Liar-type Paradoxes and the Incompleteness Phenomena

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

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Citations of this work

Incompleteness Via Paradox and Completeness.Walter Dean - 2020 - Review of Symbolic Logic 13 (3):541-592.
Paradoxes and contemporary logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Yablo’s paradox.Graham Priest - 1997 - Analysis 57 (4):236–242.

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