A critique of Malpass's argument against Supervaluationism

Abstract

Supervaluationism is one of the most discussed approaches to the semantics of future tense sentences in a branching time. In this paper, we consider the criticism advanced by Malpass against Supervaluationism. This criticism relies on the fact that supervaluationists must accept as supertrue disjunctions whose disjuncts are not only supertrue-which supervaluationists are ready to acknowledge-but also not satisfiable. In order to show this, Malpass proposes a formula, FF 1 , which shows the existence of a satisfiable disjunction with unsatisfiable disjuncts in supervaluationist models. In reply, we show that formula FF 1 cannot be expressed within a model (whether Ockhamist or supervaluationist) because it quantifies on models. It can be correctly characterised only within a meta-model that has the resources to quantify on various models. However, once that is done, FF 1 is, for the advocates of Supervaluationism, no more demanding than other disjunctions because it just generalises at the meta-theoretical level what supervaluationists already acknowledge at the theoretical level.As is well known, the semantics of future tense sentences in a branching time (BT) model is controversial. One of the most discussed approaches is Supervaluationism (Thomason, 1970). Supervaluationism is a kind of para-complete semantics; however, compared to other semantic frameworks that allow truth value gaps, Supervaluationism has the advantage of preserving the validity of formulas such as Fφ _ F¬φ and the invalidity of formulas such as Fnφ ^Fn¬φ, 1 which seem very intuitive. 1The meaning of Fn is "in n time units it will be the case that …".