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May 2021 Structural Weakening and Paradoxes
Bruno Da Ré
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Notre Dame J. Formal Logic 62(2): 369-398 (May 2021). DOI: 10.1215/00294527-2021-0018

Abstract

Recently, several authors have pointed out that substructural logics are adequate for developing naive theories that represent semantic concepts such as truth. Among them, three proposals have been explored: dropping cut, dropping contraction and dropping reflexivity. However, nowhere in the substructural literature has anyone proposed rejecting the structural rule of weakening, while accepting the other rules. Some theorists have even argued that this task was not possible, since weakening plays no role in the derivation of semantic paradoxes. In this article, I introduce a theory for naive truth based on the logic resulting from dropping the rule of weakening from classical logic, and maintaining the other structural rules.

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Bruno Da Ré. "Structural Weakening and Paradoxes." Notre Dame J. Formal Logic 62 (2) 369 - 398, May 2021. https://doi.org/10.1215/00294527-2021-0018

Information

Received: 11 July 2019; Accepted: 6 January 2021; Published: May 2021
First available in Project Euclid: 9 June 2021

Digital Object Identifier: 10.1215/00294527-2021-0018

Subjects:
Primary: 03B47
Secondary: 03B80, 03F99

Rights: Copyright © 2021 University of Notre Dame

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Vol.62 • No. 2 • May 2021
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