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Curry’s Paradox and ω -Inconsistency


In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes1. 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 ω-inconsistency in Łukasiewicz’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 ukasiewicz logic which individually, but not jointly, lack the problematic feature.

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Correspondence to Andrew Bacon.

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Presented by Jacek Malinowski

1 See, for example, [ 1,2,5].

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Bacon, A. Curry’s Paradox and ω -Inconsistency. Stud Logica 101, 1–9 (2013).

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  • Contractionless logic
  • ω-Inconsistency
  • Łukasiewicz logic
  • Curry’s paradox
  • Naïve truth theory