Pragmatic interpretation of vague expressions: strongest meaning and nonmonotonic consequence

Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. (Journal of Philosophical Logic, 41, 347–385, 2012a) we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. (Journal of Philosophical Logic, 42, 619–634, 2013) show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on a somewhat richer semantics, and show that with its help the problem can be overcome in pragmatics after all. Furthermore, we use this pragmatic interpretation rule to define a new (nonmonotonic) consequence-relation and discuss some of its properties.