Curry's paradox and omega inconsistency

Studia Logica 101 (1):1-9 (2013)
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Abstract
In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but not jointly, lack the problematic feature.
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Archival date: 2011-05-11
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The Liar Paradox and Fuzzy Logic.Hájek, Petr; Paris, Jeff & Shepherdson, John

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Fusion and Confusion.Priest, Graham
Non-Deterministic Conditionals and Transparent Truth.Pailos, Federico & Rosenblatt, Lucas

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