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Bivalence and the Challenge of Truth-Value Gaps

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Bivalence and the Challenge of Truth-Value Gaps BIVALENCE AND THE CHALLENGE OF TRUTH-VALUE GAPS By Maria Teresa Matos Ferreira Marques Philosophy Department, University of Stirling Thesis submitted for the degree of Doctor of Philosophy at the University of Stirling November 2003 THE UNIVERSITY OF STIRLING Philosophy Department Maria Teresa Matos Ferreira Marques Bivalence and the Challenge of Truth-value Gaps Thesis submitted for the degree of PhD November 2003 ABSTRACT This thesis is concerned with the challenge truth-value gaps pose to the principle of bivalence. The central question addressed is: are truth-value gaps counterexamples to bivalence and is the supposition of counterexamples coherent? My aim is to examine putative cases of truth-value gaps against an argument by Timothy Williamson, which shows that the supposition of counterexamples to bivalence is contradictory. The upshot of his argument is that either problematic utterances say nothing, or they cannot be neither true nor false. I start by identifying truth-bearers: an utterance, for instance, is a truth-bearer if it says that something is the case. Truth-bearers are evaluable items, with truth- and falsity- conditions statable in corresponding instances of schemas for truth and falsehood. A genuine case of a truth-value gap should be an utterance that is neither true nor false but says something to be the case. But it is inconsistent to accept the schemas for truth and falsehood and the existence of genuine cases of truth-value gaps. Secondly, I expound Williamson’s argument, which explores this inconsistency, and I identify two kinds of strategy to disarm his argument: those that preserve the schemas for truth and falsehood, and those that do not. Neither strategy is found to be persuasive. Thirdly, I argue that cases of reference failure causing truth-value gaps illustrate the upshot of Williamson’s argument. Fourthly, I examine Scott Soames’s account of liar sentences as counterexamples to bivalence. Soames adopts a strategy of the first kind to avoid contradictions. I argue that his solution allows some contradictions to be true, and that he fails to show that liar sentences are truth-bearers. Finally, I examine Charles Travis’s case for isostheneia: an equal balancing of reasons to evaluate a statement as true or as false, in which case a statement is neither. Travis avoids contradictions by adopting a strategy of the second kind. I argue that the schemas for truth and falsehood are immune to Travis’s objections, and that isostheneia fails to identify evaluable items. The cases examined confirm that utterances that are neither true nor false say nothing. My claim is thus that truth-value gaps are not counterexamples to bivalence. ii CONTENTS ABSTRACT.................................................................................................................................. ii CONTENTS................................................................................................................................. iii ACKNOWLEDGMENTS........................................................................................................... vi INTRODUCTION .........................................................................................................................1 Chapter 1 Truth-bearers, truth and falsehood, and truth-value gaps ............................................8 1.1 Introduction......................................................................................................................8 1.2 Truth-bearers..................................................................................................................10 1.2.1 Sentences ..............................................................................................................10 1.2.2 Sentence tokens—utterances and inscriptions.....................................................12 1.2.3 Acts and states—statements, thoughts, beliefs....................................................14 1.2.4 What is said, thought, believed – propositions....................................................15 1.3 Truth and falsehood .......................................................................................................20 1.3.1 Accounts of truth ..................................................................................................20 1.3.2 Platitudes...............................................................................................................25 1.3.3 The schemas for truth and falsehood ...................................................................28 1.4 Bivalence and truth-value gaps .....................................................................................30 1.5 Conclusion .....................................................................................................................34 Chapter 2 The argument against counterexamples to bivalence ................................................36 2.1 Introduction....................................................................................................................36 2.2 Williamson’s argument against counterexamples to bivalence............38 2.2.1 The argument........................................................................................................38 2.2.2 Williamson’s defence of the argument ................................................................40 2.3 Objections to the argument that preserve (T) and (F)...................................................47 2.3.1 Weak negation ......................................................................................................47 2.3.2 Definitely true or definitely false .........................................................................50 2.3.3 Denying versus asserting a negation....................................................................55 2.3.4 Truth as a partially defined predicate and a different interpretation of the biconditional ..................................................................................................................57 iii 2.4 Objections to the argument that do not preserve (T) and (F) .......................................59 2.4.1 Metalinguistic negation ........................................................................................59 2.4.2 Metalinguistic negation, reference and presuppositions .....................................60 2.4.3 Variations on presupposition failure....................................................................61 2.4.4 Metalinguistic negation and rejection of (T) and (F) ..........................................63 2.5 Conclusion .....................................................................................................................66 Chapter 3 Reference failure .........................................................................................................67 3.1 Introduction....................................................................................................................67 3.2 Background – reference failure as a cause of truth-value gaps....................................70 3.2.1 Frege .....................................................................................................................70 3.2.2 Russell...................................................................................................................75 3.2.3 Strawson................................................................................................................79 3.3 Object-dependency: truth-conditions and singular thoughts........................................82 3.3.1 Semantic properties and truth-conditions ............................................................82 3.3.2 Singular thoughts..................................................................................................91 3.4 Why reference failure does not provide reasons to reject (T), (F) and (PB)................97 3.5 “People who are mistaken about the existence of something are not crazy, they are just wrong!”....................................................................................................................... 100 3.5.1 Psychological and behavioural explanations.................................................... 101 3.5.2 Senses to the rescue? ......................................................................................... 110 3.6 Conclusion .................................................................................................................. 117 Chapter 4 Soames on bivalence, the liar and partially defined predicates .............................. 119 4.1 Introduction................................................................................................................. 119 4.2 Soames’s model .......................................................................................................... 121 4.2.1 The motivation for rejecting bivalence – avoidance of contradictions............ 121 4.2.2 Soames’s model of partially defined predicates............................................... 127 4.2.3 The priority requirement, the liar and bivalence .............................................. 131 4.2.4 Truth-value gaps and propositions: Soames’s case in contrast with Frege and Strawson’s................................................................................................................... 134 4.3 What is wrong with Soames’s proposal..................................................................... 139 iv 4.3.1 If logic applies to ungrounded propositions,
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