CORCORAN-SWINIARSKI ON OCKHAM’S SUMMA LOGICAE I

I1979. Loux, M. Ockham's Theory of Terms (1974). Mathematical Reviews 58#26829. (Co-author:  J. Swiniarski).In the period preceding the decidedly mathematical contributions to logic (Leibniz, Boole, etc.) but following the ground-breaking work of Aristotle and the Stoics, William of Ockham (ca. 1285{1349?) was probably the most technically competent, the most imaginative and the most prolific of the many able persons who struggled to create what we now know as modern logic. Ockham's writings contain several ideas which have only recently been fully appreciated, e.g., that an existential statement is very closely related to an “indefinitely long" disjunction, that a universal statement is very closely related to an “indefinitely long" conjunction, that the contradictory of a conjunction is the disjunction of the contradictories of the conjuncts, and that the contradictory of a disjunction is the conjunction of the contradictories of the disjuncts. By studying Ockham it is possible to gain an understanding of the enormous difficulties that had to be overcome (or set to one side) in order to achieve the degree of comprehensiveness and rigor now found in modern logic.The most important logical work of Ockham is the three-part SUMMA LOGICAE, the first part of which is translated for the first time into English in the present book.