A Note on Freedom from Detachment in the Logic of Paradox


Authors
Jeremy Seligman
University of Auckland
Jc Beall
University of Connecticut
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
Keywords LP   detachment-free logics   detachable connective   paradox   relevance logics   variable-sharing   paraconsistent logic
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DOI 10.1215/00294527-1731353
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References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Multiple-Conclusion Lp and Default Classicality.Jc Beall - 2011 - Review of Symbolic Logic 4 (2):326-336.
A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
On Dialethism.Laura Goodship - 1996 - Australasian Journal of Philosophy 74 (1):153 – 161.

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Citations of this work BETA

Lp+, K3+, Fde+, and Their 'Classical Collapse'.Jc Beall - 2013 - Review of Symbolic Logic 6 (4):742-754.

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