Supervaluationism about Vague Names Cannot Account for Statements about Those Names

Vague names, like “Everest” and “Belle Epoque” seem to refer to objects without clear boundaries. Supervaluationism claims that this vagueness is a feature of language, not of the objects referred to; vagueness in names is just ambiguity between many possible referents. This general idea admits of two more specific versions. Both give similar treatments of standard uses of vague names, but have very different results for other cases, such as reference achieved by descriptions including mentioned names. Considering two examples, I show neither variant of supervaluationism can account for the truth of all types of sentences about those names themselves. If I am right that these types exhaust supervaluationism, the theory is shown to be false. This problem closely resembles others in the super-valuationist literature about disquotation failure for truth. Treatments of vague truth and vague reference come apart though, and I show that the two problems are different enough that none of the popular solutions will succeed for reference. I consider—and reject—several specific objections, and two more general ways to recover supervaluationism following my arguments. I conclude that supervaluationism is at best a useful formalism for some kinds of vagueness reference, but fails as a general account.