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Mathematical Perspectives on Liar Paradoxes

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Abstract

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: (a) the levels of language, (b) their belonging to indeterminate compatible propositions (ICP) or indeterminate propositions (IP), (c) being based on universal antinomy and (d) the theory of dialetheism.

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  1. Eubulides (fl. 4th century BCE) of Miletus was a philosopher of the Megarian school, and a pupil of Euclid of Megara. He is famous for his paradoxes. Eubulides is most famous for inventing the forms of seven famous paradoxes some of which, however, are also ascribed to Diodorus Cronus [28].

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Correspondence to José-Luis Usó-Doménech.

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Usó-Doménech, JL., Nescolarde-Selva, JA., Segura-Abad, L. et al. Mathematical Perspectives on Liar Paradoxes. Log. Univers. 15, 251–269 (2021). https://doi.org/10.1007/s11787-021-00277-2

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