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In this article I propose a view which explains how it is possible that the disagreement concerning clear cases of a given vague predicate is genuine, whereas that concerning borderline cases is faultless. I take the possibility of faultless disagreement concerning borderline cases to be an important characteristic of vague predicates and in my view any adequate theory of vagueness should account for it. My proposal might be called “contextual supervaluationism” and it is inspired by Kölbel's relativist view from his paper “Vagueness as Semantic”. Following Kölbel I claim that the range of admissible sharpenings assumed by supervaluationism is context-dependent, but contrary to him I maintain that we need supertruth as well as truth at a sharpening. Moreover – again unlike Kölbel – I argue that utterances concerning borderline cases are permissible. I claim, however, that such utterances should be assertives rather than assertions, since they express only a weak belief of the speaker. It is the different illocutionary forces of utterances concerning clear cases and borderline cases that make it possible to explain the distinct nature of disagreements over such cases.
