Journal of Philosophical Logic

, Volume 42, Issue 5, pp 679-695

First online:

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Gödelizing the Yablo Sequence

  • Cezary CieślińskiAffiliated withInstitute of Philosophy, University of Warsaw
  • , Rafal UrbaniakAffiliated withInstitute of Philosophy, Sociology and Journalism, Gdansk UniversityCentre for Logic and Philosophy of Science, Ghent University Email author 


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.


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