There is a Logical Negation

Jc Beall agues that if FDE is logic proper, then there is no logical negation. This claim is largely based on the fact that, in standard proof systems for FDE, there are no stand-alone negation rules that suffice to capture the behavior of negation. In this paper, I show that by adopting a bilateral proof system for FDE, one can maintain that there is a logical negation, it is the very same logical negation that belongs to classical logic, and its basic function is to flip-flop between assertion and denial. I conclude by responding to the objection that it can never be coherent to both assert and deny the very same thing.

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Publication Details

Journal
The Australasian Journal of Logic
Published
2026-01-12
DOI
https://doi.org/10.26686/ajl.v23i1.9622
Citations
1
Primary Topic
Logic, programming, and type systems
Type
article
Field-Weighted Citation Impact
52.10
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article

There is a Logical Negation

Ryan Simonelli
1 citations
The Australasian Journal of Logic
Logic, programming, and type systems
52.10
article

There is a Logical Negation

Ryan Simonelli
article en
1 citations

Abstract

Jc Beall agues that if FDE is logic proper, then there is no logical negation. This claim is largely based on the fact that, in standard proof systems for FDE, there are no stand-alone negation rules that suffice to capture the behavior of negation. In this paper, I show that by adopting a bilateral proof system for FDE, one can maintain that there is a logical negation, it is the very same logical negation that belongs to classical logic, and its basic function is to flip-flop between assertion and denial. I conclude by responding to the objection that it can never be coherent to both assert and deny the very same thing.

The Australasian Journal of LogicVol. 23(1)
Wuhan University (CN)
Peace, Justice and strong institutions
Openalex Percentile: Top 1%
Logic, programming, and type systems
52.10
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