Vagueness, Truth and Permissive Consequence

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

Research output: Chapter in Book/Report/Conference proceedingChapter (Book)Researchpeer-review

27 Citations (Scopus)


We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisit of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.

Original languageEnglish
Title of host publicationUnifying the Philosophy of Truth
EditorsTheodora Achourioti, Henri Galinon, José Martínez Fernández, Kentaro Fujimoto
Place of PublicationDordrecht Germany
Number of pages22
ISBN (Electronic)9789401796736
ISBN (Print)9789401796729
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameLogic, Epistemology, and the Unity of Science
ISSN (Print)2214-9775
ISSN (Electronic)2214-9783


  • Nontransitive consequence
  • Paradox
  • Permissive consequence
  • Principle of tolerance
  • Three-valued logic
  • Transparent truth
  • Vagueness

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