Bivalence and the challenge of truth-value gaps
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.