Curry’s Paradox and ω -Inconsistency
- Andrew Bacon
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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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- Curry’s Paradox and ω -Inconsistency
Volume 101, Issue 1 , pp 1-9
- Cover Date
- Print ISSN
- Online ISSN
- Springer Netherlands
- Additional Links
- Contractionless logic
- Łukasiewicz logic
- Curry’s paradox
- Naïve truth theory
- Andrew Bacon (1)
- Author Affiliations
- 1. Magdalen College, Oxford, OX1 4AU, UK