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The Liar Paradox and Fuzzy Logic

Petr Hájek, Jeff Paris and John Shepherdson
The Journal of Symbolic Logic
Vol. 65, No. 1 (Mar., 2000), pp. 339-346
DOI: 10.2307/2586541
Stable URL: http://www.jstor.org/stable/2586541
Page Count: 8
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The Liar Paradox and Fuzzy Logic
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Abstract

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying "x is true" and satisfying the "dequotation schema" $\varphi \equiv \text{Tr}(\bar{\varphi})$ for all sentences φ? This problem is investigated in the frame of Lukasiewicz infinitely valued logic.

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