaps more accurately, it is a question on which he has revised his manner of expressing his views. The relatively early paper ‘Truth’ points out that we manifest our understanding of the logical operators by using them, and that we learn them by being trained in their use. Its conclusions are summarized in the following passage: ‘We no longer explain the sense of a statement by stipulating its truth-value in terms of the truth-values of its constituents, but by stipulating when it may be asserted in terms of the conditions under which its constituents may be asserted’ (Dummett 1959c/78c, pp. 17–18; italics original). This suggests that instead of making truth conditions central to the

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theory of meaning, we take assertion conditions or verification conditions as central.17 However, when the replacement of truth by warranted assertibility is combined with the thought that a meaning-theory with the structure of a Tarski truth theory shows how the truth conditions of more complex sentences can be derived from a finite specification of the simple elements of a language, we end up with the rather unpromising enterprise of deriving biconditionals of the form S is warrantedly assertible if and only if p

where, as before, S is a place-holder for a name in the meta-language of a sentence of the object language, and p is a sentence of the meta-language. The enterprise is unpromising because such biconditionals are, on their most obvious interpretation, false. Our understanding of warranted assertibility implies that sentences may be warrantedly asserted even though what they say is not the case. And this may be taken to imply that, once we have adopted a truth theory as the core of a theory of meaning, we are inevitably committed to classical logic. Various responses to this observation are possible, but the issues raised are complex and can be avoided by restating the conclusion.18 In order to skirt this difficulty, in 1978, when ‘Truth’ was reprinted in Truth and Other Enigmas, Dummett had decided that the conclusion of that paper should be stated not as rejecting the explanation of meaning in terms of truth conditions, but rather as giving an account of the notion of truth (1978c, p. xxii). The argument found in the early paper remains of central importance, however, and is developed at greater length in Frege: Philosophy of Language (1973a). As Dummett himself pointed out in 1978, the structure of the early paper was somewhat confusing, for it involved the rejection of an argument against bivalence which Dummett deemed at that time to be shallow, as well as a sketch of a deeper argument.19 The ‘shallow’ argument against bivalence occurs in Strawson’s discussion of sentences which involve singular terms that fail of reference (Strawson 1950, 1952). In order to account for the truth conditions of sentences which contain non-denoting singular terms, Russell had argued that sentences like ‘The current Prime Minister of England is hirsute’, which appear to have the simple subject– predicate form Fa, as does ‘Tony Blair is hirsute’, in fact have the more complex logical form $x ((Fx & Gx) & "y (Fy Æ x = y))

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Strawson had objected to Russell’s description theory that such sentences have the logical form they appear to have, and so involve singular referring expressions, but that we use such sentences on the presupposition that the singular terms that we use have a reference. Where this presupposition fails, we have uttered a sentence which is neither true nor false.20 If we allow that some statements are neither true nor false, we deny the semantic principle of tertium non datur, that no statement is neither true nor false.21 It is this argument which Dummett deemed, at this stage, to lead to a shallow reason for rejecting bivalence. One might take a quick line against the rejection of the principle of tertium non datur. Rejecting this principle seems to imply acceptance of the truth of some instance of ÿ (p ⁄ ÿp), but this is equivalent (even in intuitionistic logic) to ÿp & ÿÿp, which is a contradiction. It is for this reason that intuitionists, who refuse to assert the principle of bivalence, and who therefore do not accept that every sentence is either true or false, nevertheless do not reject tertium non datur. That is to say, they do not assert that some sentence is neither truth nor false. Alternatively, one can avoid this quick line of objection to the rejection of tertium non datur by introducing a third truth value, which one might designate by means of *. Then, when a meaningful atomic proposition p is neither true nor false, it will have this third truth value.22 The semantic principle of tertium non datur will not be true, but also, although ÿ (p ⁄ ÿp) will still imply ÿp & ÿÿp, this will not be a genuine contradiction, for when p has the value *, ÿp & ÿÿp will also have the value *. Dummett therefore took a longer route against the rejection of tertium non datur. This was intended to show that the intuitionist refusal to accept bivalence had deep metaphysical implications which were not shared by the advocate of three-valued logic who rejects tertium non datur. First he asked about the point of categorizing certain sentences as neither true nor false, and how our categorizing them thus would show up as requiring a different use from our categorizing them as false. A statement is either correct or incorrect. Here there is no place for a third option. In this regard, an assertion is different from a conditional bet. If two people make a conditional bet, such as ‘If Essendon gets into the final, it will win’, there are three possible outcomes. Either one or the other wins the bet; or, in the case where Essendon does not get into the final, the bet is off. Dummett often uses examples of this kind to illustrate what would be required in order for there to be a third option in the case of assertion

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(1959c/78c, pp. 8–10; 1973a, pp. 341–2). But in the case of assertion, and in the case of conditional assertion discussed in Frege: Philosophy of Language, we need to introduce a third truth value, not because there is a definite third outcome of the assertion of a sentence, but in order to give an account of the way in which certain simple sentences behave in more complex sentences (Dummett 1959c/78c, pp. 12–14; 1973a, p. 347). To say ‘The king of France is bald’ when there is no king of France is to mislead, and thus to say something incorrect. The pressure to say that it is neither true nor false comes from the fact that ‘The king of France is not bald’ is just as misleading. In order to give a uniform account of negation, we need to introduce a third truth value, and doing so allows us to escape the quick line of objection to the rejection of tertium non datur discussed above. From the point of view of the use that is made of sentences, however, a sentence’s having the value * amounts to a species of incorrectness or falsity. Early on, Dummett took such objections to the principle of bivalence to be relatively shallow, because the third truth value introduced is unrelated to the use that we make of sentences when used on their own to make assertions. At that time he argued that ‘every other feature of meaning must consist in its contribution to what is conveyed by the utterance of some complete sentence’ (Dummett 1973a, p. 449).23 We can see underlying this an adherence to a version of Frege’s context principle, which makes the sentence the primary linguistic unit, interpreted in the light of Wittgenstein’s critique of ostensive definition, which reinforces the idea that the sentence is the smallest unit with which one can make a move in the language game (Wittgenstein 1958, pp. 1–3).24 Dummett argued that because our use of complete sentences is primary, it is by concentrating on the notion of truth for them that we will be able to satisfy the manifestability constraint introduced above. That constraint entailed that our account of truth should enable us to show how a knowledge of truth conditions can be manifested. It was from this that Dummett’s ‘deeper’ argument for the rejection of bivalence began. This argument has two distinct elements. The first is the claim that if we are to give an account of meaning in terms of truth conditions, we will need a notion of truth that is more substantive than that provided by the redundancy theory. The redundancy theory says that the complete explanation of the meaning of ‘is true’ is captured in the equivalence ‘p’ is true iff p. The second is that the substantive notion of truth that can turn the trick of providing an account of what it is to manifest a grasp of truth conditions will be

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one according to which the truth of a sentence is to be explained in terms of some kind of potential verifiability. The first element of the deeper argument makes a point which ‘is so evident as to leave hardly any room for supporting arguments’ (Dummett 1978c, p. xxi). If we are to give an account of meaning in terms of truth conditions, then we cannot accept that the equivalence thesis gives the whole of the meaning of ‘true’.25 The equivalence thesis states that for any sentence which says that p, ‘p’ is equivalent to ‘It is true that p’. This is a thesis to which Frege subscribes when he claims that ‘It is true that I smell the scent of violets’ means the same as ‘I smell the scent of violets’ (Frege 1984, p. 354). In order for an instance of the equivalence thesis to be illuminating with regard to the meaning of the word ‘true’, one needs to understand what it means to assert ‘I smell the scent of violets’. This is particularly clear when one thinks of a Tarski truth theory which enables one to generate instances of the equivalence thesis of the form S is true if and only if p

For here we have a name of an object language sentence and a sentence of the meta-language, and unless we can already recognize that the object language sentence referred to means the same as the sentence of the meta-language that is used on the right-hand side, this will be completely unenlightening as to the meaning of the word ‘true’. In the case where the meta-language is not an extension of the object language, this is not trivial. In the case where the meta-language is an extension of the object language, we take our understanding of the sentence substituted for p for granted. But, if the whole of our understanding of the word ‘true’ consisted in our grasp of such equivalences, it would be circular to explain our grasp of the meaning of the sentence substituted for p by saying that we grasped its truth conditions (Dummett 1973a, p. 458; 1978c, pp. xx–xxi). In order to illustrate the need for a substantive theory, Dummett often introduces an analogy between giving an account of truth and giving an account of what is entailed in winning a game. One could give a formal description of the game of whist, outlining the rules and what constitutes taking a trick. Then one could describe a player who fails to take any tricks as winning a misere hand, while a player who takes all the tricks wins an abundance hand. For a person who did not yet understand the concepts of winning and losing, such a description would be indistinguishable from one which described a player who fails to take any tricks as losing a

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misere hand, while a player who takes all the tricks loses an abundance hand. It would not yet tell them what the aim or point of the game was, what a player was supposed to attempt to do in order to succeed. Similarly, a truth theory does not tell us what the point is of calling a sentence ‘true’. Part of the point of calling a sentence ‘true’ involves the close connection between asserting a sentence and asserting that it is true. This connection is captured by the equivalence thesis; but when it is captured in this way, we make the connection look less general than it is, for it is not something specific to a particular language, but something common to the notion of truth in any language (Dummett 1973a, p. 462). When we come to the second element of the deeper argument, and consider what is required of a substantive notion of truth, Dummett suggests that there are two important, intuitively plausible theses concerning truth which ought to be recognized. The first captures what is right in the correspondence theory, and although Dummett sometimes introduces it as a realist thesis, it is in fact a regulative thesis which he takes to be central to any notion of truth (1976e/93d, p. 52; 1991e, pp. 327–9). This is the thesis C, that ‘If a statement is true, there must be something in virtue of which it is true.’ This principle is sometimes called the truth-maker principle, and is held in common by Dummett and many committed realists. The second thesis is likely to be less widely agreed on. It is K, that ‘A statement cannot be true unless it is in principle possible that it be known to be true.’ Nevertheless, if we give a generous enough account of the in principle knowability of a statement, this second thesis falls out of the first.26 If there is something in virtue of which a statement is true, then it must in principle be possible for some creature, no doubt with capacities far outstripping ours, to recognize that this condition obtains (Dummett 1973a, pp. 464–6; 1976e/93d, pp. 60–2). If the knowability requirement is not to be devoid of content, however, the capacities in question must be in some sense analogous to ours. It is thus that we come to the conclusion that truth will have to be cashed out in terms of potential warranted assertibility. If the connection between truth and assertion is to be maintained, then one can justifiably assert that a sentence is true if and only if one can justifiably assert the sentence. If the knowability thesis is to be respected, one can justifiably assert a sentence if and only if there is something in virtue of which it is true, and hence it is knowably true. But, as soon as the realist endorses unrestricted bivalence, and acknowledges the existence of undecidable sentences, we will have instances of p ⁄ ÿp which will be claimed by the realist to be true, even though it is not possible

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to know which disjunct is true, or, therefore, to know in virtue of what the disjunction is true. Three distinct cases in which such a situation may arise are subjunctive conditionals, undecidable statements about the distant past or the future, and when we have quantification over an infinite domain. As should be clear from this discussion, Dummett’s characterization of realism makes the truth conditions of sentences, rather than the existence of objects, the central point of contention. Some commentators have found this feature of Dummett’s argument puzzling, and, as we will see, there are difficulties associated with it which Dummett himself has implicitly acknowledged. These difficulties are associated with the plausibility of the context principle when interpreted as it appeared to be in Dummett’s early works. In the next section we will look at Dummett’s characterization of Frege’s Platonism. This discussion will help to demonstrate the strengths and weaknesses of his early way of understanding the contrast between realists and anti-realists. It will also make explicit the connection between Dummett’s argument for anti-realism and Frege’s context principle. The context principle makes the truth of sentences primary in the explanation of the meanings of the parts of sentences. It was, therefore, in virtue of his adherence to this principle that Dummett distinguished between deep and shallow reasons for rejecting bivalence. As we will see below, Dummett now despairs of making this distinction precise, and this in turn throws some doubt on the tenability of the context principle. For the time being, however, we need to understand the part that it has played in his understanding of the issues which divide realists from anti-realists.

Frege’s Platonism The claim that Frege is a Platonist has been one of the more controversial aspects of Dummett’s interpretation of Frege’s philosophy. It needs to be discussed in some detail, because the argument for anti-realism that we have just sketched is often presented as an argument that was initially developed by intuitionists against Platonism in mathematics, but which may be capable of being extended to other cases. In this section we will distinguish between varieties of Platonism. The following section constitutes something of a digression. It takes up Sluga’s critique of Dummett’s claim that Frege is a Platonist, and argues that it rests on a misunderstanding of the variety of Platonism attributed to Frege by Dummett. In the

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last section of the chapter we turn to a direct discussion of the interpretation of the context principle and the consequences to be drawn from it concerning existence in general, and the existence of abstract objects in particular. There is considerable confusion in the literature as to what Platonism consists in. Hartry Field, for instance, defines Platonism as ‘the doctrine that there are mathematical entities and that they are in no way mind dependent or language dependent’ (Field 1990, p. 214). But a definition of this kind only raises a host of questions. What do we mean when we say that there are mathematical entities? Famously, Quine has claimed that to be is to be the value of a variable, by which he means that we are committed to the existence of the entities that we quantify over (Quine 1961a, pp. 12–15; Hookway 1988, pp. 19–25). It is undeniably the case that when we do naive mathematics, we quantify over numbers, functions, sets, relations, groups and many other mathematical entities; so, from this point of view, we would seem to be committed to recognizing the existence of mathematical entities, though they might be language- or mind-dependent. Now it might be thought that the very fact that Quine’s dictum decides the issue of our commitment to mathematical entities so quickly shows that there is something wrong with it. And indeed, Quine does not want it to be read as implying that everything that confused folk quantify over exists. Philosophers have often followed ordinary usage and quantified over meanings and properties, but Quine does not accept that there are such things. To capture Quine’s view, one should say, rather, that we should take ourselves to be committed to the existence of the objects which are values of the variables of the first-order quantifiers occurring in a scientifically adequate language. Here a scientifically adequate language quantifies only over genuine entities – that is to say, objects for which we can give precise identity conditions and which cannot be eliminated. In Frege: Philosophy of Language, Dummett argues that, in relation to ontological commitment, Frege anticipated Quine’s general outlook. For Frege, as for Quine, ‘the ontological commitment embodied in a language depends upon its quantificational structure, as revealed by logical analysis’ (Dummett 1973a, p. 480). At the same time, Frege differs from Quine in accepting second-order quantification and the entities quantified over, concepts. For the time being, this difference need not trouble us, for Frege also insists that numbers are objects, and so fall within the range of the firstorder quantifiers. So we can follow Dummett and discuss Frege’s

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Platonism as an issue which involves the existence of abstract objects such as numbers. A Platonism based on the Quinean criterion of existence, we will call ‘minimal Platonism’. The minimal Platonist says that mathematical objects exist because entities of that kind have to be introduced as the values of first-order variables in any acceptably austere adequate science. An acceptably austere adequate science is any theory which has sufficient explanatory and predictive power and a sufficiently small ontology. Of course, this leaves room for debate over the actual ontology required. As we will see below, this definition will need some fine tuning, but for the time being it will suffice. There are other forms of Platonism besides minimal Platonism. Field, for instance, rejects Platonism because, since there are no causal connections between us and the abstract mathematical objects that the Platonist believes in, the Platonist has no adequate explanation of our knowledge of mathematical truth.27 Now, it would be open to a Platonist to deny this claimed lack of causal relations in two ways. One would be to assert that there are, in fact, causal relations between us and mathematical objects. The other would be to give an explanation of our knowledge of mathematical truth in terms of the existence of causal relations between us and some entities which are not objects (for instance, Fregean concepts). Call the first of these alternatives ‘extreme causal Platonism’, and the second ‘moderate causal Platonism’. According to the first, mathematical objects exist, and our knowledge of mathematics depends on the existence of causal relations between us and those objects. I know of no one who has adopted such extreme Platonism. Numbers cannot be seen or felt; they have no effects, and are not usually thought to be entities that can enter into causal relations with us. However, the more moderate causal Platonism may be tenable. It is not completely absurd to think of truths about mathematical objects as definitionally reducible to truths about complex properties which can be instantiated by physical systems. If these properties of physical systems are themselves physical entities which can, when instantiated, be causes (a controversial assumption), then we could explain how we are caused to know simple mathematical truths which provide the basis for the deduction of more complex truths. An advantage of such a view is that it coheres with the centrality of mathematics in physical science.28 To adopt it would be to treat mathematical entities as in some sense ‘actual’, to use the term that Dummett uses to translate Frege’s ‘wirklich’. This, however, is not a version of Platonism that can be attributed to

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Frege, though something like it may be justifiable from his point of view. Frege spends a good deal of time in the Grundlagen §§21–5 showing that number cannot be a property of external things. Inter alia he asserts that number applies to ideas and concepts as well as to physical things, and since ‘It does not make sense that what is by nature sensible should occur in what is non-sensible’, numbers cannot reduce to sensible (or physical) properties (Frege 1884/1950, p. 31). He also says quite clearly that numbers are not actual. This leaves him with the difficulty of explaining how we can come to know mathematical truths and what role, if any, mathematical objects play in our acquisition of this knowledge. A more usual form of extreme Platonism gives up on ordinary causal mechanisms, and introduces some special form of mathematical intuition. It postulates quasi-causal relations between mathematical objects and the people who know mathematical truths. This was probably Plato’s view, and it seems to have been Gödel’s.29 The relationship between the mathematician and abstract entities is thought of by analogy with perception, and although no physical causation is thought to be present, the way in which abstract objects are conceived of as affecting the non-physical mind is a quasi-causal one. There are intimations of this position in Frege’s writing. When he speaks metaphorically of the mind grasping thoughts, he seems to be thinking of our relationship to abstract objects in terms of a version of such a quasi-causal model (Frege 1984, pp. 369–71). But it is somewhat anachronistic to read back into Frege’s early views about mathematical objects his later comments on the objectivity of thought. There is also much to suggest that Frege was committed, rather, to the view that there are mathematical objects, but we know about them only through logical reasoning or through what he sometimes calls ‘the logical faculty’.30 So it is reasonable to overlook these metaphorical passages and to assume that Frege was not an extreme Platonist. This, as we will see, accords with Dummett’s interpretation of Frege’s commitment to the existence of mathematical objects.31 The Platonism that Dummett finds in Frege is close to minimal Platonism. Minimal Platonism takes truth for sentences as primary, accepts as true a sufficiently austere adequate theory, and then accepts that the entities quantified over exist. From this point of view, questions about how mathematical objects affect us and result in mathematical beliefs are deemed misguided. We discover the truth of mathematical sentences through ordinary methods of proof (or whatever else convinces us of the truth of mathematical propositions), and

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there is nothing more to be said about our knowledge of the existence of mathematical entities other than that they are quantified over in sentences which are justified in this way. In the writings of Davidson and Quine this is the general view taken of the existence of the objects referred to in a language (Davidson 1977/85; Quine 1994). The truth of sentences is taken to be primary, and the objects referred to are just those things required in the domain of quantification as values of variables. As we saw above, an advantage of this view is that the truth of sentences can be connected to the practice of assertion, and so an account of the manifestability of a grasp of truth conditions becomes possible. A rather natural thought is that physical and abstract objects must be disanalogous. Even if one admits that mathematical entities exist and are, in this respect, like physical objects, they differ from physical objects in that in the case of sentences about physical objects, causal relations with the objects quantified over have a central role in the determination of the truth of sentences. Extreme Platonism might be thought to take the analogy with our ordinary ways of thinking of truth about the material world too seriously. We think of physical entities as existing independently of us, and of the truth of sentences as being determined by the way things are with those entities (and the language). When we perceive things, they themselves cause us to form beliefs, some of which are true, and if mathematical objects exist, they too must be thought of as affecting us in some way. Because numbers are quite unlike this, extreme Platonism is an unattractive doctrine. But the faults of extreme Platonism do not affect more minimal Platonisms which allow us to say that certain objects exist, but not in quite the same way as physical objects. Nevertheless, as we will see below, once we have given up the idea that there are causal relations between us and abstract objects, and have accepted that we know them through the intellect, there is some pressure to say that abstract objects do not exist completely independently of the mind. So far, we have considered Platonism as a view about entities. Yet, as we have seen, Dummett is of the opinion that, at least when it is a question of the existence of abstract objects, Platonism is essentially a view about truth. He suggests that for the Platonist, ‘mathematical statements are true or false independently of our knowledge of their truth values’, and that truth in mathematics is understood by analogy with physical truth (Dummett 1978a, p. 202). This looks as though it expresses the view that I have called ‘extreme Platonism’. But the analogy with physical truth can be

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taken more or less seriously. So, although Frege certainly appeals to the analogy between the objects of mathematical science and the objects of a physical science like astronomy, there are, according to Dummett, features of his views about the existence of mathematical objects which make his position similar to that of the minimal Platonist (Dummett 1978a, pp. 212–13; Frege 1884/1950, p. 37). Mathematical objects exist objectively, but they are not wirklich, which is to say, they are not part of the causal realm. Central to Dummett’s reading of Frege is his interpretation of the context principle. According to Dummett’s initial interpretation of the context principle, a commitment to the existence of abstract objects, such as numbers, falls out of the analysis of the truth conditions of sentences. In contrast to Quine, who would prefer a complete nominalism, and who is forced to admit the existence of sets with regret, Dummett draws the conclusion that there is nothing problematic about the existence of abstract objects. Although Dummett is known for his sympathy towards anti-realism, it is important to recognize that nominalism is a form of anti-realism that seems never to have tempted him. Indeed, he suggests that nominalism is really a crude mistake which results from failing to appreciate the context principle (Dummett 1991d, p. 183; 1956a/78c, p. 32). In Frege’s writings the context principle is enunciated as one of three fundamental principles which are laid down in the introduction to the Grundlagen. The first is to separate the psychological from the logical, the third is not to lose sight of the distinction between concept and object, and the second is ‘never to ask for the meaning of a word in isolation, but only in the context of a proposition’ (Frege 1884/1950, p. x). The principle justifies the method that Frege uses to tell us what numbers are; this method amounts to giving us the truth conditions for an identity statement, ‘The number N = the number M’. In a 1967 paper, ‘Platonism’, unpublished until 1978, Dummett interprets this as showing that for Frege, once we have laid down the truth conditions for mathematical sentences, we are committed to recognizing the singular terms of those sentences as referring to objects, and so: if an expression functions as a singular term in sentences for which we have provided a clear sense, . . . then that expression is a term (proper name) and accordingly has a reference: . . . So, then, to assert that there are, e.g., natural numbers turns out to be to assert no more than that we have correctly supplied the sentences of number theory with determinate truth conditions. (Dummett 1978a, p. 212)

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Although the emphasis here is on singular terms rather than quantifiers, this is substantially the same as the position that I have been calling minimal Platonism. When it is asked how we determine what counts as a singular term, the answer suggested by Dummett involves the relationship between such expressions and statements of generality involving quantification (Dummett 1973a, pp. 54–80, 477–8). But it is questionable whether such minimal Platonism really captures the realism that Frege espouses, as Dummett is aware (Dummett 1973a, pp. 498–9). This raises a series of complex questions which will be dealt with below. In particular, Dummett, in the 1967 paper, makes the rather cryptic comment that the implications of having to attribute to Frege such a minimal Platonism are ‘far more constructivist than is usually understood’ (Dummett 1978a, p. 213). It was only in 1991 that he filled out this hint in his Frege: Philosophy of Mathematics. There he suggests that Frege would have done better to have thought of existence for numbers as potential constructibility. But, before discussing this in detail, it is worth stepping back to take account of a general objection to attributing Platonism to Frege. We will then turn to a detailed account of Dummett’s interpretation of the place of the context principle in Frege’s thought and in philosophy in general.

Frege’s Kantian Connections Dummett’s book Frege: Philosophy of Language treats Frege’s philosophy from the point of view of the philosophy of language which descended from it. It is not so much a work of pedantic historical scholarship, as a discussion of the philosophy of language inspired by themes derived from Frege. This aspect of the book has led to criticism from some quarters. Sluga, in particular, objected that Dummett treats Frege unhistorically, and therefore deems him a realist or Platonist when, according to Sluga, his views were in fact close to Kant’s (Sluga 1976, 1977). He cites as evidence for this the influence of the Kantian, Lotze, whose work Frege had read. Dummett has accepted that the allegation of being unhistorical was partly warranted (Dummett 1991b, p. vii). He has also shown subsequently that his interpretation of Frege can almost always be substantiated. In fact, this aspect of the debate over Frege’s Platonism is something of a muddle, but it will be helpful to outline it, if only to avoid misunderstanding. In his 1976 paper ‘Frege as a Rationalist’, Sluga objected to a claim which he imputes to Dummett, that Frege was opposed to Hegelian idealism. Initially Dummett vigor-

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ously denied that he had made such a claim, and agreed with Sluga that Frege’s opposition to idealism was an opposition to the kind of subjective idealism which is the result of empiricism and naturalism, and which takes the meanings of words to be ideas in the mind (Dummett 1976b/91b). More recently, Dummett has accepted that he was wrong to imply that Frege had a part to play in the downfall of Hegelianism (Dummett 1991b, p. viii). It is now clear that both authors accept that Frege’s attack on idealism and his attack on psychologism are one and the same. Both agree that the major thrust of Frege’s objection to idealism is to argue that if mathematical entities are ideas, and if the laws of logic are empirical regularities of the working of the mind, then there is no objectivity in mathematics. But there are objective mathematical truths, just as much as there are objective physical truths, so mathematics cannot be concerned with subjective ideas or psychological processes. Some of Sluga’s other comments in this early paper seem, however, to entirely miss their mark, and do nothing to show that Frege was not a Platonist. According to Sluga, Frege’s philosophy is ‘related to the rationalist strand within modern philosophy’ (Sluga 1976, p. 31). But this observation does nothing to challenge Dummett’s view that Frege is a Platonist, for the connections between Platonism and rationalism run deep. The rationalist doctrine of innate ideas descends directly from Plato, and is connected with the central rationalist claim that the mind gives us access to a realm of objective, non-empirical truths. So there would be no contradiction in contending that Frege, like Descartes, was both a rationalist and a realist Platonist, who believed that mathematical objects exist independently of our beliefs. What Sluga seems to have in mind when he assumes that the rationalist strand in Frege’s work is opposed to Platonism is the idea that for Frege our knowledge of the objective truths of mathematics is delivered directly by reason, and does not depend on the contemplation of some independently existing objects. This is what he intends by denying that Frege’s insistence on objectivity is an ontological thesis. Thomas Ricketts similarly objects to the Platonist interpretation of Frege because it fails to recognize that for Frege, ‘ontological categories are wholly supervenient on logical ones’ (Ricketts 1986, p. 66). The independent objects are not known via some quasi-causal intuition, but are understood via a grasp of logical relations. But, from the foregoing discussion it can be seen that objections of this kind are based on a misinterpretation of Dummett’s intentions. Sluga never tells us exactly what he takes realism to be, and this makes it difficult to determine exactly what he is denying when he

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denies that Frege is a realist. He makes the following assertion with which Dummett would fundamentally agree: ‘For Frege the objects of reason are as objective as any other object; they are objects in the same sense as empirical things; even though they are not real, that is they are not spatio-temporally located, and they are not identifiable by empirical means’ (Sluga 1976, p. 43). So it appears that he has mistaken Dummett’s claim that Frege is a realist for the claim that Frege subscribes to some version of extreme Platonism. Sluga also assumes that if Frege was influenced by Kant, then he was not a realist (Sluga 1977, p. 236). But this overlooks a number of possibilities. One is the position that Putnam once adopted, and which he has called ‘internal realism’ (Putnam 1978). Such a position concedes much to Kant, in that it accepts that it is in virtue of our language, or mode of thought, that the world is understood in terms of the ontological categories that we use; but it also accepts that we think and speak of the world in a way which implies that there are objects which exist independently of individuals. Dummett, indeed, in the following passages, attributes an internal realism of this kind to Frege: For Frege, the relation of a proper name of a concrete object to that object is the prototype of the relation of reference. Even in this case, the objects which serve as referents cannot be recognized quite independently of language: it is only because we employ a language for the understanding of which we need to grasp various criteria of identity, . . . that we learn to slice the world up conceptually, into discrete objects. (Dummett 1973a, pp. 406–7) What objects we recognize the world as containing depends upon the structure of our language. . . . Thus, in a certain sense, Frege, with his insistence that proper names have sense, and that this sense comprises a criterion of identity, could endorse the second sentence of the Tractatus, ‘The world is a totality of facts not things’. Literally taken, this would be wrong for Frege, since as we have seen, for him facts belong to the realm of sense and not of reference: rather, we should say that, for Frege, the world does not come to us articulated in any way; it is we who, by the use of our language, . . . impose a structure on it. (Dummett 1973a, p. 504)32

Dummett then goes on to acknowledge that such a view must fall short of an absolute realism, particularly when we have in mind ‘pure abstract objects’ (for instance, the empty set), by which he means abstract objects which can be given to us only by reason. Unlike some other abstract objects, such as the equator, such pure abstract objects are in no way locatable in the sensible realm. The

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existence of these pure abstract objects is a result of the conceptual apparatus embodied in our language; ‘yet for just that reason it appears impossible to regard the pure abstract objects as constituents of an external reality’ (Dummett 1973a, p. 505). Frege lays down the meaning of numerical expressions by providing a criterion of identity for numbers, which enables us to determine when we are given the same number. But even concrete objects can be delimited only in virtue of a criterion of identity. So Dummett concludes that from the point of view of the context principle the possession of reference is wholly internal to the language. More recently he has associated the context principle with Putnam and ‘the internalist strain in Frege’s thinking’ (Dummett 1973a, p. 499; 1991d, p. 211n; 1995b, pp. 10–11, 18). So it would seem to be possible for Dummett to acknowledge the Kantian elements in Frege’s thought without retracting the claim that he is a realist. In some ways, doing so enhances the plausibility of the argument which Dummett develops to take us from Frege to intuitionism. For to acknowledge the influence of Kant on Frege would be to acknowledge a greater historical convergence between Frege and the intuitionists than Dummett usually implies, since, as we will see in chapter 3, historically intuitionism is explicitly a development of Kantianism.33 Sluga’s scholarship, when combined with that of Kitcher, establishes quite clearly that there are Kantian presuppositions in much of Frege’s work which were not emphasized in Dummett’s book (Kitcher 1979). The influence of Kant is recognized by Dummett, however, though differences over the nature of that influence remain (Dummett 1982a/91b). Nevertheless, the evidence does not show that Frege was not a minimal Platonist in the sense outlined. It does raise the question of whether the version of minimal Platonism that Dummett ascribes to Frege is inevitably a form of Kantianism, and whether, if it is, Dummett erred by his own lights in attributing it to Frege, and should instead have attributed to him a position closer to extreme Platonism. In the next chapter I will canvass the possibility that by reading Frege’s position as consistent with moderate causal Platonism, one can do greater justice to his insistence on the objectivity of numbers than is done by reading him as a minimal Platonist. For now it is enough to observe that, according to Dummett, Frege is a realist, because he asserts bivalence, and a minimal Platonist, because for him the existence of mathematical objects falls out of the truth of sentences that involve reference to those objects. Unfortunately, this debate has suffered from a lack of clarity in the use of terms, and recently Sluga has

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acknowledged that he and Dummett were originally using the term ‘realism’ in different senses, and so were, to an extent, arguing at cross purposes (Sluga 1993, p. xii).

The Context Principle The key to understanding what Dummett intends by his cryptic comment concerning the constructivist implications of Frege’s position is to be found, as already indicated, in his interpretation of the part played by the context principle in Frege’s philosophy. The context principle is repeated a number of times in Frege’s Grundlagen, but it is not formulated explicitly in his later works (Frege 1884/1950, §§60, 62, 106). Because the distinction between sense and reference was not introduced until some time after the publication of the Grundlagen, there has been some debate over whether Frege continued to adhere to the principle once this distinction had been drawn. Its introduction also raises the issue of whether the principle should be thought of as applying to sense or to reference.34 Dummett has always maintained that Frege continued to adhere to the principle as a principle concerning sense, but he was initially agnostic over whether he continued to hold it with regard to reference. As we will see, he is now convinced that, as a principle relating to reference, a generalized context principle continues to play an important, though destructive, role in the Grundgesetze (Dummett 1991d, p. 210). In the Grundgesetze Frege attempts to give an explicit definition of numbers which identifies them with extensions. His criterion for the identity of extensions both embodies a generalized context principle and leads to the paradoxes. So the context principle cannot give a sufficient condition for reference; it may be retained as a necessary constraint on asking after the reference of a term, but it cannot guarantee that a reference has been supplied. In §62 of the Grundlagen the context principle occurs as a premiss in an argument to the conclusion that we will have shown how to assign references to the number words if we can show how to define the sense of statements of identity involving them. In a much quoted passage Frege says: Since it is only in the context of a proposition that words have any meaning, our problem becomes this: To define the sense of a proposition in which a number word occurs . . . we have already settled that number words are to be understood as standing for self-

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subsistent objects. And that is enough to give us a class of propositions which must have a sense, namely those which express our recognition of a number as the same again. . . . When we have thus acquired a means of arriving at a determinate number and of recognising it again as the same, we can assign it a number word as its proper name. (Frege 1884/1950, p. 73)

Frege assumes that it has already been established that number words are to be understood as standing for self-subsistent objects, for they take the definite article and typically occur in identity statements (Frege 1884/1950, pp. 67–9). If a symbol stands for an object, we must have a criterion of identity; so the problem of assigning referents to number words becomes the tractable one of defining the sense of identity statements between numbers. A criterion of identity will determine whether an object a is or is not the same as an object b. As Dummett interpreted the context principle in his earlier works, when it is construed as a thesis concerning reference, it lays down that ‘if a sense has been fixed for all possible sentences in which an expression may occur, then no additional stipulation is needed to confer a reference on that expression’ (Dummett 1981c, p. 380). But, taken literally, this principle appears to conflict with Frege’s later view that an expression may have a sense but no reference. We might well think, for instance, that a sense has been fixed by Shakespeare (or at least in the language Shakespeare used) for all the possible sentences in which the expression ‘Hamlet’ may occur, and yet also think that no reference has been conferred on the expression. Dummett, aware of this difficulty, says that here the question ‘is no longer of a philosophical character’ (1956a/78c, p. 40; 1981c, p. 383). But this is not the most illuminating of comments. After all, some have thought that the question of the treatment of non-referring singular terms is an interesting philosophical question, and nothing was said in the earlier statement of the context principle about limiting its application. It is perhaps fair to Dummett’s intentions, when he made this comment, to point out that there is a difference between giving an account of the kind of reference that belongs to some class of expressions and giving an account of the reference of one particular expression of that class. To say that singular terms refer to objects is to say that expressions that fulfil the syntactic role of singular terms are apt for referring to objects. Similarly, to say that predicates refer to concepts (in Frege’s sense of functions from objects to truth values) is to say that predicates are apt for referring to concepts. It may neverthe-

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less be that in natural language a term which plays one or other of these syntactic roles is not fulfilling its normal function, and hence fails of reference. So Dummett suggests that the context principle should be read as applying to classes of expressions. Once a sense is determined for all the sentences in which an expression of a class can meaningfully occur, there is no further question to be asked concerning the kind of reference which expressions of that class can have. In the case of number words, if they behave syntactically like singular terms, and if the singular terms are apt for referring to objects, then if a number word refers, it will refer to an object. It may still be a question whether a particular number word, say 1, has a reference; but if it does have one, it will refer to an object. It will also still be a possibility that our best account of the truth conditions of sentences containing number words will lead to the conclusion that while number words are (syntactically) singular terms, they do not genuinely refer, because sentences containing number words can always be paraphrased using equivalent sentences in which the singular terms have been replaced. In chapter 9 of Frege: Philosophy of Mathematics, Dummett takes Frege to task for not having demonstrated the incoherence of an alternative strategy of this kind for explaining the analyticity of arithmetic. When this strategy is followed, apparent numerical singular terms disappear in favour of second-level concepts and higher-order quantifiers. Looked at this way, the context principle will provide at best a prima facie reason for considering a class of expressions to refer to objects, and extra argument may be required in order to establish that these singular terms cannot be paraphrased away. Dummett suggests that the real reason why Frege was forced to treat numbers as objects was that it was only thus that he could prove the theorem establishing the infinity of the sequence of natural numbers (Dummett 1991e, pp. 131–40). But even this provided Frege only with a motive for treating numbers as objects, not with a proof that they have to be so treated. The context principle, as interpreted by Dummett, is closely associated with his attribution to Frege of the recognition of the priority of language, and so with the claim that Frege should be seen as initiating the linguistic turn that led to analytic philosophy. Even Dummett has acknowledged that there is some doubt concerning his own strongest assertions on this matter. I have been unable to find a passage in which he says expressly that the route to an understanding of what is comprised by any of the

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fundamental types of entity lies through a prior grasp of the corresponding type of linguistic expression. I think that I was in error in asserting that he maintained this, and have in FPL2 altered the passages on pp. 194 and 539–40 accordingly. (Dummett 1981c, p. 235)

As already pointed out, there is a further question as to whether Dummett is right in asserting the priority of language, and what such an assertion amounts to. Since these are doctrines closely associated with Wittgenstein’s rejection of mentalism, we will return to them in the next chapter, though we will not attempt to resolve them until the last chapters of this book. Here we will ask only to what extent this attitude should be attributed to Frege, and whether the minimal Platonism which accrues to him if he did ascribe to such a view really counts as Platonism. Dummett goes on to say of his attribution of the priority of language that it captures the spirit of Frege’s enterprise: ‘We can’t immediately examine the referents of “four” and “green”; we need a syntactic analysis which is apt for a semantic account, and once such an analysis has been given, there will be no further question as to the logical type of the expressions’ (cf. Dummett 1981c, p. 237). This strongly suggests that once we have determined that in a regimented language the expressions for numbers play the syntactic role of proper names, given that the semantic account tells us that the reference of a proper name, if it has one, is an object, there is no further question as to whether number words refer to objects. But in his later book Frege: Philosophy of Mathematics, Dummett makes it clear that matters are not quite as simple as this. In 1983 Crispin Wright published Frege’s Conception of Numbers as Objects, a work which appears to follow quite closely Dummett’s early discussion of the place of the context principle in Frege’s philosophy, although Dummett is a little coy over how faithful Wright is to his earlier intentions. Like Dummett, Wright interprets the context principle as showing that nominalism is misguided, because reference to objects is internal to the language: If . . . certain expressions in a branch of our language function as singular terms, and descriptive and identity contexts containing them are true by ordinary criteria, there is no room for any ulterior failure of ‘fit’ between those contexts and the structure of the states of affairs which make them true. So there can be no philosophical science of ontology, no well founded attempt to see past our categories of expression and glimpse the way the world is truly furnished. (Wright 1983, p. 52)

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Indeed, Wright takes Dummett to task for having expressed the misgivings, discussed above, as to whether we are entitled to think of pure abstract objects as part of external reality. He argues that there are only two coherent options. One is that of a nominalist reductionist who thinks that objects which are introduced simply by laying down the senses of identity statements do not really exist, because sentences which appear to refer to them can always be replaced by other equivalent sentences in which there is no explicit reference to objects. The other follows Frege, and insists that such a method of introducing terms provides a way of being given abstract objects, which, despite being non-spatial and non-causal, are just as objective as are concrete ones. Their objectivity can be recognized in the mind-independence of the truths that can be expressed by referring to them. Dummett’s misgivings relate, according to Wright, to an intermediate position which is untenable (Wright 1983, pp. 65–84). But there are problems with Wright’s bold statement. The first difficulty looks like a minor one. Wright speaks of ‘certain expressions of our language’ which ‘function as singular terms’. But many expressions of our ordinary language function as singular terms, but are not treated as such once the language is translated into predicate logic. So, to take an example from Frege, ‘The whale is a mammal’ and ‘The number three is a prime’ are, superficially, syntactically identical. But Frege would want to say that the second does, while the first does not, involve a genuine proper name. ‘The whale is a mammal’ asserts, according to him, that a relation holds between the concept of being a whale and that of being a mammal. The logical syntax of this sentence can only be revealed through quantification. For Frege, first-order predicates are true of objects and refer to unsaturated concepts, while quantifiers are second-order predicates which apply to concepts, the referents of first-order predicates (Frege 1884/1950, p. 60). ‘The whale is a mammal’ thus has the form: (x) (Whale x … Mammal x)

This says that everything is such that, if it is a whale, then it is a mammal. But numbers are objects, so the logical form of the sentence ‘The number three is a prime’ will mirror its surface structure: Prime 3. This looks like a minor problem, which can be overcome by making our ontological commitments relate, as Quine does, to a properly regimented language; or, as Dummett says, to a language for which we have provided a syntactic analysis, apt for a semantic

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account. Yet things are not so simple. How do we determine which is the correct translation into a regimented language? One way would be to follow some sort of non-linguistic ontological intuition, but then we would not be being guided by language in the determination of ontology. Another way is to develop a syntactic criterion for genuine singular term-hood. In Frege: Philosophy of Language, Dummett argued that while we cannot take surface syntax as a reliable guide to singular term-hood, we can broaden the notion of a ‘syntactic’ criterion to include various intuitions concerning the validity of inferences, and he suggested some criteria designed to distinguish genuine singular terms from quantifier expressions, such as ‘everyone’ and ‘nothing’, which superficially play the syntactic role of singular terms, and from predicates such as ‘a policeman’ which share some of the inferential properties of singular terms (Dummett 1973a, pp. 54–80). It turns out to be quite difficult to formulate necessary and sufficient conditions for singular termhood which are intuitively correct (Wright 1983, pp. 53–64: Hale 1994). Moreover, a suspicion remains that when we formulate the appropriate ‘syntactic’ criteria, our intuitions are guided by a nonlinguistic (perhaps perceptual) understanding of the difference between material objects, which are unique and unrepeatable, and the various multiply instantiated properties that those objects instantiate. This, however, is to cast doubt on the view, common to Frege, Dummett and Wright as well as Quine, that ontological categories are simply the reflection of the logical syntax of the language that we speak, and cannot be grasped independently of it. It would take us too far afield to discuss the ultimate plausibility of this view here. In any case, even if we allow that a broadly syntactic criterion for singular term-hood is available, Wright’s claim that, when a term functions as a singular term, and a sense has been fixed for all possible sentences in which it occurs, there is no further question to be asked concerning whether it has a reference, fails. For there are further questions. First, we will need to be careful to determine that a sense has been fixed coherently for all possible sentences in which the term occurs. Second, when the sense has been fixed in such a way that the sentences containing the singular terms can always be paraphrased by others which do not contain them, a question can be raised as to the genuine existence of the objects apparently referred to. Ultimately, Frege’s attempt to say which objects the numbers are foundered, because he had not really determined a coherent sense for all possible sentences in which number terms occur. Consider again the pair of sentences ‘The whale is a mammal’ and ‘The number three is a prime’. The reason why the second sentence cannot

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have quite the same logical structure as the first is that if we were to write (x) (Three x … Prime x)

where our quantifiers range over material objects, it would be unclear what we were saying. The predicate ‘three’ doesn’t apply to the sort of object to which ordinary material predicates apply. As Frege spells out at some length, the question ‘Is this three?’, where an ordinary physical object is indicated, is indeterminate in sense. It is not until we are supplied with a concept, as in the sentence ‘Is this bundle of fur three koalas (or just one)?’, that we can answer a ‘how many’ question. This leads to the conclusion that in a sentence like ‘There are three koalas’, the expression ‘there are three’ is a quantifier, a second-order predicate of the concept of being a koala. Frege might have stopped his analysis at this point.35 Had he done so, the many identity statements and predications of arithmetic would have had to be paraphrased away. He chose instead to take the substantival grammar of number words in the expression of the truths of arithmetic seriously, and to give an explicit definition of each number N as the extension of the concept of being equinumerous (being able to be put in one–one correspondence) with a logically constructible N-membered extension. In order to give this explicit definition, he had to introduce the notion of the extension of a concept. This is an abstract object called, in Furth’s translation of the Grundgesetze, a ‘course-of-values’ and referred to by Dummett as a ‘value-range’, but more easily thought of as akin to a set.36 But now, a problem looms. As we saw above, the context principle leads Frege to assert that we will have shown how numbers are given to us if we have given a definition of identity for numbers, and thus a criterion for deciding, whenever we have a symbol a which signifies an object, whether or not the object signified by another singular term b is the same object (Frege 1884/1950, p. 73). Similarly, he assumes that he can introduce value-ranges (courses-of-values) via a criterion of identity. This he does in the Grundgesetze by introducing the abstraction operator, which allows him to construct a singular term from an expression for a concept or function, and by then giving a criterion of identity for the terms so formed: e F(e) = a Y(a) ∫ (x) (Fx ∫ Yx)

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where e F(e) is read, ‘the extension of the concept F’. The identity condition for extensions says that the extension of the concept F is identical to the extension of the concept Y if and only if every object which is F is also Y. But this is the famous Axiom V (the comprehension axiom) which leads to Russell’s paradox. Dummett, pointing out the problem, concludes that since, in the Grundlagen, Frege’s method of introducing numbers by laying down a criterion of identity resembles exactly the method of introducing the abstraction operator in the Grundgesetze, we can conclude that Frege still adhered to the context principle, but that, because of the contradiction which derives from the circularity or impredicativity of Axiom V, we must treat the method and the context principle on which it is based with suspicion. Dummett concludes that we are therefore faced with three options. We can reject the context principle. We can accept it, but argue that it does not by itself vindicate the procedure of introducing objects simply by laying down a criterion of identity. Or we can formulate a restriction on the context principle which distinguishes the cardinality operator that introduces numbers from the abstraction operator which introduces value-ranges (Dummett 1991d, p. 189). In Frege: Philosophy of Mathematics Dummett favoured the second of these options. What the paradoxes show is not that the context principle is illicit, but that the method chosen for laying down a criterion of identity does not result in a coherent sense being specified for all sentences in which expressions for value-ranges occur. By 1995, however, Dummett was undecided on the question of whether the context principle should be endorsed or rejected, but concluded that the question ‘is of prime importance to philosophy’ (1995b, p. 19). Wright’s position is that Frege’s method for introducing the cardinality operator in the Grundlagen does not lead to paradox; so he would seem to be implicitly committed to the third of Dummett’s options. But even if a coherent sense has been specified for all sentences in which a class of singular terms occur, it is not clear that this is all that is required to demonstrate that they refer to objects. A puzzle is posed by the possibility of using the abstraction operator to form a term from a predicate whenever we so desire. When we considered the logical syntax of ‘The whale is a mammal’, we followed the standard procedure of eliminating the apparent singular terms in favour of quantifier and predicates. But (x) (Whale x … Mammal x)

is equivalent to

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which will conform to the surface structure in ordinary language if we take ‘the whale’, in English, as picking out the abstract object, the extension of the predicate ‘. . . is a whale’. On this reading, the surface syntax would just be an abbreviated way of saying that the extension of the property of being a whale is contained in the extension of the property of being a mammal. Or, as Frege would say, the first property stands in the relation of subordination to the second. The popular nominalist, reductionist position is that when we have an equivalence between a sentence which does involve reference to some objects and one which does not, this shows that we do not need to countenance the objects referred to. Wright asserts that in such a case we have just as much reason to say that the sentence which does not involve reference to an object already involves commitment to the existence of the abstract objects. So why not say this in the present case? Dummett suggests that the answer is available from the point of view of the Grundgesetze. Someone impressed by Quine’s interpretation of the quantifiers will argue that the syntactic structure of (x) (Whale x … Mammal x) shows perspicuously how its truth is to be determined according to the semantic theory developed by Frege. So long as we have provided a semantics for our language and specified the domain of quantification for the quantifiers, it is enough in order for ‘The whale is a mammal’ to be true that every object which is a whale should also be a mammal. We are not required to be able to identify the whole set of whales in order to determine the truth of this sentence; nor do we need to quantify over sets or extensions.37 This would make the correct attribution of the ontological commitment of a sentence relative to our best semantic theory, and so would justify Dummett’s attribution of an intermediate position to Frege. For Dummett argues that the views that Frege expressed in the Grundlagen justify the attribution to him of such an intermediate position, because he had not then developed a semantic theory in the light of which it would be clear that the identification of a number was essential to the determination of the truth value of any sentence involving reference to that number. He had not, that is, developed a ‘robust’ notion of reference, and, indeed, had not clearly distinguished sense from reference. Dummett’s point is that when Frege wrote the Grundlagen, he did not yet have a properly developed semantic theory. This meant that the notion of reference that he was using in the early writing was not tied to a semantics, and was therefore not robust. Because Frege had

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not at this stage made clear the difference between sense and reference, when he asserted that number words refer to objects, this has to be taken as equivalent to the assertion that there are numbers. This thin notion of reference does not sustain the attribution to him of the robust picture available from the perspective of the Grundgesetze, according to which, for numbers to exist is for them to be the objects which are semantically relevant to the determination of the truth or falsity of sentences of mathematics (Dummett 1991d, pp. 189–99). But, when we look at Axiom V with an eye to the determination of the domain of quantification, it is clear that it is inadequate, because impredicative. So we have to fine-tune the notion of minimal Platonism. When the claim that we are committed to the existence of the objects quantified over by our quantifiers is made against the background of the normal semantics for first-order languages, we are committed in a robust way to the existence of those objects. When we say that entities of some kind exist without the benefit of such a background semantics, we may be using ‘exists’ in a sense so minimal as to be virtually indistinguishable from one acceptable to a reductionist.38 On such a view, abstract objects might be allowed to exist, but only as entities introduced to provide a shorthand method for asserting truths which do not fundamentally require identification of those objects in order to be ascertained. So it is only from the point of view of the Grundgesetze that we can ask whether Frege thought that the context principle entitles us to claim that we have, in the robust sense, provided referents for our terms once we have laid down the truth conditions of the sentences in which they occur. Dummett asserts that the fact that Frege assumed that, by providing a criterion of identity for value-ranges, he had established their existence shows that he still adhered to a modified context principle. It is modified because he no longer accorded priority to sentences, since, in developing the doctrine that the reference of a sentence is a truth value, he had assimilated sentences to names. His adherence to the modified context principle is evident from the method adopted for the introduction of valueranges. First the sense of the identity statement for value-ranges is laid down. Then Frege attempts to show that it can be determined for any object, whether or not it is identical with any value-range. But his method was ill founded. Value-ranges are objects which can be the values of the functions introduced. We cannot determine whether two functions determine the same value-range until we know what our domain of quantification is. But we do not know what makes up the full domain of quantification until we know which functions determine the same value-range. This impredica-

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tivity vitiates Frege’s method. It is clear that Frege did think, at this stage, that he could introduce referents for value-range terms just by determining the referents of the more complex expressions in which the value-range terms occur. However, he was not entitled to this assumption. Dummett concludes: When the notion of reference is the instrument of a serious semantic theory, serving as the base for a theory of sense, the context principle simply cannot be sustained in full generality; against that background, it is useless to mount a defence of it. The notion of reference, as applied to singular terms, is operative within a semantic theory, rather than semantically idle, just in case the identification of its referent is conceived as an ingredient in the process of determining the truth-value of a sentence in which it occurs. Hence the context principle, if it is to warrant an ascription of reference to a term, robustly understood, must include a further condition if it is to be valid. It is not enough that truth conditions should have been assigned, in some manner or other, to all sentences containing the term: it is necessary also that they should have been specified in such a way as to admit a suitable notion of identifying the referent of the term as playing a role in the determination of the truth-value of a sentence containing it. (Dummett 1991d, pp. 238–9)

Despite the difficulties which follow from Frege’s use of the principle, in 1991 Dummett still continued to maintain its importance as an antidote to ‘nominalist superstition’ (Dummett 1991d, p. 231). He further claimed that, understood as constrained by the further condition that we have a means of identifying the referents of the terms for abstract objects, it ‘rules out all grounds for cavil’ at the view that mathematics has abstract objects as its subject matter (pp. 239–40). However, it is clear in these later works that the context principle is at best a necessary constraint on the determination of reference, and does not by itself provide a sufficient condition. I began this section by asserting that Dummett attributed a form of minimal Platonism to Frege. This now needs to be modified. The Platonism which Dummett finds in Frege is not so much minimalist as constructivist. By following the context principle, Frege avoided obscure notions of causal or quasi-causal relations between immaterial objects and people. Numbers and other abstract objects are given to us as the referents of terms which occur in sentences for which we have laid down coherent truth conditions. Frege went wrong because he was mistaken in thinking that he had laid down coherent truth conditions for sentences involving value-ranges. He

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had not done so, because he had not provided a suitable method for identifying the referents of the value-range terms, the method that he attempted having been circular. But despite the problems with Frege’s application of the method, Dummett believes that he was right to begin with sentences.39 It is because the existence of abstract objects falls out, in this way, from the truth of sentences that the issue between realist and anti-realist must be fought over the notion of truth for sentences. We can now flesh out Dummett’s early comment that the implications of Frege’s thought are far more constructivist than is usually realized. In the last two chapters of Frege: Philosophy of Mathematics, Dummett argues that despite the existence of a contradiction in Frege’s system, his fundamental attitude to mathematics was correct. Frege’s logicist Platonism is the view that there are logical objects which can be proved to exist a priori. The element of logicism gives this position a great advantage over other forms of Platonism. For it dissolves the mystery over how we know about the existence of mathematical objects; we know them as we know other logical truths. This does not dissolve the mystery if we think that it is a mystery how we know logical truths, but, as we will see in chapter 3 on intuitionism, Dummett argues, against the holist, that logical truths can (up to a point) be shown to be truths in virtue of meaning. Logicism also has the advantage that it explains the applicability of mathematics. The application of mathematics just consists in the instantiation of higher-order formulas. In fact, a nonPlatonistic logicism can still be maintained which provides an interpretation of mathematics in higher-order logic. But such a view cannot prove a priori the infinity of the natural numbers; nor indeed can it show that it is true that an infinity of natural numbers exists, and for this reason it would not have been acceptable to Frege (Dummett 1991d, pp. 301–5). Frege ran into difficulties because he did not specify the domain over which his quantifiers were to range. He assumed that it was enough to provide a criterion of application and a criterion of identity for the numbers, and that reality would do the rest. But in order not to be circular, his criterion of identity required that the domain be fully specified. It is here that Dummett argues that Frege could have adopted a solution which on the one hand looks radical, but on the other can retain both the logical character of mathematics and the view that it comprises a substantive body of truths. The argument derives from Brouwer, and constitutes the traditional intuitionist response to the paradoxes. As we will see, intuitionists

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have always refused to accept that, when quantifiers range over infinite totalities, there is a guarantee that every quantified sentence will be determinately either true or false. From this perspective: Frege’s error did not lie in considering the notion of the extension of a concept to be a logical one, for that it plainly is. Nor did it lie in his supposing every definite concept to have an extension, since it must be allowed that every concept defined over a definite totality determines a definite subtotality. We may say that his mistake lay in supposing there to be a totality containing the extension of every concept defined over it; more generally, it lay in his not having the glimmering of a suspicion of the existence of indefinitely extensible concepts. (Dummett 1991d, p. 317)

What Dummett means by an ‘indefinitely extensible concept’ is one such that ‘for any definite characterisation of it, there is a natural extension of this characterisation, which yields a more inclusive concept’ (1963/78c, pp. 195–6).40 The concept of ‘ordinal number’ provides an example. Whenever we have a grasp of a totality of ordinal numbers, we can apply the concept to the totality itself, and obtain an ordinal number which is not a member of the totality. If we view ourselves as building up our understanding of the application of these concepts as we extend our use of them through the specification of wider domains of application, then we will not run into difficulties. It is when we assume that there must already be a truth about their applicability to the whole totality that paradox arises. So, When the concepts of natural number and of real number are regarded as indefinitely extensible ones, our grasp of them is beyond question; it is only when they masquerade as definite concepts that any attempt to characterise them becomes vague or circular. This diagnosis breaks the impasse; but of course at a price. Quantification over the objects falling under an indefinitely extensible concept obviously does not yield statements with determinate truth conditions, but only ones embodying a claim to be able to cite an instance or an effective operation; and the logic governing such statements is not classical, but intuitionistic. (Dummett 1991d, p. 319)

So if Dummett is right, the path to be taken in the face of the paradoxes, if we want to keep most of Frege’s intuitions intact, is the adoption of intuitionist logic. In chapter 3 we will examine what this involves in greater detail.

2 Wittgenstein and Quine

In the preface to Truth and Other Enigmas Dummett tells us that he began his philosophical career thinking of himself as a follower of Wittgenstein (Dummett 1978c, p. xii). Although he had ceased to think of himself thus by 1960, the influence of Wittgenstein nevertheless plays an important part in his philosophy. The most obvious mark of this early allegiance is the acceptance of the slogan that meaning is use; more accurately, that an account of the meanings of words will consist in an account of the uses to which they are put. Equally important is the fact that Dummett interprets Frege’s antipsychologism as a precursor of Wittgenstein’s argument against a private language. Together, these are central to Dummett’s understanding of the role of language in the account of thought, and to the verificationism that enters into the argument for anti-realism. As we saw in the previous chapter, Dummett’s view of the theory of meaning is that while it is illuminating to construct a meaningtheory for a language, such a meaning-theory will be incomplete unless we can say how knowledge of the meaning-theory is manifested – how, that is, speakers are able to manifest their knowledge of the truth conditions which the theory assigns to sentences as their meanings. This ‘manifestability constraint’ derives from Wittgenstein, and falls out of his recognition that meanings are not private mental items, but must involve publicly accessible criteria for correct use. There is, however, a certain difficulty in discussing Wittgenstein’s influence on Dummett directly. Whereas Dummett has written a voluminous quantity on Frege and a substantial amount on intui-

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tionism, the number of articles devoted exclusively to Wittgenstein is quite slight.1 Moreover, the papers which are directly concerned with Wittgenstein are often quite critical of him, and do not provide us with a clear outline of Dummett’s understanding of the content of the private language argument. Dummett’s formulations often echo Wittgenstein’s. He wants to make the workings of language clear to view, just as Wittgenstein speaks of dispersing the fog that surrounds our use of language and of commanding ‘a clear view of the aim and functioning of words’ (Wittgenstein 1967a, §§5, 122, 125). But whereas Dummett believes that the construction of a meaning-theory will contribute to an explanation of understanding, the later Wittgenstein rejects the possibility of a systematic account of language when he dismisses his earlier belief that ‘if anyone utters a sentence and means or understands it he is operating a calculus according to definite rules’ (§§81, 133). This leads him to insist that philosophy and grammar only describe and in no way explain or improve on the use of signs (§§98, 124, 496). Dummett’s understanding of the slogan ‘meaning is use’ is such that it underpins the possibility of justifying certain forms of inference in terms of their being faithful to the use that has been laid down for the logical expressions that occur in them (Dummett 1973b/78c). Wittgenstein’s understanding of ‘meaning is use’ is that meaning is determined by whatever use we happen to make of expressions. There is no such thing as a new use being faithful or unfaithful to a prior use.2 Each new use extends the meaning of the expressions involved. This picture is one which is also associated with Quine’s holism, and Dummett’s criticisms of Wittgenstein are often repeated in the context of his discussion of Quine’s indeterminacy thesis and the holism accepted by Davidson and Quine. For this reason, this chapter on Wittgenstein will also say something about Dummett’s treatment of Quine. Indeed, although the influence of Quine on Dummett is less obvious than that of Wittgenstein, Dummett tells us that when Quine visited Oxford in the early 1950s, he ‘saw a great deal of Quine . . . and had many discussions with him’; and he reports that while he was ‘not completely sympathetic to his views’, he felt ‘much more sympathetic to them than anyone else in Oxford’ (Dummett 1993b, p. 169). On one issue, Quine’s understanding of the slogan ‘meaning is use’ appears to be closer to Dummett’s than to Wittgenstein’s. For Dummett, a first step in the direction of providing a systematic account of meaning is to distinguish the theory of sense from the theory of force. One way of reading Wittgenstein is that the moral

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he wants to draw from the simplified language games that he describes in The Blue and Brown Books and the Philosophical Investigations is that no distinction can be drawn between sense and force. It is natural to think that ‘Bring me a red block’, ‘I want a red block’, ‘Do I have a red block?’ and ‘I have a red block’ share some core content. This might be identified with the truth condition, or cognitive content, of the asserted sentence ‘I have a red block’. A systematic theory would then show that in all the other cases a grasp of meaning depends on a grasp of this core content plus some transformation. ‘Bring me the red block’, for instance, might be analysed as ‘Make it the case (by your own action) that I have the red block’. ‘Do I have the red block?’ can be analysed as ‘Is it the case that I have the red block?’ One way of reading Wittgenstein is as intending to deny that we can explain the meanings of imperatives and questions in this way, building on a prior account of content. Rather, we have to give a direct account of every sentence in terms of the use that is made of it. This would undermine very quickly the possibility of a systematic account of meaning, since sentences can be put to all sorts of unusual uses (Dummett 1975a/ 78c, pp. 448–53). While Dummett takes Wittgenstein’s dictum that meaning is use to be a necessary antidote to mentalistic accounts of meaning, he interprets it as compatible with the idea that it is the use of sentences to make assertions which provides the core content that is shared between sentences that differ only in force. This is also Quine’s understanding of the dictum. Quine assumes that it is behaviour of assent and dissent which is crucial for deriving an account of meaning. So here I will simply follow Dummett and Quine in accepting that the slogan that meaning is use is compatible with the development of a theory of meaning that gives the core cognitive meaning of assertoric sentences by providing a theory of sense. Such a theory would then show, by constructing a theory of force, how the meaning of commands, questions, etc. can be derived from this core content. Yet, even if we restrict ourselves to assertoric language and assume that core meaning depends on the use of sentences to make assertions, the doctrine that meaning is use appears to come into conflict with the possibility of providing a systematic account of meaning. For Dummett, as for Davidson, the need for a systematic account of language emerges from the learnability of languages. After a relatively brief exposure to language, normal human beings acquire the ability to understand sentences which they have never heard

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before and to produce original sentences which are usually understood as intended. The most obvious explanation of this is that language is systematic, and that, Wittgenstein notwithstanding, when someone understands a language, she is doing something close to ‘operating a calculus according to definite rules’. But Wittgenstein points out that, despite elements of system in our usage, the appeal to rules gets us nowhere, for they themselves are open to differing interpretations (Wittgenstein 1967a, §§87, 198). The most that can be said is that, as a matter of fact, we usually agree with regard to the uses of expressions; but this agreement depends on context and on the fact that circumstances are standard (§42). Dummett, however, sees this rejection of systematicity as resulting in a failure to explain something (our understanding of language) which can be explained. This is the central weakness which he finds in the holism that is implicit in Wittgenstein and which becomes explicit in Quine. In the theories of both, too little account is given of the learnability of language, and the way in which we can be impelled, by a grasp of meaning, to go on in a certain way.

The Manifestability Constraint and Rejection of Mentalism Wittgenstein’s stated aim in the Philosophical Investigations is to relieve us of philosophical perplexities which arise ‘through a misinterpretation of our forms of language’ (1967a, §§109a, 111, 125, 307–9). One particular form of philosophical perplexity is that which arises about queer mental entities that we call ‘meanings’, and the most appealing aspect of the Investigations, and one which Dummett applauds, is its determination to rid us of the feeling that we need to countenance these mysterious things: ‘When I think in language, there aren’t “meanings” going through my head in addition to the verbal expressions: the language is itself the vehicle of thought’ (Wittgenstein 1967a, §329; Dummett 1978d/93d, p. 99). The arguments which lead up to this statement examine the grammar of our use of words for sensations, in particular ‘pain’, in order to convince us that the use we make of such words cannot be to designate private sensations. We are tempted into this because ‘we construe the grammar of the expression of sensation on the model of “object and designation” ’, but a simple thought experiment shows that if we construe talk of pains or sensations in this

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way, ‘the object drops out as irrelevant’ (Wittgenstein 1967a, §293). For suppose that we all had a box with something in it that we called a ‘beetle’, but we were never able to look into anyone else’s box, or find out in any way what another person’s ‘beetle’ was like; then, since it would be quite irrelevant to the use of this word whether our ‘beetles’ were the same or different, the thing in the box would cancel out as irrelevant to the meaning of the word used. Private sensations are like these ‘beetles’; introducing them merely makes a mystery of our practice of expressing hurt, which is quite unmysterious. Many of Wittgenstein’s observations here are reminiscent of Frege’s anti-psychologism. And Wittgenstein refers to Frege, suggesting that what Frege meant when he said that a word has meaning only as part of a sentence is that naming is not yet a move in the language game. ‘Naming is a preparation for description’ (Wittgenstein 1967a, §49). A thing is only a name in virtue of the part it plays in a language game, and it is pointless to attempt to explain all the variety of our linguistic practice in terms of names for simples, as was attempted in the Tractatus. The naming relation should be introduced only if it has some point in the description of what is going on. Famously, Wittgenstein criticizes ostensive definition, the idea that we can give the meaning of a term by pointing to an object. If I point to a white cup and say ‘Cha’, my audience cannot know whether ‘Cha’ means ‘white’, ‘cup’ or even ‘Bring me a cup of tea’. It is only after being exposed to this word as it is used in various sentences that its meaning will be manifest (§§27–33). These criticisms build on the insight implicit in the context principle discussed in the last chapter. However, Frege’s principle falls out of an anti-psychologism which is adopted in the service of an account of the objective truth of mathematics. Since Wittgenstein is quite unsympathetic to Frege’s insistence that language is only in order when we are dealing with precisely defined concepts, and with his related insistence that we give a single explicit definition of the concept of number, it will be useful to distinguish Wittgenstein’s conclusions from Frege’s (Wittgenstein 1967a, §§67, 71, 79, 88). So I will call Wittgenstein’s position ‘anti-mentalism’, to distinguish it from Frege’s anti-psychologism. Anti-mentalism is the claim that meanings, if they are taken to exist at all, are not subjective items. It derives from a description of our use of language which holds fast to the idea that we should be able to explain how we learn to communicate with each other, and how it can be quite clear what is being communicated. We observe

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that speaking and understanding are done by physical creatures like ourselves, and abjure any account of our practice which introduces queer entities which play no practical part in what is going on. Quine’s account of the acquisition of language in Word and Object (1960) is anti-mentalistic in this sense. This is a broader position than anti-psychologism as Frege understood it, although there is an overlap. The anti-psychologism that Frege adopted primarily served the goal of justifying belief. With regard to the truths of logic and mathematics, it amounted to the insistence that these truths are in no way relative to our psychological processes. Psychologistic accounts of logic treat logical inferences as simply transitions that we are inclined to make from one belief to another. A description of this sort cannot explain why some inferences are truth-preserving, others not. It can only describe, not justify, inference. Below I will argue that, because Dummett does not sufficiently emphasize the gap that separates Wittgenstein’s anti-mentalism from Frege’s antipsychologism, he fails to appreciate one way of interpreting Frege’s realism which makes Frege more than a minimal Platonist. In the last chapter of this book I will use this as a springboard for exploring the thesis of the priority of language which Dummett has made definitive of analytic philosophy. Wittgenstein’s considerations are largely negative; nothing is gained by introducing mental items as the referents of words for sensations. He does not attempt to give an account of what manifesting a grasp of the meaning of an expression consists in. Indeed, much of what he says suggests that he believes that no such account can be given. His advice is: ‘if you want to understand the use of the word “meaning”, look for what are called “explanations of meaning” ’ (Wittgenstein 1967a, §560). The discussion just prior to this quotation anticipates Quine’s thesis of the indeterminacy of translation. Quine’s thesis asserts that at least two equally good, but non-equivalent, translations of an expression into a second language will always exist (Quine 1960, pp. 26–79: Hookway 1988, pp. 127–45). Since translation is the translation of the expressions of one language into synonymous expressions of another language, this thesis shows, if it is true, that there is no absolutely determinate synonymy relation between languages. Wittgenstein considers the possibility that a single language has two kinds of negation; one such that double negation yields an affirmation, the other such that a double negative is a strengthened negative. He asks whether these two forms have the same meaning in sentences where they are not doubled, and suggests various possible answers. One is left with

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the impression that there are a number of different adequate answers to the question, depending on one’s interests and decisions. There is no determinate answer to the question of whether these two negations mean the same when they occur singly. Wittgenstein concludes that since questions about meaning are not fixed by anything in our heads, they are not fixed, and a systematic account of meaning cannot be given. Despite his great respect for Wittgenstein, Dummett remains convinced that an explanation of communication should be possible, and requires a systematic account of the meanings of words. When indeterminacy of translation arises, this will be because the meaning of the term in the original language is not determinate. But the existence of some terms which are indeterminate in meaning does not demonstrate a total absence of meaning; nor does it demonstrate that there are no terms that are determinate in meaning (Dummett 1974c/78c). The positive content of the manifestability constraint has been the subject of considerable debate, and has led to the charge that Dummett’s account of meaning is overly behaviouristic (Gunson 1998, p. 54).3 Behaviourism is the doctrine that statements about the mind can be reduced to statements about dispositions to behaviour. Where the particular mental state we are interested in is that of understanding a word or sentence, this will imply giving an account of that understanding as some set of behavioural dispositions. When a child begins to manifest its understanding of language, it does so by saying ‘Cat’ in the presence of cats, by using the correct word to request items of food, and by correctly answering questions like ‘What is the colour of this?’ If we interpret the manifestability constraint as requiring that we give a reductive account of what understanding any sentence consists in, in terms of observable dissent or assent to sentences in the face of perceptual stimuli, then the charge of behaviourist tendencies is warranted. But such an interpretation assumes too great a convergence between Dummett, Quine and earlier verificationists. Dummett insists that one can manifest one’s understanding of a sentence not just by responding to the observable circumstances which justify asserting or denying it, but also by drawing inferences from it, saying what would have to be observed in order for one to be justified in asserting it, and showing that one knows what it is implied by (Dummett 1973b/ 78c, pp. 298–9). We manifest our understanding largely through reasoning, and not just by responding to stimuli. So it seems fair to say that, unlike the behaviourists who want to replace talk of rationality with something more scientifically respectable, such as

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successful behaviour, Dummett accepts that we can manifest our rational understanding, but not reduce it to responses to external stimuli. Behaviourism is an anti-mentalistic form of psychologism. Skinner’s version involves reducing talk of belief and intention to talk of probabilities of behaviour. Talk of belief and intention is rejected, because it assumes rationality, instead of explaining it away in favour of scientifically respectable dispositions to behave. Quine’s version of behaviourism similarly involves abjuring talk of beliefs, meanings and intentions, because these cannot be reduced to behaviour of assent and dissent (Dennett 1979, pp. 53–70). Once one tries to explain language in these terms, logical truths will be characterized via certain patterns of behaviour. Quine suggests that they are sentences that we are prepared to assert in the face of any sensory stimulus. Logical laws are treated as nothing more than very well-established hypotheses, which ultimately have a pragmatic justification. Quine argues that the distinction between analytic truths, thought of as truths in virtue of meaning, and synthetic truths, truths in virtue of the facts, cannot be drawn. So there are no truths in virtue of meaning (Quine 1961b; 1960, pp. 57–67). Dummett thinks that Quine is unable to say what it is for some sentences to be true in virtue of meaning, because the behaviour that Quine is prepared to count as showing a grasp of meaning is too narrow. Given a broad enough definition of behaviour, the behaviour of reasoning in accordance with the specified meanings of the logical constants can be described, and the meanings laid down can be shown to justify certain inferences. Unlike the behaviourists, then, Dummett has no inclination to explain rationality away. At most he wants to make our practice comprehensible from within a rational point of view. This may seen circular, but Dummett argues that not all forms of circularity make an enterprise pointless. In his ‘The Justification of Deduction’ he discusses this circularity and its consequence, the apparent impossibility of justifying deduction. Any account of the justifiability or rationality of our deductive practice will use deduction and reason, and so be circular. To show that an attempted justification is nevertheless not pointless, he makes a distinction between a suasive and an explanatory justification of deduction. It may be impossible to persuade an irrational creature of the justifiability of deduction, but this does not mean that we cannot give an explanation, from within, of the justifiability of our deductive practice. Despite being in one sense cir-

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cular, such a justification could still be illuminating (Dummett 1973b/78c). A general model of the way in which language works, in the light of which we could see which of our inferences are justified, would indeed dispel the fog that surrounds our use of language. Although Dummett does not attempt to explain the difference between the rational and the irrational agent, his attempt to explain what a justification of our deductive practice would look like can be used to throw light on why we call the beliefs of the insane ‘irrational’. One theory of insanity is that the insane are not irrational; they are merely responding rationally to abnormal experiences, which result in abnormal beliefs. Dummett’s thoughts on justification can be used to illuminate why we nevertheless deem such beliefs irrational. We can show that our deductive practice is justified if we can construct a model of the meanings of the terms we use in the light of which our inferences would be justified. Such a model will only justify our practice if it relates to the actual uses we make of sentences, the kind of situations that justify the assertions of sentences in our mouths, and the kind of evidence that is available to creatures with our capacities. Those who are insane assert sentences which have meanings in the public language which are such that we cannot accept that the evidence that would justify asserting them is available. Someone who claims to be dead, for instance, when they are clearly able to walk, talk and breathe, strikes us as irrational, because the evidence that is available to them would normally justify the assertion ‘I am not dead’.4 Such people seem to have lost their grip on our basic shared model of the meanings of words. Dummett is not interested in the causal underpinning of such apparent loss of rationality. Rather, he is interested in the conceptual articulation of what it is that has been lost by those who are no longer comprehensible as rational agents. His revisionist argument raises the worry that our best model of what makes our practice rational implies that those who unreservedly assert bivalence have, like the insane, lost their grip on the basic shared model of the meanings of words in the light of which at least some of our deductive practice can be justified. The charge of behaviourism is misguided. The manifestability constraint makes the minimal necessary concession to the behaviourist demand that we do not rely on mysteries in giving an account of language. For what would it be for someone to understand a sentence, say, ‘Diabetics taking insulin can suffer hypoglycaemia’, who could not manifest their understanding by

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explaining what they meant in simpler terms such as ‘sugar’, ‘blood’ and ‘disease of the pancreas’, which they could use in appropriate circumstances? This minimal concession does not imply that Dummett is in any way committed to the reductionism of the behaviourist. Another issue that might cast doubt on the manifestability constraint is its apparent conflict with the linguistic division of labour, discussed in chapter 1. If we think of the manifestability constraint as applying to speakers, it may sound like the implausible demand that each speaker must manifest in their use of any word with which they are competent, a complete grasp of its meaning. An individual may manifest their understanding of the word ‘diabetes’ by saying ‘It is a disease of the pancreas’, without then being able to go on to manifest a clear grasp of the term ‘pancreas’. For instance, they may have little idea where the pancreas is, and, in these times when sweetbreads are out of fashion, no idea what a pancreas looks like. Such a person can use this sentence to convey information, and it is natural to say that they understand it, but it appears that they are not able to manifest any non-trivial grasp of the meaning of the word ‘pancreas’. What we should say about this is that a person of this kind makes manifest that their understanding of the sentence is only partial. The linguistic division of labour enables them to use the sentence successfully, and they manifest a sufficient grasp of the meaning of the words to be counted a competent speaker. But they would not be in a position to explain or justify their assertion. This kind of example shows, I think, that the manifestability constraint should really be thought of as attaching to the language, rather than to the individual speaker’s competence with the language. The meaning of an expression must be something of which a knowledge can be acquired through the normal processes of learning, and which, when the knowledge has been acquired, can be manifested by those who have acquired it. It is not the case that everyone who uses a term need demonstrate a complete grasp of the meaning of the term. Rather, in giving an account of the meaning of a term or a sentence, we will have gone wrong if it would be impossible for a speaker who has a complete grasp of the meaning of that expression to manifest that they have such a grasp. The ordinary speaker’s use may be parasitic on the expert’s capacity to make manifest what the word ‘pancreas’ means, so its meaning may not be made manifest in their use. But it can be made manifest in the uses that experts make of it.

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Dummett and Quine A fruitful way of approaching much of Dummett’s work on the theory of meaning is to see it as continuing his early debates with Quine. We saw in the last chapter that Dummett is hostile to Quine’s nominalism, but the terms within which the discussion of nominalism is couched are very much Quine’s. On the broader issue of the theory of meaning, the relationship between the two thinkers might be put like this: Quine believes that meaning must be manifest in use (Quine’s verificationism), but that the unit of meaning is the whole language (Quine’s holism). Together these two premisses lead him to reject the analytic/synthetic distinction and to adopt the thesis that questions of meaning are inextricable from questions of fact. They are claimed to result in the thesis of indeterminacy of translation, which says that two empirically adequate but nonequivalent ways of translating one language into another will always be possible (Quine 1960, pp. 26–79; 1969, pp. 80–1). The rejection of the analytic/synthetic distinction amounts to the claim that there are no truths in virtue of meaning, and the indeterminacy thesis implies that there is no clear criterion of identity for meanings. One might take Dummett’s reaction to this to have the form of a modus tollens. If there is no clear criterion of identity for meanings and no analytic/synthetic distinction, then we cannot succeed at the kind of enterprise that Frege attempted, of making the meanings of some fragment of our language clear to view by giving a systematic account of its truth conditions (Dummett 1974c/78c, pp. 414–15). We cannot, therefore, provide the sort of justification for our practice which success in this enterprise would bring. This is a very high price to pay. So, while there is hope of success, we should attempt to make the analytic/synthetic distinction precise, and to display the identity conditions of the meanings of at least those fragments of our language which can be systematized. If we can do this, we will have shown that holism is false; for Dummett agrees with Quine that meaning must be manifest in use, although he has a more generous interpretation of the way we can manifest a grasp of meaning than does Quine. This results in two different ways of understanding the idea that meaning is a matter of use. The difference can be illustrated by an example. A simple proposition of arithmetic such as 5 + 7 = 12 can be thought of in two ways. Dummett, following Frege, thinks that

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it is analytic. Although it is not language which makes it true, once the meanings (referents) of the expressions have been laid down, we see that, given what the sentence says, it could not but be true. This can be roughly spelt out in the following way. We lay down the meaning of the numeral ‘5’ in such a way that it accords with our practice of counting out five things. We lay down the meaning of the numerals ‘7’ and ‘12’ in an appropriately similar fashion. We give the natural definition of addition and of equality for numbers. Thereafter there is no further question as to the truth of the proposition; it simply follows from the meanings of the words, as laid down by our use of them in the practice of putting objects in one–one correspondence with elements in some ordered series which we generate by the process of adding one element at a time. It was this kind of explanation of the meanings of the expressions of arithmetic which Frege attempted in greater detail and precision in the Grundlagen, and more formally in the Grundgesetze. Wittgenstein, by contrast, argues that nothing forces us to accept the necessity of this truth. It is merely a convention that we accept that 5 + 7 = 12 is necessarily true.5 Nothing in our training rules out the possibility that when we count the sum of 5 and 7 it should sometimes come out as 13. When we insist on deeming any such occurrence a miscount, we are adopting a new convention. Quine, when he introduces his notion of ‘analytic hypotheses’ in translation, is giving expression to a similar thought. Quine’s ‘analytic hypotheses’ are hypotheses that a radical translator introduces concerning the meanings of key words (in particular, the quantifiers) in a native dialect (1960, pp. 68–72). The picture which Quine sketches is that these meanings cannot be uniquely determined from the observable behaviour of assent and dissent of the natives. Meanings which can be determined on the basis of such behaviour Quine calls ‘stimulus meanings’. The meanings assigned to the quantifiers are not required by the stimulus meanings which can be observed to accrue to simple observation sentences. In fact, the natives will have made a choice to accept some truths as analytic. There will have to have been a choice, because their theory of what there is, their basic ontology, is underdetermined by the evidence for it. So the translator must hypothesize as to what this choice has been. Because of the element of convention and choice which enters into every language, the more complex parts of the language will not be determined by its simpler elements. It is this slack, or ‘play’, which results in indeterminacy of translation, and which has the consequence that we cannot give determinate identity conditions

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for the meanings of the expressions in the native language in any other language. Dummett is impressed by some features of Quine’s way of thinking about language. In particular, he thinks that Quine is right to have criticized the atomistic account of meaning that characterized the early positivists. However, he argues that the model for the functioning of language that Quine sketches at the end of his famous paper ‘Two Dogmas of Empiricism’ is quite compatible with the retention of the analytic/synthetic distinction and with a systematic account of language. According to Quine’s model, language is a network of sentences connected by inferential links and related to empirical evidence at the periphery (Quine 1961b). The meanings of sentences close to the periphery will be closely associated with the sensory evidence that is taken to warrant their assertion. The meanings of the sentences in the interior will be determined by their place in the network of inferential connections, and will be related to any particular sensory evidence only indirectly. In order to give the meaning of a sentence, one may have to explain the use of the words in it by explaining the contribution they make to sentences which constitute a substantial fragment of the language. But, according to Dummett, this does not show that the unit of meaning is the whole language. If it were the whole language, one could never complete an account of the meaning of any word or sentence. But one can come to the end of an account of a word’s meaning, so Quine’s critique of atomistic accounts of language shows only that an account of meaning will have to be ‘molecular’, not that it must be holistic (Dummett 1976e/93d, p. 38).

Two Challenges: Holism and Strict Finitism The fact that the slogan ‘meaning is use’ is open to a construal different to that which Dummett wants to put on it opens two lines of objection to the possibility of succeeding in the project that Dummett identifies with making the workings of our language clear to view, and the argument against bivalence which he believes falls out of that project. These two lines of objection are first outlined in schematic form in the paper ‘Wittgenstein’s Philosophy of Mathematics’ (Dummett 1959d/78c). The first I will dub ‘the challenge from holism’, the second, ‘the challenge from strict finitism’. The challenge from holism has already been sketched. The holist’s picture of language contrasts with a traditional empiricist view

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according to which simple sentences have meanings that can be identified with the perceptible states that would verify them, and complex sentences have meanings which have been constructed out of simpler elements. According to the holist, complex theoretical sentences can impact on the meanings of simple ones, so that perceptible states that would once have been taken to verify a simple sentence may, in the light of theory, no longer do so. Words have meanings in virtue of their place in the language as a whole, and changes anywhere in the language will impact throughout the language. We accept certain sentences as fundamental to our worldview, and this impacts through the language, but nothing forces us when we make a decision to accept certain sentences as fundamental or, as we say, ‘analytic’. Adopting some such fundamental sentences means no more than treating them as not currently open to falsification on the basis of evidence. Meanings are not fixed, but are constantly changing as the pattern of acceptable assent changes over time. Dummett first outlines his central objection to holism of this kind in ‘Wittgenstein’s Philosophy of Mathematics’: If Wittgenstein were right, it appears to me that communication would be in constant danger of simply breaking down. The decision to count a particular form of statement as logically true does not affect only the sense of statements of that form; the senses of all sorts of other statements will be infected, and in a way that we shall be unable to give a direct account of, without reference to our taking the form of statement in question as logically true. Thus it will become impossible to give an account of any statement without giving an account of the sense of every statement, and since it is of the essence of language that we understand new statements, this means that it will be impossible to give an account of the use of our language at all. (Dummett 1959d/78c, pp. 176–7)

Arguments which support the claim that the holist is unable to give a coherent account of communication also occur in Frege: Philosophy of Language (Dummett 1973a, pp. 597–600) and in The Logical Basis of Metaphysics (Dummett 1991e, pp. 221–44). Some of the issues involved are connected with those that arise between Davidson and Dummett over the role of the language qua social entity in the theory of meaning, and will be discussed at the same time. However, we should notice that implicit in this quotation is a

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picture of the functioning of communication which Wittgenstein implicitly rejects when he says: ‘we are so much accustomed to communication through language, in conversation, that it looks to us as if the whole point of communication lay in this: someone else grasps the sense of my words – which is something mental: he as it were takes it into his own mind’ (Wittgenstein 1967a, §363). Dummett may seem to be objecting to the holist that we could not take the whole of language into our minds; but were he doing so, he would be slipping into something equivalent to the mentalism that Wittgenstein is warning against. If this were the only way of interpreting Dummett’s objection, it would be inadequate. A better way of making Dummett’s point is that unless we can know the meanings of some words by knowing a fragment of the language, we will be unable to make sense of the idea that some uses are faithful to those meanings, others not. Where two people disagree over the correct use of some word or expression, there will be no way of deciding who is correct, so no way of determining what was in fact said. But this consequence of his views would be accepted by Wittgenstein, so, put this way, the objection amounts simply to a refusal to be persuaded by the holist’s account of meaning. Rather than accepting that we grasp something which determines our use, Wittgenstein appears to equate understanding with our actual use. If attaching a certain meaning to certain words and phrases simply consists in being disposed to use them in a certain way, then the meanings of words will be determined by our actual usage. The actual use that we have made of terms up to some point in time will be capable of being extended in a number of different ways. There is no reason to claim that one of these extensions is the one justified by the prior uses. For there is nothing to the meaning beyond these actual uses, and those uses can, in fact, be extended in a variety of ways. This line of reasoning leads to the challenge from strict finitism. The challenge from strict finitism reflects a difficulty for intuitionism that was first raised by Bernays (1935/64, pp. 280–1). Dummett has argued that an account of meaning may be given in terms of truth conditions, but the notion of truth has to be explained in terms of its relationship to our practice of assertion, and that this leads to a notion of the truth of a sentence as residing in the existence of something which would warrant our assertion of the sentence were we to be appropriately placed. When we come to the

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realm of mathematics, it is the existence of a proof which typically warrants the assertion of a sentence. Unfortunately, some proofs are unsurveyable. When this is the case, it might be thought that it cannot be the existence of the unsurveyable proof which warrants us in accepting a theorem as true; for, since the proof is unsurveyable, we have lost the required connection between truth and the recognition of truth. As a matter of fact, we can often replace an unsurveyable proof with a proof which uses definitions, or stronger methods of proof, and this becomes our immediate justification for asserting the truth of the theorem. Wittgenstein and the holist claim that in doing this we are adopting a new criterion of truth. The strict finitist, by contrast, argues that the procedure is illegitimate. We should accept as true only those theorems for which there are canonical surveyable proofs. Truth will then be identified with the actual existence of such a proof, and the connection between truth and the conditions which warrant assertion will be strictly maintained. Strict finitism brings with it its own problems, for ‘surveyable’ turns out to be a vague term like ‘bald’. Suppose that a large number is surveyable, then its successor must be surveyable, for the addition of one cannot make it unsurveyable; but by this means the totality of the number series can be shown to be surveyable. This is not the end of the matter, for such reasoning is notoriously paradoxical. Suppose that a man is bald; the addition of one hair cannot make him non-bald. But by this means we can show that no amount of hair will make him not bald. The Sorites paradox, or the paradox of the heap, thus enters into Dummett’s philosophy, as an important side issue (Dummett 1975c/78c). In the paper ‘Wang’s Paradox’, which dates from 1970, but was not published until 1975, Dummett used it in an argument against the coherence of strict finitism. But his doing so involved endorsing Frege’s implausible rejection of the acceptability of vague concepts. More recently his reorientation towards realism has involved him emphasizing the point he first made in 1973; that the fruitfulness of deduction will bring with it a gap between truth and actual verifiability (Dummett 1973b/78c, pp. 311–18; 1991e, p. 182). Accepting this undermines the plausibility of strict finitism. However, it might be thought to undermine the argument for intuitionism as well. We will take up these complex matters again in the next chapter. For the time being we will return to the more central themes introduced in the previous chapter.

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The Manifestability Constraint and the Priority of Language In the last chapter we flagged two related issues with regard to which the influence of Wittgenstein on Dummett’s thinking is clear. The first, which we have discussed at length, was the manifestability constraint; the second, the priority of language. These two issues are related in the following way. If we are to say what the knowledge of meanings consists in, without resorting to the myth of an inner mental association between a sentence and its meaning (thought of perhaps as an idea), then we will have to do so by explaining what sort of practical ability is manifested by someone who knows the meaning of a sentence or set of sentences. But equally, to accept that knowledge of meaning must be explained as a manifestable practical ability is to accept that we cannot explain language by appealing to thoughts or ideas that are given prior to language; we must explain what it is to have a thought via our explanation of what it is to understand a language.6 Dummett argues that in his critique of psychologism, Frege had seen that we cannot explain what understanding a sentence consists in by appeal to the association between sentences and ideas. He had therefore described the meanings of sentences as thoughts, which objectively exist in a ‘third realm’. Yet, having seen the problem with an account of meanings as subjective ideas, Frege’s claim that thoughts exist in a ‘third realm’ was hopeless, for it remains a mystery in what our grasp of thoughts consists. It was Wittgenstein, according to Dummett, who provided a solution to this mystery by insisting that we explain what understanding a sentence consists in in terms of the use that is made of it. Yet, as we have seen, Wittgenstein thinks that the use of the word ‘meaning’ leaves a great deal of vagueness with regard to claims that a word has a particular meaning, and he is hostile to Frege’s search for precise concepts. Frege’s overall project, to put mathematics on a sound footing as a science, is very different from Wittgenstein’s descriptive therapy. Many issues are muddied by treating these two thinkers as though they are engaged in the same project. One such issue is the relationship between Frege’s concepts and the notion of sense. Dummett says: ‘Frege strongly attacked, in the Grundlagen and elsewhere the empiricist conception of sense as consisting in the propensity a word may have to call up in the mind of speaker or hearer any associated mental images’ (1973a,

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pp. 157–8). This suggests that at the time of writing the Grundlagen, Frege already had in mind the notion of sense as that which is known by someone who understands a sentence. But, as we have seen, the distinction between sense and reference was not drawn by Frege so early; so Dummett’s early interpretation is tendentious, as he admits in a later discussion of the context principle (1995b). The doubts raised warrant a closer inspection of the actual intention of the Grundlagen arguments. This will, I hope, provide a clearer understanding of the character of Frege’s realism and the distance, particularly with regard to normativity, that exists between him and Wittgenstein. In the last chapter I will suggest a way in which the normative project that Frege was engaged in can be developed so as to avoid the mentalism against which Wittgenstein warned, without falling foul of the descriptive truths of which Wittgenstein makes us aware. Although the account that I will offer there is not explicit in Dummett, it is, I will argue, the most coherent direction in which to develop the difficult combination of insights from Frege and Wittgenstein that Dummett wants to retain. Dummett’s view is that once Frege made it clear that understanding could not consist in the association of a subjective image with a sentence, and once his own solution of a ‘third realm’ is seen to be defective, the stage was set for Wittgenstein’s thesis that meaning is use: As a positive solution the myth of the ‘third realm’ has nothing to offer; but . . . [we should] see the importance of the negative part of the doctrine. On the one hand, it liberated Frege from seeking an account of thoughts in terms of psychological operations . . . On the other, it opened the way to analytic philosophy. For the thesis that senses are not contents of consciousness required that they be constituted by something objective, non-mental and yet not in the ordinary sense physical, and accessible to all: once the myth of the third realm is discarded, what more natural to identify as constituting them than the social institution of a common language? (Dummett 1991b, p. 226)

Frege had seen the central truth that an account of communication requires that senses are objective entities: The principle which Frege opposes to psychologism is that of communicability of sense. Of some inner experience of mine . . . I can tell you what it is like. But in the case of thought, I do not have to confine myself to telling you what it is like to have a thought that I have had: I can communicate to you that very thought. (Dummett 1993b, p. 102)

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But because he thought of these senses as objective entities existing in a third realm, he was reduced to using the metaphor of the mind grasping a sense in order to explain the relationship of a thinker to a thought. Such a ‘grasping’ is still thought of as a mental process, so mentalism is not avoided. It was up to Wittgenstein to show how to escape it, which he does, according to Dummett, in the way indicated in the following passage: Even granted that senses are not mind-dependent, still grasping a sense, or understanding a word or phrase, as expressing a sense, is surely a mental act, something that belongs within the province of psychology. Frege never found a satisfactory answer to this objection: it receives its answer from Wittgenstein’s observation (Philosophical Investigations, §154), ‘Try not to think of understanding as a mental process at all. . . . In the sense in which there are processes (including mental processes) which are characteristic of mental understanding, understanding is not a mental process.’ (Dummett 1981a/ 91b, p. 238)7

So, the Wittgensteinian view of language is taken to be the legitimate heir of Frege’s attack on psychologism. But there are reasons to doubt this. In his attack on psychologism, Frege was centrally concerned to defend the objectivity of logical truth, and to secure the position that there are truths in virtue of meaning of the kind that it was the project of the Grundlagen to display. Dummett’s reading of Wittgenstein’s anti-mentalism, and subsequent understanding of the import of the slogan that meaning is use, is that it results in a radical conventionalism which denies that there are any necessary truths which are truths in virtue of meaning. We have seen that this places Dummett in the awkward position of having to understand the slogan ‘meaning is use’ in a manner which is different from that which he believes Wittgenstein to have adopted. Yet, once the slogan ‘meaning is use’ is in place as the key to understanding the meaning of ‘meaning’, radical conventionalism is a natural outcome. For it really is difficult to see how future uses of terms can be imposed on us by past uses. How, for instance, could the proof of the independence of the parallel postulate be something which had to follow simply from the Euclidean and pre-Euclidean use of geometrical terms in measuring lines and angles? One can perfectly easily imagine a history in which the human race died out without this proof ever having been discovered, or even that the proof might

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have been discovered only to be rejected as counter-intuitive. If there is a necessity here, it seems to be a necessity either in the way things are or in features of the formal language of geometry, not something required by human practices. If we think of the axioms of geometry as analogous to the rules of a game, then it seems that we might have decided not to allow non-Euclidean geometries as legitimate.8 So the move to associating meaning with use naturally leads in the direction that Wittgenstein thought it did, and away from the acceptance of the existence of objective truths in virtue of meaning. Yet it was centrally to secure the objectivity of such truths that Frege attacked psychologism. Dummett is completely aware of these facts. However, unlike Wittgenstein, he believes that, by laying down the use of certain terms, we can demonstrate that some sentences are true in virtue of meaning. We will see in the next chapter that the negation-free fragment of intuitionistic logic is capable of being justified on the basis of an account of meaning which satisfies the requirement that meaning be manifest in use (Dummett 1991e, pp. 245–65). But despite this, the tensions inherent in this middle path render it unstable. It is interesting to note, in passing, that, if Michael Wrigley is correct, Wittgenstein’s radical conventionalist views on rule following were a response to a problem which was brought to his attention by Brouwer. So Dummett’s reinterpretation of the slogan that meaning is use in such a way as to make it compatible with the practice of intuitionists (if not Brouwer’s rhetoric) could be seen as an act of historical restitution. In a series of papers Wrigley argues that it is true that Wittgenstein’s attendance at Brouwer’s lectures in 1928 influenced him, and was part of the impetus for the rejection of the Tractatus and for the years of intellectual ferment which culminated in the Philosophical Investigations (Wrigley 1993a, 1993b, 1995).9 At the time of the Philosophical Remarks, Wittgenstein had been convinced, through the influence of Brouwer, that the actual or completed infinite is meaningless, and he claimed that our grasp of the infinite must be through a grasp of a rule or law. Wittgenstein’s (mis)understanding of intuitionism at this time was that our application of an infinite rule depends on an act of intuition, or insight, and it is because any such series of acts is necessarily finite that infinity is always only potential. Here Wittgenstein seems to have succumbed to the view that understanding is a mental process, which he was later at pains to combat. Having rejected any such mentalistic reading of what is involved in applying a rule, he ultimately developed the radical conventionalist view which is so often

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attributed to him. According to this view the application of a rule is always in some sense a decision: . . . even if the proved mathematical proposition seems to point to a reality outside itself, still it is only the expression of an acceptance of a new measure (of reality). . . . Why should I not say: in the proof I have won through to a decision? . . . The proof places this decision in a system of decisions. The proposition proved by means of the proof serves as a rule – and so as a paradigm. For we go by the rule. (Wittgenstein 1967b, p. 77)

So the historical situation might be characterized as follows. Having been convinced by Brouwer that our finite experience can provide us with no grasp of the completed infinite, Wittgenstein adopted, for a time, a position which he thought of as close to Brouwer’s. But the inadequacy of this position ultimately led him to a rather confusing amalgam involving elements of both holism and strict finitism.10 According to the first of these, there are no fixed meanings; meaning is equated with actual use, and develops as usage develops. According to the second, clear content accrues only to those portions of our practice such that the conditions for correct use are actually recognizable. Neither of these views can provide a justification or foundation for our mathematical practice. This is all to the good, according to Wittgenstein, for it is not the role of philosophers to provide such things. Dummett, however, like Frege, accepts the need for justification, and, accepting the force of the intuitionist’s views, has chosen to explore the middle position adopted by them. But the position has tensions, seeming often in danger of collapse in one of two directions: towards realism or towards the strict finitism that Wittgenstein preferred. It remains unclear whether the doctrine that meaning is use can deliver the kind of truth in virtue of meaning that is needed if mathematics and logic are to be justified.

How do Anti-Mentalism and Anti-Psychologism Stand to Each Other? Dummett often represents Frege’s anti-psychologism as essentially a doctrine concerning the communicability of sense. This obscures the distinction between anti-mentalism and anti-psychologism, however. It is clear that Frege’s realism and his anti-psychologism

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are closely connected. It is because he wants to insist that logic and mathematics are objective sciences which discover eternal truths that Frege is deeply opposed to any view that would turn the study of logic into the psychological study of the patterns of our reasoning. He is interested not in the laws by which we actually draw inferences, but in the laws of valid inference (Frege 1979, pp. 4, 175). The logical laws in which the truths of arithmetic are grounded are eternal truths, so the objects which those truths require us to recognize are themselves objectively existing non-material objects which have determinate properties (Frege 1884/1950, pp. 33–6). Since the emphasis here is on truth, the most natural way to interpret Frege’s discussion of anti-psychologism in the Grundlagen, and in other works pre-1890, is as applying to reference. Frege expresses his realism by insisting on the objectivity of arithmetical truths, the objective existence of numbers, the objectivity of concepts, and the objective nature of possible contents of judgement. The first two clearly involve reference. Yet Dummett interprets Frege’s antipsychologism as essentially a doctrine relating to the publicity and communicability of senses. If there is a doctrine of the objectivity of sense in Frege’s early writings, it must derive from what he says on the last two issues. What does Frege have in mind when he discusses the objectivity of concepts? After introducing the distinction between sense and reference, Frege continues to use the term ‘concept’ for the reference of a predicate, which is some indication that his earlier use was already intended to pick out the referents rather than the senses of predicates. This is implied by what he says in §§46–7 of the Grundlagen. There he introduces the idea that a statement of number is an assertion about a concept (Frege 1884/1950, p. 39). He goes on to reject the view that a concept is something subjective, for the following reasons. If we bring the concept of body under that of weight, by saying that all bodies have weight, we are asserting something objective. But if the concepts between which the relation of subordination held were subjective, then the relation between them would also be subjective. It is central to Frege’s metaphysics that concepts are objectively existing entities (which are not objects) between which (second-order) relations hold which we can express using sentences that involve quantifiers.11 The fact that he thinks this way means that he is committed to a doctrine which many would think Platonistic, even before he has introduced numbers as objects. Platonism is often thought of as the doctrine that there are universals. Frege’s concepts are not universals in the traditional

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sense, for they are not objects, they are functions. But they are very close to being universals, for they are the objectively existing referents of logical predicates (Frege 1971, p. 33). The doctrine of the objectivity of concepts which we find in the Grundlagen is a doctrine which is most plausibly interpreted as relating to reference rather than to sense. An indication of the strength of Frege’s realism with regard to concepts, and the way in which he understands their relationship to laws of nature, is provided by the following passage: The technical language of any science must conform to a single standard and must be judged with that standard in mind: does it enable the lawfulness of nature to be expressed as simply as possible and at the same time with perfect precision? And with this in mind I find it regrettable that the word ‘concept’ is now frequently used in phrases which are incompatible with its logical sense. A logical concept does not develop and it does not have a history. . . . a concept is something objective, we do not form it, nor does it form itself in us, but we seek to grasp it, and in the end we hope to have grasped it, though we may mistakenly have been looking for something where there was nothing. ‘The number three falls under the concept of a prime number’ is an objective truth . . . What we want to assert in using that proposition is something that always was and always will be objectively true, quite independently of our waking or sleeping, life or death, and irrespective of whether there were or will be other beings who recognise or fail to recognise this truth. (Frege 1984, p. 133)

So, while Frege is clear that concepts can exist uninstantiated, instantiated concepts correspond to the objectively existing properties of things. Senses may be ‘ways of being given’ objects or properties, but the objects and properties themselves exist independently of the ways they are given to us. It is when we come to the objectivity of possible contents of judgement that we come closest to a doctrine which seems to be that of objectivity of sense. For example, in the fairly early fragment ‘Logic’ Frege says: We do not directly observe the processes in the mind of another. Strictly speaking, therefore, we can only form a superficial judgement of the similarity between mental processes, since we are unable to unite the inner states experienced by different people in one consciousness and so compare them. If the content of the sentence 2 + 3 = 5 is exactly the same, in the strictest sense, for all those who

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Once Frege introduces the distinction between sense and reference, he replaces the notion of content with that of thought and truth value, and asserts in an exactly analogous way that the thought expressed by the sentence 2 + 3 = 5 is the same for all those who grasp it. But did he at the time of Grundlagen already implicitly think of possible contents of judgement as senses? It seems to me, for the following reasons, that he did not. Before he introduced the distinction between sense and reference, it appears that Frege thought of possible contents of judgement as made up out of the referents of the expressions which are to be found in indicative sentences. So, in ‘17 Key Sentences on Logic’, a piece which Dummett dates as fairly early, and probably earlier than 1884 (Dummett 1981b/91b), Frege has the following to say about thoughts: ‘A sentence can be true or untrue only if it is an expression for a thought. The sentence “Leo Sachse is a man” is the expression of a thought only if “Leo Sachse” designates something’ (Frege 1979, p. 175). Although Frege is here using the terminology of thoughts, what he says corresponds to his views concerning possible contents of judgement. A possible content of judgement can be split up in different ways so as to result in various concepts and relations. He suggests that this implies that the content is already articulated (Frege 1979, p. 17). Although we are never given objects or concepts independently of sentences in which the terms referring to these entities occur, still, a possible content of judgement somehow contains the objects and concepts into which it can be split. So if a word in a sentence which looks as though it is picking out an object fails to do so, there will be no content picked out by the sentence. After he has introduced the distinction between thought and truth value, Frege is able to acknowledge that a sentence containing a non-denoting name may express a thought, although it will not have a truth value. What this suggests is that early on Frege is thinking of possible contents of judgement as something like states of affairs: things in the realm of reference constructed out of objects and concepts. This way of looking at the matter means that he has to recognize the existence of false states of affairs. His fragmentary ‘Logic’ breaks off just after he has observed that ‘the content of any truth is “a content of possible judgement”, but so too is the opposite content’ (Frege 1979, p. 8). It

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is an advantage of his adoption of the view that the reference of a sentence is a truth value that he can dispense with these elements of the realm of reference which have the awkward property of being entities which do not exist.12 Perhaps they struck him as embarrassingly like the referents of non-denoting terms which he refuses to countenance in his ‘Dialogue with Pünjer on Existence’ (Frege 1979, pp. 53–67). If so, we may have an explanation of why the fragmentary ‘Logic’ breaks off just where it does. Frege’s central concern in rejecting psychologism is to secure the objectivity of mathematical truth. He wants to insist that numbers are abstract objects which are things that are the same for all of us, and with regard to which truths hold that are quite independent of our opinions. This leads him to insist that the content of a sentence cannot be a mental image. What he is insisting is that what we are talking about in mathematics are not mental images, but abstract entities (both objects and concepts) and the relations that hold between them. Near the end of the Grundlagen he expresses his view of mathematics thus: The laws of number, therefore, are not really applicable to external things; they are not laws of nature. They are, however, applicable to judgements holding good of things in the external world: they are laws of the laws of nature. They assert not connections between phenomena, but connections between judgements; and among judgements are included the laws of nature. (Frege 1884/1950, p. 99)

We should remember that at this stage judgements are possible contents of judgement plus something (symbolized in the Begriffsschrift by the judgement stroke) which changes their content. They are something like assertions that states of affair obtain.13 The connections between judgements hold because of the existence of relations that obtain between concepts, relations like that of being equal, defined in §70 of the Grundlagen. So we should keep in mind that while Frege’s anti-psychologism does lead him into anti-mentalism, the view that meanings are not mental images, this is an antimentalism very much at the service of the enterprise of showing how mathematical truths are eternal truths residing in relations between concepts which are themselves when instantiated properties that exist quite independently of human practices. Not every kind of anti-mentalism would, therefore, be congenial to Frege. It seems that the position adopted by Quine in ‘Epistemology Naturalized’ would not be. Quine’s view is anti-

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mentalistic. Indeed, he says that ‘all inculcation of meanings of words must rest ultimately on sensory evidence’. He argues, however, that since justificatory epistemology is doomed, because it is impossible to show how general statements, or even singular statements about the future, are made certain by the sensory evidence, there is no reason to eschew psychology. Since we are unable to effect a successful reduction of our beliefs to indubitable simple truths that are observable (and can be observed to be grasped), we cannot provide an epistemological foundation for our beliefs, and we might as well give up the search for any such thing, replacing justificatory epistemology with descriptive psychology (Quine 1969, pp. 71–6). This, then, is an anti-mentalistic psychologism. It obscures the distinction that Frege insisted on between the genesis of belief and its justification (Frege 1879/1970, p. 5). By making epistemology part of natural science, rather than showing how science can be justified epistemologically, it reverses the relationship of natural science and philosophy implicitly accepted by Frege and explicitly defended by Husserl in his Logical Investigations (Husserl 1900/70). In order to accord with Frege’s intentions, the account that we give of the meanings of the sentences we use must be compatible with the view that those sentences can, and sometimes do, express objective truths, and it must show how we can justify our belief in those sentences. We should recognize that, although Frege’s statement of his antipsychologism does involve a certain rejection of mentalism, it also invokes very much the picture which Wittgenstein rejected when he introduced the idea that it is the use of signs which gives them life. Dummett suggests that one of the places at which Wittgenstein is at his worst is early on in the Blue Book when he characterizes Frege’s objections to formalism thus: ‘what must be added to the dead signs in order to make a live proposition is something immaterial, with properties different from all mere signs’ (Wittgenstein 1958, p. 4; Dummett 1981a/91b, p. 239). Wittgenstein retorts: ‘But if we had to name anything which is the life of the sign, we should have to say that it was its use.’ Dummett responds by suggesting that it is plausible to interpret Frege as giving an account of the use of mathematical expressions when he shows that when we grasp the sense of a sentence, we grasp the condition for the sentence to be true (Dummett 1981a/91b, pp. 240–1). But Frege’s characterization of what it is to understand a sentence involves postulating judgeable contents and later thoughts, which are the meanings of

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sentences, and which Frege characterizes as objective but nonactual entities. So Frege’s views do fit in with Wittgenstein’s sketch, although at the same time they are partly misrepresented by it, because thoughts and concepts are identified in this sketch with mental images. If we are going to accept Frege’s outlook as one which is compatible with the slogan that meaning is use, we will have to show how talk of grasping thoughts can be reconstrued in a way which relates it to the use we make of sentences, or else how it can be disregarded as an irrelevant anomaly within Frege’s theory of meaning. Dummett’s preferred strategy appears to be the second. He rationally reconstructs what Frege says about grasping thoughts by showing that such phrases constitute a misleading and unnecessary anomaly. In the paper ‘Frege’s Myth of the Third Realm’ he argues that Frege was wrong to take thoughts as the objects of mental acts (Dummett 1986b/91b, p. 253). He claims that Frege went wrong when he thought of truth values as attaching to thoughts rather than to sentences, for this suggests that we can grasp a thought independently of assigning a reference to an expression. But what Frege in fact does in the Grundgesetze is to stipulate what the referents of primitive expressions are to be, and in so doing he specifies the conditions under which a sentence is true, and thereby shows its sense. Doing this requires that we have the notion of reference prior to that of sense, and that we understand sense as the way in which reference is given. ‘A thought should be explained as a way of referring to a truth-value’ (p. 257). One might add to this the gloss that it was because Frege initially thought of contents of possible judgements as referents that he was misled into thinking of thoughts as objects of thought. Later on he did not take his own notion of sense far enough to realize that a thought is just a way of being given something else, a truth value. If we take this path, we can then explain the rather obscure notion of a sentence referring to a truth value in terms of its being capable of being used to make an assertion: ‘if we start with thoughts, considered as merely expressed, not asserted, judgement becomes, not simply inexplicable, but mysterious, it is better to start with sentences whose utterance constitutes assertion, and explain the expression of unasserted thoughts in terms of them’ (p. 259). By taking this path we also show how, despite what Wittgenstein claimed, Frege’s theory of meaning can be seen to be interpretable as a theory grounded in the use we make of sentences. But can this strategy

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actually provide the materials for the sort of justification of our beliefs which Frege required? In part, the answer must wait until the next chapter, in which we will examine Dummett’s attempt to show under what circumstances we can justify rules of inference in the light of the use that we have laid down for the logical constants. However, there are some reasons for thinking that such a strategy is unlikely to provide the sort of justification Frege was after. Dummett argues against the view that concepts are contents of consciousness in ways which echo Wittgenstein (Dummett 1993b, pp. 132–5). Wittgenstein’s anti-mentalism is often illustrated with examples such as the understanding of words like ‘yellow’ or ‘red’. According to a theory of understanding which gets its classic exposition in Locke’s Essay Concerning Human Understanding, to understand a word of this kind is to associate with it an idea. Wittgenstein mocks this view by suggesting that it involves comparing a mental sample of yellow with things in the world in order to determine whether they are yellow. The mental image is thought of as like a painted image, but ‘why should the written sign plus the painted image be alive if the written sign alone was dead?’ (Wittgenstein 1958, p. 5). He then asks us to consider what happens when we are told to imagine something yellow. If in the first case we needed a mental sample, we would now need another one in order to check that what we had imagined was yellow. The interpolation of mental images is rejected as unexplanatory and redundant. However, it is not clear that the Lockean theory is as silly as Wittgenstein makes it out to be. Moreover, there are passages in Wittgenstein which are at least compatible with a reformulated Lockean theory. Locke distinguishes between ideas as images in our minds and ideas as powers in things to affect us in certain ways. Powers or properties of things have regular effects on our perceptual apparatus, and we can remember what these are. It is only by perceiving and remembering how things look that we are able to acquire any visual knowledge of the world at all, and when we understand a word for a colour, we do remember how things which are referred to by it look. This is particularly clear with the name of an unusual colour like puce. If you know the meaning of the word ‘puce’, you will be able to remember what puce things look like (which is not very different from imagining the colour puce). Of course, you may think that you know the meaning of the word ‘puce’ and be mistaken, which shows that the meaning is not whatever mental image crops up in your mind, but rather is the publicly

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visible power or property which characteristically looks a certain way. If Locke had not left himself open to the interpretation that he identified colours with images in our minds, rather than with the properties which we can think about through having mental images, there would have been nothing wrong with his claim that part of the process of consciously understanding colour words is having that ability to know what one knows when one knows what a colour looks like, which we call ‘imagining a colour’. Dummett’s own view of the meaning of colour predicates is that our use incorporates an embryonic theory according to which colours are propensities to affect us in certain ways (Dummett 1979a/93d, pp. 399–400). My charitable reading of Locke adds to this that we could not understand the terms for picking out such propensities unless we had the capacity to remember what it was like to be affected in the way in which colour properties affect us. The reference of the predicates may be the properties, but the capacity to refer to these properties goes by way of their effects on us. Wittgenstein’s point may be that this process, which involves the visual memory of colours, cannot be identified with understanding a colour word, for it is not essential to such understanding. The process, if it exists, is merely a means to the end of using the word correctly, and this end is what understanding consists in. We understand words for ultraviolet light without being able to imagine what it looks like, because there is no way it characteristically looks to us. Put this way, Wittgenstein’s observations are completely consonant with Frege’s views. For Frege acknowledged that in many cases mental imagery goes along with understanding, but argued that understanding could not be identified with having mental images, because we do not in general speak about our mental images, which are private, and because there are many areas of language in which no mental imagery is available. Yet there is also a way of putting Wittgenstein’s point which suggests a conflict between his characterization of understanding and Dummett’s. Wittgenstein sometimes seems to be adopting a position congenial to behaviourists, according to which talk of what is available in consciousness is irrelevant to understanding. But, as we saw, Dummett says: The theory of meaning has, as its task, to explain what language is: that is, to describe, without making any presuppositions, what it is that we learn when we learn to speak. The fact that the use of language is a conscious rational activity – we might say the rational activity – of intelligent agents must be incorporated into any such description, because

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Dummett has a desire for a philosophical understanding of the kind that Wittgenstein wants to cure. In the light of this quotation, Dummett’s view ought to be that if our conscious knowledge of the use of colour vocabulary does involve the capacity to imagine what coloured things look like, this will not be irrelevant to an account of understanding. This will not imply that mental imagery is always relevant to understanding, for clearly, in the case of our understanding of many expressions – logical constants, quantifiers, large numerals and names of abstract objects – the capacity to form mental images of their referents is not part of comprehension. However, this is not to say that some means of representing to ourselves the use of such terms may not be an important ingredient in that understanding. When interpreted as aimed at the view that meanings are mental images, Wittgenstein’s attack does not apply to Frege, for here, Frege was a trail-blazer and was strongly opposed to empiricist theories of meaning, of which Locke’s is the paradigm. In a draft of ‘On Concept and Object’ Frege accuses Kerry of having failed to distinguish ideas from concepts and properties, and he associates this ‘widespread sickness’ with empiricism: would not Locke’s empiricism and Berkeley’s idealism, and so much that is tied up with these philosophies, have been impossible if people had distinguished adequately between thinking in the narrower sense and ideation, between the parts of a content (concepts, objects, relations) and the ideas we have? Even if with us men thinking does not take place without ideas, still the content of a judgement is something objective, the same for everybody, and as far as it is concerned it is neither here nor there what ideas men have when they grasp it. In any case these are subjective and will differ from one person to another. (Frege 1979, p. 105)

But Wittgenstein’s attack is at the same time an attack on a view to which Frege did subscribe: the view that the meanings of concept words are non-material, unsaturated entities, which he calls concepts. Having introduced the study of language games as ‘the study of primitive forms of language or primitive languages’, Wittgenstein recommends such study as a means for removing ‘the mental mist which seems to enshroud our ordinary use of language’, and

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diagnoses resistance to the strategy as deriving from a ‘craving for generality’. He diagnoses this craving as the result of four tendencies: ‘the tendency to look for something common to all the entities we commonly subsume under a general term’, the tendency to think that there is a general idea of a leaf which is like a visual image, ‘the confusion between a mental state, meaning a state of a hypothetical mental mechanism, and a mental state meaning a state of consciousness (toothache, etc.)’, and lastly, ‘our preoccupation with the method of science’ (Wittgenstein 1958, pp. 17–18). The first and last of these tendencies are justly ascribed to Frege. But Wittgenstein’s treatment of them as inevitably bound up with the mentalism captured in the other two misrepresents Frege’s thought, and seems to result from Wittgenstein’s having succumbed to the ‘widespread sickness’ of equating ideas and concepts. A historical diagnosis of the situation might be as follows. Russell rejected Frege’s distinction between sense and reference, and argued in ‘On Denoting’ that the distinction was confused, and that all the puzzles that it was intended to solve could be avoided by exploiting propositional functions and interpreting problematic sentences which appeared to involve reference to proper names by using the method of descriptions (Russell 1905/56). The notion of propositional function which Russell adopted retained, however, all the confusions of traditional empiricism that Frege was trying to avoid. Propositional functions pick out properties, some of which are simples, which can be known by acquaintance, and which form the logical atoms of a reductionist account of our knowledge. Propositions are composed out of objects and these properties. They are thus ambiguously made up of things in the world and entities that we can have in mind. Wittgenstein insisted in the Tractatus that only propositions have sense. The sense of a sentence as he thinks of it is equivalent to a Russellian proposition, and contains the entities with which the sentence deals, much as Frege’s early possible contents of judgement do.14 This equally involves the rejection of the Fregean notion of sense as a way of being given a reference. Wittgenstein, in his mature period, rightly came to see this philosophy as replete with confusions and rejected it, at the same time attributing it to Frege. Emerging from his own and Russell’s confused attempts to give a reductionist account of knowledge, he announced that philosophy is really purely descriptive, and ‘it can never be our job to reduce anything to anything, or to explain anything’ (Wittgenstein 1958, p. 18).

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It is fundamental to the slogan that meaning is use as Wittgenstein understood it that we should be suspicious of accounts of meaning which explain the meanings of words in terms of reference to concepts or properties. The attempt to supply sharp definitions for words is based on a misunderstanding of the way language works: ‘We are unable clearly to circumscribe the concepts we use; not because we don’t know their real definitions, but because there is no real “definition” to them. To suppose that there must be would be like supposing that whenever children play with a ball they play a game according to strict rules’ (Wittgenstein 1958, p. 25). ‘Philosophizing mathematicians’ (surely a reference to Frege) don’t take account of all the different uses of words, which leads Wittgenstein to say: that they are obviously not aware of the difference between the many different usages of the word ‘proof’; and . . . they are not clear about the difference between the uses of the word ‘kind’, when they talk of kinds of numbers, kinds of proof, as though the word ‘kind’ here meant the same thing as in the context ‘kinds of apples’. Or . . . they are not aware of the different meanings of the word ‘discovery’, when in one case we talk of the discovery of the construction of the pentagon and in the other case of the discovery of the South Pole. (p. 28)

Yet, if it is a mistake to think of numbers as sharing properties just as we think of apples as doing, it is impossible to see mathematical truth as residing in the higher-order relations that hold between such properties, as Frege did. So, if Frege’s way of understanding the objectivity of the truth of mathematics is to be saved in a way which is compatible with the rejection of mentalism, there will have to be some significant modifications in the understanding of what is implied by the rejection of mentalism. Most importantly, it will have to be the case that rejecting mentalism does not imply rejecting the existence of concepts, as Wittgenstein assumes it does. Frege resisted mentalism by insisting on the difference between ideas which are subjective mental entities and concepts, properties, abstract objects and relations which are objective entities, some of which are unsaturated. Wittgenstein resisted mentalism, but assumed that resistance to mentalism brings with it a suspicion of the usefulness of postulating concepts, properties, abstract objects and relations as the meanings of words. If Frege’s position is to be shown to be acceptably anti-mentalistic, then, presumably, we have

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two options. Either we must show how appeal to objectively existing concepts, properties, abstract objects and relations can be made use of in the theory of meaning without lapsing into mentalism. Or we must show that, despite what Frege thought, his fundamental outlook and the objectivity of mathematical truth can be retained without appeal to objectively existing abstract entities which exist independently of language. Dummett’s strategy involves a combination of the two. On the one hand, with regard to abstract objects, he takes the first path. The context principle shows how we understand terms for abstract objects without recourse to ineffable relations to abstract ideas. Questions as to the objective existence of such objects are transformed into questions concerning the truth conditions of sentences. Then, with regard to mathematical and logical truth, he takes the second path. We can do away with Frege’s eternally existing thoughts, and explain the functioning of language in terms of the practice of assertion. If we can show how truths in virtue of meaning follow from the use that we make of sentences, we can provide a justification for our logical practice which eschews the opaque metaphysical aspects of Frege’s thought. This, then, provides a second path from Frege’s realism towards intuitionism. In the next chapter we will see that, historically, intuitionists have been sharply opposed to the realism that is characteristic of Frege’s thought. This suggests that Dummett’s constructivist version of Frege’s logicism will always be at odds with Frege’s realist rhetoric. Nevertheless, if we keep in mind Frege’s insistence on the objectivity of concepts, and accept that concepts when instantiated can be part of the causal realm, we can interpret Frege’s views in a way that is compatible with moderate causal Platonism.15 On such a view, instantiated higher-order concepts can be thought of as part of the causal realm, as are the instantiations of properties like weight and shape. Initially, we come to know simple numerical facts through interaction with concepts that fall under these higher-order concepts, and ultimately, we construct the abstract objects which are numbers through a precise characterization of these concepts and by providing identity and existence conditions for numbers, as was outlined in chapter 1. This interpretation of Frege is still compatible with Dummett’s argument that the paradoxes show that Frege’s logicism can be saved by the rejection of bivalence, but it attempts to be faithful to Frege’s realist rhetoric. In the next chapter I will argue that while it is true that rejecting

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bivalence involves some element of anti-realism, this is a degree of anti-realism that should not be offensive to one who is realist about ordinary material objects. The proffered interpretation of the realist strand in Frege shows how a strongly realist view of properties could be compatible with the denial of bivalence, and so supports this conclusion.

3 The Influence of Intuitionism

It was suggested in the Introduction that by providing an outline of the strengths and weaknesses of three possible positions within the theory of meaning Dummett has contributed much to the philosophy of language. We now come to the third of these positions, that of the constructivists. As we saw in chapter 1, Dummett has argued that if one is to adopt a realist theory, and give an account of meaning in terms of truth conditions, then, in order to avoid circularity, it will be necessary to give a substantive theory of truth which links truth to the uses we make of sentences. One response to this argument is to reject the possibility of a systematic account of meaning and to adopt the holism that Dummett associates with Wittgenstein. From this point of view, the most we can do is to describe the multifarious uses we make of language. An alternative is to give up the truth-conditional theory of meaning without giving up the attempt to provide a systematic account of meaning. On one reading, the constructivists adopt this alternative. Looked at this way, they attempt to construct a systematic theory of meaning directly in terms of the notions of provability or assertibility. Truth, if it comes in at all, is then a subsidiary, or derived, notion within the theory of meaning. However, as we saw in the first chapter, Dummett has vacillated on the relationship of truth to assertibility. His earliest important paper, ‘Truth’, interpreted the constructivist as replacing the notion of truth by that of warranted assertibility. Then, in the introduction to Truth and Other Enigmas, he characterized the constructivist as instead offering the substantive theory of truth that is required in order for a truth-conditional theory of

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meaning to be informative. Ten years on, these appear as two alternative strategies. A pure constructivist will give an account of meaning directly in terms of some notion other than truth, the classic example being the intuitionist who gives the meanings of the logical constants in terms of the notion of assertibility. A mediated constructivist, by contrast, will accept that meaning is given by truth conditions, but then accept that the notion of truth requires explication. Below we will discuss the strengths and weaknesses of these two alternatives. Given the importance of Frege for Dummett, it can seem odd that Dummett’s philosophy is at the same time so closely bound up with mathematical intuitionism, for in many ways the attitudes to mathematical truth of Frege and the intuitionists are poles apart.1 Brouwer consistently contrasts the logico-linguistic method characteristic of Hilbert and Russell with the attitude of pre-intuitionists such as Poincaré and with that of the intuitionists (Heyting 1975, pp. 123–38, 508–9; van Dalen 1981, pp. 2–4). Frege’s attempt to reduce mathematics to logic seems to place him alongside those pursuing the logico-linguistic method, and Dummett makes it central to Frege’s thought that he made the analysis of language the key for clarifying our thought about mathematics. But Brouwer describes the ‘first act of intuitionism’ as that of Completely separating mathematics from mathematical language and hence from the phenomena of language described by theoretical logic, recognising that intuitionistic mathematics is an essentially languageless activity of the mind having its origin in the perception of a move of time. This perception of a move of time may be described as the falling apart of a life moment into two distinct things, one of which gives way to the other, but is retained by memory. (van Dalen 1981, p. 4, italics in original)

The initial impetus for intuitionism comes from a thoroughly Kantian perspective which makes the source of mathematical truth reside in the categories of perception, and is expressly independent of the linguistic concerns which are central to Dummett’s treatment. Much of the linguistic orientation of Dummett’s writing derives, as we have seen, from the influence of Wittgenstein. He tells us also that it was first an interest in Strawson’s notion of presupposition which led him to study the concept of truth and the question of how it is possible to criticize fundamental logical laws (Dummett 1978c, p. xix). Coming from an environment in which language was already taken to be central, Dummett went on to emphasize that the

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debate between realists and intuitionists was one deriving from a divergence within the theory of meaning. He often justifies this focus by arguing that, when couched in purely metaphysical terms, realism and anti-realism offer two alternative pictures neither of which can be provided with a knock-down justification (Dummett 1991e, pp. 4–15; 1978c, pp. xxv–xxix). Moreover, as we saw in the first chapter, the context principle is taken to imply that questions about the existence of problematic entities can be transformed into questions concerning the truth conditions of sentences. But this focus is quite different from Brouwer’s, and this raises the question of the relationship of Dummett’s version of anti-realism to historical notions. This will be discussed in detail later in this chapter, but first a brief overview of the historical debate will be of use to readers who are not familiar with intuitionism.

Brouwer’s Intuitionism While it is true that Frege’s attempt to reduce mathematics to logic is shared by some members of the logico-linguistic school of mathematicians against whom Brouwer constructs intuitionism, this description can be misleading, for it obscures the fact that Frege was, in his own way, as opposed to Hilbert’s formalism as was Brouwer. Indeed, Frege objects to formalism that it is not enough, in order to show the existence of some mathematical entity, to prove that its postulation does not lead to contradiction, and this objection to Hilbert’s formalism can also be found in Brouwer (Frege 1971, p. 152; Heyting 1975, p. 79; Frege 1980, pp. 47–8). Frege believes in the objective existence of mathematical objects, and understands the search for mathematical truth, by analogy with the discovery of truths about the material world, as the search for the objective properties of those independently existing objects. Frege, it seems fair to say, believes that there is a logical structure of the world which can be discovered by reason. Formalists characteristically take mathematical truths to consist in no more than the derivable consequences of formal systems. While the intuitionists agree with Frege that mathematics has a subject matter that is distinct from the formal languages used for the derivation of theorems, they see this subject matter as resulting from our constructive activity. Brouwer says, ‘outside human thought there are no mathematical truths’ (van Dalen 1981, p. 6). Man creates order in nature, and the laws of counting and measuring are based on our own activities

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(Heyting 1975, pp. 51, 124). Shorn of its mentalism, this was to become Wittgenstein’s view as well. We saw in an earlier chapter that although Dummett’s characterization of Frege as a Platonist is controversial, it is substantially correct. There it was argued that the way Frege’s realism should be interpreted is as embodied in an understanding of the nature of logical truth according to which mathematical and logical truths reside in higher-order relations between objectively existing concepts and are the laws of the laws of nature. Frege never questions the validity of classical logic. Indeed his counter-intuitive rejection of vague predicates and insistence that concepts must be sharply defined are grounded in the requirement that bivalence be upheld (Frege 1984, p. 148). His faith that such logical principles give us knowledge of an independently existing reality is, it seems, simply unquestioned. But it is a faith backed up by the applicability of mathematics to an observed reality which we do naturally take to exist independently of us. The formalists also simply assume classical logic, but they are clearer about its status as an assumption. Traditionally, they may have used classical modes of reasoning to provide the rules of derivation in accordance with which each formal structure is set up. But it is just as possible to take a formalist attitude to non-classical logics, and to develop formal semantics for the languages thus derived. This then gives us the following three-way division. The early Frege and the formalists share the view that mathematics is a branch of logic, but differ in their understanding of the nature of logical truth. Brouwer argues against this that mathematics is separate from logic. Frege and the intuitionists, however, share the view that mathematical truths are not just truths about formal systems. Dummett emphasizes the fact that for Frege and the intuitionists sentences of mathematics have content; but although he is well aware of it, he does not always stress their divergence over the status of logic (Dummett 1977, p. 3; 1980a). His concentration on the intuitionists’ rejection of the law of excluded middle occasionally inadvertently gives the impression that for the intuitionists, as for the early Frege, mathematics is a branch of logic, but that intuitionists disagree with Frege over the logic which describes the structure of reality. This is misleading if it is taken to characterize Brouwer’s attitude. For, according to Brouwer, logic presupposes mathematics, and simply describes generally accepted transitions between propositions (Heyting 1966, p. 6). The failure of the law of excluded middle, in the realm of mathematics, is argued for on the

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basis of specific features of the activity of mathematical construction. He says: Suppose that, in mathematical language, trying to deal with an intuitionist mathematical operation, the figure of an application of one of the principles of classical logic is, for once, blindly formulated. Does this figure of language then accompany an actual languageless mathematical procedure in the actual mathematical system concerned? (van Dalen 1981, p. 5)

He then argues that, for the specific realm of mathematical constructions, the principle of excluded middle fails, giving as an example of such failure the existence of the sequence 123456789 in the decimal expansion of p, and linking this failure with the infinite character of the expansion of p. If the intuitionists’ rejection of the law of excluded middle is inextricably bound up with their understanding of the specific nature of mathematical truth, it is not obvious that it can be extended to a general argument for anti-realism. But Dummett’s view of intuitionism is that The first who clearly grasped that rejecting realism entailed rejecting classical logic were the intuitionists . . . The validity of the law of excluded middle does not depend absolutely on the principle of bivalence; but in this case as in many, once we have lost any reason to assume every statement to be either true or false, we have no reason either to maintain the law of excluded middle. (Dummett 1991e, p. 9)

This gives expression to his view that there is a general argument, first perceived by the intuitionists, from anti-realism, via the theory of meaning, to the rejection of bivalence. General considerations about the way in which meaning is conferred on sentences are therefore claimed to be at the heart of the metaphysical debate between realists and anti-realists (Dummett 1978c, p. xxix). Dummett’s extraction of the argument from the theory of meaning to the rejection of bivalence modifies the original intuitionist perspective to a considerable degree. Brouwer’s point of view is a development of Kant’s attitude to mathematical truth in the light of the discovery of non-Euclidean geometries. Kant thought that both geometry and arithmetic were synthetic apriori forms of knowledge, the first being grounded in the categories of outer experience. He assumed that we could not conceptualize space except by experiencing it through Euclidean geometry. But

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with the development of non-Euclidean geometries, the modern formalist attitude to geometry came to be widely accepted. Since different geometries can be developed using selected groups of mutually consistent axioms, the Kantian attitude became untenable. The formalists therefore treat geometries as formal systems which are initially studied as uninterpreted languages. It is then an independent question whether an interpretation can be found for a particular language in a given physical space or system. Brouwer admits that the development of non-Euclidean geometries shows that there is no a priori spatial intuition. But he rescues the Kantian perspective for arithmetic by insisting on the a priori intuition of time (Heyting 1975, pp. 123–9). This makes mathematics an ‘autonomic interior constructional mental activity’, and it is in the light of this that Brouwer is prepared to say that in mathematics no truths exist which have not been experienced, and that hence the law of excluded middle does not hold in this realm (Heyting 1975, pp. 551–2). At the same time, Brouwer’s claim that there is an ‘intuition of two-oneness’, which creates the numbers one and two, and all the finite ordinal numbers, in fact throws little light on our mathematical practice (Heyting 1975, p. 127). No doubt this is part of the justification for Dummett’s adoption of some of the insights of the intuitionists in the context of a very different conception of the source of mathematical truth. Dummett does not address directly the tensions which are involved in exploiting the insights of intuitionists in the service of his project of modifying Frege’s logicism in the light of Wittgenstein’s view that meaning is use. But they are considerable. There are many features of Brouwer’s conception of mathematics which are incompatible with Wittgenstein’s claim. For Brouwer, the criterion of mathematical truth is an inner feeling: I differ fundamentally from Mannoury’s conception, that mathematics when it is made less formal, will pay for it by a loss of ‘exactness’, i.e. of mathematical ‘truth’. For me ‘truth’ is a general emotional phenomenon, which by way of ‘Begleiterscheinung’ (accompanying phenomenon) can be coupled or not with the formalistic study of mathematics. (Heyting 1975, p. 451)

Mathematics, as we saw, is described as an essentially languageless activity, demonstrating Brouwer’s commitment to the notion that thoughts can exist independently of language. This conception is also evident in his discussion of communication, and here some of

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Brouwer’s more unusual commitments emerge. He rejects the common-sense view that there exists a plurality of individual minds, and claims that it flows from this that there can be no exchange of thought. What we call exchange of thought is influencing the other’s actions. So for Brouwer, words are outer signs used to indicate thoughts and to influence action. Words are instruments which have meaning only when they indicate some conscious experience, and experience is identical with truth. Reality just is the present and past experience of consciousness – a consciousness which, presumably, since there is not a plurality of minds, we all participate in. This is all very mysterious. An anti-mentalistic version of intuitionism will therefore have to give up much of Brouwer’s metaphysics, and either go some distance in the direction of realism or some way down the path which Wittgenstein travelled. It is, perhaps, worthwhile noticing that Brouwer’s intuitionism and Frege’s logicism both fall back ultimately on to a Cartesian assumption that, in the one case, the (God-given) categories of inner sense or, in the other case, the faculty of reason, are reliable guides to an intersubjective truth. Thus at some level they appear to be committed to the idea that the mind is more than merely an evolved mechanism, and so to a form of dualism. For, if our minds were organs adapted by evolution to serve the purpose of survival, there would be little reason to expect that what makes sense from our perspective is a good guide to the way the world is in itself. By contrast, Wittgenstein’s anti-mentalism, his rule-following considerations, and his remarks on certainty encourage the kind of physicalist and behaviourist reading of his work that is found in Quine. As was observed in the last chapter, the resultant naturalized epistemology seems antithetical to Frege’s foundationalism. We might think of the promise found by Dummett in intuitionism as being that it is potentially capable of being adapted, through a naturalized semantics and epistemology, to a justification of the claims of reason. Or perhaps, if a naturalized justification of reason’s pretensions turns out to be impossible, into a reason for falling back on the existence of God to ground our faith in reason’s capacity to reveal a single objective world. There are some hints that Dummett favours the second option. Brian McGuinness alludes to a paper that Dummett never chose to publish, in which, McGuinness claims, Dummett argued that realism is only defensible on a theistic basis (McGuinness 1994, p. 229). Dummett touches on these issues near the end of the discussion of

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Ayer’s philosophy, where he outlines the metaphysical commitments of verificationism. There he suggests that any verificationist theory will involve acceptance of the existence of gaps in reality. Such a consequence, he concludes, goes against our whole way of thinking. He goes on to suggest that without a belief in God we can have no guarantee that there is a single world inhabited by various creatures whose experiential worlds are partial and limited (Dummett 1992, pp. 146–8). Elsewhere, however, he draws back from the conclusion that the postulation of God’s existence would by itself justify bivalence, and hence realism (Dummett 1991e, pp. 348–51). If the single world is one which contains genuinely incomplete infinities, if there are some propositions which cannot be known to be either true or false, then God cannot know whether or not they are true or false, since ex hypothesis this cannot be known. Dummett considers these comments highly speculative, and his arguments are in general compatible with a naturalistic attitude, so my discussion will be guided by the assumption that naturalism can be defended. Yet, by interpreting Dummett naturalistically, I am surely being unfaithful to his deepest preoccupations. He makes clear in his response to McGuinness that he takes the evolutionary explanation of our existence to be no explanation at all, and suggests, indeed, that it gets matters back to front (Dummett 1994a, p. 352). Dummett has met the naturalists on their own ground, arguing in effect that naturalism cannot justify the belief that there is a way the world is in itself. This is not the same as realism in Dummett’s sense, for it is possible to accept bivalence while insisting that this is just a feature of our perspective on the world. Nevertheless, the idea that there is a way the world is in itself does capture a central motivation for realism. For those whose commitment to realism is strong enough, the thought that without God there is no way the world is in itself could motivate a rejection of naturalism. For those who find theistic explanations no explanation at all, it will not. Intuitionist logic can be explained quite independently of Brouwer’s more controversial doctrines. Essentially the meanings of the logical constants are given in terms of the existence of a proof, rather than truth; however, there is disagreement over what is meant by the existence of a proof. ‘A proof exists’ may be read as entailing the actual discovery of the proof by human beings, or its possible discovery. Heyting adopts the first reading; he is also a pure constructivist. His is the standard explanation of the meanings of the intuitionistic constants, and it is formulated directly in terms of assertibility:

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p & q is assertible if and only if both p and q are assertible. p ⁄ q is assertible if and only if either p is assertible or q is assertible. p Æ q is assertible if and only if we possess a construction r which, when joined to any construction proving p, will effect a construction proving q. ÿp is assertible if and only if we possess a construction which, from the supposition that a construction of p is carried out, leads to a contradiction. Where p(x) is a predicate of one variable and this variable ranges over a given mathematical species Q, "x p(x) is assertible if and only if we possess a general method of construction which, for any element a of Q that is chosen, will yield a construction proving p(a). Where p(x) is a predicate of one variable and this variable ranges over a given mathematical species Q, $x p(x) is assertible if and only if an element a of Q for which p(a) is true has actually been constructed. (Heyting 1966, pp. 98–103)

Heyting’s formulation involves actual assertibility, and what is assertible will change over time (1966, p. 3). It is easy enough, however, to modify his explanation of intuitionistic logic by replacing ‘assertible’ with ‘provable’, and ‘we possess a construction’ with ‘there is a construction’. This provides a mediated constructivism in which provability becomes more like truth, and can be taken to explicate it. A gap can be recognized between assertibility and provability, in that a formula may be provable even though it has not been proved. Even when it is interpreted in this more realistic way, intuitionistic logic will not recognize the general provability of p ⁄ ÿp, or the validity of ÿÿp Æ p. More recent working intuitionists seem to prefer the more realistic interpretation of the existence of a proof to that assumed by Heyting. Below we will discuss the costs and benefits of these two interpretations. But first we will return to a discussion of Dummett’s argument against bivalence.

The Intuitionist’s Case against Bivalence If Brouwer’s conception of mathematics as essentially languageless activity is incoherent, and if thought, including mathematical thought, cannot exist independently of language, then the constructivist’s argument must be recast as an argument about the way in which meaning is conferred on language. Dummett takes this to be what is essentially correct in Wittgenstein’s attitude, but believes,

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at the same time, that Frege’s analysis of number can serve to illuminate the way in which meaning is conferred on the language of arithmetic. As an account of the use, applicability and truth of mathematics, Frege’s account is superior to Brouwer’s. Rather than appealing to a mysterious ‘intuition’, it goes a good way towards providing an analysis of the meanings of number words, in the light of which the truths of mathematics can be seen to be analytic. But Frege stumbled over the paradoxes. It is Brouwer who provides a diagnosis of the source of this failure. This diagnosis is really quite independent of his claim that mathematical insight is based on intuition.2 Brouwer’s diagnosis is captured in the argument for rejecting bivalence which I called in chapter 1 ‘the traditional intuitionist response to the paradoxes’. In the paper ‘Mathematics and Logic’ Brouwer sketches this response: let us suppose that I know an ‘everything’ with a totality of relations existing between the objects, and a system of propositions which may hold for the objects. Then, given a propositional function, I can decide for any object by means of its given relations whether or not it satisfies the function, in other words, to which of the two classes defined by the function it belongs. But when I wish to decide whether the object which is the class involved in the contradiction, satisfies the given propositional function, then I see that the decision is only possible under the condition that it has already been completed. Consequently the decision cannot be taken, and hereby the contradiction is explained. We have here a propositional function which defines two complementary classes which do not satisfy the tertium non datur. (Heyting 1975, pp. 89–90)

Dummett first developed this intuitionist line of thinking in the paper ‘The Philosophical Significance of Gödel’s Theorem’, where he applied it to that theorem. This paper is important for the clues it provides with regard to the connections which Dummett perceives between the traditional intuitionist response to the paradoxes and the more general argument against bivalence for which he is famous, and which is grounded in the theory of meaning (Dummett 1963/78c). A common realist response to Gödel’s theorem is as follows. What the theorem shows is that our understanding outstrips anything which can be captured by specifiable rules for the use of language. Gödel has shown that in any consistent formal system of elementary arithmetic we can derive a statement which is expres-

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sible in the formal system, but not provable in it. At the same time, we can intuitively recognize that it is true, for it says of itself that it is not provable.3 The realist claims that our capacity to recognize the truth of this sentence must derive from a grasp of the intended interpretation of arithmetic. Since it is in virtue of this grasp of the intended interpretation that we are able to recognize the truth of the Gödel sentence, and this grasp cannot be characterized by specifying which arithmetical statements can be asserted and the forms of inference that are accepted, meaning outstrips use. Dummett adapts the intuitionist response to the paradoxes, in order to provide a different reading of the moral we should draw from Gödel’s theorem. He suggests that the realist’s interpretation rests on an illegitimate use of the notion of a model. Models have to be specified, and any specification of a model will itself involve either the notion of ‘natural number’ or of ‘set’, and so cannot be used to explain the meanings of these notions (Dummett 1963/78c). Instead of giving up the insight that meaning should be manifestable in use, as the realist does in accepting that we have an unanalysable capacity to grasp the intended interpretation of arithmetic, Dummett suggests that the moral of Gödel’s theorem is that the class of intuitively acceptable proofs is an indefinitely extensible one. In a formal system we can show the validity of induction only with respect to properties which are expressible within the system, but once a system has been formulated, we can, by reference to it, define new properties which are not expressible in the system, and by applying induction to such new properties, we can arrive at conclusions that are not provable in the system. What this shows is that the intuitionists were correct in thinking that the sense of mathematical statements is given in terms of an inherently vague notion of intuitively acceptable proof, and cannot be equated with proof in a formal system. Although there are differences between the situation with regard to the paradoxes and Gödel’s theorem, there is a similarity in the responses offered, of the following kind. Realism manifests itself in the assumption that reality must determine the truth or falsity of every proposition independently of us. In the case of set theory, this realist bias manifests itself in the acceptance of naive comprehension. This leads to a paradox which is easily dispelled when it is recognized that the problematic sentence is not well grounded, and so cannot be decided. It is only the realist insistence that bivalence must be true which blocks the general adoption of this solution. In the case of Gödel’s theorem, realism leads to the attribution to us

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of an inexplicable capacity to recognize the truth of certain sentences. But a look at what in fact goes on in the proof of Gödel’s theorem shows that we need not attribute such capacities to ourselves, for the phenomenon can be explained without them. So, without the intuitionists having had the Wittgensteinian slogan in mind, their analysis of the activity of mathematics turns out to be compatible with the view that the meaning that we have assigned to the expressions of our language should be capable of being made manifest in uses to which we put those expressions. As we have seen, Dummett is independently convinced that this principle is highly plausible. In the first chapter we saw that Dummett has a general argument from the potential knowability of truth to the rejection of bivalence. The traditional intuitionist response to the paradoxes demonstrates that this rejection enables us to dispel difficulties which result from the realist stance, and so adds force to the general argument. Interpreting intuitionism in the light of Wittgenstein’s slogan involves, as we have seen, jettisoning part of the intuitionists’ rhetoric, while accepting many of their arguments. Other important aspects of Brouwer’s attitude remain central to Dummett’s thinking. Unlike Frege and the formalists, Brouwer is not prepared to accept logic uncritically. Rather, logical principles capture principles of reasoning which we intuitively recognize as truth preserving. The principles of logic require justification, and in at least one place Brouwer gestures towards a method for providing such a justification (that of ensuring that the logical constants are a conservative extension of the language) taken up in detail by Dummett (Heyting 1975, p. 488). If we are to have an assurance that our logical principles will take us from truth only to further truth, then we will have to be certain that the truths we arrive at via the application of those principles are correct. It has seemed to many that it is impossible to justify deduction, because a semantic justification of a logic is implicitly circular, since the logical principles to be justified will be used in the justification (Dummett 1973b/78c; 1991e, pp. 200–4, 245–6; Prawitz 1974). Dummett argues that this need not always be the case, and even when it is, it need not rob semantic justifications of interest; they can be illuminating even if circular. Nevertheless, if some logical laws can be shown, by proof-theoretic means, to be self-justifying, these will be in a privileged position, because they can be justified independently of any semantic theory, and so could provide a universally accepted logic for a meta-language within which to discuss other logics (Dummett 1991e, pp. 299–300). During

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the seventies, and following the lead of Dag Prawitz and Per Martin-Löf, Dummett began to explore the possibility of providing such a proof-theoretic justification for some logical laws. Such a justification would show that we had laid down the meanings of some of the logical constants of our language in such a way that inferences employing those constants are demonstrably justifiable. Dummett mentions this possibility in Elements of Intuitionism (1977, pp. 363–4). It was also a major theme in the William James Lectures, which he delivered at Harvard in 1976, and it is discussed at length in the version of those lectures published in 1991 as The Logical Basis of Metaphysics. The more recent discussion is rather more pessimistic concerning the range of applicability of this method of justifying principles of logic than Dummett’s earlier comments suggested, and this is associated with the reorientation towards realism mentioned in the Introduction. If this project could be completed, then we would be a good way towards having provided a pure constructivist theory of meaning for the logical fragment of language. In this chapter we look at the brief early comments concerning this method of justifying deduction, and then discuss how far Dummett is successful in carrying out the project introduced. For, although the explicit use of the notion of conservative extension is a relatively late theme in Dummett’s published writing, it is illuminating to understand even his earlier versions of the case for anti-realism in the light of it. Doing so provides a reply to a fairly obvious objection to the most common way of setting out Dummett’s central argument. In Elements of Intuitionism Dummett has the following to say concerning the possibility of justifying logical principles. Logical principles will be justified if they simply fall out of the meanings of the logical constants. A given set of introduction rules will determine the meanings of the logical constants if and only if two requirements are satisfied.4 The first is that the rules should allow us to infer, from correct sentences which do not contain the constant, that a sentence containing the constant is correct. That is to say, the definition should not be circular. The second requirement, which is the one that interests us, is that the addition of the logical constants to the fragment of the language without them should be a conservative extension of that fragment. As Dummett says, there must not be any deduction from correct premisses, none of which contains any of the logical constants in question, via sentences involving the logical constants, to a conclusion not containing the constant which is not itself correct (1977, p. 363).5 Dummett suggests that the requirement

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that the logical constants are a conservative extension of the language is important for the rejection of holism. If observation sentences are to be genuinely observation sentences (rather than having verification conditions which are sensitive to all the methods of deduction that the language embodies), then the language as a whole will have to be a conservative extension of its observational fragment (Dummett 1973c/78c, pp. 220–2). The significance and scope of this constraint are elucidated in The Logical Basis of Metaphysics (Dummett 1991e, pp. 209–20). In that work, Dummett also discusses the possibility, raised by Per MartinLöf, that the meanings of the logical constants might be given by the elimination rules. In his earlier Elements of Intuitionism Dummett discusses the notion of conservative extension by speaking of the addition of the logical constants to a language. This strongly suggests the following picture. We begin with some atomic sentences for which we have criteria of correct assertion. We then introduce our logical constants. The introduction rules will have determined the meanings of those constants if and only if the atomic sentences which we are justified in asserting after the introduction of the logical constants are just those that we were justified in asserting initially. But, by this criterion, hardly any constants could be justified, and the point and fruitfulness of logical deduction would be missed. Only conjunction is plausibly thought of as conservative in this sense (Dummett 1991e, p. 220). Much of the point of logical deduction is that it can take us from sentences which have been established as correct by means of actual observations to the assertion of sentences which are likewise correct, but which have not actually been observed to be so. We express our conviction that such conclusions are correct by maintaining that we could have observed them to be correct were we to have been appropriately situated and endowed with adequate observational capacities. The important point is, as Dummett now emphasizes, that the very practice of deductive reasoning introduces a gap between truth and that which enables us to recognize truth (Dummett 1990a/93d; 1991e, p. 180). The addition of logical constants to a fragment of language containing only atomic sentences is not in general conservative in the sense just outlined. Dummett therefore now insists that the conservative extension criterion is only to be applied to one constant at a time, and to a language fragment that already contains some constants (1991e, p. 220). The need for a justification of deduction puts the manifestability constraint in a new light and provides it, and the mediated con-

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structivism introduced earlier in this chapter, with a stronger justification than was available from the perspective of the last chapter. For the pure constructivist the argument for rejecting bivalence is quite direct. If the meaning of the logical constants is laid down in terms of the notion of assertibility, and if p ⁄ q is assertible when either p or q is assertible, while ÿp is assertible when we can show that p … ^, then there is no reason to assert that p ⁄ ÿp, for many instances of this formula will not be assertible. Pure constructivists are happy to give up the gap between truth and assertibility, but just because the notion of truth that goes beyond what is actually assertible is so central to our thought, they fail to provide a compelling argument for replacing truth with assertibility. The perspective of mediated constructivism provides such an argument. As we have seen, the first premiss of this argument is the Wittgensteinian dictum that meaning must be able to be manifest in use. The next step in the argument is the claim that the way in which speakers manifest their grasp of the meanings of sentences is through their preparedness to assert, or assent to, those sentences under certain conditions. We can then identify the manifestable condition of knowing the truth conditions of a sentence with the disposition to assent to the sentence when its truth condition obtains and the speaker is in a position to recognize that it obtains. Or, when the speaker is not in a position to recognize that the truth condition obtains, with a practical knowledge of a procedure for getting into such a position (Dummett 1977, pp. 373–4). So, while we cannot directly manifest our grasp of the truth condition for a sentence like, ‘There is life on a planet less than 10 light years away from earth’, we can (presumably) manifest a knowledge of the steps that would have to be taken in order for someone to be in a position to recognize the truth of the sentence. Doing this will be largely a verbal ability, but, so long as the sentences used in describing the procedure that would lead to the recognition of its truth or falsity are themselves ones for which we can manifest our grasp of truth conditions, the understanding will reduce to a complex web of linguistic and practical abilities. The argument then proceeds with the observation that in the case of an undecidable sentence there is no way in which our purported grasp of its truth condition could be reduced to such a web of abilities. We can go some way towards demonstrating our understanding of the sentence ‘The sequence 123456789 occurs in the decimal expansion of p¢ by demonstrating our ability to calculate

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this expansion. We can manifest a grasp of the procedure that must be followed if we are to get into a position to recognize the truth of this sentence, but, since we have no guarantee that following this procedure will lead to a positive outcome, the kind of understanding that we have of this sentence does not justify us in asserting that either the sequence 123456789 does occur in the decimal expansion of p or it does not. We may never be in a position to recognize the truth of either of these disjuncts, no matter how far we develop the expansion. So, beginning from the proposition that meaning must be able to be manifest in use, we end up with the conclusion that the kind of meaning that we are able to attain for undecidable statements is such that we have no justification for assuming that the principle of bivalence holds for them. As we saw in the last chapter, concentrating on the Wittgensteinian principle as a constraint on adequate descriptions of the activity of speaking and understanding a language leads naturally to the following holist objection. We do learn how to reason in accordance with classical principles of logic, and if meaning is use, what more do we want from a demonstration of our understanding of these principles than our capacity to use them in derivations?6 Dummett rejects this objection as ‘thin’ (1977, p. 376). Yet the objection is perfectly in line with the Wittgensteinian understanding of the import of the slogan that meaning is use. Once we ask how we could justify deductive principles, Dummett has a more satisfying response to holism. For holism fails to account for the phenomenology of deduction, in which we do seem to be compelled to go on in a certain way. It also fails to offer something that we should welcome if we can get it: a rational justification of our deductive practice. So we should interpret the manifestability constraint as independently plausible, but ultimately subordinate to the need for a justification of deduction (Dummett 1973b/78c). If the notion of truth that we have for sentences prior to the introduction of the logical constants is to play the role in the explanation of our capacity to understand simple sentences that is required by Dummett, then it will have to be the case that we can manifest our grasp of the truth conditions of simple sentences. And if the addition of the logical constants to a language were to be a conservative extension of that language, then it would not lead us to assent to sentences that we could not come to assent to directly. If this were the situation for the intuitionistic constants, then clearly they would be justified. However, as Dummett admits, this is not the situation that actually obtains. Nevertheless, he maintains, there is a sense in

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which the intuitionistic constants come closer to this paradigm of justifiability than the classical constants do. A proof-theoretic justification can be given for all the laws of first-order intuitionistic logic without negation, so there is a clear sense in which these laws can be deemed self-justifying (Dummett 1991e, p. 279). Our criterion of correctness for atomic sentences in a language without logical constants is that they have been recognized to be true. Deduction puts us in the position where we can assert sentences that would not have been recognized as true apart from that deduction. Take, for example, the Königsberg bridge theorem, which shows that where there are five bridges connecting an island to the two banks of a river, a person cannot cross all bridges and return to the same spot without crossing at least one bridge twice. Having proved the theorem, we can know, on the basis of the observation that someone crossed all the bridges and returned to their starting point, that they must have crossed at least one of the bridges twice, even though we have not observed them doing so. If our logic is intuitionistic, the notion of truth, or correctness, which results is still related to recognition of truth. The deduction puts us in a position to assert that we could have recognized the truth of the deduced sentence had we been appropriately placed. But the realist who accepts excluded middle goes beyond this. He or she is prepared to assert for undecidable p, p ⁄ ÿp, even while admitting that nothing, other than the logical principles accepted, could lead us to accept the correctness of this disjunction. So the objection is not just ‘thin’; it fails to come to grips with the project of justifying our deductive practice, and amounts to the position that logical principles cannot be justified; they are simply the moves that creatures like us are disposed to follow in making transitions from one proposition to another. This is a possible position and probably Wittgenstein’s own, but it is pessimistic, and amounts to giving up on the quest for a justification of our logical principles. If one takes the meanings of the logical constants to be determined by the verification conditions of sentences containing them, then it is natural to think of these meanings as being determined by the introduction rules. As has already been mentioned, from this point of view the negation-free fragment of intuitionistic logic can be shown to involve only self-justifying laws. One might object, however, that if logical laws containing negation cannot be shown to be self-justifying, then the demand for the kind of proof-theoretic justification that is developed by Dummett, following Prawitz, is unreasonable, since so much ordinary reasoning involves negation.

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It is partly for this reason that Dummett considers supplementing the verificationist reading of the slogan that meaning is use by a pragmatist reading, according to which understanding the meaning of a sentence is understanding what one can do with it. In the context of an explanation of the meanings of the logical constants, this means grasping the elimination rules. Dummett argues that although the introduction rule for negation cannot be regarded as self-justifying, we can take the intuitionistic elimination rule for negation, the ex falso quodlibet to be so, whereas the classical rule of double negation elimination is not subject to any kind of prooftheoretic justification. The argument involves taking the meaning of ‘ÿp’ to be equivalent to ‘p Æ ^’, where ^ is absurdity, and absurdity is equivalent to the conjunction of the totality of atomic sentences of the language. This means that the meaning of negation is not, on this reading, invariant between languages. Whether this understanding of negation corresponds to the intuitive one seems to me to be doubtful. It remains the case that, as Dummett argues, intuitionistic logic is in better shape than classical logic if what we want is a justification of our deductive practice (1991e, pp. 280–300).7 Clearly, the argument just outlined is in no way limited in its application to the domain of mathematics. Brouwer’s claim that mathematics is the study of mental constructions has fallen away as irrelevant to the case against bivalence as Dummett outlines it. Everything that has been said so far is compatible with a worldview which treats ordinary physical objects as material entities which exist independently of our thoughts. But, because of this, one might question whether the case that has been mounted against bivalence really amounts to a form of anti-realism at all. This is a suspicion which is fuelled by the fact that Dummett often claims an independence between idealism and realism as traditionally conceived and the versions of these doctrines that fall out of the argument just outlined. According to Dummett’s way of speaking, the acceptance of bivalence implies a commitment to realism, and the rejection of bivalence is a mark of anti-realism. This has been like waving a red flag at a bull for some realists, who do not understand that verificationism involves the correspondence theory of truth, and who also equate realism with materialism, and assume that every anti-realism will involve a form of idealism. Dummett’s claim can be seen to involve two elements. The first is the claim that one way of making the justification of our deductive practice clear to view is to give up classical negation and bivalence. The second is

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that the rejection of bivalence is a mark of anti-realism. These two elements are to an extent independent, and below it will be argued that if we accept the second, a problem arises for the context principle. This will lead me to argue that we can accept the first element of Dummett’s conclusion without giving up anything that is required by realism concerning the physical entities recognized by common sense.

Metaphysical Debates and the Theory of Meaning Some commentators have been puzzled by Dummett’s claim that the substantive dispute between realists and anti-realists is really a disagreement within the theory of meaning. Michael Devitt (1990), for instance, claims that realism is a doctrine which is initially independent of reflexive thoughts about truth or reference. In order to be a realist about a certain class of entities, it is enough, according to Devitt, that one claims that these entities exist, and exist independently of the mind.8 Correlatively, to be an anti-realist involves being either a sceptic, denying the existence of certain entities, or an idealist. On first appraisal, Brouwer’s anti-realism fits in with such a characterization. It consists in the denial of the view that mathematical truths exist independently of human thought, and is clearly idealist in character. We have already seen in chapter 1 how, given the Quinean criterion of our existential commitment, it turns out, after all, that our claims that certain entities exist are dependent on claims concerning the truth conditions of sentences. So, unless Devitt provides an alternative account of what we are committing ourselves to when we say that entities of a certain kind exist, his objection does not get us very far. Nevertheless, there is a strong tendency to equate anti-realism with subjective idealism, and to assume that the case against subjective idealism is independent of issues within the theory of meaning. The equation of anti-realism with subjective idealism is unfortunate. We should take seriously Dummett’s comment that his arguments are intended to show how ‘we can abandon realism without falling into subjective idealism’ (Dummett 1959c/78c, p. 19). There are a variety of intermediate positions which avoid the full transcendence of truth without reducing it to subjective impressions. Part of Dummett’s project has been to categorize these (1982c/93d). It is easy to overlook this. Crispin Wright, for instance, claims that Dummett has

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given ‘anti-realism’ currency as a term for opposition to realism from the idealist (rather than the sceptical) wing of philosophy. And although he admits that ‘the depiction of Dummett’s anti-realist as a kind of latter day idealist oversimplifies in at least two important respects’, his own discussion focuses on ‘the anti-realist critique of the objectivity of truth’, thus appearing to confirm the equation (Wright 1993b, pp. 2, 29). Given the acceptance of the truth-maker principle, which we have seen is central to Dummett’s argument, it would be more accurate to speak of Dummett’s anti-realist as demanding that we provide the notion of objectivity with a determinate content. But because the relationship between traditional idealism and Dummettian anti-realism is obscure, it is worth examining in some detail. According to Dummett, idealism does not necessarily involve anti-realism of the kind that interests him. The mere supposition that mathematical entities are mental does not by itself lead to the rejection of the law of excluded middle (Dummett 1977, pp. 383–9; 1978c). One could think that numbers are mental entities, but that there is a determinate totality of mental items. Arguably Berkeley thought that although tables and chairs are ideas, statements about tables and chairs are determinately true or false, and their truthmakers exist in God’s infinite mind. But his views are deviant, since, by bringing in God, he makes the existence of ideas independent of finite minds. As we have seen, Dummett claims that metaphysical assertions are often disguised assertions involving the semantic notion of truth. He says, ‘the metaphysical question, what there really is – not so much what objects the universe contains but what facts obtain – is the very same question as the question which statements we can suppose to possess a determinate truth-value’ (Dummett 1977, p. 386).9 At first glance this looks right. The individual who has grasped the practice of assertion has understood that to assert that p is to commit oneself to the truth of p. So to assert that ‘material objects exist and exist independently of the mind’ is to commit oneself to the truth of this proposition. Implicit in any attempt to justify it will be certain presuppositions about truth. These presuppositions will themselves depend on the model of meaning assumed. But the issue is not quite so simple, because some presuppositions concerning the nature of truth, in particular the identification of truth with assertibility, may appear to result in the conclusion that the facts which obtain depend on our decision to deem sentences true. We will return to the implications of this observation below.

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It is true, as some who have wanted to argue for the independence of metaphysics and the theory of meaning have claimed, that someone can make simple assertions such as that cherries exist without having any sophisticated view about truth (Bigelow 1994, p. 14). But it is illicit to deem such a person a realist. For both the realist and the idealist are happy to make singular existence claims with regard to the objects which they believe to exist. Where they will disagree is over what such existence claims commit them to. Once one attributes to the realist the view that ‘exists’ means ‘exists independently of the mind’, Devitt’s claim that one can be a realist without having a sophisticated conception of truth is simply implausible. Indeed, the historical realism/idealism dispute emerged out of the epistemological question of what we know to be true. This is a question which cannot be framed by a person who has not made the distinction between belief and knowledge, and in order to make this distinction, the concept of truth is required. So Devitt is mistaken in his claim that the metaphysical debate is independent of thoughts about truth and reference. Although I have emphasized the plausibility of combining a strong dose of realism with the rejection of bivalence, there are ways of understanding the argument that Dummett gives for rejecting it which do appear to imply the adoption of subjective idealism. This is evident in the controversy over how we should interpret the notion of existence for proofs. It is part of the ordinary notion of truth that what is true outruns what is known to be true. If the truth of a mathematical proposition consists in the existence of a proof for it, and if truth outruns what is known to be true, then there will have to be proofs which exist but which are not yet known. It is in many ways more intuitive to follow Heyting and insist that a proof is not the kind of thing which can exist unknown. On a natural understanding, a proof comes into existence when it is constructed, and if truth is explained in terms of proof, then truth must be tensed (Heyting 1966, pp. 2–3; Dummett 1973c/78c, p. 239). However, influential contemporary intuitionists, in particular Per Martin-Löf, do not interpret the existence of a proof in this way. A distinction is drawn between a demonstration and a proof. Demonstrations come into existence as we discover proofs. They often involve the claim that a canonical proof exists, even though this has not actually been provided. Demonstrations show the existence of proofs. Proofs do not come into existence with the demonstration, but already exist given the meanings of the terms used (Martin-Löf 1998). Yet it is puzzling to claim, as Martin-Löf does, that a proposition which is

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true but unproved is one for which a proof already exists, though it is not known. Moreover, the conception of a proof which sits most easily with the manifestability constraint is one according to which proofs come into existence when discovered. For how can we manifest our capacity to recognize an as yet undiscovered proof? So, although Dummett’s starting point is quite independent of the subjectivism of historical empiricists who believe that all we can know directly are ideas, his reasoning can easily be read as implying that what exists cannot outstrip what is known to exist, and so as involving a kind of idealism after all. In the next section, we will take a detour through the historical case for idealism, in order to clarify this issue.

The Traditional Case for Nominalism and Subjective Idealism There is, in fact, a long history within the empiricist tradition of arguments from considerations concerning meaning to at least one kind of anti-realism: nominalism. As we saw in the first chapter, the standard contemporary version of nominalism is not a doctrine to which Dummett is attracted. This is nominalism as defined by Goodman and Quine: the denial of the existence of abstract objects. Yet, as we also saw, this definition of nominalism is rather unfortunate, for it obscures the possibility of a realism with regard to properties, like Frege’s, which refuses to treat them as objects. Dummett’s reasons for rejecting Quinean nominalism have to do with his interpretation of the context principle and his acceptance of the existence of those abstract objects for which identity conditions can be coherently laid down. This makes it unclear whether, regarding the referents of predicates, he accepts a Fregean realism, which, according to one plausible interpretation, involves commitment to properties existing in the world independently of us, or a Wittgensteinian nominalism, which insists that there is potentially nothing in common among the various objects which we choose to call by one general term.10 Two considerations might suggest that the latter is the more natural position to attribute to him. First, in the case of the referents of predicate expressions, it is abundantly clear that our attribution of reference must depend on the truth conditions of the sentences in which the predicates occur. If we think that these truth conditions depend on our practices (proof or verification), it will be natural to think that the referents of the predi-

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cates involved do so too. Dummett’s discussion in Frege: Philosophy of Language is critical of Frege’s extension of the notion of reference to concept expressions because it appears, for this sort of reason, that the notion of reference cannot be made to do the same sort of work in relation to predicates as it does in relation to names (Dummett 1973a, pp. 240–4). Secondly, the Wittgensteinian slogan that meaning is use has been so closely tied, in the literature, to the rejection of the existence of properties, that it is natural to assume that, in accepting the Wittgensteinian slogan, Dummett is also adopting Wittgenstein’s attitude to properties. None the less , when he considers colour vocabulary, Dummett takes a staunchly realist position. He argues that realism with regard to colours is implied by our use of expressions referring to colours. So, while further thought is needed here, we should take seriously his assertion that the rejection of realism, for which he thinks there is a good case, is not to be identified with traditional subjective idealism. Indeed, such subjective idealism usually involves mentalism, which Dummett, along with both Wittgenstein and Frege, rejects. The connection between the realism/nominalism and realism/ idealism disputes is somewhat obscure. Dummett once suggested an important analogy between them (1978c, p. 145). More recently he doubts this analogy, and claims that the scholastic realism/ nominalism dispute fits rather badly into the semantic mould (Dummett 1991e, pp. 325–6). Yet Berkeley was both an archetypal idealist and the first to tread a path from the empiricist theory of meaning to nominalism. The introduction to The Principles of Human Knowledge contains a famous argument for nominalism (which Berkeley also interprets as an argument for idealism), and is therefore the most obvious place to turn in order to clarify the relationship between the two disputes. Berkeley introduces the Principles with an attack on the belief in abstract ideas, which he thinks of as the referents of general terms. This attack is centrally a rejection of a certain model of meaning for general terms. He then argues that realism with regard to material objects is the result of this mistaken model. It is somewhat difficult to understand the point that Berkeley is trying to make when he insists that it is the doctrine of abstract ideas which results in the belief in material substance; but it is clear that he thinks that the metaphysical view is itself grounded in a mistaken model of meaning. The following sketch is intended to bring out the connection between the two kinds of dispute over realism and their common assumptions concerning meaning, rather than be an account of everything which is going on in Berkeley’s argument.

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Much of Berkeley’s argument for idealism depends on his assuming that it will be admitted that secondary qualities are ideas which exist only in the mind. So, according to one influential view, his argument is a non-starter which rests on a failure to distinguish secondary qualities from the ideas of secondary qualities.11 But, stripped of this equivocation, the argument against the doctrine of abstract ideas still has plausibility. It can be reduced to the claim that we learn to use general terms by being presented with particular instances of the qualities involved. We have no need to explain our subsequent grasp of the meanings of general terms by postulating abstract general ideas. If we do so, we are misled by a model of meaning taken from proper names, which requires a one–one correspondence between words and the objects which are taken to be their meanings. All we need, in order to explain our understanding of general terms, is to notice that it is sufficient, to know how to use a general term, that we recognize the one–many correspondence between the word and the particular instances of some recognizable quality of things. Since the only really plausible explanation of our use of language is the empiricist one, according to which we learn to use words to pick out perceptible qualities of things, the idea that we actually understand words like ‘material substance’, which is supposed to pick out something which is not a perceptible quality, must be a mistake. We use this phrase, but we use it without attaching any clear meaning to it; hence we are really not justified in asserting that material substance exists. If this is a fair paraphrase of the contribution of Berkeley’s attack on the doctrine of abstract ideas to his argument against materialism, then Dummett’s strategy for defending anti-realism is, in one way, much closer to traditional anti-realism with regard to universals than it sometimes appears. But, at the same time, anti-realism, thought of as a doctrine derived from the theory of meaning, apparently has little to do with idealism, and there is a danger that, when Berkeley or Brouwer is interpreted in this way, the metaphysical claim that objects or numbers are mind-dependent falls away as irrelevant. It is noteworthy that, in the preceding paraphrase of Berkeley, it is only the attack on the meaning of ‘material substance’ which involves a commitment to idealism, and this part of the argument could convince one to give up the notion of substance, without resulting in the slightest tendency to equate qualities with ideas. The first part of the argument is completely independent of idealism. Indeed, it would, I believe, be partially acceptable to Frege. Frege rejects the identification of the referents of predicate expres-

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sions with objects, insisting that we grasp the contribution that such expressions make to the truth of sentences without identifying objects as the referents of predicates. This has made some writers assume that Frege is a nominalist (Bergmann 1958/68). But, as we have seen, in Frege’s writing there is a rejection of the idea that the referents of general terms are objects, combined with an insistence that the unsaturated entities which are the referents of these terms exist independently of us, and can exist uninstantiated. The identification of concepts with functions allows Frege to treat predicates which are true of nothing as just as legitimate as those which are true of one or more things. Goodman and Quine also accept arguments of the kind found in Berkeley. And with them the arguments are coupled with a clear commitment to both materialism and nominalism.12 For all the argument above shows, the perceptible qualities of things could exist quite independently of any mind. The fact that they are perceptible particulars does nothing to show that they do not exist unperceived; it involves only the assumption that they can be perceived. Berkeley thinks that his version of this argument shows that only ideas exist, because he fails to appreciate the distinction between the qualities of things and our ideas of those qualities, and he assumes that it has already been accepted that it is ideas that we perceive. But this assumption is independent of the preceding argument, which is compatible with the view that the particular reds, squares and sweets that we perceive exist independently of our perceiving them. The argument could convince someone who was a realist about material objects to think of them as conglomerations of material qualities, adopting anti-realism with regard to universals only when they are thought of as objects plus anti-realism concerning substance in general. It need do nothing to convince such a person that they should be an idealist. So there is a semantic argument central to Berkeley’s thought, but it does not, by itself, lead to idealism. His idealism results from the independent and confused doctrine that the things that we perceive are ideas. But neither does the argument found in Berkeley lead in an obvious manner to the rejection of the law of excluded middle. Anti-realism with regard to abstract ideas, or abstract objects (nominalism), can be conjoined with a commitment to classical logic, as in Quine’s philosophy. Furthermore, as we saw above, a commitment to idealism can also be maintained consistently with the acceptance of classical logic, although some adjustments have to be made to this claim, as we will see below.

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Berkeley’s argument involves a kind of ‘semantic anti-realism’ which it is useful to distinguish from both idealism and the denial of bivalence. Semantic anti-realism with regard to some kinds of entity rests on considerations concerning the meaningfulness of expressions referring to entities of those kinds. Idealism with regard to a kind of entity is the doctrine that entities of that kind exist in the mind, or do not exist independently of our minds. The denial of bivalence is simply the denial that every meaningful sentence is determinately either true or false. So far the intuitive connections between these doctrines seem rather loose. Dummett has also sometimes suggested that it would be consistent to reject idealism, and to hold that natural numbers are independently existing abstract objects to which each predicate determinately either applies or not, while still maintaining, on the basis of considerations concerning meaning, that we do not possess a conception of truth for which the principle of bivalence holds (1977, pp. 383–4). So a realist appropriation of intuitionism was, at least at this early stage, considered by Dummett to be consistent. But if this is the case, and if it is also the case that an idealist might accept the principle of bivalence, it seems as though the traditional debate between realism and idealism is quite independent of the debate between realism and anti-realism as Dummett conceives it. Yet Dummett does think that his rendering of the argument in terms of the theory of meaning captures important elements in the traditional debate. In order to sort through these issues, it is helpful to make a few distinctions. Let us call the view, applied to some group of entities, that these things exist only when perceived, ‘full subjective idealism’ with regard to these entities. According to this kind of subjective idealist, it is only when perceived that a thing exists, and hence only then that there are facts as to the way it is. On this view, truths come into existence as things come to be perceived. Berkeley avoids commitment to this view, with regard to the ordinary objects of perception, only by postulating that they are always perceived by God. And Brouwer sometimes seems to be close to a commitment to subjective idealism of this kind with regard to mathematics (Heyting 1975, pp. 448, 524, 551). On this view, the existence of an object of the appropriate kind is almost as dependent on our mental perception as is the existence of a fictional object on the invention of its author. There is a difference only in the degree of freedom that we have with regard to what exists. Such subjective idealism leads naturally to the rejection of bivalence. For, just as fictional entities have only the qualities they are described as having,

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mental items will have only the qualities they are perceived as having. There is no fact of the matter as to whether Hamlet did or did not have a mole on his left shoulder. Nor, arguably, is it the case that either his nurse was a redhead or she was not. Equally, Berkeley might accept that the unperceived tree, since it does not exist, is neither deciduous nor evergreen. And one might expect Brouwer to assert that numbers have properties only once they are actually constructed. However, despite the intimations of full subjective idealism in his work, this is not the view that Brouwer takes. Just as the phenomenalist moves almost immediately from the highly implausible claim that to exist is to be actually perceived, to the more plausible claim that to exist is to be such as to be able to be perceived by a creature in the right circumstances; so Brouwer allows that when a finite domain is being considered, the law of excluded middle will hold, because it will always be possible for someone to effect the appropriate construction in a finite number of steps, and so each case can be decided (Heyting 1975, pp. 109, 130, 443, 490). The failure of excluded middle that results from subjective idealism is analogous to that which results from the failure of reference of singular terms. For in each case it is the fact that an item does not exist which leads to the conclusion that sentences which apparently refer to that item are neither true nor false. This can happen in two ways. Either there is a fictional character, or an idea, but nothing determines whether properties ascribed to that character or idea hold, because there is no object which we can examine in order to determine questions not already decided in the fiction, or contained in the idea. Or there simply is no such idea or construction or character in the first place. In such a case, there really does appear to be a ‘gap in reality’ which underpins the failure of excluded middle.13 As we saw in chapter 1, Dummett initially argued at some length that the failure of excluded middle which results from failure of reference leads naturally to a many-valued logic, but that manyvalued logics are not fundamentally less realist than is two-valued logic. But the analogy between the argument from full subjective idealism to the failure of tertium non datur, and that which reaches the same conclusion from the existence of non-referring singular terms, undermines this position. Dummett now thinks that he was mistaken in insisting on the distinction between deep and shallow reasons for rejecting bivalence, and that all rejections of bivalence involve an element of anti-realism with regard to some class of enti-

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ties (1991e, pp. 324–7). Strawson argued that a sentence like ‘The king of France is bald’ is neither true nor false, because the definite description fails of reference. This position is anti-realist with regard to Meinongian non-existent objects, though, since it is not anti-realist with regard to ordinary material objects, it is not natural for us to dub it ‘anti-realist’. Dummett suggests that Meinong’s realism ‘consists in his treating singular terms as always denoting objects’ even though some of these objects do not actually exist (1991e, p. 324). However, although this might look like a simplification of Dummett’s view, it threatens to undermine central tenets of his philosophy. We have already seen how the context principle underpins what Dummett takes to be the guiding insight of the analytic school, which is that an account of thought can be given only via an account of language. It is the context principle also which justified the assumption that questions concerning the existence of objects reduce to questions as to what ontology is required to underpin the truth conditions of sentences. But the thought that failure of reference leads to a failure of bivalence appears to break this nexus. Some sentences containing non-denoting terms appear intuitively to be true. ‘Hamlet was a ditherer’ and ‘Hera was the wife of Zeus’ are examples from fiction. ‘The novel I might have written would have been based on history’ is a modal example. Such sentences may only be true-in-the-fiction, true-in-mythology, or true in virtue of how things might have been (sometimes called true in virtue of the way things are in another possible world). But if one reads the context principle as we saw Dummett was inclined to, as asserting that it is sufficient for a name to have a reference that the sentences in which it occurs should have been given a sense, then it would seem to follow that Hamlet, Hera and the novel I might have written exist (though perhaps we would have to say that they have only fictional or possible existence). If the apparent truth of these sentences requires the existence (even if it is only in fictional or possible worlds) of the entities they refer to, then why not allow that it may well be determinately true or false in those worlds that Hamlet has a mole on his left shoulder? The argument in favour of the failure of bivalence for sentences involving fictional objects or non-existing objects assumes a criterion of existence for objects that is independent of the apparent truth of sentences containing names that are in the syntactic position appropriate for referring to objects. This criterion is something like being a potential object of public intersubjective scrutiny with

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regard to its properties. But falling back on a criterion of existence of this kind strengthens the argument developed in chapter 1 for being suspicious of the context principle, at least when it is interpreted as providing a sufficient condition for treating singular terms as referring to objects. The reasoning which takes one from subjective idealism to the failure of excluded middle is something like this. Take some unimagined and unperceived tree. Is it deciduous or not? Well, suppose that it is deciduous. In order to be deciduous, it must be able to be perceived or imagined to be deciduous; but if this is possible, the tree does exist, at least as an idea, so it is, after all, not unimagined and unperceived. An exactly parallel argument holds for its being non-deciduous. So we can conclude that it is both the case that the tree is not deciduous and the case that it is not not deciduous. But this is a contradiction. Certainly it is equivalent to the negation of excluded middle; but just because the negation of excluded middle would be absurd, the intuitionist, while refraining from asserting the principle, does not assert its negation. It is because failure of reference leads in this way to absurdity that logicians have traditionally either treated non-referring terms as illegitimate, or developed free logics in which existential generalization is restricted, or developed partial or many-valued logics. So although there is a direct route from idealism to the failure of bivalence, it is not a route that takes us to the position preferred by intuitionists. The reasoning depends on the thought that things which do not exist have no properties. And in this case the direction of explanation seems to go from a judgement about the existence of objects to a conclusion regarding the appropriateness of certain sentences. The use of sentences for making assertions no longer appears fundamental in the account of language. Rather, we will have to accept a distinction between genuine and mock or fictional assertions, in terms of a prior notion of the existence of the objects referred to by the terms in those sentences. So, while Dummett’s new position has advantages, it also raises some fundamental questions. The advantage of having renounced the distinction between deep and shallow rejections of bivalence is that it makes the connection between the rejection of bivalence, anti-realism and traditional idealism much clearer. The rejection of bivalence is almost always the mark of a form of semantic anti-realism with regard to some kind of entity. And semantic anti-realism with regard to some kind of entity may indeed fall out of the traditional idealist position that entities of that kind do not form a determinate totality which

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exists independently of our capacities. The disadvantage of rejecting the distinction is that it apparently undermines Dummett’s insistence on the centrality of sentences and assertion in the account of the functioning of language. Should we accept the centrality of sentences within the account of meaning that is captured by the context principle? As we saw in the first chapter, Dummett’s own reading of the source of the contradiction in Frege’s system puts pressure on the acceptability of the context principle. Dummett concludes that the context principle should not be read as justifying the assumption that objects automatically exist just in case it is possible to lay down a criterion of identity for them. Further, he distinguishes a thin notion of reference for number words from a robust notion according to which for numbers to exist is for them to be the objects which are semantically relevant to the determination of the truth or falsity of sentences in which they occur (Dummett 1991d, pp. 189–99). We might think that in the cases we have been discussing, the impetus towards anti-realism and the denial of bivalence comes from the prior thought that there is no object referred to by the name ‘Hamlet’ which is relevant to the determination of the truth or falsity of the sentences in which this name occurs. So the syntactic role that words play in sentences is not sufficient for us to determine whether or not they are genuine referring expressions. It is only when that role can be backed up by an account of the way in which the objects the words refer to are relevant to determining the truth or falsity of the sentences in which they occur that we have genuine referring. The context principle, then, places a constraint on questions of reference to objects, but does not provide a sufficient condition for the existence of a referent. A semantics will have to be enriched by an epistemological account of how the existence of the postulated objects is relevant to the determination of the truth or falsity of sentences. This brings Dummett closer to those who have found it odd that questions of existence should be determined via questions of truth; for it allows that where causal interaction with a physical object is relevant to determining the truth or falsity of a sentence in which a name of that object occurs, we will have a paradigm for assuming the existence of that object.14 By contrast, when one makes an assertion about a fictional object, it is not the object, but a text or set of texts, which is relevant for determining the correctness of one’s assertion. What adherence to the context principle denies, however, is that this causal paradigm constitutes the only way in which an object

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can be semantically relevant. Properly constructed abstract objects can also be shown to be semantically relevant to the truth or falsity of sentences in which they occur, in a way in which fictional objects or non-constructible numbers are not. Nevertheless, one might at the same time wonder whether the context principle, so constrained, won’t after all justify nominalism. If all questions concerning the truth of statements about directions, for instance, are ultimately decided by answering questions concerning the parallelism of lines, then it seems, on the proffered account of robustness, that directions will not enter robustly into the semantics of the sentences which contain them. And if all questions concerning facts about numbers can be reduced to facts about the relations such as being equinumerous which hold between extensions, then numbers, thought of as the extensions of the properties of being equinumerous with some logically constructible Nmembered extension, will not enter robustly into the semantics of the sentences which contain them. Perhaps a Fregean attitude to the existence of properties can mitigate this nominalism, by insisting on the fact that the properties themselves are objective and enter into the truth conditions of sentences, but before considering this, we will look at a more plausible version of idealism than full subjective idealism.

Moderate Idealism and the Denial of Bivalence We have seen that, although it is possible to be an idealist and accept bivalence, there is a natural path from full subjective idealism to the denial of bivalence. But for many classes of entity, subjective idealism is not an intuitively plausible position. Moreover, as was discussed in the last chapter, in the case of mathematics, the analogue of subjective idealism, strict finitism, appears to be incoherent. There is, however, a version of idealism which, on balance, comes closer to the standard intuitionist view than the radical position we have been considering. Let us call ‘moderate idealism’ the view that to exist is to be capable of being perceived by a creature in the right circumstances. Moderate idealism is a much more plausible position than full subjective idealism. Indeed, it might even be thought to be tendentious to describe it as a form of idealism, for one way of arriving at this position is that outlined in the first chapter. There we saw that Dummett derives a version of moderate idealism from the realist assumption that, in order for a sentence to be true, there

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must be something in virtue of which it is true, plus the epistemological constraint that if a sentence is true, it must be possible to know that it is. This position allows that objects can exist without actually being perceived, and that they exist independently of particular minds. In this sense it is objectivist (Dummett 1982c/93d, p. 235). At the same time, according to it, there is no sense to be made of the idea that something exists without it being possible for some creature, which is in the right circumstances and sufficiently like us, to have some way of knowing that it exists.15 Many intuitionists are moderate idealists in this sense. As was mentioned, one interpretation of the intuitionistic logical constants allows that a statement is true if we possess a means for obtaining a canonical proof of it, even if the proof has not actually been developed. For instance, the intuitionist will allow that 101000 + 3 is determinately either prime or not prime, even if we have not proved which, because there is a method which we could apply which would result in a proof. The intuitionist is therefore prepared to assert the subjunctive conditional; if we were to carry out the procedure for determining whether 101000 + 3 is prime, then there would be a determinate outcome. And this is taken as evidence that it is already the case that this number is prime or not, as the case may be. By contrast, the full subjective idealist must be resolutely sceptical concerning the truth of such subjunctive conditionals, insisting that there is no truth of the matter until the number is actually constructed (Dummett 1973c/78c). So the moderate idealist goes some way towards realism, but not so far as to embrace unrestricted bivalence. It is in Dummett’s early paper ‘Truth’ that he first develops an argument which takes us from moderate idealism of this kind to the rejection of bivalence. In this paper the argument is applied to character traits (Dummett 1978c, pp. 14–16). There Dummett begins with the observation that the correspondence theory expresses an important feature of the concept of truth not captured by the law ‘It is true that p if and only if p’. This is the feature captured by what has been called the truth-maker principle.16 It is the interpretation placed on the claim that a truth-maker exists, which constitutes the difference between the realist and the anti-realist, as emerges from Dummett’s example. Dummett discusses this principle in relation to the question of the validity of the statement ‘Either Jones was brave or Jones was not brave’, where Jones is a man who is dead and was never in a situation of danger. If we accept that the sort of thing which makes an attribution of bravery true is the manifestation of brave

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behaviour in the face of danger, then the instance of excluded middle in question amounts to the assertion that either it is the case that, had Jones encountered danger, he would have acted bravely, or it is the case that if Jones had encountered danger, he would not have acted bravely. The anti-realist with regard to character traits is then characterized as someone who refuses to acknowledge the truth of this disjunction, because it may well be that nothing exists or existed which makes either of the disjuncts true. The realist, by contrast, argues that although there is nothing which now exists which would justify us in asserting either of the disjuncts, nevertheless there must have existed something, an underlying character trait, for instance, which now makes it the case that Jones either was brave or was not. What really divides the realist from the anti-realist in this case is that the realist is happy to countenance the existence of a truth-maker which may in principle be imperceptible, while the anti-realist can make no sense of the claim that something exists which makes one or other of these disjuncts true, yet it is not in principle possible for anyone to put themselves in a position to judge which one is true. One way of putting this is to say that the realist’s purported semantics fails Dummett’s epistemological constraint, because whatever it is which is claimed to determine the truth or falsity of this statement cannot be relevant to the use that we make of the statement and the actual means we employ for determining whether or not it is true.17 This particular example is made rather complex by the fact that, although it is ostensibly about character traits, it also involves a statement in the past tense. So two questions arise: whether it would have been possible for someone in the past to determine which of these disjuncts was true, and whether it is now possible to determine which of the disjuncts is true. Dummett recognizes ‘three principal sentence-forming operations which are responsible for our capacity to frame undecidable sentences: the subjunctive conditional; the past tense (or more generally, reference to inaccessible regions of space-time); and quantification over infinite or unsurveyable infinite totalities’ (1976e/93d, p. 60). We have seen that the traditional intuitionist argument concerns the last of these. We will discuss the issue of anti-realism with regard to the past in the next chapter. Abstracting from the issues raised by the past tense, we have here a subjunctive conditional, and it is the first question that we should answer: whether it would have been possible for someone in the past to determine which of these disjuncts was true.

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It might seem that in this, and in similar cases, the anti-realist’s argument for doubting this instance of excluded middle is weaker than Dummett assumes; for if someone had existed in the past who was interested in the question of Jones’s bravery, they could have put him in one or more situations of danger until the issue was definitely decided. But, of course, such an intervention would have resulted in a completely different situation. The way in which we should understand the question that is posed is to allow that all the information is still available that was ever available, given the actual history of Jones’s life. Under these circumstances the antirealist will refuse to countenance the truth of either disjunct, given that no perceptible state of affairs ever existed which made either disjunct true, while the realist will insist that one or other disjunct must be true, and claim further that the fact that the truthmaker cannot be, and could not be, perceived makes no difference. Nevertheless, because it is natural to assume that, had someone wanted to test Jones in the past, they would have been able to determine whether or not he was brave, the denial of excluded middle may seem, in this case, a fairly unattractive doctrine. For it is tempting to suppose that the behaviour would be the manifestation of some already existing mechanism, the existence of which could be discerned by some other means. The crudest picture would be that bravery is something which is already present in the genes, so that, even though Jones’s bravery was not manifest in his behaviour, yet it could be detected by doing an appropriate genetic test. But the relationship between genes and behaviour may be quite complex. A person might have acted bravely if faced with certain kinds of danger, or when in certain moods, or at certain periods of their life, while they would have been cowardly in other circumstances. Given these facts, it may still seem more plausible that nothing exists which makes it true that Jones either was or was not brave. So realism with regard to character traits could manifest itself in the insistence that bivalence holds because of the existence of some categorical base for our dispositions, while the anti-realist who identifies character traits with, in principle, observable behaviour ought to be led to refrain from asserting bivalence. This form of realism involves reductionism. Bivalence is asserted because the conditional is assumed to be made true by some categorical base. Dummett suggests that it would also be possible to be a naive realist with regard to conditionals of this kind and to maintain the truth of bivalence for them while taking them to be ‘barely true’

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(1976e/93d, p. 57). However, he does not offer an example of such a naive realism with regard to subjunctive conditionals, and since it is difficult to understand what a direct apprehension of counterfactual reality would be like, the position appears implausible (p. 62). Realism in this area usually takes the reductionist form. So the example illustrates rather well Dummett’s claim that reductionism should not be identified with anti-realism. It also illustrates how easily reductionism can lead to a denial of bivalence. It does this in a way which reopens the question whether all routes to the denial of bivalence should be deemed forms of anti-realism. If we think that ‘Jones was brave’ is true just in case the categorical basis for bravery existed in Jones, then we can think of the negation of its negation in two ways (corresponding to wide and narrow scope). On one reading, the lack of a categorical basis for bravery is asserted; on the other reading, the existence of the categorical basis for cowardice is asserted. The second way of reading ‘Jones is not brave’ will lead, by reasoning similar to that which was used in the case of non-denoting descriptions, to a three-valued logic. The fact that Jones was neither brave nor cowardly would, in this case, be made true by the lack in Jones of any sufficient categorical base for either of these dispositions. This kind of reasoning is quite realist in character, since it accepts that the things that do exist, exist independently of us. It may seem to be an oversight that Dummett has ignored the most influential contemporary analysis of counterfactuals: that offered in terms of possible worlds by David Lewis (1973). If we give an analysis of counterfactual conditionals in terms of possible worlds, we might deem ‘Jones was brave’ to be true just in case in any possible world in which Jones was faced with danger, he would have acted bravely. On such a view, the law of excluded middle could be affirmed, since in any possible situation in which he faced danger, Jones would have been brave or not brave; but since absolute truth is identified with truth in all possible worlds, bivalence would lapse, since it might not be the case either that in every possible world Jones was brave, or that in every possible world he was not brave. Dummett is quite aware of this possibility, and suggests that any theory of this kind, which replaces the notion of absolute truth with some notion of truth relativized to a world, moves some distance away from the classical realist semantics. Nevertheless, the move to a relativized truth predicate does not by itself take us far from realism, as Dummett acknowledges in relation to tense logic (1982c/93d, p. 268). Whether it does depends on the

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interpretation that one places on the quantifiers which range over times, or possible worlds, or whatever else truth is relativized to. If one admits possible worlds, one could have a strongly objectivist reading of the counterfactual conditional ‘If Jones had encountered danger, he either would or would not have acted bravely’ which departs from the standard two-valued semantics. But Dummett is in general dismissive of semantic theories of this kind, because they are not really able to provide the foundation of a theory of meaning: that is, an account of what understanding consists in (1991e, pp. 154–7). One way in which such semantics fail this requirement is that it is impossible to see how our grasp of the use of a sentence like ‘Jones was brave’ could relate to the way things are in possible worlds which are causally inaccessible to us. Another is that we have no way of specifying which worlds are possible independently of our prior grasp of the meanings of words. Suppose that there is a world in which Jones is faced with danger and always avoids it by sneaking away. Everybody else in that world is so terrified by danger that, whenever they are faced with it, they fall into a blubbering heap. Is this a world in which Jones is brave or not? Being brave is partly relativized to a population. Thus a child might be deemed brave for standing up to a danger which a soldier would be expected to take in her stride. In any case, postulating the abstract structure of possible worlds does not decide this question for us, since it is our grasp of the meanings of words which guides us in our decisions as to which worlds are possible, which not. In the 1963 paper ‘Realism’, unpublished until 1978, and elsewhere, Dummett indicates the possibility of adapting the moderate idealism, discussed above, to cover a central case of anti-realism: that of phenomenalism (1978b, p. 150). More recently he has argued that the phenomenalists ought to have rejected bivalence, although in general they did not; for, according to the phenomenalist, the truth of a material object statement reduces to a subjunctive conditional (Dummett 1991e, pp. 329–31). The moderate idealist with regard to the material world does not equate the existence of material things with their actually being perceived, but claims that to exist is to be capable of being perceived by a creature in the right circumstances, with appropriately extended perceptual powers. A disjunction like ‘Either there is intelligent life on a planet less than ten light years away from earth, or there is not’ is thought to be true in virtue of the truth of one or other of the subjunctive conditionals: ‘Were we to examine all the planets less than ten light years

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away from earth, we would discover intelligent life’ or ‘Were we to examine all the planets less than ten light years away from earth, we would not discover intelligent life’. Dummett sometimes calls such a pair a pair of ‘opposite counterfactual conditionals’. If one assumes that one or other of such a pair is true, then a dilemma arises. Either one takes the counterfactual conditional to be true in virtue of some categorical base (say the existence of a planet on which there is intelligent life), in which case the claimed reduction becomes circular, or one is committed to treating these subjunctive conditionals as barely true. As Dummett reports, Isaiah Berlin (1950) once offered this argument as a refutation of phenomenalism. But Dummett offers the phenomenalist another way out. The phenomenalist can reject bivalence with regard to such subjunctive conditionals. This does not necessarily save phenomenalism, however. For the phenomenalist is hardly likely to want to refrain from asserting the truth of a disjunction such as ‘Either there is or there is not gold on the moon’. If we were to look, we surely would be able to discover that this either is or is not the case. What degree of difficulty of verification is necessary in order to make it illegitimate to assert such a disjunction? How like us does the creature that could verify one or other disjunct need to be? How great is the extension of the perceptual powers allowed to be? Presumably the creature cannot have infinite perceptual powers, for in that case the anti-realist phenomenalist’s judgements will coincide with the realist’s. But presumably, also, the creature will not be subject to all the limitations of an actual human being, for this would restrict the range of cases in which we were justified in asserting instances of excluded middle far more narrowly than is suggested by the practice of intuitionists. Dummett characterizes those who are opposed to scientific realism as attempting to reveal the world as it presents itself to us with ‘our particular observational capacities, conceptual equipment and location in time and space’ (1978c, p. 152). But if we take this seriously, it seems to imply that ‘Either there is intelligent life on a planet less than ten light years away from earth, or there is not’ cannot be asserted. For there is nothing which now warrants the assertion of either disjunct. It is tempting to assert that the creature’s powers should be thought to be extended just as far as one likes, so long as they still count as finite. But this looks like gerrymandering in order to end up with an analogue of intuitionism. And once one brings up this worry for the case of phenomenalism, it becomes obvious that even in the case of mathematics it is not clear that the argument

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Dummett gives from considerations concerning meaning to the adoption of intuitionism might not justify a more restricted logic. As we have seen, the position that Dummett ascribes to the intuitionist is not a stable one. If phenomenalism is thought of along these lines, as a form of moderate idealism, it looks as though it will collapse back into the subjective idealism which is the analogue of the strict finitism briefly discussed in the previous chapter. This brings home the need for some independent reasons for rejecting strict finitism and the analogous subjective idealism.

The Case against Strict Finitism In the paper ‘Wang’s Paradox’ Dummett attempts to face the challenge from strict finitism head on. There he argues that ‘surveyable’ is a vague predicate, and so subject to the incoherence demonstrated by the Sorites paradox, or paradox of the heap. A proof which is just a little bit longer than an actually surveyable proof will still be surveyable, yet not all proofs are surveyable. So transitivity fails. Similarly, the property of being a small number is a vague property. If n is a small number, then n + 1 is surely also a small number; but, by a series of such inferences, one can reach the contradictory conclusion that some very large number is small. The situation with regard to these predicates is exactly analogous to phenomenal predicates like ‘is red’, where the existence of non-discriminable difference will likewise lead to inconsistency. Dummett concludes that the use of vague predicates is intrinsically inconsistent, and that this gives a reason for rejecting strict finitism. An unpalatable consequence of this rejection of vague predicates is that the phenomenal predicates of ordinary language are taken to infect it with inconsistency, and Dummett is forced to conclude there are no phenomenal qualities (1975c/78c, pp. 264–8). One may, because of this, wonder whether this response is satisfactory. First, it seems to require that we purge our language of phenomenal predicates; yet such predicates are absolutely fundamental. There is no problem with their use in ordinary discourse, and one might take this as evidence that Wittgenstein is right to insist that our ordinary usage is perfectly in order, and that it is only the misguided attempt to turn everything into a science which leads to our puzzlement here (1967a, §98). If the rejection of strict finitism brings with it the rejection of phenomenal predicates, is not the price too high? Dummett does not explicitly meet this challenge.

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Indeed, his most recent writing on vagueness and bivalence concludes with a sharp condemnation of the realist outlook which he appeared earlier to be endorsing (1995a). On the surface, vague predicates provide a clear counterexample to the general position that Dummett is now prepared to defend, according to which the denial of bivalence for an area of discourse is always associated with some retreat, though possibly a minimal one, from a realist semantics for statements of that kind. Someone who denies bivalence because of the existence of vague predicates could consider themselves to be a realist, and insist that vagueness in language derives from vagueness in reality. Such a person would deny bivalence for sentences containing vague predicates, but might claim to be adopting a fully realist attitude. Dummett argues, however, that such a position does not constitute a thoroughgoing realism. The out-and-out realist will insist that every unambiguous predicate is precisifiable in one unique, determinate way. In order to fully retain bivalence they will have to insist, as Frege did, that only predicates of this kind are acceptable in a scientific language where meanings are well defined, because only predicates of this kind latch on to determinate properties. Such an out-and-out realism is, Dummett suggests, not a plausible doctrine. But the fact that it is not plausible does not detract from the fact that, by contrast, the theorist who accepts that there is vagueness in nature has moved some distance from out-and-out realism. Since Dummett himself seems no longer to have the dismissive attitude that he earlier expressed with regard to vague predicates, the question might be raised whether he has any longer any good reason for rejecting strict finitism. I suspect, however, that he now believes that there are ways of making our use of phenomenal predicates coherent which do not lend themselves to being extended in such a way as to provide a solution to the strict finitist’s problem. In The Logical Basis of Metaphysics he discusses, in a rather different context, the method of supervaluations which provides a semantics for phenomenal predicates by replacing them with a system of sharpenings (Dummett 1991e, pp. 73–4). Truth for vague predicates, on such a semantics, is not absolute, but is relativized to a sharpening. The Sorites series is blocked because in each sharpening, or precisification, there will be a clear demarcation between things for which the predicate holds and those for which it does not. Vagueness is preserved, because it is admitted that no one of the sharpenings determinately captures the meaning of the vague predicate. If this semantics were to give us a coherent way of dealing with

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phenomenal predicates, but could not be extended in such a way as to save strict finitism, then Dummett’s conclusion in ‘Wang’s Paradox’ would look less unpalatable. The strategy which suggests itself is first to apply the method of supervaluations to the notion of surveyability, and then, if it can be shown that in this case the method does not lead to coherence, to reject strict finitism as subject to irredeemable vagueness. There will be a number of possible sharpenings of the notion of surveyability. If our sharpenings involve the idea that a proof is ‘surveyable’ relative to a person and a time, then very few proofs will be surveyable, since virtually no proof will be surveyable in every sharpening. Absolute truth in mathematics will be truth under all sharpenings, and virtually no arithmetical truth will be absolutely true. Truth will become relativized to a person and a time, and arguably this conclusion is incoherent, or at least, so at odds with our generally accepted views concerning mathematical truth, and so at odds with the use that we make of mathematical discourse, as to be unacceptable. So Dummett’s rejection of strict finitism on account of its vagueness can be defended up to this point. There is a further worry. In his paper ‘Strict Finitism’ Crispin Wright argues that if Dummett is right and the notion of surveyability is incoherent, this conclusion must infect his own use of notions like decidability. He claims that ‘ “decidable in practice”, like “surveyable” and “intelligible” is, if Dummett is right, irremediably Sorites-susceptible’ (Wright 1982/93, p. 124). Wright’s own conclusion, on the basis of this observation, is that it is tendentious to assume that predicates that are Sorites-susceptible are in any way incomprehensible, and that they should therefore be disallowed. Phenomenal predicates are perfectly comprehensible; there is no reason to reject them just because of the possibility of Sorites reasoning. The strict finitist can take the same attitude to the predicate ‘surveyable’. Moreover, it is not clear that any incoherence could ever be derived by strict finitist methods. So Dummett’s conclusion that the Sorites susceptibility of ‘surveyable’ renders it unacceptable is premature (Wright 1982/93, pp. 152–60). Wright argues further that it is not possible in principle for the intuitionist to distinguish finite from infinite totalities. Therefore, for those who are convinced of the legitimacy of the manifestability constraint, strict finitism, rather than intuitionism, should fall out as the natural philosophy of mathematics. There is a great deal of complicated reasoning behind these conclusions, and it is beyond the scope of this book to delve further

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here. But if one is to be able to defend Dummett’s conclusion that the intuitionist’s outlook is the most coherent position to adopt on the basis of the argument from manifestability and learnability, it will, I suspect, be because one has been convinced that the intuitionists are right to insist that there is a sharp disanalogy between finite and infinite totalities. For the intuitionist, ‘the whole essence of infinity . . . lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed’ (Dummett 1977, p. 57). Earlier, we saw how this conception of infinity as never completed results in the traditional intuitionist response to the paradoxes. The realist’s mistake was to treat an infinite totality as though it was already completed, rather than seeing that some concepts are indefinitely extensible. The finitist’s mistake might be characterized as similar. It is to fail to recognize that the concepts of being a natural number, or being an ordinal number, are indefinitely extensible. Because we can continue with the process of construction as long as we like, there is no natural stopping place to the process of construction. To attempt to specify a point beyond which we could not effect the construction of a natural number will lead to paradox. Wright attempts to show that the intuitionist cannot give an adequate definition of a finitude, because it is not in principle possible to show that a set could be put in one–one correspondence with an initial segment of the series of possible integers. It is not practically possible to enumerate the finite initial segment of the natural numbers up to 101000. But if the intuitionists are right, we can have the concept of infinity without being able to enumerate each finite number in practice. We can see that, were we able to complete the enumeration of 101000 numerals, the process would ultimately come to an end. By contrast, the enumeration of all the natural numbers would never come to an end. The intuitionist’s position thus entails recognizing the truth of certain subjunctive conditionals even though we are not in practice in a position to fulfil the antecedent of the conditional.18 This involves moving a considerable distance towards realism and away from the full subjective idealism that we considered above. If the argument which Dummett is exploring is cogent, it takes us just as far in this direction as we should be willing to go. Dummett’s case for anti-realism starts from considerations about meaning, and this has raised the question of the relationship between the doctrines that have traditionally been opposed to realism, in particular Berkeley’s idealism and Dummett’s brand of semantic anti-realism. We have seen that the connection is fairly

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loose. It is quite possible to believe in a material world which exists independently of any observer, and to be convinced by Dummett’s version of the intuitionist’s argument that we have not conferred a meaning on the sentences of the language such that the principle of bivalence holds without exception. If we call the view that the ordinary objects accepted by common sense, such as trees and cherries, exist, and exist independently of human minds, ‘common-sense realism’, then we can say that one can be a common-sense realist and accept the argument against bivalence for certain areas of discourse.19 It would also be possible to be an objective idealist and to think that reality is determinate though not material. Nevertheless, the following connections between attitudes to bivalence and traditional doctrines do appear to be established. Someone who asserts the general validity of excluded middle is committed to realism (or at least an objective idealism which amounts to a kind of realism). It is also the case that full subjective idealism naturally leads to failure of bivalence, as does the position I have called moderate idealism. There is one area of language, vague predicates, in which interpreters who accept the failure of bivalence tend to think that they are realists; but Dummett would now argue that even rejecting bivalence because of vagueness involves some retreat from realism. The price of giving a coherent semantics for such an area of discourse is that truth simpliciter is replaced by a relativized notion: truth relative to some sharpening of the vague predicates. So Dummett is now inclined to argue that the refusal to assert bivalence is in general the mark of some kind of anti-realism with regard to some kind of entity. By developing such connections, Dummett has shown us a way in which ‘we can abandon realism without falling into subjective idealism’. And the abandonment of realism comes to look, in many areas of discourse, to be the common-sense view.

Pure vs Mediated Constructivism, Truth Theories and Semantics In the preceding chapters we have characterized three possible positions within the theory of meaning. Their strengths and weaknesses, as Dummett has exposed them, can be summarized in the following way. Three propositions with regard to meaning strike us as initially plausible:

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The meaning of a sentence is given by its truth conditions. What someone understands when they understand the expressions of a language is something that should be capable of being made manifest in the use that they make of its sentences. It must be possible to give a systematic account of the meanings of the sentences of a language which shows how a speaker’s ability to understand new sentences is grounded in their grasp of the meanings of a finite number of simpler sentences and modes of sentence construction.

The realist accepts the first and third of these propositions, but is not, according to Dummett, able to satisfy the second. The holist, according to Dummett, gives up on (3), and if Wittgenstein is taken to be the paradigm, they will also give up on (1). There is, however, an influential theory which has holistic elements while maintaining both (1) and (3). This is Davidson’s version of the truth-conditional theory. But since Davidson’s own views have now evolved, and since many of the issues that arise have to do with what we know when we know a language, Davidson will not be discussed until chapter 5. The pure constructivist replaces truth with verifiablity, and adopts propositions (2) and (3), but gives up on proposition (1). The strength of mediated constructivism, which retains the notion of truth but gives an account of it in terms of possible verifiability, is that it apparently manages to satisfy all three of the initially plausible propositions concerning meaning. Whether it actually does so depends on whether the manifestability constraint is genuinely satisfied and whether the resulting theory is descriptively adequate. It may seem, for reasons first touched on in chapter 1, that the position here called ‘mediated constructivism’ is not really tenable. If we are committed to the view that meaning is given by truth conditions, we will accept that the construction of a truth theory which states the truth condition of each sentence will play a central role in the theory of meaning. But if we explain ‘is true’ by ‘is provable’ or ‘is verifiable’, then it may seem that we have only masked and not genuinely solved the difficulty discussed in chapter 1 that replacing ‘is true’ with ‘is verifiable’ in S is true if and only if p converts a truth into a falsehood. One way around this problem is to insist that a truth theory for an intuitionist object language, in which truth is cashed out as provability, is given in an intuitionist metalanguage. If ‘if and only if’ is interpreted intuitionistically, then

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says that a proof that S is true can be converted into a proof of p, and a proof of p can be converted into a proof that S is true, which, by the intended intuitionistic meaning of ‘is true’, is clearly the case. In The Logical Basis of Metaphysics Dummett calls this a ‘programmatic’ or ‘internal’ interpretation, and argues that nothing is done to explain the meanings of the intuitionistic logical constants by such a truth theory; they are simply assumed as understood. In the case where the meta-language is classical, the standard semantics for the classical constants is the only natural contender, and the meanings of the constants can be explained in terms of the truth or falsity of sentences. In the case of the intuitionistic constants there is no standard semantics. There is a semantics in terms of Beth trees or Kripke trees, and another in terms of the assignment of propositions to sentences, and species to predicates. The first corresponds to the notion of provability according to which provability is identified with assertibility and leads to a tensed truth predicate. The second is more in line with an untensed notion of provability. But Dummett complains that, since the notion of a proposition is completely obscure, a programmatic interpretation of the intuitionistic constants does not help to explain the meanings of the intuitionistic constants (1991e, pp. 20–39). These observations do not show that mediated constructivism is untenable, but they do show that those who are developing the semantics for intuitionistic languages have a good deal of work ahead of them if they are to show how the semantics which they construct relate to the activity of using and understanding a language, and so to the development of a theory of meaning. This is not a criticism which applies only to constructivists, however, since many logicians who construct ‘semantics’ of various sorts pay little heed to the question of how the semantic value T in their theories relates to our actual use of the notion of truth and its place in the activity of speaking and understanding language.

A Common-Sense Realist Appropriation of the Argument against Bivalence In the last section of this chapter I want to suggest that Dummett’s current view, that the rejection of bivalence is always associated with some form of anti-realism, should not be taken to foreclose the

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possibility of developing what I think is the most attractive position in the philosophical landscape that he has mapped. This is the common-sense realist appropriation of the argument against bivalence. As we have seen, the manifestability constraint brings with it the disadvantage that it seems to justify strict finitism and more radical forms of idealism than the moderate idealism that the intuitionists propose. In order to justify the moderate intuitionist position, we need to insist on the special character of infinite totalities. But this leaves it open to the common-sense realist to accept the special status of infinite totalities and subjunctive conditionals, and the failures of bivalence which result from them, without leaving the ground of realism except for the denial of the existence of the completed infinite and of a determinate counterfactual reality. In the first chapter we saw that Frege’s logicism can be saved by modifying his Platonism. But the modification consisted not so much in a rejection of the thought that mathematical truth resides in the existence of structures which have determinate properties independently of anybody’s recognition of them, but in the recognition that the concepts of mathematics are infinitely extendable. A person who understands the language of arithmetic will be able to manifest their understanding in the use of symbols to speak of finite sets of things, but will never be in a position to show that they have grasped the completed totality, for our understanding that it is an infinitely extendable one precludes this possibility. The commonsense realist who appropriates the intuitionist’s rejection of the law of bivalence will accept a mild epistemological constraint on truth claims. Although we may often have only indirect means of recognizing truth, and truth will outstrip our actual capacities to recognize it directly, nevertheless, we have no justification for asserting unrestrictedly the principle of bivalence. One reason is that in the case of infinitely extendable totalities, accepting it leads to paradox. Moreover, the real existence of infinitely extendable totalities brings with it the real possibility that the truth of a sentence and its negation may never be decided. We have seen that Dummett’s restrictions on the applicability of the context principle amount to an admission that, where an existence claim is robust, this will involve the idea that the existence of the object is relevant to the truth or falsity of sentences containing reference to the object.20 In the case of ordinary physical truth, this relevance will go by way of the causal perceptual relations we have with the object. So, in the case of ordinary talk about physical objects, there is no reason for the common-sense realist and the intu-

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itionist to disagree. Disagreement may arise when undecidability creeps in. It has been argued that the denial of bivalence when counterfactual conditionals or infinitely extendable totalities are involved does not involve anti-realism with regard to anything that a common-sense realist should want to acknowledge. Past- and future-tense statements are another matter, however, and in the next chapter we will look at this third source of undecidability. Past- and future-tense statements provide a particular challenge for the argument against bivalence that Dummett has developed. For tense brings with it undecidability, along with both strong intuitions that bivalence holds with regard to past-tense statements and, for those who believe in the openness of the future, an inclination to deny bivalence for future-tense statements. Anti-realism with regard to the future is mentioned by Dummett as a central example of the non-reductive anti-realism that he finds most interesting. Both pastand future-tense sentences may be undecidable, but the most natural position to take is the asymmetric one which accepts the truth of bivalence with regard to simple past-tense statements, but not with regard to future-tense ones. It may be impossible to now determine whether or not there were ten geese on the Capitol on the day that Caesar was murdered, but there is a strong inclination to insist that this sentence was either true or false independently of our capacity to decide it. By contrast, the undecidability of the statement that there will be ten geese on the Capitol on the 2500th anniversary of the murder of Caesar does tend to make us claim that this sentence is not now either true or false. What makes the difference between pastand future-tense sentences? Are there features of past-tense statements which render them immune to the general argument against bivalence that has been developed? Or can this case be developed to show where, in general, that argument breaks down? Dummett has tended to remain agnostic on this issue, preferring simply to set out the strengths and weaknesses of realism and anti-realism about the past and the future. In the following chapter I will argue that the implausibility of anti-realism about the past is a special case which does not undermine the general argument against bivalence, though it helps to explain why accepting bivalence is so natural. If I am right, this strengthens the case for the common-sense realist’s appropriation of the rejection of bivalence.

4 The Reality of the Past

As we saw at the end of the last chapter, the question of anti-realism with respect to the past and the future introduces a line of objection to the general anti-realist argument so far developed. If the general anti-realist argument implies that we should deny bivalence for simple past-tense statements which are undecidable, and if this conclusion is untenable, then there must already be some defect in the general argument, or specific reason why it fails in this instance. Just as in the case of the challenge from strict finitism, which threatens the cogency of the argument for intuitionism, so here too, Dummett has been the best critic of the anti-realist’s position. It is he who first raised the thorny problem that if the argument against bivalence is generally adopted, we will be committed to refraining from asserting that undecidable past- and future-tense sentences are determinately either true or false (Dummett 1969/78c, p. 368). While this is natural enough in the case of future-tense sentences, and coheres with the common-sense thought that the future is open, denying bivalence with regard to undecidable past-tense sentences is counter-intuitive. So the past and the future become an important testing ground for the overall cogency of the argument against bivalence and for the claim, made in the last chapter, that the conclusions of this argument need not be anathema to the common-sense realist. Taking seriously Dummett’s proposal that we see the general argument for anti-realism as laying down the basis of a research programme that involves looking at the use of particular areas of discourse in detail, we can, I will argue, ultimately justify our realist

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presuppositions in the case of past-tense statements. This will not involve an objection to the general anti-realist argument. It will involve accepting the challenge of showing how we can manifest in our use of past-tense statements a grasp of truth conditions which transcend verification conditions, and the kind of justification that we can give for doing so. It is clearly a possibility envisaged by Dummett that the pursuit of the explanation of meaning for different areas of discourse will have different results (1993d, p. 473). We may conclude that we are justified in adopting a realist attitude to material object statements about inaccessible regions of space, for instance, while abjuring realism with regard to character traits. The case for realism with regard to the past is then of particular interest, because it helps to explain why it is so natural to adopt a realist attitude. But, I will argue, the justification for adopting realism in this case does not impugn the general demand that one shows how one could ideally manifest a grasp of truth conditions.

Anti-Realism with Respect to the Past In two early papers, ‘The Reality of the Past’ and ‘A Defence of McTaggart’s Proof of the Unreality of Time’, Dummett sets out the interrelated issues of the reality of the past and the reality of time. In the first of these, he argues that while the general argument for antirealism ought to make us anti-realists about the past, there are good reasons for thinking that anti-realism about the past is implausible (Dummett 1969/78c, pp. 367–8). The standard view is that past and future are asymmetrical: the past is determinate, the future indeterminate. But this standard view is surprisingly difficult to defend, since the general anti-realist argument suggests that we should think of statements about the past as being made true by the present or future evidence that we may have for them, as are present- and future-tense statements.1 At the same time, the arguments for the truth of bivalence and realism with regard to the past seem to work equally well with respect to the future. So looking at this case will help us see how the apparent cogency of denying bivalence can be blocked in a particular instance. It will also help demonstrate just how sophisticated is Dummett’s demand that we give an account of the meaning of sentences by showing how they are used. Following Dummett’s general argument, the consistent antirealist with regard to past-tense statements ought to refrain from asserting that an undecidable past-tense statement is either true or

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false. The problem for this kind of anti-realism, as Dummett sees it, is the ‘truth-value link’. There are various links between the past truth of sentences and the present truth of past-tense statements, as well as between the truth value of present-tense statements and the future truth values of past-tense statements. These truth-value links go along with the natural idea that truth is timeless. If it is now true that I am drinking a cup of tea, it will be true in the future that I was drinking a cup of tea at this time, even though all evidence for this may in the future be lost. So ‘Karen Green was drinking a cup of tea at 3.30 on Tuesday 2 June 1998’ will in the future be determinately either true or false, although undecidable. If one accepts the cogency of this refutation of the failure of bivalence for undecidable past-tense statements, there are two ways of taking it. On the one hand, one might argue that the particular failure of the argument in this case does not impugn the general argument for antirealism, because the existence of truth-value links is a special feature of tensed statements. This looks like an attractive response, but it threatens to undermine the plausible asymmetry between past and future. On the other hand, one might take the objection in this case to point to a generalizable objection to the style of argument that has been outlined. But before dealing with the consequences of accepting the cogency of this argument for bivalence, and hence of realism with regard to the past, we need to demonstrate that the argument is cogent. Dummett does not allow the antirealist with regard to the past to give up without a fight. In his paper on McTaggart, Dummett makes anti-realism about the past a more plausible position than it initially appears to be by arguing that we should recognize that the implication of McTaggart’s argument is that we have a choice between anti-realism with regard to time and anti-realism with regard to the past. The antirealist with regard to the past takes time and our immersion in it seriously, and is prepared to conclude that ‘true’ always means ‘now true’. The realist about the past, as characterized by Dummett, assumes that there is a point outside time from which the temporal series can be observed (1969/78c, pp. 369–70). So the price of realism with regard to the past is the conclusion that time, and the passage of time, are unreal.2 Since anti-realism with regard to the past and with regard to time are interrelated in this way, we will look briefly at Dummett’s discussion of McTaggart’s proof before returning to the implications of the reality of the past for the argument against bivalence. McTaggart’s argument for the unreality of time can be summarized as

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follows. We first distinguish between what McTaggart calls the A series and the B series. The A series is made up of past, present, future. Moments of time change with regard to the properties of the A series; a moment was future, is now present, and will be past. The B series involves relations of earlier and later; moments of time do not change with regard to the properties of the B series. Two moments of time which are related as earlier and later are always related in that way (so long as time is not cyclical). McTaggart’s first conclusion is that it is essential to time that events should form an A series as well as a B series. This follows from the following argument: 1

2

3

4

5

A universe in which nothing ever changed would be a timeless universe. Therefore, time involves change. A universe in which there was a B series without an A series would be a universe in which there was no change. Therefore, if there were no A series, there would be no B series, and no time, since the relations of earlier and later are temporal relations. There would, however, be a C series: a series of permanent relations between events; but it would not be a temporal series. In order to have time, we need a C series, the fact of change, and the fact that change happens in one direction. Therefore, the C series and the A series are both essential to time. Every event is present, past and future, but these are incompatible predicates. Therefore, the distinctions of past, present and future cannot be true of reality. We cannot get out of the contradiction by saying that every event will be past, is present, and was future, because this assumes the existence of time.

Dummett points out that it is natural to think that McTaggart’s argument is a sophism based on a failure to recognize the properties of token reflexive expressions – words such as ‘I’, ‘now’ and ‘here’. The reference of such expressions depends on the context in which they are uttered. It is impossible for two incompatible token reflexive predicates to apply to an entity in the same context, as one can see in the case of space. So one might object to McTaggart: could we not show that space is unreal, for every position in space is both here and there, but these are incompatible predicates? We do

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not conclude that space involves a contradiction, because we are inclined to say the following: for any position, there are positions which can be designated as ‘here’ relative to the first position, or as ‘there’ relative to that first position, and these are incompatible; but we never have both of these applying to a position relative to a single point of view. A position that is ‘here’ relative to a context of utterance in which I am somewhere may be ‘there’ relative to a different context of utterance. So there is no contradiction. Dummett suggests that the difference between time and space emerges when we consider the first part of McTaggart’s argument. Token reflexive expressions are essential to the description of time, but they are not essential to the description of space. We could imagine a complete description of all the spatial relations between objects without introducing into the description any ‘here’ or ‘there’ or other token reflexive expressions. So a reformulation of McTaggart’s argument is that it is impossible to give a description of events as occurring in time unless token reflexive expressions are imported. Then his claim that time is unreal depends on the assumption that reality is something of which there exists a complete description. What is temporal cannot be described without the use of token reflexive expressions; but if anything is real, it must be possible to give a complete – that is to say, observer-independent – description of it. Since it is impossible to eliminate token reflexivity from the account of time, time must be unreal. Dummett concludes that McTaggart’s argument shows that if we are convinced that time is real, we must abandon our prejudice that there must be a complete description of reality. In this early writing Dummett was inclined to identify the claim that there is a complete description of reality with realism. Indeed, the idea that there is a way things are in themselves which would be captured in a complete description of reality, and would incorporate and explain all the partial perspectives of finite and temporally located beings, is surely a realist one. Yet Dummett is now careful not to identify this view with realism, which he characterizes in terms of the acceptance of bivalence. If we assume that realism involves the assumption that there is a complete description of reality from, as it were, ‘outside time’, we can see that anti-realism about the past is not as counter-intuitive as it at first appeared. Realism concerning time naturally leads to what I will call ‘presentism’. This is the view that we will misrepresent the nature of time if we attempt to stand outside it and describe it as a series of points ordered in a sequence. We should take seriously the idea that we are immersed in time and can only

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ever know the past or the future from the point of view of the present. To say that it was the case that there were ten geese on the Capitol on the day that Caesar was murdered is to say that the present evidence warrants the assertion of this past-tense statement. To say that it will be false in the future that I had just finished drinking a cup of tea when I wrote this sentence is to say that I now have evidence that this will be false in the future. As we saw, it is partly the existence of truth-value links which makes anti-realism with regard to the past implausible. But the existence of truth-value links is not decisive against presentism. For the truth-value link can be reinterpreted. When I say that it will be true in the future that I had not just finished drinking a cup of tea when I wrote these sentences, I will be making a claim concerning what is now true about the future. So the truth-value link is preserved, but without the implication that this link implies that in the future it will be definitely false that I had just finished drinking a cup of tea at this time, since in the future this claim may be undecidable (Dummett 1969/78c, pp. 368–9). On the standard view, the past provides us with a multitude of examples where we are prepared to assert an instance of excluded middle although we are not in a position to assert either disjunct. Many of them are quite trivial. I am prepared to assert that either Michael Dummett walked along Cornmarket Street on 5 May 1976 or he did not, although there may now be no evidence for the truth of either of the disjuncts, and it may be the case that in the future nothing will turn up to decide the question. Still, there is a very strong temptation to believe that even if nothing would decide the question, the disjunction must be true, and true in virtue of the past obtaining of a state of affairs which it now transcends our powers to recognize as having obtained if it did (Dummett 1969/78c, pp. 363, 368; Wright 1993a, pp. 178–9; Weiss 1996, p. 579). But the future appears to be open. It is natural to express this by saying that it is now (that is, in 1998) neither true nor false that I will walk along Cornmarket Street on 5 May 2006. But, as we will see below, there are difficulties with the cogency of such a remark. The conclusion of the anti-realist argument, that we are not justified in assuming bivalence for past-tense sentences, even if they are no different from decidable present-tense sentences except for being in the past tense, is extremely counter-intuitive. Is there, then, a relevant difference between statements about the past and the mathematical statements for which the general argument goes through? Or can we show that the argument will break down in the

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general case for the same reasons that it breaks down in the case of the past? Or should we simply accept that our intuitions in this case need to be overridden? Dummett does not decide this issue, but he gives the following analysis of the situation. The reason why the realist has such a strong case when we consider statements about the past is because of the truth-value link. The realist and the anti-realist agree that the only kinds of evidence that we ever have for the truth of past-tense statements are the present and future traces of past happenings. Sometimes these are fairly direct, as with memory; sometimes the traces are quite indirect evidence of a past which we surmise on the basis of a theory about the causes of our evidence. Even the evidence of memory is not totally reliable, for our memories contain traces of past misperceptions as well as traces of accurate past judgements, which means that, insofar as we accept memories as direct evidence of the past, we are hypothesizing a certain undistorted causal chain connecting the past occurrence with our present memory. The realist will say that although the only evidence we have of the truth of past-tense sentences is present traces, what makes a past-tense sentence true is not the present trace of the past, but the way things were. In this case we have a paradigm of a situation in which knowing the meaning, when thought of as knowing the truth condition, cannot be equated with knowing the assertibility condition, because the assertibility conditions of a past-tense sentence always consist in present evidence; but it seems plausible to argue that a person who thinks that what makes a past-tense sentence true is something about the present will simply have failed to grasp the meaning of the past tense. The anti-realist must say that this misrepresents the situation. It is within the present that we distinguish what justifies us in asserting a present-tense statement from that which justifies us in asserting a past-tense statement; so our grasp of the meaning of a past-tense sentence must consist in whatever we now take as justifying the assertion of the past-tense sentence. As we saw, Dummett proposes that the anti-realist therefore expresses the truth-value link, emphasizing that the truth of a pasttense statement consists in the present assertibility of the past-tense statement. So ‘A’ is true iff ‘F(P(A))’ is true

expresses our current warrant to assert ‘In the future it will be the case that A was true’ iff we now have a warrant to assert A; but it does

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not imply that in the future we will have a warrant for asserting ‘A was true’. It will only be from the perspective of the future time, when we get there, that we will be able to judge the truth of ‘A was true’ at that time. Dummett thinks that the anti-realist can reinterpret these facts about truth-value links. They relate to the truth or falsity of pasttense statements whenever made, not to the evidence available for them at the time of utterance, but to the evidence that is now, or may later become, available for ascribing to those statements the property of being true when they are uttered. So it was once true (i.e. assertible) that in the future the sentence ‘I was in the library on the third Tuesday of April 1991’ would still be true in twenty years, and I could assert it on the basis of the evidence then available to me, even though I recognized that that evidence might not be available in twenty years, and that when the twenty years had elapsed, I would be justified in asserting this sentence only if there were then evidence available to me. I cannot now assert uncontentiously what will then be true (all I can do is assert what the current evidence indicates will be true in the future about the past). The anti-realist is thus forced to give up something that has been central to philosophy since Plato: the timelessness of truth. This is made only slightly more palatable if one agrees with Dummett that McTaggart’s proof of the unreality of time shows that we have a choice. We can think of reality as a timeless eternal realm, but at the cost of making time an illusion, or we can take our immersion in time seriously, recognizing that the truth, even about the past and the future, is the truth available from the perspective of a time. The choice which Dummett seems to offer is rather a stark one. In order to conform to the manifestability constraint, the anti-realist must insist that the evidence available for the truth of a sentence is present evidence. This leads to the rejection of timeless truth. On the other hand, the realist will have to forgo manifestability in order to save timeless truth. This need not, however, be the end of the matter. In the paper ‘What is a Theory of Meaning? (II)’ there is a suggestion that the extension of verificationism to empirical statements might involve some divergence from the constructivist picture. According to the intuitionist, a statement of the form p ⁄ q is provable if and only if either p is provable or q is. Moreover, in the mathematical case we never have sentences which were true becoming false; provability is an enduring feature of mathematical statements. But verifiability is not an enduring feature of empirical statements. The trivial past-tense statements that we have been considering were all decidable, but are no longer. Moreover, it is often

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the case that the present evidence for the truth of past-tense statements is itself such as to warrant the assertion of Pp or Pÿp even when it is undecidable which. For instance, one may remember very well that one intended to switch off the stove before leaving, and that one either did or did not carry out this intention, but not remember which. These observations open up the possibility of two slightly different intermediate positions. Dummett suggests that ‘we may wish to lay down that a disjunctive statement is conclusively established by a demonstration that an effective procedure would, if it were or had been applied at a suitable time, yield or have yielded a verification of one or other disjunct’ (1976e/93d, p. 73). In a paper on the metaphysics of verificationism, he throws out a slightly different hint as to how one might make one’s common-sense realist prejudices cohere with the benefits, from the point of view of a scientific understanding of communication, of verificationism. There he discusses the possibility of a ‘composite’ view according to which ‘the meaning of a sentence has two distinct components: what is required to verify a statement made by uttering it; and our conception of what would render such a statement true’ (Dummett 1992, p. 141). Such a composite view would have to be adopted by a verificationist who rejects phenomenalism. Such a person would not identify the existence of a material object with the existence of appropriate sense data, but would nevertheless insist that the method of verifying a material object statement is an essential part of its meaning. As we saw in chapter 3, a phenomenalist is unlikely to equate the existence of a material object with the actual existence of sense data, and will say, rather, that for a material object to exist is for it to be the case that, were there a suitably placed observer, the appropriate sense data would be experienced. But it is plausible to go further and to say, given our background theory about material objects and the way in which material objects cause sense data, that a material object could exist such that we could never have direct sensory evidence of its existence. A black hole is like this. At most, we can have sensory evidence from the behaviour of other objects that a black hole exists in a region of space. We cannot see it directly, since the energy that would allow us to do so cannot escape from the black hole. The exterior of our time cone is another such example. So a verificationist who wants to admit that the sentence ‘The exterior of our light cone may exist, but its existence can never be verified directly by sense-data’ is meaningful, will have to admit as possibly true, and so meaningful, some sentences which are unverifiable.

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A similar situation seems to obtain in the case of past-tense statements. A verificationist will want to say that the verification condition of a past-tense statement is the present evidence for it; but if they are also convinced that the past is not gappy, they will want to say that certain past-tense statements are no doubt true but not verifiable. The truth condition of a past-tense statement such as ‘Michael Dummett walked along Cornmarket Street on 5 May 1976’ will consist in the past existence of evidence which would have warranted the assertion or denial of this sentence, even if no evidence now exists which warrants the assertion or denial of the sentence. Our conviction that we are justified in attributing to ourselves a grasp of such a truth condition has to do with our background theory about the nature of the world. Given the possibility of such a composite view, Dummett may be being unfair to the realist by lumbering him or her immediately with a conception of reality as laid out from some eternal perspective. Let us call that picture ‘extreme realism’. Classical realism involves the acceptance of classical logic, and of truth conditions which we can in some sense grasp, while at the same time admitting that it may now transcend our capacity to recognize them as obtaining if they do. In the case of the past, however, this is an odd thing to say, for only a committed four-dimensionalist will say that the past exists. A more moderate realist will insist that the past did exist, and exist independently of us, but that it no longer exists. The more moderate realist will say that the truth conditions of past-tense sentences may transcend our capacities to recognize them as obtaining if they did, because we cannot go back to the past. The truth condition of a past-tense sentence is something which no longer exists, but we do have a capacity to recognize how the past must have been if a sentence in the past tense is true. In order for the manifestability constraint to be satisfied, this capacity must be something we can manifest in the present. We do this in two ways: we are capable of manifesting our grasp of the present-tense sentence from which the past-tense sentence is derived, and we are able to manifest in our behaviour a general grasp of what it is for an event or state of affairs to be past and how this differs from its being present or future. The common-sense realist can, therefore, accept the picture of our immersion in time, and at the same time insist that, in this case, accepting the general truth of bivalence for simple empirical assertions in the past tense does not conflict with an extended verificationism. The case for this depends partly on the nature of the direct

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evidence supplied by memory and partly on general features of our understanding of causation and its place in the world. Dummett says that the global anti-realist ‘cannot . . . attach any sense to the supposition that there was evidence a year ago which would then have justified the assertion of present tense “P” other than as the supposition that we now had (or might later acquire) evidence that a year ago there was such evidence’ (1969/78c, p. 371). Let us unpack this with the help of an example. What counts as evidence that there was evidence more than twenty-five years ago that I was in the seminar room of the Philosophy Department at Monash University on the third Tuesday in April 1971? I have good evidence that I existed at that time, and was a student in the department; all of this is evidence that in 1971 there was evidence for the truth or falsity of the sentence. But the evidence that I now have is only general evidence that either I was in the library on the third Tuesday of April 1971 or I was not; it is evidence that in the past this sentence was decidable, but it does nothing to make the sentence decidable now. What we actually have in the evidence that is available to us from the past is evidence of much missing evidence. We now have evidence that dinosaurs were coloured, without having evidence that dinosaurs were any particular colour. We have evidence that they were either brightly coloured or not, but we have no evidence that any particular dinosaur was brightly coloured – or that none of them were. So the realist who wants to take our immersion in time seriously will want to agree with Dummett. We can’t make sense of the claim that there was evidence twenty years ago that p other than as the supposition that we now have evidence that twenty years ago there was evidence that p; but the kind of evidence that we have of the existence of past evidence for p falls well short of evidence for p itself. For this reason we feel confident in asserting p ⁄ ÿp without being able to assert either p or not p. Dummett suggests here that it is in the spirit of the anti-realist’s arguments to allow that under such circumstances ‘p ⁄ q’ is true because there is evidence for the truth of the disjunction without there being evidence for either disjunct. The special nature of the evidence supplied by memory seems to justify the adoption of bivalence in this case. But if the adoption of bivalence is taken to be the general mark of realism, we have an apparent conflict between the remark that such a strategy is ‘in the spirit of the antirealist’s argument’ and the claim that accepting bivalence is always a mark of a realism. The conflict can be resolved by noticing that

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what is in the spirit of the anti-realist argument is that, in this case, we are given an explanation of what warrants the assertion of such undecidable disjunctions. The special nature of the kind of evidence that we have of the past suggests that there is a specially strong case for a moderately realist attitude in this case – one which does not show the general failure of the argument against bivalence. This is another place in which the ‘minimal undeniable concession to realism’ that was needed to explain the informativeness of deduction has to be adopted (Dummett 1991a, p. 267). If this is accepted, we can see that in this instance the common-sense realist can accept verificationism, but resist the argument that its adoption will lead to the unpalatable conclusion that we should think past truth indeterminate. A different argument for asserting bivalence for past-tense sentences also suggests itself. Insofar as we have evidence for the existence of causation, we have evidence that the way things are in the present is a consequence of the way things were in the past. It seems plausible to suppose that the cause of the way things are could not be less determinate than the way things are. This leads to the moderate realist picture which is compatible with verificationism. It accepts our immersion in time, but builds into the representation of the past the idea that things were determinately one way or another, even though it may transcend our capacities to recognize which way they were from the point of view of a different time. We can acquire an understanding of these transcendent truth conditions from the character of the evidence about the past that is available to us in the present – in particular, the evidence that the cause of the current state of affairs cannot be less determinate than its effects. So we can be realists about the past without infringing the general anti-realist argument. I have argued that a moderate realist with regard to the past need not be lumbered with the four-dimensionalist doctrine that the past exists, but can continue to assert the law of excluded middle, when it occurs within the scope of the past-tense operator, because of the nature of the evidence that we have for past-tense statements. Moreover, the general causal conceptual framework within which we understand the world is sufficient to justify the assertion of P(p ⁄ ÿp) even when we are not justified in asserting either Pp or Pÿp. We make this judgement from within a theory of the material world according to which it is governed by causal laws which require that the material past which led to the present was as determinate as is the present. This overarching theoretical conception of nature may

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not be capable of being absolutely justified by inductive evidence. But we take it to provide the best explanation of our experienced situation, and we cannot help but rely on it when we interpret the significance of the present traces of the past that form the evidence for our beliefs concerning what was the case. This takes us some distance away from an atomistic conception of our capacity to understand language, without going all the way to a holism which violates Dummett’s strictures on the learnability of language. Having rejected the argument that verificationism must lead us to deny bivalence with respect to simple past-tense statements, can we still adhere to the standard view with regard to the future? There are difficulties in maintaining the standard view, but Dummett has an ingenious and surprising argument to show how an asymmetry in our use of past- and present-tense statements underpins it.

Anti-Realism with Respect to the Future I argued that in the case of the past we have present evidence for the assertibility of P(p ⁄ ÿp) without present evidence for the assertibility of Pp or of Pÿp. This forces a gap between truth and assertibility, for it also seems undeniable that ‘P(p ⁄ ÿp)’ is true iff ‘Pp’ is true or ‘Pÿp’ is true

for ‘P(p ⁄ ÿp)’ is true iff ‘(p ⁄ ÿp)’ was true

and ‘(p ⁄ ÿp)’ was true iff ‘p’ was true or ‘ÿp’ was true

and since ‘p’ was true iff ‘Pp’ is true

and ‘ÿp’ was true iff ‘Pÿp’ is true

we are entitled to assert that one or other of these disjuncts is true, even when neither is assertible. This underpins a retreat from anti-

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realism, in this instance. But a comparison with statements about the future suggests that the truth-value links, here assumed, are not all that is involved. In the case of the future, there are equally truthvalue links: ‘F(p ⁄ ÿp)’ is true iff ‘(p ⁄ ÿp)’ will be true.

And when the moment of the future which is relevant comes about, ‘p ⁄ ÿp’ will be true, which apparently justifies us in asserting that now the future-tense sentence ‘F(p ⁄ ÿp)’ is true although we have no reason to assert ‘Fp’ or ‘Fÿp’. But now a difference emerges. In the case of the past tense there is no reason to deny that ‘P(p ⁄ ÿp)’ is true iff (‘Pp’ is true ⁄ ‘Pÿp’ is true). So we are committed to its now being true that either Pp or Pÿp, although we do not know which. But someone might well admit, on the basis of the truthvalue link, that it is now true that F(p ⁄ ÿp) while refusing to accept that it is now true that Fp or that it is now true that Fÿp. This is one way of interpreting Aristotle’s claims in De Interpretatione (Wright 1993a, p. 177). Aristotle can be read as claiming that the general experience that has been acquired is enough to convince one that the evidence now available warrants the assertion of any instance of the law of excluded middle in the future tense, where the tense operator has wide scope, but also suggests that it might now be quite open which of the future-tense disjuncts is true. One might nevertheless wonder whether this position is coherent. Clearly something in our use of past- and future-tense statements inclines us to treat them asymmetrically. But, from the point of view of logic, it is difficult to justify this. If it is now true that F(p ⁄ ÿp), then, since (p ⁄ ÿp) will be made true in the future by one or other of these disjuncts, how can we deny that it is now true that Fp or now true that Fÿp? The argument for such logical determinism is well known, as is the further move to fatalism. As discussed in chapter 3, Dummett claims that metaphysical disputes are in general semantic disputes, by which he means disputes grounded in the use that we make of sentences. His response to the argument just canvassed demonstrates what he intends by this, and what kinds of consideration can be brought into play if one is to work through an argument for or against realism in a particular case. It may seem that in this instance, something like a general metaphysical difference underlies a semantic dispute, or at least a dispute about the truth conditions for future-tense statements. Those who want to refrain from asserting that it is now either

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true that Fp or true that Fÿp often do so by saying things like ‘The future does not yet exist’. Yet, as Dummett points out, it is not clear how this distinguishes the future from the past. Neither future nor past exists now. But the past did exist, and the future will do so. Metaphysically, there seems to be symmetry. Yet a common-sense realist with regard to the past may well want to adopt the standard view according to which it is not yet determined which of two opposite claims about the future is true. This is a natural position, captured in the idea that one cannot change the past, but that the future is still open, and will be determined partly by random accidents and free choices. What Dummett shows is that if we look closely enough at the way in which we use past- and future-tense statements, we can identify the features of our use which impose this metaphysical picture on us. These features are not sacrosanct – we can imagine things being different – but they are what underpins the asymmetric metaphysical picture. What lies behind our conviction that present evidence warrants us in asserting that it is either now the case that Pp, or now the case that Pÿp, although it transcends our ability to determine which, while the present evidence gives us no such certainty with regard to the future? In the case of the future, we manifest our belief that the future is open by trying to bring about a future which fits in with our desires. We do not try to bring about the past, and although it is not impossible to conceive such behaviour, the fact that we do not engage in it is enough to show that we can, in our general behaviour, manifest our commitment to a view which then has an impact on the semantics we accept for our language. In three papers which initially appear to be rather remote from questions concerning the semantics of natural language, Dummett shows how features of our use of sentences about the past and the future in fact underpin the metaphysical asymmetry that is commonly accepted (1954a/78c; 1964/78c; 1986a/93d). This is not to say that he accepts the metaphysical asymmetry. If the future were genuinely open, even God could be surprised by what happens. Dummett cannot believe in such a God, and since he does believe in God, he does not believe in the asymmetry of past and future (1994a, p. 354). This need not deter unbelievers from accepting it. I will not here attempt to summarize Dummett’s complex arguments with regard to the cogency of the idea of bringing about the past. I will merely report what I take to be his conclusion. It is that were we to think that it is possible to bring about a past event, we would not be justified in assuming that we could know the truth of

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past-tense sentences independently of our intentions. We think with regard to future-tense sentences that, in many cases, we cannot now know whether or not some future event will take place independently of our intention to bring it about. But in the case of past-tense statements we do take ourselves to be in a position to know their truth or falsity independently of any intention of ours. Were we able to bring about the past, we would have to change our behaviour in this respect, since we would not be able to know what was the case in the past independently of our intention to do something which might bring about a past event. The tendency that we have to refrain from asserting bivalence with regard to future-tense sentences is therefore justified not by a metaphysical picture, as it seemed to be, but by our adherence to a difference in the way in which we use past- and present-tense sentences and the different constraints which surround what we count as good reasons for asserting them. Once again, we might see this difference of use as arising from the fact that the meaning of material object statements is partly derived from their embeddedness in a causal account of the world. But it is not sufficient to say this. The notion of backwards causation is not absolutely incoherent, but it does not cohere with other features of our use of language. So, although Dummett himself does not accept the conclusion, it seems that he has a plausible explanation of how one can consistently be a verificationist and hold the standard view with regard to past and future. The standard view accepts determinacy and bivalence with regard to past-tense statements, but refrains from asserting that it is now necessarily the case that either Fp or Fÿp, although admitting that F(p ⁄ ÿp). Saying this does little more than express our conviction that it may be impossible to know which of these disjuncts is true independently of a present or future intention to bring it about. This is a position which, as we have seen, looks incoherent from the point of view of logic. But if Dummett is right, our intuition that we should refrain from asserting bivalence in this kind of case, and the metaphysical picture of the openness of the future which follows from it, derives from the relationship that holds between the verification conditions of future-tense sentences and our present intentions. It is the practical ability to use past- and present-tense sentences differently in this respect which underpins the metaphysical picture, rather than the other way around.

5 What do we Know when we Know a Language?

Dummett makes Wittgenstein’s private language argument pivotal to the justification of the manifestability constraint. Yet he differs markedly from Wittgenstein in accepting that our knowledge of language must be systematic. This systematicity is expressed in the idea that knowledge of a language involves implicit knowledge of some specifiable rules. A meaning-theory such as Davidson proposed captures at least some of this systematicity. In the mid-1970s Dummett described such a meaning-theory as giving a theoretical representation of a practical ability (1976e/93d, p. 37). But by the early 1990s he was dissatisfied with this formulation, because it obscures the extent to which knowing a language is a conscious rational activity (1993b, pp. 159–61). Nevertheless, Dummett still agrees with Davidson that the construction of a truth theory for a language will be a central element in the construction of a theory of meaning for that language. He continues to hold that the meaning-theory, or theory of reference, will need to be supplemented by a theory of sense. The theory of sense ‘will lay down in what a speaker’s knowledge of any part of the theory of reference is to be taken to consist, by correlating specific practical abilities of the speaker to certain propositions of the theory’ (Dummett 1976e/93d, p. 40). The theories of sense and reference then require further supplementation by a theory of force, which will give an account of ‘the various kinds of linguistic act which may be effected by’ the utterance of a sentence. It is the combination of the two assumptions, first, that speaking and understanding a language is a practical ability which involves

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knowledge of the truth conditions of the sentences of the language as laid down by a meaning-theory, and second, that this knowledge must be something that can be manifest in the use that speakers make of sentences, which gives the argument for anti-realism its purchase. But as we saw as early as the first chapter, the suggestion that there is something, the meaning of the word or sentence, which every speaker who understands that word or sentence knows, is highly debatable. If we think of a language as a precise formal object, with a definite vocabulary, syntax and semantics, then there is no single language which will provide an accurate description of the linguistic output of the millions of people who speak various forms of the vaguely defined entity that is called ‘English’. Individuals differ too widely in the vocabulary they understand, the sentences they accept as grammatical, and the inferences that they deem acceptable for there to be any one truth theory which could encompass what any speaker knows.

Languages and Idiolects Two major responses to this problem have developed in the literature. One is to shrink the notion of a language, as used in the explanation of speakers’ competence, to that of an idiolect. Each speaker invokes a particular formal object which is made up of the vocabulary which they use, the rules of sentence formation that result in the judgements of grammaticality which they make, and the inferences they are inclined to accept. The idiolect of a speaker will be a changing, developing structure. Within a language community there will be considerable similarity among idiolects, but no two need be the same. If Chomsky is right, there will be the same kind of variation that we find among other biological entities, such as human bodies. The linguist will study the parameters within which idiolects develop, but there will be no place within the science of language for languages as social entities (Chomsky 1993, pp. 16–26, 34; 1995). The point of view adopted is purely descriptive. From this perspective, If my grandmother were to say ‘I brang the book,’ we would not hesitate to say she is following the rule for ‘sing-sang-sung,’ contrary to ‘common agreement.’ True, her internal language may change, replacing ‘brang’ with ‘brought.’ If it does not, she’ll be speaking a language which differs from mine in this among many other respects,

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and speaking it ‘correctly,’ insofar as the word means anything. Questions of meaning are usually considered different, and somehow more profound. That has to be argued; in fact they seem merely more obscure, but no different in relevant respects. (Chomsky 1993, pp. 20–1)

This naturalistic descriptivism is in line with Davidson’s early claim that the theory of meaning is an empirical theory which takes up the task of describing language rather than improving it or reforming it (Davidson 1967/85, pp. 24, 29). So it is perhaps not surprising that Davidson too has given up his early view according to which speakers communicate in virtue of knowing a common language (Davidson 1986, pp. 437, 446). Communication is now described by him as taking place through the construction of passing theories, which are truth theories constructed in the light of the utterances of speakers at particular times. Chomsky and Davidson have made what may be designated ‘the internalist response’ to obvious problems concerning speakers’ knowledge of meaning (Chomsky 1993, p. 26). There is a pretty unobjectionable sense in which speakers know their own usage, and at least tacitly know some rules which result in their speech patterns. Hearers understand speakers by latching on to this pattern. Speakers follow some pattern of usage, and attributions of knowledge of meaning to speakers is taken to imply no more than that they implicitly know the rules that generate their own pattern of use. The other dominant reaction to the observation that there is no single language which every speaker knows is externalist, and involves giving up altogether the hypothesis that understanding a language involves knowledge of a meaning-theory. Pressure for this conclusion comes from at least three different sources, which need to be dealt with separately. First, there is pressure on the idea that speakers know the meanings of the vocabulary they use. Kripke emphasizes the fact that speakers often do not know enough to be able to uniquely identify the referents of the names they use; so if by ‘meaning’, we mean what Frege called ‘sense’, that which determines reference, speakers do not know the meanings of the names they use (Kripke 1980). Putnam has pointed out that there is a linguistic division of labour, and individual speakers do not know the precise application conditions of general terms they use (Putnam 1975). Next, there is pressure on the idea that speakers know the facts stated by a theory of syntax for their language. Last, there is pressure on the claim that speakers construct and understand sen-

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tences according to the rational principles that would be laid down in a theory of logical form for the language. Stephen Stich has been central in applying the latter two forms of pressure (Stich 1971; Stich and Nisbett 1980; Stich 1985). Pressure from this direction has seemed to some to undermine Dummett’s whole conception of the nature of the project that he calls ‘the theory of meaning’. As we saw early in the first chapter, Dummett rejects the view that what is wanted from a theory of meaning is merely a description of the causal mechanisms which result in speech. He insists that speaking and understanding a language is a rational activity. But it appears to be the coherence of this conception of the actual practice of speakers that is undermined by Stich’s observations. A representative statement of Dummett’s insistence on the need to explain understanding language as a rational activity is the following: Any adequate philosophical account of language must describe it as a rational activity on the part of creatures to whom can be ascribed intention and purpose. The use of language is, indeed, the primary manifestation of our rationality: it is the rational activity par excellence. . . . To represent speech as a rational activity, we must describe it as something on to which the ordinary procedures of estimating overt motive and intention are brought to bear. This requires a place, for which a purely causal theory allows no room, for the distinction, essential to the comprehension of an utterance between why a speaker says what he does and what it is that he says, that is, what his words mean, as determined by the linguistic conventions that have to be specially learned. The concept of intention can in turn be applied only against the background of a distinction between those regularities of which a language speaker, acting as a rational agent engaged in conscious, voluntary action, makes use from those that may be hidden from him and might be uncovered by a psychologist or neurologist; only those regularities of which, in speaking, he makes use characterize the language as a language. He can make use only of those regularities of which he may be said to be in some sense aware; those, namely, of which he has at least implicit knowledge. (Dummett 1978d/93d, p. 104)

We can separate out a number of claims in this passage. First, there is the claim that the use of language is a rational activity. Second, because it is a rational activity, we need to be able to give explanations of the use of language in terms of motives and intentions. This in turn is claimed to require a distinction between why a speaker

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says what he does and what the words that he uses mean. Last, it is claimed that in order to explain language use as intentional, we must be able to distinguish hidden regularities from those of which a speaker makes use. All this suggests that Dummett sees the philosophy of language as a sort of armchair linguistics in which we give a phenomenological or philosophical account of the practice of speaking and understanding a language as that practice appears to a rational agent engaged in it. For those who are thoroughly committed to the study of linguistics and cognition from the naturalistic point of view, this attitude can seem prejudiced and oldfashioned. To use Chomsky’s phrase, it involves a kind of methodological dualism (Chomsky 1995, p. 34). The methodological dualist argues that science explains the behaviour of objects, but that it cannot explain the behaviour of those entities which are rational unless it uses a style of intentional explanation which involves the attribution of conscious (or nearly conscious) reasons. The thoroughgoing naturalist disagrees. Moreover, results which Stich cites from the scientific study of human behaviour apparently undermine the methodological dualist’s faith that we are rational intentional agents. But before considering what we should conclude from this evidence, it is worth first considering the case of our knowledge of syntax. We saw above that Chomsky claimed that the case of meaning is not substantially different from that of syntax. If we can show that it is different, we may be on the path to justifying the methodological dualism which Dummett wishes to maintain. As Chomsky now admits, different speakers speak according to different grammatical rules. Nevertheless, one might think that there is an idealization of the performance of speakers of a language which corresponds to the correct grammar of the language. This appeared to be the position outlined in the first pages of Aspects of the Theory of Syntax. There it was claimed both that ‘linguistic theory is concerned primarily with an ideal speaker-listener, in a completely homogeneous speech community’, and that ‘linguistic theory is mentalistic, since it is concerned with discovering a mental reality underlying actual behaviour’ (Chomsky 1965, pp. 3–4).1 Although Chomsky spoke there of ‘a generative grammar specifying what the speaker actually knows’, this was not conscious knowledge of the kind that Dummett is assuming; for, according to Chomsky, a ‘generative grammar will be dealing, for the most part, with mental processes that are far beyond the level of actual or even potential consciousness’ (Chomsky 1965, p. 8). The method assumed to be used in constructing the grammar of the ideal

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speaker-listener has been dubbed the ‘method of reflective equilibrium’.2 A theory is constructed which predicts the sentences that speakers will accept as grammatical; it is tested against the actual judgements of speakers, and then modified if its predictions are ‘too bad’. It is not required that the theory be a perfect predictor, since individuals are acknowledged to make ‘performance errors’, but the best theory will be the one which most nearly approximates speakers’ actual practice. The tensions inherent in this picture are manifest. Speakerlisteners in a linguistic community follow different rules. There simply does not appear to be one ideal theory which will be more predictively accurate than any one of a number of others. Take, as an example, the use in English of ‘they’ as a singular, sex-indefinite pronoun. Is this grammatical or not? It turns out that in some contexts the use of singular, sex-indefinite ‘they’ is standard. For instance: Either Mary or John should bring some wine with them.

But many authorities on the grammar of English would deem the following sentence to be incorrect: A person who believes in the objectivity of grammatical correctness may well have their beliefs shaken.

It turns out that prescriptive grammarians who have judged this usage incorrect have not engaged in anything like the method of reflective equilibrium. Rather, they have been motivated by extraneous social views (Bodine 1975). Moreover, nothing other than explicit attempts to impose the convention that correct English uses ‘he’ as the singular, sex-indefinite pronoun lies behind their pronouncements. It is difficult to see how, in this sphere, correctness of grammar could depend on anything other than the influence of various kinds of social power. The speech patterns of actual speakers of English are just too various, and probably not even always internally consistent. So Chomsky has chosen to resolve the conflict inherent in his initial description by retaining its mentalism and giving up a good bit of the idealization. A grammar will be an idealization of an individual’s speech. Linguistic theory will study the shared features of such grammars, and ‘correctness’ becomes the scientifically irrelevant imposition of uniformity by social pressure groups.

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Are meaning and logical form no different? Dummett’s contention is that we cannot interpret the speech of another unless we can make sense of them as a rational agent who intends to say something in uttering a sentence. Acts of meaning are intentional in two senses. They are largely conscious and deliberate. They are also directed towards some content. Let us concentrate on the speaker who intends to utter a truth, rather than intending to lie, to amuse, or to solicit information or obedience. Being able to interpret what a speaker says involves being able to make sense of the speaker’s overall behaviour by assigning an interpretation or content to their words, the one they intended to convey. Sometimes, as Dummett suggests, this will involve distinguishing what is intentional from what is not. What he means might be illustrated in the following way. We hear a caller on talk-back radio who says: About twenty per cent of men will suffer from prostrate cancer at some time in their life.

We laugh, but immediately make sense of their speech by assuming that an unconscious slip has made the caller substitute ‘prostrate’ for ‘prostate’. Although what they said was literally nonsense, we assume that they meant to convey a fact about the prevalence in the community of prostate cancer. But does this kind of case really cohere with Dummett’s statement? And can this kind of example really provide us with an account of what speakers know which will bear the weight of Dummett’s normative argument? Dummett, remember, claimed that ‘The concept of intention can in turn be applied only against the background of a distinction between those regularities of which a language speaker, acting as a rational agent engaged in conscious, voluntary action, makes use from those that may be hidden from him and might be uncovered by a psychologist or neurologist’. And I have assumed that, in the case of the talk-back radio caller, we make sense of his speech by assuming that, were he a fully conscious rational agent, he would have said ‘prostate’, but that an unconscious mechanism resulted in the substitution ‘prostrate’. This is certainly possible; the caller could recognize his slip in an instant. But it might equally be the case that this speaker always uses ‘prostrate’ in this context. In this case he is acting as a rational agent who is suffering from a mistaken belief concerning the name in English of a certain male gland. This is a case where he speaks consciously, and is perfectly rational; he just speaks a slightly different idiolect from the bulk of knowledgeable English speakers.

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Dummett appears to face a dilemma. If he insists too heavily on the connection between the regularities of which a speaker consciously makes use and intentional speech, he will be forced in the direction Chomsky has taken, and will have to accept that in some idiolects of English, ‘prostrate cancer’ means what is usually called ‘prostate cancer’. Whereas if we insist that this speaker is mistaken about the name of this gland in the language he speaks, then it would seem that he is unaware of the meanings of some of the words in the language, and we cannot explain understanding a language entirely in terms of the knowledge of regularities of which the speaker consciously makes use. Dummett wants to insist, as we have seen, that the language is a social entity. But this insistence itself undermines any simple description of the ability to speak and communicate in terms of the knowledge of a language. The tenor of Dummett’s comments, in the passage with which we began, is not unlike that of Daniel Dennett’s description of the intentional stance. According to Dennett, if we are to interpret an organism as acting intentionally on the basis of beliefs and desires, then we will have to interpret it as rational. It was against this view of Dennett’s that Stich explicitly directed his objections. But, as we will see, the implications of the debate between Stich and Dennett seem to be that it is only on the basis of a very weak notion of rationality that it is plausible to claim that it is necessary to interpret speakers as rational in order to make sense of their behaviour. In a series of papers Stich has used the results of psychological studies of human reasoning to undermine the claim that, in order to interpret human behaviour, we must describe ourselves as rational agents. Dennett has suggested that if we are able to take the intentional stance towards a creature, then we will be able to explain its behaviour as rational in the light of its beliefs and desires. But if the psychological studies referred to by Stich are accurate, many people are less than fully rational. So, after all, we will not be able to explain human behaviour by taking the intentional stance (Stich 1981; 1985, p. 121). Dennett’s response to Stich has been to backtrack. When we adopt the intentional stance, we idealize. We interpret a system as though it were rational. Closer inspection of the system is likely to reveal that the system is not fully rational. For instance, although a person believes that 20 - 17 = 3, and believes that $20 was tendered in payment for a $17 dollar item, and believes that they gave the correct change, they may only have given $2. There are a number of ways of describing what may have gone on in this sort of situation (Dennett 1981/87, pp. 84–8). Perhaps the change-giver thought that one of the $1 coins tendered was a $2 coin. Perhaps they mis-

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takenly believed for a second that 20 - 17 = 2. In this kind of case, Dennett is now happy to accept that there is just no fact of the matter as to what the beliefs really were (Dennett 1987, p. 116). Intentional description involves idealization, even to an extent misrepresentation, since it represents speakers as having beliefs described in one precise way when another way of describing their beliefs might be equally good. Dennett and Stich therefore appear to agree that interpretation involves the attribution of some minimal rationality, but this is a minimum compatible with a good deal of irrationality (Stich 1990, pp. 29–54). But a response like Dennett’s looks to be hopeless from Dummett’s point of view. It amounts to accepting the indeterminacy of translation which goes hand in hand with Quine’s holism. If there is often no single precise way of assigning content to a speaker’s beliefs, then how will we assign a single precise content to the sentences which express those beliefs? If there is no precise content that can be assigned to the sentences of our language, how can we conclude that its logical operators correspond precisely to those of the intuitionist rather than those of the classical logician? This statement of the problem suggests a reply on Dummett’s behalf. Perhaps the difficulty arises from attempting to assign content to beliefs prior to assigning content to language. As we have seen, Dummett takes it as definitive of the analytic tradition that it gives a philosophical account of thought in terms of a philosophical account of language. This is what he means when he says that the notion of language is philosophically primary. If we examine the messy internal states of an actual individual, we may only be able to give an imprecise account of the content of those states. We use the same sentences both to speak of the world and to assign beliefs to speakers and prelinguistic thinkers. But, as Frege pointed out, we have to understand the content of these sentences rather differently when they are put to these two different uses. For, in the first case, as long as a sentence does not contain intensional operators, any extensionally equivalent sentence will provide an equally true (though perhaps less informative) way of conveying the information about the world that we want to convey. But because speakers, and other thinkers, have beliefs about things only ‘under modes of presentation’, in the second case what looks superficially like an extensionally equivalent substitution may be false. Frege tries to avoid this superficial failure of extensionality through his hypothesis that sentences in opaque contexts have an unusual ‘indirect’ reference. This solution brings with it many problems. We do not need to solve all the difficulties which are involved in the attribution of

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belief, however, in order to see that it might be possible to design a language which was precise in terms of its ability to convey content about the world, but imprecise as a vehicle for conveying the contents of people’s beliefs, just because the idiosyncratic contours of an individual’s beliefs about the world need not match the contents of the sentences of the most carefully crafted language. The fact that the attribution of belief is indeterminate does not, by itself, imply that the assignment of content to the sentences of language need be indeterminate. It only does so if we make the content of sentences depend directly on the beliefs expressed by them. However, if we do construct an ‘ideal’ language, the sentences of which have determinate content, it will still be an open question whether this construction will throw any light on our ordinary capacity to speak and understand language. In a paper contributed to a collection on Chomsky, Dummett comes close to adopting this position. There he follows Strawson, who had pointed to two dominant schools of thought with regard to meaning. The Gricean, communication-intention theorists make up one school; Fregean theorists interested in constructing a formal semantics for a language, the other (Strawson 1971, p. 171; Dummett 1989a/93d, p. 174). Communication-intention theorists take the primary function of language to be the communication of belief. Because of this, they are inclined to fall into a conception of language according to which it is a code for thoughts which exist independently of language. But this conception of language cannot be entirely adequate, for it fails to accord with the fact that there are many new thoughts which we can have only in virtue of understanding the sentences that express them. This is not to say that there is no possibility of prelinguistic thought. But prelinguistic thought is indeterminate in structure in a way that thought in language is not. Further, many sophisticated thoughts, thoughts about numbers, theoretical entities, aesthetic and ethical values simply could not be entertained except in language. We do not have non-linguistic thoughts of these kinds and then clothe them in language. Rather, having them involves having learned how to use sentences which express them. Looked at this way, indeterminacy of belief need not be taken to imply indeterminacy of language. The thought that it does so rests implicitly on the view of language according to which language has meaning in virtue of its role in conveying beliefs and other mental states which exist independently of language. However, the contrast that Strawson draws does not adequately cover the field of possible positions within the theory of meaning.

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As Dummett points out, Chomsky both takes for granted the view that language is the vehicle for the expression of thoughts which do not exist independently of language and has a thoroughly internalist and psychologistic account of meaning. Language is, according to Chomsky, dependent on an innate biological structure of the brain which allows communication, but does not necessarily encode thoughts which exist independently of that mechanism. Davidson has aptly captured one form of this Chomskian idea by saying that ‘Language is the organ of propositional perception’ (Davidson 1997, p. 22). Davidson, like Dummett, objects to versions of Chomskian linguistics which adopt the code conception of language and which, usually following Fodor, postulate a prelinguistic mentalese.3 Instead, he suggests that language brings with it propositional perception. The logical structure of this propositional perception is to a great extent shared in common, but the details are individual. Each of us thinks in a unique idiolect, which is one version of a shared structure. So, if a psychologist were interested in a predictive account of our responses to language, it is knowledge of each unique idiolect which would be required. Both the code conception of language and Davidson’s more sophisticated idea that language is the organ of conceptually articulated perception are, at least prima facie, open to the objections that Dummett levels at Chomsky. Dummett complains that if meaning is thought of in the Chomskian fashion, it becomes essentially private, and communication will rest on faith (Dummett 1989a/93d, p. 177). The communication-intention theorist makes the primary function of language the communication of beliefs and other psychological attitudes. Chomsky makes the primary function of language the expression of belief and other psychological attitudes. Davidson makes language necessary for having conceptually articulated belief. Each of these underplays the function of conveying either accurate or inaccurate information about the world. The utterance of a sentence can communicate both information about the beliefs of the utterer and information about the world. And the information about the world may be quite different from that conveyed concerning the content of the utterer’s belief. The most striking case of this is parroting, where a speaker repeats a true sentence which they do not understand, but which is nevertheless informative for their audience. Perhaps the opposite happens when a speaker shows by their utterance that they have an incoherent belief. But, more usually, we often learn more about the world from a person’s utterances than

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they intended to convey. At other times we learn about a speaker’s beliefs, even though what they say makes little sense, and so tells us nothing about the world. We have seen that Dummett is convinced that Frege is basically correct in asserting that, on an account of meaning which makes meanings inner mental items, communication cannot be explained, and will, indeed, always be in danger of breaking down (Dummett 1959d/78c, pp. 176–7). On Chomsky’s account of language, how will we know that we have understood a speaker as they intend to be understood? Dummett suggests that the only thing we have to go by is the way in which the speaker speaks and responds. He then poses a dilemma for Chomsky. We either think of this linguistic behaviour as evidence for the correctness of our hypothesis that the speaker has internalized a certain language, or we take the behaviour as constituting their understanding of a particular language. If we think of the behaviour as evidence for an internalized theory, then we could always be wrong, and the success of our communication will rest on faith: a conclusion Dummett deems absurd. But if behaving in a certain way constitutes understanding the sentences used in accordance with the meanings captured by a particular truth theory, then the hypothesis of internalization will fall away as irrelevant (Dummett 1989a/93d, pp. 180–1). By the same token, the hypothesis that truth needs to be brought in is also in danger of falling away as irrelevant. For, if a person’s attaching a certain meaning to sounds which they utter simply consists in their using those sounds in a certain way, we could give a direct description of that use, bypassing the notion of truth altogether. This was half of Wittgenstein’s position, the other half being that no systematic account of use could be provided. This argument makes it appear as if Dummett’s central objection to an account of language which makes idiolects primary consists in its inadequacy to ground a theory of communication and, in particular, its failure to demonstrate the connection between an account of truth conditions and the various uses that we make of language. But is Dummett correct in contending that, by reducing the notion of language to an idiolect, writers like Chomsky and Davidson have failed to provide an explanation of communication? Is it in fact absurd to think that communication rests to a certain degree on faith? Davidson agrees with Chomsky that a language, thought of as a social entity, is simply a philosophically uninteresting group of idiolects, and that communication does not take place in virtue of knowledge of a shared language. Indeed, in Davidson’s

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case, it is a commitment to seeing communication as primary which leads him to conclude that the notion of a language is redundant: ‘what matters, the point of language or speech or whatever else you want to call it, is communication, getting across to someone else what you have in mind by means of words that they interpret (understand) as you want them to’ (Davidson 1994, p. 11). So if Davidson is correct, Dummett would seem to be wrong in his assumption that an account of communication requires the social concept of language. The issues are complex, and I have argued elsewhere that Dummett has not managed to demonstrate, on the basis of what is required for communication, that the social conception of language is prior (Green 1991). The difficulty is that the model of communication outlined by Davidson in papers such as ‘Radical Interpretation’ and ‘Belief and the Basis of Meaning’ is, with certain amendments, perfectly adequate (Davidson 1973/85, 1974/85). Briefly stated, this is the view that when I interpret another, I first understand their words as having the meaning they have in my idiolect, then, in so far as this interpretation makes no sense of the other person’s utterances in the light of their behaviour, I adjust my interpretation, adopting the principle that they are at least minimally rational, but are likely to have made mistakes of the kind which are comprehensible to me because they are of the kind to which I am also prone. Communication, on this view, will rest partly on faith. It will rest on the faith that others are sufficiently similar to me that I can make sense of them by my lights. But this need not be a disadvantage. Communication is often a rather partial and imprecise matter, as anyone who has written an article and been misunderstood, or attempted to teach first-year students, will be aware. Moreover, we may just be hard-wired to expect that others will have similar experiences to us in similar situations, and our best theory of our evolution convinces us that this is roughly right. Dummett’s attempt to show that those who reduce language to a series of idiolects cannot give an account of the functioning of communication is therefore not convincing. This is not the end of the matter, however. For accepting that there are idiolects, and that communication involves sensitivity to differences among idiolects, is compatible with a number of different ways of understanding the relationship between idiolects and languages, thought of as social entities. Davidson’s views as outlined in his earlier papers were consistent with the idea that each idiolect consists in a partial knowledge of a language which exists

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as a social entity. The situation might be compared with that which relates individuals to the law. The law is a social entity that is independent of any particular person’s beliefs, and different individuals have different partial understandings of it; but each understands that their behaviour is expected to conform to it. This way of understanding the relationship helps explain why it is that, in general, interpreting the words of a speaker from one’s own linguistic community as meaning what one would oneself mean by those words, in that context, is a good strategy. One usually expects that they, like you, are attempting to speak in conformity with the socially determined rules of language. However, in more recent papers Davidson has radicalized his picture of communication, in one place concluding that ‘there is no such thing as a language, not if a language is anything like what many philosophers and linguists have supposed. There is therefore no such thing to be learned, mastered or born with’ (Davidson 1986, p. 446). This radical conclusion is the result of his analysis of malapropism, which is extended to give an account of James Joyce’s linguistic virtuosity. According to Davidson, Joyce takes us back to the foundations of communication (Davidson 1991, p. 11). In the following section I will examine the interchange between Davidson and Dummett over the interpretation of malapropism and the social character of language in some detail, and will argue that Davidson fails to show that language as a social entity is unimportant in an account of communication. Some years prior to writing on malapropism, Davidson developed an account of metaphor according to which there is no need to think of words used metaphorically as having changed in meaning. He rejected the idea of metaphorical meanings, and argued that metaphor can be explained by exploiting the distinction between word meaning and speakers’ meaning (Davidson 1978/ 85). Words have (socially determined) literal or usual meanings, but speakers can do unusual things with them. In his paper on metaphor he argued that this is all the apparatus we need to account for metaphor. In the paper on malapropism, by contrast, we are told that malapropism is different, for in malapropism words actually change their literal meanings. I will argue that Davidson has not established that, in order to explain our capacity to understand malapropism, we need any more apparatus than is required to explain our capacity to understand metaphor.4 The outcome of my discussion will be a partial vindication of Dummett’s claims for the conceptual priority of language. The vindication is only partial, however, because of an ambiguity which emerges in the notion of

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the conceptual priority of language. On the one hand, what may be being claimed is the priority of the existence of a language in the explanation of, and possibility for, complex beliefs. On the other hand, what might be being claimed is the conceptual priority, in the explanation of understanding, of knowledge of a language. Dummett is correct to insist on the conceptual priority of language in the first sense; Davidson is correct in denying the conceptual priority of language in the second.5

Davidson on Malapropism and the Social Character of Meaning It is usually assumed that literal meaning is the same as linguistic meaning, and that while a person may use words in all sorts of deviant ways, what the words mean depends on the conventions accepted by the community. It is also usually assumed that literal meaning is systematic. Indeed, early Davidson, like Dummett, made it a central virtue of the truth-conditional account of meaning that it gave a systematic account of meaning. If one understands the meaning of a word or phrase, then one knows how it contributes to the meanings of various sentences in which it occurs, and in virtue of knowing a grammar, one understands the systematic relationship between different grammatical forms of a word. So a person who understands the meaning of ‘avatar’ will understand it in the various usages ‘Hindu avatars’, ‘I don’t believe in avatars’, and ‘Is Christ an avatar?’ If two words have the same meaning, one will be able to be uniformly substituted for the other without there being a change of meaning in the whole, though there may be some change in informativeness. So to say that ‘avatar’ literally means ‘incarnate deity’ is to commit oneself to the good sense of the appropriate substitutions. Not all meaning is systematic. Metaphor, which many theorists have thought allows words to take on meanings other than their literal meanings, looks as though it involves a breakdown of systematicity. In ‘The wolf is a social animal’ and ‘Man is a wolf’ we have literal and metaphorical uses of the term ‘wolf’, but the metaphorical contribution of a word is not systematic between metaphors. In ‘He wolfs his food’ the meaning conveyed by ‘wolfs’ is rather different from that conveyed by ‘wolf’ in ‘Man is a wolf’. Moreover, metaphor often collapses if a synonym is substituted. ‘Man is an erect-eared, wild, gregarious canine’ is

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simply false, not metaphorical. It seems that, with metaphor, part of what is encompassed by saying that the meaning is not literal is that it is not systematic. And part of what is implied by Davidson’s denial that there are metaphorical meanings is that no systematic account can be given of the contribution of a metaphor to the meaning of a sentence in which it occurs, beyond the systematic meanings of the words taken literally (Davidson 1978/85, p. 245). So there is much to be said for identifying literal meaning with systematic meaning, and I will argue that so long as this is accepted, Davidson has failed to show, as he claims to have, that the analysis of malapropism demonstrates that literal meaning should not be identified with conventional meaning (1986, pp. 442–3). According to Davidson, speaker and hearer come to communication armed with a prior theory of their co-conversationalist’s language. Each adjusts their expectations of the other’s linguistic intentions in the face of the evidence. Proper names are assigned a reference appropriate to the context and the background knowledge of the individuals involved. Words like ‘wicked’ and ‘cool’ are assigned the appropriate one from among their various extensions. Speaker and hearer come to share a passing theory. A passing theory is something like the language of a two-member linguistic community at a certain time. Davidson reports that, at the end of a paper on referential and attributive uses of definite descriptions, Donellan used the sentence ‘There’s glory for you’ to say ‘There is a nice knock-down argument’. In Sheridan’s play, Mrs Malaprop used ‘There’s a nice derangement of epitaphs’ to say ‘There’s a nice arrangement of epithets’. In order to explain these linguistic acts, Davidson suggests that, in the passing theory that we construct to understand them, the sentences literally mean what they are used to mean. But does our understanding of these utterances require the construction of a passing truth theory? A truth theory is a systematic theory. If I conclude that ‘formidable’ in French means the same as ‘great’ in current English, I will assign the same interpretation to the word in other contexts. My interpretation will be systematic. In his paper on metaphor Davidson insists that it is because literal meanings can be assigned to words independently of contexts that they have explanatory power (1978/85, p. 247). But suppose that I am sitting with my friend who has just developed a knock-down argument against realism. ‘There’s glory for you,’ he says. ‘Indeed,’ say I. At this very moment a great goal is scored by France in the soccer game that we happen to be half watching on the television. ‘There’s true glory for you,’ say I. There is no need to readjust one’s

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theory in order to interpret this utterance. The first use of the sentence required some extra background information in order to be interpreted. But success in this interpretation does not lead to a systematic readjustment to one’s theory. Rather, one’s default setting for interpretation remains the conventional meaning. There is an ambiguity in Davidson’s proposal which emerges out of a disagreement between Dummett and Hacking over how it is to be interpreted. Davidson suggests that we come to interpretation with a prior theory of the speaker’s language. In the face of the speaker’s utterances, increasing information about the speaker’s competence, the context we share, and so on, we construct a passing theory. But how does the passing theory relate to the prior theory? One might think that it replaces it and enriches it. In this case we might think of the prior theory as being given by a truth definition for L-prior. In L-prior, let us say, ‘John’ is ambiguous. ‘Cool’ refers to coldish temperatures. ‘Prostrate’ means prostrate. Conversation with Bloggs may then result in a passing theory which consists in a truth definition for L-passing in which ‘John’ means John Bigelow, ‘cool’ refers to approved characters, actions and fashions, and ‘prostrate’ means prostate. That this is the right way to interpret Davidson is suggested by his remark that he persists in calling what the interpreter has at any moment of a speech transaction a theory, because a description of the interpreter’s competence requires a recursive account (Davidson 1986, p. 441). But, as Hacking points out, ‘once the passing theory is made essential, recursivity, as a demand, is doomed’ (Hacking 1986, p. 455). By which he means that the demand that literal meaning be systematic must be relinquished. Passing meanings cannot be assigned to words independently of context, and so appeal to them cannot explain how we interpret utterances in context. Rather, the passing theory seems to involve ad hoc, one-off revisions to the prior theory, which is the theory of the systematic and conventional uses of the words of the language that is being spoken. This is how Dummett suggests that Davidson intended to be interpreted. In his comments on Davidson and Hacking, Dummett argues that Hacking has misunderstood Davidson. The prior theory is not replaced by the passing theory; rather, the prior theory is a theory about how, in general, to understand the speaker, whereas the passing theory is a theory about how to understand some specific utterance. Dummett therefore replaces the terms ‘prior’ and ‘passing theory’ with the terms ‘long-range’ and ‘short-range theory’. Dummett says that we should take a speaker’s short-range

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theory ‘to relate to how he intends, and expects, H to understand particular utterances he makes during the conversation, when he does not intend, or expect, H to incorporate his interpretations of those utterances into his long-range theory’ (Dummett 1986c, p. 460). I suspect that Dummett has not characterized Davidson’s intentions correctly, but I am not certain of this, since Davidson does not correct Dummett in the paper in which he continues the debate with Dummett over the existence of a language. One reason for this suspicion is that Dummett’s characterization no longer covers words like ‘wicked’ and ‘cool’, which may well be incorporated into a hearer’s long-range theory for interpreting certain speakers. But, either way, my point is made. A short-range theory in Dummett’s sense does not involve conventional meanings; but neither does it involve literal meanings, for the meanings of words in a short-range theory do not make a systematic contribution to interpretation, but are once-, or twice-off, interpretations for the duration of a conversation with a particular speaker. If we incorporate these one-off meanings into our theory, replacing L-prior with L-passing, then, as Hacking claims, we will have renounced the virtues of having a meaning-theory which was claimed to give us a systematic account of the contribution of the meanings of words to the meanings of sentences. One might object to this line of reasoning in the following way. All that has been shown is that, insofar as Davidson is right when he claims that malapropisms force us to give up the idea that first meanings are conventional, they also force us to relinquish the thought that first meanings are systematic. If I am right that our use of the notion of literal meaning involves an implication of systematicity, then we will have some reason to deny that what Davidson calls ‘first meaning’ is literal meaning. Here what Davidson means by ‘first meaning’ is the first intention in a sequence of intentions to affect one’s audience’s behaviour through speech (1986, p. 435). But this amounts to a dispute over whether we should use the term ‘literal meaning’ for conventional or, rather, first meanings. Davidson’s fundamental claim – that conventions are not necessary for communication – will not be affected; nor will his related claim that Joyce and malapropism take us back to the foundations of language. These are connected with Davidson’s general thesis that a language as a social entity is not prior in the explanation of communication. But can we really make sense of the idea that in malapropism the first meaning of the words used is not the conventional meaning?

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Davidson equates first meaning with the first intention in a chain of intentions to affect the behaviour of another. But take, for an example, my young son, who once wrote, ‘Hitler was the leader of the nasty party’. Did he intend his audience to acquire the belief that Hitler was the leader of the Nazi party by uttering a sentence which he believed his audience would recognize as having that meaning? Surely he did not. He didn’t have a clear concept of the Nazi party. He wrote a sentence which he thought made sense, which he hoped would be understood and be taken as evidence of his understanding, but in this case he was wrong. Perhaps his first intention was to copy a sentence which he had heard. The sentence he produced was evidence that he could not yet have any clear intentions with regard to conveying information about the Nazi party. Difficulties emerge here because the attribution of intentions introduces opaque contexts. Some theorists are inclined to argue that, so long as my son had, say, seen Hitler and the Nazis on film, or looked at photos from the Second World War, he was causally connected with the Nazi party, and so did intend to speak of the Nazi party when he used the expression ‘nasty party’. We should recognize, however, that opaque contexts are characteristically ambiguous. We can either focus on what is consciously available to the speaker, or concentrate on the state of affairs which the speaker intends, without being concerned to capture exactly the information that is available to them (Green 1985). So there is a sense in which my son intended to speak of the Nazi party when he said ‘nasty party’, and I recognized this when I interpreted and corrected him. At the same time, it is misleading to attribute to him the intention of referring to the Nazi party by using the term ‘nasty party’, for an intention to refer is usually a conscious intention, and since my son did not intend to make a mistake, he cannot have intended to use a word which he understood to mean nasty to refer to a party with a quite different name. This case is, I think instructive. It shows one reason why one might insist that languages are conceptually primary. A language is a great articulated social instrument. It encodes information about the world, and enables us to exchange that information across vast distances. It provides us with a means of affecting the behaviour of others in relatively predictable ways, and it delivers detailed predictions of other people’s behaviour. Its use must be mastered in order for individuals to be able to have certain thoughts. This claim is central to what Dummett understands as the conceptual priority of language. As we have seen, he insists that a philosophical

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account of thought will require a philosophical account of language (Dummett 1993b, p. 4). Davidson does not disagree with the view that thought depends on language, but in order to make it the case, he turns language into something psychological, an organ of propositional perception. For Dummett the priority of language is the priority of a social institution, the use of which has to be mastered before publicly expressible thought is available. My son may have heard the name ‘Hitler’, he may have parroted sentences about the nasty party, but it was not until he had internalized enough of the information that he acquired through working on his project that he was able to have thoughts that could clearly be identified as about the Nazi party. If internalization of a sufficient portion of a language, taken as a social entity, is a necessary condition for the possession of clearly articulated thoughts and intentions, then the language must be conceptually primary. The case of the man who spoke of ‘prostrate cancer’ may seem a little more difficult. Perhaps this man does have a concept of the prostate (he knows well enough where that gland is). But is he really aware of what he is saying? What, for instance, does he think it is to be knocked prostrate? Does he think it has something to do with blows below the belt? There is implicit confusion here too, which undermines the thought that the speaker had a clear intention. Indeed, in the example that I heard, the speaker used the word ‘prostate’ when speaking of the gland, but nevertheless used ‘prostrate’ in the phrase ‘prostrate cancer’. This suggests that he was not fully conscious of what he was saying. He knows that the language is systematic. Words do not acquire ‘r’s when they are used as adjectives rather than as nouns. This background knowledge may well have made him blush later, when he suddenly realized what he in fact said. In these cases Davidson’s sloppiness with regard to who is constructing the theory of meaning leads to confusion (Davidson 1994, p. 4). It is misleading to attribute to this speaker an intention that his audience interpret ‘prostrate’ as prostate, for if he could consciously formulate this intention, he would not be an example of an inept speaker, but would fall into the same category as those who construct malapropisms for comic effect. A theorist can describe this speaker as meaning prostate by ‘prostrate’, but only with the proviso that this is not a way of representing the deviant utterance that is available to the speaker. Once again, the speaker does not intentionally make this mistake. Indeed, our use of language is governed by a general intention to use words in the correct way, relative to our audience.6 It is true that this person intended to use this

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sentence to talk about that gland. But now, correct them, and they will say, ‘Oh I didn’t mean to say that’. So again the ambiguity in the attribution of intentions undermines any clear attribution of intentions, and this was the strongest case for Davidson’s view. James Joyce, Goodman Ace and Sheridan, who knowingly and cleverly construct meaningless sentences which will nevertheless be understood by a sufficiently astute listener or reader, intend to produce sentences which will be recognized as deviant in virtue of the linguistic meanings of the words used, with the intention that their audience should recognize their similarity in sound to sentences which are not meaningless, in order to entertain by the ludicrousness of the sentence constructed, or in Joyce’s case to communicate while apparently disobeying the conventional rules of language. Unless the first intention was to construct a deviant, meaningless sentence, their aim would not be to entertain or impress. This presupposes a shared knowledge of the literal meanings of the words which make up the deviant sentences. These practitioners know that the deviance of the sentences produced will alert their audience to the need for further interpretive activity. So I conclude that Davidson has not established that malapropisms in general, or Joyce’s language games in particular, force us into much more radical adjustments to our notion of literal or word meaning than do metaphors. Either the agent is so confused that no clear first intention can be attributed to them, or the agent is aware of what they are doing, in which case their first intention is to produce a meaningless or deviant sentence. Words in malapropism have their ordinary literal meanings, but they are used to say something which would normally be said by using other words which happen to be similar in sound to the actual words used. What bearing does this conclusion have on the broader debate over the priority of languages over idiolects? Davidson’s claim was that shared conventions are not necessary for communication. I have argued that the case of malapropism does not establish his case. There may, however, be other arguments which do establish that shared conventions are not required for linguistic communication. But I think that the most important moral to be drawn from this argument is that there is an ambiguity in the claim that shared conventions are not necessary for communication. It sometimes sounds as though what Davidson is arguing is simply that there is no precise formal object with a fixed vocabulary and syntax such that knowledge of that clearly defined abstract object is necessary

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for communication. Clearly nothing that has been said here counts against this. Indeed, it is difficult to believe that anyone ever could have held such a view, although Davidson suggests that the position he is denying is one to which he once adhered. What I have argued is that the existence of a public shared institution of conventional associations of sounds with things, properties and linguistic functions, etc. is necessary for communication, because speakers need to acquire a knowledge of a sufficient portion of this public entity to be counted as speakers of the language and to be ascribed precise linguistic intentions. It is this, I believe, that Dummett intends when he talks of the conceptual priority of languages over idiolects. But this looks very close to a doctrine that Davidson himself accepts. The suspicion that there is an ambiguity in the claim that shared conventions are necessary for communication becomes evident from an examination of an earlier paper of Davidson’s (1981/85). Davidson feels pressure to deny the conceptual priority of a knowledge of conventions, because if we are to attribute knowledge of conventions to a creature, we must be able to attribute beliefs to it. If it is also the case that we cannot attribute beliefs to a creature which does not have a language, we cannot make the attribution of conventions a condition of language, or we will be caught in a tight circle of explanation. Three connected lines of response suggest themselves. First, we could break this tight circle by giving up the claim that we can only attribute beliefs to a creature that has a language. Second, we could insist that the priority of linguistic conventions lies not in the priority of the attribution to speakers of knowledge of conventions, but rather in the priority of the existence of conventions. Third, we could deny that knowledge of conventions is prior to the acquisition of language, but insist that having propositional beliefs and acquiring knowledge of conventions come into existence contemporaneously. This view is Davidson’s own. Peacocke calls it ‘the no priority thesis’ (1997, p. 3). The no priority thesis accepts that the capacity to have precise intentions is the same as the capacity to speak in accordance with conventions, but denies that this shows that language is prior. Pressure to take the first path comes from the fact that children must acquire beliefs about the purpose and use of language before they can acquire a mastery of a conventional language. The conventional language is, after all, something that is perceived as an element of the environment like music, the wind in the trees, pictures, patterns and artefacts. Those who believe in mentalese think

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of these prelinguistic beliefs as couched in an innate language of thought which has a similar computational structure to conventional language. But, from an evolutionary perspective, perception pre-dates linguistic conception, and there is no reason to suppose that the kind of proto-thought available to an animal that has perception, but no language, already anticipates the computational structure of language (Macphail 1998). While the point remains that if children are to be able to acquire beliefs about the conventions that make up the language to which they are exposed, these beliefs cannot themselves be beliefs that require a knowledge of the language to be acquired; it simply pushes back the need for explanation to claim that this is done in some already available language of thought. Even if we accept this argument for the existence of prelinguistic proto-belief, we can still insist that without the prior existence of the conventions that make up a conventional language, children would not be able to acquire the highly structured beliefs which a creature must have if we are to attribute to it precise intentions.7 So, while linguistic conventions cannot be prior in one sense, the sense in which knowledge of linguistic convention could be prior to knowledge of language, linguistic convention can be prior in another sense, the sense in which the existence of linguistic conventions is prior to the acquisition of the knowledge of those conventions. The resulting picture would, like Davidson’s, make full propositional thought and the acquisition of language codependent; but, unlike his conception of language as an organ of propositional perception, it would emphasize that language is a publicly perceptible institution which comes to be understood and manipulated much as are other items that we perceive. Although Davidson’s ostensible purpose in ‘A Nice Derangement of Epitaphs’ was to reject a simplistic view of interpretation according to which a recursive theory systematically grinds out interpretations, there is a sense in which he is still wedded to vestiges of this view. Since there is no precise L which speakers and hearers need bring to communication, and since a language, when it is thought of as a social entity, is a vast, vague, historical accretion of various uses, the only place left for a precise L is the passing theory which speakers and hearers share at a particular time. But if we think of knowledge of language according to a different model, we will make the existence of conventions conceptually prior for communication, while asserting in a stronger sense than Davidson does that to know a language is not different from knowing one’s way around the world in general.

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In Wittgenstein’s Philosophical Investigations an analogy is drawn between our language and a city (Wittgenstein 1967a, §18, p. 8). A city is a human artefact that serves a purpose. Knowing a city involves a certain amount of knowledge how. Someone who knows a city knows how to get around the city. It also involves a certain amount of knowledge that. A person who knows how to find their way around a city knows that in order to get, for instance, from the Pont Neuf to the Pantheon, they will have to walk up the hill on the south side of the Seine, and that the most direct route will take them up Boulevard St Michel. Someone could know their way around a city without knowing the names of the streets they use, however. They would still have some knowledge that, but perhaps it would not be described appropriately in the terms just used. A person who knows a city does not in general know everything there is to know about getting around the city. ‘I know Paris well’ can be true, uttered by someone who does not know how to get to the Santé prison from the Pantheon. Many people know Paris, but in one sense, what each of them knows differs. In another sense of course, they know the same entity, Paris. Suppose that we were to give a recursive characterization of this entity. We would list the streets of Paris, and say which streets intersected. We might provide an account of the orientation of the streets and the addresses of important landmarks. A fuller account would tell us the length of each street, identify its beginning and end on a grid, list the numbers of the houses, and even, perhaps, the size and kind of each building. Once we have given the axioms of our theory of Paris, we could introduce logical principles which would allow us to deduce more complex facts about Paris from these simple ones. If our theory tells us that F is a fact about Paris, and G is a fact about Paris, then F and G will be a fact about Paris. Now, in one sense, this is a theory about what it is that people who know Paris know. It is a theory about Paris. In another sense, this theory captures much more than any person who knows Paris knows, and perhaps much less. Someone who knows Paris may know where in the Latin Quarter the best orange tart is to be bought. Facts of this sort are unlikely to be included in our official recursive description of Paris. Paris is a structured entity which people know. It changes over time, and has vague boundaries. Languages, I want to suggest, should be thought of in the same way. We could not give our theory of Paris unless we had the convention of naming streets, buildings, directions, distances, relations and positions. A language is a set of such conventions. In a particu-

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lar location a practice exists of associating particular sounds with particular things, properties and events. Unless a child is exposed to such a practice, they will never know a language. In order to learn a language and learn how to use it, children must first find out some structured facts about the world in which they live. Where they live, ‘Milk’ may be used to bring about the appearance of milk. The association of this sound with this stuff is fairly reliable in their environment – nearly, though perhaps not quite, as reliable as the association between cold white fluids and the taste of milk. A child has to learn a lot about language before he or she can use it to communicate successfully. So, in the explanation of linguistic communication, the existence of language as a set of conventions is prior. A child could not communicate linguistically unless it had recognized that sounds in its environment are associated with things and events and can be used to manipulate the environment. Discovering conventional language is not unlike discovering other regularities which make the world predictable and manipulable. If we think of language in terms of this analogy as a public institution which has been developed by human beings, then the normative element in the theory of meaning can be understood as analogous to town planning. Cities are places in which people live, work and relax. They grow up haphazardly, but can also be planned, improved and regulated in order to serve their functions better. Languages are vehicles for acquiring and expressing more precisely structured beliefs about the world. They thus help us in reasoning about the world. They are also vehicles for communicating information to other people, as well as for affecting their behaviour. The normative element in Frege’s thinking about language derives from the conception of language as an instrument for conveying information about the objects of our thought, the universe of concrete and abstract objects about which we communicate. Since acquiring the ability to have precisely structured thoughts of this kind depends on the conventions that constitute the language we use, normative questions arise concerning the reliability of certain systems of conventions for conveying information and for reasoning. Unless we retain some vestiges of a representationalist account of language, we will not be able to do justice to the demand for normativity. Where, then, does this leave us in relation to the question of what we know when we know a language? We have seen that there is a tension between Dummett’s claim that what someone knows when they know a language must be manifest in their use of it and the

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claim that language is a social entity that transcends the verbal behaviour of any particular individual and which they will understand only partially. In the first chapter I suggested that Dummett could resolve this tension by acknowledging that, while it is not the case that coherent sense is already implicit in the language we use, it is implicit in the way we use language that one important aim of language is to make coherent sense of the world. We have seen how, in the case of past-tense statements, making coherent sense of the world seems to involve the adoption of a theory according to which the past, which is the cause of the present, was as determinate with regard to the properties of material objects as is the present. The sense which we make of the world by adopting a realist conception of the past, in this case, involves the postulation of past truth conditions which transcend any present verification conditions. There is an element of meaning which potentially transcends use, and this, I want to suggest, is the element that Frege identified as reference. We show in our behaviour that we have adopted, in a particular area of discourse, a realist interpretation of the sentences involved by showing that we take it that our assertions are made true by the objects we are referring to, whether or not those objects are accessible to us. But, as Dummett insists, whether we make best sense of our own usage and place in the world by adopting a realist attitude in a particular area of discourse depends on specific features of the case. With regard to the past, our behaviour implicitly involves a commitment to the determinate truth or falsity of a past-tense statement independently of our capacity to know it. This comes out in our insistence that what is true of the past is independent of our intentions. But in other cases, such as the attribution of character traits, or quantification over infinitely extendable totalities, it may be that nothing in our relationship to the reality about which we are communicating, or our behaviour, or our best theories concerning the possibility of judging the truth or falsity of these sentences, need force on us a commitment to bivalence. In the next chapter I will argue that we can resolve the tension between the Fregean and Wittgensteinian elements in Dummett’s philosophy by focusing on the publicity of the language as itself an object of experience. Meanings are not internal ideas in the mind, but properties of publicly accessible linguistic items. Speakers only have a partial knowledge of these meanings. Still, any speaker who understands a language must know a sufficient amount concerning the meanings of the words of that language. What counts as sufficient is vague. Bad reasoners count as understanding the language,

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as do those who misuse unusual words. But when we listen to the bizarre utterances of a schizophrenic, we may wonder whether they have a clear grip on what words actually mean. All speakers know only a fragment of the language they speak. Furthermore, the meanings of words are partially determined by the natures of the things that the words are used to refer to. These things need not be fully known by any individual. While an individual must know enough to be able to make practical use of the social instrument for talking about the world that is language, no two speakers of a language have exactly the same knowledge. Rather, speakers have a general grasp of the structure of their language and a particular grasp of many of its names, predicates, indexicals and connectives. They also have a general grasp of its purpose. In constructing a truth theory, we attempt to outline an idealized version of this public institution, one which would serve its purposes better. Speakers implicitly recognize that such an idealized theory should be able to be constructed. If it is pointed out to them that their use of language leads to ambiguities or inconsistencies, they will attempt to modify it. And many speakers would be happy to attempt to conform to the idealized language. But no one yet knows what such an idealized language would be, since no one knows entirely the natures of the objects and properties about which we mean to speak. It is this view which I believe is faithful to both Frege’s anti-psychologism and Wittgenstein’s anti-mentalism, and so it is the view that someone impressed by Dummett’s arguments ought to adopt. If we also tie the construction of an ideal language to the possibility of its practical use, we can accept Dummett’s arguments for being suspicious of bivalence, without being committed to anti-realism with regard to the common-sense entities of the world.

6 Psychologism, Phenomenology and Philosophy of Mind

We have seen that Dummett takes it to be constitutive of the analytic tradition to which he belongs that, according to it, a comprehensive philosophical account of thought can be obtained only through a philosophical account of language. He presses Frege into service as the first philosopher to have recognized this, although, as was noted earlier, some commentators find this reading strained. Others have argued that it was Wittgenstein who, in the Tractatus, first clearly made the linguistic turn, and Dummett agrees that the Tractatus played an important part in its completion (Hacker 1997). Yet, as with Frege, not everything Wittgenstein says implies the priority of language. In one place he claims that language disguises thought, and that the form of the language can obscure the form of the thought (Wittgenstein 1961, p. 37). This suggests that thought is independent of language. At the same time, Wittgenstein adopts a method in which the form of thought is clarified via an analysis of the logical structure of language. It is natural to interpret Frege as having a similar view. He was from the outset distrustful of ordinary language. He saw it as containing false analogies which had led philosophers astray. In particular, he insisted that the similarity between ‘Theaetetus flies’ and ‘Theaetetus exists’ resulted in the mistaken belief that existence is a first-order predicate, with all its paradoxical results (Frege 1979, pp. 53–67). He complained as well that the grammatical similarity between ‘This flower is red’ and ‘Red is a colour’ had led to the conflation of the logical relation of an object’s falling under a concept with the relation of subordination that holds between concepts (p. 18).1 Frege’s logical language

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was intended to overcome such defects in our ordinary way of talking, so as to enable us to grasp more firmly the laws of truth or, if you like, the logical structure of the world. He says, ‘however true it is that thinking, at least in its higher forms, was only made possible by means of language, we have nevertheless to take great care not to become dependent on language; for very many of the mistakes that occur in reasoning have their source in the logical imperfections of language’ (p. 143). So there is a definite sense in which Frege did think that we can give an account of thought through an account of language. He believed that we can give a philosophical account of the objects of thought, and of the epistemological basis for the logical truths which hold of them, by constructing a language which makes perspicuous the logical structure of the judgements we make. Yet it also seems quite clear that he believed that this logical structure exists quite independently of any particular language. Whether it resides in the structure of reality or the structure of the mind depends on whether one takes Frege to be a realist rationalist, in the tradition of Leibniz, or a Kantian. But whichever is the case, he approaches the task of constructing a logical language as a task which aims at something, truth, which exists independently of language. It is this which accounts for the normativity of his project. As we saw in chapter 2, Dummett argues that, although Frege saw that the objective logical structures that we grasp when we think are not ideas, or private mental items, he left our capacity to grasp these structures mysterious. Dummett therefore argues that it is by following Wittgenstein’s injunction to examine the use of words that we will show in an unmysterious way what grasping a thought, or knowing a meaning, consists in. But we saw that this strategy for illuminating what a grasp of thoughts consists in comes at a price. For the Wittgensteinian slogan that meaning is use undermines the idea that what we aim for in language are properties, relations, relations between properties, and logical structures which exist independently of language. Meanings apparently become immanent in our actual finite practice. Normativity is then impossible to explain. In chapter 3 I argued that the most plausible argument for the adoption of intuitionist logic turns out to be a version of the traditional intuitionist case, and that this argument is largely independent of those versions of the manifestability constraint which tie it to individuals’ actual usage. The manifestability constraint constrains our model of what rational understanding consists in. In the last chapter also, we saw that Dummett’s insistence

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that language is fundamentally social led us back to a basically Fregean conception of language as an instrument for capturing and conveying information about the world. The capacity of this great social instrument to convey information depends on a history of reasonably consistent usage, and of constant modification in the light of developing theories of the world. From this point of view also, the manifestability constraint should not be thought of as applying to individual usage, but should rather be thought of as a constraint on the normative construction of an ideal language. If language is a tool that humans are to be able to use in order to communicate about the world, it must be possible, in principle, to know what it is being used to say. As a social entity, however, language is independent of any particular individual’s knowledge or intentions. Moreover, since the world about which we wish to convey information embodies structures which are quite independent of us, there is plenty of room for the normative project on which Frege and Dummett are engaged. This way of developing Dummett’s ideas at first appears to privilege its Fregean elements over those which derive from Wittgenstein. This may appear to overlook the fundamental weakness that Dummett finds in Frege: the fact that he leaves it mysterious as to what a grasp of thoughts consists in. Frege has a robust sense that the objects of our mathematical thought exist independently of our grasping them. But once he distinguishes thoughts, the senses of sentences, from the truth values that are their referents, he fails to provide an account of how we grasp thoughts and of how we convey them to others. Wittgenstein has an appealing explanation of how we manifest our grasp of meanings: we do it by using language. But he cannot give a satisfactory explanation of the normativity of our practice. If one could show how the realist appropriation of intuitionism that I suggested in chapter 3 can fill these lacunae, then the case for adopting it would begin to look much stronger than the case for assimilating the rejection of bivalence to the idealist strand in the anti-realist tradition that Dummett has been taken to endorse. In this last chapter we will use Dummett’s discussion of the relationship between Frege’s notion of sense and Husserl’s noema as a vehicle for inquiring into our capacity to grasp thoughts, the relationship of linguistic understanding to prelinguistic thought, and the further interpretation of the dictum that an analysis of thought must proceed via an analysis of language. The outcome of my discussion will be that, while Dummett suspects that the turn towards

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cognitive science will bring with it the mentalistic baggage that he deplores in Husserl, an untenable mentalism need not be an essential feature of more psychologically oriented attempts to explain our understanding of language. Indeed, the more realistically interpreted version of the model of understanding that has been extracted from Dummett’s thought should be congenial to those who seek both a naturalistic account of linguistic understanding and a model for comprehending the nature of rationality.

On the Relationship of Phenomenology to Analytic Philosophy In a book devoted to the relationship between phenomenology and the analytic tradition, Richard Cobb-Stevens argues that because the analytic tradition fails to account for the continuity between predication and perception, it is unable to provide a coherent account of the relationship between words and the world. He suggests that it is only by exploring Husserl’s phenomenology – in particular his theory of categorical intuition – that such an account can be provided (Cobb-Stevens 1990, pp. 1–2). Earlier, Mohanty had similarly concluded that an adequate theory of meaning and reference would need to enrich Frege’s ideas with elements from Husserl (Mohanty 1982, p. 116). Dummett’s Origins of Analytical Philosophy (1993b) is based on lectures delivered in 1987, so its basic argument pre-dates Cobb-Stevens’s book. However, it can be read as a response to the kind of challenge to the analytic tradition that is posed by his and Mohanty’s reasoning. Any attempt to characterize thought independently of language, so as to provide the basis for an explanation of language, will falter, largely because it will be mentalistic and invite the code conception of language. Dummett claims to accept Føllesdal’s account of Husserl’s noema, according to which it is a generalization of the Fregean notion of sense to all intentional acts, including acts of perceiving (Føllesdal 1969; Dummett 1993b, pp. 73–4). But he argues that, rather than being an improvement on Frege’s account, Husserl’s account of meaning involves a version of the incoherent Humpty-Dumpty theory according to which speakers give words meaning by intending them to have certain meanings. Since these meanings are implicitly thought of as existing independently of language, this tends in the direction of subjective idealism, and so, by implication, lapses

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into the mentalism that Frege was at such pains to avoid (Dummett 1993b, pp. 43–51, 82–3). The interpretive issues raised by Dummett’s discussion of Husserl are complex. Commentators have offered various readings of Husserl’s notion of noema (Smith and Smith 1995, pp. 22–7). So it is not surprising that Dummett’s short book does not always appear to do justice to the complexity of Husserl’s ideas and their development. Dummett is suspicious of any attempt to give an account of the understanding of language in terms of prelinguistic mental acts, because he assumes that any such account will succumb to the code conception of language, which, as we saw, can be found in one interpretation of Chomskian linguistics (Dummett 1993b, p. 67). Such a conception takes for granted the existence of mentalese or some alternative set of mental representations, and gives an account of linguistic meaning according to which linguistic items have meanings because they are associated with particular, already meaningful, mental items. Fodor’s language of thought hypothesis provides the contemporary archetype of such an account of linguistic meaning (Fodor 1975). But this hypothesis merely pushes back the difficulty of explaining what meaning something consists in, from the fairly tractable problem of giving an account of the meanings of publicly accessible linguistic items to that of giving an account of the representational properties of inner mental items. Such a method involves methodological solipsism, the study of representations construed narrowly as representational structures in the mind (Fodor 1982, pp. 295–6). Since at least one influential discussion of Husserl suggests a similarity between Fodor’s representational theory of mind and Husserl’s early views concerning intentionality, Dummett assumes, with some justification, that criticisms of the code conception of language which apply to Fodor will extend to Husserl (Dreyfus 1982, pp. 3, 15–17). He objects that it is simply not the case that mathematicians first have individual thoughts concerning the concept of integration and then, having come to recognize the similarity between these thoughts, group them together as thoughts that can share a mode of expression. Rather, it is through learning what integration is, and by learning to use the sign for integration, that mathematicians acquire thoughts about integration (Dummett 1993b, pp. 67–8). So a grasp of the use of language is essential to the capacity to have thoughts of this kind. There are, however, two weaknesses in this line of objection to Husserl. First, it depends on accepting the basic correctness of the

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analogy drawn between Fodor and Husserl. In doing this, it overlooks the fact that Husserl, unlike Fodor, was not attempting a naturalistic reduction of intentionality (Smith 1999, p. 84). It also underplays the development of Husserl’s ideas, which arguably resulted in the development of the notion of noema, under the influence of Frege, towards a notion close to Frege’s concept of sense (Küng 1973, pp. 675–6). Second, it may seem to do too little justice to the plausibility of the idea that some kinds of thought must exist independently of language, even if there are higher levels of abstract thought which cannot exist without it. Dummett in fact admits the need to introduce proto-thoughts in order to give an account of perception. Indeed, he criticizes both Husserl and Frege for having given an account of perception which ties it too closely to the grasping of senses, and so fails to account for the prelinguistic capacity for perception characteristic of babies and dogs (Dummett 1993b, pp. 121–6). Yet, when he discusses our grasp of observational terms like ‘red’, he says, ‘It is only those who have received a certain training in the use of colour words who can manifest their colour impressions; and it is only to them that we can confidently ascribe colour-impressions’ (p. 90). Someone who wants to insist on the existence of thought which is independent of language will object that we can confidently attribute some kind of colour impressions to monkeys that unerringly pick out the ripe fruit on a tree, and even to bees who unerringly locate flowers among the leaves. Moreover, we humans can manifest capacities for making fine distinctions between shades of colour for which we have no (standard) names. Understanding a language presupposes some kind of prelinguistic capacity to comprehend the world. Written and spoken words are themselves items that we perceive, as are the objects and properties that they pick out. The capacity to recognize a linguistic mark as having a particular conventional meaning is a capacity which must build on certain kinds of prelinguistic perceptual capacities. So the complaint that pure logical analysis leaves something out of the theory of meaning appears to be well taken. Dummett might respond that these issues belong to psychology, the description of how knowledge of language is acquired, not to philosophy, the description of what is known by one who understands a language. But a philosophical account of what it is that is known by one who understands a language should at least be constrained by psychological evidence. Psychology is largely irrelevant when we are engaged in the normative task of constructing a language ideal

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for a certain purpose, as Frege was; but it is a presupposition of Dummett’s argument that even such an ideal language will only be ideal if it can be internalized and successfully used by creatures with our psychological capacities. This is what lies behind the plausibility of the revised manifestability constraint. Frege’s logical investigations have been influential for the theory of meaning, thought of as a descriptive enterprise, because one can only construct an ideal language from the background of an implicit theory of the way in which language works (Dummett 1975a/78c, p. 441). The view that the cognitive content of a sentence can be equated with its truth conditions is implicit in Frege’s construction of an ideal language, and the language is ideal because, in it, truth conditions are perspicuous. This idea has, as we have seen, guided the development of twentieth-century analytic philosophy of language. And the fruitfulness of Frege’s logic suggests that his presuppositions were, at least up to a point, accurate. But this guiding idea can only be fully developed into a descriptive account of the way language actually works if it is integrated into a plausible psychological account of the way in which truth conditions are grasped. Such an account would explain how a grasp of truth conditions relates to perception and other means of judging truth; how what we perceive can be evidence for or against the truth of a sentence that we understand, or, to use Husserlian language, how something perceived can provide an intuitive fulfilment for an intentional content (Husserl 1900/70, Investigation I, §10, pp. 282–4). This is one place where those who advocate phenomenology claim that Husserl has much to offer. Dummett might be assumed to agree that this connection needs to be made, since his critique of classical truth-conditional semantics involves the observation that it fails to show how a grasp of truth conditions can be cashed out in terms of recognitional capacities. He argues that it is by following Wittgenstein that this need can be met. In what follows, I develop the realist interpretation of Frege’s concepts, and combine it with a particular reading of the moral that we should draw from Wittgenstein’s claim that meaning is use, to argue that there is no reason why Frege’s logical notions should not be given an analysis which ties some of them quite tightly to our capacity for perceptual judgement. I will also argue that the distinctive features of Frege’s understanding of sense and reference make his account superior to Husserl’s. By developing the idea of language as a publicly accessible institution (discussed at the end of the last chapter), we can

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illuminate what is meant by talk of the priority of language, and how this need not be incompatible with the existence of either prelinguistic thought or of a mind-independent reality. If we understand the point that Wittgenstein was attempting to make when he insisted that we should answer the question ‘What is the meaning of a word?’ by describing its use, in the light of the concept of language as a social institution sketched above, we can provide a solution to a deep obscurity in Husserl’s account of intentionality. Husserl treats intentionality as an irreducible property of inner acts. Wittgenstein’s slogan can be read as resisting such inner acts of meaning or intending, and as insisting that intentionality comes into existence with the development of conventional signs which are used to perform various functions. It is the public existence of signs with a certain use which makes possible the idea that a sign, or a thought, could be of the kind to refer to an object or property, yet not do so. When we use such signs we appear to be thinking of things which do not exist. This is the problem of intentional inexistence. So the doctrine that meaning is use provides a solution to the problem of intentional inexistence which Husserl found so difficult. In the next section we will examine the problem of intentional inexistence and the notions of sense and meaning which are introduced to solve it.

How Close are Frege and Husserl on Sense and Reference? While the relationship between Fregean sense and Husserlian noema is an issue that has to be addressed, giving a truly satisfactory account of it would require a long monograph. First one would need to establish exactly what Frege’s and Husserl’s views on sense and reference were, then discuss their similarities and differences. This is no mean task, since there is considerable exegetical disagreement with regard to the views of both authors, and they both changed and developed their views during their lifetimes. So, to simplify the discussion, I will sketch a number of different ways in which one can understand the relationship between sense and reference. These have been extracted from Frege, Husserl and their interpreters. I will offer an interpretation which I take to be the most charitable way to read Frege’s version of the distinction, and argue that it is not as arid as some phenomenologists have claimed.

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Dummett suggests that by 1894 both Husserl and Frege had come to essentially the same conclusion with regard to the meanings of empty referring expressions (Dummett 1993b, p. 37). Each had made a distinction between the object referred to by an expression and something else – in Frege’s case, its sense. This enabled them to say of a sentence that contains a referring expression which picks out nothing, that in one sense it has no meaning (no reference), while in another sense it has a meaning; it contributes via its sense to the expression of a thought. Husserl arrived at a similar conclusion by considering the problem of intentional inexistence. Frege was more directly concerned with the informativeness of identity statements. A look at the writings of Frege and Husserl shows, however, that despite some similarities in their views, there are important differences which amount to very different ways of understanding the concept of sense. In this connection, it is worth noting that Frege was not unaware of the problem of intentional inexistence, but he did not see the need to introduce senses in order to solve it. In his ‘Dialogue with Pünjer on Existence’ he argued that a sentence like ‘Centaurs don’t exist’ does not predicate something (not being able to be experienced) of the non-existent objects, centaurs, but rather says of the concept of being a centaur that nothing falls under it (Frege 1979, p. 54). Interestingly, at this juncture he seems to equate a statement about a concept with a statement about an idea; assigning the concept ‘man’ to the class of concepts under which something falls is equated with classifying an idea (Frege 1979, pp. 54–5). Here, everything he says points to a Russellian solution to the problem of intentional inexistence, although the full-blown Russellian position is not developed. Names, Frege asserts, presuppose existence, so ‘Leo Sachse exists’ is self-evident if true; but ‘Men exist’ is not self-evident – it means the same as ‘There are men’. The word ‘exists’, when used as a predicate, is pleonastic. For, if one tries to give it a content, one will be led into contradiction. Anything that is thought of is an object of thought; so when one thinks of something and says that it does not exist, one both presupposes and denies existence in the same breath. His solution to this paradox is the Kantian one of giving up the notion that ‘exists’ is a first-order predicate (that is, an expression that refers to a concept under which objects fall).2 Given Russell’s further development of this solution, one might well wonder with Russell whether anything further is to be gained by bringing in senses as well as concepts.3

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Frege’s discussion in this dialogue bears remarkable similarities to Husserl’s discussion in his paper ‘Intentional Objects’. Husserl states the paradoxes with which Frege berates Pünjer in very similar terms (Frege 1979, pp. 58–9; Husserl 1996, p. 347). But Husserl’s solution looks quite different. He suggests that talk of the objects of representations is inauthentic when those representations have no existing objects. Rather, ‘the entire distinction between “real” and “intentional,” reduces to certain peculiarities and distinctions in the logical function of the representations, i.e., in the forms of possible valid contexts into which the representations, considered exclusively in terms of their objective content (objektiven Gehalt), can enter’ (Husserl 1996, p. 353). He elucidates this by saying that the classification of objects into existing and non-existing is a ‘classification of representations into representations A, which fit into valid existential judgements of the form “A exists,” and again into representations B, which fit into valid existential judgements of the correlative form “B does not exist” ’ (p. 355).4 Superficially, this looks like a very different view to Frege’s. Rather than being the denial of the claim that existence is a predicate, it amounts to the claim that existence is a predicate of representations. However, one needs to exercise caution here. Husserl is speaking of representations ‘considered in terms of their objective content’. He is concerned with ideal, rather than psychological, contents. So it is possible that his claim that what is involved is a classification of representations amounts to the same thing as Frege’s claim that what is involved is a classification of ideas. Then his view would be the same as Frege’s, but expressed in a more garbled and less precise manner.5 As noted above, Frege too, early on, used the German word ‘Vorstellung’ for what he would later call a ‘Begriff’, and this ambiguity between a property or concept and our idea or representation of it has been ubiquitous in the philosophical tradition. On the other hand, insofar as it suggests that what looks like a classification of objects is really a classification of representations, Husserl’s treatment is reminiscent of Frege’s early account of the informativeness of identity statements. In the Begriffsschrift Frege offers a meta-linguistic account of the content of identity statements. Signs in this context refer not to their normal contents but to themselves (Frege 1879/1970, pp. 20–1). In ‘On Sense and Reference’ Frege criticizes his earlier account, but it is not immediately clear whether his criticisms amount to a revision or a rejection of his earlier account. He introduces the notion of sense, having observed that, if a = b says of two signs that they designate the same

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thing, the sentence a = b ‘would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means’ (Frege 1984, p. 157). One way of understanding how the introduction of senses solves this problem is to think that signs are associated with senses, and identity statements then say of these senses that they designate the same thing. This was Russell’s interpretation of Frege’s strategy, and his complicated rejection of the notion of sense in ‘On Denoting’ (1905/56) hinges on the observation that expressions do not function as designations of their senses. A better way of understanding Frege is to see him as retracting his former view. Words in identity statements do not refer to themselves at all, they refer to objects; but two expressions can refer to the same object in different ways, and because of these different modes of presentation, it need not be immediately obvious just from understanding the expressions that the same object is being referred to. If we interpret Frege in this way, it becomes natural to take senses as somewhat derivative entities in his philosophy. When we think of an object in a certain way, we think of it as falling under particular concepts. But we can also think of concepts in different ways, for concept expressions can be formed by combining words for concepts, and in this case too, there may be different ways of being given the same concept. Predicates which are true of nothing are a case in point. Each of these refers to the same concept – that is to say, the same function from objects to truth values, one which takes every object to the false – but they do so in different ways. Being a unicorn involves the marks of being horse-shaped and having a horn, whereas being a mermaid involves the marks of having a fish’s tail and a woman’s head and torso. Still, on this view, our capacity to grasp senses is dependent on our capacity to grasp concepts. The mode of presentation of an object that is associated with an expression will be a complex property of any object which falls under that mode of presentation. It will be the property through which the object is known. This reading explains Frege’s otherwise obscure comment that ‘Comprehensive knowledge of the thing meant would require us to be able to say immediately whether any given sense attaches to it’ (1984, p. 158). Thought of this way, Frege’s notion of sense develops out of his earlier claim that a content can be analysed in various ways (Beaney 1996, pp. 223–45). Some rather different models for thinking about the notion of sense have now emerged. The first will be dubbed the ‘metalinguistic’ conception of sense. On this conception, senses are

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thought of as belonging to signs, and signs are interpreted as ambiguous, referring sometimes to their normal referents, sometimes to their own semantic properties, their senses. This is roughly Carnap’s (1947) understanding of the relationship between a sign, its extension and its intension.6 At the other extreme is a view which starts with objects and concepts as two different kinds of entity in the realm of reference which are associated with signs according to the syntactic function of the sign as it occurs in a logically wellformed sentence. Names of objects can be constructed out of unsaturated concept expressions by the use of the definite article. Such names have senses which are grasped through a grasp of the senses of the concept expressions from which they are constructed. The fact that one grasps the complex concept involved does not ensure that one knows whether or not something falls under it, so one’s understanding of sentences containing non-denoting names is explained. Gareth Evans makes much of the fact that senses are ways of thinking of objects, and some of what he says concurs with this way of thinking about senses. Senses may be features (or properties) of objects associated with the words which name them, and which provide our ways of thinking of those objects. A virtue of Evans’s way of speaking, and one with which Dummett concurs, is that we can also think of objects in ways which are essentially indexical. Evans argues, however, that Frege was mistaken in thinking that non-denoting names could have senses, on this conception, for there is no way of being given something which doesn’t exist (Evans 1982, pp. 22–33). However, if one admits that one can understand the sense of a complex singular term in virtue of understanding the senses of the concept expressions out of which it is constructed, one will have a solution to this difficulty. Nevertheless, since the reference of a complex is a function of the referents of the parts of the complex, sentences containing such non-denoting terms will be ill-formed unless a reference is supplied.7 This was, I think, Frege’s view. On such an account, complex singular terms will have a sense that is a function of the senses of their parts. Simple singular terms, proper names, will not have a precise sense unless they have been introduced by definition.8 I will call this the ‘objectivist’ notion of sense. Senses are ultimately constructed out of the referents of simple concept expressions, and concepts exist independently of us. On a third way of conceiving senses, senses become intermediary objects of intentional acts. They are like Locke’s ideas, entities thought of as in the mind, and as representations of a world which

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is known only indirectly. I will call this the ‘subjectivist’ notion of sense. This subjectivist view may be combined with the first conception, resulting in the idea that one is related to a reference by way of a sense which is both the meaning of an expression and a transparently known mental entity. The sense seems to be something which is in consciousness, and which may or may not determine an entity in the world. Many interpreters read Frege this way. But, although some of Frege’s doctrines suggest it, it is ultimately an incoherent doctrine, and one which he ought to have rejected in the light of his insistence on the objectivity of sense. The strongest evidence that Frege thought of senses as intermediary intentional objects comes from his claim that in belief contexts words refer not to their ordinary referents but to their senses. However, Frege’s claim that words in belief contexts refer to senses, plus the thought that co-referring terms ought to be able to be substituted salva veritate in such contexts, tends, when it is thought through, to lead to a notion of sense which is private and idiosyncratic, and to jar with the claim that senses are not mental items, but public thought contents that can be shared (Green 1985). It is highly probable that the various remarks concerning sense that Frege makes cannot be melded into a single consistent whole (Beaney 1996, §8.1; Dummett 1981c, p. 124). But, as long as one takes the thought that senses are in general public entities to be essential to Frege’s notion, this way of thinking of senses as basically private and internal meanings should not be attributed to him. On our second way of understanding Frege’s senses, they would be aspects or features of the objects, concepts or truth values which are referents. They would be the properties of objects, associated with a word or expression by one who understands it, through which the objects or concepts referred to may be known. In the case of concepts, they will be the various different ways one can think of a property via its marks. Thinking of senses in this way makes it possible to connect Frege’s thinking with the tradition of Leibniz, to which he refers in the introduction to the Begriffsschrift. Leibniz’s attempt to construct a lingua characteristica was based on the idea that complex concepts, or properties, can be analysed into other concepts or properties which are had by any object that possesses the first. These are what Frege calls ‘the marks of a concept’. By characterizing the marks of the concept being a man as being rational, human and male, for instance, one gives necessary and sufficient conditions for something’s being a man. One may be able to characterize this concept in some other way, for instance as being

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an ape nearly devoid of body hair except for the head and chin, with an XY chromosome pair, in which case the same concept or property will be given in a different way, through different marks. In an ideal language, every complex predicate expression will be introduced by a definition, so each complex expression designating a concept will encode information about the marks of the concept which can then be used in inferences. Husserl’s early views concentrate on representations as structures in the mind; thus they appear to involve a version of the subjectivist view of meanings. At this stage he thinks of meanings as standing to mental acts as species stand to individuals. Meanings are features, parts or moments of mental acts which they share with other mental acts just when, as we would say, two acts are acts of meaning the same thing (Husserl 1900/70, §§31–5, pp. 329–33; Smith and Smith 1995, pp. 18–20). As mentioned above, Dummett rejects any such view, because it illegitimately makes inner mental items primary. But Husserl in fact says very little at this stage about the principles which group thoughts into kinds with the same meaning. Presumably, it would be possible to group representations into species in virtue of their capacity to be expressed using intertranslatable expressions. Or, alternatively, it would be possible to group them in terms of the objects to which they correctly apply, or the situations in which the words that express them are correctly used. So Dummett may have been too quick in assuming that the early Husserl has a subjectivist notion of sense. Indeed, in a famous passage Husserl rejects the fundamentally subjectivist idea that an image stands ‘in the same relation to consciousness as a statue does to a room in which it is set up’ (Husserl 1900/70, appendix to §§ 11 and 20, p. 595). According to some commentators, once he has developed the concept of noema, Husserl has come to a position rather like the objectivist notion that I have just ascribed to Frege. Gurwitsch, for instance, claims that perceptual noema are aspects of objects: We recall the definition of the perceptual noema as the thing perceived appearing from a certain side, under a certain aspect, in a certain orientation – briefly, in a one-sided manner of adumbrational presentation. The decisive point is that notwithstanding the onesidedness of its appearance, it is the thing itself that presents itself, stands before our mind, and with which we are in contact. Noetically speaking, perceptual consciousness is an original (albeit incomplete because one-sided) experience of the thing perceived appearing in ‘bodily presence’ (in Leibhaftigkeit). (1982, p. 67)

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Although Dummett accepts Føllesdal’s equation of senses with noema, he restricts his criticisms of Husserl to the earlier account of the meaning of intentional acts, and does not comment on this way of interpreting noema and sense. This may be because his own understanding of the notion of sense lies somewhere between the subjectivist and objectivist positions that I have outlined. Dummett’s own understanding of the concept of sense escapes the idea that senses are intermediary objects by exploiting a formulation of Geach’s, derived from Wittgenstein, according to which, in saying something about a reference, we show our grasp of a sense. As Evans remarks, Dummett thinks of these senses as methods or procedures for identifying objects or determining truth values (Evans 1982, p. 17n). He further attributes this view to Frege. A sense is like a recipe or instruction for locating the referent associated with the words that have that sense (Dummett 1993b, p. 113).9 If one understands the sense of the expression ‘greatest prime number’, one knows a method for determining of any number whether or not it is the greatest prime number. Such methods can be known by different people, hence they are public. But they are also things that one can have in mind even when there is not in fact anything which will be determined as a result of applying the method. It is important that senses, in this sense, are not the objects of intentional acts, but ways of getting to objects. Nor are they, as in the previous conception, ultimately reducible to features or aspects of objects through which they are known. There are elements of Dummett’s conception in Husserl, as well. In his early paper on intentional inexistence Husserl insists that the intentional content of an act is not its object, and that, although every act is directed in virtue of such a content, an act may fail to have an object. Like the subjectivist conception, this one makes meanings entities that we have in mind; but they are not objects of acts, they are means of getting to the objects of acts, if such exist. As discussed in chapter 2, Dummett interprets Frege’s antimentalism as originating in considerations to do with the possibility of communication. If we are to communicate in virtue of a shared grasp of the senses of words, senses must be intrinsically communicable. Because of this, he is led to fault Frege for saying that when Dr Lauben says ‘I have been wounded’, Dr Lauben has an incommunicable thought which only he can grasp (Dummett 1981c, pp. 120–6; 1993b, p. 140). If Frege’s claim is that thoughts or senses are intrinsically communicable, then he has contradicted himself. However, if Frege’s anti-mentalism was, as I have suggested, sub-

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sidiary to his anti-psychologistic view of mathematical truth, he need not be seen as having contradicted himself. In general, we communicate about publicly accessible items which are given to us in ways that are accessible to all. But sometimes, as when we speak of ourselves, we speak of items that we experience from a perspective that no one else can share. The fact that Frege speaks this way about our thoughts about ourselves is evidence that in general he is thinking of senses as features or aspects of objects through which they are known and thought about by us. Nevertheless, Dummett’s notion of sense can be related to the notion of sense as an aspect of an object in the following way. If an object is a purple rhododendron, it instantiates the concepts being purple and being a rhododendron. A particular rhododendron might also be the only flowering plant in my garden. These two expressions could provide two ways of being given one object. At the same time, ‘purple rhododendron in Karen Green’s garden’ provides a recipe for locating the object under discussion. It is the capacity to grasp a concept which is mysterious. How is it that exposure to a number of objects that instantiate the property of being a rhododendron can lead to a grasp of what it is to be a rhododendron which remains a recognitional capacity even when no rhododendrons are present? It is no doubt because having a recipe for recognizing things as purple rhododendrons is so closely connected to perceiving that an object is a purple rhododendron that Husserl was inclined to introduce the notion of noema by extending the notion of sense and equating grasping the sense of an expression with seeing an object as of the kind to be picked out by a word with that sense. But Frege does not identify senses with concepts. For if concepts are in the world, at least when instantiated, then what is instantiated is a property which may be only partially grasped by us. My understanding of the words ‘is a purple rhododendron’ involves a rather vague grasp of the property of being a rhododendron. I am not certain of being able to distinguish a rhododendron from an azalea. I am given this property in a certain way, which is usually good enough for picking out rhododendrons, but if I were a horticulturalist, the sense that I could supply through a definition of being a rhododendron would have to fully capture what it is to be a rhododendron. If we can make sense of our capacity to understand language, and do so in such a way that we provide ourselves with a model of what we are doing when we reason, in the light of which we can justify our deductive practice, we will have to integrate this model

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into our account of ourselves as evolved beings which interact causally with the world around us. Evans and others who have moved from armchair philosophy of language to empirically informed cognitive science see the need for integrating the account of language into a more general account of thought. Dummett suggests that as soon as we begin to discuss ‘what occurs within our minds, inaccessible to other speakers’, there is a danger, to which Evans’s programme is not immune, of lapsing back into mentalist conceptions of incommunicable thought. But this worry does not itself do justice to the anti-mentalist conception of a concept that Frege developed. If concepts are largely objective, and the words in the public language are associated with concepts which, when combined, enable us to think of objects under modes of presentation, then we can understand how we interact causally with these concepts without making the mistake of identifying the meanings of words with the effects on us which are ideas in our minds, rather than with the properties of things which we have come to recognize. The public language is a huge repository of information, in which senses have been laid down for many descriptive words. With the senses that we associate with words, we attempt to mirror the marks of the properties that are found in the world. By learning what a word like ‘rhododendron’ means, one can come to determine of particular plants whether or not they are rhododendrons. An animal might also manifest a perceptual capacity to recognize rhododendrons. It would not have a word with a sense which corresponds to ours, but it might nevertheless unerringly distinguish members of this species as a source of food, flowers or nesting sites. It might be responding to some feature of these plants which is imperceptible to us, yet still choose all and only rhododendrons. Because he distinguishes senses from concepts, Frege has at hand the materials for explaining how such a prelinguistic sensitivity to the presence of properties can develop into a full linguistic capacity to grasp concepts via the decomposition of sentences and the understanding of the senses of words, even when those concepts are not present or even instantiated. If, as I maintained in the first two chapters, we can understand Frege’s concepts as not entirely abstract, but as sometimes causally active when instantiated, then we can accept that we initially come to grasp concepts through our causal interaction with the properties of things. As Frege says, white is an objective quality which we can identify with a power of reflecting light of certain wavelengths (1884/1950, p. 36). At first we know

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this power through its effects on us, and the ordinary sense of the word ‘white’ is tied up with the ordinary visual way of being given the power; but a scientist interested in reflectance properties could give us this same property through an expression with a very different sense. Our proto-thought is sensitive to similarities among things, similarities in their effects both on us and on other things. It is also sensitive to similarities among sounds. Learning, or perhaps being born knowing, that some sounds indicate the presence of certain birds, some smells indicate the presence of predators, is fundamental to the prelinguistic, natural meaning that underpins protothought. In the early evolution of language, conventional signs mimic such natural signs. But once conventional signs become established, a new property or concept can be recognized: that of signification. Full-fledged linguistic signification imposes a structure of object and concept on the world, allowing us to distinguish between particular things and repeatable properties; and once this vehicle of thought has evolved, it is almost impossible to perceive the world except through the categories of language. This is what Davidson expresses by saying that language is an organ of propositional perception. It is also why Frege insists that even perception has a logical aspect. But, as Dummett points out, there is much spatial thought which is not linguistic, and many properties which we unerringly respond to, like the speed and trajectory of a ball, but could not adequately characterize in language. It is therefore not so much that we cannot perceive the world except through the categories of language, as that we cannot communicate or make public what we perceive except through such categories.10 Proto-thought involves sensitivity to the presence or absence of properties in objects and expectations built up on the basis of regularities in the relations among properties. Red colour is a sign of ripeness in apples. A bear that picks a red apple no doubt has an expectation of the sweet juice, white crunchy flesh, and other properties which are marks of being an apple. But does the bear grasp the thought ‘This is an apple’? There are some reasons for thinking so. The bear has a proto-thought very similar to our thought. It brings the apple to its mouth. If the apple is wax, it may stop, and suddenly throw it away in disgust. We want to say that it was disappointed, it had expectations that were not fulfilled. But what makes our thought different is the very consciousness in our grasp of the sense of ‘This is an apple’ that under certain circumstances we will be disappointed. Having introduced conventional lan-

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guage, we have become familiar with the concept of a sign. A sign may be misleading. It can always point to something which does not exist. And this is the feature of intentionality that Brentano latched on to as the distinguishing character of full-fledged thought. Frege can, I think, give an explanation of how we come to grasp concepts through ordinary causal interaction with the instantiations of those concepts that affect us. We develop sentences with truth conditions sensitive to the presence of these properties, and then, by building up complex signs, we construct signs for complex concepts which may never have been instantiated, but which we grasp through the marks that we have used in the construction. Ultimately for Frege, as for Dummett, a grasp of concepts will be grounded in recognitional capacities; but according to Frege, these recognitional capacities will themselves be explained in terms of the existence of properties and laws of nature.

Wittgenstein and Intentionality What Wittgenstein adds to the picture is an account of intentionality which makes the existence of language prior in the account of what it is to be in an intentional state. As we saw in the last chapter, it is impossible to attribute precise intentions to people whose grasp of the meanings of words is too confused. A child or animal can manifest sensitivity to the presence of a property, but this is not sufficient for manifestation of a grasp of the precise way of being given that property that is associated with the sense of a word. People acquire precise intentions through internalizing the use of signs which have precise functions to pick out properties of things in certain ways, manifest in the way the sign is naturally analysed by anyone who understands it. For Husserl, the nature of intentionality is quite mysterious. As was mentioned, Husserl is famous for rejecting the picture according to which an image in the mind is like a statue in a room, something which represents by resemblance; yet his account of representation reduces it to a mysterious act. Resemblance is not sufficient for representation, and this leads Husserl to conclude: This can only mean that the constitution of the image as image takes place in a peculiar intentional consciousness, whose inner character, whose specifically peculiar mode of apperception, not only constitutes what we call image-representation as such, but also, through its pecu-

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liar inner determinateness, constitutes the image-representation of this or that definite object. (1900/70, p. 594)

It is not so much, as Dummett claims, because individual acts of meaning are seen as instances of a general kind of mental act that Husserl leaves us with a mentalistic account of intentionality, but because, when he comes to explain what these acts have in common, he is reduced to claiming that intentionality is a ‘phenomenological essence of consciousness’. He then goes on to explain the representational qualities of all signs in terms of certain conscious acts, saying: Our exposition extends, mutatis mutandis, to the theory of representation in the wider sense of a theory of signs. To be a sign, likewise is no real (real) predicate; it requires a founded conscious act, a reference to certain novel characters of acts, which are all that is phenomenologically relevant. (p. 595)

What Husserl means by ‘real predicate’ is an intrinsic property. It is not an intrinsic property of a sign or mental image that it is a representation of something else. So Husserl concludes that a certain mental act makes a sign a sign. This is very like the HumptyDumpty theory of meaning, according to which words have the meanings that we consciously assign to them. But this is totally mysterious and unexplanatory. Words do not in general have meanings because of our intentional acts; we are able to engage in intentional acts because we have latched on to the use of words which are signs that have meanings. We can now appreciate that a good deal of Wittgenstein’s great leap forward, in insisting that the meaning of a word is its use, was to see that the intentional character of the sign is not any inner state of consciousness, but comes simply from the use to which it is put. This leads us back to the priority of language thesis. On the proffered account, it is only when some objective items – sounds, shapes, patterns – come to be used to represent other objective items – situations, places, objects – that intentionality arises. Perception, on this way of thinking, is not yet fully intentional. Davidson (1975/85) has made much of the idea that to have a belief, it is necessary that one have the concept of a belief. This can be made more precise and plausible by saying that, in order for something to be a communicable conscious belief, it must be recognized by the believer that the belief could be mistaken. Although a belief func-

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tions as a representation of the way things are, because it is a representation, it may misrepresent, and it is central to believing that one recognize this. Beliefs have the fundamental property of signs, which is to be potentially misleading. On this way of looking at the matter, it is only after a creature has become familiar with the existence of the kind of conventional sign which develops in language that it can acquire full intentional states of believing. Animals surely have proto-thoughts, but on this view, they do not have full intentional thoughts, because they have not come to see their own mental states as signs – that is, as intentional states which may be misleading. It may seem to be a mistake to drive too great a wedge between animal perception and our thought. Although perception is causal, misperception certainly exists. A greyhound chases a rabbit that doesn’t exist. Cats look for food which may not be available. Clearly such creatures have expectations about the world, and there is a sense in which the map of expectations about the world that a cat or a dog possesses is a representation or belief. But these representations seem not to be able to be used by the cat or dog as representations. The greyhound has no way of thinking that this scent is misleading. So although the scent is only a sign of a rabbit, it is not treated, by the greyhound, with the distrust that those who recognize signs as signs bring to interpretation. A sign indicates because it is used to indicate; a mental image can be thought of by us as a sign because our familiarity with linguistic and pictorial signs makes it possible for us to treat our own mental images as signs. But a creature that has not latched on to the use of arbitrary items to represent other items cannot treat its own mental images as signs. It cannot ask itself of its mental images whether they represent correctly. Its mental images are not representations for it (whatever they may be for us). For it, there is no gap between what is and what is represented. It is for this reason that one cannot say of a frog whether the ‘content’ of its representation is ‘fly there’ or ‘small black object there’. For the frog, the difference in satisfaction conditions between these two different representations does not exist. Conscious representation of the kind that counts as full publicly expressible thought is more than evolutionally primed reaction to perceptible properties. It involves the capacity to envisage representational states themselves as having different senses, even though in some cases the very same situation would fulfil them. We have different words for flies and other small black objects. Seeing that these are signs which are used differently enables us to have

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thoughts with the different contents, ‘That’s a fly’, and ‘That is a flying speck of dirt’. It enables us to wonder, ‘Is it a fly or just a flying speck of dirt?’ When we do so, we treat our own perceptual input as a potentially misleading sign of the way things are. One should agree with Husserl that having fully intentional representational states involves having expectations as to what would count as a fulfilling perception (intuition). One should disagree, however, with the obscurantism of his claim that intentionality is grounded in a peculiar mode of apperception. Rather, it is a mode of thinking about the world which has internalized the possibility that one item can be used as a sign for something else, and which treats its own mental states, whether these be experienced as images of linguistic items or as images of perceived things (or as a fusion of the two), as themselves signs. Since it is always a possibility that a sign will be misused, this raises doubts about the veridicality of internal images. It is noteworthy that language provides the analogy on which Locke draws when he questions the adequacy of ideas of secondary qualities to represent the powers that cause them.11 He suggests that the ideas in our minds are like words which God has placed in our minds to represent things. It is because the nature of words that are signs for things is so different from the nature of the things for which they are signs that the possibility arises that ideas of secondary qualities are not good guides to the natures of the properties of things that they represent. From our perspective, we could question whether, at this point, human self-consciousness with regard to its own intentional states has not gone too far. The relationship between the power in an object which affects our perceptual apparatus and the idea in the mind which is an effect of that power is not a purely arbitrary one. Although an image may be stimulated in circumstances which are not those that normally cause it, and so be misleading, if there were not a ground in the nature of things and in the nature of our perceptual apparatus such that similar properties had similar effects, and importantly different properties had different effects, perception would not work, as it does, as a pretty reliable guide for distinguishing among kinds of things. The regularities which hold between conventional signs and things are arbitrary; they depend on us. Locke extends this arbitrariness to the relationship between secondary qualities and their effects, but this may well be a mistake. For our purposes, the important thing is not so much the nature of this mistake, or the consequences of recognizing it, but the fact that it provides

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indirect evidence that it is from recognizing that certain linguistic items act as signs that we acquire the capacity to treat our own mental states as signs, and not vice versa. Language is conceptually prior in the account of thought, because it is with language that we are first made consciously aware of the possibility that one item may be used as a sign for something else. We understand representation in general via language, and are even prone to overgeneralize from the linguistic to the perceptual case in the way in which Locke does. If we interpret Wittgenstein in this way, his claim that meaning is use becomes an injunction not to look for the source of intentionality in some special feature of the mental act, but to find it in the use that is made of signs. Such a way of understanding him would be compatible with nevertheless agreeing with Frege that signs have different kinds of use according to their logical role, some signs being used to pick out objects, others indicating concepts. ‘The life of a sign is its use’ need not preclude there being different kinds of use, and indeed, a great deal of use being the conveying of information about objects, concepts and their relations. If one fundamental use of language is to encode information about the properties of things which has been acquired by generations of humans over centuries of exploration of the world, then we can see why an account of meaning will always be in part normative. And if the use of the logical constants is fundamentally to enable us to make reliable inferences, we can see why Dummett thinks we should be impressed by the constructivist’s arguments for thinking that a logic that fails to endorse bivalence is preferable. In the Introduction I raised the question whether the linguistic turn had taken us up a blind alley. The continuity between animal proto-thought and our own cognitive capacities, and the need to explain the understanding of language as grounded in prelinguistic capacities for thought, seemed to suggest so. In this chapter I have argued that even if one takes seriously the fact that linguistic thought grows out of prelinguistic perception, and that there are properties of things which are being responded to by both language-using humans and language-less brutes, this does not undermine the fruitfulness of what Dummett takes to be the central proposition of analytical philosophy: that an account of thought can be given only via an account of language. If we attempt to account for intentionality directly as a feature of mental acts, as Husserl does, we are reduced to saying that intentionality is a sui generis feature of conscious acts. If we follow Fodor and attempt to give an

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account of the content of perceptual acts directly in terms of causal correlations, we are left with unanswerable questions about ‘real’ content. But if we begin with language as the paradigm of a representational system in which signs have been developed as instruments that can be used to encode and convey information about the world, its furniture and regularities, we can explain our capacity for conscious communicable thought as involving the self-conscious recognition of the possibility of representation, which is manifested in our capacity to use linguistic signs as signs. Such full-blown intentional thought has a complexity of structure derived from the language which it internalizes. This complexity comes into existence with language, and although it is no doubt grounded in complex perceptual capacities for dealing with the world, it cannot be fully explained in terms of them. Some of our capacities – in particular, our capacity to treat our own mental states as representations – are plausibly dependent on our having first learned to use conventional signs as representations. The context principle, whether it is interpreted as providing a sufficient condition for the determination of reference or only a necessary condition, as I have urged, can now be seen, as Dummett has always suggested it should be, as acknowledging that the structure of communicable thought has to be understood via the structure of language. There must be cognitive processes which underlie our ability to recognize that linguistic signs are being used as signs. But these cognitive processes need not involve the structure of object and concept which is integral to thought as it is capable of being shared by us. It is an interesting empirical question whether the structure of proto-thought already involves something akin to this distinction. The importance of boundaries in visual perception suggests that visual perception already involves the capacity to pick out material objects. On the other hand, Chomsky’s hypothesis that there is a special language module responsible for our capacity to speak may support the alternative hypothesis that thought only begins to structure the world into objects and concepts after the evolution of languages with an appropriate syntactic structure. This question, however, cannot be answered a priori. Nor do we need to attempt to answer it. All that needs to be recognized, at this point, is that Dummett’s thesis of the priority of language in the analysis of thought need not be deemed a philosophical anachronism belonging to an outdated methodological dualism, as Chomsky suggests. Rather, it can be incorporated into cognitive science in a perfectly respectable way via the hypothesis that it is the evolution

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of language which is necessary for the development of full intentionality, and that it is therefore only through the analysis of language that we are able to gain a grip on the structures of those parts of our capacity to think which we are able to make accessible to others and fully conscious to ourselves.12 While Dummett is surely right that it has been definitive of the analytic tradition that an account of communicable and conscious thought needs to proceed via an account of language, this observation is by no means unique to the analytic tradition. In a remarkable passage, Nietzsche argues that the development of speech and the development of consciousness go hand in hand. We become conscious because we need to communicate our wants and beliefs; by communicating them, they become as available to us as they are to others. He cites in favour of this theory the fact that conscious thinking is done in words (Nietzsche 1964, pp. 296–300). Descendants of this thought are also to be found in many poststructuralists; and indeed, one should acknowledge that the linguistic turn is as much a feature of the ‘Continental’ tradition as of the analytic tradition.

Conclusion

I claimed at the beginning of this book that we should not see Dummett as a determined advocate of any particular brand of antirealism, but rather should value his work for the way in which it maps the semantic terrain, exploring the strengths and weaknesses of various theories of meaning. We have now completed our overview of the evolving map that Dummett has provided. At times we have had to leave out details, and I have occasionally argued that Dummett has underemphasized important features of the landscape. But the map which has emerged is far more profound and illuminating than any other currently in our possession. Unlike many philosophers with a logical bent, Dummett demands that if logic is to advertise itself as of importance in the theory of meaning, it should earn its keep. Formal languages can be provided with interpretations via the construction of appropriate algebraic structures; but if such a structure is to be called a semantics, it should be possible to show both that it is capable of providing the basis for a theory of meaning and that the theory of meaning which is so derived is adequate. According to the most recent map that Dummett has provided, theories of meaning can be seen as occupying three broad and overlapping regions: those occupied by the holist, the realist and the constructivist. Holists can be of the radical kind epitomized by Wittgenstein’s dictum ‘language is a motley’, and reject the possibility of a systematic theory of meaning at all. They can, alternatively, take the position adopted by McDowell, that only a modest, unexplanatory semantics is possible. Such a view sees itself as realist, insofar as bivalence is asserted, but takes

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the principle of bivalence to be unjustifiable and simply part of our practice. Other realists, and various anti-realists, accept that an explanatory, systematic meaning theory is possible. A thoroughgoing realist semantics involves the interpretation of all singular terms at face value, as referring to objects, and the assumption that every predicate is determinately true of or false of every object. Such a semantics will be adequate only for a tiny fragment of natural language: that which assigns determinate and decidable predicates to presently existing, accessible objects. As soon as vagueness, the past and future tense, quantification over infinite domains or subjunctive conditionals are introduced, things become complicated. I have argued that it is reasonable to interpret Dummett as concurring with those who assume that the inaccessibility of the past does not constitute a reason for giving up on a realist semantics for past-tense statements. Moreover, the fact that the meaning of a past-tense statement is naturally identified with its truth condition, which needs to be distinguished from the condition which warrants its assertion, is surely part of the explanation of why it is so natural to extend realist semantics to other cases. But, as Dummett has so thoroughly argued, there are good reasons to believe that in other cases the extension is difficult to justify, if what is wanted is the basis for a genuine theory of meaning. The smallest deviation from a thoroughgoing realist semantics maintains bivalence, but involves the reinterpretation of some singular terms as not genuine, as in Russell’s theory of descriptions. The next-smallest deviation involves the enrichment of the notion of absolute truth with some notion of relativized truth, truth relative to a sharpening or relative to a possible future course of events, for instance. Such objectivist relativized semantics involve giving up bivalence for absolute truth, which is identified with truth in every possible future or in every sharpening, although the law of excluded middle is assumed to hold in any possible future or sharpening. Semantics of this kind can then be given a more realist or anti-realist cast, according to the interpretation placed on the existence of a possible future or adequate sharpening. Dummett makes clear that he takes realist interpretations of such semantics as highly defective from the point of view of a genuine explanation of our capacity to use language, since it is only on the basis of our use of language to talk about this world that we can determine what is an adequate sharpening or possible future. A further step in the direction of anti-realism may be the result of a reductionist thesis. For instance, it is quite

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natural to assert that truths about fictional characters can be reduced to truths about what is explicitly stated in, or directly implied by, the stories written about those characters. Such a reductionist thesis naturally leads to the denial of bivalence. But bivalence can also be denied without any clear reductionist thesis. Neutralism about the future is, Dummett suggests, a case of this. It is not the case that a statement about the future can be translated into some statement about the present; but we manifest our general belief that the future is open, and that what will happen is partly the result of our intentions, by refraining from asserting bivalence for future-tense statements. Similarly, in the case of mathematics, intuitionists refrain from asserting bivalence, because mathematical reality as we know it does not warrant the assertion that every mathematical truth will ultimately be able to be shown to be either true or false. Such objectivist anti-realisms are to be distinguished from subjectivist anti-realisms. I have argued that Dummett has, to a certain extent, done a disservice to those who deny bivalence from an objectivist stance, by deeming their views forms of anti-realism, and thus appearing to assimilate them to subjective idealism. These are forms of anti-realism which are perfectly compatible with realism with regard to common-sense physical objects, and if Dummett is correct that many of the objects recognized by science are merely extensions of our common-sense views about the world, they are compatible with realism with regard to the majority of the entities postulated by science. Nevertheless, subjectivist views naturally lead to the denial of bivalence; so, in this respect, objectivist anti-realisms share a common feature with subjective idealism. Whatever one’s choice of nomenclature, objectivist anti-realisms are naturally located between the extremes of thoroughgoing realism and subjective idealism. Dummett has not shown that any particular semantics, or metaphysical account of what there is, provides a basis for an adequate theory of meaning. He has, however, raised a challenge and cleared some of the path towards meeting it. If we are to make the workings of our language clear to view, we will need some account of the way in which the semantic value of complex expressions depends on the semantic values of their parts. If such a semantic account of the structure of language is genuinely going to contribute to our understanding of the way in which language works, and the nature of rationality, it will have to relate to the way in which we interact with our surroundings and come to grasp the meanings of words.

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In an autobiographical essay Bertrand Russell once wrote that it struck him that the aim of philosophy should be to show how one could get from what is available from the subjective point of view to the scientific world-view, and to show how one could get back again from the scientific world-view to an explanation of what is available from the subjective point of view. Russell’s own attempts at this project foundered on his atomism, but the goal he outlined is still worth aiming at. We have common-sense and scientific theories about the way the world functions. Can we, in terms of those theories, make our capacity to represent and communicate about the world comprehensible? In this book I have suggested that because he is influenced by post-Fregean understandings of semantics, Dummett’s approach to this question concentrates too heavily on reference to objects, rather than on reference to properties or concepts. If the kernel of truth in Locke’s dictum that the immediate objects of perception are ideas involves ideas as they are powers in objects, and reduces to the claim that it is the properties of things which immediately affect us, then an important part of the theory of meaning will have to explain what is involved in the transition from merely being affected by particular properties, as are many living and non-living things, to having a grasp of concepts which includes the capacity to represent those properties, whether or not they are instantiated. What cognitive scientists have found interesting in Husserl is that, with notions such as the intuitive fulfilment of a noema, he attempted to relate aspects or properties of things with the ways in which we expect things to be in virtue of our understanding of them as things of a certain kind. However, although Husserl himself recognized a distinction between meanings and concepts, those who have developed Husserl’s philosophy have continued to conflate the properties of things with the senses of words (1900/70, §33, pp. 331–2). Frege began to see that one should distinguish between the senses of predicate expressions, which are ways in which concepts are given to us, from the properties in the world which we only partially grasp through those senses. He left us an intriguing idea which has been largely overlooked. Nevertheless, even if I am right, and Dummett has paid too little attention to this particular Fregean idea in his pursuit of a theory of meaning, he has been much clearer about this Fregean distinction than have most other commentators, and he has done a great deal to insist that the theories that we introduce into semantics are actually applicable to the activity we want to explain – the activity of consciously thinking and communicat-

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ing about the world that impinges upon us. Contemporary thought about language often falls into two opposing and untenable camps. Those who follow either a Whorfian or a structuralist path attribute to cultures a virtual freedom in the construction of concepts. Those who follow a naive representationalism think that the world will magically provide a fit between the causal impingement of a property on our perceptual apparatus and our representation of that property. Dummett has shown that there are paths between these extremes. Like the representationalists, he insists that if a sentence is true, there must be something in virtue of which it is true. Like those who believe that we create concepts, he recognizes that meaning is dependent on the uses to which language is put. The correct use of words tracks at a basic level communally recognizable features of things; but when we take seriously the extent to which this is the case, our unquestioned faith that bivalence holds in all areas of discourse should be undermined.

Notes

Preface 1 2

Some testimonials to this influence are to be found in Heck 1997. Thus, in a review of The Logical Basis of Metaphysics, Gregory Currie complains: ‘the case as he has stated it has had very much the appearance of work in progress. It has often been presented as tangential to the central topic (as in his writings on Frege), it has not been easy to understand, and it has had about it the air of something incomplete – some part of the argument seems to be missing’ (1993, p. 465).

Introduction 1

Dummett’s characterization of analytic philosophy is by no means uncontroversial. A collection of essays on analytic philosophy, edited by Hans-Johann Glock, is devoted to arguing that it is either too narrow or inaccurate because paradigmatic analytic philosophers do not fit the bill (Glock 1997). I have argued elsewhere that Dummett’s characterization is essentially correct and that the case made by the authors of these essays is not compelling (Green 2000a). 2 Classical logic has as a theorem the law of excluded middle, p ⁄ ÿp, and assumes the principle of bivalence, that every meaningful sentence is either true or false. In intuitionistic logic the law of excluded middle is not a theorem, and bivalence is not asserted. 3 Chomsky expresses puzzlement over what such a ‘philosophical account’ could be, and suggests that it involves a kind of methodological dualism which has not been explained or justified (Chomsky 1995, pp. 34–5).

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4

Göran Sundholm introduces this metaphor when contrasting MartinLöf’s approach to philosophy with Dummett’s (Sundholm 1994, p. 146). 5 One might question the assumption that some sentences are undecidable. This is not an issue that I explore, but it is discussed at length in Tennant 1997, pp. 161ff. 6 A statement is taken to be barely true when only a trivial statement of its truth condition is possible, or, equally, when no reductionist account of its truth condition can be provided.

Chapter 1 Fregean Foundations 1 2

3 4 5 6

7 8

9

Dummett reports that earlier he had written a book on intuitionism, but on being asked to revise it for publication, he became dissatisfied with it. Logicism is the claim that the truths of arithmetic are truths of logic. In The Foundations of Arithmetic Frege argued that Kant was wrong in his claim that arithmetic is a synthetic a priori science and that, properly understood, arithmetical truths are analytic or logical truths (Frege 1884/1950). An excellent and thorough introduction to Frege’s development of his logic, its background and motivation, is provided by Beaney (1996). See however Green 1992 for an attempt to draw out the implications of this schema. This is not to imply that Dummett ignores Frege’s introduction of concepts: two chapters of Frege: Philosophy of Language (1973a) are devoted to it. But the notion does not become central to his thought. Wolfgang Carl discusses this comment in Carl 1994, pp. 53–75. Dummett has suggested recently that Frege became more disillusioned with language after the discovery of the paradoxes, and he quotes a 1906 letter to Husserl in which Frege says that ‘the main task of the logician consists in the liberation from language’ (Dummett 1993b, p. 6). The quotation I have given, however, dates from between 1879 and 1891, well before the discovery of the paradoxes. Dummett provides an account of the relationship between an account of sense and an account of force, and arguments for distinguishing between them, in 1975a/78c; 1976e/93d, pp. 38–42. I use the expression ‘cognitive part’ of language to denote the part of language standardly used for the expression and conveying of truths. This usage might be objected to. It is probable that the interpretation of metaphor involves cognitive processes, as does the recognition of force. Therefore this usage may not be ideal, but it is standard, and should not be misleading in this context. The first part of Husserl’s Logical Investigation is devoted to teasing apart the various elements in meaning (1900/70, pp. 269–333).

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10 There is some debate over the extent to which Frege should be credited with the development of semantics. Dummett’s most recent discussion of this debate is in 1995b, pp. 10–17. 11 The distinction between intensions and extensions that Davidson was working with was derived from Carnap (1947). Unfortunately, Carnap failed to preserve the distinction between senses and concepts, and identified senses with properties. For Frege, a theory of reference already involved reference to concepts, which are unsaturated entities, and which he claimed had some affinity with intensions. When Davidson claims that all we need is a theory of reference, he is assuming that singular terms refer to objects, and predicates refer to sets. In my view Carnap’s conflation has done a great deal of harm (Green 1992). 12 As is well known, Kripke (1980) has argued that not even this is the case, and that speakers do not, in general, know anything which uniquely identifies the referents of the expressions they use. 13 See also Dummett 1973a, p. 381. 14 Indeed, Dummett himself sometimes mentions Chomsky when discussing the implicit grasp that we have of the principles that govern the use of language (Dummett 1975a/78c, p. 451). 15 In ‘What is a Theory of Meaning? (II)’ Dummett used the phrase ‘theoretical representation of a practical ability’. But soon after he recognized that this was misleading, since it did not sufficiently capture the fact that understanding is different from riding a bicycle, because the first, unlike the second, involves the acquisition of conscious knowledge (1976e/93d, p. 36; 1978d/93d). 16 See, for instance, Dummett 1974c/78c, p. 379; also Lavine 1994, p. 173. 17 In other places we have similar assertions suggesting that we replace the notion of truth with that of proof or verification (Dummett 1973c/78c, p. 227). 18 Hilary Putnam shows one way in which the intuitionistic connectives can be translated into classical logic, and a truth theory for an intuitionist language derived, in his paper ‘What is Realism?’ (1976). An alternative is to derive a truth theory for non-classical logic in a nonclassical meta-language (Dummett 1976e/93d, pp. 67–9). The problem is discussed at length by Wright (1976/93, 1984/93). 19 In deeming this argument shallow, Dummett seemed to be suggesting that it did not provide reasons for disputing realism. He now asserts that, in rejecting bivalence, Strawson is evincing an anti-realism with regard to Meinong’s non-existent beings. This involves retracting the view that the argument is shallow. In conversation Dummett has indicated that he struggled for a long time to clarify the distinction between shallow and deep reasons for rejecting bivalence. Ultimately he came to the conclusion that any rejection of bivalence involves the adoption of some element of anti-realism with regard to some sort of entities. It should be noted that such an element of anti-realism is still compatible with considerable realism.

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20 In fact there are two ways of interpreting the consequences of the failure of this presupposition: on one interpretation, no statement is made; on the other, a statement is made, but it is neither true nor false. 21 See introduction to Truth and Other Enigmas for a useful summary of the relevant terms (Dummett 1978c, p. xix). 22 The qualification ‘meaningful’ is important here. Frege, for instance, suggested that sentences which contained non-denoting names were neither true nor false, but he did not clearly reject bivalence. Rather, he was expressing the opinion that such sentences were really ill-formed, so not properly meaningful. He should probably be placed with those who deny that such sentences make statements. 23 This assumption also echoes Wittgenstein, who says in the Brown Book: ‘Let us now look at the different kinds of signs which we have introduced. First let us distinguish between sentences and words. A sentence I will call every complete sign in a language game, its constituent signs are words’ (Wittgenstein 1958, p. 82). This assumption is endorsed by Davidson (1977/85). 24 See Wright 1983, pp. 41–52, for an example of the way in which Wittgenstein’s critique of ostensive definition can be used to disarm a certain kind of empiricist suspicion of the context principle and so render it more plausible. 25 The most influential contemporary advocate of the redundancy theory agrees, and for this reason believes that a theory of meaning has to be given in terms of use (Horwich 1990). 26 For a discussion of the interpretation and plausibility of principles C and K which emphasizes the fact that the verificationist notion of truth is a correspondence notion, see Martin-Löf 1998. 27 Field seems to assume that in rejecting extreme Platonism he has given us reasons for rejecting minimal Platonism. This is a mistake. Crispin Wright discusses at some length purported objections to the existence of abstract objects based on our lack of causal relationship with them (1983, pp. 84–103). 28 See as an example the philosophy of mathematics outlined in Bigelow 1988. I have also argued for the compatibility of this way of thinking with Frege’s fundamental doctrines in Green 1999. 29 See e.g. Gödel 1947/64, pp. 271–2. 30 See e.g. Weiner 1990, pp. 180–1. I do not entirely agree with the conclusions that Weiner draws from this observation, but she is surely right to claim that for Frege it is the logical faculty which gives us knowledge of logical objects. 31 In a recent paper Erich Reck introduces the term ‘contextual Platonist’ to characterize Frege’s position. Minimal Platonism as I understand it corresponds pretty well with contextual Platonism as Reck describes it, for it makes the existence of objects depend on the truth conditions of sentences (Reck 1997).

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32 Joan Weiner has recently echoed this interpretation of Frege (Weiner 1990, p. 184). 33 In ‘Objectivity and Reality in Lotze and Frege’ Dummett rejects much of the textual evidence offered by Sluga (Dummett 1982b/91b). In a companion paper on Frege and Kant, Dummett discusses Frege’s use of the word ‘intuition’, and establishes that, although Frege accepted that the source of our knowledge of geometrical truth is intuition, he nevertheless thought that this was knowledge of objective and mindindependent truth. This discussion confirms the interpretation of Frege according to which what he means by ‘objective existence’ is independence of minds (Dummett 1982a/91b). 34 Some evidence that it is the latter which Frege intended is provided by his comments in a letter to Husserl (Frege 1980, p. 63). 35 David Bostock (1974) attempts a Fregean account of arithmetic along these lines. 36 Extensions, however, are derived from concepts, whereas on the iterative conception of a set, sets can be formed by applying set-forming operations to a domain of individuals, and there will be many sets such that no concept of which the set is an extension can be found. 37 Interestingly, Frege’s own interpretation of his logic involves the assumption that properties are already referred to in the first-order quantification. But these properties are not objects; they are the concepts which are the referents of predicate expressions. One might argue that Frege’s analysis gets the natural interpretation of the truth conditions of this sentence correct. Insofar as one is asked to establish this sentence as true, one will show that the property of being a whale essentially involves the property of being a mammal. That is to say, nothing could count as an instantiation of ‘being a whale’ unless it also counted as an instantiation of ‘being a mammal’. 38 Our quantifier may be effectively a substitutional quantifier. 39 Dummett’s commitment to this aspect of the context principle is reiterated in Dummett 1975b/78c, p. 126. 40 Dummett tells us that the idea of an indefinitely extensible concept originated with Russell (Dummett 1991d, p. 317n.).

Chapter 2 Wittgenstein and Quine 1

Just three papers have Wittgenstein’s name in the title (Dummett 1959d/78c, 1981a/91b, 1993f/93d). The bulk of the discussion of Wittgenstein is scattered throughout Dummett’s writings. The paper ‘Can Analytic Philosophy be Systematic and Ought it to Be?’ contains an extended discussion of Dummett’s understanding of what should be kept and what jettisoned from Wittgenstein (Dummett 1975a/78c). 2 Here I am following Dummett’s interpretation of Wittgenstein. By contrast, P. M. S. Hacker (1996) insists that Wittgenstein has a nor-

Notes to pp. 59–77

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mative conception of meaning which differs substantially both from Quine’s behaviourist conception and from the characterization which Dummett provides. Gunson derives this problem from two papers of McDowell’s which discuss a distinction Dummett once drew between modest and fullblooded theories of meaning (McDowell 1981, 1987). I have chosen not to address this literature directly, largely because I find it excessively dense, and too confusing to be helpful in an introductory text. Dummett has also expressed dissatisfaction with the papers in which he initially introduced the distinction (1993d, pp. vii–xv). I have argued elsewhere that McDowell is insensitive to the distinction between anti-psychologism and anti-mentalism, and that this vitiates his criticisms (Green 1986). For a general discussion of this and other delusions see Davies and Coltheart 2000. This is the way in which Dummett interprets Wittgenstein (Dummett 1959d/78c) as do Saul Kripke (1982) and Crispin Wright. Christopher Peacocke disagrees. If it is possible to provide a direct account of the possession conditions for a concept, then there is no need to give an account of thought by way of language (Peacocke 1992, 1997). Dummett gives another version of this argument in 1993a, pp. 22–5. The discovery of non-Euclidean geometry leads naturally to conventionalism, and once one has come to see geometrical axioms, such as the parallel postulate, as a convention that one may choose to adopt for certain purposes, it is natural to think of logics as similar conventionally adopted rules of inference. For an account of Wittgenstein’s attendance at these lectures and Russell’s comments on the influence of Brouwer, see Monk 1990, pp. 249–51, 293. For Wittgenstein’s commitment to finitism, and his recognition of the connection between finitism and behaviourism, see Wittgenstein 1967b, p. 63. See also Frege 1971, p. 70, for a clear expression of this. Discussing Wittgenstein’s semantics in the Tractatus, Carruthers says: ‘The possible situation which the proposition directs us towards is called a “state of affairs” (“Sachverhalt”). If that state of affairs exists then the proposition is true, if it does not then the proposition is false (2, 2.12–2.15, 2.201–2.221)’ (1989, p. 30). This is the natural thing to say, but what does it then mean to say that there is something, a state of affairs, which does not exist? This is exactly analogous to the problem of the being of the non-existent entity which Frege solves by insisting that ‘exists’ is a second-order predicate which says that a concept is instantiated. It is noteworthy that Monk reports that Frege’s reaction to the Tractatus was to insist that he did not understand what a ‘Sachverhalt’ could be (Monk 1990, p. 163). Nevertheless, Frege never

212

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solves this problem totally satisfactorily, for in the paper ‘Negation’ he still feels the need to attribute ‘being’ to a false thought, and thus reproduces the problem at the level of sense (Frege 1984, pp. 373–89). 13 See Carl 1994. 14 For a discussion of the semantics of the Tractatus see Carruthers 1989, and for this point in particular p. 25. 15 I argue for this interpretation in greater detail in Green 1999.

Chapter 3 The Influence of Intuitionism 1 2

3

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8

See also Heyting’s description of mathematics as expressing empirical facts concerning mental constructions. This would have been anathema to Frege (Heyting 1966, pp. 8, 10). See in particular the last page of ‘The Philosophical Significance of Gödel’s Theorem’, where Dummett argues that accepting the intuitionist claim that the classical explanation of the logical constants is faulty, because circular, is independent of the intuitionist’s insistence that the notion of truth has to be replaced by that of proof (1963/78c). Wright, following Putnam, argues that the most we should conclude from Gödel’s theorem is that if the formal system of arithmetic is consistent, the undecidable sentence will be true, but that we cannot recognize its truth unless we demonstrate the consistency of the formal system (Wright 1994; Putnam 1975, pp. 362–84). Dummett responds that since every arithmetical proposition is true only on the assumption that the axioms are true and the formal system consistent, we are in no worse position with regard to the undecidable sentence than with regard to other arithmetical propositions (1994a, p. 333). A rule of inference is an introduction rule for a logical constant c if its conclusion is required to have c as its principal operator; it is an elimination rule if one of its premisses is required to have c as its principal operator (Dummett 1991e, pp. 256–8). Two classic papers discussing the notion of conservative extension are Prior 1960; Belnap 1961. I discuss this objection in Green 1991. Neil Tennant has argued that the correct logic for a constructivist to adopt is intuitionistic, relevance logic. In such a logic it will always be possible to transform a proof that involves ex falso quodlibet into one that does not involve this rule of inference (Tennant 1997, pp. 304–54). The classical logician might wonder whether the fact that taking a proof-theoretic path to the justification of deduction leads to such a radical revision of our practice does not show the questionability of the demand. A little fine-tuning is required to allow for the possibility that one might be a realist about mental items such as qualia or fears.

Notes to pp. 106–28 9

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In one of his latest papers Dummett (1997) admits that the semantics of tense do not seem to resolve all the metaphysical issues that arise concerning the existence of the past. This suggests that he would now not unreservedly endorse the quoted sentence. There has been some debate over whether this is the right way to interpret Frege; see Weiner 1990; Burge 1992; Weiner 1995. This view is expressed in Mackie 1976, p. 12. Dummett discusses these arguments in a number of early papers (1978c, pp. 29–65). Quine and Goodman seem to have believed that materialism leads to the rejection of abstract objects, because abstract objects are not causally active. Frege, on the other hand, since he thought of laws of nature as involving relations between concepts, may well have assumed that at least instantiated concepts are causally active. In a paper discussing Ayer’s verificationism, Dummett suggests that any verificationist theory of meaning involves the idea that there are gaps in reality; yet, as he goes on to comment, this goes against the grain of our thinking (1992, p. 146). In the next chapter I will argue that it is just the implausibility of the idea that there are gaps in reality that pushes us towards bivalence with regard to many areas of discourse. Dummett notices that this brings him closer to those who have thought the issues at the centre of the debate between realists and anti-realists concern the existence of objects (1993d, p. 468). The requirement that the creature is sufficiently like us is intended to rule out the possibility of this position collapsing into realism through allowing that the creature might be a god with the capacity to survey an infinite totality. For a more recent repetition of this view see Dummett 1991e, p. 331. David Armstrong has popularized the slogan that every truth needs a truth-maker. In his A Materialist Theory of Mind he applied it to Ryle’s dispositional theory of mind. Assuming that a person must either have or not have a disposition, even when it is not being manifested (just as a glass either is or is not brittle), he argued that the truth-maker of an attribution of a dispositional property must be the underlying categorical base. Dummett had already offered a response to this argument, before Armstrong’s book was published. It was that the antirealist should deny the assumption of bivalence. So the truth-maker argument is not decisive against the dispositional theory of mind (Armstrong 1968, p. 85). Thus I am in agreement with Samual Mitchell and Neil Tennant, who offer defences of intuitionism against the strict finitist along these lines (Mitchell 1992; Tennant 1997, pp. 143–58). Neil Tennant argues in his first book on anti-realism that the semantic anti-realist should have no difficulty in accepting scientific realism of the sort advocated by Richard Boyd. This, however, is too strong a claim. The semantic anti-realist may well be forced into some form of

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instrumentalism with regard to theoretical entities. It is the commonsense objects of ordinary perception which can be recognized equally well by both a semantic realist and a semantic anti-realist who is not tempted, for independent reasons, by phenomenalism (Boyd 1983; Tennant 1987). 20 Frege’s rejection of bivalence for sentences containing non-denoting terms could now be taken to be a paradigm of the common-sense realist rejection of bivalence in the service of anti-realism with regard to obscure, non-causally active but material entities (Dummett 1991e, pp. 324–5).

Chapter 4 The Reality of the Past 1 2

This was A. J. Ayer’s early view (1946, pp. 101–2). There are surely fruitful fields to be reaped, by those interested in post-analytic philosophy, in the relationships between Dummett’s and McTaggart’s thinking on these issues and Heidegger’s. Heidegger comes down strongly for the reality of time and its passage, and rejects the realist view of the past according to which it is ‘levelled off’ into a series of points imagined via a spatial metaphor. The price is an anti-realist concept of truth as what appears at a point in time. A reading along these lines might help both to domesticate Heidegger for analytic readers and to show neo-Heideggerians that not all analytic thinking neglects temporality.

Chapter 5 What do we Know when we Know a Language? 1

What Chomsky means by ‘mentalistic’ is in line with my use of the term ‘psychologistic’. The mental reality underlying linguistic behaviour is no more than a disposition to behave in a certain way, so it is not a mentalism which offends against Wittgenstein’s strictures. 2 The use of this term originates with John Rawls, A Theory of Justice, p. 20, though he refers to Nelson Goodman, Fact, Fiction and Forecast, pp. 65–8, for a description of the method. He then suggests the analogy with grammar on p. 47 of Theory of Justice, though nothing like the method of reflective equilibrium is discussed in the pages of Chomsky to which he refers. 3 This version of Chomsky is lucidly developed by Pinker (1995). 4 Another version of this argument appears in Green 2001. The argument should not be taken as an unqualified endorsement of Davidson’s treatment of metaphor; the claim is merely that a slight modification of that treatment will account for malapropism.

Notes to pp. 163–85

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5

Christopher Peacocke (1997) has pointed out various other ambiguities in the priority of language thesis. 6 This is what Dummett means when he says that ‘a speaker holds himself responsible to the accepted meanings of words’. Davidson has objected that some linguistic communities deliberately adopt deviant usages, but, relative to those communities, a new standard of correctness has evolved (Dummett 1986c, p. 462). 7 The issues raised here are complex. For example, the cognitive capacities of deaf-mutes who have never learned sign language are considerable (Pinker 1995, pp. 67–8). Visual perception is highly structured, and it would not be surprising if language rides piggyback on cognitive structure already available in vision. Nevertheless, a great deal of determinacy in structure and content is acquired with language; in particular, it is plausible to claim that the distinction between objects and properties has a linguistic foundation, and this is all that is being claimed. Indeed, Euan Macphail (1998) argues that there is little evidence for anything other than associative reasoning in animals which have not evolved language.

Chapter 6 Psychologism, Phenomenology and Philosophy of Mind 1

2 3 4 5

It might be thought by someone who endorsed Crispin Wright’s reading of the context principle that Frege would treat ‘red’ in this context as a singular term referring to an object. In fact, he does not do so. This provides indirect evidence that Dummett is correct in arguing that the reasons that Frege gives for taking numerals to refer to objects are weak. Dummett indicates in a footnote that he has been convinced that this is an inaccurate characterization of Kant’s view (Dummett 1983a/93d, p. 277). Russell (1905/56) uses the term ‘propositional function’ for Fregean concepts, and argues that the method of descriptions obviates the need to introduce senses. By ‘valid’, Husserl merely means true. In support of this interpretation, it should be noted that Husserl says: ‘if, now, the extension is defined as the entirety of objects that can be truly subsumed under a representation, it nonetheless seems unnatural to say that the general representation represents the objects in its extension’ (1996, p. 359). This strongly suggests that he has in mind Fregean concepts (which Frege identifies with the referents of the signs which represent them), rather than words or images which themselves represent. This impression is also borne out by the fact that he speaks of representations entering into hypothetical

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Notes to pp. 187–200 relationships, where Frege would speak of relations between concepts (pp. 362–3). Only roughly, because Carnap also equates intensions with properties, thus obliterating the Fregean distinction between concepts and senses (Green 1992). In ‘Appendix 2: Frege’s Logical Notation’ Michael Beaney provides a lucid account of Frege’s method of dealing with definite descriptions (Beaney 1997, pp. 384–5). This fits in with Frege’s footnote concerning the sense of an actual proper name such as ‘Aristotle’ (Frege 1984, p. 158). One might object to this as an analysis, however, because, according to it, a sentence like ‘Aristotle existed’ has no precise sense. As I have interpreted it, Frege’s theory does not account for the meaningfulness of existential statements involving ordinary proper names. Dummett discusses this problem at length in (1983a/93d). Thinking of senses in this way leads Dummett to make the rather odd claim that ‘In view of Frege’s realism, the instruction must be thought of as addressed, not to us, but to reality’ (1993b, p. 113). But how could an instruction be addressed to reality? The bizarreness of this thought suggests that Dummett has not characterized Frege’s thinking correctly. This is perhaps too strong, and is only a contingent feature of us. It seems that creatures like dolphins and bats, that use echolocation in order to perceive the world, can literally get their conspecifics to perceive what they are perceiving. Even we do something similar when we get others to see what we are seeing directly, by putting them in the right position. He says that ideas of secondary qualities are ‘no more the likeness of something existing without us, than the names, that stand for them, are the likeness of our ideas, which yet upon hearing, they are apt to excite in us’ (Locke 1690/1975, bk 2, ch. viii, §7). Since first writing this, I have come across Euan Macphail’s The Evolution of Consciousness (1998), in which he argues for a very similar conclusion. In some ways, Macphail’s position is more extreme than that for which I am arguing. Moreover, our interpretations of the fruitfulness of Fodor’s approach differ. Nevertheless, his argument that there is little evidence for the existence of conscious thought without language is highly suggestive.

References and Bibliography

Works of Dummett Relevant to the Philosophy of Language. Where a work has been reprinted, page references are to the reprint (1953). Review of Waisman Introduction to Mathematical Thinking. Mind 62: 535–45. (1954a/78c). Can an Effect Precede its Cause? Proceedings of the Aristotelian Society 28: 27–44. Reprinted in Dummett 1978c, pp. 319–32. (1954b). Review of P. Geach and M. Black Translations from the Philosophical Writings of Gottlob Frege. Mind 63: 102–5. (1955a/78c). Frege on Functions: A Reply. Philosophical Review 64: 96–107. Reprinted in Klemke 1968, pp. 268–83, and Dummett 1978c, pp. 74–84. (1955b/78c). The Structure of Appearance. Mind 64: 101–9. Reprinted in Dummett 1978c, pp. 29–37. (1956a/78c). Nominalism. Philosophical Review 65: 491–505. Reprinted in Klemke 1969, pp. 321–36, and Dummett 1978c, pp. 38–49. (1956b/78c). Note: Frege on Functions. Philosophical Review 65: 229–30. Reprinted in Klemke 1968, pp. 295–7, and as ‘Postscript (1956)’ in Dummett 1978c, pp. 85–6. (1957/78c). Constructionalism. Philosophical Review 66: 47–65. Reprinted in Dummett 1978c, pp. 50–65. (1959a/78c). George Boole: Review of Studies in Logic and Probability. Journal of Symbolic Logic 24: 203–9. Reprinted in Dummett 1978c, pp. 66–73.

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(1959b). A Propositional Calculus with Denumerable Matrix. Journal of Symbolic Logic 24: 97–106. (1959c/78c). Truth. Proceedings of the Aristotelian Society 59: 141–62. Reprinted, with postscript, in Dummett 1978c, pp. 1–24. (1959d/78c). Wittgenstein’s Philosophy of Mathematics. Philosophical Review 68: 324–48. Reprinted in Dummett 1978c, pp. 166–85. (1960a/78c). A Defence of McTaggart’s Proof of the Unreality of Time. Philosophical Review 69: 497–504. Reprinted in Dummett 1978c, pp. 351–7. (1960b/78c). Oxford Philosophy. New Blackfriars 42. Reprinted in Dummett 1978c, pp. 431–6. (1960c/78c). Presupposition. Journal of Symbolic Logic 25: 336–9. Reprinted in Dummett 1978c, pp. 25–8. (1963/78c). The Philosophical Significance of Gödel’s Theorem. Ratio 5: 140–55. Reprinted in Dummett 1978c, pp. 186–201. (1964/78c). Bringing About the Past. Philosophical Review 73: 338–59. Reprinted in Dummett 1978c, pp. 333–50. (1967/78c). Frege’s Philosophy. In The Encyclopedia of Philosophy, ed. P. Edwards, New York: Macmillan, 225–37. Reprinted in Dummett 1978c, pp. 87–115. (1969/78c). The Reality of the Past. Philosophical Review 78: 239–58. Reprinted in Dummett 1978c, pp. 358–74. (1972–3). Frege’s Way Out: A Footnote to a Footnote. Analysis 33: 139–40. (1973a). Frege: Philosophy of Language. London: Duckworth. (1973b/78c). The Justification of Deduction. Proceedings of the British Academy: 201–31. Reprinted in Dummett 1978c, pp. 290–318. (1973c/78c). The Philosophical Basis of Intuitionistic Logic. In Logic Colloquium ’73, ed. H. E. Rose and J. C. Shepherdson, Amsterdam: North-Holland, 5–40. Reprinted in Dummett 1978c, pp. 215–47. (1974a). Postscript. Synthèse 27: 523–34. Reprinted as ‘The Social Character of Meaning’ in Dummett 1978c, pp. 420–30. (1974b). Reply to W. V. Quine. Synthèse 27: 413–16. (1974c/78c). The Significance of Quine’s Indeterminacy Thesis. Synthèse 27: 351–97. Reprinted in Dummett 1978c, pp. 375–419. (1975a/78c). Can Analytical Philosophy be Systematic and Ought it be? Congress on the Philosophy of Hegel at Stuttgart, Stuttgart: Reprinted in Dummett 1978c, pp. 437–58. (1975b/78c). Frege. Teorema 5: 149–88. English version, ‘Frege’s Distinction between Sense and Reference’, in Dummett 1978c, pp. 116–44.

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(1975c/78c). Wang’s Paradox. Synthèse 30: 301–24. Reprinted in Dummett 1978c, pp. 248–68. (1975d/93d). What is a Theory of Meaning? In Mind and Language, ed. S. Guttenplan, Oxford: Oxford University Press, 97–138. Reprinted in Dummett 1993d, pp. 1–33. (1976a). Comment on Czesl¢aw Lejewski. In Philosophy of Logic, ed. S. Körner, Oxford: Blackwell, 28–43. (1976b/91b). Frege as a Realist. Inquiry 19: 455–68. Reprinted in Dummett 1991b, pp. 79–96. (1976c/91b). Frege on the Consistency of Mathematical Theories. In Studien zu Frege I: Logik und Philosophie der Mathematik, ed. M. Schirn, Stuttgart: Friedrich Frommann Verlag, 229–42. Reprinted in Dummett 1991b, pp. 1–16. (1976d/78c). Is Logic Empirical? In Contemporary British Philosophy, ed. H. D. Lewis, London: George Allen and Unwin, 45–68. Reprinted in Dummett 1978c, pp. 269–89. (1976e/93d). What is a Theory of Meaning? (II). In Truth and Meaning: Essays in Semantics, ed. G. Evans and J. McDowell, Oxford: Clarendon Press, 67–137. Reprinted in Dummett 1993d, pp. 34–93. (1977). Elements of Intuitionism. Oxford: Oxford University Press. (1978a). Platonism. In Truth and Other Enigmas, London: Duckworth, 202–14. (1978b). Realism. In Truth and Other Enigmas, London: Duckworth, 145–65. (1978c). Truth and Other Enigmas. London: Duckworth. (1978d/93d). What do I Know when I Know a Language? Centenary Celebrations, Stockholm University, Stockholm. Reprinted in Dummett 1993d, pp. 94–105. (1979a/93d). Common Sense and Physics. In Perception and Identity: Essays Presented to A. J. Ayer, ed. G. F. Macdonald, London: Macmillan, 1–40. Reprinted in Dummett 1993d, pp. 376–410. (1979b). Was Frege a Philosopher of Language? Revue Internationale de Philosophie 33: 786–810. (1979c/93d). What Does the Appeal to Use Do for the Theory of Meaning. In Meaning and Use, ed. A. Margalit, Dordrecht: Reidel, 123–35. Reprinted in Dummett 1993d, pp. 106–16. (1980a). Critical Notice of E. J. Brouwer Collected Works. Mind 84: 605–16. (1980b). Review of H. Sluga, Gottlob Frege (London, 1980); David Bell, Frege’s Theory of Judgement (London, 1980); G. Frege, Philosophical and Mathematical Correspondence, ed. B. F. McGuinness

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(Oxford, 1980) and P. Geach and M. Black, Translations from the Philosophical Writings of Gottlob Frege, 3rd edn. (Oxford 1980). London Review of Books 18(2): 13–15. (1981a/91b). Frege and Wittgenstein. In Perspectives on the Philosophy of Wittgenstein, ed. I. Block, Oxford: Oxford University Press, 31–42. Reprinted in Dummett 1991b, pp. 237–48. (1981b/91b). Frege’s Kernsätze zur Logik. Inquiry 24: 439–48. Reprinted in Dummett 1991b, pp. 65–78. (1981c). The Interpretation of Frege’s Philosophy. London: Duckworth. (1982a/91b). Frege and Kant on Geometry. Inquiry 25: 233–54. Reprinted in Dummett 1991b, pp. 126–57. (1982b/91b). Objectivity and Reality in Lotze and Frege. Inquiry 25: 95–114. Reprinted in Dummett 1991b, pp. 97–125 and Sluga 1993, pp. 203–22. (1982c/93d). Realism. Synthèse 52: 55–112. Reprinted in Dummett 1993d, pp. 230–76. (1983a/93d). Existence. In Humans, Meanings and Existences, ed. D. P. Chattopadhyaya, Delhi: Macmillan, 221–58. Reprinted in Dummett 1993d, pp. 277–307. (1983b/93d). Könnte es Einhörner Geben? Conceptus 17: 5–10. English version, ‘Could there be Unicorns?’, in Dummett 1993d, pp. 328–48. (1983c/93d). Language and Truth. In Approaches to Language, ed. R. Harris, Oxford: Pergamon, 95–125. Reprinted in Dummett 1993d, pp. 117–46. (1984/91b). An Unsuccessful Dig. Philosophical Quarterly 34: 377–401. Reprinted in Dummett 1991b, pp. 158–98. (1985). Corrections to Hacking on Frege. Philosophical Quarterly 35: 310. (1986a/93d). Causal Loops. In The Nature of Time, ed. R. Flood and M. Lockwood, Oxford: Blackwell, 135–69. Reprinted in Dummett 1993d, pp. 349–75. (1986b/91b). Frege’s Myth of the Third Realm. Untersuchungen zur Logik und zur Methodologie 3: 24–38. Reprinted in Dummett 1991b, pp. 249–62. (1986c). ‘A Nice Derangement of Epitaphs’: Some Comments on Davidson and Hacking. In Truth and Interpretation: Perspectives on the Philosophy of Donald Davidson, ed. E. LePore, Oxford: Blackwell, 459–76. (1987). Replies to Essays. In Michael Dummett: Contributions to Philosophy, ed. B. Taylor, Dordrecht: Martinus Nijhoff, 219–313.

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(1988a). The Origins of Analytical Philosophy. Lingua e Stile 23: 3–49. (1988b/91b). Second Thoughts. Philosophical Quarterly 38: 87–103. Reprinted in Dummett 1991b, pp. 199–216. (1989a/93d). Language and Communication. In Reflections on Chomsky, ed. A. George, Oxford: Oxford University Press, 192–212. Reprinted in Dummett 1993d, pp. 166–87. (1989b/91b). More about Thoughts. Notre Dame Journal of Formal Logic 30: 1–19. Reprinted in Dummett 1991b, pp. 289–314. (1990a/93d). The Source of the Concept of Truth. In Meaning and Method. Essays in Honour of Hilary Putnam, ed. G. Boolos, Cambridge: Cambridge University Press, 1–15. Reprinted in Dummett 1993d, pp. 188–201. (1990b/91b). Thought and Perception: The Views of Two Philosophical Innovators. In The Analytic Tradition, ed. D. Bell and N. Cooper, Oxford: Blackwell, 83–103. Reprinted in Dummett 1991b, pp. 263–88. (1991a/93d). Does Quantification Involve Identity? In Peter Geach: Philosophical Encounters, ed. H. A. Lewis, Dordrecht: Kluwer Academic Publishers, 161–84. Reprinted in Dummett 1993d, pp. 308–27. (1991b). Frege and Other Philosophers. Oxford: Clarendon Press. (1991c). Frege and the Paradox of Analysis. In Frege and Other Philosophers, Oxford: Clarendon Press, 17–52. (1991d). Frege: Philosophy of Mathematics. London: Duckworth. (1991e). The Logical Basis of Metaphysics. Cambridge, Mass.: Harvard University Press. (1991f). The Relative Priority of Thought and Language. In Frege and Other Philosophers, Oxford: Clarendon Press, 315–26. (1991g/93d). Review of David Bell, Husserl. Philosophical Quarterly 41: 484–8. Excerpt reprinted in Dummett 1993d, pp. 224– 9. (1992). The Metaphysics of Verificationism. In The Philosophy of A. J. Ayer, ed. L. E. Hahn, La Salle, Ill.: Open Court, 129–48. (1993a). Mood, Force and Convention. In The Seas of Language, Oxford: Oxford University Press, 202–29. (1993b). Origins of Analytical Philosophy. London: Duckworth. (1993c). Realism and Anti-Realism. In The Seas of Language, Oxford: Oxford University Press, 462–78. (1993d). The Seas of Language. Oxford: Oxford University Press. (1993e). Truth and Meaning. In The Seas of Language, Oxford: Oxford University Press, 147–65.

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Index

abstract ideas, 85, 109–11 abstract objects, 12, 31–6, 38–9, 44–6, 48–52, 108, 111–12, 116, 173, 209 n.27, 213 n.12 abstraction operator, 46–7 Ace, Goodman, 169 acquisition of language, 55–6, 58, 81, 127, 170 analytic hypotheses, 64–5 analytic philosophy, 1–4, 21, 42, 70, 114, 157, 176, 179–82, 198–200, 206 n.1 analytic truth, 60–1, 66, 96, 207 n.2 analytic/synthetic distinction, 60, 63–5 anti-mentalism, 43, 57–8, 71, 73–84, 93, 175, 190–1, 211 n.3 anti-psychologism, 37, 53, 57–8, 69–84, 175, 211 n.3 anti-realism and idealism, 105–7 argument for, 6, 28–30, 35, 53, 91, 99–105 global, 3 outright, 9, 11 reductive, 9, 11 with respect to future, 132–3, 145–8

with respect to past, 8, 119–20, 132–48, 213 n.9 Aristotelian logic, 13 Armstrong, David, 213 n.17 assertion, 16, 24–30, 34 atomistic accounts of meaning, 2, 9–10, 65, 73, 100–1, 145 Ayer, Alfred, 8–12, 94, 213 n.13, 214 n.1 backwards causation, 147–8 Beaney, Michael, 207 n.3 Berkeley, George, 82, 106, 109–13, 127 Beth trees, 130 Bigelow, John, 209 n.28 bivalence and realism, 29–30, 40, 96–8, 104, 130–2, 133–48, 201–2, 208 n. 19 arguments against, 24–30, 95–104, 117–24, 130–2, 208 n.19 argument against and antirealism, 7–8, 85–6, 91, 99–105, 128, 175, 178 failure to endorse, 12, 198, 206 n.2, 209 n.22 Boole’s logic, 13 Bostock, David, 210 n.35

232

Index

Brouwer, L. E. J., 7, 51, 72–3, 88–93, 96, 98, 104–5, 110, 112–13, 211 n.9

criterion of identity, 38–9, 41, 46–9, 51, 63, 116 Currie, Gregory, 206 n.2

Carl, Wolfgang, 207 n.6 Carnap, Rudolph, 187, 208 n.11, 216 n.6 Carruthers, Peter, 211 n.12 causal theory of reference, 167 Chomsky, Noam, 3–4, 22–3, 150–4, 158–60, 199, 206 n.3, 208 n.14, 214 n.1 classical logic, 6, 23, 25, 90–1, 104, 111, 142, 208 n.18 cognitive science, 178–9, 192, 199 colour, 10–11, 80–2, 109, 181, 192–3, 215 n.1 communication, 16, 21, 59, 66, 70, 92–3, 141, 160–2, 164–71, 173, 190–1 communication-intention theorists, 158–9 comprehension axiom, 47 concepts, 3, 14–15, 31–3, 35, 41–2, 44, 46, 52, 57, 68–9, 73–85, 90, 108, 111, 127, 176, 182, 184–9, 191–4, 198–9, 204–5, 207 n.5, 208 n.11, 210 nn.36, 37 conditional counterfactual or subjunctive, 9, 30, 117–24, 127, 131–2, 203 intuitionist meaning of, 95 conditional assertion, 27 conditional bet, 26 conjunction, 95, 100 conservative extension, 98–102 constructivism, 7, 36, 40, 51, 85, 87–95, 99–101, 128–30, 201, 212 n.7 convention, 152–4, 163–73, 181, 183, 193, 196–9 conventionalism, 64, 71–3, 211 n.8 context principle, 13, 27, 30–1, 34–6, 39–52, 209 n.24 course-of-values, 46

Davidson, Donald, 2–3, 17–19, 34, 54–5, 66, 129, 149, 151, 159– 71, 193, 195, 208 n.11, 209 n.23 definite descriptions, 2, 25–7, 114, 216 n.7 definition of number, 40–1 Dennett, Daniel, 156–7 Descartes, René, 37 Devitt, Michael, 105, 107 disjunction, 95 double negation, 58, 104 elimination of metaphysics, 2, 8, 11 elimination rule, 100, 104, 212 n.4 Evans, Gareth, 3, 187, 190, 192 ex falso quodlibet, 104 extension of a concept, 40, 46–8, 52, 208 n.11, 210 n.36 fatalism, 146 fictional existence, 112–17, 202 finitism, 65, 67–8, 73, 117, 124–7, 131, 211 n.10, 213 n.18 Fodor, Jerry, 159, 180–1, 198–9, 216 n.12 Føllesdal, Dagfin, 179, 190 force, 16–17, 19, 54–6, 149, 207 nn.7, 8 formalism, 78, 89 Frege, Gotlob, 1–3, 7, 12–20, 23, 27–52, 57–8, 63–4, 69–86, 89–93, 96, 98, 108–11, 116–17, 125, 131, 151, 157–8, 160, 173–94, 198, 204–5, 207 nn.2, 3, 5, 6, 208 nn.10, 11, 209 nn.22, 30, 31, 210 nn.33, 37, 213 n.12, 214 n.20, 215 nn.1, 5, 216 nn.7, 8, 9 Fregean functions, 14–15, 42, 46, 49–50, 74–5, 82–3, 111, 186–7

Index geometry, 91–2, 71–2, 211 n.9 Glock, Hans-Johann, 206 n.1 God, 93–4, 106, 112, 147, 197, 213 n.15 Gödel, Kurt, 33 Gödel’s theorem, 96–8, 212 nn.2, 3 Goodman, Nelson, 108, 111, 213 n.12, 214 n.2 grammar ideal, 54, 153–4 knowledge of, 22, 150–4, 163 logical, 14–15, 45–8 subject/predicate, 14, 56–7 universal, 22 Hacker P. M. S., 210 n.2 Hacking, Ian, 165–6 Heyting, Arend, 94–5, 107, 212 n.1 Hilbert, David, 88–9 holism, 7, 10, 54, 56, 63–7, 73, 87, 99–102, 145, 157 Horwich, Paul, 209 n.25 Husserl, Edmund, 78, 178–91, 194– 8, 204, 207 nn.6, 9, 215 nn.4, 5 idealism Hegelian, 36–7 moderate, 117–24, 131–2 subjective, 37, 82, 104–17, 127–8, 179–80, 203 identity statements, 16, 35, 40–1, 44, 46, 49, 184–6 idiolects, 22, 150–3, 155–6, 159–62, 169–71 implicit knowledge, 20–4, 149–53, 208 n.14 impredicative definition, 49–52 indefinitely extensible concept, 52, 97, 127, 210n indeterminacy of translation, 54, 58–9, 63–5, 157–8 infinity, 23, 30, 42, 51–2, 72–3, 91, 94, 119, 126–7, 131, 213 n.15 instrumentalism, 9, 213 n.19 intentional inexistence, 182–94

233

intentional stance, 155–7 intentionality, 60, 152–3, 182–3, 193–200 introduction rule, 99–100, 103–4, 212 n.12 intuition, 33, 37, 179, 197, 210 n.33 intuitionism, 3, 6–9, 11, 26–30, 39, 51–2, 67–8, 72, 85, 87–105, 107–8, 112, 115, 117–18, 126–32, 140, 177–8, 203, 212 n.2, 213 n.8 Joyce, James, 169 justification of deduction, 6, 19–20, 60–1, 63–5, 73, 85, 93, 98–104, 212 n.7 Kant, Immanuel, 207 n.2, 210 n.33, 215 n.2 Kantianism, 36–40, 88, 91–2, 177, 184 Kitcher, Paul, 39 Königsberg bridge theorem, 103 Kripke, Saul, 151, 208 n.12, 211 n.5 Kripke trees, 130 language and games, 27–9, 55, 57, 82 knowledge of, 15–24, 128–30, 149–75 learnability of, 55–6, 127, 145 social character of, 66, 150, 156, 160–2, 166, 173–5, 177–8 law of excluded middle, 26–7, 90–2, 95, 96, 103, 106, 112–15, 118–23, 128, 138, 144, 146–8, 202, 206 n.2 Leibniz, Gottfried, 177, 188 Lewis, David, 121–2 linguistic priority thesis, 1, 4, 42–3, 53–4, 56, 58, 69–71, 157–63, 167–71, 176–7, 181–3, 191–200 linguistic turn, 1–3, 176 Locke, John, 80–2, 187, 197–8, 204, 216 n.11

234

Index

logic intuitionist, 6, 8, 13, 23, 26, 51, 72, 94–5, 103–4, 115, 118, 130, 177, 198, 206 n.2, 208 n.18, 212 n.7 many valued, 26, 113–15, 121 predicate, 13–14, 44 tense, 121 two valued (classical), 6, 23, 25, 90–1, 102–4, 111, 113, 130, 142, 206 n.2 logical constants, 20, 60, 80, 82, 88, 94–5, 99–104, 118, 130, 198, 212 n.4 logical positivism, 2, 8–11 logicism, 13, 51–2, 85, 88–93, 131, 207 n.2 logico-linguistic method, 88–9 Lotze, Hermann, 36, 210 n.33 McDowell, John, 201, 211 n.3 McTaggart, J. M. E., 134–7, 140, 214 n.2 malapropism, 15, 155, 162–70, 214 n.4 manifestability constraint, 18, 27, 34, 53, 56–62, 69, 100–2, 108, 126–7, 129, 131, 140, 142, 149, 177–8, 182 Martin-Löf, Per, 100, 107–8 meaning and truth conditions, 3, 17–19, 24–5, 28, 87–8, 128–30, 139–40, 149–51 and use, 3, 53–5, 62–8, 71–3, 78–9, 84–5, 87, 92, 97–8, 101–4, 109, 134, 177–8, 182–3, 195–8, 209 n.25 first, 166–7 literal, 162–6, 169 molecular, 65 theory of, 3–8, 12–13, 15, 17–19, 21–3, 81–2, 87, 91, 96, 99, 105–7, 109–10, 112, 122, 128–30, 152, 158–60, 179, 182, 195, 200–3, 209 n.25, 211 n.3

meaning-theory, 18–19, 22, 24–5, 53–4, 149 Meinong’s jungle, 7, 114, 208 n.19 mentalism, 1, 67, 71, 89–90, 104, 109, 154, 158–60, 178–80, 214 n.1 metaphor, 15, 19, 162–4, 169, 207 n.8, 214 n.4 names see singular terms negation, 27, 58–9, 95, 104–5 negation free intuitionistic logic, 72, 103–4, 212 n.7 Nietzsche, Friedrich, 200 noema, 178–84, 189–91, 204 nominalism, 35, 43, 63, 108–11, 117 non-Euclidean geometry, 72, 91–2, 211 n.8 non-existent objects, 114, 184, 208 n.19, 211 n.12 no priority thesis, 170 normativity, 19–23, 70, 173 ontological commitment, 31–9, 44–5, 48 opaque contexts, 157, 167 ordinary language philosophy, 2–3 paradoxes intuitionist response to, 51–2, 96–8 set-theoretic (Russell’s) 2, 23, 47, 58, 207 n.6 Sorites, 68, 124–7 Peacocke, Christopher, 170, 211 n.6, 215 n.15 perception, 3, 11, 33, 88, 112, 170–1, 179–82, 193–9, 204, 215 n.7 phenomenalism, 2, 9–11, 141, 122–4, 213 n.19 phenomenology, 3–5, 176–200 Plato, 33, 140 Platonism, 1, 13, 30–9, 43, 49–52, 58, 74–5, 85, 90, 131, 209 nn.27, 31 possible content of judgement, 74–7, 83

Index Prawitz, Dag, 99, 103 predicate logic see logic, predicate predicates phenomenal, 11, 124–6 reference (semantic value) of, 14, 41, 44, 74–5, 81, 108–12, 130, 186, 208 n.11, 210 n.37 second order, 46, 208 n.11, 211 n.12 sense of, 74, 204 vague, 7, 68, 90, 124–6, 128 presupposition, 26, 88, 209 n.20 priority of language see linguistic priority thesis private language argument, 53–4, 56, 149 propositional functions, 83, 96, 215 n.3 proto-thought, 171, 181, 193–4, 198 psychologism, 5, 37, 53, 57–8, 60, 69–72, 78, 175 Putnam, Hilary, 22, 38–9, 151, 208 n.18, 212 n.3 Quine, Willard van Orman, 4, 7, 9, 31–2, 34–5, 44–5, 48, 53–6, 58–60, 63–5, 77–8, 93, 108, 111, 157, 213 n.12 rationalism, 37 realism and correspondence, 29 common sense, 7–8, 142 mathematical see Platonism naive, 9 reorientation towards, 6 semantic, 12, 30 sophisticated, 9 with regard to future, 145–8 with regard to past, 134–48, 174, 202, 214 n.2 with regard to time, 135–40, 214 n.2 Reck, Eric, 209 n.31 reductionism, 9–11, 62, 121

235

reference of proper names, 12–17, 35, 38, 41–3, 83, 114–16, 164, 174, 186–7, 204 of sentences, 14, 49, 76–9 robust notion of, 48–50, 116 theory of, 17, 149, 179, 208 n.11 Russell, Bertrand, 2, 26, 83, 88, 184–5, 204, 210 n.40 Russell’s paradox see paradoxes, set-theoretic sense and reference, 12–20, 22–3, 35–6, 38–50, 82–3, 113–14, 151, 182–92, 216 n.9 metalinguistic conception of, 186–7 of concept expressions, 14, 187, 204 of proper names, 14–16, 216 n.8 of sentences, 14, 75–7, 79–80, 84 relation of to concepts, 14, 69–71, 74–5, 194, 196–7, 204–5, 208 n.11, 215 n.3, 216 n.6 subjectivist conception of, 188–9 theory of, 17–19, 23–4, 50, 54–5, 140 sentences as primary see linguistic priority thesis singular terms, 14, 16, 19, 25–6, 35–6, 40–50, 113–15, 187, 202, 215 n.1 Sluga, Hans, 30, 36–40, 210 n.33 Sorites paradox see paradoxes, Sorites Stich, Stephen, 152–3, 156–7 stimulus meaning, 64 Strawson, Peter, 25–6, 88, 158, 208 n.19 strict finitism, 65, 67–8, 73, 117, 124–7, 131, 133 subjunctive conditionals see conditional, counterfactual or subjunctive

236

Index

systematicity of language, 56, 149, 163 Sundholm, Göran, 207 n.4

prior and passing (long-range and short-range), 151, 164–6 truth-value links, 135–40, 146

Tarski, Alfred, 17 Tennant, Neil, 212 n.7, 213 nn.18, 19 tertium non datur see law of excluded middle theory of descriptions, 2, 25–6, 83, 202, 215 n.3 theory of meaning see meaning, theory of time, 134–8, 140, 214 n.2 token reflexive expressions, 136–7 tone, 16–17, 19 truth constructivist, 87–8, 128–30 correspondence theory of, 29, 104, 118, 209 n.26 definition of, 17 redundancy theory of, 27–8 substantive theory of, 28–9, 87 timelessness of, 135–8, 140 truth-maker principle, 29, 106, 118–20, 213 n.17 truth theory as theory of meaning, 2–3, 17–21, 24–5, 27–8, 53, 67–8, 128–30, 149–51, 160–6, 171–5

undecidable sentences, 7, 29, 101–3, 119, 132–5, 138, 141, 143, 207 n.5 universals, 74–5, 110–11 unsaturated entities, 14, 44, 82, 84, 110–11, 208 n.11 vagueness, 7, 52, 68, 90, 97, 124–6, 128, 202 value-range, 46–51 verificationism, 2, 8–13, 24–5, 53, 59, 63–5, 94, 100, 103–4, 123–4, 140–5, 148, 209 n.26, 213 n.13 warranted assertibility, 24–5, 29, 87–8, 129–30 Weiner, Joan, 209 n.30, 210 n.32 Wittgenstein, Ludwig, 2–3, 7, 18, 27, 43, 55–9, 64, 66–73, 78–85, 86–7, 90, 92–3, 95–6, 98, 101–3, 108–9, 124, 129, 149, 160, 172–8, 183, 190, 194–5, 198, 200, 209 nn.23, 24, 210 nn.1, 2, 211 nn.5, 9, 10, 12 Wright, Crispin, 43–7, 105–6, 126–7, 208 n.18, 209 n.27, 212 n.3, 215 n.1 Wrigley, Michael, 72