Pythagoreanism

"The theory that the proper motion of the sun, moon, and planets is from west to east, and that they also share in the motion from east to west of the heaven of the fixed stars, makes its first appearance in the in Plato’s Republic, and is fully worked out in the Timaeus. In the Republic it is still associated with the "harmony of the spheres,"..."

"In the Timaeus... the slowest of the heavenly bodies appear the fastest and vice versa; and, as this... is... a Pythagorean [speaking], we might suppose the theory of a composite movement to have been anticipated by some... [in] that school."

"Pythagoreans were... open to new ideas."

"[T]he theory is... emphatically expressed by the Athenian Stranger in the Laws, who is... Plato... expounding a novel theory."

"[A] view... Aristotle sometimes attributes to the Pythagoreans... things were "like numbers." He does not appear to regard this as inconsistent with the doctrine that things are numbers..."

"Aristoxenos represented the Pythagoreans as teaching that things were like numbers, and there are other traces of an attempt to make... this... the original doctrine. A letter... purporting to be... Theano... wife of Pythagoras... says... she hears many of the Hellenes think Pythagoras said things were made of number, whereas he... said they were made according to number. ...[T]his fourth-century theory had to be explained away... later... and Iamblichos... tells... that it was Hippasos who said number was the of things."

"Aristotle seems to find only a verbal difference between Plato and the Pythagoreans. The metaphor of [numbers'] "participation" was merely substituted for that of [numbers'] "imitation." ...Aristotle’s ascription of the doctrine of "imitation" to the Pythagoreans is... justified by the Phaedo."

"The arguments for immortality ...come from various sources. Those derived from the doctrine of Reminiscence... sometimes... supposed... Pythagorean, are only known to the Pythagoreans by hearsay, and Simmias requires to have the whole psychology of the subject explained... When... we come to the question what it is that our sensations remind us of, his attitude changes. The view that the equal itself is alone real, and that what we call... things are imperfect imitations of it, is... familiar to him. He requires no proof... and is... convinced of the immortality of the soul... because Sokrates makes him see that the theory of forms implies it."

"Sokrates does not introduce the theory as a novelty. The reality of the "ideas" is the... reality "we are always talking about," and they are explained in a peculiar vocabulary... of a school."

"Whose theory is it? It is usually supposed... Plato’s... though nowadays it is... his "early theory of ideas,"... that he modified... profoundly in later life. But there are serious difficulties in this view."

"Plato... was not present at the conversation... in the Phaedo. Did any philosopher ever propound a new theory of his own by representing it as already familiar to... distinguished living contemporaries? It would be rash... to ascribe the theory to Sokrates, and there seems nothing... but to suppose that the doctrine of “forms” originally took shape in Pythagorean circles, perhaps under Sokratic influence. ... Simmias and Kebes were not only Pythagoreans but disciples of Sokrates; for... Xenophon has included them in his list of true Sokratics."

"We have... ground for believing... the Megarians had adopted a like theory under similar influences, and Plato states... that Eukleides and of were present at the conversation recorded in the Phaedo. ...[U]se of the words εἴδη and ἰδέαι to express ultimate realities is pre-Platonic, and it seems most natural to regard it as of Pythagorean origin."

"Parmenides had already called the original Pythagorean "elements" μορφαί, and Philistion called the "elements" of Empedokles ἰδέαι. If the ascription of this terminology to the Pythagoreans is correct, we may say that the Pythagorean "forms" developed into the atoms of Leukippos and Demokritos on the one hand, and into the "ideas" of Plato on the other."

"We... exceeded the limits... by tracing the history of Pythagoreanism... to... where it becomes practically indistinguishable from the earliest form of ; but it was necessary... to put the statements of our authorities in their true light."

"Aristoxenos is not likely... mistaken with regard to the opinions of the men he had known personally, and Aristotle’s statements must have had some foundation."

"We must assume... a later form of Pythagoreanism... was closely akin to early . [T]he fifth-century doctrine was of the more primitive type..."

"Whether or not we accept the hypothesis of direct influence from Persia on the Ionian Greeks in the sixth century, any student of Orphic and Pythagorean thought cannot fail to see that the similarities between it and Persian religion are so close as to warrant out regarding them as expressions of the same view of life, and using the one system to interpret the other. The characteristic preoccupation of Pythagoreanism with astronomy and the contemplation of the heavens becomes transparently clear, when we see it in the light of notions like , , and ."

"The School of Pythagoras, in our opinion, represents the main current of that mystical tradition which we have set in contrast with the scientific tendency. The terms 'mystical' and 'scientific,' ...are ...not to be understood as if ...all the philosophers we class as mystic were unscientific. The fact that we regard Parmenides, the discoverer of Logic, as an offshoot of Pythagoreanism, and Plato... as finding in the Italian philosophy the chief source of his inspiration, will be enough to refute such a misunderstanding. Moreover, the Pythagorean School... developed a scientific doctrine closely resembling the Milesian Atomism; and Empedocles, again, attempted to combine the two types of philosophy."

"Behind the School of Pythagoras, we can discern, in the socalled Orphic revival, one of these reformations of Dionysiac religion. ...[T]the Pythagorean philosophy... is always passing from mysticism to science, as its religion had passed from Dionysus to Apollo. Yet, philosophy and religion alike do not cease to be mystical at the root; and the attempt to hold the two ends together involves religion in certain contradictions, and leads philosophy to corresponding dilemmas..."

"[T]hroughout the mystical systems inspired by Orphism, we... find the fundamental contrast between... principles of Light and Darkness, identified with Good and Evil. This cosmic dualism is the counterpart of the dualism in the... soul; for... physis and soul... are... identical in substance. The soul in its pure state consists of fire, like the divine stars from which it falls; in its impure state, throughout... reincarnation, it... is infected with the baser elements, and weighed down... In the cosmologies... the manifold world of sense will be viewed as a degradation from the purity of real being. Such systems will tend to be other-worldly, putting all value in the unseen unity of God, and condemning the visible world as false and illusive, a turbid medium... obscured in mist and darkness. These characteristics are common to all the systems which came out of the Pythagorean movement—Pythagoreanism proper, and the philosophies of Parmenides, Empedocles, and Plato."

"The doctrines of mysticism are secret, because they are not cold, abstract beliefs, or articles in a creed, which can be taught and explained by intellectual processes... The 'truth' which mysticism guards is... only... learnt by being experienced (παθεῖν μαθεῖν); it is... not an intellectual, but an emotional experience—that invasive, flooding sense of oneness, of reunion and communion with... the life of the world... Being an emotional, non-rational state, it is indescribable, and incommunicable save by suggestion. To induce that state, by the stimulus of collective excitement and all the pageantry of dramatic ceremonial, is the aim of mystic ritual. The 'truth' can only come to those who submit themselves to these... because it is... to be immediately felt, not conveyed by dogmatic instruction. For that reason only... 'mysteries' are reserved to the initiate, who have undergone 'purification,' ...a state of mind which fits them for the consummate experience. Pythagoreanism presents... an attempt to intellectualise... Orphism, while preserving its social form, and... spirit... Orphism ceases to be a cult, and becomes a Way of life. As a revival, Pythagoreanism means a return to an earlier simplicity... simple enough to adapt itself to a new movement of the spirit. Pythagoreanism is... a complex phenomenon, containing the germs of several tendencies... philosophies that emerged from the school... separating towards divergent issues, or intertwined in ingenious reconciliations. Our analysis must take account of three strata, superimposed... Dionysus, Orpheus, Pythagoras. From Dionysus come the unity of all life, in the cycle of death and rebirth, and the conception of the or collective soul, immanent in the group as a whole, and yet something more than any or all... To Orpheus is due the shift of focus from earth to heaven, the substitution for the vivid, emotional experience of the renewal of life in nature, of the worship of a distant and passionless perfection in the region of light, from which the soul, now immortal, is fallen into the body of this death, and which it aspires to regain by the formal observances of asceticism. But the Orphic still clung to the emotional... reunion and... ritual that induced it, and... to the passionate spectacle (theoria) of the suffering God. Pythagoras gave a new meaning to theoria... as the passionless contemplation of rational, unchanging truth... a 'pursuit of wisdom' (philosophia). The way of life is still also a way of death; but now... death to the emotions and lusts... and a release of the intellect to soar into the untroubled of theory... by which the soul can 'follow God' (ἕπεσθαι θεῷ)... beyond the stars. Orgiastic ritual... drives a... nail into the coffin of the soul, and binds it... to its earthly prison-house. ...[O]only certain ascetic prescriptions of the Orphic askesis are retained, to symbolise a turning away from lower desires, that might enthral... reason."

"To this society men and women were admitted without distinction; they had all possessions in common, and a 'common fellowship and mode of life.' ...[N]o individual... was allowed to claim the credit of any discovery... It was vulgarly supposed that the school must have wished to keep its knowledge to itself as a 'mysterious' doctrine, as if there were any conceivable reason for hiding a theorem in geometry or harmonics. ...What is to be gathered from the story of Hippasos is that the pious Pythagoreans believed that the Master’s spirit dwelt continually within his church, and was the source of all its inspiration. ...The impiety lay, not in divulging a discovery in mathematics, but in claiming to have invented what could only have come from... a group-soul... living on after [Pythagoras'] death as the Logos of his disciples."

"[T]he Pythagorean One, or Monad, splits into two principles, male and female, the Even and the Odd, which are the elements of all numbers and so of the universe. ...One is not simply a numerical unit, which gives rise to other numbers by ...addition. That conception belongs to the later atomistic number-doctrine ...In the earlier Pythagoreanism, we must think of the One (which is not itself a number at all) as analogous to Anaximander’s ἄπειρον. It is the primary, undifferentiated group-soul, or physis, of the universe, and numbers must arise from it by a process of differentiation or 'separating out' (ἀπόκρισις). Similarly, each of these numbers is not a collection of units, built up by addition, but itself a sort of minor group-soul—a distinct 'nature,' with various mystical properties. In the same way, it is by dividing up the whole interval of the octave that the harmonic proportions are determined."

"Pythagorean science... will inevitably reproduce the later and inconsistent conception of the atomic, indestructible, individual soul. This... was... present in Orphic religion, fallen from its first Dionysiac faith in the one continuous life in all things, towards the Olympian conception of athanasia. The later Pythagoreans of the fifth century 'construct the whole world out of numbers, but they suppose the units to have magnitude. As to how the first unit with magnitude arose, they appear to be at a loss.' ...at a loss, because they could not realise that this physical doctrine was ...a reflection of the belief in a plurality of immortal souls, which contradicted their older faith that Soul was a Harmony—a bond linking all things in one. This Soul had formerly been the One God manifest in the logos; now it is broken up into a multitude of individual atoms, each claiming an immortal and separate persistence. And the material world suffers a corresponding change. In place of the doctrine of procession from the Monad, bodies are built up out of numbers, now conceived as collections of ultimate units, having position and magnitude. Thus, Pythagoreanism is led... from a temporal monism to a spatial pluralism—a doctrine of number-atoms hardly distinguishable from the atoms of Leukippus and Democritus, who, as Aristotle says, like these Pythagoreans, 'in a sense make all things to be numbers and to consist of numbers.' But the development of this number-atomism was predestined by religious representations of the nature of soul older than Pythagoreanism itself, and already contained in the blend of Dionysiac and Olympian conceptions inherited by Pythagoras from Orphism."

"The tendency which impelled Pythagorean science towards a materialistic atomism is only the recoil of that same tendency which exalted Pythagoras, from his position as the indwelling daemon of his church, to the distant heaven of the immortals. It is the tendency to dualism. When God ceases to be the immanent Soul of the world, living and dying in its ceaseless round of change, and ascends to the region of immutable perfection, it is because man has acquired a soul of his own, a little indestructible atom of immortality, a self-subsistent individual. 'Nature' likewise loses her unity, continuity, and indwelling life, and is remodelled as an aggregate of little indestructible atoms of matter. But note the consequence: she, too, is now self-subsistent. The world of matter becomes the undisputed dominion of Destiny, or Chance, or Necessity—of Moira, ', . There is no place in it for the God who has vanished beyond the stars."

"Not one of the philosophical ideas in Part I of the commentary is peculiarly Neoplatonic. The doctrine of the Threeness of things... is found in Aristotle and goes back to the early Pythagoreans or to Homer even; paragraph 8 is mathematical in content rather than philosophical... although there is an allusion in it to the Monad as the principle of finitudes, again a very early Pythagorean doctrine; and these two paragraphs are the source of [Heinrich] Sitter's suggestion of the authorship of Proclus. As a matter of fact, the philosophical notions in Part I have been borrowed for the most part directly from Plato, with two or three exceptions that are Aristotelian... Plato's Theaetetus, Parmenides, and the Laws, are specifically mentioned. The Timaeus forms the background of much of the thought. And the Platonism of a mathematician of the turn of the third century A. D. need not surprise us, if we but recall Aristotle's accusation that the Academy tended to turn philosophy into mathematics."

"§1. The aim of Book X of Euclid's treatise on the Elements is to investigate the commensurable and incommensurable, the rational and irrational continuous quantities. This science (or knowledge) had its origin in the sect (or school) of Pythagoras, but underwent an important development at the hands of the Athenian, Theaetetus, who had a natural aptitude for this as for other branches of mathematics most worthy of admiration."

"§2. Since this treatise (i. e. Book X of Euclid.) has the aforesaid aim and object, it will not be unprofitable for us to consolidate the good which it contains. Indeed the sect (or school) of Pythagoras was so affected by its reverence for these things that a saying became current in it, namely, that he who first disclosed the knowledge of surds or irrationals and spread it abroad among the common herd, perished by drowning: which is most probably a parable by which they sought to express their conviction that firstly, it is better to conceal (or veil) every surd, or irrational, or inconceivable in the universe, and, secondly, that the soul which by error or heedlessness discovers or reveals anything of this nature which is in it or in this world, wanders [thereafter] hither and thither on the sea of nonidentity (i. e. lacking all similarity of quality or accident), immersed in the stream of the coming-to-be and the passing-away, where there is no standard of measurement. This was the consideration which Pythagoreans and the Athenian Stranger held to be an incentive to particular care and concern for these things and to imply of necessity the grossest foolishness in him who imagined these things to be of no account."