Editing Ancient Greek philosophy (section)

=== Pythagoreanism ===

{{Main|Pythagoreanism}}

[[Pythagoras]] lived at approximately the same time that Xenophanes did and, in contrast to the latter, the school that he founded sought to reconcile religious belief and reason. Little is known about his life with any reliability, however, and no writings of his survive, so it is possible that he was simply a [[mysticism|mystic]] whose successors introduced rationalism into Pythagoreanism, that he was simply a [[rationalism|rationalist]] whose successors are responsible for the mysticism in Pythagoreanism, or that he was actually the author of the doctrine; there is no way to know for certain.<ref>Burnet, ''Greek Philosophy'', 37–38.</ref>

Pythagoras is said to have been a disciple of [[Anaximander]] and to have imbibed the [[cosmology|cosmological]] concerns of the Ionians, including the idea that the cosmos is constructed of spheres, the importance of the infinite, and that air or aether is the ''arche'' of everything.<ref>Burnet, ''Greek Philosophy'', 38–39.</ref> Pythagoreanism also incorporated [[asceticism|ascetic]] ideals, emphasizing purgation, [[metempsychosis]], and consequently a respect for all animal life; much was made of the correspondence between mathematics and the cosmos in a musical harmony.<ref>Burnet, ''Greek Philosophy'', 40–49.</ref> Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.<ref>C.M. Bowra 1957 ''The Greek experience'' p. 166"</ref>