SOURCE: "Greek Mathematics and Greek Logic," in Ancient Logic and Its Modern Interpretations, edited by John Corcoran, D. Reidel Publishing Company, 1974, pp. 35-70.

In the following essay, delivered as a paper in 1972 and published in 1974, Mueller examines the nature of Euclidean reasoning (as evidenced in Elements), and its relationship to Aristotle's syllogistic logic (a type of logical argument). Mueller concludes that Euclid demonstrates no awareness of syllogistic logic or of the basic concept of logic—that is, that an argument's validity depends on its form.

Introduction

By 'logic' I mean 'the analysis of argument or proof in terms of form'. The two main examples of Greek logic are, then, Aristotle's syllogistic developed in the first twenty-two chapters of the Prior Analytics and Stoic propositional logic as reconstructed in the twentieth century. The topic I shall consider in this paper is the relation between Greek logic in this sense...