Ritter, Heinrich 1838. The Pythagorean philosophy, pp. 326-420. In, The History of Ancient Philosophy. Vol. 1.pdf - Heinrich Ritter

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BOOK IV. HISTORY OF THE PRE-SOCRATIC PHILOSOPHY . PART SECOND : THE PYTHAGOREAN PHILOSOPHY. CHAPTER I. PYTHAGORAS AND THE PYTHAGOREANS. NEARLY at the same time with the opening de velopment of Ionian philosophy in Asia Minor, a spirit of scientific inquiry was evolved in the Greek colonies of Lower Italy. These Italian colonies had been planted principally by Achæans and Dorians ; and although they were destitute of a common political centre, they nevertheless consti tuted at times a variety of alliances and confedera tions, as is clear even through the general obscu rity of their history ; and they appear to have carried on a very active and considerable com merce with the neighbouring Greeks of Sicily. The Doric elements seem to have predominated in these parts ; at least the spoken language inclined more or less, with local peculiarities, to Dorism. The early activity of mind displayed in these co lonial states is sufficiently attested by the cele brated codes of Zaleucus and Charondas ; the polished culture of poetry and rhetoric, in Sicily especially ; and lastly, the medical school esta blished at Croton . To judge from the number of citizens of these states who were crowned in the PYTHAGORAS AND THE PYTHAGOREANS. 327 Olympic games, their wealth and prosperity must have been considerable : it, however, degenerated into luxury and effeminacy. Now it is singular, that in these colonies philo sophy was not the original production of indige nous mind, but was introduced by strangers from Ionia ; afterwards, however, when the first impul sion had been given, it found many native ad mirers and promoters. This procedure, however, was strictly conformable with the general course of the development of Greek mind. Of the philo sophy of Magna Græcia, that which was diffused in the Dorian and Achæan states must engage our attention before that which grew up in the Ionian colony of Elea ; not merely because, in all appear ance, it was earlier in time, but also on account of its greater affinity to the Ionic system ; an assertion which will perhaps startle those who maintain the constant validity of the inference from identity of race to identity of opinions : but it is even so man bears within a sensibility keenly and quickly alive to every impression ; and diversified relations of life educe and bring to light very opposite phases of his thought. Croton, an Achæan colony, received an illus trious accession in the person of Pythagoras, who was born at Samos, 49th Olymp.,' -a — a sage whose · Clemens Alex. Strom . i. 309. Cf. Diod. Sic. xii. 9. This assumption is not well warranted : indeed , the whole chronology of Pythagoras, and of the stories connected with him, is extremely vague. His story travelled through tradition, to be afterwards treated as an historical romance. That this was the case in some degree with the disciples of Plato and Aristotle, but still more so with the new Pythagoreans and Neo-Platonists, is, I think, unquestionable. Krische (de Societatis a Pythagora in urbe Crotoniatarum 328 PYTHAGOREAN PHILOSOPHY. descent is traced back to the Tyrrhenian Pelas gians. His biography is enshrouded with a thicker veil of mythical obscurity than that of any other of the earliest philosophers ; and the fabulous le gends of which he is the subject are nearly as ancient as history itself. Little light, consequently, is thrown upon his real history by the minute details of his fortunes and deeds transmitted from the last days of antiquity, which are a mere tissue of vague and varying anecdotes and fables, rarely furnishing any information as to the per sonal character of the man. The intellectual attainments of Pythagoras were, according to the concurrent testimony of the different traditions, far from ordinary .* Of the particular objects which attracted his inquiries a pretty general notion may be formed, although we are unable to measure the extent to which his acquaintance with them may have reached . Pythagoras is usually classed among the most eminent founders of scientific mathe conditæ Scopo Politico, Gott. 1830-4 ) builds too much on the credibility of Aristoxenus, Dicæarchus, and Apollonius. ' According to Aristoxenus, Aristarchus, Theopompus, Cleanthes. Clem . Alex. Strom . i . 300 . Diog. L. viii . 1. Porphyr. Vita Pyth. i. 2. cf. Kessling ad h. 1. Pythagoras is also called a Phliasian, which appears to refer to the descent of his family from Phlius. Lyc. a Porp. V. Pythag. 5. Paus. ii. 13. cf. Krische, p. 3. When Lycus calls him a Metapontine, he alludes probably to his residence at Metapont. Herodot. iv . 95. 3 Porphyrii Vita Pythagoræ ; Jamblichus de Vita Pythagoræ ; Diog. L. viii. 1-50 ; Phot. Bibl. Cod . cclix. contain but little about the life of Pytha- . goras ; and upon the doctrines of the Pythagoreans scarcely any thing of importance. 4 Ηerodot. iv. 95. και Ελλήνων ου το ασθενεστάτη σοφιστή Πυθαγόρη. Heraclitus, ap. Diog. L. ix. 1 , ascribes to Pythagoras modupadinu, and says of him, Diog. L. viii. 6 : Πυθαγόρης Μνησάρχου ιστορίην ήσκησεν ανθρώπων μάλιστα πάντων και εκλεξάμενος ταύτας τας συγγραφάς εποιήσατο εαυτού σοφίην, πολυμαθίην , κακοτεχνίην. PYTHAGORAS AND THE PYTHAGOREANS . 329 matics ; ' and the common account is in some de gree confirmed by the general scope of his philo sophical labours, and by the particular statement that Pythagoras was chiefly occupied with the determination of extension and gravity , and in measuring the ratios of musical tones, as well as by the many astronomical discoveries ascribed to him . Nevertheless, the probability of all these statements depends more on the consideration of the course of scientific development pursued by the Pythagorean school than upon the individual autho rities on whom they rest. And it is on similar grounds that we are not indisposed to attribute to Pythagoras certain essays on the healing art, which, however, seem to have been confined to a few experiments upon the effects of music on the human mind. And when we consider that the scope of all his labours was to train and educate man by the moral and conventional habits of life , and that gymnastics were by the Greeks generally, and by the Pythagoreans especially, regarded as an essential part of education, it becomes exceedingly probable that he did advance some precepts on the " Cic. de Nat. D. iii. 36. Diog. L. i. 25 ; viii. 11 , 12. These and other similar passages shew that later writers were unable to give any precise statement of the mathematical merits of Pythagoras. · Aristoxenus, ap. Diog. L. viii. 14, in very exaggerated terms. 3 Porphyr. in Ptolem. Harm. 3. p. 213. Diog. L. viii. 12. Boeth. de Mus. i. 10, 11 . * Diog. L. viii. 14. Plin. Hist. Nat. ii. 8 , 21 . * Diog. L. viii. 12. Cels. de Medic. i. præf.; cf. iii. 4. 6 Porphyr. V. Pyth. 30, 33. Jamb. V. Py. 164, 244. It is sufficient barely to mention , that the practice of magical forms and other devices of the art has been imputed to Pythagoras. ? Plat. de Rep. x. 600. 330 PYTHAGOREAN PHILOSOPHY. art of training, or at least in his lectures insisted on the recognition of their general importance in the moral direction of life .' But in all this diversity of acquirements and skill, there is less, seemingly, that is indicative of the central point of interest — his personality —than in the cycle of tradition which is spread around his story. On this head, all the fables and anecdotes recited reveal to us the saint the worker of miracles the teacher of a divine wisdom : his very birth is marvellous and won derful; some accounts making him a son of Apollo, others of Hermes. Whenever he ap peared, a divine glory shone around him : he is said to have exhibited a golden thigh ; Abaxes the Scythian came to him flying on a golden arrow ; he was seen at different places at the same time ; wild beasts were obedient to his call ; the river-god held converse with him ; he re ceived from Hermes the gift of the recollection of his previous existence, and the power to awaken the same remembrance in others ; he heard the harmony of the spheres ; and his sayings passed for unerring wisdom. Who now will wonder that he received from the Crotoniats the title of Hy perborean Apollo ? At all events, it is clear that such fables and opinions could only have for their ' In the statements concerning his musical and gymnastic skill, it possible that some confusion may exist, and that the philosopher has been confounded with the athlete and musician of the same name. There were also others of this name. Diog. L. viii. 46, 47. Aristox. Harm. Elem. ii. 36. ap. Meibom. ? The anecdotes are well known ; and need only remark, that the authority of Aristotle is pretended for some of them . Ælian. Var. Hist. ii. 26. Apoll. Dysc. Hist. Mir. 6. PYTHAGORAS AND THE PYTHAGOREANS . 331 object one who either himself laid claim to, or to whom at least his associates and followers attributed, a more than human fellowship with the divine. On this point there are yet on record the most unques tionable testimonies of antiquity, of which we shall only adduce the earliest — the deposition of Hero dotus, who speaks of a certain secret worship of the Pythagoreans — the Pythagorean orgies — and of a holy legend or formulary of this worship.' Now , when we find that among the Pythagoreans the science of numbers, geometry, and music, and even medicine and gymnastics, including dancing, were in the closest manner connected with their sacred rites, we cannot well doubt that the central point of all the science and knowledge of the Py thagoreans, and of Pythagoras himself, is to be found in the secret worship which he instituted, and which his followers regarded as holier than the public service of the gods as regulated and established by the state. When we contemplate an individual so singular and so remarkable as Pythagoras, we naturally long to know the mode and processes in and through which his mental character, such as it subsequently shewed itself, was forthformed , and the means by which he acquired his widely extended influence. This desire has led to the formation of many con jectures, which, in part, may probably have been founded on traditionary grounds. When, however, we reflect on the mass of fable which, in the course ii. 31. Cf. Arist. ap . Jamb. V. Pyth. Still more ancient is the testi mony of Xenophanes ( Diog. L. viii. 36 ) concerning Pythagoras, which, however , is only indirectly available for our purpose . 332 PYTHAGOREAN PHILOSOPHY. of time, grew up out of the traditions concerning Pythagoras, and, on the other hand , how meagre and scanty was the knowledge of him possessed by even the earliest authorities, we can scarcely hope to be able to discriminate between the true and the fictitious. The accounts given by later writers of the formation of his mental character introduce us into a field so wide, that we are lost in its bound less expansion. In geometry , his teachers were the Egyptians; in arithmetic, the Phænicians;' in astronomy, the Chaldæans ; in holy things and morality, the Magi : thus nothing is left for Greece to do, and Pythagoras is presented as one wholly taught and formed by the wisdom of the East. On the other hand, again, teachers have been assigned to him from among the Greek learned : first of all, two sages of the olden time, Creophilus: and Hermodamas," names otherwise wholly unknown ; and Bias“ and Thales of the seven sages, besides Anaximander the physiolo ger ;' and, according to the opinion most exten sively current, Pherecydes the mythograph. Of 1 Connected herewith is the statement, that Pythagoras was the disciple of the Phænician Moschos or Mochos, the first author of the atomic doc trine, according to Posidonius. Moschos is by some taken to be Moses, which is again connected with the assertion that Pythagoras must have had an acquaintance with the Jewish religion. ? Porphyr. V. P. 6. Apulei. Flor. i. fin . I pass by other statements. 3 Jambl , V. P. 9 . Porph . V. P. 2. Diog. L. viii. 2. Cf. Jambl. V. P. 11. Diog. L. ut sup. cum not. Menag. Creophilus and Hermodamas seem to have been but one and the same person. 5 Jambl. V. P. 11 . 6 Ib . ? Ib. Porph. ut sup. Apulei. Flor. ut sup. & According to Andron, Duris, and Aristoxenus. Diog. L. i. 118, 119. Cic. de Divin . i. 50, PYTHAGORAS AND THE PYTHAGOREANS. 333 these rumours and opinions, two only deserve a detailed examination ; that which represents Pythagoras to have been taught by the Egyp tians, and that which makes him the scholar of Pherecydes. When we consider that Egypt was, in an espe cial wise, the wonder-land of the olden Greeks, and that even in later times, when it was better known, the singular character of its people — which, how ever reserved and retiring of itself, the stupendous structures of the national architecture protruded so prominently upon the observer's attention — was well calculated to preserve, and even to jus tify their wonderment , — we cannot feel much sur prised that the Greeks should have sought to establish some connexion between the Egyptians and their singular countryman , Pythagoras. The attempt was much facilitated by the numerous points of resemblance to Egyptian tenets and cus toms presented by the Pythagorean doctrine ofme tempsychosis, and many of his ascetical precepts at least as they were latterly understood. Whence, then, could they be more fitly derived than from Egypt ? Furthermore, there was a legend, some what ancient, that Pythagoras had , before he ar rived at Croton, been on long and distant travels ; which indeed, so far as probability is at stake, there is no ground to question. Moreover, Samos was in constant intercourse with Egypt, partly through the commerce ofprivate individuals, partly through the political relations maintained therewith by the tyrant Polycrates, with whom Pythagoras is brought into connexion by tradition. We can 334 PYTHAGOREAN PHILOSOPHY. not, therefore, deny the probability that Pytha goras may have been in Egypt. But we must be cautious in arguing further, that therefore he was initiated in all the secret lore of the Egyptian priesthood , both because the evidence is very insufficient, and the Egyptian institution of castes deprives the inference of all likelihood. Besides, a very superficial acquaintance, on the part of Pythagoras, with Egyptian usages and opinions, is quite sufficient to account for all that is usually referred to that source. Again , the geometry - of which Herodotus is of opinion that it was brought into Greece from Egypt -- was in its very infancy, and the Greeks were the first who gave to it a scientific form ; so that they could not have bor 1 rowed from the Egyptians any thing beyond a few practical rules and applications. The doctrine of metempsychosis was, it is true, a public doctrine among the Egyptians; but Pythagoras needed not to go to them for it. As for the funeral cus toms, and the abstinence from particular sorts of food, which were common to the Pythagoreans and to the Egyptians, they are but external things, wholly destitute of any noticeable influence on the inner character of man's mind, and are very far from implying any acquaintance with priestly mysteries : moreover, the inventive skill and ima gination of later times has been very busy on 3 these points. On this head we have only one point more to notice — that symbolical mode of expression common to the Pythagoreans and Egyp 1 Antiphon ap. Porph . V. P. 7, 8. Jambl. V. P. 18, 19. ? See above, 141 . 3 See below, p. 335. PYTHAGORAS AND THE PYTHAGOREANS . 335 tians. Now , a symbolical language may naturally grow out of any cult, whether public or mystical ; with this single difference, that in the former the meaning of the symbol is open and evident to all, in the latter intelligible by the adept alone. Now , so far as we are able to judge, there was only a very distant resemblance between the Egyp tian and Pythagorean symbolism . In the Pytha gorean the predominant symbol is numerical ; there are, it is true, other symbolical rules of life, but they have completely the colour of Greek practical wisdom and Greek relations of life ; and it is only in the geometrical symbols that a remote corre spondence with the Egyptian hieroglyphics can be discovered. But a slight consideration of the intimate connexion between the geometrical and numerical symbols of the Pythagoreans is suffi cient to stop at once any wish or attempt to ollow out to a great length this merely accidental agreement. With Pherecydes, Pythagoras is brought into connexion by certain statements, in which, how ever, any other name might as felicitously be substituted for that of Pherecydes. Among the opinions of Pythagoras, the doctrine of metempsy chosis is by these accounts referred to the instruc tions of Pherecydes. Thus, we are at liberty to choose whether to derive his acquaintance with this tenet from Egypt or Pherecydes ; otherwise no trace can be discovered that Pythagoras adopted into his philosophemes aught else from the mythic narratives of Pherecydes. On the contrary, the opinions as to the origin of things attributed by 336 PYTHAGOREAN PHILOSOPHY. Aristotle to Pherecydes and the Pythagoreans respectively are widely opposed to each other. It is clear, then , that the formation of the mind of Pythagoras cannot, with any likelihood, be traced by means of the accounts transmitted to us on the subject. Its principal features must be attributed to himself, as the results of his own independent researches, and to the influence of the age in which he lived, which was impelled by a strong stimulus to the pursuit of scientific knowledge. If, indeed, we do but duly and rightfully appreciate the effects operated on the mind of Pythagoras by the character of his age, we shall be able satisfac torily to account for the manner in which, by his own scientific efforts, he was enabled to become, what it is impossible not to regard him , -- one who exercised no little influence on the scientific intelli gence and moral sentiments, not merely of contem poraries, but even of after - times. Already had the Greeks attained to the first principles of scientific mathematics ; in connexion with which astronomical observation had commenced , and a question had been started as to the origin and import of the stars in the mundane economy ; music and gymnastics were practised as a means of improving body and mind ; in the gnomes of the poets and sages a cer tain practical wisdom had found its appropriate expression ; and a religious view of the system of things was as yet livingly present in the popular mind, and capable of a farther and better develop ment. Now, finding, as we do, the labours and I Met. i . 7. Stob. Ecl. i. 380. Cf, Diog. L. i . 119. Arist. Met. xiv. 4 ; cf. xii . 7 . PYTHAGORAS AND THE PYTHAGOREANS . 337 efforts of Pythagoras all concentrated in this reli gious scope and aim, it is only with extreme diffi culty that we can dispose ourselves to believe in the foreign origin of his knowledge and wisdom. For the whole period of the advancement of Greek mind , extending from before Pythagoras to long subsequent times, displays so many and such obvious signs of similar attempts to seize and apprehend, in a mysterious point of view, the good and the holy, as evidently prove that it was the direct and natural offspring of the pure Greek mind. We find , moreover, that tradition itself allows Pythagoras to draw his religious conceptions from a Greek source ; for besides that his secret lore is not seldom associated with the Orphic mys teries, he is also represented as having in Crete been initiated in all the mystical secrets of the Idean cave ;' and another statement makes him to receive from the Delphic priestess, Empedoclea , his ethical doctrines — i. e. his ascetical precepts, which have more or less a religious reference .? Moreover, we would hazard the conjecture that Pythagoras might have received from his ancestors, the Tyrrhenian Pelasgians, some holy legend, which, as available for his purpose, he may have adopted, and given to it a completer form and 3 larger application . " Jambl. V. P. 25. Porphyr. V. P. 17. Diog. L. viii. 3. 2 Aristoxen. ap. Diog. L. viii. 8, 21. Porphyr. V. P. 41 . * Lobeck, in the Aglaoph., has, it is well known, referred the Orphic Bacchic mysteries to the Pythagoreans and Pythagoras. There is perhaps too much asserted or denied in this. When, however, in opposition to this view, the connexion of Pythagoras and the worship of Apollo is adduced as decisive, and, with Krische (p. 22, &c., 33, &c. ), it is asserted that Pytha goras never in any respect, but only after his death certain degenerated Z 338 PYTHAGOREAN PHILOSOPHY . That his religious views were promulgated in a system of secret doctrines, is indeed implied in the very term orgies, by which Herodotus denominates them : but we are further expressly and credibly in formed that the Pythagoreans adopted the maxim, “ Not unto all should all be made known .”‫ا]ور‬ These orgies seem to have found their way into Greece Proper- at least Herodotus speaks of them as of something commonly known — but it was in the Italian colonies that they were most extensively diffused. Why Lower Italy should have been the chosen scene of the exertions of Pythagoras, is variously accounted for by a diversity of legends, the most probable of which it would indeed be dif ficult to select. This, at all events, we know, that he migrated from Samos to Croton -- an event which is placed as happening in his fortieth year.? We shall pass over the miraculous stories of his appearance in Croton - of the god-like veneration he there received of the moral change his pre cepts and example suddenly effected — and shall merely observe, that he seems to have enjoined a peculiar mode of private life on all who sought disciples, had any thing to do with Bacchic mysteries, we must in that case form a very different opinion of Pythagoras from that which has been re corded by the mouth of his disciples. We do not pretend to determine the matter ; yet we would call attention to the fact, that not merely the cult of Apollo, but that of Hermes also, is mentioned in several important legends about Pythagoras, which would seem to refer to a connexion with Samo thracian mysteries ; and that in Philolaus, the truest disciple of the Pytha gorean philosophy, a reference to the Bacchic cult occurs ( Böckh, p. 36). All this favours a conjecture in itself probable, that these new -coined mys teries consisted of an eclectical combination and more general interpretation of earlier cults. · Aristox. ap . Diog. L. viii. 15. Arist. ap. Jambl. V. P. 31 . ? Aristox. ap. Porph. V. P. 9. Cicero, de Rep. ii. 15, places it in Olymp. 62. PYTHAGORAS AND THE PYTHAGOREANS . 339 his society. The mere designation of this institu tion, which was afterwards observed by his fol lowers, is sufficient to convict of exaggeration those statements of later writers, which represent Pytha goras himself as operating an entire revolution in the form of government, not only in Croton, but likewise in the other Italian cities. This, however, does not exclude the probability that Pythagoras did communicate to his followers principles of politics, the aim and object of which was a change in the constitution of the several states : at least, much is told us of the political maxims of Pytha goras, which appear to have had a leaning to wards aristocracy ;8 and if we call to mind the fate of the later Pythagoreans, both appear probable ; which indeed the intimate connexion of ancient religion with politics would also lead us to expect in the case of the Pythagorean orgies. Only we must guard against entertaining an opinion that the secret society of the Pythagoreans was wholly of a political nature ; on the contrary, all the probable accounts on this head justify us in seeking the bond and centre of the Pythagorean community in some secret religious doctrine. The association founded by Pythagoras appears to have been a secret society : several traditions refer to this, the greater part of which were, how ever, in later times exaggerated into the improbable, if not the impossible. The complete initiation in the orgies, as in all similar institutions, was pre 1 Plat. de Rep. x. p. 600. ? Varro ap. August. de Ordine, ii. 54. Posidon. ap. Senec. Ep. 90 . 3 Diog. L. viii. 3. Jambl. V. P. 257. 340 PYTHAGOREAN PHILOSOPHY. ceded by certain courses of probation and minor inductions. A peculiar practice is imputed to Pythagoras : that he first of all examined the phy siognomy of the candidates for initiation ;' he then habituated them, during the period of probation , to a long silence (exeluvdia). The periods of the several initiations are given differently ; and indeed in such matters we must not expect to be able to speak with positive certainty. It is probable, how ever, and indeed consistent with the general consti tution of such associations, that the Pythagoreans were divided, according to the grade of initiation, into different classes, the denominations of which we are utterly ignorant of, except that very general classification into Exoterici and Esoterici. In such holy fraternities it is not surprising that much should have been supported by an appeal to the respect entertained by the associates for the original founder ; and this, in all probability, is the explica tion of the far -famed autos épa of the Pythagoreans. There is, moreover, nothing remarkable in the admission of women to the mysteries — those much famed female Pythagoreans. The institution was maintained by its members living in common, by common customs, by bodily and mental exer cises : there were certain precepts for the direc tion of the associates delivered, partly in symbo lical aphorisms, the import of which may indeed be guessed at, but cannot be accurately given ;' partly in plain and clearly expressed rules of conduct, I Gell . Noct. Att. i. 9. ? Gell. ibid. Jamb. V. P. 68, 72, 226. 3 Cic. de Nat. D. i. 5 . 4 Jambl . V. P. 267 fin . 5 On this point at great length, Jambl. Protrep. 21 . PYTHAGORAS AND THE PYTHAGOREANS . 341 some of which, it is not unlikely, have come down to us in the so -called golden verses of Pythagoras. To the community of living practised by the Pytha goreans belonged the common meals (ouoostia ), for which particular sorts of food appear to have been enjoined by their first founder ; though, indeed, the statements on this point are far from unanimous.' Lastly, they had also certain peculiar ordinances to be observed in the burial of adepts. The asserted community of property: looks like an ex aggeration of later days ; for it is contradictory of many anecdotes of the private wealth of individual members, which are more probable than the general accounts. The Pythagorean league was highly favourable to the carrying out to perfection a peculiar scien tific system. The various objects to which it was directed we have already indicated , when we spoke of the literary attainments of Pythagoras. The religious sentiment must be regarded as forming 1 The prohibition of beans for food, according to a probably spurious work of Aristotle ( Diog. L. viii. 34), which was an Egyptian custom, ac cording to Herodotus, ii. 37. Aristoxenus, on the other hand, says, Pytha goras recommended beans before all other food : Gell. iv. 4. The absti nence from fish is another resemblance to Egyptian customs ; but the tra dition on this point is not very extensive, and rests on fables. On absti nence from flesh there are a variety of traditions, Eudox. ap. Porph. V. P. 7. Jambl. V. P. 85, 108. Diog. L. viii. 20. It is safest to follow Aristotle , according to whom the Pythagoreans only abstain from particular kinds of fish . Gell. ib. Diog. L. viii. 19. Cf. Porph. de Abst. i. 126. The statement of Aristoxenus, that they only abstained from the ploughing ox and the wether, evidently on account of their usefulness, appear to be a later ver sion. Diog. L. viii. 20. Cf. Ath . x. 13. p. 418. 2 Herod. ii. 31 . 3 Gell. Noc. Att. i. 9. The statement might have originated in part in the custom of the Pythagoreans of contributing to the expense of the com mon meal, and in part from their maxim , All things are common among friends. 342 PYTHAGOREAN PHILOSOPHY . the connecting and pervading thread of the dif ferent branches of the scientific labours, of which the principal were music and mathematics, and which were, indeed, so closely entwined with their whole view of science, that we confess there is some ground for the assertion that their whole system was concentrated in mathematics and music. That the religious sentiment, falling in with and meeting the desire for scientific stimulus, should give rise to philosophical speculations, is but natural; so that we are justified in assuming for Pythagoras himself a certain degree of philosophical develop ment. Beyond this, we must confess entire igno rance as to what may have been the subject or the result of the philosophical labours of Pythagoras ; for those of ancient writers who were best and most critically acquainted with the doctrinal sys tems of the earlier philosophers, Plato and Aris totle, do not attribute to Pythagoras any particular philosopheme ; and, on the other hand, the state ments of later times, which give to Pythagoras personally the doctrines of all the Pythagoreans, do not deserve the slightest consideration on this head. The utmost that even conjecture can hazard , is to suppose that the germ of the philosophical view which was subsequently carried out by his disciples and followers was pre-existent in the earlier lessons of Pythagoras. An opinion has been put forward, that the gra dations in the Pythagorean fraternity had reference to the communication of philosophy, and that par ticular doctrines were revealed to the esoterici alone, and others to the exoterici ; but to all abso PYTHAGORAS AND THE PYTHAGOREANS . 343 lutely without the pale it was not allowable to communicate any philosophical tenet. Many allu sions to this point are contained in various stories of members expelled the society on the grounds of talkativeness, and of the unhappy destiny of those who divulged the mystic doctrines. When , however, we reflect that the more ancient authorities speak, it is true, of Pythagorean mysteries, but not as if they were of a philosophical character ;' and that it is only later writers, that are so fond of intruding into philosophy their favourite mysteries, who speak of a secret philosophy of the Pythagoreans,—the impure source of the traditions becomes imme diately evident. Unquestionably, all that was intimately connected with the religious lore of the Pythagoreans would naturally be kept secret ; but contrariwise, there could not exist any motive to keep in secrecy whatever was of a purely scientific character, and admitted of being exhibited freely and in a manner intelligible to all. Now, it is but natural, that with the longer cultivation of philo sophy by the Pythagoreans, its scientific results would be the more widely diffused ; whereas in the earlier times they would be more mixed up with the source from which they sprung — the legends | Aristoxenus merely remarks generally, that the Pythagoreans had a rule, not to communicate all to all : but the passage is from a treatise on education, where it most probably had a particular application. Diog. L. viii. 15. Aristotle, according to Jambl. V. Py. 31 , states that, among the deepest secrets of the Pythagoreans, it was taught there are three species of intellectual creatures, God and man , and an intermediate, to which class Pythagoras belonged : this, it is to be hoped, no one will consider to be philosophical. There is more of a philosophical character undoubtedly in what Plato ( Phæd. p. 22) instances as a secret doctrine ; but yet this is only in a mythical garb, and cannot with certainty be referred to the Pythago reans . Cf. Cratyl. p. 400. 344 PYTHAGOREAN PHILOSOPHY, and precepts of religion — and consequently kept the more rigidly within the narrow precincts of the holy brotherhood. This is in some degree con firmed by the traditionary statement that Pytha goras and his immediate followers left no written work behind them' by which their peculiar tenets might have become commonly known ; and that it was only long subsequently that Pythagorean doc trines were first diffused and rendered current in Greece. This diffusion in Greece Proper of Pythagorean doctrines was occasioned by the disastrous fate of their society. The Pythagoreans, we are told ( for the truth of all particulars we cannot pretend to vouch ), had acquired considerable influence in the politics of Croton, and given to its constitution an almost perfect form of aristocracy. Their influence is also represented as extending to Metapontum , Locri, Sybaris, and Tarentum , and as especially inimical to all tyrannical governments. About this time one Tetys had established himself in the tyranny of Sybaris, and the unfriendly nobles had fled to Croton . The refusal of the Crotoniats, at the instance of the Pythagoreans, to deliver up the fugitives when demanded by Tetys, occasioned a war between these two neighbouring states : the Crotoniats, under the command of the Pythagorean Milo, defeated the once -powerful but effeminated Plut. de Alex. Fort. i. 4. Porph. V. P. 57. Diog. L. i. 16 ; viii. 15. Jambl. V. P. 199. All the writings attributed to Pythagoras and the old Pythagoreans are supposititious, with the exception, perhaps, ofcertain mys tagogic works, which were very early in use for all sorts of superstitious practices. Some of them probably belong to the very first times of the Py thagoric league. Cf. Diog. viii . 7. c. not. Menagii. PYTHAGORAS AND THE PYTHAGOREANS. 345 Sybarites, and destroyed their city. This success, however, entailed the ruin of the Pythagoreans. In the division of the spoil a dispute arose from among the popular party, led on by Cylon, who had, it is said, on account of the impurity of his morals, been refused admission into Pythagorean society. The discontented attacked the Pythago reans who were assembled in the house of Milo, where the greater number were slain . Pythagoras himself is represented as having escaped the danger, and fled into other cities of Lower Italy ; but as the persecution of the Pythagoreans rapidly ex tended thither also , he met his death , according to the story, at Metapontum ,' B.c. 358. After his decease, his memory was held in the greatest respect by the Italian Greeks ;' and even in the time of Cicero, the spot was pointed out where he was said to have perished .” This persecution of the Pythagoreans was fol lowed by a great political movement throughout all the Italian states. Every where the Pythago rean houses of assembly were burnt to the ground, and the leading citizens banished ; until at last the friendly intervention of the Achæans effected a reconciliation of parties, and an Achæan constitu tion --i. e. a democracy - was introduced . In all likelihood, this persecution of the Pythagoreans and their political principles was the cause and occa 1 Diod . Sic. xii. 9. Plut. de Gen. Socr. 13. De Repugn. Stoic. 37. Porphyr. V. P. 56. Jambl. V. P. 255. · Arist. Rhet. ii. 23. Justin. xx. 4. Porphyr. V. P. 4. Jambl. V. P. 170. 3 Cic. de Fin. v . 2. • Polyb. ii. 39, where the Achæan polity is expressly stated to be demo cratic. 346 PYTHAGOREAN PHILOSOPHY . sion of the appearance of so many philosophers of this sect in Greece Proper. Some, however, re mained in Italy, and there enjoyed, for the most part, high political consideration . There are many statements, manifestly fictitious, of the successive transmission of the Pythagorean system . The persecutions which the society un derwent appear to have cast a deep shade of obscurity over its history immediately after the death of its founder. We find, moreover, pre tended lists of Pythagoreans, by which an undue and incredible extension is given to their school, and in which many are reckoned as its members who could never have been, in the remotest de gree, connected with it. The causes which led the writers of later times, and even of a very early date , to attribute to the Pythagorean school a wider sphere of influence than it actually pos sessed, were mainly three : a desire on the part of Pythagoreans to accumulate honours upon their sect ; the historical confusion by which those who took a part in the Pythagorean orgies were mis taken for professors of its philosophy ; and lastly, the indifference with which the terms Italic and Pythagorean were used to indicate the same sys tem of philosophy. The zeal which burst out shortly before the birth of Christ for the myste rious and wonder -working in philosophy, which was usually designated as Pythagorean, gave rise to a multitude of compositions which were falsely put forward under the names of earlier philoso phers of that school. Modern criticism has clearly Jambl. V. P. 265, 6. Diog. L. i . 15. Herodot. iv. 95. PYTHAGORAS AND THE PYTHAGOREANS , 347 shewn that the works attributed to Timæus and Archytas are spurious ; and that the treatise on the nature of the All, which has been assigned to Ocellus Lucanus, cannot even have been written by a Pythagorean. Similarly, also, the many frag ments pretendedly of Archytas, as also those which are usually given to Brontinus Euryphemus, and other ancient Pythagoreans, are manifestly spurious. Furthermore, it can be satisfactorily shewn that Alcmæon the Crotoniat physician, the contemporary of Pythagoras, many of whose opi nions are yet extant, has been erroneously classed among the Pythagoreans ; and also that Hippasus, Ecphantus, Empedocles, and Eudoxus, do not belong to that series of philosophical development which we ` designate by the name of the Pytha gorean school. There would be much less diffi culty in proving this assertion, did we still possess the work of Aristotle against the Pythagoreans and Archytas; however, the slightest comparison of the pretended works and fragments of Pythago reans with the information we may derive as to the Pythagorean doctrines from the scattered notices of Aristotle, leaves no room to hesitate what decision our judgment must come to on this point. It is only from the time of Socrates that we first derive any account of the Pythagoreans pos sessing the slightest title to the certainty of his tory. This information is, however, limited to four or five names — Philolaus, Lysis, Clinias, Eurytus, | The present place admits not of critical discussions. On this point my History of the Pythagorean Philosophy may be consulted. 348 PYTHAGOREAN PHILOSOPHY. Archytas ; of these, three are mentioned by Aris totle — Philolaus, Eurytus, and Archytas ; ' the first and the last lived at Thebes, and the latter of the two was the teacher of Epamonidas :' of Clinias all that is told is not so well warranted, notwithstanding its high degree of probability. As to the age in which these individuals respectively lived, thus much only can be affirmed with cer tainty, that Philolaus was the teacher at Thebes of Simmias and Cebes, before they came to So crates at Athens :: that, somewhat later, Lysis was the instructor of Epamonidas; and somewhat later still, Archytas was the contemporary of the younger Dionysius and of Plato . The dates of the others are consequently determined ; for they are all more or less connected together. There is yet another statement, apparently very credible to a certain point, which tells that Philolaus, Clinias, and Eurytus, were the disciples of one Aresas, a teacher in Italy of the Pythagorean philosophy.* By this the efformation of that system of doctrines which we designate as the Pythagorean is traced backward another generation ; not, however, that we pretend for one moment to deny, that the first lineaments may even previously be recognised in I Met. viii. 2, xiv. 5 ; Probl. xvi. 9 ; Rhet. iii. 11. Eth. Eud. ii. 8. Cf. Theophr. Met. 3. Diog. v. 25 . ? ' Corn. Nep. Epam . 2. Plut. de Gen. Socr. 13. 3 Plat. Phæd, p. 61. On this authority Böckh ( Philolaus, p. 5, &c.) places the life of Philolaus between Olymp. 70 and 90. * Jambl. V. P. 266. There is much unquestionably that is incorrect mixed up with this account ( Böckh's Phil. 13 ) ; but it stands distinctly apart from the other fabulous narratives of the succession of the Pythagorean school ; on which account it will deserve some credit. Plutarch , de Gen. Soc. , means possibly Aresas, when he talks of the Pythagorean Arkesos. PYTHAGORAS AND THE PYTHAGOREANS. 349 the general character of the Pythagorean fraternity. However, it has been only transmitted to us in the shape given to it by the labours of Philolaus, Eurytus, and Archytas ; for although there is a fragment under the name of Aresas,' its spurious ness is proved by its subject matter; besides which, we are no where told that Aresas committed his thoughts to writing ; on the contrary , there exists a tradition, apparently very old and well- founded , that Philolaus or his contemporaries were the first to give a written expression to the tenets of the Pythagorean philosophy. Of the five individuals previously enumerated, Lysis and Clinias do not appear to have left behind them any written monu ment ;' and we may well believe the same of Eurytus, since an ancient writer speaks of his doctrines on the merely oral authority of Archytas.* Of Philolaus, on the contrary, fragments have come down to us, the genuineness of which Böckh has satisfactorily established ; and of Ar chytas there cannot be a question, notwithstanding the many supposititious works in his name, that he left behind him many and important treatises. It was the doctrines of these men, and of a few others whose names are not so well known, that Plato and Aristotle had in view in their statements of the Pythagorean philosophy. The general description portrays these Pytha goreans as men, the chief aim of whose action and I Stob. Ecl. i. 846. ? See Böckh's Philol. 16. 3 The fragments attributed to Clinias are doubtful. 4 Later writers adduce, it is true, fragments of his : Stob. Ecl. i. 210 ; where the name, however, is Eurysus ; and Syrian ad Arist. Met. fol. 118 a, where also the name is corrupt. 350 PYTHAGOREAN PHILOSOPHY. thoughts was to attain to a perfect blamelessness of life .The important influence their example operated on the morals and science of their times is clearly shewn in the anecdotes of Archytas. The obscurity of their history , however, is strikingly proved by the inconsistency of all that is told of this celebrated statesman and scholar ; an obscu rity which is undoubtedly attributable in the main to the oblivion into which the Greek colonies so rapidly fell. Archytas, the most distinguished citi zen, and a native of Tarentum , who six or seven times discharged the responsible office of general, and never experienced either check or defeat, and deservedly enjoyed the unlimited confidence of his fellow-townsmen, was eminently distinguished for his self -command and purity of conduct ; and as uniting with a rare and prudent knowledge of man kind, such a child-like feeling of universal love and such simpleness of manners , that he lived with the inmates of his house a real father of a family ; ' and, amid all his public avocations, still found leisure to devote to the most important discoveries in science, and to the composition of many works of a very diversified character. His discoveries were exclu sively in the mathematical and kindred sciences.” He was occupied not merely with theoretical, but also practical mechanics ;: and his inventions in this department of study imply a considerable I The anecdotes from which these traits of character are taken are to be found in Plutarch, Ælian, Diogenes Laërtius, Athenæus, and others, and for the most part are marked with a character of peculiarity which attests their truth . ? Diog. L. viii. 83. Vitruv. ix . 3. 3 Diog . L. ut sup. Arist. xy 9 ; Polit, viii. 6. G x. 12. PYTHAGORAS AND THE PYTHAGOREANS, 351 advance in their cultivation . He also published a musical system, which was referred to by all suc ceeding theoretical students of the art ." He wrote, moreover, a treatise on agriculture. Of his philo sophical doctrines many accounts have come down to us ; but wherever our information on this head is derived exclusively from writers of a later date, we cannot be too much on our guard , lest we should adopt any thing which rests merely on suppositi tious writing, since nearly all the fragments attri buted to him are spurious .' With regard to the local diffusion of Pytha gorean views in its later times, the nativity and residence of those last-mentioned Pythagoreans respectively affords the best and directest infor mation. Philolaus, according to the majority of witnesses, was a Tarentine ; according to Diogenes, a Crotoniat. Thebes, as already mentioned, was | Ptolem. Harm. i. 13. Boeth . de Mus. v . 16. 2 Varro de Re Rust. i. 1. Colum. i. 1 . · See my History of the Pythagorean Philosophy, p. 67. Hartenstein has recently produced a most valuable and useful monography upon Ar chytas, which, however, is, I believe, as yet unpublished . He acknowledges that the fragments in Stob. Ecl. 710, & c. 720, &c, cannot have come from the hand of Archytas in their present shape. But their seeming profound ness has at all times excited attention, and created a wish for their being made available for the purposes of the history of philosophy ; and Hartenstein has not been able to resist making the attempt. He considers himself to be justified in classing the fragments into original, and into restorations of Archytic doctrines. This is, to my mind, too artificial a procedure. It has been suggested to me that these fragments may possibly be re-translations into the Doric dialect from Aristotle's extracts from the works of Archytas (Tà ék toll Trualov kal Tôv ’APXutelwr, Diog. L. v. 25 ) ; and hence the many Peripatetic terms. Against this hypothesis I must remark, that the use of ovola for únń, without any nicer limitation, decidedly belongs to the Stoical phraseology, and suggests a time at which Stoical and Peripatetic terms were employed eclectically. Hartenstein , from Arist. Met. i. 5 , claims otoixeiov for a Peripatetic term ; but the philosophical use of the word dates from Plato. 352 PYTHAGOREAN PHILOSOPHY. the seat of his instructions, but his residence there seems to have been only temporary ; ' and according to a very probable statement, he resided for some time at Heraclea in Lucania . Clinias also, a Ta rentine, lived at Heraclea. Eurytus, a native of Croton, or of Tarentum , dwelt at Metapontum ; Archytas at Tarentum . We have already said that Lysis, by birth a Tarentine, taught at Thebes; previously, however, he is stated to have been in the Peloponnese . Among the later Pythagoreans there are also mentioned Xenophilus of the Thra cian Chalcis, Echecrates, Diocles, and Polymnas tus, the common birth -place ofwhich three was the little town of Phlius : with these it has been as serted that Aristoxenus , the disciple of Aristotle, was acquainted .* From these philosophical Pythagoreans we shall no doubt be justified in distinguishing certain other Pythagoreans, who brought into Greece manifold superstitious practices and pretended magical powers. It is true, the testimonies to this perversion of the Pythagorean orgies — for such it is necessary to consider the most, if not the whole of such practices — are not very ancient, the earliest belonging to the time of Cicero. But when we reflect, that it was at this period that superstition first began openly to shew itself, and that the secret customs and associations of the Pythagoreans presented a fitting stock for the en grafting of the grossest superstitions; that there 1 Plat. Phæd. p. 61 . ? Jambl. V. P. 266. Plut. de Gen. Socr. 13. 3 Jambl . V. P. 250. 4 Diog. L. viii. 46. Jambl. V. P. 251 . 5 In earlier times it was usual to call them Orphic mysteries. PYTHAGORAS AND THE PYTHAGOREANS. 353 was, moreover, a natural germ of superstition in their mystical rites; and that, lastly, traces of deep corruption were very early discovered in this school, — we cannot well hesitate to admit that, even in the olden times, there were some, among those usually reckoned as Pythagoreans, who sought by such fraudulent artifices to make a profit of the popular superstition. It is likewise far from improbable that so -called Pythagorean works were early in existence, having for their object the accre diting and diffusion of particular superstitions — such as the holy legend, and the descent into the lower world - of which, so early as in the age of Augus tus, critical investigation attempted to prove that they were not the composition of Pythagoras, but of very ancient Pythagoreans — Cercops or Bronti nus. Similarly, many sentiments and opinions quoted by ancient writers as those of Pythagoreans are quite open to the question, whether they be longed to philosophers of that name, or to these same religious tricksters.* Now , believing, as we do, that the first develop ment of philosophy by this school began with Pythagoras, and maintained a truly philosophical character down to Archytas, we must necessarily suppose a series of gradual and successive advance " Hereto belong the tricks with the arithmetic symbols, and the cynism of the later Pythagoreans. Athen. iv. 161 , &c. Diog. L. viii. 37, 38, from the comic writers. 2 Comp. Lobeck. Agl. p. 904. 3 Upon these works consult Diog. L. viii. 7. not. Menag. The katáßaois eis çdov was the subject of the allusions of the comic writer Aristophanes : Diog. L. viii. 38. 4 I am disposed to see traces of this in Aristotle, Anal. Post. ii. 11 ; Meteor. i. 8. 2 A 354 PYTHAGOREAN PHILOSOPHY . ments . But as the Pythagoreans anterior to Phi lolaus did not, to all appearance, commit their opinions to writing, the first commencements of this method of philosophising are not so well known as its results. Wholly different is it with the question, whether there are not usually com prised in the Pythagorean , as in the Ionian school, views which, in their fundamental character, are widely distinct ; and consequently , under the name of Pythagorean philosophy we assume the oneness of what, as essentially different in character, cannot rightfully be comprehended under a single doctrinal term . In answering such a question, we must admit that very opposite tendencies are indeed dis coverable in the Pythagorean philosophy, but still not so directly counter to each other as to defy all attempts to refer them to the same fundamental position. In this respect the Pythagoreans must not be likened to the Ionians, but to the Eleatæ , by whom we shall presently see a single primary view carried out on its different aspects. This unity of opinion among the Pythagoreans on all important points was strongly promoted by the close bonds of their fraternity : indeed it is not improbable that the stories of the expulsion of cer tain members on account of their doctrines were so far founded on truth, that the Pythagoreans were scrupulous to preserve the purity of their doctrine ; and to this there is an evident allusion in the dis tinction so expressly drawn between the genuine Pythagorean and the spurious expositions of their theory of numbers.' An appeal, however, has been " Hereto belongs the doctrine of Hippasus : vide Jambl. in Nicom. p. 11 . PYTHAGORAS AND THE PYTHAGOREANS. 355 made to Aristotle in behalf of the pretended co existence of different fundamental views among the Pythagoreans ; ' — in my opinion, most fruitlessly. It is true, Aristotle does at times say, “ this or that Pythagorean was thus or thus of opinion :" but this expression is either used by him when speaking of subordinate matters ; or if he does occasionally apply it to leading principles, it is apparent, from his elsewhere attributing the same doctrines to the Pythagoreans collectively, that he is speaking of the genuine and recognised philosophising Pytha goreans, whom he elsewhere distinguishes from those other -- rightfully or wrongfully so called-- Pythagoreans. It is quite another question, whether Aristotle does or not attribute any important tenet to some only of the Pythagoreans, as distinct from others who taught differently . This would indeed be sufficient to call for a careful distinction of dif fering and opposite views, unless, in fact, these statements of doctrines, so expressly denied to be the opinions of the collective school, were confined V. 81. Villois. Anecd . ii. 216. Syrian. in Arist. Met. xii. fol. 71 b, 85 b. Simpl. Phys. fol. 104 b ; and the doctrine of Ecphantus, Origen. Phil. 15. Stob. Ecl. Phys. i. 308 , 448-486. Brandis on the doctrine of numbers of the Pythagoreans and Pla tonists, in the Rhein. Mus. 2. 210. Hoffmeister in the Kritischen Biblio thek f. der Schul- und Unterrichts -wesen , 1828, n. 51. Brandis, in his Gesch. d. Gr. Röm . Phil. p. 445, has given his views on this point more pre cisely. “ That the Pythagoreans, notwithstanding these differences, agreed in the grounds of their system , is plain from Aristotle, who invariably talks either of Pythagoreans generally, or ofsome Pythagoreans, without entering into any precise distinctions.” Now this differs little, if at all, from my own view . ? Meteor. i. 6, 8 ; de Anim. i. 2 ; de Sensu et Sensil. 5. 3 De Cælo, iii. 1 . 4 Met. i . 5. 356 PYTHAGOREAN PHILOSOPHY. entirely to wider applications of the fundamental doctrine of contraries, universally admitted by the Pythagoreans. Such being actually the case , we are only driven to suppose that the Pythagorean philosophy did not receive until later times a defi nite shape and form . Aristotle'— who, if his state ments relative to this philosophy be considered in the aggregate, and not in detail, is our best autho rity - evidently regarded their doctrines as forming a system perfectly one, which in this respect stands in direct contrast not only with the Ionic and Ele atic, but also with the Platonic system : this, how ever, manifestly does not exclude the possibility of the existence of different grades of perfection, and diversified points of view. This seems to be strongly confirmed by the fact, that Aristotle no where allows an individual philosopher to stand prominently forward out of the general body of the Pythagorean sect. Generally speaking, it would appear that the acquaintance possessed by the ancients with this doctrinal system was con fined to the writings of Philolaus and Archytas. Even of the philosophical doctrines of Philolaus little has been expressly quoted ; and of all the 1 Of course, we do not deny, that there is much in the accounts given by Aristotle of the Pythagorean doctrine which needs confirmation . On the contrary, we are disposed to think that the wish to find points of re semblance between the Pythagorean and Platonic systems had led Aristotle to many distorted views of the former. When we compare his extracts together, it is impossible not to perceive that he was, to a certain degree, undecided as to the meaning of the Pythagorean doctrine. As he has often misinterpreted the Platonic, so too he has the Pythagorean, and, generally, every doctrine in which there was aught of the mystical in the exposition, and thereby required greater quickness of fancy than Aristotle possessed. PYTHAGORAS AND THE PYTHAGOREANS. 357 Pythagoreans, he alone presents himself before us in any degree of distinct personality. On this account, it is perfectly impossible to trace histori cally the divers tendencies and advances of the Pythagorean philosophy. CHAPTER II. DOCTRINES OF THE PYTHAGOREANS . If, in our exposition of these doctrines, we confine ourselves to Aristotle and the more ancient autho rities, and the fragments of Pythagorean writings still extant, and only with extreme caution make any use of the statements transmitted through later channels, this will occasion no surprise to those who are in any degree acquainted with these later traditions. Besides their usual inaccuracy and want of precision, all the writers upon the Pythagorean philosophy, subsequent to the birth of the Christ, exhibit a strange confusion of the most opposite views ; arising in part from their having been deceived by supposititious works, and in part from their confounding with the old and genuine the doctrines of the more modern Pytha goreans, which, however, had nothing in common with the ancient Pythagorism beyond the mere outward form . It is undoubtedly no easy matter to separate, in these later traditions, what belongs to the old system, and what to the new ; but another, perhaps greater difficulty, lies in the sym bolical mode of indication employed by the Pytha goreans, and which is capable of being taken in a variety of ways, in consequence of the very imperfect correspondence of the symbol and the DOCTRINES OF THE PYTHAGOREANS . 359 object it stood for. We even find that they employed the same symbol in different senses ; and it is far from easy to determine the particular sense they gave it in each formula respectively. Even the formula in which they advanced their leading position , “ The number is the essence (ovoia ) or the first principle (agxá) of all things ," can only be taken symbolically. And the question to be determined is, what did they understand by number as the principle of things. This much, at all events, is clear, that in this doctrine they started from the mathematical, consequently from the form , not from the matter of the sensible. On this account, Aristotle has derived their whole system from a fondness for mathematical studies, which had first engaged their attention , and which they had greatly advanced, since they also considered numbers to be principles of the mathematical. In this light we must look upon the Pythagorean doctrine of numbers as one of those modes of re presentation which have originated in a peculiar bias, in the prosecution of which, the first authors, misled, as is often the case, by their prepossession, employ many forced similitudes and lame reason ings in support of their favourite theory. Many are the instances, besides , this of the Pythago reans, where a predilection for the mathematical has led to an attempt to reduce all things to number and measure , or where a deep -seated tend ency of man's nature has suspected it could dis cover some deep mystery in figures and numbers ; and in all these instances alike the theorist, in order to establish his hypothesis, has had recourse 360 PYTHAGOREAN PHILOSOPHY . to manifold fantastical and empty analogies. We cannot wonder, therefore, at the remark of Aris totle, that the Pythagoreans, whenever, in the many points of resemblance they adduced in con firmation of their system , some cases did not exactly tally, did not scruple to draw upon fancy for the deficiencies of reality.' Their mode of pro ceeding was mainly this : they first endeavoured to give probability to the dogma, “ all is number," by calling attention to the many phenomena whose qualities are dependent on numerical relations, and then sought to accumulate instances by the aid of the most arbitrary assumptions. Nevertheless, it would not seem that the philosophical element in their doctrine was originally the result of observa tion of the constant recurrence in nature of certain numerical relations. Now, we find yet many other and similar for mularies expressive of the Pythagorean doctrine of numbers ; and it is above measure necessary to notice, that in some numbers, in others the num ber, or the elements of number, are made to be 1 Arist. Met. i . 5. οι καλούμενοι Πυθ. των μαθημάτων αψάμενοι πρώτοι ταύτα προήγαγον και έντραφέντες εν αυτοίς τάς τούτων αρχάς φήθησαν είναι πάντων. επει δε τούτων οι αριθμοί φύσει πρώτοι , εν δε τούτοις έδόκουν θεωρείν ομοιώματα πολλά τοίς ούσι και γιγνομένοις, μάλλον και εν πυρί και γη και ύδατι, ότι το μέν τοιονδί των αριθμών πάθος δικαιοσύνη, το δε τοιονδί ψυχή και νούς, έτερον δε καιρός και των άλλων ως ειπείν έκαστον ομοίως· έτι δε των αρμονικώνv εν αριθμούς δρώντες και τα πάθη και τους λόγους, επειδή τα μεν άλλα τους αριθ μοίς εφαίνετο την φύσιν αφομοιωθήναι πάσαν, οι δε αριθμοί πάσης της φύσεως πρώτοι , τα των αριθμών στοιχεία των όντων στοιχεία πάντων είναι υπέλαβαν και τον όλον ουρανόν αρμονίαν είναι και αριθμόν, κ. τ. λ . Cf. ib. c. 6. - Brandis , in the Rhein . Mus. ib. p. 212. sq., makes unnecessarily a distinction be tween the doctrine, " things are duocámara of numbers," and the other, " they are viunoer twv åpı@uwv.” This doctrine is very old. In Philolaus there is much verbal play of this kind. In later times it was probably mul tiplied into a greater variety of forms. DOCTRINES OF THE PYTHAGOREANS. 361 the principles of things. That these several ex pressions are not identical or tantamount, is of itself evident ; and it becomes us now to enter upon a particular explanation of the proper sense of each. We begin with the expression : Number is the principle of things. In the fragments of Philolaus, mention constantly occurs of the essence of num ber. That this should be conceived as one and the same with number itself is natural. But in the Pythagorean doctrine, number comprises within itself two species - odd and even : it is therefore the unity of these two contraries ; it is the odd and the even . Now, the Pythagoreans said also that one, or the unit, is the odd and the even ; and thus we arrive at this result, that one, or the unit, is the essence of number, or number absolutely. As 1 In Böckh's collection, n . 18. 2 Arist. ibid . φαίνονται δή και ούτοι τον αριθμόν νομίζοντες αρχήν είναι και ώς ύλην τοϊς ούσι και ως πάθη τε και έξεις, του δε αριθμού στοιχεία το τε άρτιον και το περιττόν, τούτων δε το μέν πεπερασμένον, το δε άπειρον, το δε εν εξ αμφοτέρων είναι τούτων (και γάρ άρτιον είναι και περιττόν) , τον δ ' αριθμόν εκ του ενός . οι δε Πυθ. δύο μεν τας αρχάς κατά τον αυτόν ειρήκασι τρόπον , τοσούτον δε προσετέθεσαν, ο και ίδιον αυτών εστίν, ότι το πεπερασμένον και το άπειρον και το εν ουχ ετέρας τινάς φήθησαν είναι φύσεις, οιον πύρ ή γήν ή τι τοιούτον έτερον, αλλ ' αυτό το άπειρον και αυτό το εν ουσίαν είναι τούτων, ών κατηγορούνται διό και αριθμόν είναι την ουσίαν πάντων. From these passages it may be seen how Aristotle, after the manner of the Pythagoreans, puts άρτιον for άπειρον, πεπερασμένον, or, as elsewhere still better, πέρας for Tregittdy and also for év, and reciprocally. This phraseology deserves notice. But in this passage åp.Quòs also is put for év, as the ground or principle of the contrariety of odd and even ; so that from this alone it results, that with the Pythagoreans the one had a double signification, indi cating both the unit which stands for the representative of the odd, and the one, which is the odd and the even. The argument of Aristotle in the latter part is as follows : that ofwhich unity and infinity may be predicated, is in its essence nothing else than one and infinite ; now unity and infinity may be predicated of all, therefore all is nothing else than one and infinite. But farther : one and infinite, or odd and even, is number in general ; conse quently all is number. The following may serve to confirm what is said in 362 PYTHAGOREAN PHILOSOPHY. such , it is also the ground of all numbers, and is therefore named the first one, of whose origin no thing further can be said.' In this respect the Pythagorean theory of numbers is merely an ex pression for “all is from the original one” — from one being, to which they also gave the name of God ; for, in the words of Philolaus, “ God em braces and actuates all, and is but one." Nothing essential is there in that the Pythagoreans deno minated the primary one as number preeminently ; but it did undeniably afford a connecting point whereon much that was essential attached itself. The same thought, which we have here sup posed to form the basis of the Pythagorean doctrine of numbers, occurs again, though differently ex pressed in other formulæ . Thus Philolaus is re the text. Philol, ap. Stob. i. 456. Böckh, n. 2. 8 Ya Hày cptuos .xet suo μεν ίδια είδη, περισσόν και άρτιον, τρίτον δε απ ' αμφοτέρων μιχθέντων αρτιοπέ ρισσον, εν εξ αμφοτέρων τούτων does not mean resulting from, but consisting of, both . For number, i.e. even and odd, are supposed to have their origin from the odd : Arist. ap. Theon. Smyrn. i. 5. p. 30. 8id kal åptionégITTOV καλείσθαι το έν συμφέρεται δε τούτοις και Αρχύτας. Brandis, Hist. d . Gr. Röm. Phil. p. 445, 465, adduces another far less attested interpretation of the άρτιοπέριττον,, which, however, might very well have subsisted alongside of the one already given. 1 Arist. Met. xiii . 6. όπως δε το πρώτον εν συνέστη έχον μέγεθος απορείν εοίκασιν.- όσοι το ένα στοιχείων και αρχήν φασιν είναι των όντων . Cf. ib. xiv. 3. Philol. ap. Jambl. ad Nic. Arithm. p. 109. Böckh, n. 19. êv åpxà névtwv. Brandis, ib. not. 60, thinks that an extended one - as a derivatory — is meant by the above passage of Aristotle : but in that case Aristotle could not say they gave no derivation of them. The addition εκείνοι δ' έχοντα μέγεθος completely refutes this opinion , after Arist. Met. xiii. 6. In this passage , Aristotle, proceeding from the Pythagorean assumption, that sensible things consist of numbers, infers therefrom that they posited their units as ex tended, and not as mathematical , quantities. That the Pythagoreans called the one itself an extended magnitude, is, for reasons hereafter to be adduced, at least doubtful. 2 Phil. de Mundi Opif. p. 24. εντί γάρ, φησίν, ο αγεμών και άρχων απάν TWw Deós, els del dúv. Vid. Böckh, n. 19. DOCTRINES OF THE PYTHAGOREANS. 363 presented as saying, Number is the eternal, self originated bond of the eternal continuance ofmun dane things. Another form of this doctrine, which regarded ten as the essence of number, displays an equally active endeavour to exhibit the same thought. For, inasmuch as the unit was regarded by the Pythagoreans as the ground of multiplicity, but all numbers were , according to the decenary scale, based upon the decade, the decade and the unit consequently were held by them to be symbols of the ground of all things. Of the decade, therefore, they taught that it em braces every number, comprising within itself the nature of all, of the even and the odd, of the moved and the unmoved, of the good and the evil : that the work and the essence of number must be seen in the energy which is contained in the decade ; for it is great, perfecting all, working all, the prin ciple and the director of all life, divine, heavenly, or human. They likewise expressed the essence of number by the tetractys, or quadrate, which, ac cording to them , is the root of the eternally flow ing nature of what they understood by the grand tetractys, whether the sum of the first four num bers, i. e. ten, or the sum of the first four odd and | Jambl. ad Nic. Arithm . p. 11. Syrian. in Arist. Met. fol. 71 b, 85 b. Böckh, n. 17. 2 Theon. Smyrn. Plat. Math. ii. 49. 3 Philol. ap. Stob. Ecl. i . 8. Böckh, n. 18. Dewgeîv dei tà dpya kal tàu έσσίαν τώ αριθμώ κατταν δύναμιν , άτις έντι έν τα δεκάδι μεγάλα γαρ και παν τελής και παντοεργός και θείω και ουρανίω βίω και ανθρωπίνω αρχά και αγεμών.. * According to the famous oath of Pythagoras, the teacher of the tetractys. Carm . Aur. v. 47. Jambl. V. P. 162. ου μα τον αμετέρα γενεά παραδόντα τετρακτύς , παγάν αεννάου φύσεως ρίζωμά τ' έχουσαν.. 364 PYTHAGOREAN PHILOSOPHY. of the first four even, i. e. thirty-six,' is unimport ant ; for the essential is not the symbol, but what the symbol represented. Lastly, they also called the triad the number of the whole, inasmuch as it has beginning, middle, and end. All these dif ferent symbols evidently express the same, -that a unity, which has at the same time within itself multiplicity, is the cause of all things ; and such a unity was equally understood by them under the first one, the decade, the tetractys, and the triad. But in the essence of number, or in the first original one, all other numbers, and consequently the elements of numbers, and the elements of the whole world, and all nature, are contained . The elements of number are the even and the odd : on this account, the first one is the even -odd, which the Pythagoreans, in their occasionally strained mode of symbolising, attempted to prove thus ; that one being added to the even makes odd, and to the odd even.3 The primary elements of nature, or the universe, were arranged by some of the Pytha goreans in a table of opposite notions, which , as given by Aristotle, stands as follows : The limit and the limitless, The odd and the even, The one and the many, The right and the left, The male and the female, The quiescent and the moving, 1 Plut. de Isid, et Os. 76 ; de Anim. Procr. 30 . Arist. de Cælo, i. 1 . 3 Arist. ap. Theon. Smyrn. i. 5. The Pythagoreans, however, took the expressions even -odd and odd - even in yet another sense : vid. Nicom. Inst. Arithm. i . 9, 10. DOCTRINES OF THE PYTHAGOREANS. 365 The right line and the curve , Light and darkness, Good and evil, The square and the oblong .' We must not, however, imagine that all the simple elements which enter into the composition of things were supposed by the Pythagoreans to be contained in this table ; for it is manifest that its limit has been determined by a wholly external cause — the opinion that ten is the perfect number, such being the number of the contrarieties it contains. On this account, it would seem that much has been omitted from the table, which, nevertheless, the very Py thagoreans, who drew it up, elsewhere stated to be of the utmost importance in the exposition of the mundane contraries. But the most remarkable point in the table is, that among the mundane contraries we find that which the Pythagoreans held to be the ground of all contraries — the one, namely, which in the table is opposed to multi plicity, as if not contained therein . This leads us to remark, that the Pythagoreans do not always employ the notion of the one and of the cause in the same sense, but in two very opposite applica 1 Arist. Met. i. 5. έτεροι δε των αυτών τούτων τας αρχάς δέκα λέγουσιν. είναι γάρ κατά συστοιχίαν λεγομένας πέρας και άπειρον, περιττών και άρτιον , εν και πλήθος, δεξιών και αριστερόν, άρρεν και θηλυ, ήρεμούν και κινούμενον, ευθύ και καμπύλον, φώς και σκότος, αγαθών και κακόν , τετράγωνον και ετερόμηκες. That Aristotle did not distinguish the Pythagoreans who composed this table from the others, on account of their whole doctrine, but that by at tributing the table to some only of the Pythagoreans, he merely meant that it was some only of them who had drawn up these contraries in a definite table, is clear from the simple fact, that he does not impute to those who drew it up any peculiar tenet, and that in Eth. Nicom. i. 4, ii. 5, he attri butes to the Pythagoreans indiscriminately the series of contraries.