Different formal tools are useful for different purposes.  For example, when it comes to modelling degrees of belief, probability theory is a better tool than classical logic; when it comes to modelling the truth of mathematical claims, classical logic is a better tool than probability theory.  In this paper I focus on a widely used formal tool and argue that it does not provide a good model of a phenomenon of which many think it does provide a good model: I shall argue that while supervaluationism may provide a model of probability of truth, or of assertability, it cannot provide a good model of truth -- truth cannot be supertruth.  The core of the argument is that an adequate model of truth must render certain connectives truth-functional -- and supervaluationism does not do so.