Logical Consequence and the Paradoxes

Journal of Philosophical Logic 43 (2-3):439-469 (2014)

Authors
Edwin Mares
Victoria University of Wellington
Abstract
We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics
Keywords Paradoxes  Structural contraction  V-Curry paradox  Informational semantics  Substructural logics
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DOI 10.1007/s10992-013-9268-4
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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
Spandrels of Truth.J. C. Beall - 2009 - Oxford University Press.

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Citations of this work BETA

Generalized Revenge.Julien Murzi & Lorenzo Rossi - forthcoming - Australasian Journal of Philosophy:1-25.
The Logics of Strict-Tolerant Logic.Eduardo Barrio, Lucas Rosenblatt & Diego Tajer - 2015 - Journal of Philosophical Logic 44 (5):551-571.
Contractions of Noncontractive Consequence Relations.Rohan French & David Ripley - 2015 - Review of Symbolic Logic 8 (3):506-528.

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