supervaluation

An approach to the problems of vagueness. Suppose a vague predicate has things to which it definitely applies (things in its positive extension) things to which it definitely does not (in its negative extension) and a penumbra. Then we imagine a plurality of interpretations or precisifications, each of which has no penumbra, but behaves classically. However, each may put the division between the positive and negative extensions in different places. Then the assignment of truth value for all such interpretations is a supervaluation. Anything true in all precisifications is supertrue; anything false is superfalse. A nice property is that classical laws such as (p ∨ -p) are supertrue—true in all interpretations, in spite of their variation in placing the boundaries.