Connexive implication

Abstract

This paper contains a rigorous treatment of the species of implication described in [8] and [9], where it was given the name of connexive implication . A brief historical survey will lay bare its roots in antiquity, and it will be shown that none of the well-known systems of propositional logic serves to formalize it. 1 In this paper a new system of ‘connexive’ logic will be presented, the system being shown to be (a) consistent, (b) independent of two-valued logic, (c) Post-complete.