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November 2019 Noncontractive Classical Logic
Lucas Rosenblatt
Notre Dame J. Formal Logic 60(4): 559-585 (November 2019). DOI: 10.1215/00294527-2019-0020

Abstract

One of the most fruitful applications of substructural logics stems from their capacity to deal with self-referential paradoxes, especially truth-theoretic paradoxes. Both the structural rules of contraction and the rule of cut play a crucial role in typical paradoxical arguments. In this paper I address a number of difficulties affecting noncontractive approaches to paradox that have been discussed in the recent literature. The situation was roughly this: if you decide to go substructural, the nontransitive approach to truth offers a lot of benefits that are not available in the noncontractive account. I sketch a noncontractive theory of truth that has these benefits. In particular, it has both a proof- and a model-theoretic presentation, it can be extended to a first-order language, and it retains every classically valid inference.

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Lucas Rosenblatt. "Noncontractive Classical Logic." Notre Dame J. Formal Logic 60 (4) 559 - 585, November 2019. https://doi.org/10.1215/00294527-2019-0020

Information

Received: 6 July 2017; Accepted: 24 March 2018; Published: November 2019
First available in Project Euclid: 6 September 2019

zbMATH: 07167758
MathSciNet: MR4019862
Digital Object Identifier: 10.1215/00294527-2019-0020

Subjects:
Primary: 03A05
Secondary: 03B47

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 4 • November 2019
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