PYTHAGORAS (c. 570-c.494)
Born on the Island of Samos (off the coast of Asia Minor, not far from Miletus); his father was supposed to have been a gem-cutter or engraver. He left Samos in 530 to escape rule under Polycrates, a tyrant. He reportedly traveled in Egypt and Babylonia. Pythagoras later settled in Croton, on the Bay of Tarentum, in southern Italy, where there were Greek colonies.
He was a mathematician as well as a philosopher and a religious leader. He founded a philosophical/religious monastic order (the "Pythagoreans") of three hundred young men (reports differ as to whether the order included women; certainly, Pythagoras famously lectured to an all-women audience) that had strict rules of conduct and diet. They also held their property in common.
He believed that the study of mathematics could convert the soul from the world of the senses to the contemplation of the eternal. Pythagoras divided the soul from the soma (body) (which was considered the sema (prison)). The soul was immortal and transmigrated from one body to another (metempsychosis), including the bodies of other creatures (reincarnation). (According to one version of this theory, after leaving the human body, soul goes through all of the different animal bodies, which takes 3,000 years, before returning to a human body).
Today he is best remembered for Pythagoras' Theorem. It is believed that he did not write a book. There was an uprising in Croton against the Pythagoreans; many were killed and the rest were driven out. Pythagoras fled to a temple in the nearby town, Metapontum, where he starved to death.
Sometime close to his death or after the Pythagoreans divided into the akousmatikoi (from akousmata, "things heard"), who venerated his teachings on religion and the proper way to live but had little interest in philosophy and mathematics, and the mathematikoi (from mathema, "study" or "learning"), who were interested in philosophical, mathematical, musical, and astronomical knowledge. These three areas were connected, for they believed that mathematics was the key to understanding the kosmos: the kosmos is a harmonious (from harmonia, a carpenter's joint, and also a "musical fitting together") arrangement ordered by number.
(1) 'Empedocles too bears witness to this, writing of him [Pythagoras]: "And there was among them a man of surpassing knowledge, master especially of all kinds of wise words, who had acquired the utmost wealth of understanding: for whenever he reached out with all his understanding, easily he saw each of the things that are, in ten and even twenty generations of men."'
-- PP, p. 219
(2) 'At any rate, Timaeus says in book VIII: "So when the younger men came to him wanting to associate with him, he "did not immediately agree, but said that they must also hold their property in common with whoever else might be admitted to membership." Then after much intervening matter he says: "And it was because of them that it was first said in Italy: "What belongs to friends is common property."'"'
-- PP, p. 227
(3) 'Three hundred of the young men, bound to each other by oath like a brotherhood, lived segregated from the rest of the citizens, as if to form a secret band of conspirators, and brought the city [Croton] under their control.'
-- PP, p. 227
(4) "<Pythagoras ordered his followers> not to pick up <food> which had fallen, to accustom them not to eat self-indulgently or because it fell on the occasion of someone's death... not to touch a white rooster, because it is sacred to the Month and is a suppliant. It is a good thing, and is sacred to the Month because it indicates the hours, and white is of the nature of good, while black is of the nature of evil... not to break bread, because friends long ago used to meet over a single loaf just as foreigners still do, and not to divide what brings them together. Others <explain this practice> with reference to the judgment in Hades, others say that it brings cowardice in war, and still others that the whole universe begins from this."
-- Aristotle, quoted in Diogenes Laertius, Lives of the Philosophers (8.34-35)
(1) 'The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides enclosing the right angle. [If we pay any attention to those who like to recount ancient history, we may find some of them referring this theorem to Pythagoras, and saying that he sacrificed an ox in honor of his discovery.]'
-- PP, 1st ed., p. 281
Metempsychosis and Reincarnation
(1) 'On the subject of reincarnation Xenophanes bears witness in an elegy which begins: "Now I will turn to another tale and show the way." What he says about Pythagoras runs thus: "Once they say that he was passing by when a puppy was being whipped, and he took pity and said: "Stop, do not beat it; for it is the soul of a friend that I recognized when I heard it giving tongue.""'
-- PP, p. 219
(2) 'Moreover, the Egyptians are the first to have maintained the doctrine that the soul of man is immortal, and that, when the body perishes, it enters into another animal that is being born at the time, and when it has been the complete round of the creatures of the dry land and of the sea and of the air it enters again into the body of a man at birth; and its cycle is completed in 3,000 years. There are some Greeks who have adopted this doctrine , some in former times, and some in later, as if it were their own invention; their names I know but refrain from writing down.'
-- PP, p. 220
(3) 'What he said to his associates, nobody can say for certain; for silence with them was of no ordinary kind. Nonetheless the following became universally known: first, that he maintains that the soul is immortal; next, that it changes into other kinds of living things; also that events recur in cycles, and that nothing is ever absolutely new; and finally, that all living things should be regarded as akin. Pythagoras seems to have been the first to bring these beliefs into Greece.'
-- Porphyry, Life of Pythagoras (19)
(1) 'And by way of indicating this the Pythagoreans are accustomed sometimes to say 'All things are like number', and sometimes to swear this most potent oath: 'Nay, by him that gave to us the tetractys, which contains the fount and root of ever-flowing nature.' By 'him that gave' they mean Pythagoras (for they deified him); and by 'the tetractys' a number which, being composed of four primary numbers, produces the most perfect number, as for example ten (for one and two and three and four make ten). This number is the first tetractys, and it is called 'fount of ever-flowing nature' inasmuch as the whole universe is arranged according to attunement, and the attunement is a system of three concords, the fourth, the fifth and the octave, and of these three concords the proportions are found in the four numbers just mentioned -- in one, two, three and four.'
-- PP, p. 233-234
Pythagoras and Harmony (David Harrison)
(2) 'At the same time as these [Leucippus and Democritus] and before them, those called Pythagoreans took hold of mathematics and were the first to advance that study, and being brought up in it, they believed that its principles are the principles of all things that are. Since numbers are naturally first amongst these, and in numbers they thought they observed many likenesses to things that are and that come to be... and since they saw the attributes and ratios of musical scales in numbers, and other things seemed to be made in the likeness of numbers in their entire nature, and numbers seemed to be primary in all nature, they supposed the elements of numbers to be the elements of all things that are.'
-- Aristotle, Metaphysics (1.5 986a17-21)
(3) 'The elements of number are the even and the odd, and of these the latter [odd] is limited and the former [even] unlimited. The One is composed of both of these (for it is both even and odd) and number springs from the One; and numbers, as I have said, constitute the whole universe.'
-- Aristotle, Metaphysics (1.5 987a13-19)
(4) 'They supposed the elements of numbers to be the elements of all existing things.'
-- Aristotle, Metaphysics (1.5 986a1-2)