Notre Dame Journal of Formal Logic

Variations on a Theme of Curry

Lloyd Humberstone

Abstract

After an introduction to set the stage, we consider some variations on the reasoning behind Curry's Paradox arising against the background of classical propositional logic and of BCI logic and one of its extensions, in the latter case treating the "paradoxicality" as a matter of nonconservative extension rather than outright inconsistency. A question about the relation of this extension and a differently described (though possibly identical) logic intermediate between BCI and BCK is raised in a final section, which closes with a handful of questions left unanswered by our discussion.

Article information

Source
Notre Dame J. Formal Logic Volume 47, Number 1 (2006), 101-131.

Dates
First available in Project Euclid: 27 March 2006

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1143468315

Digital Object Identifier
doi:10.1305/ndjfl/1143468315

Mathematical Reviews number (MathSciNet)
MR2211186

Zentralblatt MATH identifier
1107.03018

Subjects
Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
Secondary: 03B05: Classical propositional logic

Keywords
Curry's Paradox truth-functions fixed points conservative extension substructural logics BCI logic

Citation

Humberstone, Lloyd. Variations on a Theme of Curry. Notre Dame J. Formal Logic 47 (2006), no. 1, 101--131. doi:10.1305/ndjfl/1143468315. http://projecteuclid.org/euclid.ndjfl/1143468315.


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