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May 2020 A Note on FDE “All the Way Up”
Jc Beall, Caleb Camrud
Notre Dame J. Formal Logic 61(2): 283-296 (May 2020). DOI: 10.1215/00294527-2020-0007

Abstract

A very natural and philosophically important subclassical logic is FDE (for first-degree entailment). This account of logical consequence can be seen as going beyond the standard two-valued account (of “just true” and “just false”) to a four-valued account (adding the additional values of “both true and false” and “neither true nor false”). A natural question arises: What account of logical consequence arises from considering further (positive) combinations of such values? A partial answer was given by Priest in 2014; Shramko and Wansing had also given a partial result some years earlier, although in a different (more algebraic) context. In this note we generalize Priest’s (and indirectly Shramko and Wansing’s) result to show that even if one considers ordinal-many (positive) combinations of the previous values, for any ordinal, the resulting consequence relation (the resulting logic) remains FDE.

Citation

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Jc Beall. Caleb Camrud. "A Note on FDE “All the Way Up”." Notre Dame J. Formal Logic 61 (2) 283 - 296, May 2020. https://doi.org/10.1215/00294527-2020-0007

Information

Received: 3 September 2019; Accepted: 20 November 2019; Published: May 2020
First available in Project Euclid: 9 April 2020

zbMATH: 07222692
MathSciNet: MR4092536
Digital Object Identifier: 10.1215/00294527-2020-0007

Subjects:
Primary: 03B20
Secondary: 03A99, 03B50, 03B53

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 2 • May 2020
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