Abstract: Supervaluational treatments of vagueness are currently quite popular among those who regard vagueness as a thoroughly semantic phenomenon. Peter Unger's 'problem of the many' may be regarded as arising from the vagueness of our ordinary physical-object terms, so it is not surprising that supervaluational solutions to Unger's problem have been offered. I argue that supervaluations do not afford an adequate solution to the problem of the many. Moreover, the considerations I raise against the supervaluational solution tell also against the solution to the problem of the many which is suggested by adherents of the epistemic theory of vagueness.