When regimenting a vague, natural language it is common for philosophers to introduce an operator Def with the intention of equipping the language with the means to express its own vagueness. But, despite this clear role, there is no well accepted logic or semantics for the modality. And, indeed, if it is plausibly assumed that the locution is itself vague, that this higher-order of vagueness can also be expressed in the language, and that the logic governing it is a normal modal system, then one can apparently derive revenge, higher-order paradoxes. In this paper, a new approach to the semantics of higher-order vagueness is presented. I intend initially to be neutral about the interpretation of the operator—whether the operator is epistemic or semantic—and to investigate structural questions about its logic. I suggest that the formal structure of a logic for higher-order vagueness should be that of higher-order probability. It is argued that the resulting system is a much more natural account of higher-order vagueness, and that it affords a solution to one of the strongest versions of the paradox of higher-order vagueness.
