Two Kinds of Consequential Implication

Studia Logica 106 (3):453-480 (2018)
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Abstract

The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength and \). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system for \, CI\, is definitionally equivalent to the deontic system KD and is intertranslatable with the minimal consequential system for \, CI. The main drawback ot the weaker operator \ is that it lacks unrestricted contraposition, but the final section of the paper argues that \ has some properties which make it a valuable alternative to \, turning out especially plausible as a basis for the definition of operators representing synthetic conditionals.

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Claudio Pizzi
Università degli Studi di Siena

Citations of this work

Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
Axioms for a Logic of Consequential Counterfactuals.Claudio E. A. Pizzi - 2023 - Logic Journal of the IGPL 31 (5):907-925.
Situation-Based Connexive Logic.Alessandro Giordani - 2023 - Studia Logica 112 (1):295-323.

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References found in this work

Connexive implication.Storrs Mccall - 1966 - Journal of Symbolic Logic 31 (3):415-433.
A propositional logic with subjunctive conditionals.R. B. Angell - 1962 - Journal of Symbolic Logic 27 (3):327-343.
Strong Boethius' thesis and consequential implication.Claudio Pizzi & Timothy Williamson - 1997 - Journal of Philosophical Logic 26 (5):569-588.
On systems containing Aristotle's thesis.R. Routley & H. Montgomery - 1968 - Journal of Symbolic Logic 33 (1):82-96.

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