So far, the method of supervaluations has been mainly employed to define a non-gradable property of sentences, supertruth, in order to provide an analysis of truth. But it is also possible, and arguably at least as plausible, to define a gradable property of sentences along the same lines. This paper presents a supervaluationist semantics that is quantitative rather than qualitative. As will be shown, there are at least two distinct interpretations of the semantics — one alethic, the other epistemic — (...) which can coherently be adopted to address key issues such as vagueness and future contingents. (shrink)