## Notre Dame Journal of Formal Logic

### A Note on Freedom from Detachment in the Logic of Paradox

#### Abstract

We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$, except trivially. We derive this as a corollary of a more general result concerning variable sharing.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 54, Number 1 (2013), 15-20.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1355494519

Digital Object Identifier
doi:10.1215/00294527-1731353

Mathematical Reviews number (MathSciNet)
MR3007958

Zentralblatt MATH identifier
1272.03115

#### Citation

Beall, Jc; Forster, Thomas; Seligman, Jeremy. A Note on Freedom from Detachment in the Logic of Paradox. Notre Dame J. Formal Logic 54 (2013), no. 1, 15--20. doi:10.1215/00294527-1731353. https://projecteuclid.org/euclid.ndjfl/1355494519

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