Tolerant, Classical, Strict

Pablo Cobreros, Paul Egré, David Ripley, Robert van Rooij

Research output: Contribution to journalArticleResearchpeer-review

126 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)347-385
Number of pages39
JournalJournal of Philosophical Logic
Volume41
Issue number2
DOIs
Publication statusPublished - 1 Apr 2012
Externally publishedYes

Keywords

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

Cite this