Unsharpenable Vagueness

Philosophical Topics 28 (1):1-10 (2000)
Abstract
A plausible thought about vagueness is that it involves semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. Where there is incomplete specification of extension there is indeterminacy, an indeterminacy between various ways in which the specification of the predicate might be completed or sharpened. In this paper we show that this idea is bound to founder by presenting an argument to the effect that there are vague predicates which cannot be sharpened in such a way as to meet certain basic constraints (of penumbral connection and public accessibility) that must be imposed on the very notion of a sharpening.
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