Supervaluationism and Its Logics

Mind 116 (463):633 - 675 (2007)
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 recast. There are several ways of doing this 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 (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion
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