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An Argument for Minimal Logic

Kürbis, N; (2019) An Argument for Minimal Logic. Dialectica , 73 (1-2) pp. 31-63. 10.1111/1746-8361.12267. Green open access

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Abstract

The problem of negative truth is the problem of how, if everything in the world is positive, we can speak truly about the world using negative propositions. A prominent solution is to explain negation in terms of a primitive notion of metaphysical incompatibility. I argue that if this account is correct, then minimal logic is the correct logic. The negation of a proposition A is characterised as the minimal incompatible of A composed of it and the logical constant ¬. A rule‐based account of the meanings of logical constants that appeals to the notion of incompatibility in the introduction rule for negation ensures the existence and uniqueness of the negation of every proposition. But it endows the negation operator with no more formal properties than those it has in minimal logic.

Type: Article
Title: An Argument for Minimal Logic
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/1746-8361.12267
Publisher version: https://doi.org/10.1111/1746-8361.12267
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10078502
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