Pythagoreanism

"We are told that the other book which passed under the name of Pythagoras was really by Lysis."

"Aristotle... was... out of sympathy with Pythagorean ways of thinking, but took... great... pains to understand them. This was... because they played so great a part in the philosophy of Plato and his successors, and he had to make the relation of the two doctrines as clear as he could to... his disciples."

"[T]he religious revival... suggested the view that philosophy was above all a "way of life." Science too was a "purification," a means of escape from the "wheel." This is the view expressed so strongly in Plato’s Phaedo, which was written under the influence of Pythagorean ideas."

"In Copernicus time Pythagoreans still believed that the only way to truth was by mathematics."

"[W]e cannot safely take Plato as our guide to the original meaning of the Pythagorean theory, though... from him alone... we can learn to regard it sympathetically."

"None of Pythagoras own work has survived, but the ideas fathered on him by his followers would be the most potent in modern history. Pure knowledge, the Pythagoreans argued, was the purification (catharsis) of the soul... rising above the data of the human senses. The pure essential reality... was found only in the realm of numbers. The simple, wonderful proportion if numbers would explain the harmonies of music... [T]hey introduced the musical terminology of the octave, the fifth, the fourth, expressed as 2:1, 3:1, and 4:3. ..."

"It has been no easy task to revise this volume in such a way as to make it more worthy of the favour with which it has been received. Most of it has had to be rewritten in the light of certain discoveries made since the publication of the first edition, above all, that of the extracts from Menon’s Iατρικά, which have furnished, as I believe, a clue to the history of Pythagoreanism."

"They [the Pythagoreans] say the things themselves are Numbers and do not place the objects of mathematics between forms and sensible things. ...Since again, they saw that the modifications and the ratios of the musical scales were expressible in numbers—since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number... and the whole arrangement of the heavens they collected and fitted into their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory coherent."

"This sufficiently justifies... regarding the "fragments of Philolaos" with... more than suspicion."

"[W]e must not impute to the Pythagoreans... that even numbers can be halved indefinitely. They had... studied the properties of the decad, and... must have known that... 6 and 10 do not admit of this."

"It is... probable that we should ascribe to Pythagoras the Milesian view of a plurality of worlds, though... not... infinite ...Petron, one of the early Pythagoreans, said there were ...a hundred and eighty-three worlds arranged in a triangle; and Plato makes Timaios admit, when laying down ...only one world, that something might be urged in favour of ...five, as there are five regular solids."

"The Pythagoreans had... a great veneration for the... words of the Master... but... veneration is often accompanied by a singular licence of interpretation."