From heaps and gaps to heaps of gluts

Abstract

One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the recognition of cases of overdetermination and truth value gluts has few supporters. This imbalance lacks justification. As it happens, Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature. A simple dualisation of supervaluation semantics results in a paraconsistent logic of vagueness based on what has been termed subvaluational semantics.