Vagueness without truth functionality? No worries

Abstract

Among theories of vagueness, supervaluationism stands out for its non–truth functional account of the logical connectives. For example, the disjunction of two atomic statements that are not determinately true or false can, itself, come out either true or indeterminate, depending on its content—a consequence several philosophers find problematic. Smith (2016) turns this point against supervaluationism most pressingly, arguing that truth functionality is essential to any adequate model of truth. But this conclusion is too strong. Here, I argue that the problem with standard forms of supervaluationism is not the failure of truth functionality per se, but rather that they lack the structural resources necessary to algorithmically assign truth values to sentences based on their respective subject matters. However, recent developments of supervaluationism, which draw upon the cognitive science framework of conceptual spaces, resolve this issue. By incorporating conceptual information directly into their model-theoretic representations of the subject matters of sentences, these newer frameworks retain sensitivity to conceptual relations while providing consistent, content-based valuations of truth. Hence, their lack of truth functionality is nothing to worry about.