On the provable contradictions of the connexive logics C and C3
- Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely N4, as well as its non-constructive extension C3. For these systems, various observations concerning provable contradictions are made, using mainly a proof-theoretic approach. The topics covered in this paper include: how new contradictions are found from parts of provable contradictions; how to characterise provable contradictions in C3 that are constructive; how contradictions can be seen from the relative viewpoint of strong implication; and as an appendix an attempt at generating provable contradictions in C3.
| Author: | Satoru NikiORCiDGND, Heinrich WansingORCiDGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-107124 |
| DOI: | https://doi.org/10.1007/s10992-023-09709-4 |
| Parent Title (English): | Journal of philosophical logic |
| Publisher: | Springer Nature |
| Place of publication: | Berlin |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/09/12 |
| Date of first Publication: | 2023/07/29 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | ConLog, Projekt ID: 101018280 Connexive Logic; Non-Trivial Contradictory Logics; Provable Contradictions; Strong Implication |
| Volume: | 2023 |
| Issue: | 52 |
| First Page: | 1355 |
| Last Page: | 1383 |
| Note: | 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 |
| OpenAIRE: | OpenAIRE |
| faculties: | Fakultät für Philosophie und Erziehungswissenschaft |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
