Vagueness

Vagueness

Vagueness

Vagueness

Synopsis

When did Rembrandt get old? If you keep removing single grains of sand from a heap when is it no longer a heap? These questions and the many others like them will eventually lead us to the problem of vagueness. Timothy Williamson traces the history of the problem from discussions of the heap paradox in classical Greece to modern formal approaches, such as fuzzy logic. He shows the problems with views which have taken the position that standard logic and formal semantics do not apply to vague languages and defends the controversial realist view that vagueness is a kind of ignorance - there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is.

Excerpt

This book originated in my attempts to refute its main thesis: that vagueness consists in our ignorance of the sharp boundaries of our concepts, and therefore requires no revision of standard logic. For years I took this epistemic view of vagueness to be obviously false, as most philosophers do. In 1988 Simon Blackburn, then editor of the journal Mind, asked me to review Roy Sorensen's intriguing book Blindspots, which includes a defence of the epistemic view. It did not persuade me; I could not see what makes us ignorant, and Sorensen offered no specific explanation. An alternative treatment of vagueness, supervaluationism, looked more or less adequate-unlike other popular alternatives, such as three-valued and fuzzy logic, which on technical grounds have always looked like blind alleys. However, I continued to think about the epistemic view, for the standard objections to it did not seem quite decisive. It was not clear that they did not assume a suspect connection between what is true and what we can verify. It then struck me that the notion of a margin for error could be used to give a specific explanation of ignorance of the sharp boundaries of our concepts, and the epistemic view began to look more plausible. A limited version of it was tentatively proposed in my book Identity and Discrimination (Oxford, Blackwell, 1990). The more closely the objections to it were analysed, the weaker they seemed. The next step was to focus on the fact that the meaning of vague expressions can be stated only in a language into which those expressions can be translated; it is a mistake to treat the language in which one theorizes about vagueness as though it were precise. Mark Sainsbury's inaugural lecture at King's College London, 'Concepts without Boundaries', helped to bring the

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