If the semantic values of predicates are, as Williamson assumes (_Philsophical Perspectives,_ _13_, 505–517, 1999, 509) properties in the intensional sense, then epistemicism is immediate. Epistemicism fails, so also this properties account of predicates. I deploy examination of Williamson’s account as a foil against properties as semantic values, showing that his two positive arguments for bivalence fail, as do his efforts to rescue epistemicism from obvious problems. In Part II I argue that, despite the properties account’s problems, it has an (...) important role to play in compositional semantics. We may separate the problem of how smallest parts of language get attached to the world from the problem of how those parts compose to form complex semantic values. For the latter problem we idealize and treat the smallest semantic values as properties (and referents). So doing functions to put to one side how the smallest parts get worldly attachment, a problem that would just get in the way of understanding composition. Attachment to the world must be studied separately, and I review some of the options. As a bonus we see why the requirement of higher order vagueness is an artifact of taking properties as semantic values literally instead of as a simplifying idealization. (shrink)