for both plato and aristotle, then, pythagoreanism is almost the closest philosophy to their own, and yet to be distinguished from their own.

for both plato and aristotle, then, pythagoreanism is almost the closest philosophy to their own, and yet to be distinguished from their own. pythagoreans look for a reality that is eternal and superior to the one immediately surrounding us, and they find it through the study of such s as music and astronomy. so far, plato and aristotle follow. there they diverge from both the pythagoreans as from each other. in both cases the pythagoreans are guilty, as it were, in producing too much music. for plato, the mistake is in the attention to concrete, heard sounds; for aristotle, the mistake is the attention to abstract, unheard sounds. in both cases, music is suggestive of the more basic principle, of duality — one thing being simultaneously something else. this is the principle plato wishes to exploit, and aristotle to deny and reduce to mere metaphor.

for both plato and aristotle, the pythagoreans are somewhat admired, they are somewhat sublime—but, evenmore,made fun of. they display a certain absurdity, paying attention to the tiny details, whether these are the quarter-tones that plato’s pythagoreans stretch their ears to hear, or the three consonants that aristotle’s pythagoreans describe in musical terms. this special position—sublime, and ridiculous—is perhaps what makes them most ‘pythagorean’. after all, this duality of the sublime and the ridiculous is central to the tradition of pythagoras himself, the prophet of metempsychosis—and the hermit of beans.

once again: it is not so much the contents of the pythagorean life itself that is important, as its very otherness. the pythagoreans insist on living differently, and, in this way, they reach a different reality. plato wishes to go beyond them into that reality, aristotle wishes to stay nearer to ordinary reality, but both sense that the way to eternal, higher metaphysical realms is through a certain distance from ordinary reality; and that mathematics, in
particular music, may lead the way.

so here is the formula we gain from plato’s and aristotle’s reception (or, perhaps, construction) of the pythagoreans. othern