Intuitionistic views on connexive constructible falsity

  • Intuitionistic logicians generally accept that a negation can be understood as an implication to absurdity. An alternative account of constructive negation is to define it in terms of a primitive notion of falsity. This approach was originally suggested by D. Nelson, who called the operator constructible falsity, as complementing certain constructive aspects of negation. For intuitionistic logicians to be able to understand this new notion, however, it is desirable that constructible falsity has a comprehensive relationship with the traditional intuitionistic negation. This point is especially pressing in H. Wansing’s framework of connexive constructible falsity, which exhibits unusual behaviours. From this motivation, this paper enquires what kind of interaction between the two operators can be satisfactory in the framework. We focus on a few naturallooking candidates for such an interaction, and evaluate their relative merits through analyses of their formal properties with both proof-theoretic and semantical means. We in particular note that some interactions allow connexive constructible falsity to provide a different solution to the problem of the failure of the constructible falsity property in intuitionistic logic. An emerging perspective in the end is that intuitionistic logicians may have different preferences depending on whether absurdity is to be understood as the falsehood.

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Author:Satoru NikiORCiDGND
Parent Title (English):Journal of applied logics
Publisher:College Publications
Place of publication:Rickmansworth
Document Type:Article
Date of Publication (online):2024/04/24
Date of first Publication:2024/03/31
Publishing Institution:Ruhr-Universität Bochum, Universitätsbibliothek
Tag:ConLog, Projekt ID: 101018280
Basic systems; Connexive logic; Constructible falsity; Contradictory logics; Intuitionistic logic
First Page:125
Last Page:157
ConLog, Projekt ID: 101018280
Relation (DC):info:eu-repo/grantAgreement/EC/H2020/101018280
Institutes/Facilities:Institut für Philosophie I
Dewey Decimal Classification:Philosophie und Psychologie / Philosophie
faculties:Fakultät für Philosophie und Erziehungswissenschaft
Licence (English):License LogoCreative Commons - CC BY-NC-ND 4.0 - Attribution-NonCommercial-NoDerivatives 4.0 International