 (2) Pythagoreanism is the philosophy of a group of philosophers active in the fifth and the first half of the fourth century BCE, whom Aristotle refers to as “the so-called Pythagoreans” and to whom Plato also refers. Aristotle’s expression, “so-called Pythagoreans,” suggests both that at his time this group of thinkers was commonly called Pythagoreans and, at the same time, calls into question the actual connection between these thinkers and Pythagoras himself. Aristotle ascribes no specific names to these Pythagoreans, but the philosophy which he assigns to them is very similar to what is found in the fragments of  Philolaus  of Croton (ca. 470-ca. 390 BCE). Thus, Philolaus and his successor Eurytus are likely to have been the most prominent of these Pythagoreans. Philolaus posits limiters and unlimiteds as first principles and emphasizes the role of number in understanding the cosmos. Aristotle also identifies a distinct group of these so-called Pythagoreans who formulated a set of basic principles known as the table of opposites. Plato’s sole reference to Pythagoreans cites their search for the numerical structure of contemporary music and is probably an allusion to  Archytas  (ca. 420-ca. 350 BCE), who is the first great mathematician in the Pythagorean tradition. Starting from the system of Philolaus he developed his own sophisticated account of the world in terms of mathematical proportion.