Presocratic philosophy, for all its diverse features, is united by the quest to understand the origin and nature of the world. The approach of the Pythagoreans to this quest is governed by their belief, probably based on studies of the numerical relations in musical harmony, that number or numerical structure plays a key role for explaining the world-order, the cosmos. It remains questionable to what extent the Pythagoreans, by positing number as an all-powerful explanatory concept, broke free from Presocratic ideas (...) that certain stuffs or material elements sufficed to account for the source and constitution of the world, but apparently number found such a universal application with them that Aristotle could summarize the Pythagorean position as ‘numbers…are the whole universe’ . Historians of Greek philosophy have generally accepted Aristotle's assessment. Of late, however, certain scholars have argued that the Pythagorean number doctrine is Aristotelian interpretation, unjustly foisted upon the Pythagoreans. Enlisted in support of their arguments are the fragments of Philolaus of Croton. Here we have the foremost representative of fifth-century Pythagoreanism, who states as his basic principles, not numbers exactly, but ‘limiters’ and ‘unlimiteds’, and who, it is argued, regards number solely as an epistemological aid for understanding the structure of reality. So Philolaus is called upon as a witness against Aristotle. The rationale goes something like this: Aristotle most likely had written sources for his knowledge of Pythagorean teachings; the only texts we know of with any certainty are Philolaus' book and the writings of Archytas; since Aristotle treats Archytas separately, he is mainly relying on Philolaus; because Philolaus does not expressly state that things are numbers, Aristotle's interpretation is wrong. (shrink)