2
How to theorise about vagueness

In this chapter I shall examine in more detail the project of constructing a theory of vagueness. The apparent simplicity of its central question, 'what are the logic and semantics of a vague language?', masks considerable unclarity in the nature of the project and what would count as success. I shall discuss matters of methodology, the aims and constraints of the project and the standards by which we should judge candidate theories. And in §3 I shall investigate an important distinction between two attitudes to elements of a theory.


1. ESTABLISHING A REFLECTIVE EQUILIBRIUM

A theory of vagueness deals with the semantic structure of vague languages and the logical relations that hold between their sentences. It must specify the range of truth-values, or any alternative truthvalue status, that a sentence can have. And it should capture the distribution of them among borderline cases, in particular through a sorites series. But, as we saw in chapter 1, §4, it may not be theoretically possible to assign some determinate truth-value status to each member of the series in turn — for that would commit us to sharp boundaries between any two semantic categories. The best description of the distribution of truth-values may have to be of some other form, where, for example, we take a step back from describing assignments case by case and describe the general structure of truthvalues (see chapter 8, §1). Similarly, if we require of a theory of vagueness that it specifies truth-conditions for vague sentences, then we must allow such conditions to be stated in vague terms in such a way as not to settle a truth-value status for every sentence.

The theory is also concerned with the logical principles governing our language — with, for example, specifying how the truth-value of a complex sentence is determined by, or otherwise related to, its

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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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