Curry's paradox and omega inconsistency

Studia Logica 101 (1):1-9 (2013)
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.
Keywords Lukasiewicz logic  Curry's paradox  Semantic paradoxes  Non-classical logic  contraction
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