Higher-Order Vagueness and the Vagueness of ‘Vague’

Sorensen (1985) has argued that ‘vague’ is itself a vague predicate; it is just as sorites-prone as its positive instances. This result has been exploited by Hyde (1994) in an ingenious attempt to establish that vague predicates must necessarily suffer from higher-order vagueness. More precisely, Hyde has argued that the vagueness of ‘vague’ ensures that the “paradigmatic conception”, according to which predicate vagueness is characterized by the presence of border cases, need not be revised or further elaborated upon in order to account for the phenomenon of higher-order vagueness: if a predicate has border cases, it has border border cases. Tye (1994) has objected (convincingly I think) that this is too strong: all that follows from Sorensen’s result is that there are some border border cases, but not necessarily border border cases of every vague predicate. I shall argue that this is still too strong: Sorensen’s proof presupposes the existence of border border cases, hence cannot be used to establish that fact on pain of circularity.