Notre Dame Journal of Formal Logic

Disarming a Paradox of Validity

Hartry Field

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Notre Dame J. Formal Logic, Volume 58, Number 1 (2017), 1-19.

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03A99: None of the above, but in this section
Secondary: 03B99: None of the above, but in this section 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52} 03F45: Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]

Curry paradox substructural logic validity


Field, Hartry. Disarming a Paradox of Validity. Notre Dame J. Formal Logic 58 (2017), no. 1, 1--19. doi:10.1215/00294527-3699865.

Export citation


  • [1] Beall, J. C., Spandrels of Truth, Oxford University Press, Oxford, 2009.
  • [2] Beall, J. C., and J. Murzi, “Two flavors of Curry’s paradox,” Journal of Philosophy, vol. 110 (2013), pp. 143–65.
  • [3] Boolos, G., The Logic of Provability, Cambridge University Press, Cambridge, 1993.
  • [4] Cobreros, P., P. Egré, D. Ripley, and R. van Rooij, “Reaching transparent truth,” Mind, vol. 122, pp. 841–66.
  • [5] Field, H., Saving Truth from Paradox, Oxford University Press, Oxford, 2008.
  • [6] Field, H., “What is logical validity?,” pp. 33–70 in Foundations of Logical Consequence, edited by Colin Caret and Ole Hjortland, Oxford University Press, Oxford, 2015.
  • [7] Kripke, S., “Outline of a theory of truth,” Journal of Philosophy, vol. 72 (1975), pp. 690–716.
  • [8] Whittle, B., “Dialetheism, logical consequence, and hierarchy,” Analysis, vol. 64 (2004), pp. 318–26.