Editing Vagueness (section)

=== Supervaluationism ===
{{main|Supervaluationism}}
Another theoretical approach is known as "[[supervaluationism]]". This approach has been defended by [[Kit Fine]] and Rosanna Keefe. Fine argues that borderline applications of vague predicates are neither true nor false, but rather are instances of "[[truth value]] gaps". He defends an interesting and sophisticated system of vague semantics, based on the notion that a vague predicate might be "made precise" in many alternative ways. This system has the consequence that borderline cases of vague terms yield statements that are neither true, nor false.<ref>Kit Fine, ''The Limits of Abstraction'' (2002).</ref>

Given a supervaluationist semantics, one can define the predicate "supertrue" as meaning "true on all [[precisification]]s".  This predicate will not change the semantics of atomic statements (e.g. "Frank is bald", where Frank is a borderline case of baldness), but does have consequences for logically complex statements. In particular, the [[tautology (logic)|tautologies]] of sentential logic, such as "Frank is bald or Frank is not bald", will turn out to be supertrue, since on any precisification of baldness, either "Frank is bald" or "Frank is not bald" will be true.  Since the presence of borderline cases seems to threaten principles like this one (excluded middle), the fact that supervaluationism can "rescue" them is seen as a virtue.