Introduction

Aristotle's reports on the philosophy of the “so-called Pythagoreans” are among our earliest sources for the history of Pythagoreanism. According to Aristotle, these Pythagoreans championed both a theory of principles (ἀρχαί) in which numbers (or the elements of numbers) play a fundamental role, and an astronomical system in which not only the five ordinary planets, the sun and the moon, but also the earth itself and even an additional counter-earth orbit around a central fire. The purpose of this chapter is to analyze the most comprehensive account of the Pythagorean theory of principles in Aristotle's extant work: the first part of Metaphysics A5.

Aristotle's treatment of “the so-called Pythagoreans” is distinguished from the rest of Metaphysics A by a feature which previous scholarship has tended to underrate: the focus here is on the intellectual development of the Pythagorean school. Aristotle's sketch of this development, however, is based on a much fuller treatment, which Aristotle had included in his monograph on the Pythagoreans. Whereas the monograph itself is now lost, Alexander of Aphrodisias, in commenting upon our chapter of the Metaphysics, supplies ample additional information gathered from the monograph. This evidence should be used in order to supplement the picture emerging from an analysis of Metaphysics A5.