Tolerant, Classical, Strict

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. P. Cobreros (B) Department of Philosophy, University of Navarra, 31011 Pamplona, Spain e-mail: [email protected] P. Egré (B) · D. Ripley Institut Jean-Nicod (CNRS-EHESS-ENS), Département d’Etudes Cognitives de l’ENS, 29, rue d’Ulm, 75005, Paris, France e-mail: [email protected] D. Ripley (B) Department of Philosophy—Old Quad, University of Melbourne, Parkville, VIC 3010, Australia e-mail: [email protected] R. van Rooij (B) Institute for Logic, Language and Computation, Universiteit van Amsterdam, P.O. Box 94242, 1090 GE, Amsterdam, The Netherlands e-mail: [email protected]