The maxim of minimal mutilation, as applied to non-classical theories of truth by Hjortland, recommends preferring logical theories that retain as much classical logic as possible. Connexive logics, by contrast, are typically understood as contra-classical, as they invalidate some classical principles in order to validate the Aristotle and Boethius theses without collapsing into triviality, a threat posed by the Post-completeness of classical logic. In this article, we show that these two desiderata (i.e., validating every connexive principle while validating every classicaly valid inference) are compatible. We introduce CST, a connexive logic defined by transplanting the strict-tolerant validity relation of ST into the possible worlds semantics of Wansing’s connexive logic C. We prove that CST validates every classically valid inference while also validating all four connexive principles, i.e., Aristotle’s Thesis, its variant, Boethius’ Thesis, and its variant, and that its conditional is non-symmetric. CST is therefore supraclassical and connexive in Wansing’s minimal sense, yet non-trivial. The key to avoiding triviality lies in the strict-tolerant character of the validity relation: just as ST recovers classical inferential behavior while departing from it at the metainferential level, CST recovers classical and connexive principles while invalidating Cut and related metainferences. We also present a sequent calculus LKcst for the logic and discuss possible interpretations of this logic and reassess the classical logic’s Post-completeness result.
Activities > Extra talks > Supraclassical connexive logic
Supraclassical connexive logic
Federico Pailos (U. Tübingen/CONICET)
