Journal of Philosophical Logic

, Volume 41, Issue 2, pp 347-385

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Tolerant, Classical, Strict

  • Pablo CobrerosAffiliated withDepartment of Philosophy, University of Navarra Email author 
  • , Paul EgréAffiliated withInstitut Jean-Nicod (CNRS-EHESS-ENS), Département d’Etudes Cognitives de l’ENS Email author 
  • , David RipleyAffiliated withInstitut Jean-Nicod (CNRS-EHESS-ENS), Département d’Etudes Cognitives de l’ENSDepartment of Philosophy—Old Quad, University of Melbourne Email author 
  • , Robert van RooijAffiliated withInstitute for Logic, Language and Computation, Universiteit van Amsterdam Email author 


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.


Vagueness Sorites paradox Tolerance Logical consequence Truth Non-transitivity Trivalent logics Paraconsistent logics