Disarming a Paradox of Validity

Notre Dame Journal of Formal Logic 58 (1):1-19 (2017)
  Copy   BIBTEX

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 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.

Author's Profile

Hartry Field
New York University

Analytics

Added to PP
2014-06-26

Downloads
696 (#12,037)

6 months
52 (#30,954)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?