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The Liar paradox and fuzzy logic. (English) Zbl 0945.03031
Summary: Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate \(\text{Tr}(x)\) saying “\(x\) is true” and satisfying the “dequotation schema” \(\varphi\equiv \text{Tr}(\overline\varphi)\) for all sentences \(\varphi\)? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.

MSC:
03B50 Many-valued logic
03F30 First-order arithmetic and fragments
03B52 Fuzzy logic; logic of vagueness
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