Truth [Course Book ed.] 9781400838691

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Truth

P RI NC ETON FOuNdaTIONs OF CON T E MP ORaRY PhIlOsOPhY

Scott Soames, Series Editor Philosophical Logic by John P. Burgess Philosophy of Language by Scott Soames Philosophy of Law by Andrei Marmor

trUtH Alexis G. Burgess & John P. Burgess

P r i n c eto n U n i v e r S i ty P r eS S P r i n c eto n A n d ox fo r d

Copyright © 2011 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved Library of Congress Cataloging-in-Publication Data Burgess, Alexis, 1980–  Truth / Alexis G. Burgess and John P. Burgess.    p. cm. — (Princeton foundations of contemporary philosophy)  Includes bibliographical references and index.  ISBN 978-0-691-14401-6 (hardcover : alk. paper) 1. Truth. I. Burgess, John P., 1948– II. Title.  BD171.B85 2010  121—dc22 2010041439 British Library Cataloging-­in-­Publication Data is available This book has been composed in Archer and Minion Pro Printed on acid-­free paper. ∞ Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

To Anna and Aigli

Contents

Starred (*) technical sections optional Preface Acknowledgments

xi xiii

CHAPTER ONE Introduction 1.1 Traditional Theories 1.2 Contemporary Theories 1.3 Paradoxes 1.4 Plan 1.5 Sentences 1.6 Propositions

1 2 4 5 7 10 12

CHAPTER TWO Tarski 2.1 “Semantic” Truth 2.2 Object Language vs Metalanguage 2.3 Recursive Definition 2.4* Direct Definition 2.5* Self-­Reference 2.6* Model Theory

16 16 18 22 24 28 29

CHAPTER THREE Deflationism 3.1 Redundancy 3.2 Other Radical Theories 3.3 Disquotation 3.4 Other Moderate Theories 3.5 Sloganeering 3.6 Reference

33 34 38 41 44 47 49

Contents

viii

CHAPTER FOUR Indeterminacy 4.1 Presupposition 4.2 Vagueness 4.3 Denial, Disqualification, Deviance 4.4 Doublespeak, Dependency, Defeatism 4.5 Relativity 4.6 Local vs Global

52 53 54 55 59 61 65

CHAPTER FIVE Realism 5.1 Realism vs Deflationism 5.2 Correspondence Theories 5.3 Truthmaker Theories 5.4 Physicalism 5.5 Utility 5.6 Normativity

68 68 70 72 74 77 79

CHAPTER SIX Antirealism 6.1 Meaning and Truth 6.2 Davidsonianism 6.3 Dummettianism vs Davidsonianism 6.4 Dummettianism vs Deflationism 6.5 Holism 6.6 Pluralism

83 84 87 90 93 96 97

CHAPTER SEVEN Kripke 7.1 Kripke vs Tarski 7.2 The Minimum Fixed Point 7.3 Ungroundedness 7.4* The Transfinite Construction 7.5* Revision 7.6* Axiomatics

102 103 105 107 109 112 113

CHAPTER EIGHT Insolubility? 8.1 Paradoxical Reasoning 8.2 “Revenge”

116 116 118

Contents



8.3 8.4 8.5 8.6

Logical “Solutions” “Paraconsistency” Contextualist “Solutions” Inconsistency Theories

Further Reading Bibliography Index

120 123 124 127 135 143 153

ix

Preface

This volume is, in accordance with the aims of the series in which it appears, a somewhat opinionated introductory survey of its subject, at a level suitable for advanced undergraduate or beginning graduate students of philosophy, or the general reader with some philosophical background. The subject is truth, and more specifically, what it is for something to be true, with special emphasis on the question whether there is anything interesting all truths have in common, besides their all being true. We set aside the postmodernist answer, “All truths are enforced by the hegemonic structures of society,” on the grounds that it confuses something’s passing for true in a given society with its actually being true, overlooking the question, “What is something that passes for true in a given society passing for?” Questions about what passes for true but isn’t, and how it is able to do so, are needless to say of great importance, but writers addressing them have not been lacking. We also leave to others the question of “the value of truth,” at least insofar as it is a question of intrinsic value, not just practical utility. The important issues that have been extensively discussed under this heading seem to us really about the intrinsic value, not so much of truth itself, as of something else related to it: of discovering the truth, or of speaking the truth. That one should value knowledge and honesty, rather than contenting oneself with what Harry Frankfurt calls bullshit, we take for granted without comment, and we take for granted that the reader takes it for granted, too. The issues about truth that remain, the ones we do address, have in recent years been made the subject of dozens of monographs and anthologies, as well as scores of journal articles not yet anthologized. Any survey of this large volume of material will inevitably give more attention to some parts of it than others, with more than a few subtopics getting merely a passing mention (plus references to further literature for the interested reader). Though other authors would doubtless make different judgments about

Preface

xii

what to emphasize and what not, we do not consider our judgment to be at all eccentric. We do give especially detailed attention to the pros and cons of so-­called deflationism, and its claim that there is nothing interesting all truths have in common; but then it is hard to think of an issue that has been more intensively debated in the recent specialist literature on truth. Though not eccentric, our emphases are not entirely conventional, either. Though for expository purposes we first treat the question of the nature of truth in isolation from consideration of such paradoxical utterances as “What I am now saying is false,” our real opinion is that the two topics are inseparable. One can go a long way toward the goal of an adequate theory of truth while ignoring the bearing of the paradoxes, but not all the way, and so we have devoted our last two chapters to the paradoxes and attempted solutions. The least conventional aspect of our choice of topics is perhaps our giving attention to a position often treated as unmentionable, the defeatist view that the paradoxes admit no solution. The paradoxes nonetheless remain for us a subordinate issue. The literature on them fairly quickly gets involved in technicalities, but our discussion goes only as far as is possible without requiring any deep knowledge of technical notions. Moreover, the more technical parts of the material we do include have been placed in sections starred as optional reading, whose omission should not seriously impede understanding of the remainder of the book. About the division of labor in producing this volume the following may be said. We have drawn on previous work by both of us, especially AGB’s doctoral dissertation on fictionalism about truth and public lectures of JPB on Tarski and Kripke. We began with a literature search, making a list of topics needing coverage, with AGB and JPB taking responsibility for the more philosophical and the more technical material, respectively. AGB then undertook extensive drafting, and JPB intensive rewriting to condense to fit the publisher’s word limits. As a result of this way of working, JPB is mainly to be blamed for any faults in the condensed style, though AGB did undertake a final editing. In matters of substance rather than style, we stand together.

Acknowledgments

Thanks to Scott Soames, for organizing the present series and inviting us to contribute to it. Thanks as well to the staff at Princeton University Press, especially Ian Malcolm, Heath Renfroe, and Leslie Grundfest; to our copyeditor, Jodi Beder; and to the two readers who provided comments on the manuscript.

chapter one

Introduction

Inquiry, it is said, aims at the truth. Yet it’s doubtful there is any such thing as the truth. So it might be better to say that inquiry aims at truths, and better still to say that different inquiries from archeology to zoology aim at different truths from archeological to zoological. Such inquiries have had many successes, but in many cases inquiries are still underway, and success has not yet been achieved. Thus some truths are known, others unknown. But what, if anything, do the different truths, known and unknown, about different topics have in common, to make them all truths? If we knew the answer to this question we’d at least have a better understanding of the nature of inquiry, and perhaps even a better chance of finding what we’re looking for when we inquire. But with so many kinds of truths, the project of coming up with a unified conception of what truths are might seem hopeless. Perhaps that is why other inquiries leave it to philosophy. This little book is about recent philosophical inquiries into what it is for a thing to be true. There are other philosophical questions about truth—Is truth of value in itself or only as a means to other ends? How much sense can be made of the idea of one untruth’s being closer to truth than another?—but there are so many such questions that it would take a book longer than this even just to introduce them all. The question on which we focus—“What is it for a thing to be true?”—has a certain priority simply because some sort of answer to it has to be presupposed by any serious attempt to answer almost any of the others.

Chapter One 1 .1  Traditional

Theories

If the best-­known saying about truth is Pilate’s question, “What is truth?” (John 18:38), probably the best-­known saying about truth by a philosopher is Aristotle’s assertion (Metaphysics, 1011b25): (1) To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true. This saying, like others of Aristotle’s, has been interpreted in more than one way; and it is not the only thing Aristotle said about truth, either. The definition modern philosophy inherited from medieval Aristotelianism ran along the following lines: (2)  Truth is agreement of thought with its object.

2

Most early modern philosophers from Descartes to Kant professed to accept something like (2) as a definition of truth. Some, however, even as they did so, complained, in a terminology itself inherited from medieval Aristotelianism, that (2) was only a “nominal” definition, revealing the meaning of the word “truth,” and not a “real” definition, revealing the essence of the thing, Truth. The supposed contrast between real and nominal definition was in deep disrepute through much of the last century, but in recent decades its reputation has recovered somewhat, and we will see in later chapters that there is a fundamental division today among writers on truth over the question whether, once it has been explained what it means to call something true, there remain any further questions about what it is to be true. Be that as it may, (2) was as diversely interpreted as it was widely endorsed. By a century or so ago at least three interpretations had emerged, differing over the location of the objects of thought—in an external world, in the mind along with thought itself, or in the interaction between the two—and therewith over the nature of agreement. In surveys of philosophical thought about truth one typically encounters early on a list of “theories” of truth represented by slogans loosely based on things that were said in a three-­cornered debate over truth about a century ago, in which the realist insurgent Bertrand Russell attacked the

Introduction

dominant British idealism and American pragmatism of the day, as represented by the now-­forgotten H. H. Joachim and the ever-­ famous William James. The slogans are biconditional in form, involving “if and only if ” (henceforth abbreviated “iff ”). They read as follows: (3) Realist or correspondence theory: A belief is true iff it corresponds to reality. (4) Idealist or coherence theory: A belief is true iff it coheres with other ideas. (5) Pragmatist or utility theory: A belief is true iff it is useful in practice. By bringing in the notions of reality and idea and practice, whose homes are metaphysics and epistemology and ethics, such views tend to suggest truth is a metaphysical or epistemological or ethical notion. Both (4) and (5) invite immediate objections: May not a paranoid’s delusions of persecution be frighteningly coherent? May not a patient’s faith that a mere placebo is a wonder drug be therapeutically useful? Russell was quick to claim in opposition to Joachim that multiple systems of beliefs may be internally consistent, though incompatible with each other. Nietzsche had already suggested well before James that false beliefs may be not merely useful but indispensable for life. These objections are so obvious that the reader will likely guess that Joachim and James must have held more interesting views than a simplistic reading of the coherence and utility slogans would suggest. Indeed, idealists understood that multiple belief systems, including crazy ones, might be classifiable as coherent if one meant by coherence just bare logical consistency; but they meant something more. Likewise, pragmatists recognized that there might be counterexamples to the principle of the utility of truth if one understood it as a purported exceptionless universal law; but they understood it as something less. Both groups also made cogent criticisms of crude “copy” versions of the correspondence theory. And the coherence and utility views put two questions on the agenda for any inquiry into the nature of truth: to explain why

3

Chapter One

consistency is at least a necessary condition for truth, and why, as a general rule subject to particular exceptions, true beliefs tend to be more useful than false ones. Still, Joachim leaves quite obscure what beyond mere consistency is required for a system of beliefs to constitute a “significant whole,” and thus be coherent in his sense; and James does not satisfactorily explain how utility, or any feature that only claimed to hold “in the long run and for the most part,” could be definitive of truth. 1 .2

4

 Contemporary Theories

Any historical treatment of our subject would have a great deal more to say about the figures already mentioned and several others. Gottlob Frege, the great precursor of the analytic tradition in philosophy, held that truth could not be defined as correspondence or in any other way. G. E. Moore, cofounder with Russell of that tradition, held like Russell that truth is correspondence, and unlike Russell that correspondence is unanalyzable. C. S. Peirce, the philosopher and logician from whom James took the word “pragmatism,” defined truth roughly as what would come to be believed if inquiry were pursued to its ideal limit; John Dewey, a younger pragmatist whom James frequently cited, eventually concluded that one should simply avoid talk of truth in favor of talk of “warranted assertability.” This book, however, in accordance with the aims of the series in which it appears, must be concerned mainly with the status of the question among philosophers in the analytic tradition in the early twenty-­first century, and so, after taking note of the debates of the first years of the twentieth, must leave those earlier debates behind. Henceforth the coherence and utility theories will be mentioned only as occasional foils for views having a significant number of present-­day defenders. But note the plural: “views having a significant number of present-­day defenders.” The analytic tradition has become the mainstream in Anglophone philosophy, wholly supplanting idealism and largely absorbing pragmatism, but in achieving this

Introduction

status it has ceased to represent, if it ever did, a uniform doctrine. Its founders’ realist or correspondence view of truth is by no means universally accepted, and the reader should not infer from our indication that (4) and (5) are no longer widely defended that there is now a consensus in favor of (3). The problem with (3) is not that what it tells us seems obviously wrong, as with (4) or (5), but rather that it tells us so very little, pending specification of what its key terms (“reality” and “correspondence”) are supposed to mean, and that every attempt to say something more specific has proved highly contentious. The rival theories that attract philosophers today are not, however, those that attracted philosophers a century ago. Today the kind of idealism that predominated a century ago is dead, its heir being an idealism that dares not speak its name, and calls itself “antirealism.” Antirealism holds a distinctive view of the nature of truth, but it resembles the traditional idealist Joachim’s view less than it resembles Peirce’s. Pragmatism survives, but some of its most noted recent adherents have been, like many nonpragmatists, attracted to a view of the nature of truth, called deflationism, that attributes no interesting common property to all truths. In this respect deflationism is unlike the view of James; it derives, rather, from F. P. Ramsey, the most talented British philosopher of the generation after Russell and Moore. So in place of the traditional three-­cornered realist-­idealist-­ pragmatist debate, one has today a three-­cornered realist-­ antirealist-­deflationist debate, complicated by each of the three positions coming in several variant versions and by the presence also of several less popular views on the scene. That debate will be the primary topic of this book. 1 .3  Paradoxes

Russell’s work in logic became very influential among philosophers in the decades following the First World War, especially among the logical positivists, the dominant school of the period. But many positivists’ views on truth were less like Russell’s than like Dewey’s, in that they tended to hold that the concept of truth

5

Chapter One

6

has no role to play in a scientifically oriented philosophy. Ironically, one of Russell’s own discoveries contributed to the spread of this tendency, which was also found among logicians and mathematicians. In the background was a crisis in the then-­novel branch of mathematics known as set theory, where antinomies or paradoxes had emerged. Some of these (Burali-­Forti’s, Cantor’s) were quite technical, but Russell discovered one that is easily stated. Consider the set R of all sets that are not elements of themselves. Then R is an element of R, which is to say, is one of the sets that is not an element of itself, iff R is not an element of R—a contradiction! Russell’s paradox reminded many of a fact long known but little cited in the realist-­idealist-­pragmatist debate, that the notion of truth, too, is subject to paradoxes. In particular it reminded many of a paradox attributed to ­Aristotle’s contemporary Eubulides, called the pseudomenos or liar. Suppose I say, “What I am now saying is not true.” Then it seems that what I am saying is true iff what I am saying is not true—another contradiction! Medieval logicians had added similar examples, under the label insolubles: Suppose Socrates says, “What Plato is saying is true,” while Plato says, “What Socrates is saying is false.” Modern mathematicians and logicians and philosophers now added more examples, finding that truth is but one of a family of related notions, all of which involve what seem to be similar contradictions. One member of this family of notions—called alethic, from the Greek for “truth”—is that of a predicate or an adjective being true of something. This notion gives rise to an exact parallel to Russell’s paradox of the set of all sets that are not elements of themselves, namely, Grelling’s paradox of the adjective that is true of all adjectives that are not true of themselves. “English” is English, “short” is short, and “polysyllabic” is polysyllabic. Hence these three are autological or true of themselves. By contrast, “French” is not French, “long” is not long, and “monosyllabic” is not monosyllabic. So these three are heterological, or not true of themselves. What about “heterological”? Another member of the family of alethic notions is that of definability, where an object is definable iff it is the one and only

Introduction

thing of which some predicate is true. This notion likewise gives rise to several paradoxes, of which Berry’s, the easiest to state, goes somewhat as follows: “The smallest natural number not definable in English in twenty-­six syllables or fewer” defines a natural number in English in twenty-­six syllables. Other definability paradoxes (Richard’s, König’s) were more technical, and became entangled with debates over the status of set theory. Many mathematicians were only too happy to join those philosophers who classed alethic notions as unacceptably “psychological” if not damnably “metaphysical” in character. However, one important mathematician and logician, Alfred Tarski, and following him quite a few philosophers, attempted to rehabilitate the notion of truth by “solving” or “resolving” or “dissolving” or at least blocking the paradoxes. Debate over the solution (or insolubility) of the paradoxes and debate over the nature (or lack of nature) of truth proceeded separately over most of the last century, but it has become increasingly clear in recent years that the two questions cannot really be kept apart. (For instance, some think deflationism makes it harder, while others think it makes it easier, to deal with the paradoxes.) Accordingly, the paradoxes will be a secondary topic of this book. 1 .4  Plan

It is with Tarski, probably still today the writer most often cited in discussions of truth by philosophers in the analytic tradition, that we begin our survey of theories of truth. To accommodate readers differing in their degree of background and interest in technical matters, we divide our account of Tarski’s work in two. The first half of chapter 2 gives a nontechnical account of the most often discussed aspects of Tarski’s views, which should be enough to enable the reader to follow allusions to those views later in the book. More technical material is confined to the starred sections making up the second half of the chapter, which readers who so choose may postpone or omit. We then turn to the deflationism-­realism-­antirealism debates, taking deflationism first. Tarski gave a central role in the theory of

7

Chapter One

8

truth to the principle that saying something and saying it is true are equivalent. Common to all forms of deflationism is the claim that, roughly speaking, this equivalence principle is all there is to the theory of truth. Chapter 3 is devoted to the exposition of various deflationistic positions from Ramsey’s time to the present; a half-­dozen variants, some more radical, some more moderate, are described. The present authors are sympathetic to the general idea behind deflationism, but not fully satisfied with any of the existing versions. It is our dissatisfaction with existing versions that will be most evident in this chapter, while our sympathy with the general idea will become more evident when we turn in later chapters to deflationism’s “inflationist” (realist and antirealist) rivals and critics. One popular objection to the equivalence principle, and hence to any theory of truth, such as deflationism, that embraces it, goes as follows. If you have never practiced cannibalism, then neither “Yes” nor “No” is an appropriate answer to “Have you stopped eating people?” since the question seems to presuppose that you at least used to eat people. This suggests that “You have stopped eating people” is neither true nor false. But if it is not true (as well as not false), then to say that it is true is to say of what is not that it is, which is false, and we have a case where saying something is not equivalent to saying that it is true, because the latter is false while the former is not false (though not true, either). Similar purported counterexamples turn on the phenomena of vagueness and relativity, which we lump together with presupposition in chapter 4 under the bland label “indeterminacy.” We survey various lines of defense deflationists have taken against purported indeterminacy counterexamples, without pretending to achieve a full resolution of the issues. Paradoxical examples like the liar are often viewed as further cases of indeterminacy, and the discussion of presupposition and vagueness is in some respects a warm-­up for tackling the paradoxes later in the book, though it will be seen when we come to them that the paradoxes involve an additional twist. Chapter 5 is devoted to views we classify as “realist,” namely, views taking truth to involve standing in some appropriate relation to some portion(s) or aspect(s) of reality. Russell and Moore were realists about truth in this sense at key stages in their careers,

Introduction

though each changed his mind about truth more than once—our attaching just one view to Russell’s name in §1.1 and to Moore’s in §1.2 was a caricature—and though their versions of realism were distinct and incompatible. Among the heirs of Russell and Moore there is even more disagreement than there was between those pioneers themselves. There is disagreement both over the nature of the “appropriate relation” involved (which some do and some don’t call “correspondence”) and over the “portion(s) or aspect(s)” of reality involved (which some do and some don’t call “truthmakers”). Moreover, there is a division between those satisfied with a fairly abstract and metaphysical account of these matters, and those who see a need for a more concrete and physical account. Along with the different realist views we consider also a realist objection to deflationism alleging that the latter cannot explain why true beliefs are useful, and an objection to realism and deflationism alike alleging that the notion of truth has an evaluative role that both groups wrongly neglect. Chapter 6 is devoted mainly to those who call themselves “antirealists.” They reject both deflationism and what we call “realism,” though they do not much discuss either. What they do discuss at length, and most emphatically reject, is something else that they call “realism,” which amounts to what others call truth-­ conditional semantics, to which they oppose something called verification-­conditional semantics. (Explaining the tangled usages of “realism” will be one of our tasks in this chapter.) Along with antirealism we take note in the same chapter of a more recent position, pluralism, which holds that a realist view of truth may be more appropriate for some “domains of discourse” and an antirealist for others. The discussion of pluralism concludes our survey of contemporary theories of the nature of truth, insofar as those can be discussed without bringing in issues about the paradoxes. We begin our examination of views on liar-­style paradoxes in chapter 7, with an account of the work of Saul Kripke, whose “Outline of a Theory of Truth” (1975) has probably been the most influential work on its topic since Tarski’s “The Concept of Truth in Formalized Languages” (1935). Our Kripke chapter is organized like our Tarski chapter, with a nontechnical account, containing what is needed to follow discussions in our next and final chapter,

9

Chapter One

coming in the first half, followed in the second half by sections starred as optional reading, containing more technical material. Tarski held that it is impossible to avoid paradox unless one distinguishes the language for which one is formulating a theory of truth from the language in which one is formulating that theory. Kripke in the end seems to concede, however reluctantly, that he has been unable to avoid something like Tarski’s split or the “ghost” of it. It is on this point that several subsequent writers have sought to improve on Tarski and Kripke alike. Several proposals are considered in chapter 8, especially views advocating deviation from classical logic and views emphasizing the role of context in communication. Also considered is the defeatist view that no proposed solution to the paradoxes can ever be wholly successful, because the intuitive notion of truth ultimately is simply incoherent. Finally, a connection between this issue of the solvability or unsolvability of the paradoxes and the issues between deflationism and inflationism is briefly sketched. The book then ends, not with a final verdict on the issues, but with suggestions for further reading. Before launching into our survey we must address a question that we have sidestepped so far, but can hardly hope to continue evading when we get down to closer consideration of the views of specific authors. The question is this: What kinds or sorts of things or items are true, or as is said, are bearers of truth? Presumably the same kinds of things are false as are true, so what we are really asking is: What kinds of things bear truth or falsehood, or as is said, bear truth values? Or if (as is surely the case) more than one kind of thing can do so, which are the fundamental truthbearers? An early confrontation with this question is unavoidable, since the writers whose work we survey often have quite strong opinions on the matter, so that the position adopted on it can affect the whole character of an author’s account of truth. 1 .5  Sentences

10

One answer quickly suggests itself. Some truths have been written down. (The preceding remark provides an example.) Other truths

Introduction

have only been spoken. (Readers will have to provide their own examples.) When truths are written or spoken it is sentences that are written or spoken, and so it may seem that it is sentences that are the truths, the bearers of truth. The same conclusion can also be reached in a different way. Consider the following dialogue: (6) X:  Where there’s a will, there’s a won’t. Y:  That’s true. Z:  What’s true? I didn’t hear. Y may answer Z with a direct quotation, thus: (7)  Y: X said, “Where there’s a will there’s a won’t,” and that’s true. It seems that the quotation of a sentence designates a sentence, the one quoted. If so, it seems to be a sentence that Y is calling true in (6). But what are sentences? The distinctions that have to be made in response to this question, though they may at first seem pedantic, have proved fundamental to the study of language. Sticking with speech rather than writing for the moment, suppose each of ten greeters on a reception line says successively to each of ten guests, “I’m glad to see you.” Is that a hundred sentences or one sentence a hundred times? The usual answer is that it is one sentence type and a hundred sentence tokens. Does our language have one sentence type “The post office is near the bank” with two meanings, or two with the same pronunciation? Using Greek-­derived words for pronunciation and meaning, we may say there is one phonological type but two semantic types. A phonological type is a sound pattern, a semantic type a sound pattern plus a meaning. Once made, the distinction phonological vs semantic can be seen to apply to tokens as well: Producing a phonological token amounts to emitting sounds, as both parrots and people can do, but only the people and not the parrots can thereby speak meaningfully, which is what producing a semantic token amounts to. Writing (or recorded as opposed to live speech) complicates the story. If the greeters have laryngitis and each greeter writes on a card, “I’m glad to see you,” and successively shows it to each

11

Chapter One

guest, then there is one type, ten inscriptions of the type, and one hundred presentations of the inscriptions to a potential reader. Usually the word “token” is used with writing for what there are ten of, but to maintain parallelism with speech it might better be used for what there are one hundred of. As with speech one distinguishes phonological from semantic, so with writing one must distinguish orthographic from semantic, since two meanings may share a spelling. Ambiguity can prevent an orthographic or phonological type from having a fixed truth value: “A bank is an especially dangerous place to be during a flood” is true if riverbanks are meant but false if moneybanks are meant. An even more common phenomenon than ambiguity is so-­called indexicality, the kind of dependence on features of context (such as who is speaking to whom) that is signaled by what are called indexicals (such as “I” and “you”). It can prevent even a semantic type from having a fixed truth value: “I’m glad to see you” is true when said by a greeter sincerely glad to see the guest, and false when said by one merely being polite. In general, a sentence can be the bearer of a fixed truth value only if we understand “sentence” in the sense of semantic token. Where indexicality is absent, and any possible semantic token would have the same truth value, there will be no harm if we say that the semantic type has that truth value in a secondary sense, and if ambiguity is absent as well, that the orthographic or phonological type has that truth value in a tertiary sense. Thus some types may be recognized as derivative truthbearers even if semantic tokens are recognized as the primary truthbearers. There is, however, a rival proposal. 1 .6  Propositions

Returning to the dialogue (6), Y may answer Z with an indirect rather than a direct quotation, thus:

12

(7)  Y: X said that where there’s a will there’s a won’t, and that’s true.

Introduction

What is called a that-­clause, the word “that” with a sentence coming after it, is often held to designate a proposition, the proposition expressed by that sentence. If so, it is a proposition that Y is calling true in (7), and that we are calling true when we use the form of expression “That     is true” or its stylistic variant “It is true that     .” Many take propositions to be the primary bearers of truth, with sentences being called “true” only in a derivative sense, a sentence being true if it expresses a true proposition. According to this propositionalist view, what we took earlier to be reasons for giving first place to semantic sentence tokens as bearers of truth are better taken as reasons for giving them first place as ­expressers of propositions (but only second place, after propositions, as bearers of truth). Some proponents of the rival sententialist view, while still insisting on sentences as the primary truthbearers, allow that a proposition may be called true in a derivative sense if it is or could be expressed by a true sentence. Many sententialists, however, are suspicious of the whole idea of propositions, not least on account of the frequency of disagreements about them among propositionalists themselves. Propositionalists generally agree that, just as different tokens of the same sentence type may express different propositions, so inversely the same proposition may be expressed by tokens of different sentence types. If Jack says to Jill, “I am younger than you are,” and Jill says back to Jack, “You are younger than I am,” they have expressed the same proposition, that he is younger than she is. Similarly if Jack says to Jill in English, “I love you,” and then in French «Je t’aime.» But here agreement ends. A sentence like “Jack fell down” has a certain grammatical structure. Does the proposition it expresses have a structure as well? One of us may say “Jack loves Jill,” calling them by name, and another of us, “He loves her,” pointing first to the one, then to the other. Have we expressed the same proposition? To each question, some say yes and some say no. And then there are embarrassing questions asked by linguists. If “that the earth moves” designates the same thing that “the proposition that the earth moves” denotes, why is it that we can say

13

Chapter One

(8a) Copernicus hypothesized that the earth moves, while the Inquisition anathematized the proposition that the earth moves. but not (8b) Copernicus hypothesized the proposition that the earth moves, while the Inquisition anathematized that the earth moves.

14

(Evidently designating a proposition by a that-­clause is not quite the same as denoting one by a noun phrase beginning with “the proposition that.”) But despite doubts and difficulties, it seems that propositionalists outnumber sententialists. It also seems that, though many other kinds of things are spoken of as true and false—from assertions and beliefs and conjectures and declarations to remarks and statements and thoughts and utterances—there are at present no serious candidates for the role of fundamental truthbearers beyond propositions and sentences (the latter in the sense of semantic tokens). In particular, while the traditional theories (3)–(5) were formulated in terms of beliefs, few today regard beliefs as the primary bearers of truth and falsehood, for the following sort of reason, among others: It is possible to believe a disjunction (for instance, that it was either Professor Plum or Colonel Mustard who killed Mr. Boddy) without believing either disjunct, and such a belief may be true; but a disjunction cannot be true unless one disjunct is; so there must be truths that are not believed. Similar considerations apply to assertions. In any case, the very notions of “assertion” and “belief ” are ambiguous, since we must distinguish the act or state or event or process or whatever of asserting or believing from the content thereof, from what is asserted or believed. The most common view today seems to be that the content is a proposition, and that if the act or state or event or process can be called “true” at all, it is only in a derivative sense. Items of yet other sorts are also spoken of as true or false. One speaks, for instance, of false teeth or false friends. But here we are clearly dealing with different senses of the key words “true” and “false,” roughly synonymous with “genuine” and “fake,” as can be

Introduction

seen from the fact that while a false sentence or proposition is as much a sentence or proposition as a true one, false teeth or friends are no teeth or friends at all. (What is false about them is the proposition that they are teeth or friends.) In sum, other truthbearers beyond sentences and propositions can be and will be more or less ignored for the remainder of this book. But the division between sententialists and propositionalists, which cuts across the division of theorists into realists and antirealists and deflationists, must be borne in mind as we turn to the examination of the views of particular authors, beginning with Tarski.

15

chapter two

Tarski

Tarski was, by his own account, primarily a mathematician, though also “perhaps a philosopher of a sort.” He foresaw important applications for a notion of truth in mathematics, but also saw that mathematicians were suspicious of that notion, and rightly so given the state of understanding of it circa 1930. In a series of papers in Polish, German, French, and English from the 1930s on he attempted to rehabilitate the notion for use in mathematics, and his efforts had by the 1950s resulted in the creation of a branch of mathematical logic known as model theory. This fact alone makes Tarski’s work an enduring achievement, even if its philosophical bearing remains in dispute. What follows is a simplified account (telescoping earlier and later developments) of the most basic features of Tarski’s influential work. 2 .1  “Semantic”

Truth

Tarski held that almost all words of ordinary language, “true” included, are ambiguous, and his first task was to distinguish the sense of “true” that concerned him, and to give it a label. To give a somewhat facetious example, a follower of Williams James might hold that “Snow is white” is true on the grounds that it is useful for people to believe so, while a follower of William Jennings Bryan might hold that “Snow is white” is true on the grounds that the Bible often uses the phrase “white as snow.” Tarski considered himself a follower of Aristotle, because he held that “Snow is white” is true on the grounds that snow is white (and that “to say of what is that it is, is true”).

Tarski

He gave his notion of truth the label “semantic” truth, which could mislead readers familiar only with the present-­day usage of “semantics” for the branch of linguistics concerned with meaning. Tarski was following a usage current among positivistically inclined philosophers in the 1930s, on which “semantic” was one of a trio of terms. A notion was called syntactic if it pertains to relations among words, semantic if it pertains to relations between words and things, and pragmatic if it pertains to relations among words and things and people. Thus a notion involving only words and compilations of words (such as the Bible) would count as syntactic, while a notion that brought in people (as believers, for instance) would count as pragmatic. By contrast, Tarski’s notion of truth was “semantic” simply because his principle (1)  “Snow is white” is true iff snow is white. involves words and a thing, snow, but not people. No more should be read into the “semantic” label than that. Anything of the same form as (1) is called a T‑biconditional. The general pattern (2)  “    ” is true iff     . where the same sentence goes into each blank, is called the T‑scheme. Tarski is famous for the emphasis he places on the T‑scheme, but against a background of classical logic, which Tarski assumes without question, the scheme is equivalent to a pair of rules, T‑introduction and T‑elimination: (3a)  from “    ” to infer “ ‘    ’ is true” (3b)  from “ ‘    ’ is true” to infer “    ” Tarski’s whole discussion could be recast in terms of these rules. Nonetheless we will stick to formulations in terms of the scheme in what follows. Another notion Tarski counted as “semantic” was that of the satisfaction of a condition by a thing or things. Parallel to (1) Tarski held, for instance, (4a)  “x is white” is satisfied by snow iff snow is white.

17

Chapter Two

(4b) “x is the same color as y” is satisfied by snow and milk iff snow is the same color as milk. Yet another notion Tarski counted as “semantic” was that of denotation, as illustrated by (5)  “snow” denotes snow. Tarski’s ambition was to rehabilitate for use in rigorous mathematics the whole list of what he called “semantic” notions. (Note, however that these are more or less what we called “alethic” notions in §1.3, and meaning is not on Tarski’s list, though it would be at the head of any list of “semantic” notions in present-­day linguistics.) 2 .2

18

 Object Language vs Metalanguage

Before going further we need to look at how quotation marks are being used in (1). The sequence of letters es, en, oh, double-­yu, and so on, is an orthographic type that is used in English to express the truth that snow is white, but that could be used in some other language to express the falsehood that grass is red. Setting aside complications owing to ambiguities within a single language, there are two ways we could acknowledge this fact in a reading of (1). One way would be to take the quotation marks with what they enclose to designate the semantic type consisting of the orthographic type together with its English meaning. The other way would be to take it to denote the orthographic type, but take “true” to be elliptical for “true in English.” The latter is Tarski’s way. For him quotation marks are used to designate orthographic types, and what he is concerned with under the label “truth” is truth-­in-­English, or truth-­in-­L for some other language L. Tarski calls the language L for which truth is being discussed the “object language,” and the language L* in which truth is being discussed the “metalanguage.” So far we have been writing as if both languages L and L* were just English. But Tarski insists that paradox will be inevitable if one takes both L and L* to be the whole of some natural language, including the word “true” itself. For then one can write down something like this:

Tarski

(6)  The sentence numbered (6) is not true. One then has (7a) The sentence numbered (6) is “The sentence numbered (6) is not true.” which together with the T‑biconditional (7b) “The sentence numbered (6) is not true” is true iff the sentence numbered (6) is not true. yields the contradiction (7c) The sentence numbered (6) is true iff the sentence numbered (6) is not true. If, however, one distinguishes the object language L from the metalanguage L*, and takes “true sentence of L” to belong only to the latter and not the former, then while one can still write down this: (6)  The sentence numbered (6) is not a true sentence of L. it will be only a sentence of L*, and there will be no paradox in the conclusion that it is neither a sentence of L that is true nor a sentence of L that is not, since it will not be a sentence of L at all. Thus for Tarski, though it is sentences of one language L that go into the blanks in (2), what results from filling the blanks is a sentence of another language L*. Three points should be noted about the relationship between L and L* as described so far. First, since for any instance of (2) the same sentence of L that is mentioned on the left side is used on the right side as a clause in a biconditional sentence of L*, the metalanguage must contain the object language. Second, in order to be able to mention sentences of L, the metalanguage must contain the device of quotation. Third, the metalanguage must contain something more besides, namely, the truth predicate “is true-­in-­L.” But the first two requirements can be relaxed. First, L* need not literally contain L, so long as one can translate L into L*. In subsequent mathematical applications of Tarski’s work, often L and L* are each a fragment of some natural

19

Chapter Two

language, today most often English, but with L being abbreviated and written in symbols rather than words, while L* is not. Thus items of nonlogical vocabulary that may be written “less than” or “perpendicular” in L* might be abbreviated to “