Liar-type Paradoxes and the Incompleteness Phenomena

Journal of Philosophical Logic 45 (4):381-398 (2016)

Abstract
We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s Paradox in this framework. Furthermore, we define explicit and implicit self-reference in paradoxes in the incompleteness phenomena.
Keywords Gödel’s incompleteness theorem  The Liar Paradox  Modal logic  Arithmetical realization
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DOI 10.1007/s10992-015-9378-2
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References found in this work BETA

Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
The Logic of Provability.George S. Boolos - 1993 - Cambridge University Press.
Yablo’s Paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.
Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.

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