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2018 Second-Order Logic of Paradox
Allen P. Hazen, Francis Jeffry Pelletier
Notre Dame J. Formal Logic 59(4): 547-558 (2018). DOI: 10.1215/00294527-2018-0011

Abstract

The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, concluding that it will be extremely difficult to appeal to second-order LP for the purposes that its proponents advocate, until some deep, intricate, and hitherto unarticulated metaphysical advances are made.

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Allen P. Hazen. Francis Jeffry Pelletier. "Second-Order Logic of Paradox." Notre Dame J. Formal Logic 59 (4) 547 - 558, 2018. https://doi.org/10.1215/00294527-2018-0011

Information

Received: 8 January 2016; Accepted: 31 May 2016; Published: 2018
First available in Project Euclid: 11 September 2018

zbMATH: 06996543
MathSciNet: MR3871900
Digital Object Identifier: 10.1215/00294527-2018-0011

Subjects:
Primary: 03B53, 03C85
Secondary: 03B50, 03E70

Rights: Copyright © 2018 University of Notre Dame

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Vol.59 • No. 4 • 2018
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