(Joint work with P. Cobreros, D. Ripley and R. van Rooij)
This paper is a response to N. Smith's claim in his book "Vagueness and Degrees of Truth" (2008) that an adequate account of vagueness requires a large number of degrees of truth, and more specifically, more than three degrees of truth in order to accommodate what Smith calls the closeness principle. This paper compares Smith's fuzzy account with a 3-valued version of the strict-tolerant account proposed by Cobreros, Egré, Ripley and van Rooij (2012). It is shown that such an account meets all of Smith's desiderata, while avoiding a mismatch between the number of truth values needed in relation to assertion and those needed in relation to inference. The paper is also an occasion to discuss the notion of truth value and its role in semantic theory.