The mystical tradition

co rnford, | Francis .!t. London, 1912,5 1.1957 a FROM RELIGION TO PHILOSOPHI Ch. VI The mystical tradition 106 _ st Arn y| ves 2 Pythagoras 108 The Pyth.reformatíon Pyth. Ethics, Pyth,Science, P. tar . Pe 194 = 214. a LAr how paie A A\L CDYEN SSIS x MA Philes D PH

106. PYTHAGORAS 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,’ which have been chosen in default of better, are, of course, not to be understood as if we supposed that 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 himself as finding in the Italian philosophy the chief source of his inspiration, will be enough to refute such a misunderstanding. Moreover, the Pythagorean School itself developed a scientific doctrine closely resembling the Milesian Atomism; and Empedocles, again, attempted to combine the two types of philosophy. What we do hope to establish is that the philosophy of the western Greek colonies, however much its individual thinkers may be influenced by the Milesians and their followers in the East, however far they may severally go to join hands with ‘science,’ has at its root a different and opposed view of life, a different type of religion, and, consequently, a different conceptual scheme of the nature of things, which lies behind all its manifestations, and is the point of departure which they all have in common. What this was, we have already tried at some length to describe. It was that type of religion, centred in Greece round the figure of Dionysus, which has some claim to be called the only form of religion that possesses the secret of vitality, just because it is, at bottom, the religion of the Life of earth and man, the life which, though it dies, is perpetually reborn. Asif because its faith has been rooted in this life, mystical religion has itself been reborn a thousand times. Its history is a series of revivals ; and every such revival is heralded by the doctrine of regeneration : ‘Ye must be born again.’ But he that would save his life must lose it ; this religion is also the religion of death and renunciation : Hades and Dionysus are the same. Herein lies its almost irresistible attraction for a certain type of emotional ascetic—the man whose nature demands intensity of passion, and who yet rejects ‘ bodily ’ passions as impure.

107. The Orphic Revival Behind the School of Pythagoras, we can discern, in the socalled Orphic revival, one of these reformations of Dionysiac religion. It is important for us to grasp its nature, because the reforming principle, represented in the figure of Orpheus, is Apolline in character, and therefore drawn partly within the circle of Olympian theology. Orpheus, the ideal of the Orphic, is a Dionysus tamed, and clothed, and in his right mind—in a word, Apollinised.1 When we come to the Pythagorean School, which carries on this representation into philosophy, the same combination of Dionysiac with Apolline elements will reappear ; and we shall see, moreover, that (as we should expect) there is, between the two ideals, a deep-lying contradiction, which defies reconciliation. Dionysus may become Orpheus, without losing all his life and mystery ; but, if he takes the further step (which perhaps, in a sense, he actually did take at Delphi *) and becomes Apollo, then he ceases to be Dionysus. He has left the earth and her cycle of life, which dies and is born again, and ascended to his seat among the ‘deathless’ ones, above the reach of mortality. He is no longer a daemon in communion with his church, but a God beyond the great fixed gulf of Moira, This fatal sequence, from the group-daemon to the personal God, is reflected in a curious way in the Pythagorean philosophy, which 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, which it will be our business to bring to light. It is important to observe that the Orphic movement was a revival, as well as a reformation ; that is to say, it was a return to a type of religion more primitive than the prevailing Olympianism. It must have been caused by one of those outbursts of mystic fervour which, from time to time, upheave and shatter the crystallised forms of theology and ecclesiasticism, when the 1 For Orpheus as son, or épôgevos, or #raspos of Apollo, see Roscher Lex. 8.v. ‘Orpheus’; Eisler, Weltenmantel, ix. p. 681. 2 See J. E. Harrison, Themis, p. 443.

life that created them has died out of them, and they have drifted away from all touch with genuine emotion. The rule in such cases is that, with much clearing away of lumber, there is a return to the simple, primitive type of organisation shaped by the first impulse of the same spirit, which now resurges and seeks once more to clothe itself in the bare essential form. The Orphic movement was thus, in some degree, a return to Dionysus and his thiasos—the daemon and his church, held in one by the unique, mystical relation. It is the organisation of the magical secret society, adapted once more to a reviving human need. But history never repeats itself. The Dionysus to whom the Orphics return, is not the old Dionysus of a group of satyrs, but the Orpheus who was more at home with the Muses than with the Maenads. It was the Maenads, indeed, that tore him, the Muse’s enchanting son, to pieces. Thus, Dionysus, though revived, is also reformed; the more savage parts of his ritual are expurgated, or toned down to a decent symbolism. Above all, what had formerly been the religion of earth and of the life and death of her trees and plants in the circling seasons, becomes now a religion of the heavenly bodies, and especially of the Sun. The Sun also moves through the circle of the year, waxing in summer and waning in winter; but he too easily comes to be conceived as an immutable and deathless God.! The Olympian notion of immortality (athanasia), as a life that negates change and death, intrudes itself. With the doctrine of the fall of the soul from the stars, went, as we have seen, the belief in an indestructible individual soul, persisting throughout its round of reincarnation. After what has been said above of Heracleitus, it will be clear that this Orphic notion of individual immortality is in contradiction with the other mystic representation, to which Heracleitus remains true, that there is no life without death, and that there is only one life, which dies and is reborn in every shape of existence. This representation is the older, for it goes back to days when only the group had a soul, and the atomic individual soul was not yet invented. The soul of Heracleitus’ world is like the soul of the tribe which passes from the 1 Heracleitus characteristically protested against this, declaring that the Sun, hke everything else, changes, and is ‘new every day’ (frag. 32).

living state to the dead, and round again. This was no ‘ sorrowful weary wheel,’ from which any escape was either possible or to be desired. The cyclic movement simply was the movement of life, and life could take no other course, no upward flight to a mansion in the stars. Thus, the Orphic religion already contains two contradictory notions of the nature and destiny of the soul, one Dionysiac, the other Ouranian. Modern writers have failed to see this contradiction, because they have been blinded by the compromise in which Orphism attempts to ‘reconcile’ the incompatible. Further, throughout the mystical systems inspired by Orphism, we shall find the fundamental contrast between the two principles of Light and Darkness, identified with Good and Evil. This cosmic dualism is the counterpart of the dualism in the nature of the soul; for, as always, physis and soul correspond, and are, indeed, 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 the period of reincarnation, its substance is infected with the baser elements, and weighed down by the gross admixture of the flesh.! In the cosmologies inspired by this conception, we may expect to find, first, that the element of fire will be set in contrast with the other three, and second, that 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 in which the rays of heavenly light are broken and 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. 1 All this is very clearly brought out by Socrates in Plato’s Phaedo; see below, p. 246. 2 It must be remembered, too, that Fire is the element of which the Diog. Laert. viii. 1, 27 Measurers of Time (the heavenly bodies) consist. (Pythagoras): Ardy re rai aeArvnw nai rods AA ous dorépas elvas Oeobs* Erınpareiw yao rd Oepudy Ev avrois, rep Earl {wis alrior . . . Kai dvOpwros elra pds Geods ovyyéverar, karà 7d pertyew dvbpwwor Oeppod Bò nal mpovoeiadaı Tov Oedr fuor. So, in aboriginal America, ‘the Fire-God was especially associated with the lapse of time,’ and his vital force, enfeebled by use, was periodically renewed by the kindling of new fire. Payne, History of the New World, ii. 830.

108. The Pythagorean reformation of Orphism As Orphism was a reformation of Dionysiac religion, so Pythagoreanism may be regarded as a further reformation of Orphism,! which takes yet another step, away from Dionysus, away even from Orpheus, towards Apollo. It is a further movement from emotion towards intellect and reason, from religion towards philosophy. Orphism was still a cult, in which the initiate, as Aristotle ? says, ‘ was not expected to learn or understand anything, but to feel a certain emotion and get into a certain state of mind, after first becoming fit to experience it.’ The means to that emotional state of mind had formerly been ‘ orgiastic ’ ritual, and especially those dramatic representations of the passion and resurrection of the life-daemon, which point back to the old mimetic dances of magic, and forward to the tragic drama. The state of mind is that of passionate sympathetic contemplation (Aewpia), in which the spectator is identified with the suffering God, dies in his death, and rises again in his new birth. By these and other ritual means—the eating of flesh or the drinking of wine—the old sense of mystical oneness and participation can be renewed, and the daemon-soul of the group re-created in collective emotion. The only doctrine is the myth, the verbal counterpart of the action of the rite, the life-history of the God, which is also the life-history of the soul. 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 ; such beliefs no one has ever desired to conceal, except from fear of persecution. The ‘truth’ which mysticism guards is a thing which can only be learnt by being experienced (zraGeiv pabeiv); it is, fundamentally, not an intellectual, but an emotional experience—that invasive, flooding sense of oneness, of reunion and communion with the 1 For Pythagoras’ relation to the Orphic communities in Western Greece see Eisler, Weltenmantel, ii. p. 679. 2 Arist. frag. 45, 1483a 19: xaddwep’Aprororéhys dEroi rods rehouuérous où nadeiv Ti Seiv, ¿AMA wade Kal GiareBñræ Önkorbrı yevouévous erirndetovs. Cf. Burnet, E.G.P.?, p. 91, who, however, ignores the importance of the emotional state of mind. thing. This, surely, not the ritual action, is the essential

life of the world, which the mystical temperaments of all ages seem to have in common, no matter in what theological terms they may happen to construe it afterwards. 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 influences, because it is a thing to be immediately felt, not conveyed by dogmatic instruction. For that reason only—a very sufficient one—‘ mysteries’ are reserved to the initiate, who have undergone ‘ purification,’ and so put themselves into a state of mind which fits them for the consummate experience. Pythagoreanism presents itself as an attempt to intellectualise the content of Orphism, while preserving its social form, and as much as possible of the spirit which that form had originally clothed. Like Orphism itself, it is both a reformation and a revival. Like all reformations, it means that much of the ceremonial overgrowth is shaken off: Orphism ceases to be a cult, and becomes a Way of life. As a revival, Pythagoreanism means a return to an earlier simplicity, a disinterring of the essential form, whose outline is simple enough to adapt itself to a new movement of the spirit. Pythagoreanism is thus, from the very first, a complex phenomenon, containing the germs of several tendencies, which, when we come to the philosophies that emerged from the school, we shall find separating towards divergent issues, or intertwined in ingenious reconciliations. Our analysis must take account of three strata, superimposed in the order we have described—Dionysus, Orpheus, Pythagoras. From Dionysus come the unity of all life, in the cycle of death and rebirth, and the conception of the daemon or collective soul, immanent in the group as a whole, and yet something more than any or all of the members that partake of it. 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 experience of reunion and the ritual that induced it, and, in particular, to the passionate spectacle (theoria) of the suffering God. Pythagoras gave a new meaning to theoria ; he reinterpreted it as the passionless contemplation of rational, unchanging truth, and converted the way of life into a ‘ pursuit of wisdom ” (philosophia). The way of life is still also a way of death ;1 but now it means death to the emotions and lusts of this vile body, and a release of the intellect to soar into the untroubled empyrean of theory? This is now the only avenue by which the soul can ‘follow God’ (Emeodaı des), who has ascended beyond the stars.’ Orgiastic ritual, which plays upon the emotions, only drives a new nail into the coffin of the soul, and binds it by a new chain to its earthly prison-house. All that must go; only certain ascetic prescriptions of the Orphic askesis are retained, to symbolise a turning away from lower desires, that might enthral the reason. Such, in our opinion, is the trend of this new movement, called But, though it moves further from Dionysus Pythagoreanism. towards Apollo, it remains Dionysiac at the root, and keeps alive something of the faith first delivered to the saints of mysticism. Hence, in the analysis to which we now turn, we shall try to distinguish what Pythagoreanism preserves from each 1 Plato, Phaedo, 644: xiwbuvevovo: yap doo Tvyxdvovow dphüs amrönevor puocoglas NeXn0évar Tous dddous, Ere oúder Lo avrol Enırmdevoow 4 érobrporew Te xal reOvdvat, 2 Not to be confounded with the 0ewpía of Ionian science, which characteristically means curios:ly, such as led Hekataeus or Solon to travel about the world as spectators of ita marvels. The @ewpia of Pythagoras meant especially contemplation of the heavens. Cf. his sermon on the Three Lives, Heracl. Pont. ap. Cic. Tusc. v. 3; Iambl. Vit. Pyth. 58: eiduxpuwéorarov dè elvas roûroy dvßpurou tpbrov, Tov dmodefänerov Thy Tüv xadAlorwr Bewplar, dv al mposovondfew pidóropor. na pèv oiv elvas Ty TOD céuravros ovpavoî Oday kal rv Ev adrg popouuérur dorépur, el Tis xaBopyn tiv Tdtw . . . Plato, though impatient of this star-gazing (Rep. 529 4), and of those who study the ‘ proportion (cvpperpla) of day to might, and of day and night to month, and of month to year, and of the other stars to sun and moon’ (5304), still speaks of the philosopher as the ‘ spectator of all time.” 3 For the escape of the soul from the wheel of birth, as Pythagorean doctrine, see Rohde, Psyche,? 1i. 165. Plato, Theaet. 1764: 5 xal veıpäcdas xp évOdvde exeiae pebyew dre réxuoTa. puy dè duolwors Bey card 7d Öhvaror. 4 Plato's rejection of the drama and of the orgiastic kinds of music is partly motived by a similar condemnation of violent states of non rational emotion.

of the two strata—Dionysiac and Orphic—that lie below it. In the actual history of the school, all the elements are, of course, present from the outset and blended together ; but, in analysis, it is worth while to isolate them, with a view to following out their shifting combinations in the systems which derive from the Pythagorean tradition. 109. Pythagoras as Daemon of his School Dikaiarchos,! after describing the founding of the community at Kroton, says that it is hard to get any @rtain knowledge of what Pythagoras taught his disciples; but his best known doctrines were, ‘first, that soul is an immortal thing, and that it is transformed into other kinds of living things; further, that whatever comes into existence is born again in the revolutions of a certain cycle, nothing being absolutely new; and that all things that are born with life in them ought to be treated as kindred ’ (ouoyevi). We have already dwelt at length on the significance of these doctrines, of the unity and kinship of all life or soul, and its continuous rebirth in periodic revolutions. Later legend told how Pythagoras, like Francis of Assisi and the Spanish Carmelites, preached to animals; ? and, when we remember that Orpheus before him had made the wild things gather to his music, there is no reason to doubt the substantial truth of the tradition. What specially concerns us is to note that, for anything Dikaiarchos says, the Master himself, like Heracleitus, 1 Ap. Porph. Vit. Pyth. 18, 19: rpòrov pév ds ¿Bávaro elral bye hr Yuxtr, elra peraBdddovoay eis dra yévy Suv, pds de rovras dre Karà wepibsous rivas tà yevbueré wore wad ylyvera, véov de ovdtr ar\os deri, xal Bri wdvra rà ywbueva Eupuxa óuoyev dei vonlfew. 2 Iambl. Vit. Pyth. xm. ; Porph. Vit. Pyth, 24; G. Cunninghame Graham, Compare also the Golden race of the Age of Santa Teresa (1907), p. 51. Kronos in the Polsticus of Plato (272 8), who “have the power to converse not only with men but with beasts,’ and use their opportunity eis gi\ovogla», ‘inquiring from all nature’ (rapà wdons péceus), in case any part of nature may have some peculiar faculty, so as to perceive, better than any other, what might contribute to the ingathering of wisdom. In the Meno, 810, where the Orphio doctrine of palingenesia 18 stated, 1t is the ‘kinship of all nature’ (re rijs purews drdons ouyyerois ofcys) that makes it possible for the soul, which has learnt all things in the other world, to recover its knowledge here by reminiscence (anamnesis).

may have held, more closely than his later followers, to the primitive Dionysiac belief in one all-pervading Soul, the substratum of kinship which unites all forms of life into ‘ one clan’ (ouoyerñ).! It seems probable that he dwelt upon this unity, rather than upon the inconsistent idea of a plurality of indestructible, atomic souls, which always asserts itself in the popular mind as soon as the sense of individuality has grown strong enough to insist upon a personal immortality. Not that we are convinced that Pythagoras himself saw the inconsistency or tried to avoid it; only, the very form which he gave to his community embodied the value he set on®nity and his attempt to keep in check the self-assertion of individualism. To this society men and women were admitted without distinction ; they had all possessions in common, and a ‘ common fellowship and mode of life”? In particular, no individual member of the school was allowed to claim the credit of any discovery he might make. The significance of this rule has not been fully understood. 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 1 Sextus Emp. Math. ix. 127: ol pév oîv wept rdv Ilvôayépar xal roy * EuredoxAéa xal rev 'Ira\üv m\ÿ60s paot pù ubvor quiv pds dddHous Kal Tpds Toùs Ocods elval ria Kowwvlav, &ANG Kal mpds Ta Eoya riv Spur. Ev yap Urápxew veda TO dia wavrds rod xóouov deñxop Ppuxis Tphrror, Td Kal évoür Yuûs mpôs éxeiva. Tamblichus (Vit. Pyth. 108) well expresses the doctmne in the following words: Pythagoras ‘taught them to abstain from things that had life (soul) in them (€uyixwr) ; for, if they wished to reach the height of just behaviour, they must of course do no wrong to any of the living things that were their kindred (ovyyerür fúwv). How could they induce others to behave justly if they themselves were convicted of aggression (rAcovetla), although bound in the participation of kinship (ovyyerırfı peroxñe) with living things, which are linked to us, as it were, in brotherhood by fellowship (xowwvlay) in the same life and elements and the same mixture composed of them.’ If Aristoxenus (see Burnet, £.G.P.?, p. 102) 18 right in stating that Pythagoras only prohibited, among animals, the ploughing ox and the ram, he probably did so because the ram stood for the male fertilising principle of animal life, and the ox which ploughs the earth for the same principle in vegetation, which springs from the ploughed earth. animals would be symbols of all life. The two Compare the doubtful fragment of Empedocles 1545 (D.F. V.?) which says that the first miserable men who ate flesh Body éxdcayr’ dporfjpwr. 2 ko ouvovola al ölarra, Iambl. Vit. Pyth. 246. The admission of women was ‘Dionysiac’ (the Maenads) rather than Orphic. feminine. Orphism was anti-

for hiding a theorem in geometry or harmonics. The truth comes out in the story of Hippasos of Metapontion, who ‘ was of the Pythagoreans, but, because he published a treatise on the sphere of the twelve pentagons, was cast away at sea, as having committed an impiety and taken glory to himself for his discovery, whereas all discoveries belonged to “ Him ” (éxelvov Tod avdpos), for so they call Pythagoras. They say that a supernatural vengeance overtook (ro Satpoviov veueoÿoai) those who published what belonged to Pythagoras’! This supernatural or daemonic anger was the wrath of Pythagoras himself, who after his death remained what he had been in life—the daemon in whom all the life of his church was centred and incarnated. That Pythagoras worked miracles and was conscious of supernatural power, there is no reason whatever to doubt; he was probably the author of the doctrine: ‘ There are Gods, and men, and beings like Pythagoras ”—beings who are half-divine, daemons in human shape.? 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 ‘ Hi m.’ Thus Pythagoras seems to have held to the conception of a group-soul, incarnate in himself, but living on after his death as the Logos of his disciples. Heracleides, who preserves the famous story of his previous incarnations, reports him as saying that Hermes had offered him anything he wished for, except deathlessness (athanasia) ; and that he chose to preserve, through life and death, the memory of what happened to him.* The legend may enshrine the truth that the ‘immortality ’ Pythagoras desired and claimed was not the deathless continuation 1 Iambl. Vit. Pyth. 88=D.F.V." s. tit. ‘ Hippasos,’ 4. 2 D.F.V.®, p. 24. Cf. the Introd. to the Hindu Tales of Somadeva: ‘The Gods have perpetual happiness, men are in constant unhappiness ; the actions of those who are between men and Gods are, by the diversity of their lot, agreeable. Therefore I will recount to you the life of the Vidyädhäras,’ ie. demons and magicians (Kátha-Sára-Sárit-Sagara, 1. i. 47). 3 Cf. Procl. in Hud. i. p, 419: Lori pév dpyaîa, paoir ol wept ròv Edónuov, kal ris rüv Ilvdayopelwv Movons ebpipara. + Heracl. Pont. ap. Diog. vii. 4 (D.F. V.*, p. 24).

of individual personality, but the older Dionysiac continuity of the one life that is born again in every generation of the group.! But, as usual, his followers could not be content to live in communion with a spirit of like passions with themselves, but must needs exalt their daemon to the highest grade of divinity. Pythagoras soon becomes the son of Apollo by a virgin birth,? and even an incarnate God, Apollo Hyberoreios himself. But, through all the overgrowth of decadent superstition in the later legend, enough remains of the older faith to warrant us in refusing to attribute these frigid inventions to the Master himself. Apotheosıs and athanasia are precisely the fatal steps in the career of a ‘ being like Pythagoras,’ because they put an end to the reality of that communion in which the originators of such churches find the very meaning of the common hfe. I our view, then, be correct, the society of Pythagoras, so long as the influence of his own ideal survived, realised once more the primitive type of religious group, and that peculiar relation, best called ‘ participation’ (methex:s), ın which such a group stands to ıts immanent collective soul. The passage from the divine plane to the human, and from the human to the divine, remains permeable, and is perpetually traversed. The One can go out into the many; the many can lose themselves in reunion with the One. This essential conception is the key to the understanding of the number doctrine, on which rests Pythagoras’ claim to be a philosopher, as well as a founder of mathematics. 110. The Tetractys * The misguided followers who reckoned Pythagoras among the Gods, were accustomed, Porphyry tells us,? to swear by 1 It will be remembered how Diotima im Plato's Symposium (207 D) explains this immortality of perpetual renewal Plato, too, thought of his logoi as living on in the souls of his school and perpetually giving birth to new thoughts in each generation that arose and passed away. 2 His mother 18 called Parthems, in legend. See Eisler, Weltenmantel, ıi. p. 679 ff ; W. Schultz, Altromsche Mystik, p. 97 3 Arıst. frag. 186; Porph. Vit. Pyth. 20: pera riv Oeüv rdv IIvdaydpav karmplüpour. 4 For the tetractys see W. Schultz, ATTOZ, Memnon, 1910; Weltenmantel, n. p. 684. 5 Vat. Pyth. 20. Eısler,

him, as the God who had left with them a symbol applicable to the solution of many problems in nature—the tetractys. ‘ The so-called Pythagoreans,’ says Aristotle,! ‘attached themselves to the mathematics, and were the first to advance that science by their education, in which they were led to suppose that the principles of mathematics are the principles of all things. So, as numbers are logically first among these principles, and they fancied they could perceive in numbers many analogies of what is and what comes into being, much more readily than in fire and earth and water . . . and since they further observed that the properties and determining ratios of harmonies depend on numbers—since, in fact, everything else manifestly appeared to be modelled in its entire character (dow) on numbers, and numbers to be the ultimate things in the whole universe, they became convinced that the elements of numbers are the elements of everything, and that the whole “ Heaven ” is harmony and number.’ Aristotle adds that the decad was held to be perfect, and to embrace the whole ‘ nature ’ of number? We may therefore look for the ‘nature’ of all things in the decad,as expressed in the symbol called the tetractys, which, we have every reason to believe, goes back to Pythagoras himself. The original tetraciys appears to have been the ‘ tetractys of the decad,’ obtained by the addition, 142+3-44=10: ‘This tetractys,’ says Theon of Smyrna,? ‘is of great importance in music, because all the consonances are to be found 1 Met. a5, trans, A. E. Taylor. 2 Met. 15, 986 a: éme rédecov 9 Sexds elvas doxei Kal wacay mepieiindevau Thy Tôv apôuèv pio. Cf. Philolaus, frag. 11: ewpeiv dei ra Epya kal Thy ovolay TO dpOud array duvapu Uris doriv Ev ra derdò peydha yop Kal wavredis Kai wavröepyos xal Belt Kat odpavlw Blw xal dvOpumivw dpyà kal ayepòv xowwvoiga, Lévy-Bruhl (Fonct. ment. p. 237) has an interesting discussion of the mystic properties of numbers. He remarks that the numbers so enveloped with a mystical atmosphere rarely go above 10. The higher numbers have not, together with their names, passed into collective representations, but have generally been mere arithmetical numbers from the first. 3 repl rerpaxréos, p. 154, Dupuis (1892).

contained in it. But it is not only on this account that it has been held in the highest honour by all Pythagoreans ; but also because it is held to contain the nature of the universe. Hence it was an oath by which they swore : ‘By him who gave to our soul the teiractys, which hath the fountain and root of ever-springing “ nature ” (physis). 1 Theon proceeds to enumerate other forms of the tetractys. The second is that used by Plato in the Timaeus to symbolise the harmonic constitution of the world-soul : 8 27 These two tetractyes ‘contain the musical, geometrical, and arithmetical ratios, of which the harmony of the whole universe is composed.’ The later Pythagoreans delighted in using this symbol as the master-key to the interpretation of the world. The third tetractys is point, line, surface, solid ; the fourth is fire, air, water, earth; the fifth is pyramid, octahedron, eikosahedron, cube; the sixth is ‘of things that grow’ (ra puouévwr) : the seed, growth into length, into width, into height; ? the seventh is that of societies: the individual, the family, the village, the 1 où pa röv auerépg Yuxa (yevég, al.) rapadbvra rerpaxriv, mayday devdov purtos plfwud T’ Exovear. Diels, Arch. f. Gesch. d. Phil. ini. 457, conjectures that these lines were the opening of the poem often cited as the'Iepds Adyos or IIepl 0e@v, in which, according to Theol, Arith. p. 17, the might of the number 4 was celebrated, and Metaphysics connected with it. Cf. Payne, History of the New World, ıi. 283, 410: ‘Nauh-, the Mexican particle for this number (4), in the abstract form “* Nahui” probably embodies some conception analogous to ‘‘ Nahua,” the Command or Rule of Life, and suggesting wholeness, perfection, or indefeasibility; these austere and orderly barbarians recall the Pythagorean philosophers, who held the number 4 to be the root or source of all things.’ Nahuatlacá is a general name used by the Mexicans to denote ‘tribes living mainly by agriculture in accordance with a settled Nahua or Rule of Life, dictated by a custom administered by hereditary chiefs.’ 2 Note this as the primitive form of the three ‘dimensions’ (atta, ‘ growths’).

state; the eighth is the four cognitive faculties: reason, knowledge, opinion, sense ; ! the ninth is the rational, spirited, and appetitive parts of soul, and the body; the tenth is spring, summer, autumn, winter—the seasons by which all things come into being; the eleventh is the four ages of man: infancy, youth, manhood, old age. ‘The cosmos composed of these tetractyes is geometrically, harmonically, and arithmetically adjusted, potentially containing every nature of number, and every magnitude and every body, whether simple or composite. It is perfect because all things are parts of it, and itself is not a part of anything. That is the reason why the Pythagoreans swore by it, and said “all things are like number.” ’ The details of some of these interpretations of the tetractys are, of course, late; they are expressed partly in Platonic terms.” But they are in a line with the earliest traditions of Pythagoreanism, and are typical of the whole tendency of the school. They satisfy the mystic’s passion for unity, his desire to find the meaning and nature of the whole in every part. 111. The Procession of Numbers The real significance of the tetractys comes out in the second line of the Oath, which describes it as ‘ containing the fountain and root of ever-springing nature (physis)” No words could better express what we take to be the genuine Pythagorean conception of the process by which the One goes out into the manifold world. The tetractys is not only a symbol of static relations linking the various parts of the cosmos; it contains also the cosmogonical movement of life, evolving out of primal unity the harmonised structure of the whole. It is a fountain of ever-flowing life. The tetractys of the decad is a numerical series, the sum of which is the perfect number, ten, which we are told that Pythagoras regarded as ‘the nature of number, because all men, 1 Arist. de Anim. a2, 4045 21. 2 Cf. Arist. de Anim. a 2, 404018. ‘It was explained in (Plato’s) lectures on philosophy that the self-animal (universe) is composed of the form of One, and the first length (Two), breadth (Three), and depth (Four),’ etc.

whether Hellenes or not, count up to ten, and, when they reach it, revert again to unity.’! The word ‘revert’ (dvarrodow) recalls the fragment, already quoted, of the Pythagorean Hippodamus, which tells us that this reversion is to be conceived as the revolution of a wheel. ‘ All mortal things under constraint of Nature revolve in a wheel of changes. . . . When they are born they grow, and when grown they reach their height, and after that they grow old, and at last perish. At one time, Nature causes them to come to their goal in her region of darkness, and then back again out of the darkness they come round into mortal form, by alternation of birth and repayment of death, in the cycle wherein Nature reverts upon herself’ (dvarrodi fovras). We have seen that the whole nature of things, all the essential properties of physis, were believed by the Pythagoreans to be contained in the tetractys of the decad; and it now appears that, just as we should expect, this ‘fountain of ever-flowing nature’ contains the periodic movement of life, evolving out of unity and reverting to unity again, in the recurrent revolution of a wheel of birth. It embodies the fundamental Dionysiac representation of palingenesta. But there is something more in it than this. Pythagoras inherited the music of Orpheus, as well as the reincarnation doctrine of Dionysus. From the Orphics he inherited also the doctrine of the fall of the soul from its first perfect state of union with the divine, its degradation into the darkness of this life and of the underworld, and its final restoration to peace and unity. Now, on the model of this doctrine of the fall of the soul, the Pythagorean philosophy must hold that all existence proceeds out of the One and returns to it again; and that the One alone is perfect, while the manifold world of visible body is a turbid medium of appearance, in which the one truth is half-revealed and half-concealed, as the divine soul is manifest in the flesh and yet obscured by it and degraded. There is thus, inherent in the representation handed down 1 Aetius, i. 3, 8: ela: dè tiv Piow Tod dpibuoò Séxa" nexpı ydp rar dla mdvres"E\\mves, wávres BépBapor dpibuoîow, ep’ & ¿Mbvres rádiv dvamodoucır ¿rl ri povdda. Professor Burnet (£.G.P.?, p. 114) thinks we are probably justified in referring this to Pythagoras himself. For xporodiouds (‘ procession’), the opposite of éraroëoués, see below, p. 209, note 1. 3 Hippodamus, ap. Stob. Flor. 98, 71, see above, p. 167, note 1,

from Orphism to Pythagoras, not only the primitive wheel of birth, but another aspect of the movement of life, which is best pos) out of unity described as a processional movement (mpo7rodvc into plurality, out of light into darkness.! This movement, also, must be revealed in the nature of numbers, and contained in the tetractys. Pythagoras found it in the procession of numerical series, the study of which he originated, thereby founding the science of number. It is practically certain, also, that in music he discovered the ratios of the octave, the fifth, and the fourth, contained in the harmonic proportion 12:8:6.2 Now a progression like those contained in the tetractys of Plato’s worldsoul (p. 206)—the series, 1:2:4:8, 1:3:9:27—is what the Pythagoreans called an harmonia ; it is a continuous entity knit together by a principle of unity running through it, namely the logos or ratio ($ or 4) which links every term to its predecessor by the same bond.? Both series, moreover, radiate from the One, which in Pythagorean arithmetic was not itself a number, but the source in which the whole nature of all numbers was gathered up and implicit. When we note, further, that every number is not only a many, but also one number, we can see how Pythagoras would find the whole movement of cosmic evolution contained in the procession of series, in which the One passes out of itself into a manifold, yet without losing all its unity, and a return from the many to the One is secured by that bond of proportion which runs, backwards and forwards, through the whole series and links it into a ‘harmony.’ It is thus that we must understand the doctrine that ‘the whole Heaven is harmony and number.’ The processional movement of physis is modelled upon that of soul, which falls from its first state of union with the divine, but yet remains linked to the One life 1 Theon Smyrn. p. 29 (Dupuis): dpidubs dor: ovornua uordôwr (the atomic view discussed below, p. 212) 4 xpowodi uds \400vs dd povddos dpybperos Kai dvarobig uds els pordda karakıyywr. 2 See Burnet, E.G.P.?, p. 118. 3 Aotius, i. 3. 8: Mudaydpas . . . dpxds rods dpidpoùs Kai rds ouuuerplas ras év rodros, As xal ápuorias xadeí. Compare the logos of Heracleitus, as constancy of ‘measures’ preserved throughout transformation, above, p. 188. Plato, Tim. 31 0, on the ‘ bond of proportion: Geouür dè xéAlioros ds Ar abréy Te nal rà cuvdovuera Bri pddiora lv wary" Touro dì xéguxer dvadoyla «dora drorekeiv.

by mysterious bonds of harmony, and can return to it again, purified by music.’ Indiscussing the segregation of opposites and its possible origin, as reflecting the exogamous segmentation of the undifferentiated human herd, we have already pointed out that the 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? The analogy reminds us that the One is not simply a numerical unit, which gives rise to other numbers by a process of addition. That conception belongs to the later atomistic number-doctrine, presently to be considered.” In the earlier Pythagoreanism, we must think of the One (which is not itself a number at all) as analogous to Anaximander’s areipov. 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’ (d7oxpuots). 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.* 1 See Theon Smyrn p 18 ff. (Dupuis) for philosophy as purification and initiation; Procl. Médooa, Ance. Gr. et Lat. ii. p. 25: 7 pév ye pupids, iris écriv appovia xpelrrwv, ex Tis Tpuwdovpérns yevopévn povddos émiorpageions eis éaurm (i.e. 100x100), aroxaraorarin) ris ¿ori Kai Tedeovovpyds ris Yrxis, éraréyoura rerovaay els Tv olxnow mél dber Hee deupo, nudárep pnoir O dv Palôpy Zuwxparns. The reference is to Phaedrus, 248 E, els pév yap To avrò dev Fee Y Puy éxdory oùx dpuxveiras ¿rav prpiwy, and, since this agrees with Empedocles’ doctrine that the fallen soul 18 exiled for 30,000 dpa: = 10,000 years (sce below, p. 228), it 18 probable that Proclus' connection of the return of the soul with the return to the monad is of old Pythagorean origin, as indeed the character of the doctrine would lead us to expect. 4 Above, p. 70. Also Theon Smyrn. p. 34 (Dupuis): ’ApiororAns dv rw TlvOa-yopixy ro tv grow éuporépur (äprlou al weplrrov) peréxcw Tis péews. 3 The methods of Eurytos described by Burnet (£ G.P.?, p 110) belong, as he points out, to the fourth century. By that time the atomistic doctrine was developed. 4 Cf. the division of the soul in Plato’s Tsmaeus, 35 B, and the distribution of the whole mass of soul-substance, firat into a number of portions, one for each star, and secondly into individual souls (ıbıd. 41 ).

112. Pythagorean Ethics The Pythagorean conception of goodness (dpern), including both moral virtue and the physical excellences of health and strength, is based entirely on the notion of ‘ arrangement’ (rétis) and ‘order’ (cosmos). The best expression of it is to be found in Plato’s Gorgias. Socrates there argues that the good artist will not work at random, but always with reference to an ideal or pattern. Guided by this model, he will put his material into a certain arrangement, making one part suitable and fitting to another, until he has marshalled the whole into ‘an arranged and ordered thing.'! Trainers of the body and physicians order and systematise the body (xoopotcr ro copa «al ouvrärrovat), and this cosmos is health and strength. The similar cosmos that is introduced into the soul, is Law, which makes men law-abidıng and orderly; and this is Justice and Temperance. The source from which this conception is derived is acknowledged later, where Socrates says that ‘ the wise say that heaven and earth and Gods and men are held together by fellowship, and friendship, and orderliness, and Temperance, and Justice, and, for that reason, call this universe Cosmos.’ Their knowledge of geometry has taught them the great power, among Gods and men, of Proportion; whereas the ignorant believe in grasping more than one’s due share.? 1 Gory. 503E: eis ráfo tiva Ékaoros TOnow $ Av Tin, Kai wposavayndger Tè Erepov rq érépw wpérov Te elvas cal dpubrtew, ¿ws dy TO drav ovorionru Terayuévoy re xal kexooumuévor rpayna. lambl. V.P. 182, after Aristoxenus (D.F.V.2, p. 284). cupwapéwec Pas Tp Tod Kaspoî ices tiv TE érouajouérmr pay kal TO wpérov Kai To dpportov. 2 504D: rats dè ris puxos rdêcor Kal roo uroeo: vopipov Kai vôuos, ó0ev al vipupor ybyvovras ai xbomo‘ rabra È éore Stxacootvy Te Kai cwdpootwy. Cf. Rep. 4324, where Temperance is the concord (äpuoria), compared to the harmony of the octave (4° d\ns drexvas reraraı, did raro» rapeXouérn cuvgdovTas), an oubroca, ouupurla. See also Phaedo, 93 c, for virtue as harmonra. 8 507E: paol 8 oi copoi (Pythagoreans and Empedocles, Olympiod.) xal ovpardr xal ya» nal Beoùs xal d»@pwrovs Tir Kowwriay ovvéxew Kai gidlav xal koomörnra Kai awppocivyy Kai dixacéryra, Kai 7d Sho» roîro da Tatra xbo uo» xadovow . . . AlAnde oe Bri 7 ioôrns 7 yewperpixi Kai du Ocois Kai dv dv0pywos péya Suvarac’ où de wAeovetlar oleı deiv doxeiv’ yewuerplas yap dueheïs. Plutarch, Symp. Q. viii. 2. 2, says that this principle of proportion is called Aixy and Néuecis (Aristotle's ‘distributive justice,’ X.N. v. 3. 13). Alex. in Anat. Met. a5, 9855 26- rijs uer yap Scxacootvns (Sov dwohauBdvovres elvas rò ävrırewovdös re Kal (oor (ol Iluhaybpeın), Ev rois dpêpois rovro euplanovres Lv,

113. Pythagorean Science The earliest ‘science’ of the Pythagoreans is simply a transcript of the procession of numbers into terms of space and space-filling matter; or, rather, we should say that they were at first unable to conceive number and its behaviour except under the forms of space and motion, and hence did not distinguish at all between the procession of numbers out of the Monad and the process which generates the visible world in space. This process presented itself in the only possible way—as the progressive conquest of a formless and unlimited field (y#pa) of darkness (the dark and cold air) by the light and warmth radiating from a central nuclear unit.! We may note, by the way, that this led to the displacement of earth from the central position in the universe, which must be occupied by the nuclear Fire, Hesha. The first great step away from geocentric astronomy was thus due to the bold acceptance of the consequences of an a prior: theory, which simply restated a purely mythical representation. Its importance for us is the way it illustrates once more the truth of our hypothesis, that the nature and behaviour of physis reproduce mythical and religious beliefs about the nature and behaviour of Soul. 114. Number Atomism Guided by the same hypothesis, we can predict the final stage of Pythagorean science. It will inevitably reproduce the later and inconsistent conception of the atomic, indestructible, individual soul. This, as we saw, was already 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 Bd roro ral róv loans lrov dpiBubv (either 4 or 9) xpüror Eheyov elvar Biraroobvn». The mathematical education in Rep. vii. (530 A) culminates in the conceptions of cvugwrla in harmonics and cupperpla in astronomy, and these provide a bridge to dialectica and the study of beauty and goodness (531 c). 1 See Burnet, E.G.P.?, p. 120.

appear to be at a loss.’ ® They might well be at a loss, because they could not realise that this physical doctrine was nothing but 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 correIn place of the doctrine of procession from the sponding change. Monad, bodies are built up out of numbers, now conceived as collections of ultimate units, having position and magnitude. Thus, Pythagoreanism is led on 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,3 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 per1 Arist. Met. 46, 10805 18 ff. Sce Burnet, F.C. P.?, p. 336 ff. 2 Burnet (Æ.G.P.?, p. 343) says that the view that the soul is a harmony cannot have belonged to the earliest form of Pythagoreanism, ' for, as shown in Plato’s Phaedo, it is quite inconsistent with the idea that the soul can exist independent'y of the body.’ The inference would hold, if it were impossible for religious, or even philosuphic, representation to be inconsistent. I doubt, however, if it is even inconsistent; see below on Empedocles’ logos-soul, p. 235. The doctrine that the soul 18 a harmony is attributed to Pythagoras by Maorobius, Soma. Scip. i. 14, 19. Cf. Rohde, Peyche’, ii. 3 De Cuelo, y4, 303a 8. Cf. de Amm. a5, 409% 7, on the monads of Xenocrates and their likeness to atoms,

fection, 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, 18 now self-subsistent. The world of matter becomes the undisputed dominion of Destiny, or Chance, or Necessity—of Moira, Lachesis, Ananke. There is no place in it for the God who has vanished beyond the stars. We shall watch, in the sequel, the mystic philosophers, who cannot dispense with God, exhausting their ingenuity in devices to get him back into touch with Nature, to restore to him the raison d'être which he lost from the moment that he ceased to animate the world from within, to be the ‘nature of things’ itself. All such attempts seem now to us like efforts to draw down Apollo from the skies, and change him back into Dionysus ; or, if that is impossible, to find a mediator between God and Nature, some daemonic power, half-natural, half-divine, an Eros who will fill up the chasm, and bind all things again into one. But the time for these efforts is not yet. We have first to consider two systems that emerged from the Pythagorean tradition, before that tradition went all the way to join hands with scientific Atomism, and so became fatally Olympianised. These are the systems of Parmenides and Empedocles. 115. PARMENIDES Parmenides wrote what he had to say ‘about the Nature of Things’ (mepi guoews) in hexameter verse, which combines a certain oracular dignity and earnestness with the closely knit sequence of logical argument. He is the first philosopher, so far as we know, who cast his theory of Nature into the form of a deduction, in this respect justifying the historians who throw him into the sharpest contrast with the cryptic and interjectional Heracleitus. But it is characteristic of him, too, that his theory is stated as a revelation, accorded to him by the Goddess who governs all things in person. Certain features of the proem call for our attention. Like Orpheus, Parmenides seeks wisdom by a descent, through the western gate of the sunset, into the darkness of the under-