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.

Similar books and articles

Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
Validity Curry Strengthened.Lionel Shapiro - 2013 - Thought: A Journal of Philosophy 2 (1):100-107.
There is No Paradox of Logical Validity.Roy T. Cook - 2014 - Logica Universalis 8 (3-4):447-467.
Natural deduction and Curry's paradox.Susan Rogerson - 2007 - Journal of Philosophical Logic 36 (2):155 - 179.
Variations on a Theme of Curry.Lloyd Humberstone - 2006 - Notre Dame Journal of Formal Logic 47 (1):101-131.
Validity and Truth-Preservation.Lionel Shapiro & Julien Murzi - 2015 - In T. Achourioti, K. Fujimoto, H. Galinon & J. Martínez-Fernández (eds.), Unifying the Philosophy of Truth. Springer Verlag. pp. 431-459.
Computer implication and the Curry paradox.Wayne Aitken & Jeffrey A. Barrett - 2004 - Journal of Philosophical Logic 33 (6):631-637.
A revenge-immune solution to the semantic paradoxes.Hartry Field - 2003 - Journal of Philosophical Logic 32 (2):139-177.

Analytics

Added to PP
2014-06-26

Downloads
695 (#13,395)

6 months
52 (#30,984)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Hartry Field
New York University

Citations of this work

Logical Partisanhood.Jack Woods - 2019 - Philosophical Studies 176 (5):1203-1224.
Generalized Revenge.Julien Murzi & Lorenzo Rossi - 2020 - Australasian Journal of Philosophy 98 (1):153-177.
Faithfulness for naive validity.Ulf Hlobil - 2019 - Synthese 196 (11):4759-4774.

View all 15 citations / Add more citations

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.

Add more references