The mathematical origins of Aristotle's syllogistic

Abstract

In 1936, BENEDICT EINARSON called attention to a number of similarities, terminological and otherwise, between the language of ARISTOTLE'S logical writings and that of ancient Greek mathematics) The significance of this research has not, I think, generally been recognized; indeed, EINARSON's paper has not elicited much comment from other scholars. 2 I want to propose an interpretation of the syllogistic theory presented in Prior Analytics 1.4-7 which takes account of EINARSON'S work. I claim that this syllogistic theory is more properly regarded as mathematics than as logic as understood by most contemporary logicians. These results, if correct, will require some major revisions in our interpretation of ARISTOTLE'S logical works and in our account of his development as a logician: in particular, the profusion of recent work 3 interpreting the syllogistic by constructing formal models for it in the style of contemporary logic must be given a hard second look. Moreover, some questions will be raised about the place of the syllogistic theory in ARISTOTLE's conception of logic. I would like to suggest what I think some of the answers might be, although this is a problem that must await further research. EINARSON has gathered from the Organon an impressive list of terms with technical mathematical associations. Some of these terms concern the techniques