Contenability and the Logic of Consequential Implication

Logic Journal of the IGPL 12 (6):561-579 (2004)
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Abstract

The aim of the paper is to outline a treatment of cotenability inspired by a perspective which had strong roots in ancient logic since Chrysippus and was partially recovered in the XX Century by E. Nelson and the exponents of so-called connexive logic. Consequential implication is a modal reinterpretation of connexive implication which permits a simple reconstruction of Aristotle's square of conditionals, in which proper place is given not only to ordinary cotenability between A and B, represented by ¬, but to its “secondary” variant ¬ . After showing that logics of strict implication, of Stalnaker-Lewis conditionals and of relevant implication do not satisfy the intuitive properties required for cotenability , it is proved that such conditions are satisfied by consequential cotenability and by its secondary variant . The notions of strong cotenability and of bilateral cotenability are then introduced: the latter stands to standard cotenabilty as contingency stands to possibility, and in Section 9 it is shown to be a useful tool in the reconstruction of Boethius' theory of adjuncta

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Claudio Pizzi
Università degli Studi di Siena

Citations of this work

Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
Connexive Negation.Luis Estrada-González & Ricardo Arturo Nicolás-Francisco - 2023 - Studia Logica (Special Issue: Frontiers of Conn):1-29.
Counterfactuals and modus tollens in abductive arguments.C. Pizzi - 2013 - Logic Journal of the IGPL 21 (6):962-979.
Axioms for a Logic of Consequential Counterfactuals.Claudio E. A. Pizzi - 2023 - Logic Journal of the IGPL 31 (5):907-925.

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