The liar paradox and Godel's first incompleteness theorem

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The article critically analyzes the example of the incorrect application of metamathematics, in particular, Gödel's First incompleteness theorem, to the explication of the Liar Paradox by J. Barker. It is shown that an explication of this kind, doubting well known Tarki's definition of truth, is based on the erroneous use of key Gödel constructions - substitution idea and the diagonal lemma. The criticism of the proclamation by Barker of the explication of the Liar as a mathematical theorem shows certain limitations in demonstrating the heuristic analogy between the Liar's sentence and the Godelian sentence.

Original languageEnglish
Pages (from-to)415-427
Number of pages13
Issue number2
Publication statusPublished - 1 Jan 2017


  • Explication
  • Godel's theorem
  • Liar paradox
  • Self-reference
  • Truth predicate
  • self-reference
  • truth predicate
  • explication

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