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Vagueness is a special case of indeterminacy—semantical indeterminacy. It may be indeterminate whether a sentence is true or false, indeterminate whether a term denotes a certain object, and indeterminate whether a given set is the extension of a certain predicate. I take the word ‘vague’— my universe of discourse here comprises only linguistic items—to be entirely appropriate only in application to predicates and certain of their constituents.1 A predicate is vague if it is indeterminate, or, at any rate, possibly indeterminate, which set is its extension—or if it is possible that, for at least one object, it is indeterminate whether that object belongs to the extension of that predicate. In other words, a predicate is vague if it admits of (potential) borderline cases. In the case of one-place predicates, this comes down to saying that the term ‘vague’ applies primarily to verbs and adjectives and prepositions, the main constituents of predicates. (Of course, if it applies to verbs and adjectives, it applies to adverbs as well— that is, to representatives of the grammatical categories “takes a verb and makes a verb” and “takes an adjective and makes an adjective.”)

Indeterminacy and Vagueness: Logic and Metaphysics