Describes a semantic approach to problems of vagueness and truth value gaps due to Bas van Fraassen (1941– ) in which sentences are evaluated by sets of classical valuations (called ‘precisifications’). One can say that a formula is supertrue with respect to a set of classical valuations if every evaluates as true (and superfalse if every evaluates it as false). Then borderline or vague cases are those in which two valuations and disagree, i.e., those formulae that are not supertrue. Likewise, validity on the supervaluationist account can be defined as preservation of supertruth from premisses to conclusions, that is:
The supervaluationist account of validity is in a weak sense paracomplete insofar as is not a consequence of all sets , although the set is in fact a consequence of all sets .