The last generation of “Presocratics” includes two further prominent philosophers: Philolaus and Diogenes of Apollonia. They both offer important lessons for any attempt to offer a general account of the development of early Greek philosophy.

Philolaus of Croton

Philolaus' philosophy brings us back, almost full circle, to the Ionian beginnings of our story and the Pythagoreans' interest in number, harmony and the nature of the soul. Perhaps the first self-proclaimed Pythagorean to compose a treatise, Philolaus combines Pythagorean interests evident from the earliest periods of the movement, some hundred years before, with a familiar form of cosmological account, no doubt influenced by the similar attempts of thinkers such as Empedocles and Anaxagoras a few years earlier. It is possible that Philolaus' work is the principal source for Aristotle's account of Pythagoreanism in general.

Philolaus' cosmology begins as follows: ‘The nature in the cosmos was fitted together from unlimiteds (apeira) and limiters (perainonta), both the cosmos as a whole and everything in it” (DK 44 B1). DK 44 B2 then goes on to argue further for this dualist system, insisting on the necessity of both “unlimiteds” and “limiters” to generate the cosmos and the things in it. The obscure identity of these “unlimiteds” and “limiters” has been one of the principal puzzles in interpreting Philolaus' account and commentators have often made a link between this apparently abstract ontology and Pythagorean ideas about number and shape, identifying the “limiters” as numbers (or numbers of a certain kind) or abstract geometrical shapes that are then somehow imposed on the “unlimiteds”, perhaps conceived as a kind of unformed matter.