Studia Logica

, Volume 100, Issue 4, pp 855–877

Tolerance and Mixed Consequence in the S’valuationist Setting

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


In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that sentences of the form ‘\({p {\vee} {\neg} p}\)’ and ‘\({p {\wedge} {\neg} p}\)’ are not automatically valid or unsatisfiable, respectively. Some philosophers might take this commitment as a negative outcome of our previous proposal. We think, however, that the general ideas underlying our previous approach to vagueness can be implemented in a variety of ways. This paper explores the possibility of defining mixed notions of consequence in the more classical super/sub-valuationist setting and examines to what extent any of these notions captures non-transitive tolerant reasoning.


Vagueness Tolerance Logical Consequence Super- and Sub-valuationism 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Pablo Cobreros
    • 1
  • Paul Egré
    • 2
  • David Ripley
    • 3
  • Robert van Rooij
    • 4
  1. 1.Department of PhilosophyUniversity of NavarraPamplonaSpain
  2. 2.Département d’Etudes Cognitives de l’ENSInstitut Jean-Nicod (CNRS-EHESS-ENS)ParisFrance
  3. 3.Department of Philosophy – Old QuadUniversity of MelbourneMelbourneAustralia
  4. 4.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands

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