Abstract

Extending Lukasiewicz's approach of axiomatization to the modal syllogistic, McCall develops a system of fourteen axioms with decision procedure, in which exactly those necessity syllogisms recognized by Aristotle are provable. Primitives, besides those of propositional logic, are Necessity and the A and I statement forms. The approach thus contrasts with that of the "structuralists", who would analyze Aristotle's modal statements further in terms of contemporary logic systems. The seemingly insurmountable problems of the contingency syllogisms are circumvented by taking contingency as an additional primitive requiring fourteen further axioms. In the resulting system, all of Aristotle's contingency syllogisms, as well as twenty-four which he overlooked, are provable. Although a "structuralist" analysis would seem indispensable for an ultimate understanding of the modal syllogistic, McCall's formalization is more faithful to Aristotle than any hitherto proposed.--J. B. B.