Gödelizing the Yablo Sequence
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.
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- Gödelizing the Yablo Sequence
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Journal of Philosophical Logic
Volume 42, Issue 5 , pp 679-695
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- Springer Netherlands
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- Yablo’s paradox
- Author Affiliations
- 1. Institute of Philosophy, University of Warsaw, Warsaw, Poland
- 2. Institute of Philosophy, Sociology and Journalism, Gdansk University, Gdansk, Poland
- 3. Centre for Logic and Philosophy of Science, Ghent University, Ghent, Belgium