 Williamson (1994a) points to two further problems apparently afflicting the supervaluationist account. First, classical inferences like conditional proof, constructive dilemma, and reductio ad absurdum no longer hold in a language extended to express vagueness by the addition of a determinately operator ‘D’ or similar. The logic of the extended language is decidedly non-classical. (Dummett [1975] offers an alternative definition of validity that does not encounter this problem, but Williamson raises other objections to it. However, Graff Fara [2003] shows that if we strengthen the notion of consequence to penumbral consequence, we get failures of these principles even in the absence of a determinately operator.) Second, problems arise also with regard to the phenomenon of higher order vagueness. In accommodating higher order vagueness, the supervaluationist must admit that his proffered concept of truth, viz., super-truth, lacks properties that truth is standardly thought to possess. Contrary to claims by supervaluationists, then, truth is not super-truth (see Keefe 2000 for a rebuttal).