The liar paradox and fuzzy logic

JC Shepherdson, J Hajek, P & Paris,

Research output: Contribution to journalArticle (Academic Journal)

41 Citations (Scopus)


It is well known that the liar paradox shows that crisp Peano arithmetic PA cannot be consistently extended by adding a truth predicate Tr(x)satisfying 's iff Tr(s')' for all sentences s, where s' is the goedel number of s. We show that such a consistent extension is possible if Tr is allowed to be many valued with truth values in [0,1]. However such a theory has no standard model, and it becomes inconsistent if Tr is required to commute with propositional connectives.
Translated title of the contributionThe liar paradox and fuzzy logic
Original languageEnglish
Pages (from-to)339 - 346
Number of pages8
JournalJournal of Symbolic Logic
Publication statusPublished - Mar 2000

Bibliographical note

Publisher: Association for Symbolic Logic

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