Restall’s Proof-Theoretic Pluralism and Relevance Logic

Erkenntnis 81 (6):1243-1252 (2016)
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Abstract

Restall :279–291, 2014) proposes a new, proof-theoretic, logical pluralism. This is in contrast to the model-theoretic pluralism he and Beall proposed in Beall and Restall :475–493, 2000) and in Beall and Restall. What I will show is that Restall has not described the conditions on being admissible to the proof-theoretic logical pluralism in such a way that relevance logic is one of the admissible logics. Though relevance logic is not hard to add formally, one critical component of Restall’s pluralism is that the relevance logic that gets added must have connectives which mean the same thing as the connectives in the already admitted logic. This is what I will show is not possible.

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Teresa Kouri Kissel
Old Dominion University

Citations of this work

Logical Pluralism from a Pragmatic Perspective.Teresa Kouri Kissel - 2018 - Australasian Journal of Philosophy 96 (3):578-591.
Proof-theoretic pluralism.Filippo Ferrari & Eugenio Orlandelli - 2019 - Synthese 198 (Suppl 20):4879-4903.

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References found in this work

Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan Ross Anderson & Nuel D. Belnap - 1975 - Princeton, N.J.: Princeton University Press. Edited by Nuel D. Belnap & J. Michael Dunn.
Logical Pluralism.J. C. Beall & Greg Restall - 2005 - Oxford, GB: Oxford University Press. Edited by Greg Restall.
Logical pluralism.Jc Beall & Greg Restall - 2000 - Australasian Journal of Philosophy 78 (4):475 – 493.
Display logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.

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