7
Supervaluationism

In this chapter and the next I shall defend a supervaluationist theory of vagueness and seek its best possible version. I believe that, unfortunately, there is no straightforward argument for the correctness of this view — there is no simple demonstration that the truthconditions of our vague sentences must quantify over precisifications, for example. The case for it must be made by showing the success with which it fulfils the tasks facing any theory of vagueness and the effectiveness of its reflective equilibrium in balancing our intuitions, judgements, explanations of our linguistic practices and theoretical considerations of simplicity and so forth. I claim that on this costbenefit method of assessment, it does vastly better than its rivals. The main rivals have been rejected in previous chapters. Theories offering no modification to classical logic or semantics are unacceptable, I have argued (even if they deny that there is a vague language and characterise vagueness via our pragmatic relations to a range of precise languages). But theories offering a truth-functional manyvalued logic are at least as bad. We should propose a non-truthfunctional semantics and regard sentences that do not take classical values as falling into a truth-value gap instead. And the only viable way I can see of doing these things is with a supervaluationist theory. This leaves logical space for theories that I have not considered, in particular ones deviating from classical semantics in some other way and/or deviating from classical logic as well. In §7 I consider and reject some of those possibilities, namely those that can be seen as variants on the standard supervaluationary theory. I do not think that there is any hope for as yet undiscovered alternatives differing radically from all the considered options. So although I may not have eliminated, or provided comparisons with, every possible account of vagueness, I maintain that I have dealt with all those with any plausibility.

-152-

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Theories of Vagueness
Table of contents

Table of contents

  • Cambridge Studies in Philosophy - Theories of Vagueness *
  • Cambridge Studies in Philosophy *
  • Title Page *
  • For My Parents, Sheila and Terry *
  • Contents ix
  • Acknowledgements xi
  • Introduction 1
  • 1 - The Phenomena of Vagueness 6
  • 2 - How to Theorise About Vagueness 37
  • 3 - The Epistemic View of Vagueness 62
  • 4 - Between Truth and Falsity: Many-Valued Logics 85
  • 5 - Vagueness by Numbers 125
  • 6 - The Pragmatic Account of Vagueness 139
  • 7 - Supervaluationism 152
  • 8 - Truth is Super-Truth 202
  • References 221
  • Index 229
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