Supervaluationism and Its Logics

Abstract

If we adopt a supervaluational semantics for vagueness, what sort of logic results? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between ‘global’ construals (e.g., an argument is valid if and only if it preserves truth-under-all-precisifications) and ‘local’ construals (an argument is valid if and only if, under all precisifications, it preserves truth). The former alternative is by far more popular, but I argue in favour of the latter, for one, it does not suffer from a number of serious objections, and two, it makes it possible to restore global validity as a defined notion.