A Note on Freedom from Detachment in the Logic of Paradox

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Notre Dame Journal of Formal Logic 54 (1):15-20 (2013)
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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

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10.1215/00294527-1731353

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Author Profiles

Jeremy Seligman
University of Auckland
Thomas Forster
Cambridge University
Jc Beall
University of Notre Dame

Citations of this work

What Is an Inconsistent Truth Table?Zach Weber, Guillermo Badia & Patrick Girard - 2016 - Australasian Journal of Philosophy 94 (3):533-548.
Lp+, k3+, fde+, and their 'classical collapse'.Jc Beall - 2013 - Review of Symbolic Logic 6 (4):742-754.

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References found in this work

The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Logic for equivocators.David K. Lewis - 1982 - Noûs 16 (3):431-441.
A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
Multiple-conclusion lp and default classicality.Jc Beall - 2011 - Review of Symbolic Logic 4 (2):326-336.
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.

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