Unsharpenable Vagueness

Philosophical Topics 28 (1):1-10 (2000)
Abstract
A plausible thought about vagueness is that it involves a form of semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. And where there is incomplete specification of extension there is indeterminacy—an indeterminacy between various ways that the specification of the predicate might be completed or, as some like to say, sharpened (or precisified). We shall argue that this idea is defective insofar as there are vague predicates that cannot be sharpened. At least, there are predicates that are vague but that cannot be sharpened in such a way as to meet certain basic constraints that we think must be imposed on the very notion of a sharpening.
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