Abstract

The first serious attempt in the West at analyzing a mathematical proof according to syllogistic theory was carried out by Alessandro Piccolomini in 1547. Aristotelian scholars had claimed that mathematics was to be considered most certain because it used “scientific” (“demonstrative”) syllogisms which, among other features, were supposed to connect the major and the minor term of the premises by means of a middle term that provided the “cause” of the conclusion. Piccolomini argued that mathematics did not make use of causal syllogisms and thus that it did not satisfy the criteria set by Aristotle for “scientific” syllogisms. In order to prove his claim, Piccolomini reconstructed the first proposition of Euclid’s _Elements_ according to syllogistic logic but then objected that the syllogisms used in the proof were not “causal,” and hence not “scientific.” The chapter presents Piccolomini’s syllogistic reconstruction of the first proposition of Euclid’s _Elements_ and points out its shortcomings.