Supervaluationism

Supervaluationism is a semantic theory of vagueness in philosophy of language and logic. It was developed by Jon N. Fine in the 1970s and subsequently refined by other philosophers. The core idea is that vague predicates do not have a single sharp extension. Instead, there are many admissible precisifications, which are precise, nonvague readings of the sentence. A sentence is evaluated relative to a precisification: under every admissible precisification, a given sentence may be true or false. A sentence is supertrue if it is true under every admissible precisification; superfalsity if false under every admissible precisification; and otherwise it is neither supertrue nor superfalsity.

Precisions are not arbitrary: they must respect the context and the intended use of the vague terms. The theory thus treats truth as a range across possible sharp meanings rather than a single fixed value. The truth conditions are defined by a satisfaction relation with respect to each precisification. Consequently, the law of the excluded middle and other classical inference rules can be preserved at the level of precisifications; however, individual vague sentences may lack a determinate truth value across all precisifications.

Example: for "x is tall," there are precisifications with a high threshold and low threshold. A borderline person may be tall under some precisifications and not tall under others; the sentence "x is tall" would be neither supertrue nor superfalsity, even though in every precisification the context makes either it or its negation true.

Evaluation: Supervaluationism can explain why border cases seem indeterminate without adopting many-valued truth values. It also faces criticisms, such as dependence on a chosen set of admissible precisifications and difficulty handling higher-order vagueness. It remains a central approach in the philosophy of vagueness and has inspired variants and applications in formal semantics.