Liar-type paradoxes and the incompleteness phenomena

• Autores: Makoto Kikuchi, Taishi Kurahashi
• Localización: Journal of Philosophical Logic, ISSN-e 1573-0433, Vol. 45, Nº. 4, 2016, págs. 381-398
• Idioma: inglés
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• Resumen

  • 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.