Rosser-Type Undecidable Sentences Based on Yablo’s Paradox

Journal of Philosophical Logic 43 (5):999-1017 (2014)
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Abstract

It is widely considered that Gödel’s and Rosser’s proofs of the incompleteness theorems are related to the Liar Paradox. Yablo’s paradox, a Liar-like paradox without self-reference, can also be used to prove Gödel’s first and second incompleteness theorems. We show that the situation with the formalization of Yablo’s paradox using Rosser’s provability predicate is different from that of Rosser’s proof. Namely, by using the technique of Guaspari and Solovay, we prove that the undecidability of each instance of Rosser-type formalizations of Yablo’s paradox for each consistent but not Σ1-sound theory is dependent on the choice of a standard proof predicate

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Citations of this work

Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
Liar-type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
On the Depth of Gödel’s Incompleteness Theorems.Yong Cheng - forthcoming - Philosophia Mathematica.
On Rosser's provability predicates.Taishi Kurahashi - 2014 - Journal of the Japan Association for Philosophy of Science 41 (2):93-101.

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References found in this work

Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
Yablo’s paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.

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