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2017 Disarming a Paradox of Validity
Hartry Field
Notre Dame J. Formal Logic 58(1): 1-19 (2017). DOI: 10.1215/00294527-3699865

Abstract

Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi (“Two flavors of Curry’s paradox”) call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they recommend a radical solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction.

In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem.

Citation

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Hartry Field. "Disarming a Paradox of Validity." Notre Dame J. Formal Logic 58 (1) 1 - 19, 2017. https://doi.org/10.1215/00294527-3699865

Information

Received: 6 December 2013; Accepted: 20 March 2014; Published: 2017
First available in Project Euclid: 17 November 2016

zbMATH: 1360.03028
MathSciNet: MR3595339
Digital Object Identifier: 10.1215/00294527-3699865

Subjects:
Primary: 03A99
Secondary: 03B47, 03B99, 03F45

Rights: Copyright © 2017 University of Notre Dame

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Vol.58 • No. 1 • 2017
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