A propositional logic with subjunctive conditionals

Abstract

In this paper a formalized logic of propositions, PA1, is presented. It is proven consistent and its relationships to traditional logic, to PM ([15]), to subjunctive (including contrary-to-fact) implication and to the “paradoxes” of material and strict implication are developed. Apart from any intrinsic merit it possesses, its chief significance lies in demonstrating the feasibility of a general logic containing the principle of subjunctive contrariety, i.e., the principle that ‘If p were true then q would be true’ and ‘If p were true then q would be false’ are incompatible.