Gödelizing the Yablo Sequence

Journal of Philosophical Logic 42 (5):679-695 (2013)
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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

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Author Profiles

Cezary Cieslinski
University of Warsaw
Rafal Urbaniak
University of Gdansk

Citations of this work

Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
Rosser-Type Undecidable Sentences Based on Yablo’s Paradox.Taishi Kurahashi - 2014 - Journal of Philosophical Logic 43 (5):999-1017.
Yablifying the Rosser Sentence.Graham Leach-Krouse - 2014 - Journal of Philosophical Logic 43 (5):827-834.
Liar-type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.

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References found in this work

Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
An Introduction to Gödel's Theorems.Peter Smith - 2007 - New York: Cambridge University Press.
An Introduction to Gödel's Theorems.Peter Smith - 2009 - Bulletin of Symbolic Logic 15 (2):218-222.
Yablo’s paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.

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