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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DOI 10.1007/s11225-012-9373-3
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References found in this work BETA
Saving Truth From Paradox.Hartry H. Field - 2008 - Oxford University Press.
Spandrels of Truth.J. C. Beall - 2009 - Oxford University Press.
How to Be Really Contraction Free.Greg Restall - 1993 - Studia Logica 52 (3):381 - 391.
The Liar Paradox and Fuzzy Logic.Petr Hájek, Jeff Paris & John Shepherdson - 2000 - Journal of Symbolic Logic 65 (1):339-346.

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Citations of this work BETA
Fusion and Confusion.Graham Priest - 2015 - Topoi 34 (1):55-61.
Paths to Triviality.Tore Fjetland Øgaard - 2016 - Journal of Philosophical Logic 45 (3):237-276.

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