Journal of Philosophical Logic

, Volume 42, Issue 5, pp 679–695

Gödelizing the Yablo Sequence

Open Access
Article

Abstract

We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo paradox. We also look at a formulation which employs Rosser’s provability predicate.

Keywords

Incompleteness Omega-liar Yablo’s paradox Paradox Provability Arithmetic Goedel 

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of PhilosophyUniversity of WarsawWarsawPoland
  2. 2.Institute of Philosophy, Sociology and JournalismGdansk UniversityGdanskPoland
  3. 3.Centre for Logic and Philosophy of ScienceGhent UniversityGhentBelgium

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