Studia Logica

, Volume 101, Issue 1, pp 1–9 | Cite as

Curry’s Paradox and ω -Inconsistency

Article

Abstract

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.

Keywords

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

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Magdalen CollegeOxfordUK

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