Mathematical Perspectives on Liar Paradoxes

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 inte...

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Published inLogica universalis Vol. 15; no. 3; pp. 251 - 269
Main Authors Usó-Doménech, José-Luis, Nescolarde-Selva, Josué-Antonio, Segura-Abad, Lorena, Alonso-Stenberg, Kristian, Gash, Hugh
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2021
Springer Nature B.V
Subjects
Computer Science
Logic
Mathematics
Mathematics and Statistics
Paradoxes
Philosophy
Sentences
Paradox
03B42
Determined compatible propositions
Incompatible propositions
01A20
Liar paradox
Logic
Metalanguage
Systems
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Summary: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.
ISSN:1661-8297
1661-8300
DOI:10.1007/s11787-021-00277-2