Higher-Orders of Vagueness Reinstated

The role of higher-order vagueness in creating apparent difficulties with attempts to formulate a sentence capable of characterizing the vagueness of a predicate, that is, its role in appearing to undermine a characteristic-sentence approach to defining vagueness, has led some to question the very existence of such a phenomenon. Hyde () sought to put the existence of higher-order vagueness beyond doubt and to do so in a way that showed it to be unproblematic. Varzi (), though sympathetic to the existence claim, argues that the reasoning of Hyde () for that claim is ultimately circular, depending as it does on an argument for the vagueness of 'vague' which itself supposedly assumes the very point at issue. To avoid circularity the vagueness of 'vague' must be argued for independently of this argument of Sorensen () or be taken as obvious. Such is the dialectic so far. By way of rejoinder I think the charge is mistaken. Sorensen's argument is sound and its conclusion available for use in a non-circular argument for higher-order vagueness. Before dealing with the specific charge of circularity it is worthwhile pausing briefly to bolster the central argument of Sorensen () for the vagueness of 'vague'. After all, doubts surrounding its soundness would undermine the value of any subsequent debate concerning its legitimate use in establishing higher-order vagueness, including the present one. Both Deas () and Tye () have expressed just such doubts but for reasons already outlined by Varzi I think we can safely put aside the concerns expressed by Deas. Tye's concerns are also misguided but a little more work is required to show this. Tye argues that Sorensen's argument is unsound; 'vague' is not vague, rather it is vaguely vague. The argument proceeds as follows. If 'vague' is vague then it follows that there are predicates which are vaguely vague (Tye , p. ). Assuming Sorensen's argument for the vague-ness of 'vague' is sound then it follows that there are vaguely vague predicates; and now we are presented with an alternative explanation of