Zeller, Eduard 1881. A history of Greek philosophy from the earliest period to the time of Socrates: with a general introduction. Vol. 1. Translated from the German with the Author's sanction by S. F. Alleyne. London: Longmans, Green, and Co. [Internet Archive]
A more restricted significance seems first to have been given to it in the time of the Sophists, when it became usual to sook after a wider knowledge by means of more special and adequate [|] instruction than ordinary education and the unmethodical routine of practical life could of themselves afford. By Philosopy was now understood the study of things of the mind, pursued not as an accessory employment and matter of amusement, but exclusively and as a separate vocation. (Zeller 1881: 1-2)
Thus, "the striving after intellectual and, more especially, after scientific culture" (Ueberweg 1889: 2).
Pythagoras indeed, according to a well-known anecdote, had previously assumed the name of philosopher; but the story is in the first place uncertain; and in the second it keeps the indeterminate sense of the word according to which philosophy signified all striving after wisdom. (Zeller 1881: 2, fn1)
"But the most pure and unadulterated character, is that of the man who gives himself to the contemplation of the most beautiful things, and whom it is proper to call a philosopher" (Iamblichus 1818: 28).
Those who maintain that Greek Philosophy originally [|] came from the East, support their opinion partly on the statements of the ancients, and partly on the supposed internal affinity between Greek and Oriental doctrines. The first of these proofs is very unsatisfactory. Later writers, it is true, particularly the adherents of the Neo-Pythagorean and Neo-Platonic Schools, speak much of the wisdom which Thales, Pherecydes ad Pythagoras, Democritus and Plato, owed to the teaching of Egyptian priests, Chaldeans, Magi, and even Brahmans. But this evidence could only be valid if we were assured that it rested on a trustworthy tradition, reaching back to the time of these philosophers themselves. (Zeller 1881: 31-32)
The same question of Oriental influence that Ritter and Ueberweg wrestled with, the latter even having to negate Chinese influence on Pythagoras.
Indeed, when anything, otherwise unknown to us, is related by them Plato, Pythagoras, or any of the ancient philosophers without any reference to authorities, we may take for granted that the story is founded, in the great majority of cases, neither on fact nor on respectable tradition, but at best on some unauthenticated rumour, and still oftener, perhaps, on a misunderstanding, [|] an arbitrary conjecture, a dogmatic presupposition, or even a deliberate invention. (Zeller 1881: 32-33)
Why it's best not to rely on any single source but to collect various instances and trust the judgment of the most prudent commentators.
Thales may have been in Egypt: we have no certain evidence of the fact; but it is not likely that he there learned more than the first rudiments of mathematics. That Pythagoras visited that country, and that his whole philosophy originated thence, was first asserted by Isocrates, in a passage which is more than suspected of being a rhetorical fiction. Herodotus says nothing about his having come to Egypt, and represents him as having derived from the Egyptians only a very few doctrines and customs, and these at third hand. (Zeller 1881: 33)
"The oldest testimonies are nearly two hundred years younger than Pythagoras. [...] Isocrates first mentions his Egyptian travels" (Ritter 1836: 155).
It must have been very astonishing to the followers of Alexander to find among the Brahmans not only their Dionysus and Heracles, but also their Hellenic philosophy; to hear of wtaer being the origin of the world, as with Thales; of Deity permeating all things, as with Heracleitus; of a transmigration of souls, as with Pythagoras and Plato; of five elements, as with Aristotle; of the prohibition of flesh diet, as with Empedocles and the Orphics; and no doubt Herodotus and his successors must have [|] been often inclined to derive Greek doctrines and usages from Egypt. But for us, all this is not sufficient proof that Heracleitus, Plato, Thales and Aristotle borrowed their theorems from the Hindoos or Egyptians. (Zeller 1881: 42-43)
Indeed, quite astonishing parallels.
Several writers mention Pherecydes as the first who taught immortality, or more precisely, transmigration; but the testimony of Cicero and other later authors is not sufficient, in the absence of older evidence, to prove this statement. Even if we admit the probability that Pherecydes spoke of transmigration, the assertion of his having been the first to do so rests only on the fact that no previous writings are known to contain that [|] doctrine. Still more uncertain is the theory that Pythagoras was the first to introduce it. Heracleitus clearly presupposes this; Philolaus expressly appeals to the ancient theologians and soothsayers for the theory that souls were fettered to the body, and as it were buried in it, as a punishment. Plato derives the same theory from the mysteries, and more particularly from the Orphic mysteries; and Pindar teaches that certain favourites of the gods are to be permitted to return to the upper world, and that those who thrice have led a blameless life will be sent to the islands of the blest in the kingdom of Cronos. (Zeller 1881: 69-70)
If would not be surprised if the figure of Pherecydes is so closely connected with Pythagoras in tradition for this sole point of common doctrine. That the islands of the blest are placed in "the kingdom of Cronos" is new information.
Pindar's eschatology follows no fixed type (cf. Preller's Demeter und Persephone, p. 239), while, in many places, he adopts the usual notions about Hades, in Thren. 2 it is said that after the death of the body, the soul, which alone springs from the gods, remains alive; and in two places transmigration is alluded to, viz. in Thren. Fr. 4 (110), quoted by Plato, Meno, 81 B. (Zeller 1881: 70, fn4)
"SOCRATES: They were certain priests and priestesses who have studied so as to be able to give a reasoned account of their ministry; and Pindar also and many another poet of heavinly gifts. As to their words, they are these: mark now, if you judge them to be true. They say that the soul of man is immortal, and at one time comes to an end, which is called dying, and at another is born again, but never perishes. Consequently one ought to live all one's life in the utmost holiness." (Meno 81b, p. 301 in Lamb's translation)
In this last representation, we perceive an alteration in the doctrine; for whereas the return to corporeal life is elsewhere [|] always regarded as a punishment and a means of improvement, in Pindar it appears as a privilege accorded only to the best, giving them an opportunity of earning higher happiness in the islands of the blest, instead of the inferior happiness of Hades. But this use of the doctrine presupposes the doctrine itself, and according to the quotations from Plato and Philolaus, we must assume that Pindar derived it from the Orphic mysteries. It is certainly conceivable that it might still have reached the mysteries through Pythagoreanism, which must early have been connected with the Orphic cult. But the most ancient testimonies, and the Pygoreans themselves, refer it solely to the mysteries; and it is besides very doubtful whether the Pythagorean doctrines could have been prevalent in Thebes, in the time of Pindar, whereas that city is, on the other hand, known to have been an ancient seat of the Bacchic and Orphic religion. Lastly, the doctrine of metempsychosis is ascribed to Pherecydes, and regarded as anterior to Pythagoras, not only by the writers we have quoted, but indirectly by all those who make Pherecydes the teacher of Pythagoras. We have, therefore, every reason to believe that it was taught in the Orphic mysteries prior to the date of Pythagoras. (Zeller 1881: 70-71)
In other words, there is no good reason to suppose that Pythagoras introduced the doctrine of metempsychosis from Egypt - it was already in Greece at the time.
According to Herodotus, iv. 94 sq., the Thracian Getæ believed that the dead came to the god Zalmoxis or Gebeleïzin; and every five years they sent a messenger to this god by means of a special human sacrifice, entrusted with communications to their departed friends. That the theory of transmigration was involved in this cannot be deduced from the statement of the Greeks of the Hellespont, that Zalmoxis was a scholar of Pythagoras, who had taught the belief in immortality to the Thracians. Herodotus says that it was the custom of another Thracian tribe (Her. v. 4) to bewail the newly born, and to praise the dead as happy; because the former are about to encounter the ills of life, while the latter have escaped from them. But this custom proves even less than the other in regard to metempsychosis. (Zeller 1881: 73, fn1)
The story of Zalmoxis turns out to be unreliable, as nearly all things pythagorean do.
However this may be, it appears certain, that among the Greeks the doctrine of transmigration came not from the philosophers to the priests, but from the priests to the philosophers. Meantime it is a question whether its philosophic importance in antiquity was very great. It is found, indeed, with Pythagoras and his school, and Empedocles is in this respect allied with them; a higher life after death is also spoken of by Heracleitus. But none of these philosophers brought the doctrine into such a connection with their scientific theories as to make it an essential constituent of their philosophic system: it stands with them all for a self-dependent dogma side by side with their scientific theory, in which no lacuna would be discoverable if it were removed. A philosophic basis was first given to the belief in immortality by Plato; and it would be hard to maintain that he would not have arrived at it without the assistance of the myths which he employed for its exposition. (Zeller 1881: 74)
Here I think we may be restricted by not having any lengthy philosophical treatises from genuine pythagorean philosophers, whereas we have a whole shelf of books from Plato.
If we consider that fire, wind and water are formed in the atmosphere during tempests, and that the fertilising rain is represented in the mythus of Uranus as the seed of the god of heaven; that Chronos, according to this original import, was not the god of Time in abstracto, but the god of the warm season, of the time of harvest, of the sun-heat (Preller, Griech. Mythol. i. 42 sq.), and, as such, was a god of heaven - that he was so regarded by the Pythagoreans when they identified the vault of heaven with Χρόνος, and called the sea the tears of Chronos (vide infra, Pythagorean system) - if we consider all this, the opinion given above, concerning which even Conrad's (p. 22) and Brandis's adverse judgment (Gesch. der Entw. der Griech. Phil. i. 59) have not shaken me, will appear to have far the most probability in its favour. (Zeller 1881: 91, fn2)
In this light it does indeed make sense that the islands of the blest are placed in "the kingdom of Cronos" (Zeller 1881: 69, above).
It would, therefore, be more connect to speak of three philosophic tendencies instead of two: a realistic, an idealistic, and an intermediate tendency. We have really, however, no right to describe the Italian philosophers as Idealists. For although their first principle is, according to our ideas, incorporeal, the precise discrimination of spiritual from corporeal is with them entirely wanting. Neither the Pythagorean Number, nor the Eleatic One, is a spiritual essence, distinct from the sensible, like the Platonic ideas; on the contrary, these philosophers maintain that sensible things are according to their true essence, numbers; or that they are one invariable substance. Number and Being are the substance of the bodies themselves, - the matter of which the bodies consist, and for this reason they are apprehended sensuously. Conceptions of number and conceptions of magnitude interpenetrate one another with the Pythagoreans; numbers become something extended; and among the Eleatics, even Parmenides describes Being as the substance which fills space. So in the further development of the systems, there is a confusion of spiritual and corporeal. The Pythagoreans declare bodies to be numbers; but virtue, friendship and the soul are also numbers, or numerical proportions; nay, the soul itself is regarded as a corporeal thing. (Zeller 1881: 188)
This is clearly picking up the thread from Uberweg (cf. 1889[1863]: 30-31) and explodes those treatments which describe pythagoreanism as the first idealistic philosophy.
The Pythagoreans say that magnitudes are derived from numbers, and from magnitudes, bodies; but on what this process was based, how it came about that matter was moved and transmuted, that numbers produced something other than themselves, - they make no scientific attempt to explain. What they seek is not so much to explain phenomena from general principles, as to reduce phenomena to their first principles. Their scientific interest is concerned rather with the identical essence of things, the substance of which all things consist, than with the multiplicity of the phenomena and the causes of that multiplicity. (Zeller 1881: 203)
"The principles of numbers, limit and the unlimited, were viewed by the Pythagoreans, according to Aristotle, not as predicates of another substance, but as themselves the substance of things; at the same time things were looked upon as images of these principles immanent in them" (Ueberweg 1889: 46-47).
The Pythagoreans [pp. 306-533]
1. Sources of our knowledge in regard to the Pythagorean philosophy [p. 306-323]
Among all the schools of philosophy known to us, there is none of which the history is so overgrown, we may almost say, so concealed by myths and fictions, and the doctrines of which have been so replaced in the course of tradition by such a mass of later constituents, as that of the Pythagoreans. (Zeller 1881: 306)
An all-too-familiar beginning: the tradition of Pythagoras is overgrown with lore.
The recent literature concerning Pythagoras and his school is given by Ueberweg, Grund. i. 48. Of more comprehensive works, besides the accounts of Greek philosophy in general, and Ritter's Gesch. de Pythag. Phil (1826), we have the second volume of Röth's Gesch. d. Abendlichen Philosophie, which treats at great length (Abth. 1, pp. 261-984, and 2, pp. 48-319) of Pythagoras; and Chaignet's work in two volumes, Pythagore et la Philosophie Pythagorienne. (Zeller 1881: 306, footnote 1)
Ritter and Ueberweg I've now read. Zeller himself dismisses both Röth and Chaignet.
The little that can be quoted respecting them from Xenophanes, Heracleitus, Democritus, Herodotus, Io of Chios, Plato, Isocrates, Anaximander the younger, and Adron of Ephesus, will be noticed in the proper place. (Zeller 1881: 306, fn2)
A quick run-down of the most important secondary sources. In due time I may come to have a clear picture of what each of these contributed to the discourse on Pythagoras and the pythagoreans.
Pythagoras and his school are seldom mentioned by writers anterior to Aristotle, and even from Plato, whose connection with them was [|] so close, we can glean very few historical details respecting them. Aristotle, indeed, bestowed much attention on the Pythagorean doctrine; not only discussing it in the course of his more comprehensive researches, but also treating it in separate treatises: yet when we compare what he says with later expositions, it is found to be very simple and almost meagre. While later authors can expatiate at length upon Pythagoras and his doctrines, he is never mentioned, or at most once or twice, by Aristotle; his philosophic doctrines are passed over in silence, and the Pythagoreans are everywhere spoken of as if the writer were ignorant whether, and how far, their theories were really derived from Pythagoras himself. (Zeller 1881: 306-307)
The further back you go, the quieter it gets. Plato seems to hint at various pythagorean doctrines fairly frequently but it is indeed difficult to call them "historical details". Aristotle's own treatment of pythagoreanism is markedly meagre. Perhaps this indeterminacy as to Pythagoras himself is the reason for the frequent exposition that the pythagoreans attributed their theories to Pythagoras himself.
Even the accounts which we get from the writings of the older Peripatetics and their contemporaries - Theophrastus, Eudemus, Aristoxenus, [|] Dicæarchus, Heracleides, and Eudoxus - are far slighter and more cautious than the subsequent tradition; nevertheless, from them we can see that legend had already taken possession of Pythagoras and his personal history; and that the later Peripatetics had begun to develop the Pythagorean doctrines according to their fancy. (Zeller 1881: 307-308)
On all of these, likewise, I expect to gather much more information from subsequent readings of later works.
These sources (of which it is true we possess only fragments) give us scarcely a single detail which we did not already know through Aristotle. Farther developments of the Pythagorean legend, which relate, however, rather to the history of Pythagoras and his school, than to their doctrines, appear during the third and second senturies, in the statements of Epicurus, Timæus, Neanthes, Hermippus, Hieronymus, Hippobotus, and others. (Zeller 1881: 308)
It would appear that very early on, the life of Pythagoras was much more fascinating than his specific philosophical doctrines.
But it was not until the time of the Neo-Pythagoreans, when Apollonius of Tyana wrote his Life of Pythagoras, when Moderatus compiled a long and detailed work on the Pythagorean Philosophy, when Nicomachus treated the theory of numbers and theology in accordance with the principles of his own school - that the authorities concerning Pythagoras and his doctrines became copious enough to make such expositions as those of Porphyry and Iamblichus possible. (Zeller 1881: 308)
Apollonius' Biography of Pythagoras is no longer extant. Fragments of Moderatus' work are included in Porphyry. As I recommended before to time-travelling bibliophiles - make sure to cop as many different biographies of Pythagoras as possible. Wrestle the ancient hellenes if need be, out of the contents of their libraries. Maybe even set a great library on fire to hide your immense theft of texts (*cough* Alexandria *cough*).
Thus the tradition respecting Pythagoreanism [|] and its founder grows fuller and fuller, the farther removed it is from the date of these phenomena; and more and more scanty, the nearer we approach them. With the range and extent of the accounts, their nature likewise changes. At first many miraculous stories about Pythagoras were in circulation. In course of time his whole history developes into a continuous series of the most extraordinary events. In the older statements, the Pythagorean system bore a simple and primitive character, in harmony with the general tendency of the pre-Socratic philosophy; according to the later representation, it approximates so greatl to the Platonic and Aristotelian doctrines that the Pythagoreans of the Christian period could even maintain that the Philosophers of the Academy and the Lyceum had stolen their so-called discoveries, one and all, from Pythagoras. (Zeller 1881: 308-309)
It is quite possible that nearly all we know about Pythagoras and his school is in some measure an invention of later authors. As to the accusation that Plato and Aristotle plagiarized Pythagoras, Zeller refers to "Porhpry, V. Pyth. 53, probably after Moderatus" (ibid, 309, fn1).
It is clear that precisely the opposite was actually the case, and that the ancient Pythagorean doctrine contained none of the accretions which afterwards made their appearance. This is betrayed by the author when he says that Plato and Aristotle collected all that they could not adopt, and omitted the remainder, called that the whole of the Pythagorean doctrine; and also in the statements of Moderatus (loc. cit. 48) that the number theory with Pythagoras and his disciples had been only symbolical of a higher speculation (cf. Part iii. b, 96 sq., second edition). (Zeller 1881: 309, fn2)
It is certainly a tantalizing idea: that the highest and most productive philosophical authorities cannibalized the pythagorean doctrine, took everything valuable for their own, and left behind beans and talking rivers.
But if the untrustworthy and unhistorical character of these expositions is in the main indisputable, we cannot venture to make use of the statements they contain, even where these statements are not in themselves opposed to historical probability, and to the more ancient and trustworthy authorities; for how can we, in regard to minor particulars, trust the assertion of those who have grossly deceived us in the most important matters? (Zeller 1881: 310)
On this account I'm of the "unscientific" or "unhistorical" mind - these academics wish to exclude everything they can identify as forgery and folly. I would like to take the opposite tack and scrape together the craziest stuff (as probably did Iamblichus).
In all cases therefore the later authorities, subsequent to the appearance of Neo-Pythagoreism, are unsupported by other testimony, their statements may generally be supposed to rest, not on real knowledge or credible tradition, but on dogmatic presuppositions, party interests, uncertain legends, arbitrary inventions, or falsified writings. (Zeller 1881: 310)
Yeah - that's the good stuff. Give me that.
What has just been said in regard to the indirect authorities for the Pythagorean doctrine, equally applies to the so-called direct sources. Later writers, belonging almost without exception to the Neo-Pythagorean and Neo-Platonic period, speak of an extensive Pythagorean literature, the nature and compass of which we may gather not only from the few writings we possess, but far more from the numerous fragments which exist of lost works. (Zeller 1881: 311)
Lost to time, that gluttonous bastard.
A very small fraction, however, of these writings may with any probability be ascribed to the ancient Pythagorean school. Had this school possessed such a mass of written works, it would be hard to understand why the ancient authors should not contain more distinct allusions to them, and especially why Aristotle should be so entirely silent as to Pythagoras' own doctrine, when several of these [|] writings bear his very name. (Zeller 1881: 311-312)
A mystical sect with a several-year-long initiation period... Why indeed would not their books be in general circulation?
Diogenes, viii. 6, mentions three works of Pythagoras: a παιδευτικὀν, a πολιτικὀν, and a φυσικόν. Heracleides Leinbus (about 180 B.C.) besides these speaks of a treatise, περἰ τοῡ ὂλου, and a ίερὀς λόγος, in hexameter. How this last is related to the ίερὀς λόγος, consisting of twenty-four rhapsodies which, according to Suidas, must be attributed to Orpheus, and according to others, was written be Theognetus the Thessalian, or Cercops the Pythagorean, and is probably identical with the Orphic Theogony (Lobeck, Aglaoph. i. 714) cannot be discovered. That the fragments of the Πυθαγόρειος ὕμνος about number [.|.] This ίερὀς λόγος, as appears from the above quotations, is chiefly concerned with the theological and metaphysical import of numbers. In Diod. i. 98 there is mention of a ίερὀς λόγος of Pythagoras, by which we must probably understand the one in verse, and not the prose work which seems to have been later. Besides the above-named writings Heracleides, loc. cit., notices others; περἰ φυχῆς, περι εὐσεβείας, 'Helothales," and "Croton" (these last were dialogues, as it would seem), καἰ ἄλλους; Iamblichus (Theol. Arithm. p. 19) a σύγγραμμα περἰ θεῶν, probably to be distinguished from the ίεροἰ λόγοι; Pliny, Hist. Nat. xxv. 2, 13; xxiv. 17, 156 sq., a book on the influences of plants; Galen, De Remed. Parab. vol. xiv. 567 K, a treatise περἰ σκίλλης; Proclus, in Tim. 141 D, a λόγος πρὀς 'Αβαριν; Tzetzes. Chil. ii. 888 sq. (cf. Harless, in Fabr. Bibl. Gr. i. 786), προγνωστικἀ βιβλί; Malal. 66 D; Cedren. 138 C, a history of the war between the Samians and Cyrus; Porphyry, p. 16, an inscription on the grave of Apollo in Delos. Io of Chios (or more probably Epigenes, to whom Kallimachus attributed the τριαγμοί) asserted that he composed pseudo-Orphic writings (Clemens, loc. cit.; Diog. viii. 8), and that Hippasus had stolen from him a μυστικὀς λόγος, and from Asto, the Crotonian, a whole series of works (Diogenes, viii. 7). A κατάβασις εἰς ἅδου seems to have given rise to the tale of the philosopher's journey to Hades [...] and Iamblichus, V. P. 158, 198, speaks in a general manner of many books embracing the whole of philosophy, which were some of them written by Pythagoras himself, and some under his name. (Zeller 1881: 311-312, fn2)
So many god damn books we cannot read.
For the story of the concealment [|] of these writings (vide infra, note 4), which, according to Iamblichus, was no longer believed, even in the time of Aristotle, cannot be brought forward, more especially if Io had already been acquainted with them (vide preceding note). Röth's groundless statement that Aristotle and the other ancient authorities knew only of the Pythagoreans, the exoterics of the school, and not of the esoteric doctrines taught to the Pythagoreans - (an indispensable and fundamental presupposition of his whole exposition) will be examined infra. (Zeller 1881: 312-313, fn1)
How convenient - they didn't hide their books because Iamblichus didn't believe they did so. Eduard Maximilian Röth's thesis sounds even interesting - no wonder Zeller disparages his Geschichte unserer abendländischen Philosophie. Naturally it has not been translated into English (yet?). A library in München has made a good scan of the book available - so if I ever learn to read German, hold your pipe and classes.
Those consequently who escaped from the persecution wrote summaries of the Pythagorean doctrine for their adherents. But Porphyry himself presupposes that there were ancient Pythagorean writings, and, therefore, adds that the Pythagoreans collected them. (Zeller 1881: 313, fn2)
This sounds like the story I'm familiar. But then again, it might be just a story.
Iamblichus says that Pythagorean writings were in existence, but that until the time of Philolaus they were scrict preserved as secret by the school, but this assertion can have no weight against the evidence we have just cited; it is rather indeed a confirmation of the fact that the later writers themselves could find no authentic traces of the existence of Pythagorean writings previous to Philolaus. (Zeller 1881: 313-314)
Oh, Philolaus sold his pythagorean books? Let me sell mine, then.
To begin with, as regards the tradition concerning the writing of Philolaus, the existence of a work under that name is presupposed by Hermippus (ap. Diog. viii. 85) and Satyrus (ibid. iii. 9) about 200 B.C., for they tell us that Plato bought the work of Philolaus, and copied his Timæus from it. Both speak of this work as well known, and it is difficult to see how, if it did not exist, the statement could have arisen. Besides, Hermippus borrowed the assertion from an older writer. Already about 240 B.C. the book was known to Neanthes, as is shown by the statement of this author in Diog. viii. 55, that up to the time of Philolaus and Empedocles the Pythagoreans admitted everyone to their instructions, but that when Empedocles had made known their doctrines in his poem, they resolved never to impart them to any other poet. (Zeller 1881: 315, fn2)
"Hermippus says that Philolaus wrote a book which Plato bought in order to copy from it his Timaeus; Satyrus speaks of three books" (Ueberweg 1889: 46). "The common statement makes [Empedocles] a Pythagorean; but the authorities on which the assertion rests are in part of a late date, partly fabulous and opposed to all consistent chronology" (Ritter 1836: 489).
It is true that Philolaus is never mentioned by Aristotle, though a word is quoted from him in Eth. Eud. ii. 8, 1225 a, 33; and Plato in the Timæus places his physical theories, not in the mouth of Philolaus, but of a Pythagorean otherwise unknown. But Plato had every reason to do this, supposing there existed a writing of Philolaus which would immediately have exhibited the great difference of his physical doctrines from those of the Pythagoreans. And with regard to Aristotle, though it is impossible that he can have derived his numerous and minute statement about the Pythagorean doctrines merely from oral tradition, yet he never mentions his authorities; just as elsewhere he quotes much from the ancient philosophers [|] without saying whence he gets it. We cannot, therefore, argue from his silence respecting Philolaus, that no work of his was known to him. (Zeller 1881: 315-316, fn2)
Both Plato and Aristotle sucked at proper citations.
On the other hand, if we compare Metaph. i. 5, 986 b, 2 sqq. with the fragment of Philolaus in Stob. Ecl. i. 454 sq. (vide infra, 371. 2); Metaph. xiii. 6, 1080 b, 20; xiv. 3, 1091 a, 13 sq., with Stob. i. 468; Metaph. i. 5, 985, b, 29 sq. with the fragment in Iambl. Theol. Arithm. p. 56, 22 (vide infra, § iii.), it will appear very probable that Aristotle in these passages is referring to the work of Philolaus; and considering the scanty number of the fragments we possess, it is not surprising that further proofs are not forthcoming. (Zeller 1881: 316, fn2)
Quite likely I'll have to find a way to search out these specific passages. Not now, though - this is just an introduction to pythagoreanism, not yet a deep dive.
He [Schaarschmidt] says, for instance (p. 32 sqq.), that the passage in Stob. Ecl. i. 360 contradicts the statement of Aristotle (De Cœlo, ii. 2, 285 a, 10), that the Pythagoreans assumed only a right and a left in the world, and not an above and a below, a before and a behind; but this latter statement is explained by another from the work on the Pythagoreans (Schol. in. Arist. 492 b, 39), which even, were it spurious, we could scarcely assign to a period so recent as the Neo-Pythagorean. The Pythagoreans (we there read) admitted no above and below in the ordinary and proper sense, because they identified the above with the left side of the world, and the below with the right; and at the same time the above with the circumference, and the below with the centre. This last conception seems to be precisely the meaning of the mutilated passage in Stobæus; it resolves the opposition of the above and the below into that of the outward and inward. (Zeller 1881: 317, fn2)
It may very well be that the table of fundamental oppositions Aristotle gives in his Metaphysics is a random selection of his own making, limited to 10 in order to make it believably pythagorean. Such is the hint: "Aristotle seems, rather, at times to be expressing in his own language conceptions which he only found implied in their doctrines" (Ueberweg 1889: 46-47).
Nor can we with Schaarschmidt (p. 65) consider it un-Pythagorean that the ἄπειρον and περαῖνον should be distinguished from the ἄρτιον and περισσόν; for we find the same thing in the table of contraries (Arist. Metaph. i. 5, 986 a, 23). (Zeller 1881: 317, fn2)
At some point I'll have to look up the table in Greek.
First, the Pythagoreans no doubt put numbers in the place of material substances as the ultimate ground of things; but certain Pythagoreans, for example Philolaus, may nevertheless have sought to explain more precisely how things arise from numbers, by reducing the qualitative fundamental difference of bodies to the difference of form in their constituent atoms. Plato does this from a similar standpoint. [|] The Pythagorean doctrine does not assert that there are no bodies, but only that bodies are something derived. (Zeller 1881: 317-318, fn2)
Ritter tried to explain their "determination of extension" (1836: 374-376), but it went far above my head, and still does. This curious role of the number in the formation of corporeal bodies is probably also why Ueberweg places pythagoreanism as an intermediate stage between Palmenides' sensuous (materialist) and Plato's non-sensuous (idealist) positions.
Second, in regard to Empedocles, that philosopher was unquestionably some decades anterior to Philolaus; why then may not his theory of the elements (as I suggested in my second edition, p. 298 sq., 508 sq.) have given rise to the theory of Philolaus? (Zeller 1881: 318, fn2)
Hmm, could Empedocles, who is not considered among the rank of the pythagoreans, be the ground for Philolaus, our most distinctive pythagorean philosopher?
But such a reflection does not seem impossible at a period when the conception of νοῦς had already been discovered by Anaxagoras; more especially as we find Aristotle (Metaph. i. 5, 985 b, 30) naming νοῦς and φυχἠ among the things which were reduced by the Pythagoreans to particular numbers; while, on the other hand, it is deserving of note, that the Platonic and Aristotelian theory of the multiplicity of the parts of the soul which was known to other so-called Pythagoreans (vide Part iii. b, 120, 2nd ed.) is absent from this fragment; the differences which exist between the phenomena of life and those of the soul are here directly connected with the corporeal organs. The same argument tells in favour of the genuineness of most of these fragments. The influence of the Platonic and Aristotelian philosophy, which is so unmistakeable in all pseudo-Pythagorean writings, is not perceptible in them. (Zeller 1881: 318, fn2)
Sadly, here it looks like the exact point that interests me the most (the division of the soul into three) is a platonic/aristotelian addition, the lack of which can be used to identify genuine pythagorean sources.
Opinions are likewise unanimous as to the spuriousness of the treatise on the World-soul, attributed to Timæus of Locris, but obviously an extract from the Tomæus of Plato. (Zeller 1881: 319)
"Timæus Locrus [...] is credited with a work περἰ φυχᾶς κόσμω, which is only an abstract of Plato's Timaeus, of late origin" (Ueberweg 1889: 43).
This judgment is not to be set aside by the fact that Petersen, in order to explain the undeniably Platonic element in the so-called books of Archytas, regards him as having anticipated the Platonic doctrine of Ideas, and Beckmann makes him out in this respect a disciple of Plato; for not a single ancient authority alludes to this pretended Platonism of Archytas. Wher the relation between PLato and Archytas is mentioned, we hear only of a personal relation, or a scientific intercourse which would by no means involve a similarity in philosophic theories. (Zeller 1881: 320)
Perhaps it is the other way around, and there is an Archytanic element in the books of Plato.
On the contrary, where the philosophic [|] opinions of Archytas are spoken of, he is always described as a Pythagorean, and that not only by the more recent writers subsequent to Cicero's time, but even as early as Aristoxenus, whose acquaintance with the later Pythagoreans is beyond question; indeed Archytas clearly calls himself a Pythagorean, in a fragment the authenticity of which can scarcely be disputed. (Zeller 1881: 320-321)
"Aristoxenus, on the other hand, says, Pythagoras recommended beans before all other food" (Ritter 1836: 341, fn1).
If, however, Archytas was a Pythagorean, he cannot have been at the same time an adherent of the doctrine of Ideas; [|] for it is not merely impossible to prove that this doctrine was known to the Pythagoreans, but Aristotle's evidence is most distinctly to the contrary. Since therefore in the fragments of the so-called Archytas we encounter Platonic as well as Peripatetic doctrines and expressions, we must consider these a sure sign of a late origin, and consequently reject by far the greater number of the fragments. (Zeller 1881: 321-322)
The philologists are sometimes kinda nutty. Plato spoke of ideas, hence the fragments Archytas containing the word cannot be authentic.
A contemporary of Archytas, Lysis the Tarentine, has latterly been conjectured by Mullach to be the author of the so-called Golden Poem; but the corrupt passage in Diogenes viii. 6 is no evidence for this, and the work itself is so colourless and disconnected, that it laaks rather like a later collection of practical precepts, some of which had perhaps been long in circulation in a metrical form. (Zeller 1881: 322)
That's one guess for the authorship of the Golden Verses.
In regard to the remaining fragments, with few and unimportant exceptions, those which bear the names of well-known ancient Pythagoreans, such as Theano, Brotinus, Clinias, and Ecphantus, are certainly spurious. Most of them, however, are attributed to men of whom we either know nothing at all, or are ignorant when they lived. But as these fragments precisely resemble the rest in their content and exposition, we cannot doubt that they too claim to be of ancient Pythagorean origin. If they have no such origin, they must be considered deliberate forgeries, and not the genuine productions of a later Pythagoreanism approximating to the Platonic or Peripatetic philosophy. (Zeller 1881: 323)
Too bad. Wikipedia stoked my hopes that Plato may have borrowed some of his key psychological terms from Theano. Perhaps the 150 years spanning betwen Zeller and us, another view has arisen.
II. Pythagoras and the Pythagoreans [p. 324-368]
We know that his father's name was Mnesarchus, [...] Heracleitus, ap. Diog. viii. 6, Herodotus, iv. 95, and most of the other authorities. The name, Marmacus, given to him, according to Diog. viii. 1, by several writers, is perhaps founded merely on a scriptural error. Justin (xx. 4) calls him Demaratus, which is most likely also founded on some confusion or another. (Zeller 1881: 324)
I'm starting to think that the Greek language is not the best written language.
[...] Neathes (instead of which our text of Porphyry, as we have seen, gives Cleanthes) ap. Porph. V. P. 1, makes Mnesarchus a Tyrian, who, account of his services at samos, received the right of citizenship there (Clemens and Theod. loc. cit. say incorrectly that he asserted Pythagoras himself to have been a Tyrian or a Syrian); but the statement is of little consequence, since it may be explained partly by a [|] confusion of Τύριος and Τυῤῤηνὀς, and partly from an attempt to account for the supposed oriental wisdom of the philosopher by his extraction. Probably in reference to this story, Iamblichus, V. P. 7, represents him as having been born during a journey of his parents to Sidon. (Zeller 1881: 324-325, fn2)
Iamblichus inventing something? Unimaginable! /s
The well-known story of Heracleides of Pontus, and of Sosicrates (ap. Cic. Tusc. v. 3, 8; Diog. i. 12; viii. 8; cf. Nicom. Arithm. sub. init.) about Pythagoras' conversation with the tyrant Leo of Phlius, in which he declared himself to be a φιλόσοος, points to a connection with Phlius. (Zeller 1881: 325, fn2)
The "well-known anecdote" (mentioned above).
Röth (p. 287 sq.) combines with this last statement the assertion of Iambl. (V. P. 11, 19) that Pythagoras left Samos at the age of eighteen, received instruction from Pherecydes, Thales, and Anaximander; was 22 years in Egypt, and after its conquest by Cambyses (525 B.C.), 12 more in Babylon; and at the age of 56 again returned to Samos. Consequently he places his birth in 569 B.C.; his return to Samos in 513 B.C.; his arrival in Italy in 510; and his death in 470. But these statements are entirely destitute of evidence. Röth supposes that Iamblichus may have borrowed them from Apollonius (of Tyana), but even if this were true, we must still ask where Apollonius obtained them? There is no mention even of the so-called Crotonian memoirs on which Apollonius (ap. iambl. 252) founds his narrative of the expulsion of the Pythagoreans from Croton. (Zeller 1881: 326, fn1)
The whole story of the expulsion of the pythagoreans rests on a no longer extant biography by Apollonius?
According to Cleanthes (Neanthes), in Porphyry, V. P. 1, Pythagoras was brought as a boy to Tyre by his farther, and there instructed by 'the Chaldæans.' Iambl. V. P. 14, says that when he left Samos on his great travels, he first went to Sidon, and there met with prophets, the descendants of the ancient Mochus (vide supra, p. 48, and infra, chapter on the Atomists, note 2), and other hierophants; that he visited Tyre, Biblus, Carmel, &c., and was initiated into all the mysteries of the country. Porphyry (V. P. 6) is more moderate; he merely states that Pythagoras is said to have gained his arithmetic knowledge from the Phœnicians. (Zeller 1881: 328, fn1)
Young Pythagoras was all over the place.
Many maintain that Pythagoras was taken prisoner by Cambyses in his Egyptian campaign, and was only set at liberty a long time after by Gillus the Crotonian; and that in consequence of this he had the benefit of the instructions of the Persian Magi, especially Zoroaster. (Zeller 1881: 328)
Could this also have influenced his decision to set up his school at Croton?
This statement of Hippolytus, however, is hardly sufficient to prove that Aristoxenus asserted a personal acquaintance between Pythagoras and Zoroaster. He may, perhaps, have observed the similarity of the two doctrines, and hazarded the conjecture that Pythagoras was acquainted with Zoroaster; for there is no certainty at all that Hippolytus himself knew the work of Aristoxenus. What he says about the Zoroastrian doctrines which Pythagoras adopted cannot have been taken as it stands from Aristoxenus, because it presupposes the story about Pythagoras' prohibition of beans to be true, while, as we shall presently find, Aristoxenus expressly contradicts it. (Zeller 1881: 329, fn3)
According to Wikipedia we don't even know when Zoroaster lived: "By any modern standard of historiography, no evidence can place him into a fixed period".
Our most ancient authority for this relationship is Alexander (Polyhistory), who, according to Clemens, Strom. i. 304 B, said in his work on the Pythagorean symbols: Ναζαράτῳ τῷ 'Ασσυρίῳ μαθητεῦσαι τὀν Πυθαγόραν. (Zeller 1881: 329, fn3)
Dang, another one: "None of Alexander's works survive as such: only quotations and paraphrases are to be found, largely in the works of Diogenes Laertius" (Wiki).
The Pythagorean doctrine of Transmigration was found, or supposed to be found (vide supra, p.73, 1), among the Gauls, as every such similarity was thought to be based upon a relation of teacher and taught, either Pythagoras was made a disciple of the Gauls, as by Alexander, or the Druids were made disciples of the Pythagorean philosophy, as by Diodorus and Ammian (vide supra, 73, 1), into which, according to Hippolyt. Refut. hær. i. 2, 9 E; ibid. e. 25, they were regularly initiated by Zalmoxis. Iambl. (151) says also that Pythagoras was instructed by the Celts, and even by the Iberians. (Zeller 1881: 330)
Pythagoras sure got around. The road between Celtic Druids and Indian Brahmins is not a short one.
The first known author who speaks of Pythagoras being in Egypt is Isocrates, Bus. 11: ὂς (Πυθ.) ἀφικόμενος εἰς αῖς Αῖγυπτον καἰ μαθητἠς ἐκεἰνων γενόμενος τήν τ' ἅλλην φιλοσοφίαν πρῶτος εἰς τοὐς ''Ελληνας ἐκόμισε, καἰ τἀ περἰ τἀς θυσίας καἰ τἀς ἁγιστείας τἀς ἐν τοῖς ἱεροῖς ἐπιφανέστερον τῶν ἅλλων ἐσπούδασεν. (Zeller 1881: 331, fn1)
Mentioned by both Ritter and Ueberweg. Man, I hate transcribing ancient Greek. Most times I'm merely guessing (probably wrongly) which way the double diacritics might be pointing. Also, while I'm already bitching, fuck the Greek s. Especially in the Encyclopædia Britannica I'm frequently left guessing if it's an a, o, or s.
Plut. Qu. Conv. viii. 8, 2, 1, makes out that Pythagoras was a long while in Egypt, and adopted the precepts concerning the ίερατικαἰ ἀγιστεῖαι, such as the prohibition of beans and fish. (Zeller 1881: 331, fn1)
Which one is it - did he learn the prohibition of beans from the Magi or from Egypt? Or is Aristoxenus correct and it was more like Pythagoras reached Croton, said fuck 'em all and shovelled beans for every meal?
Antipho (Diog. viii. 3 and Porph. V. P. 7 sq.) relates how Polycrates introduced him to Amasis, and Amasis to the Egyptian priests; and how he thus after many difficulties, which his perseverance at length overcame, gained admittance to the Egyptian mysteries and holy rites. He says also that he learned the Egyptian language. (Zeller 1881: 331, fn1)
A nice story retold in one of the better (and longer) videos about Pythagoras (by Delphic Philosophy channel). Makes one wonder, though, why Pythagoras should thus ungratefully escape from Polycrates' tyranny.
From this author, Clemens, Strom. i. 302 c, and Theodoret, Gr. aff. cur. i. 15, p. 6, no doubt derive their statement that he was circumcised in Egypt. (Zeller 1881: 331, fn1)
Haha, "Pythagoras olnud isegi ümberlõigatud juut" (Tammsaare 1924: 119). Clemens, you cray-cray.
Iamblichus, V. P. 12 sqq. (cf. p. 325, note), gives a circumstantial account of his wonderful voyage from Mount Carmel to Egypt (whither, according to Theol. Arithm. 41, he had fled from the tyranny of Polycrates), and goes on to tell of his 22 years' intercourse with the priests and prophets, in which he learned all that was worth knowing, visited all the temples, gained access to all the misteries, and devoted himself to astronomy, geometry, and religious exercises. (Zeller 1881: 311, fn1)
Iamblichus could just as well have written that then Pythagoras fucked all them hoes, rolled up in all the most pimped out rides, and made stacks on stacks on stacks, bought his momma a house and a candy paint Cadillac and went out like a gangster, middle finger in the air.
The most ancient evidence for this journey, that of Isocrates, is more than a hundred and fifty years later than the event to which it refers, and moreover is contained, not in a historical work, but in a rhetorical oration which itself makes no pretension to historical credibility. (Zeller 1881: 332)
It's like me writing the biography of Eduard Zeller.
The Rhetor Polycrates had written an apology for Busiris. Isocrates shows him how he should have handled his theme. He explains his points of view very candidly, c. 12. The adversary of Busiris, he says, has ascribed wholly incredible things to him, such as the diverting of the Nile from its course, and the devouring of strangers. (Zeller 1881: 332, fn1)
In other words, the story of Pythagoras studying in Egypt originates from a pretty fabulous piece of writing.
Herodotus, it is true, remarks on the analogy of one Pythagorean usage with a custom of the Egyptians; [...] ii. 81. The Egyptian priests wear linen trousers under their woollen garments, in which they were not allowed to enter the temple, or to be buried. (Zeller 1881: 332)
That is indeed an all-too-familiar trope about the pythagoreans. This is also, amongst the present crowd (including Ritter and Ueberweg) the first mention of Pythagoras' notorious trousers.
As to the presence of Pythagoras in Egypt, though there was every opportunity for mentioning it, he [Herodotus] preserves so strict a silence that we can only suppose he know nothing of it. Nor does Aristoxenus seem to have been aware of it. Thus there is an entire dearth of all trustworthy evidence respecting the supposed [|] journeys of Pythagoras in the East; our authorities become more copious as we recede from the philosopher's own time, and more meagre as we approach it; before the beginning of the fourth century they entirely fail. Each later writer has more to tell than his predecessor; and in proportion as the acquaintance of the Greeks with the Oriental civilised nations increases, the extent of the journeys which brought the Samian philosopher to be instructed by them likewise increases. This is the way that legends are formed and not historical tradition. (Zeller 1881: 333-334)
I'm - for the time being - convinced. This explodes Pythagoras' Egyptian studium pretty adequately.
Though it is probable that Herodotus, in the passage just quoted, when speaking of the later philosophers who adopted the doctrine of Transmigration, was especially referring to Pythagoras, he does not necessarily mean that Pythagoras himself acquired it in Egypt. Herodotus names Melampus as having imported the Egyptian Dionysiac cultus into Greeke (vide supra, 71, 4); it would seem, therefore, that Melampus is primarily alluded to among the 'ancients' who introduced the doctrine of Transmigration into the Orphic Dionysiac mysteries. In that case Pythagoras would not have required to go to Egypt, in order to become acquainted with this doctrine. (Zeller 1881: 333, fn2)
"[Melampus] was the introducer of the worship of Dionysus, according to Herodotus, who asserted that his powers as a seer were derived from the Egyptians and that he could understand the language of animals."
There is no English equivalent for the German word Pragmatismus, which may perhaps be explained as the tendency to explain the history of thought by imaginary combinations of fact. - Note by Translater. (Alleyne 1881: 334)
Not the case only a few short years later after Peirce and James employed it to signify a type of philosophy. Pierce's 1878 pragmatic maxim - "Consider the practical effects of the objects of your conception. Then, your conception of those effects is the whole of your conception of the object." - reads quite differently in light of this translator's note.
There is quite enough to account for such a presupposition, even if it were founded on no actual contemporary tradition, in the syncretism of later times, in the false pragmatism which could only explain the similarity of Pythagorean doctrines and usages with those of the East by the theory of personal relations between Pythagoras and the Orientals, and in the tendency to [|] panegyric of the Pythagorean legend which loved to concentrate the wisdom of the whole human race in its hero. The statement that Pythagoras visited Crete and Sparta, partly to become acquainted with the laws of those countries, partly that he might be initiated into the mysteries of the Idæan Zeus, stands on no better foundation. (Zeller 1881: 334-335)
Indeed, Pythagoras was either the wisest man to ever live, who taught or learned from everyone, or an idiot who plagiarized Persian mathematics and was afraid of beans because they make you fart out your soul or something.
Because Pythagoras could scarcely have attained that 'polymathy,' for which he is extolled by Heracleitus (vide infra, p. 336, 4), otherwise than by travels (Chaignet, i. 40; Schuster, Heracl. 372), it does not at all follow that he went to Egypt, or visited non-Hellenic countries. Moreover, Heracleitus rather derives his learning from writings which he studied; it is possible, however, that these may have been collected by him previously on his journeys. (Zeller 1881: 335, fn1)
That he studied writings extensively does not easily show from translations such as that he "practiced inquiry" (Ueberweg 1889: 44), but it is a good indication that Pythagoras was not, like Socrates, illiterate, and may indeed have originated some pieces of writing himself.
The statements of the ancients are probably mere arbitrary conjectures. Most of them assert with Aristoxenus (ap. Porph. 9) that the tyranny of Polycrates occasioned his migration [...] and that this assertion contradicts the uncertain story of Polycrates's commendatory letters to Amasis is no argument against it. But it cannot be considered as proved, since the combination was perfectly obvious. Others (Iambl. 20, 28) say that he emigrated because the Samians had too little taste for philosophy. On the other hand, Iambl. 28 says he did so in order to avoid the political activity, which the admiration of his fellow-citizens would have forced upon him. (Zeller 1881: 336, fn2)
A run-down of the three possible reasons Pythagoras might have left Samos for Croton.
Again, the well-known and often quoted narrative of Zalmoxis presupposes that Pythagoras had already played the same part in his own country that he afterwards played in Magna Græcia. In this story a Gætic divinity takes the form of a man and communicates with Pythagoras. The motive of that fiction evidently is to explain the presumed similarity of the Gætic belief in immortality with the Pythagorean doctrine (vide supra, p. 73, 1); yet the story could never have been invented if the name of the philosopher had been unknown to the Greeks on the Hellespont, from whom Herodotus received it, and if in their opinion his activity had first commenced in Italy. (Zeller 1881: 337)
Put this way, the story of Zalmoxis reads like the angel Gabriel taking human form to have an illuminating conversation with Mohammed.
Whether among his countrymen he found less appreciation than he had hopes for, or whether other reasons, such as the tyranny of Polycrates or the fear of the Persian invasion, had disgusted him with his native city, in any case he left it and took up his abode in Crotona, a city with which he may possibly have had some personal connections, and which may well have commended itself to him on account of the far-famed salubrity of its site and the vigorous activity of its inhabitants. (Zeller 1881: 337)
"To judge from the number of citizens of these states who were crowned in the Olympic games, their [Crotoniats'] wealth and prosperity must have been considerable" (Ritter 1836: 326-327).
But this portion of his life is still so much obscured by fabulous legends that it is hard to discover anything with a historical foundation in the mass of pure invention. If we may believe our informants, even the person of Pythagoras was surrounded with miraculous splendour. A favourite, and even a reputed son, of Apollo, he is said to have been revered by his followers as a superior being, and to have given proof of this his higher nature by prophecies and miracles of all kinds. (Zeller 1881: 338)
"Whenever he appeared, a divine glory shone around him" (Ritter 1836: 330).
According to Ælian, loc. cit. cf. iv. 17, Aristotle had already related that Pythagoras had been simultaneously seen in Crotona and Metapontum, that he had a golden thigh, and had been spoken to by a river god. This statement, however, has such a suspicious sound, that one might be tempted to conjecture an error in the words, κἀκεῖνα δἐ προσεπιλέγει ό τοῦ Νικομάχον, with which Ælian introduces it, and to suppose that Nicomachus, the celebrated Neo-Pythagorean, and not Aristotle, was Ælian's authority; had not Apollon. Mirabil. c. 6, likewise quoted the same thing from Aristotle. It cannot possibly have been Aristotle himself, however, who stated these things. He must have mentioned them merely as Pythagorean legends, and then himself have been taken by later writers as the authority for them. (Zeller 1881: 338-339, fn4)
"That Pythagoras had a golden thigh is the testimony of history. It is asserted by Aristotle, of all possible authorities the highest, by both Porphyry and Jamblichus after Nicomachus, by Herodotus, by Plutarch, Diogenes Laertius, Aelian, Apollonius, etc." (CP 1.88)
[...] Apul, De Magia, 31; Porph. 23 sq.; Iambl. 36, 60 sqq., 142, who unfortunately, however, have not named the 'trustworthy ancient writers' to whom they owe their information; [...] (Zeller 1881: 339, fn4)
Dammit, Porphyry and Iamblichus... What were you thinking?
He alone among mortals understood the harmony of the spheres; and Hermes, whose son he was in a prior state of existence, had allowed him to retain the remembrance of his whole past amidst the various phases [|] of his existence. There is mention even of a descent into Hades. His doctrines are said to have been imparted to him in the name of his divine protector by the mouth of the Delphic priestess Themistoclea. (Zeller 1881: 339-340)
Understood or heard? - "he heard the harmony of the spheres" (Ritter 1836: 330
According to A. Gellius, iv. 11, Clearchus and Dicæarchus, the disciples of Aristotle, asserted that Pythagoras maintained that he had formerly existed as Euphorbus, Pyrander and others; but the verses of Xenophanes, ap. Diog. viii. 36, say nothing of any recollection of a previous state of existence. He is also said to have kept up constant intercourse with the soul of a friend who had died (Herm. in Joseph. Con. Ap. i. 22). (Zeller 1881: 340, fn1)
Even this comes down to us third-hand. Keeping up a constant intercourse with a dead friend is new information for me.
By Hieronymus, no doubt the Peripatetic, ap. Diog. viii. 21, cf. 38; Hermippus, vide Diog. viii. 41, in imitation of the story of Zalmoxis (Herod. iv. 95), puts an insipid natural interpretation upon this legend, about which Tertullian, De An.. c. 28, is unnecessarily angry. Its true origin is probably to be found in a work attributed to Pythagoras, called Κατάβασις εἰς ἅδου. (Zeller 1881: 340, fn2)
I wonder if Tertullian got equally angry at the story of Jesus rising from the dead after three days.
Dicæarchus, ap. Porph. 18; cf. Justin. Hist. xx. 4; speaks of lectures, which, in the first instance, he delivered before the Council of Elders (τὀ τῶν γερόντων ἀοχεῖον), and then by command of the authorities before the youths, and finally the women. A lengthy and declamatory account of the contents of these lectures is given in Jambl. V. P. 37-57, and a modernised paraphrase in Röth, ii. a, 425-450. I do not believe that this enlarged version is taken from Dicæarchus; partly because it seems too poor in content for this philosopher, and partly because Dicæarchus, according to Porphyry, makes Pythagoras appear first before the ruling council, and then before the youths; whereas in Iamblichus he is represented to have made his first [|] appearance in the gymnasium, and then on the report of his lecture there, to have been commanded to speak before the council. It would seem that a later biographer of Pythagoras had added to the statements of Dicæarchus; and it is probable that this was none other than Apollonius; since iamblichus in his V. P. 259 sq. adduces a narrative from him in a similar style, and (as Rohde, Rhein. Mus. xxvii. 29, remarks) Apollonius, ibid. 264, expressly makes mention of the temple of the Muses, to the building of which, according to section 50, these discourses of Pythagoras had given occasion. (Zeller 1881: 340-341, fn4)
The story of different lectures held by Pythagoras is familiar from Iamblichus. That a temple to the Muses was built as a result is news to me.
According to Plutarch, loc. cit., and Pliny, Hist. Nat. xxxiv. 6, 26, a pillar was subsequently, at the time of the Samnite war, erected to him in Rome as the wisest of the Greeks. (Zeller 1881: 341, fn2)
Likewise, complete news to me.
Cf. as to the Pythagorean women, Diog. 41 sq.; Porph. 19 sq.; Iambl. 30, 54. 132, 267, end. As to the most celebrated of them, Theano, who is generally called the wife, but sometimes the daughter of Pythagoras, [...] (Zeller 1881: 341, fn4)
Wikipedia has her as either a wife or student, but not daughter.
The Pythagorean school is represented to us not merely as a scientific association, but also, and principally, as a religious and political society. Entrance into it was only to be obtained by a strict probation, and on condition of several years' silence. (Zeller 1881: 342)
Themes all too familiar. A strict probation = range järelekatsumine. (Given the physiognomical associations, a direct probing of the head?)
Now Zaleucus was certainly a hundred years earlier than Pythagoras, and so probably was Charondas (cf. Hermann, Griech. Antiquit. i. section 89); if, on the other hand, we recognise this Charondas (vide Diodorus, xii. 11; Schol. in Plat. p. 419), as the lawgiver of Thurii (445 B.C.), he would be much too young for a personal disciple of Pythagoras. The appearance of such statements, therefore, in the above-mentioned writers, is a fresh proof how little real historical foundation exists, even for ancient and widely spread accounts of Pythagoras. (Zeller 1881: 342, fn1)
Perhaps someone should remove from the Wikipedia entry for each legislator that they were disciples of Pythagoras?
Some other Pythagorean lawgivers are named in Iambl. 130, 172. The story of Numa's relations with Pythagoras is discussed in vol. iii. b, 692, second edition. (Zeller 1881: 342, fn1)
Heavy emphasis on "story".
The tests themselves, among which that of physiognomy is mentioned (Hippolytus called Pythagoras the discoverer of physiognomy), and the duration of the silent novitiate, is variously given. The countenance of the teachers was hidden from the novices by a curtain, as in the mysteries. (Zeller 1881: 342, fn4)
Put this way, it sounds fairly odd indeed that Pythagoras should first lay hands on newcomers and then separate himself from them with a veil.
The members recognised each other by secret signs; [...] Iambl. 238. The Pentagon is said to have been such a sign (Schol. in Aristoph.; Clouds, 611, i. 249, Dind.; Lucian, De Salut. c. 5). Krische, p. 44, thinks the gnomon also. (Zeller 1881: 342)
I can't even tell what a "gnomon" is, yet. But I am surprised that the prevalent sign was not the tetractys.
[...] only a certain number of them were admitted into the inner circle and initiated into the esoteric doctrines of the school: persons not belonging to the society were kept at a distance, unworthy members were excluded with contumeyl. (Zeller 1881: 343)
Define:contumely - "harsh language or treatment arising from haughtiness and contempt". In other words, unworthy members were cussed out.
Gellius, loc. cit., names three classes of Pythagorean disciples: ἀκουστικοἰ or novices; μαθηματικοἰ, φυσικοί; [...] (Zeller 1881: 343, fn1)
Markedly different from the customary two-fold distinction (acous-/mate- or eso-/exo-).
[...] And Villoison's Anecd. ii. 216-two, the Esoterics and Exoterics; the former were also called Mathematicians, and the latter Acousmaticians; according to Hippolytus and Iamblichus, the Esoterics were called Pythagoreans, and the exoterics Pythagorists. The unknown writer, ap. Phot. Cod. 249, distinguishes Sebasti, Politici, and Mathematici; also Pythagorici, Pythagoreans, and Pythagorists; calling the personal scholars of Pythagoras, Pythagorici; the scholars of these, Pythagoreans; and the ἃλλως ἒξωεν ζηλωταἰ, Pythagorists. (Zeller 1881: 343, fn1)
This transliteration kinda vindicates my own Estonian matemaatikud and akusmaatikud. But the source is surprisingly late, especially for Zeller - Jean-Baptiste-Gaspard d'Ansse de Villoison (1753-1805). By this token it looks like a wholly modern invention. On the other hand, he might very well have been one of Charles Fourier's French sources on pythagoreanism. Iamblichus' terms are familiar: "he called some of them Pythagoreans, but others Pythagorists" (1818: 42). But, now, what the hell is a "Sebasti"?
The members of the inner Pythagorean school (he [Röth] says) were called Pythagorics, and those of the outer circle Pythagoreans; there was an important distinction between their doctrines, all the systems of the Pythagoreans being founded on the Zoroastrian dualism, which (according to p. 421 sq., it was imported into Crotona by the physician Democedes) is not to be found in the conceptions of Pythagoras, which are genuinely Egyptian. These were the Pythagoreans, and these alone (to them belonged Empedocles, Philolaus and Archytas, and Plato and his followers were allied to them), to whom the accounts of Aristotle have reference, and who were generally recognised by the ancients before the period of the Ptolemies. Now all the authors who mention such a distniction call the exoterics Pythagorists, and the esoterics, the true disciples of Pythagoras, Pythagoreans; and the anonymous writer in Photius applies this name only to the second generation. (Zeller 1881: 343, fn1)
Unsurprisingly none of the ancients respected Iamblichus' rather elegant designations. They are all the more suitable because all so-called (by none, other than on the basis of Peirce) koino-pythagoreans, i.e. modern pythagoreans, are exoteric "pythagoreans" rather than esoteric "pythagorics". // Seda eristust on eesti keeles veel rasked järgida: pütaagorlased vs kes? "pütagoristid"?
[...] Apuleius, De Magia, c. 56; Philostr. Apollon. i. 32, 2, who adds to the prescripts of linen clothing aprohibition to cut the hair. Others speak only of white garments, e.g. Ælian, V. H. xii. 32. (Zeller 1881: 344, fn2)
The prohibition against cutting one's hair is news to me.
According to Hermippus and others, ap. Diog. 39 sq., Pythagoras was slain in his flight, because he would not escape over a bean field. Neanthes (ap. Iambl. 189 sqq.) relates the same of Pythagoreans in the time of Dionysius the elder. (Zeller 1881: 344, fn4)
This is the story that makes an appearance in every Youtube video about Pythagoras, especially from younger folk who obviously find it funny and absurd. That it was initially spoken about some random pythagoreans is reported by Iamblichus and even on Wikipedia. But I guess Pythagoras himself refusing to trot on bean plants and dying because of it is just funnier.
Aristoxenus, ap. Athen. x. 418 sq.; Diog. viii. 20; Gell. iv. 11, expressly denies that Pythagoras abstained from meat: he only refused the flesh of ploughing oxen and bucks (the former probably on account of their utility, and the latter on account of their lustfulness). (Zeller 1881: 345, fn5)
I cannot eat these animals... They are too horny! - Pythagoras, probably.
The sacrifice of a bull is ascribed to Pythagoras on the occasion of the discovery of the Pythagorean principle, and other mathematical discoveries (Apollodor. ap. Athenæum, x. 418 sq., and Diog. viii. 12; Cic. N. D. iii. 36, 88; Plut. Qu. Conv. viii. 2, 4, 3; N. P. Suav. v. 11. 4, p. 1094; Procl. in Eucl. 110 u, 426 Fr. Porph. V. P. 36, infers from this the sacrifice of a σταίτινος βοῦς), and he is also said to have introduced meat diet among the athletes: vide infra. (Zeller 1881: 364, fn5)
The sacrifice of "a bull" is very modest - the later anecdote has him sacrificing a hecatomb (a hundred oxen). It is indeed odd that a reputed vegetarian should sacrifice masses of oxen and recommend meat diet to athletes.
In regard to beans, Aristoxenus (ap. Gellius, loc. cit.) maintains that Pythagoras, far from prohibiting them, particularly recommended this vegetable. It is, therefore, probable, that Hippol. Refut. i. 2. p. 12, and Porph. 43 sqq., derived their absurd account (mentioned also by Lucian, Vit. Auct. 6) of the prohibition of beans, not from Aristoxenus, but from Antonius Diogenes, from whom Joh. Lydus, De Mens. iv. 29, p. 76, quotes it in the same words as Porphyry; and though the contradiction of Aristoxenus itself presupposes that such a prohibition was even at that period attributed to Pythagoras, it nevertheless shows that it was not acknowledged by those Pythagoreans whose tradition he followed. Gell. loc. cit. explains the story of the beans as a misunderstanding of a symbolical expression; the most probable explanation is that a custom, which really belonged to the Orphics, was transferred to the ancient Pythagoreans; cf. Krische, p. 35. (Zeller 1881: 364, fn5)
It turns out that the bean story might have resulted from confounding the Pythagoreans with Orphics, who - from what I've seen here - were more in line with the Egpytian mysteries.
According to Nicomachus, Harm. i. 10; Diog. viii. 12; Iambl. 155 sqq. and others (vide infra). Pythagoras himself invented harmony. What is more certain is, that it was first developed in his school, as is shown by the name and the theories of Philolaus and Archytas, on which more hereafter. Plato says in Rep. vii. 530 D, that the Pythagoreans regarded Harmony and Astronomy as two sister sciences. (Zeller 1881: 348, fn1)
How does one invent harmony?
The Harmony of the Pythagoreans presupposes a diligent study of music. The moral application of this art corresponds to the character of the Doric life and of the cultus of Apollo; and we elsewhere find that that cultus was connected with music as a medicinal cure. In accordance with this the Pythagorean music is represented as grave and quiet, and the lyre as their chief instrument. (Zeller 1881: 348, fn2)
Not surprising in the least.
According to Iamblichus, 97, the hours after meals were devoted to politics, and Varro, vide Augustin. De Ord. ii. 20, maintains that Pythagoras only communicated his political doctrines to the ripest of his scholars. (Zeller 1881: 349, fn5)
Let's talk politics after we eat.
Cicero, indeed (De Orat. iii. 15, 56; cf. Tusc. v. 23, 66), includes Pythagoras with Anaxagoras and Democritus among those who renounced political activity in order to live entirely for science; but this does not destroy the former evidence, since in the first place it is uncertain whence Cicero derived his information; and in the second, Pythagoras himself held no public office. Still less does it follow from Plato, Rep. x. 600 C, that the Pythagoreans abstained from political activity; though, according to this passage, their founder himself worked, not as a statesman, but by personal intercourse. The strictly aristocratic character of the Pythagorean politics appears from the charges against them in Iambl. 260; Athen. v. 213 f (cf. Diog. viii. 46; Tertull. Apologet. c. 46), and from the whole persecution by Cylon. (Zeller 1881: 350, fn1)
In politics, Pythagoras was, quite literally, the man behind the curtains.
They no less rigorously maintained the doctrine of their master, and silenced all opposition with the famous dictum αὐτὀς ἄφα. We are told, however, that [|] this doctrine was carefully kept within the limits of the school, and that every transgression of these limits was severely punished. In order that the doctrine might be quite incomprehensible to the unitiated, the Pythagoreans, and in the first instance the founder of the school, are said to have employed that symbolical mode of expression in which are contained most of the maxims handed down to us as Pythagorean. (Zeller 1881: 350-351)
Indeed, why should "autos epha" have any effect on anyone who doesn't know who the "autos" is?
Aristoxenus, Diog. viii. 15, says it was a principle of the Pythagoreans, ηἠ εἶναι πρὀς πύντας πάντα ῤητά, and, according to Iambl. 31, Aristotle reckons the saying about Pythagoras, quoted p. 338, 3, among the πάνυ ἀπόῤῤητα of the school. (Zeller 1881: 351, fn1)
Yeah, this contains wholly two impossible diacritics (einai and reta) that lexilogos.com can't handle. Google Transalte refuses to translate it, and thus here I sit, unaware of how "every transgression of these limits was severely punished".
Further, it seems certain that the Pythagorean society distinguished itself above all other similar associations by its ethical tundency; but we can get no true idea of its ethical aims and institutions from the later untrustworthy authorities. Pythagoras doubtless entertained the design of founding a school of piety and morality, temperance, valour, order, obedience to government and law, fidelity to friends, and generally for the encouragement of all virtues belonging to the Greek, and particularly to the Doric conception of a good and brave man; virtues which are particularly insisted on in the sentences attributed with more or less probability to Pythagoras. For this purpose he appealed first to the religious motives which resulted from the belief in the dominion of the gods, and especially from the doctrine of transmigration; then he had recourse to the educational methods and usages of his native country, such as music and gymnastics. We are assured by the most trustworthy traditions that these two arts were zealously practised in the Pythagorean school. (Zeller 1881: 353)
A very sober estimation.
The division of esoteric and exoteric (if this indeed existed among the ancient Pythagoreans) was purely a religious distinction. It resulted from the traditional distinction between greater and lesser initiations, between complete and preparatory consecrations. [...] In regard to the later conception of the importance of this distinction, I cannot agree with Rohde (Rh. Mus. xxvi. 560 sq.) in explaining it from the supposed fact that after there appeared a Pythagorean philosophy the adherents of this philosophy regarded the original Pythagoreanism, which was limited to religious prescripts and observances, as merely a preparatory stage of the higher knowledge; this seems to me to be an invention of the Neo-Pythagoreans, who thus attempted to represent as the opinions of Pythagoras what they themselves had foisted upon him, and to explain away the entire silence of ancient traditions on the subject. It is only in their writings that these two classes of Pythagoreans are recognised; and it is they who, in the passage discussed p. 309, 2, declare the celebrated propositions of the Pythagoreans to be something exoteric, the true meaning of which can only be discovered by regarding them as symbols of deeper doctrines kept up as a mystery by the school, and lost from general tradition. That the true philosophy of the Pythagoreans should be represented as an occult doctrine, only imparted to a select minority even of the disciples, is quite in harmony with this tendency, which, indeed, is its most obvious explanation. (Zeller 1881: 356)
Some worthwhile background for the interpretation of CP's koino-pythagoreanism as a sort of exoteric extra-neo-pythagorean philosophy (extra-neo in the sense of new new). The point here being, I guess, that the esoteric/exoteric distinction is not particularly important, and is presumably in line with other contemporaneous mystery cults (Bacchic, Orphic, etc.). "That philosophical or even mathematical propositions," continues Zeller, "apart from their possible religious symbolism, should have been held secret, is in the highest degree improbable" (ibid, 356), though sadly on this front he refers to Ritter's German-language Pyth. Phil, p. 52.
The political tendency of the Pythagorean community was fatal to its material existence and to a [|] great part of its members. The democratic movement in opposition to the traditional aristocratic institutions, which in time invaded most of the Greek States, declared itself with remarkable rapidity and energy in the populous and independent Italian colonies, inhabited by a mixed population, excited by ambitious leaders. The Pythagorean συνέδρια formed the centre of the aristocratic party: they therefore became the immediate object of a furious persecution which raged with the utmost violence throughout lower Italy. The meeting houses of the Pythagoreans were everywhere burnt; they themselves murdered or banished, and the aristocratic constitutions overthrown. This continued until at length, through the intervention of the Achæans, an agreement was brought about by which the remainder of the exiles were allowed to return to their homes. (Zeller 1881: 356-357)
A bit more context to the political turbulence that brought about the destruction of the Pythagorean league.
So much we can gather from the detailed accounts presently to be noticed, and also from the statements of Polybius, ii. 32, who says (unfortunately only incidentally, and without any mention of date): [...] On this rests the assertion that the Achæans united Crotona, Sybaris, and Caulonia in a league and convention, and thus introduced their constitution into those cities. (Zeller 1881: 357)
That "the remaineder of the exiles were allowed to return to their homes" (above), which other accounts thus far consulted (Ritter & Ueberweg) leave out, originates from Polybius and might be somewhat dubious. The following pages go on to detail the indeterminacy of Pythagoras' death.
The various accounts are these: 1st, according to Plut. Stoic. Rep. 36, 3, p. 1051; Athenag. Supplic. c. 31; Hippolyt. Refut. i. 2, sub fin.; Arnob, Adv. Gent. i. 40; Schol. in Plat. p. 420, Bekk. and a passage in Tzetz. Chil. xi. 80 sqq., Pythagoras was burned alive by the Crotoniates. Hippolytus adds that Archippus, Lysis, and Zamolxis escaped from the [|] conflagration, and Plutarch's words seem to admit the possibility that he only meant an attempt at burning. 2. Nearest to this comes the account of Diog. viii. 39, that Pythagoras and his people were in the house of Milo when the enemy set fire to it; that he escaped indeed, but was intercepted in his flight, and killed; the greater number of his friends (forty of them) were also put to death: only a few, among whom were Archippus and Lysis, escaped. 3. According to Porph. 57 and Tzetz. loc. cit., others think that Pythagoras himself escaped from the attack in Crotona to Metapontum, his disciples making a bridge through the fire for him with their bodies; and all, except Lysis and Archippus, being destroyed; that he there starved himself to death, being weary of life, as Porphyry says; or died of want, according to Tzetzes. 4. According to Dicæarchus, ap. Porph. 56 sq., and Diog. viii. 40, Pythagoras at the time of the attack on the forty Pythagoreans, was in the town, but not in the house; he fled to the Locrians, and thence to Tarentum, and was rejected by both. Proceeding to Metapontum, he there, after forty days' starvation (ἀσιτήσαντα, says Diogenez; ἐν στάνει τῶν ἀναγκαίων διαμείναντα, says Porphyry; hence, no doubt, Tzetzes' theory), died. [...] 5. According to the mutually complementary accounts of Neanthes, ap. Porph. 55; of Satyrus and Heracleides (Lembus), ap. Diog. viii. 40; and of Nicomachus, ap. Iambl. 251, Pythagoras at the time of Cylon's attack was not in Crotona at all, but in Delos with Pherecydes, to tend in his illness and bury him; when on his return he found that his followers, with the exception of Archippus and Lysis, had been burned in Milo's house or slain, he betook himself to Metapontum, where (according to heracleides, ap. Diogenem) he starved himself to death. 6. According to the account of Aristoxenus (ap. Iambl. 248 sqq.), Cylon, a tyrannical and ambitious man, being angry that Pythagoras had refused him admission into his society, commenced [|] a violent struggle with the philosopher and his followers during the last years of Pythagoras's life. In consequence of this, Pythagoras himself emigrated to Metapontum, where he died; but the struggle continued, and after the Pythagoreans had maintained themselves for some time longer at the head of the states, they were at last attacked at Crotona during a political consultation in the house of Milo, and all, except the two Tarentines, Archippus and Lysis, were destroyed by fire. Archippus retired to his native city, and Lysis to Thebes; the rest of the Pythagoreans, with the exception of Archytas, abandoned Italy and lived together in Rhegium (which, however, is also in Italy), until the school, as the political conditions became worse and worse, gradually died out. [...] 7. The account of Apollonius, ap. iambl. 254 sqq., resembles that of Aristoxenus. According to this, the Pythagorean aristocracy very early excited dissatisfaction; after the destruction of Sybaris and the death of Pythagoras (not merely his departure; ἐπεὶ δὲ ἐτελεύτησεν, it is said, and in connection with ἐτελεύτησεν, the previous ἐπεδήμει and ἀπῆλθε are to be explained), this dissatisfaction was stirred up by Cilon and other members of noble families not belonging to the society, and on the partition of the conquered [|] lands broke out into open hostility. The Pythagoreans were dispersed during one of their assemblies, then defeated in combat, and after ruinous disturbances, the whole Pythagorean party was driven out of three neighbouring cities by the judges, who had been corrupted, and a distribution of lands and remission of debts was decreed. Not till after many years did the Achæans accomplish the return of the exiles, of whom about sixty came back; but even these fell in an unfortunate encounter with the Thurians. 8. Lastly, Hermippus (ap. Diog. viii. 40; cf. Schol. in Plat. loc. cit.), differing from all other accounts, says that Pythagoras was with his friends, fighting at the head of the Agrigentines against the Syracusans, and was killed in flight, while the remainder of the Pythagoreans, to the number of thirty-five, were burned in Tarentum. (Zeller 1881: 357-360, fn2)
Okay, so there are only 8 different accounts of how Pythagoras died. How come none of them appear to involve beans, though?
Apollonius, Mirab. c. 6, makes Pythagoras fly to Metapontum before the attack which he foretold. In Cic. Fin. v. 2, we are told that the dwelling of Pythagoras and the place of his death were shown in Metapontum; in Valer. Max. viii. 7, ext. 2, that the whole city of Metapontum attended the funeral of the philosopher with the deepest reverence; in Aristid. Quint. De Mus. iii. 116 meib. that Pythagoras before his death recommended the use of the monochord to his disciples. These accounts agree best with the present version, as they all presuppose that the philosopher wsa not personally threatened up to the time of his death, and when Plut. Gen. Socr. 13, p. 583, speaks of the expulsion of the Pythagoreans from various cities, and of the burning of their house of assembly in Metapontum, on which occasion only Philolaus and Lysis were saved - though Metapontum is substituted for Crotona, and Philolaus for Archippus - the silence in regard to Pythagoras himself, and the placing of the whole persecution in the period after his death, are both in accordance with the statements of Aristoxenus. (Zeller 1881: 359, fn2)
Not at all surprised that Apollonius would add something miraculous. Zeller seems to be clearly of the opinion that the more believable versions are those in which Pythagoras himself was somewhat removed from the actions, i.e. away tending to Pherecydes. Perhaps his quiet death elsewhere was merely conflated with the attack on the Crotonian school to tie things together with a neat bow. If Jesus of Nazareth had retired to Syria after being accused like Hamdan Qarmat did, we probably wouldn't have Christianity, much like we don't have living pythagoreanism.
The party struggles with the Pythagoreans, thus begun, may have repeated themselves at different times in the cities of Magna Græcia, and the variations in the statements may be partially accounted for as recollections of these different facts. The burning of the assembled Pythagoreans in Crotona and the general assault upon the Pythagorean party most likely did not take place until the middle of the fifth century; and, lastly, Pythagoras may have spent the last portion of his life unmolested in Metapontum. [...] The above suppositions are chiefly based on the following grounds: Firstly, by far the greater number, and the most creditable authorities, maintain that Pythagoras died in Metapontum (cf. Iambl. 248); and even those who place the burning of the house in Crotona in his life-time, for the most part assert that he himself escaped. Although it is clear from the contradictoriness of these latter statements that no universally accepted tradition existed at the time, yet the fact itself that Pythagoras fled to Metapontum [|] must have been pretty firmly established, since the most improbable expedients were resorted to by the authors of these statements to reconcile it with their other theories. Other accounts say that he was put to death in Crotona or Sicily, but this is no doubt an instance of what so often happens in regard to Pythagoras - that facts about his school, or a portion of his school, are transferred to him personally. Secondly, the occasion of Pythagoras's retreat to Metapontum could not have been the incendiary attack on the assembly at Crotona; the attack must have occurred many years after his death. Aristoxenus and Apollonius say this expressly. Aristoxenus, however, is the authority whom we should most expect to reproduce the Pythagorean tradition of his time. (Zeller 1881: 360-361)
Zeller thus explodes the story of Pythagoras dying in the disturbances at Croton. Pythagoras is generally held to have died "c. 495 BC" (Wiki). In contrast, "the Crotonian massacre must be placed about 440 B.C., or even later" (ibid, 361, fn2). That is, there is an approximately half a century between these events.
It matters not that the Pythagorean assembly which was burned is universally placed in the house of Milo, and that the authors of the deed are also called by Aristoxenus Cylonians; for Milo's house may have remained the meeting place of the Pythagoreans after the death of its owner, as Plato's garden was that of the Academy; and 'Cylonians' seems, like Pythagoreans, to have been a party name, which survived the chief from whom it was derived; cf. Aristox. loc. cit. 249. Thirdly. It is nevertheless probable that before the death of Pythagoras, a party adverse to the Pythagoreans was formed by Cylon in Crotona, which party may have been strengthened mainly by the demand for a division of the conquered lands, and by the victorious conflict with the Sybarites; and that this disturbance may have determined Pythagoras to remove to Metapontum. This is admitted by Aristoxenus and Apollonius, though the former makes the burning of Milo's house take place an indefinite time after the death of Pythagoras; and the latter, instead of the burning, relates another incident in the time of Cylon. (Zeller 1881: 362, fn2)
Very curious to see if other accounts contest this interpretation. The "division of the conquered lands" is summarized by Ritter thus: "In the division of the spoil a dispute arose from among the popular party, led on by Cylon" (1836: 345).
Even Aristotle (ap. Diog. ii. 446, cf. viii. 49) incidentally mentions Cylon's enmity against Pythagoras, which had become proverbial. These earlier conflicts, however, cannot have occasioned the overthrow of the Pythagoreans in Lower Italy. This can only have happened (even according to Polybius) when the burning of the council house in Crotona gave the signal for similar acts in other places, and a universal storm broke out against the Pythagoreans. When, therefore, Aristoxenus says that the Pythagoreans kept the lead of public affairs in the cities of Magna Græcia for some time after the first attack upon them, there is every reason for crediting the statement. (Zeller 1881: 362, fn2)
This Aristoxenus of Tarentum indeed seems like the most creditable source: there are fragments extant fragments from 4 of his books concerning pythagoreans: "Life of Pythagoras", "On Pythagoras and his pupils", "On the Pythagorean life", and "Pythagorean maxims/negations".
Fourthly. If the first popular movement against the Pythagoreans was confined to Crotona, and if they finally maintained themselves there, it is not probable that Pythagoras, contrary to the principles of his school, should have starved himself to death, or even have died of hunger. It rather seems as if, even in Aristotle's time, tradition had been silent as to the particular circumstances of his death, and that sThe lacuna was subsequently filled by arbitrary conjectures; [...] (Zeller 1881: 362, fn2)
It is indeed just a bit suspicious that a leader who taught his students to subsist on simple foods and only water, so as to accustom the body to withstand material lack, should starve himself to death.
Vide the expression of Heracleitus, quoted p. 336, 5, and the assertion of Thrasyllus, Glaucus, and Apollodorus, ap. Diog. ix. 38, according to which Democritus was acquainted with Philolaus, that he spoke with admiration of Pythagoras in a treatise called after him, and, in general, had made industrious use of the Pythagorean doctrines. Democritus, however, was certainly younger than Philolaus, and it is doubtful how far Heracleitus had knowledge of Pythagoras as a philosopher. His words seem rather to refer to the founder of the religious association. He charges Pythagoras with κακοτεχνίν; and the συγγραφαὶ, from which he is said to have gained his false wisdom, may either mean Orphic hymns, or the ancient mythological poems, of which Heracleitus generally speaks so slightly; or, at any rate, the writings of Pherecydes and Anaximander. The passage concerning Pythagoras and his universal knowledge pershaps stood in the same connection as the polemic against the ancient poets. (Zeller 1881: 363, fn3)
Diogenes of course knows all. Democritus "highly extolled Pythagoras" (Ritter 1836: 545). The resemblance between his atomism and "the Pythageroan physics" (Ritter 1836: 539) requires further examination. Heracleitus might have been wholly ignorant on the details of Pythagoras' philosophy when he wrote that famous estimation that "his own wisdom was eclectic and nothing better than polymathy and perverted art" (Ueberweg 1889: 44-45), which may indeed signify that Heracleitus thought that Pythagoras perverted "Orphic hymns, or the ancient mythological poems". If "Heraclitus was equally opposed to all objects of popular belief" (Gomperz 1901a: 60), it would make perfect sense that he would deride someone who seemed to have been steeped in Greek religion, even taking it to its extremes.
Of Xenophilus we are told (Plin. Hist. Nat. vii. 50, 168; Valer. Max. viii. 13, 3; Lucian, Macrob. 18) that he attained the age of 105 in perfect health. The two last authorities appeal to Aristoxenus in support of this statement. (Zeller 1881: 365)
Ritter must have thought this unworthy of mention, Ueberweg skims over it with "Xenophilus is reported [...] to have died at an advanced age" (1889: 48). On Wikipedia, on the other hand, it is approximately 1/4 of the information about him: "In the Macrobii of Pseudo-Lucian, Aristoxenus is supposed to have said that Xenophilus lived 105 years. Xenophilus enjoyed considerable fame in the Renaissance, apparently because of Pliny's claim that he lived 105 years without ever being sick."
In the first half of the fourth century, it even attained, in the person of Archytas, to new political importance. We know [|] little, however, with certainly concerning his scientific theories; nor can we determine how far a philosophic impulse was connected with this renewed life of the school. Soon after the period of Archytas the Pythagorean school, even in Italy, seems to have died out, or at any rate, to have been represented only by some isolated followers. Aristoxenus, at least, speaks of it as an entirely extinct phenomenon, and we have no information from other sources as to the longer continuance of the school, although the knowledge of its doctrines was not confined to the sages of Greece. (Zeller 1881: 366-367)
Thus ends the saga of early pythagoreanism.
Besides those Pythagoreans we have spoken of, [|] many others are named in the confused and ill-arranged catalogue of Iamblichus, and elsewhere. But several of these names evidently do not belong to the Pythagoreans at all; others have possibly been introduced by subsequent interpolators; and all are worthless for us, because we know nothing further about the men they designate. There are, however, some few men who are connected with the Pythagorean school, but do not properly belong to it, whom we shall have to notice later on. (Zeller 1881: 367-368)
Thus the neat little niche which Leonid Zhmud has carved out for himself, correcting the various false attributions.
3. The Pythagorean philosophy: its fundamental conceptions: Number and the Elements of Number [p. 368-419]
In order to estimate rightly the philosophy of the Pythagoreans, it is of the highest importance that we should distinguish in their doctrines and institutions that which is philosophical in the narrower sense from that which has arisen from other sources and motives. The Pythagorean constitute primarily not a scientific, but a moral, religious, and political association; and though a definite tendency of philosophic thought was developed in this association at an early period, and probably by its very founder, yet its members were not all philosophers, nor were all the doctrines and opinions [|] which they entertained the result of philosophic enquiry. On the contrary, many of these may have arisen independently of such enquiry, and may have related to objects with which the Pythagorean philosophy never concerned itself. Although, therefore, in considering these doctrines and opinions, we ought not to lose sight of their possible connection with the purely philosophic doctrines, yet we must not reckon all that is Pythagorean as belonging to the Pythagorean Philosophy. (Zeller 1881: 368-369)
Thus the sad affair of Peirce categorizing Pythagoras in his "Study of Great Men" as mere "Moralist & Reformer" (W 5: 37). (Though there is a footnote saying that Pierce wrote a manuscript in which one half was dedicated to the chronology of Plato's dialogues and the other half "concerns the life of Pythagoras" - cf. CP 7.255.)
The most generally distinctive doctrine of the Pythagorean philosophy is contained in the proposition that number is the essence of all things, that everything, in its essence, is number. [...] Aristot. Metaph. i. 5: Ἐν δἐ τούτοις καἰ πρὀ τούτων οί καλούμενοι Πυθαγόρειοι τῶν μαθεμάτων ἁφάμενοι πρῶτοι ταῦτά τε προήγαγον, καὶ ὲντραφέντες ὲν αὺτοῑς τὰς τούτων ὰρχἀς τῶν ὄντων ἀρχὰς ὼήθησαν εἶναι πάντων ἐπεὶ δὲ τούτων αἱ ἀριθμοὶ φύσει πρῶτοι, ἐν δὲ τούτοις ἐδόκουν θεωρεῖν ὁμοιώατα πολλὰ τοῖς οὖσι καὶ γιγνομένοις, μᾶλλον ἢ ἐν πυρὶ καὶ γῇ καὶ ὕδατι, ὄτι τὸ μὲν τοιονδὶ τῶν ἀριθμῶν πάθος δικαιοσύνη, τὸ δὲ τοιονδὶ φυχὴ καὶ νοῦς, ἔτερον δὲ καιρός, καὶ τῶν ἄλλων ὡς εἰπεῖν ἕκαστον ὁρῶντες τὰ πάθη καὶ τοὺς λόγους, ὲπεὶ δὴ τὰ μὲν ἄλλων ὡς εἰπεῖν ἕκαστον ὁμοίως ἔτι δὲ τῶν ἁρμονικῶς ἐν ἀριθμοῖς. Cf. ibid. iii. 5, 1002 a, 8: οἱ μὲν πολλοὶ καὶ οἱ πρότερον τὴν οὐσίαν καὶ τὸ ὂν ᾢοντο τὸ σῶμα εἶναι [...] οἱ δ' ὕστερον καὶ σοφώτεροι τούτων εἶναι δόξαντες ἀριθμούς. Cf. the following note. It seems unnecessary to add to these Aristotelian passages the explanations of later writers, such as Cicero, Acad. ii. 37, 118, Plut. Plac. i. 3, 14, &c. (Zeller 1881: 369)
"At the same time, however, and even earlier [|] the so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principle are the principles of everything. And since numbers are by nature first among these principles, they fancied that they could deterct in numbers, to a greater extent than in fire and earth and water, many analogues of what is and comes into being justice, and such and such soul or mind, another opportunity [...]" (pp. 39-40 in Hugh Tredennick's edition); "This is why the vulgar and the early thinkers supposed that substance and Being are Body, and everything else the madifications of Body; and hence also that the first principles of bodies are the first principles of existing things, whereas later thinkers with a greater reputation for wisdom supposed that substance and Being are numbers." (p. 188 in Tredennick)
On the one side, Aristotle frequently asserts that, according to the Pythagorean theory, things consist of numbers, or of the elements of numbers; that numbers are not merely qualities of a third substance, but immediately, and in themselves, the substance of things; and form the essence of things; yet for that very reason, do not exist apart from things, like the Platonic ideas. He, therefore, in considering the relation of the Pythagorean numbers to his four kinds of causes, places them among the material, as well as the formal causes; for the Pythagoreans, he says, sought in numbers at [|] once the matter and the qualities of things. (Zeller 1881: 370-371)
I'm so done with transcribing ancient Greek - the previous quote has me beat. (Even more so because various presentations of the Greek text present very different versions, with spaces in differenc places, different diacritics, etc. It is horrible to witness!) The only way I can get past this is by just recording where the relevant passages are and then, at some point, compile all the different English translations into something like what I did with the Golden Verses. Substantially, numbers being both "the matter and the qualities of things" is why Ueberweg placed Pythagoreanism between the Ionian sensuous and the Doric non-sensuous (cf. 1889: 30). That is, pythagoreanism occupies as-if a curious intermediate position between idealism and materialism. Or, you know, perhaps Aristotle
With this Philolaus in substance agrees; since he not only describes number as the law of the universe, and that which holds it together, the power that rules over gods and men, the condition of all definition and knowledge, but he calls the Limit and the Unlimited, which [|] are the two constituents of numbers, the things from which all is formed. On the other hand, however, Aristotle likewise says that the Pythagoreans represent things as arising from the imitation of numbers, the manifold similarities of which with things they perceived. In another place he seems to confine the immanence of numbers in things to one portion of the Pythagorean school; and in later accounts the statement that all things consist of numbers, is opposed by the assertion that things are formed, not out of numbers, but after the pattern of numbers. (Zeller 1881: 371-372)
That number is "the power rules over gods and men" is echoed in the Golden Verses: "you will come to know the essence of immortal gods and mortal men" or "Thou wilt know the constitution of the Immortal Gods and of men". I'll note that footnotes on these pages quote Philolaus in Greek. But since Google Translate can't make heads or tails of Ancient Greek, it seems, I'll just note that they're there.
In the commencement of the fragment the words αὐτἀ μὲν ά φύσις are not very good sense, and even Meineke's amendment, μόνα ἁ φύσις, does not satisfy me. I would sooner (as already observed in Hermes, x. 188) discard the μὲν as a repetition of the words before ἐστώ, but it would be better still to read ἀίδιος ἔσσα καὶ ἀεὶ ἐσομένα φύσις: the essence of things, as a nature which is eternal and which will always exist, is divine. (Zeller 1881: 372, fn1)
Likewise, more or less reflected in the Golden Verses: the tetractys or "the Mystick FOUR" is the "fountain and root of the Eternal Nature".
The pseudo-Pythagoras is represented [|] as saying the same thing in the ἱερὸς λόγος, vide Iambl. in Nicom. Arithm. p. 11, and Syrian in Metaph. (Schol. in Ar. 902 a, 24), when he describes number as the ruler of forms and ideas, the standard and the artistic faculty by which the Deity created the world, the primitive thought of the Deity. (Zeller 1881: 372-373, fn4)
In other words God or Demiurgos created the universe based on mathematical principles - the essence of numbers, Limited and Unlimited. One instance in Zeller, that I either forgot to mark down or imagined, is that the the other oppositions in that table may be variations on the limited and unlimited.
We are [|] also informed that the Pythagoreans distinguished between numbers and the things numbered, and especially numbers and the things numbered, and especially between Unity and the One. From this it has been inferred that they developed their doctrine of numbers in different directions; one division of the school holding numbers to be the inherent ground of things, and another seeing in them merely prototypes. (Zeller 1881: 372-373)
My immediate philistine-Kantian reading of this would be that this pythagorean "One" stands for the kantian "Unity" and this pythagorean "Unity" for the kantian "Totality". The difference between numbers being the inherent ground of things and their prototypes eludes me at the moment.
Because the Pythagoreans discovered many similarities between numbers and things, he says (Metaph. i. 5; xiv. 3) they held the elements of numbers to be the elements of things; they perceived in number (he adds in the same chapter) both the matter and the qualities of things; and in the same place that he ascribes to them the doctrine of the imitation of things by numbers, Metaph. i. 6, he asserts that they differed from Plato in considering numbers, not as Plato did the ideas as separate from things, but as the things themselves. From this it is evident that the two statements 'numbers are the substance of things,' and 'numbers are the prototypes of things,' do not, in Aristotle's opinion, exclude one another; the Pythagoreans, according to his [|] representation, considered things to be the copies of numbers, for the very reason that numbers are the essence of which things consist, and the properties of which must therefore be cognisable in them. Philolaus places number in the same relation to things when he describes it (loc. cit.) as their law and the cause of their properties and relations; for there is the same relation between law and its fulfilment as between prototype and copy. Later writers, indeed, conceive the Pythagorean numbers entirely after the manner of the Platonic ideas - as models external to things. (Zeller 1881: 374-375)
The distinction from Platonic ideas is significant enough - Zeller himself says that we need to distiguish "the Pythagorean doctrines from those of the Platonists and Neo-Pythagoreans" (ibid, 375). The materiality of numbers is already a familiar theme - and why the pythagoreans are not strictly idealistic/materialistic but somewhere inbetween (having an "intermediate" position). Zeller points out three different aspects here: (1) numers are the law of things - the prototype/copy relation; (2) numbers are the cause of the properties of things - by which we may perhaps understand magnitudes or measure ("qualitative"); and (3) numbers are the cause of the relations of things - by which we mean "number" in as in amount ("quantitative"). What to do with these interpretations, I do not yet know - but in time some glimmer of insight may arise from this variety attached to the "All is number" question.
The meaning of the Pythagorean fundamental doctrine then is this: - All is number, i.e., all consist of numbers; number is not merely the form by which the constitution of things is determined, but also the [|] substance and the matter of which they consist. It is one of the essential peculiarities of the Pythagorean standpoint that the distinction of form and matter is not as yet recognised. We regard numbers only as an expression for the relation of substances, they directly seek in them the essence and substance of the real. The Pythagoreans (as we are told by Aristotle, and also by Philolaus), were doubtless led to this theory by perceiving that all phenomena are ordered according to numbers; that especially the relations of the heavenly bodies, and of tones, and, generally speaking, all mathematical conceptions, are governed by certain numbers and numerical proportions. (Zeller 1881: 375-376)
The most significant part here is that the pythagoreans did not distinguish form and matter: it is not only the case that things can be measured (determininng their relations externally) but things are as if internally constituted by numbers or the essence of numbers (limited/unlimited). My feeling that Pythagorean physics is almost like that of modern computer game designers with their polygons (cf. remark on Ritter 1836: 374-376) is by no means novel. Evidently, Nietzsche, in his lectures on pre-socratic philosophy, concerning the pythagoreans, spoke of the "Eternal Computer".
This observations is itself connected with the ancient use of symbolic round numbers, and with the belief in the occult power and significance of particular numbers, which belief was current among the Greeks as among other nations, and probably existed from the very commencement in the Pythagorean mysteries. (Zeller 1881: 376)
Indeed, regardless whether Pythagoras actually travelled to Egypt and was held captive at Persia, or communicated with the ancient Indian mathematicians, as Peirce still held (it was a timely view, what with Schroeder's Pythagoras und die Inder, 1884) - in any case this numerical symbolism does feel as if it could have been the stuff of Egyptian priests and Persian magi.
In proof of this we need only call to mind the importance of the number seven (so celebrated among the Pythagoreans), especially in the cult of Apollo (vide Preller, Myth. i. 1550; the many triple orders in the Mythology - Hesiod's exact prescriptions concerning lucky and unlucky days of the year (Έρ. καὶ ἡμ., 763 sqq.); Homer's preference for certain numbers, and the like, mentioned in Ps. Plut. V. Hom. 145. (Zeller 1881: 376)
Somewhat surprising, because the pythagorean number that has kept me up at night with how much obscure sense it makes is number 5 (physical body, health, life in general - propagation, union of male and female - 2+3, and the pythagoreans using the pentagram as a sign of recognition, rather than the holy tetractys). A quick google search gives the answer from Wikipedia: "The number seven was considered to be particularly interesting because it consisted of the union of the physical (number 4) with the spiritual (number 3). In Pythagorean numerology the number 7 means spirituality." - thus my bafflement, that in Ritter's interpretation of Philolaus, 7 stands for animals, basically, but not only; evidently the crucial thing there is that animals have a soul. There are layers to this numerical symbolism.
All numbers are divided into odd and even, to which, as a third class, the even-odd (ἀρτιοπέρισσον) is added, and every given number can be resolved either into odd or even elements. [...] Philol. Fr. 2. ap. Stob. i. 456, &c. ὃ γα μὰν ἀριθμὸς ἔχει δύο μὲν ἴδια εἴδη, περισσὸν καὶ ἄρτιον, τρίτον δὲ ἀπ' ἀμφοτέρων μιχθέτων ἀρτιοπέϲιννοτ. ἑκατέρω δὲ τῶ εἴδεος πολλαὶ μορφαί. By the ἀρτιοπέρισσον we must understand either the One, which was so called by the Pythagoreans (vide infra, p. 379, 1), but which we should scarcely expect to be described as a separate species; or those even numbers, which, when divided by two, give an uneven results. (Zeller 1881: 377)
The latter case being... irrational numbers? Or... like 6 ÷ 2 = 3?
Among numbers, of which Philolaus is chiefly thinking, those which result from uneven factors only belong to the first [|] class; those which result from even and uneven factors, to the second; those which result from even factors only, to the third. (Zeller 1881: 377-378, fn2)
What does this mean?
These words were explained by the Greek commentators (Alex. ap. Simpl. 105 b; Schol. 362 a, 30 sqq. and Simplicius himself; Themist. loc. cit. Philop. K. 13) unanimously as follows: A gnomon is a number which, being added to a square, gives another square; and as this is a property of all uneven numbers (for 12 + 3 = 22, 22 + 5 = 32, 32 + 7 = 42 and so on) such numbers (as Simpl. 105 a, Philop. K. 13, expressly assert) were called by the Pythagoreans γνώμονες. By the addition of odd numbers to one, we get only square numbers (1 + 3 = 22; 1 + 3 + 5 = 32 and so on), and therefore numbers of one kind; whereas in any other way - whether by adding together odd and even numbers (so Philop. says), or by adding even numbers only to the one (so say Alexander, Simplicius, and Themist.), we obtain numbers of the most different sorts, έτερομήκεις, τρίγωνοι, έπτάγωνοι, &c., and consequently an unlimited plurality of εἔδη. (Zeller 1881: 378, fn1)
Ritter is infinitely more simplistic on this: "one being added to the even makes odd, and to the odd even" (1836: 364). The meaning of "gnomon" seems to be more ancient than the one given by google (something to do with the sun-dial). Either Ritter or Ueberweg mentioned the mystery of the gnomon being a part of pythagorean initiation, but I cannot find the exact passage.
From this the [|] Pythagoreans concluded that the odd and the even are the universal constituents of numbers, and furthermore, of things. They identified the uneven with the limited, and the even with the unlimited, because the uneven sets a limit to bi-partition, and the even does not. Thus they arrived at the proposition that [|] all consists of the Limited and the Unlimited. (Zeller 1881: 377-379)
In support of the thesis that all the rest in the table of oppositions are really based on this one.
There is, in fact, no difference between these various appellations; they are all intended to denote the idea of Limitation, which, however, as a rule, is apprehended, after the manner of the ancients, as concrete, and might be expressed either actively or passively, either as Limiting or Limited, for that which limits another by its admixture with it must in itself be something Limited (cf. Plato, Tim. 35 A, where the indivisible substance as such is the binding and limiting principle). (Zeller 1881: 379, fn1)
Timaeus 35a concerns the intermixture of body and soul.
These characteristics they tried to reduce to the fundamental opposition of the limited and the unlimited, odd and even. The limited and the uneven was held, however, by the Pythagoreans, in agreement with the popular belief, as the better and more perfect, the unlimited and the even as the imperfect. Wherever, therefore, they perceived opposite qualities, they regarded the better as limited or uneven, and the worse as unlimited and even. Thus, according to them, all things were divided into two categories, of which one was on the side of the limited, and the other on that of the unlimited. (Zeller 1881: 380)
Thus, the right side, masculinity, rest, straightness, light, goodness, and squareness are all, in some sense, limited and uneven, as opposed to the left side, femininity, motion, being bent, darkness, badness, and oblogness are somehow unlimited and even.
The number of these categories was then more precisely fixed by the sacred number ten, [|] and the ten fundamental oppositions were as follows: - 1. Limited and Unlimited; 2. Odd and Even; 3. One and Many; 4. Right and Left; 5. Masculine and Feminine; 6. Rest and Motion; 7. Straight and Crooked; 8. Light and Darkness; 9. Good and Evil; 10. Square and Oblong. It is true that this classification belongs only to a portion of the Pythagoreans, who were probably later members of the school; but [|] it is universally admitted both by earlier and later Pythagoreans that things are compounded out of opposing elements; and ultimately, out of the odd and the even, or the limited and the unlimited; and therefore they must all have reduced the given phenomena to these and similar opposites. (Zeller 1881: 380-382)
How certain the number of these oppositions is we can never know, having only Aristotle's report to consult? It looks here like the only certainty here is that the pythagoreans did indeed put a premium on a third being compounded of two opposing elements.
Arist. Metaph. i. 5, 986a, 22 (directly after the quotation on p. 379, 1): ἕτεροι δὲ τῶν αὐτῶν τούτων τὰς ἀρχὰς δέκα λέγουσιν εἶναι τὰς κατὰ συστοιχίαν (in two series directly opposed to one another, the Good and the Evil) λεγομένας, πέρας καὶ ἅπειρον, περιττὸν καὶ ἄρτιον, ἒν καὶ πλῆθος, δεξιὸν καὶ ἀριστερὸν, ἄῤῤεν καὶ θῆλυ, ἠρεμοῦν καὶ κινούμενον, εὐθὺ καὶ καμπύλον, φῶς καὶ σκότος, ἀγαθὸν καὶ κακὸν, τετράγωνον καὶ ἐτερόμηκες. (Zeller 1881: 381, fn1)
"Others of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong" (Perseus).
There is all the less reason to contest the assertion of Eudemus (with Chaignet, v. 146), since, according to Alcmæon, the gods and the stars are always moving (vide infra), and the soul, too, is in constant motion. The ceaselessness of this motion, the fact that, as Alcmæon says, it connects the beginning with the end, might be considered a perfection, even though motion itself were an imperfection; it shows that the heavenly bodies themselves consist of the Limiting and Unlimited. (Zeller 1881: 381, fn1)
An interesting contradiction.
[...] granting that the slight difference to be found in the enumeration in Plutarch (De Is. c. 48) is to be regarded as unimportant, and that the septuable table of Eudorus (ap. Simpl. Phys. 39 a; vide infra, p. 388, 1) as well as the triple table, Diog. viii. 26, prove little, because these writers evidently mix up later doctrines; granting that, for the same reason, we cannot attach much weight to the text of Ps. Alex. in Metaph. xii. 6, 668, 16; and lastly, that the different arrangements of the several members in Simpl. Phys. 98 a, and Themist. Phys. 30 b, 216, is immaterial to the present question; yet it lies in the nature of things that even those who had not the decuple table, must have applied and developed the doctrine of opposites; not, indeed, according to that fixed scheme, but in a freer manner. (Zeller 1881: 382, fn1)
Thus, there are other tables but they are later and mixed up with other schools of thought.
The drawing up of a [|] table of such opposites was nothing more than a formal development; for the comprehension of the fundamental doctrines of Pythagoreanism this table is of the less importance, since in it the separate numbers are not the result of any deduction according to a definite principle, but out of all the opposites that are given to us empirically, certain of the most prominent, chosen in a somewhat arbitrary manner, are enumerated, until the number ten is complete, so also the apportionment of the particular concepts to the several series is is to a great extent arbitrary, although generally speaking we cannot mistake the leading point of view, which consists in an attempt to assign the uniform, the perfect, the self-completed, to the Limited; and the opposite categories of these, to the Unlimited. (Zeller 1881: 382-383)
That the positions of the oppositions in Aristotle's table should bear some significance on the numerical symbolism is indeed difficult to gras. It would mean that (1) the point/dot/monad has something to do with the limit and the unlimited; (2) the line with odd and even; (3) surface/triangle with unity and plurality; (4) cube/geometrical body with right and left; (5) health, life or propagation with male and female [checkmark here]; (6) plants with rest and motion [also check]; (7) animals/soul with straightness and crookedness; (8) man with light and dark [which maybe has some connection with virtue?]; (9) daemons with good and evil [check?]; and (10) perfection/God/wisdom with squareness and oblongness.
It is said that Pythagoras designated odd numbers, and especially the Monad, as male; and even numbers, especially the Dyad, as female, vide Ps. Plut. V. Hom. 145; Hippol. Refut. vi. 23, i. 2, p. 10; Alex. ad. Metaph. i. 5, 29, 13; Bon. Schol. 540 b, 15; Philop. Phys. K. ii. cf. Sext. Matt. v. 8. (Zeller 1881: 383, fn1)
For some time I've had trouble remembering which was male and which was female - 2 or 3. That is no longer an issue. Consider, too, that "the number two was with them the symbol of opinion" (Ritter 1836: 400) - Women be opinionated, amiright guys? Guys? You have no opinion. Oh, okay then.
But, as with the Pythagoreans, the perception of the inherent contradictions in things primarily connects itself with the idea of number, so the recognition of the harmony which reconciles these contradictions is connected with the idea of musical relations; harmony as conceived by [|] them is nothing else than the octave, the relations of which therefore Philolaus proceeds at once to expound, when he wishes to describe the essential nature of harmony. Strange as this may seem to us, it was natural enough to those who were not as yet accustomed to distinguish definitely general concepts from the particular phenomena, through which they arrived at the perception of these concepts. (Zeller 1881: 384-386)
I.e. the ordeal with 220, 440, and 880 Hz.
Böckh. Philol. 65. has rather a different interpretation of this. He says: 'Unity is the Limit, but the Unlimited is indefinite Duality, which becomes definite Duality since twice the measure ofUnity is included in it; Limitation is, therefore, given through the determination of Duality by means of Unity; that is, by fixing the proportion, 1 : 2, which is the mathematical proportion of the Octave. The Octave is, therefore, Harmony itself, through which the opposite primitive causes were united.' What prevents me from adopting this ingenious view is my inability absolutely to identify the Limit and Unlimited with Unity and DUality. (Zeller 1881: 385, fn3)
This does sound awfully plausible, at least more so than Ritter's vacuum-interpretation. Yet, understandably, taking One/Many as Unity/Duality may be a bit of a stretch.
Many of our authorities, however, represent the matter indifferently. They assert that the entire system was founded on the opposition of unity and duality, which is then reduced to the opposition of spiritual and corporeal, of form and substance, of the Deity and matter, and is itself derived from the Deity as the original Unity. According to another theory, the starting point of the system was not the arithmetical conception of number and its constituents, but the geometrical conception of the limits of space and of unlimited space. A third opinion bases the system not on the consideration of number, but on the distinction of the limited and unlimited. (Zeller 1881: 386)
The first sounds like neoplatonism, the second like kantianism (or the stuff of William Hamilton).
The first of the above-mentioned theories is found [|] soon after the commencement of the first century before Christ in Alexander Polyhistor. The Pythagoreans, he tells us, appealing to statements of the Pythagoreans, regarded Unity as the beginning of all things; from Unity arose indefinite Duality, which was related to Unity as matter to the efficient cause; from Unity and Duality sprang numbers, and from numbers, points, &c. This view is developed in the extensive excerpts in Sextus from a Pythagorean work. According to it, the Pythagoreans, in a full discussion of the subject, maintained that the causes of sensible phenomena can lie neither in what is sensibly perceptible, nor in anything corporeal, nor even in mathematical figures, but only in Unity and indeterminate Duality, and that all logical categories are in the end reducible to these two principles. They, therefore, regarded Unity as efficient cause, and Duality as passive matter, and supposed not merely numbers, but also figures, bodies, elements, and the world itself, to originate from the co-operation of the two principles. (Zeller 1881: 386-387)
Somewhat new stuff, as Ritter and Ueberweg breathe nothing on Duality.
In the same sense the mythical Zaratas, the instructor of Pythagoras, ap. Plut. Procr. An. 2, 2, p. 1012, called the One the father, and indeterminate Duality the mother of numbers, cf. p. 389, 3. (Zeller 1881: 387, fn1)
Makes sense as far as odd numbers are masculine, and even numbers feminine. This evidently may originate from the principles of numbers (Unity and Duality) being likewise gendered.
The Pythagoreans, says Eudorus, reduced all things ultimately to the One, by which they understood nothing else than the highest Deity; they derived from this two principles, the One and indefinite Duality, God and matter; under the former they classed everything thta is good, under the latter everything evil. Consequently they used various names to designate these principles. The One they called the uneven, the masculine, the ordered. That which is opposed to unity they called the even, the feminine, the unordered, &c. Inasmuch, however, as this second element is derived from the One, the One alone is to be regarded as first principle in the true sense of the word. (Zeller 1881: 388)
Thus begins the long line of philosophies which decry matter as evil - e.g. Proclus.
In agreement with this, we read in the Plutarchic Placita that of the two principles of Pythagoras, Unity denoted the good, reason, or deity; and indefinite Duality, evil, matter, and the dæmons. Of these two writers, the former only is at the pains to tell us that the doctrines he ascribes to the Pythagoreans were not stated by them in so many words, but are merely hinted at in their number-theory. Other writers of later times express themselves to the same effect. (Zeller 1881: 389)
Confirmed: women are demons.
Most of the Pythagoreans call the cause of all things the Monad and the Dyad; [|] Pythagoras himself in the ἱερὸς λόγος calls it Proteus (from πρῶτος) and the Dyad or Chaos. Other Pseudo-Pythagorean fragments, of which the contents are similar, are given in Part iii. b, 99, second edition. (Zeller 1881: 389-390, fn3)
"In Greek mythology, Proteus is an early prophetic sea-god or god of rivers and oceanic bodies of water, one of several deities whom Homer calls the "Old Man of the Sea" (halios gerôn)."
The pseudo-Archytas differs only from this interpretation in making the distinction more prominent between the primitive essence and the two derived principles, and in apprehending the latter not in the Pythagorean, but in the Aristotelian form. He indicates as the most universal principles, form and matter; form corresponds to the regulated and determinate, and matter to the unregulated and indeterminate; form is a beneficent, and matter a destructive nature; but he discriminates both from the Deity, which, standing above them, moves matter towards form, and moulds it artistically. (Zeller 1881: 390)
Reminiscent of Peirce's triad of Matter, Mind, and God - here Matter, Form, and Deity.
It [|] is affirmed in more than one place that the Pythagoreans exalted the Deity above the opposition of principles, and derived the principles from Deity. Unity and Deity, and antecedent to this opposition, was called the One. Unity as opposed to duality, and as a member of the opposition, was called the Monad. (Zeller 1881: 390-391)
Hence the difficulty with identifying Unity with One, noted somewhere above.
The expositions, too, which Sextus and Alexander Polyhistor have followed, bear unmistakeable marks of the eclecticism which after the second half of the second century before Christ began to blend the philosophical systems together, and to confuse the ancient with the recent. For these reasons the testimonies [|] in question are valueless; and neither the doctrine of Unity and indefinite Duality, nor the identification of the primal Unity with Deity, and all that depends upon it, can any longer be attributed to the ancient Pythagoreans. (Zeller 1881: 393-394)
Quite possibly why Ritter and Ueberweg are mum on this indeterminate Duality.
Among the later Pythagoreans whose tendencies were Platonic, Unity and Duality, as we see from what has been quoted above, play an important part; but among the earlier philosophers, Plato is the first who can be proved to have employed them, and the Aristotelian [|] passages which might seem to ascribe them to the Pythagoreans, and which were constantly explained in this sense by the ancient commentators, relate entirely to Plato and the Academy. (Zeller 1881: 394-395)
Thus the Unity/Duality ordeal might not be pythagorean at all.
Aristotle and Philolaus always cite the odd and the even, or the limited and the unlimited, and these alone as elements of number. Even where Aristotle speaks of numbers being produced from the One, he understands by the One only the number one and never adds to it duality, which he could not possibly have omitted if the One were incapable of producing number except in combination with duality; lastly, many authorities expressly deny that the Pythagoreans held the theory of Unity and Duality. (Zeller 1881: 396)
Limit/Illimitation and Odd/Even being the first rows in the table, this makes me wonder if they do not somehow act in concert to produce numbers.
Aristotle on the contrary emphatically declares that Anaxagoras was the first philosopher who discriminated spirit from matter, and he on this account includes the Pythagoreans among those who recognised only sensible existence. (Zeller 1881: 397)
Cue the folly of calling Pythagoras the first idealist philosopher, as the Lexikon der Antike did (cf. Estonian translation).
The Deity, it is thought by some, was distinguished by the Pythagoreans as absolute unity, from unity conceived as in opposition, or from the limit; consequently, it was also distinguished from the world, and exalted above the whole sphere of opposites. Others say that the first one, [|] or the limited, was at the same time apprehended as Deity. This, however, is asserted only by Neo-Pythagorean and Neo-Platonic authorities, and in fragments of interpolated writings emanating from the same circle. Aristotle, in the various passages where [|] he expounds the Pythagorean theory of the ultimate reasons of things, never says a word about their doctrine of God. (Zeller 1881: 398-400)
And now even the pythagorean monotheism falls flat on its face.
This objection is based upon a manifest confusion: the Even and the Odd number is not the Even and the Odd; the expression, 'that is to say,' is consequently not legitimate, and the only sense which the words of Aristotle can have, according to the context, is the following: first, the One arises out of the Odd and the Even, and then the other numbers proceed from the One. (Zeller 1881: 401, fn1)
Some well-deserved clarity on this otherwise fairly confusing issue.
Röth (ii. a, 769 sqq.) himself, repugnant as this assertion naturally is to him, is obliged to confess that the sacredness and inviolability of Pythagoras' circle of ideas, in regard to religious speculation, left little room for the free intellectual development of his school; and that among the writings (authentic according to Röth) left to us by the Pythagoreans, there is none which has properly a speculative character; but that they are all religious and popular works. Is not this to say, as I do, that theological convictions here appear primarily as the object of religious faith, and not scientific enquiry? (Zeller 1881: 404)
This is not a problem for me. The separation between religious and scientific, at least during the time period at hand, seems arbitrary.
I am consequently the less able to believe that the Pythagoreans taught a development of God in the universe, by which He gradually arrived at perfection through imperfection. This theory is closely connected [|] with the statement that they held the One to be the Deity. For the One is described as the Even-Odd, and as the Odd is the perfect, and the Even the imperfect, so, it is argued, they supposed not only the perfect but the imperfect, and the reason the imperfection, to be in God, and accordingly held that the perfect good can only arise from a development of God. I must protest against such an inference, if only upon the ground that I dispute the identity of the One with the Deity. (Zeller 1881: 404-405)
Others would object over the supposition that there is something imperfect in God. God must be perfect because that's what everybody say. How they know so does not matter.
Aristotle says the Pythagoreans treated numbers as space-magnitudes; he often mentions the theory that geometrical figures are the susbstantial element of which bodies consist, and his commentators go further, [|] declaring that the Pythagoreans held mathematical figures to be the principle of the corporeal, and reduced them to points or units; that they regarded these units partly as something extended in space, and partly also as the constituents of numbers; and consequently taught that corporeal things consist of numbers. (Zeller 1881: 407-408)
Polygons.
Philolaus attempts to derive sometimes the corporeal in general, and sometimes the physical fundamental qualities of bodies from figures, and figures from numbers. From this Ritter concludes, and Hermann and Steinhart agree with him, that the Limiting principle of the Pythagoreans was the unit, or, viewed in regard to space, the point; and the Unlimited, the interspaced or the void; when, therefore, they said that all things consist of the Limit and the Unlimited, they meant that all things are composed of points and empty interspaces, and when they asserted that all things are number, this was only to express that these points together form a number. (Zeller 1881: 409)
"If, therefore, the void is a principle of numbers, and numbers are principles of things, it is clear that the Pythagoreans supposed vacuum to be a principle of things" (Ritter 1836: 381).
To anyone accustomed to discriminate between corporeal and incorporeal, it must seem evident that bodies can [|] only to be compounded out of bodies, and so it inevitably follows that numbers and their elements must be something corporeal if bodies are to consist of them. The special characteristics of the Pythagorean Philosophy however lies in this, that such a distinction is as yet unrecognised, and that, in consequence, number as such is regarded not only as the form, but as the matter of the corporeal. (Zeller 1881: 410-411)
Another gentle reminder that the pythagorean philosophy is one of the earliest, and hence somewhat primitive.
Yet number itself is not on that account necessarily conceived as corporeal; for it is clear that qualities and relations which no one except the Stoics, or before their time, ever considered as bodies, were expressed in the Pythagorean Philosophy by numbers. The Pythagoreans not only defined man, or plants, or the earth by numbers, but asserted that two is opinion, four justice, five marriage, seven the opportune time, etc. Nor is this simple comparison. The meaning in both cases is that the specific number is properly and directly the thing with which it is compounded. It is a confounding of symbol and concept, a mixture of the accidental and the substantial, which we cannot discard without mistaking the essential peculiarity of Pythagorean thought. (Zeller 1881: 411)
In other words, pythagorean philosophy is markedly more symbolical than some others.
We are expressly told that Ecphantus, a later philosopher, who scarcely can be numbered among the Pythagoreans at all, was the first to explain the Pythagorean Monads as something corporeal. The ancient Pythagoreans cannot have held such an opinion, for in that case they must have believed the corporeal to have been something original, instead of deriving it, as we have just shown that they did, out of mathematical figures. (Zeller 1881: 415)
Good to know.
The proposition that all is number, and composed of the odd and the even, cannot possibly be derived from the theories concerning the limited and unlimited; but these might very easily and naturally have arisen out of that proposition. The exposition, therefore, of Aristotle, is fully justified. The fundamental conception from which the Pythagorean philosophy starts, is contained in the proposition that all is [|] number; in the next place, the opposite determinations in number - the odd and the even - were distinguished and compared, at first indeed very unmethodically, with other opposites, such as right and left, masculine and feminine, good and evil; the more abstract expression of the limited and unlimited, although at a later time this opposition was placed by Philolaus at the head of the system, and so appears in the decuple table of categories, must belong to a more developed stage of reflection. (Zeller 1881: 418-419)
Thus, while on Ritter's advice we'd have to flip the columns around to put "right" on the right, here we find out that Odd and Even should properly be placed as the first row.
4. Systematic development of the number system, and its application to Physics [p. 419-480]
After the remarks on p. 312, 1; 343, 4, I think it is unnecessary to append a criticism of the exposition of the theory of numbers and of the Pythagorean theology given by Röth (ii. a2 632 sq., 868 sq.). It is impossible to enter on a discussion of the primitive form of the Pythagorean doctrine with an author who seeks true Pythagoreanism in the Orphic fragments, and sees in the texts of Aristotle and Philolaus only spurious Pythagoreanism. Such a discussion becomes absolutely out of the question when the historian intermingles in an entirely arbitrary manner his own ideas with the sources he adopts. (Zeller 1881: 419, fn1)
Glad I'm not a historian.
Thus they said that justice consisted of the equal multiplied by the equal, or in the square number, because it returns equal for equal; and they therefore identified justice with four, as the first square number, or nine, as the first unequal square number. (Zeller 1881: 420)
There is also some symbolism in this: "Justice was defined by them [...] as [...] (square-number), by which it was intended to express the correspondence between action and suffering [...] or, in other words, retribution" (Ueberweg 1889: 47).
So seven was the critical time, because in the opinion of the ancients, the climacteric years were determined by it; five, as the union of the first masculine with the first feminine number, was called marriage; one was reason, because it is unchangeable; two, opinion, because it is variable and indeterminate. (Zeller 1881: 420)
"Climacteric is the period of life starting from the decline in ovarian activity until after the end of ovarian function", i.e. puberty commencing around 14 years of age. That 1 stood for reason because of its immutability is novel.
By further combinations of such [|] analogies, there resulted theorems like these: that this or that conception had its seat in this or that part of the world; opinion, for example, in the region of the earth; the proper time in that of the sun, because they are both denoted by the same number. In a [|] similar manner, certain numbers, or certain figures and [|] their angles, were assigned to particular gods; here [|] again, only isolated and arbitrary points of comparison are in question. It was unavoidable from the capricious irregularity of this whole procedure, that among all these comparisons there should be numerous contradictions; that the same number or figure should receive various significations, and on the other hand, that the [|] same object or concept should sometimes be denoted by one figure and sometimes by another; what whimsical vagaries were permitted in regard to this subject even in the ancient Pythagorean school, we can see from the example of Eurythus, who attempted to prove the signification of particular numbers by putting together the figures of the things they designated out of the corresponding number of pebbles. (Zeller 1881: 420-425)
Very keen to find out what the pebble-figures exactly looked like.
The assertions of Moderatus in respect of the numbers one, two, seven, and eight, are confirmed by Plutarch De Is. c. 10, p. 354; in part also by Alexander (vide the note before the last). Alexander says in the same place, c. 75 (cf. Theol. Arith. p. 9), that the Dyad was also called Eris and τόλμη. On the other hand, Philo, De Mundi Opif. 22 E, affirms that the other philosophers compare the [|] number seven to Athene, but that the Pythagoreans compare it to the Supreme God, which they do for the same reason, because it neither begets nor was begotten. This last interpretation is manifestly of later origin. As to the general fact, that numbers were designated by the names of the gods, there seems no doubt. (Zeller 1881: 422-423, fn1)
"Eris is the Greek goddess of strife and discord. Her Roman equivalent is Discordia, which means the same. Eris's Greek opposite is Harmonia, whose Roman counterpart is Concordia.[3] Homer equated her with the war-goddess Enyo, whose Roman counterpart is Bellona." - "In the disorderly changes of the earth they found the reason why so much appears to us to be purely accidental" (Ritter 1836: 399).
The truth is that we are ignorant of the source of these strange assertions: it does not follow that they may not have had some foundation which Philolaus, from his own point of view, may have thought sufficient. If we once enter the region of imagination, it is difficult to set bounds to arbitrary caprices. (Zeller 1881: 424, fn1)
Once again, this is only a problem for the historian.
[...] the spirit by the monad, the soul by the dyad, opinion (δόξα) by the triad, the body or sensation by the tetrad (Theo of Smyrna, c. 38, p. 152; Asclep. loc. cit. 541 a, 17, cf. p. 420, 2). It is true that the last-mentioned passage is certainly posterior to Plato; and that, as regards the rest, it is impossible to say what really belonged to the ancient Pythagoreans. (Zeller 1881: 425)
I was just thinking that this makes a bit too much sense, so may be tainted by platonism (cf. Zeller 1881: 318, fn2, above).
The importance of the decuple system in relation to the Pythagoreans is much greater. For as they considered numbers over ten to be only the repetition of the first ten numbers, all numbers and all powers of numbers appeared to them to be comprehended in the decad, which is therefore called by Philolaus, great, all-powerful and all-producing, the beginning and the guide of the divine and heavenly, as of the terrestial life. According to Aristotle, it is the [|] perfect and complete, which includes in itself the whole essence of number; and as nothing, generally speaking, would be knowable without number, so in particular, we are indebted solely to the decad that knowledge is possible to us. (Zeller 1881: 427-428)
Now this is new! 1 = 11 = 21 = 31, etc., 2 = 12 = 22 = 32, etc., etc.
Nicom. Inst. Arithm. p. 9 sq.: Theo. Math. i. c. 8 sq. Three kinds of numbers are here distinguished among the even numbers, the ἀρτιάκις ἄρτιον (the numbers that can be divided by even numbers down to Unity, like 64); the περισσάρτιον (the numbers which, divided by 2, give even numbers, but which, divided by any even number higher than 2, give uneven numbers like 12 and 20); and the ἀρτιοπέρισσον (vide supra, p. 377, 1). Similarly three kinds of numbers are distinguished in regard to uneven numbers, the πρῶτον καὶ ἀσύνθετον (the first numbers); the δεύτερον καὶ σύνθετον (numbers which are the product of several uneven numbers, and are, therefore, not divisible merely by unity, as 9, 15, 21, 25, 27); and lastly, the numbers divisible separately by other numbers than unity, but [|] the relation of which to others is only to be defined by unities, as 9 and 25. (Zeller 1881: 426-427, fn1)
This I'm sure to meet again, and will have to construct a table (ideally, it already exists somewhere).
Four has a similar importance, not merely because it is the first square number, but chiefly because the four first numbers added together produce the perfect number, ten. In the famous Pythagorean oath, Pythagoras is therefore celebrated as the revealer of the quaternary number (Tetractys), and this in its turn is praised as the source and root of the eternal nature. Later Pythagoreans are fond of arranging all [|] things in series of four: how far this is derived from the ancient Pythagoreans cannot be determined. (Zeller 1881: 428-429)
What is the pythagorean oath? Is it just those few lines (46-47) in the Golden Verses: "By that pure, holy, four lettered name on high, / nature's eternal fountain and supply, / the parent of all souls that living be, / by him, with faith find oath, I swear to thee." (Wiki:Tetractys) - or is the whole of the Golden Verses, or what? The tendency to arrange everything in a series of four is familiar from Taylor (cf. e.g. 1818: 238).
On this oath and the quaternary number vide Carm. Aur. v. 47 sq.; Hierocles in Carm Aur. v. 166 f. (Fragm. Phil. i. 464 sq.); Theo, Math. c. 38; Lucian, De Salut. c. 5; V. Auct. 4; Sext. Math. 94 sqq.; iv. 2; Plut. Plac. i. 3, 16; Iambl. Th. Ar. p. 20; cf. Ast. on the passage and Müllach in loc. cit. of the golden poem. The date of these verses cannot be determined with certainty. According to the Theol. Ar., they were found in Empedocles, and from his point of view the four elements should be regarded as the four roots of the universe. But in this case, instead of γενεᾷ, it would be necessary to read with Sextus, iv. 2, and others, ψυχᾷ (cf. Fabricius in loc. cit. of Fabricius), and by the word, παραδοὺς to understand (with Mosheim, in Cudworth. Syst. Intell. i. 580) the Deity. It seems to me more likely that Pythagoras is here celebrated as the inventor of the Tetractys. (Zeller 1881: 428, fn3)
The oath appears as if it follows from line 47 of the Golden Verses - until the end? Codworth citation very valuable - indeed, on page 580 he discusses the "Pythagorick Trinity".
But each of the other numbers has its particular value. One is the first from which all the other numbers arise, and in which the opposite qualities of numbers, the odd and the even, must therefore be united; two is the first even number; three the first that is uneven and perfect, because in it we first find beginning, middle and end; five is the first number which results by addition from from the first even and the first uneven number. Six is the first number which results from them by multiplication. Six multiplied by itself gives a number which again ends in six; all the multpiles of five end either in five or ten; three, four, and five, are the numbers of the most perfect right-angled triangle, which together form a particular proportion; [|] seven is the only number within the dead which has neither factor nor product; this number is moreover compounded out of three and four, the significance of which has just been discussed; lastly, to pass over other things, it is together with four the mean arithmetical proportion between one and then. Eight is the first cube, and the great Tetractys is formed out of the four first uneven and the four first even numbers, the sum of which (36) equals the sum of the cubes of one, two, and three. Nine, as the square of three, and the last of the units, must have had a special importance. (Zeller 1881: 429-430)
The information up to five is already all too familiar. That 6 × 6 = 36 is significant makes some sense, given the repetition of symbolic series (cf. above). This "mean arithmetical proportion" I take to be limits dividing the ten first numbers up into three: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. / The actual significance is revealed in the footnote: "For 1 + 3 = 4, 4 + 3 = 7, 7 + 3 = 10." (ibid, fn2), which seems to put the premium on adding the number 3. The "special importance" of number nine is not availed - the footnote refers us to Iamblichus in latin.
The Pythagoreans called the harmonic theory κανονικὴ, according to Porphyry, in Ptol. Harm. (in Wallisii Opp. Math. ii.), p. 207, and Ptolemais of Cyrene, who is cited by Porphyry. Notwithstanding, the word, ἁρμονική, must also have been in use among them. Aristoxenus (Harm. Elem. sub init.; ibid. p. 8) gives this as the ordinary designation for the theory of tones (ἡ καλουμένη ἁρμονικἠ). In the same way he constantly calls the adherents of the Pythagorean theory οἱ ἁρμονικοὶ, οἱ καλούμενοι ἁρμονικοὶ; we find even in Archytas the expression, ἁρμονικὴ ἀναλογία, for a certain numerical relation. (Zeller 1881: 431, fn1)
Harmooniline analoogia.
After tones, the number theory was next applied to geometrical figures, and it is not necessary to be a Pythagorean to see that the form and relations of figures are determined by numbers. If, therefore, the Pythagorean and the Greek mathematicians in general were accustomed to apply geometrical terms to numbers, and to discover arithmetical and harmonical proportions in figures, the habit was perfectly natural. The Pythagoreans, however, did not stop here, but as they saw in numbers generally the essence of things, they sought to derive figures and bodies immediately from definite numbers. (Zeller 1881: 434)
Controversial, "for from the composition of the unextended, extension cannot possibly result" (Ritter 1836: 378).
It is true that a very improbable reason is given for this, viz., because 6 = 2 × 3, and that the even designates the body, and the uneven the soul. (Zeller 1881: 435, fn2)
Footnote to the clause that "Philolaus we know explained four as the number of the body" (ibid, 435). By this token, 3 designates the soul?
That Pythagoras regarded the world as never having had a beginning is often affirmed by later writers, [...] who for that reason accused Pythagoras of setting the necessity of nature in the place of Providence. (Zeller 1881: 439, fn2)
(1) Possibility; (2) Necessity; (3) Providence. - Nah.
Chaignet and Rohr consider that they have found in the testimony of Stobæus sufficient evidence as to the doctrine of Pythagoras and the ancient Pythagoreans. But we cannot trust writers, whose sources it is impossible to trace beyond the Neo-Pythagorean epoch; and least of all, can we trust so recent a compiler. (Zeller 1881: 441, fn2)
"Fragments of these forgeries are preserved in Stobæus" (Ueberweg 1889: 48).
According to the Pythagoreans, the central fire was first formed in the heart of the universe; this is also called by them the One or the Monad, because it is the first body of the world; the mother of the Gods, because it is this which engenders the heavenly bodies; they also call it Hestia, the hearth or the altar of the universe, the guard, the citadel or the throne of Zeus, because it is the central point in which the world-sustaining energy [|] has its seat. How this beginning of the world itself came about, Aristotle (loc. cit.) says they were unable to explain, and we cannot certainly discover from his language whether they even attempted an explanation. After the formation of the central fire, the nearest portions of the unlimited, which according to the obscure notions of the Pythagoreans signified at once infinite space and infinite matter, were constantly being attracted to this centre, and becoming limited through [|] this attraction, until by the perpetual continuation and extension of that process (thus we must complete the accounts) the system of the universe was at last finished. (Zeller 1881: 442-444)
To me this reads like a cryptic account of cosmic gravitation, or the formation of galaxies and planetary systems.
The universe was conceived by the Pythagoreans as a sphere. In the centre of the whole they placed, as we have seen, the central fire; around this ten heavenly bodies moving from west to east describe their orbits; farthest off, the heaven of fixed stars, next the five planets; then the sun, the moon, the earth, and tenth, and last, the counter-earth, which the Pythagoreans invented in order to complete the sacred number of ten. The extreme limit of the universe was formed by the fire of the periphery, which corresponded to the central fire. (Zeller 1881: 444)
That the whole universe is spherical, and that there's a fiery periphery both come as news to me. The order: (1) central fire, (2-6) the five planets, (7) the sun, (8) the moon, (9) earth, (10) counter-earth. Shouldn't Earth be 8, in correspondence with "human life, such as it exists on the earth, to eight" (Ritter 1836: 404)?
Among the bodies of the universe the central fire occupies the first place, not only from its position, but because, on account of this position, it is the centre of gravity and support of the whole, the measure and bond of the universe, which indeed sprang solely from it and through its operation. (Zeller 1881: 446)
Difficult to imagine, as the central fire as-if shines through the fixed stars and the sun: "the central light of fire reaches us mediately only through the sun and the stars; whereas these receive it immediately from the universal mundane fire" (Ritter 1836: 399).
[...] is certainly Stoic and the Demiurgus Platonic; but the comparison of the central fire with the keel of the ship of the universe seems to be truly Pythagorean. Nicom. (ap. Phot. Cod. 187, p. 143 a, 32) also, among many later documents, brings forward a statement, according to which the Monad was called by the Pythagoreans Ζανὸς πύύργος, which must have come from some ancient tradition. (Zeller 1881: 446, fn1)
What is this now?
Plut. Plac. Qu. viii. 4, 3, p. 1007; to the question, 'What is Time?' Pythagoras replied, 'The Soul of the World.' (Zeller 1881: 447, fn1)
A correspondence with Peirce, who connects time with soul.
Aristotle, in discussing the theories of the ancient philosophers about the soul, quotes from the Pythagoreans only the celebrated assertion that the particles emanating from the sun are souls, and he infers from hence, not without difficulty, that they regarded the soul as the moving principle. (Zeller 1881: 448)
Somewhat different interpretation: "the statement of Aristotle, that some of the Pythagoreans called the floating particles in the sunbeam, others that which sets them in motions, souls; and remarking, at the same time, that the souls which float in the air were what the Pythagoreans called heroes and demons" (Ritter 1836: 407).
In the exposition of Alexander, and in the short statement of Sextus, the Stoic element is equally apparent; witness the πνεῦμα διὰ παντὸς διῆκον, the conception of the human soul originating from the Divine Soul by emanation, the cosmology, so different from that of the Pythagoreans, which we shall discuss further on, and the number four applied to the element. (Zeller 1881: 448, fn2)
As per, reportedly, Cicero: "God with the Pythagoreans is the soul which is diffused through and governing in all things, and from which our souls derive their origin. (Ritter 1836: 369-370). Zeller's explanation is that Cicero "did not hesitate to use the most recent and most convenient documents" and "clearly did not know how to distinguish the original doctrines of Pythagoreanism from the new" (ibid, 448, fn2).
The first loses any probability it might seem to have, if we consider with what care and completeness Aristotle quotes everything which his predecessors have said on the subject of the soul. (Zeller 1881: 449, fn1)
Hmm. Did not know that Aristotle was so thorough on the subject of the soul.
The objections made by Chaignet and Rohr have no great weight. The former says (ii. 176): Since Aristotle concludes from the Pythagorean conception of solar corpuscles that the soul is endowed with motive force (404 a, 21, ἐοίκασι γὰρ οὗτοι πάντες ὁπειληφέναι τὴν κίνησιν οἰκειότατον εἶναι τῇ ψυχῇ), it necessarily follows from this that he attributes to the Pythagorenas a World-soul. Rohr speaks in a similar manner (l. c.., p. 21). But the fact that Aristotle is here making a simple deduction, of which he himself is not certain, is enough to show the impossibility of his having had in his possession so precise an explication as that of our fragment. (Zeller 1881: 449, fn1)
A nice phrase in itself - noted for the motive force (Chase's motivity).
Around the central fire, the earth, and between the two, the counter-earth, revolve in such a manner, that the earth always turns the same side to the counter-earth and the central fire; and for this reason, the rays of the central fire do not come directly to us, but indirectly from the sun. When the earth is on the same side of the central fire as the sun, we have day; when it is on the other side, night. (Zeller 1881: 450)
Okay, if they're constantly lined up, then mayhaps it makes some sense. But does this imply that the central fire, too, is in constant rotation and not in a fixed position? But then, the central fire rotates around the sun?
Arist. De Cœlo, ii. 13; [...] According to this passage the side of the earth which we inhabit is always turned away from the central fire and the counter-earth. (Zeller 1881: 450, fn1)
So the central fire and counter-earth are always behind us and the sun always in front of us? How is the sun then illuminated by the central fire? And whence comes the alternation of night and day? I'm having real trouble imagining this cosmos now (Ritter's explanation was vague but more persuasive).
As to the sun and the solar light, Achilles Tatius (as well as Stobæus and the author from whom he takes his information) seems to admit that the solar light is the reflection of the fire of the circumference. (Zeller 1881: 451, fn1)
Oh lawd. How or why is the fire of the circumference not visible to us? Same objection by Zeller himself on the next page: "Only it would seem that if this latter fire can enlighten the sun, it must also be visible to us" (ibid, 451, fn1).
Böckh (Philol. 124 sq.) thinks that this opinion is erroneous, and believes that the central fire is the luminous source, the rays of which the sun reflects to us; he afterwards (Unters. üb. d. kosm. Syst. d. Platon, 94) gave the preference to the opinion of Martin (Eiudes sur le Timée, ii. 100), according to which [|] the sun concentrates and reflects, not only the light of the central fire, but also that of the external fire. (Zeller 1881: 451-452, fn2)
This does not make more sense.
But we shall see further on that the Pythagoreans perhaps really thought they saw this fire in the milky way. This belief accords with the opinion (contained in all the passages quoted) that the rays of this fire, as well as those of the central fire, are concentrated and sent back by the sun, as by a sort of burning glass. It is not stated whether the Pythagoreans supposed that the other planets and fixed stars were foci of the same kind, but less intense, for these rays. (Zeller 1881: 452, fn1)
The sun's glassy essence. (A little play on Peirce.)
Clemens (Strom. v. 614 C), even thinks that the Pythagoreans meant by the counter-earth, heaven, in the Christian sense of the word. (Zeller 1881: 452, fn1)
Why not? Neither exists.
It is now universally recognised that Copernicus and others were wrong in attributing to the Pythagoreans the doctrine of the rotation of the earth on its axis, and the revolution of the earth round the sun. (Zeller 1881: 453, fn3)
Boom.
The Pythagoreans held the sun and moon to [|] be virtreous spheres, which reflected back light and warmth to the earth. At the same time we are told that they conceived the stars as resembling the earth, and surrounded like the earth by an atmosphere; [|] they attributed to the moon, plants and living beings far larger and fairer than those on the earth. This theory was founded, it would seem, partly on the appearance of the moon's disc, which resembles the earth; and partly on the desire to discover a special abode for the souls who had quitted the earth, and for the dæmons. Also they thought that the stars, which like the earth were planets, but which belonged to a better portion of the universe, must possess everything that serves to adorn the earth, in a more perfect manner. (Zeller 1881: 455-457)
Define:vitreous - "like glass in appearance or physical properties", "(of a substance) derived from or containing glass".
As regards the form of the sun, the Placita (ap. Euseb. Pr. Ev. xv. 23, 7) describe it as a vitreous disc (δίσκος); but this description is not found in any other text, and expressly contradicts what is said in Stob. i. 526: οἱ Πυθ. σφαιροειδῆ τὸν ἥλιον. Moreover, the Pythagoreans must have attributed to the sun the same shape as to the moon, the spherical form of which is never disputed. We must, therefore, consider the statement of Eusebius as erroneous. (Zeller 1881: 456, fn1)
Erroneous or not, it is a pretty funny image: a disk Sun reflecting light on a flat Earth.
[...] that the 59 years and 21 months are equal to 729 months; and are 364½ days of the solar year are equal to 729 half days; lastly that 729 is the cube of 9 and the square of 27, or the first cube of an uneven number (hence the number 729 has for Plato also - Rep. ix. 587 E - an especial significance). (Zeller 1881: 459, fn2)
Cool.
They supposed the acuteness of these tones to be according to the rapidity of motion, and this again to be in proportion to the distance of the several planets, the intervals of the planets corresponded with the intervals of sounds in the octave. Thus they arrived at the theory that the heavenly bodies in their [|] rotation produce a series of tones, which together form an octave, or, which is the same thing, a harmony. The [|] fact that we do not hear these tones, they explained by saying that we are in the condition of people who live [|] in a smith's forge; from our births we are unceasingly hearing the same sound, and are so never in a position to take note of its existence from the contrast of silence. (Zeller 1881: 460-463)
The smith's forge situation recalls Plato's cave analagoy. The important contrast with silence was mentioned: "a harmony of sound, unnoticed, indeed, by us, in consequence of our habitually hearing it from our birth, and of the law of our auditory perception, which depends on the contrast with silence" (Ritter 1836: 396).
Simplicius, it is true, De Cœlo. 211, a, 14; Schol. 496 b, 11 sqq. thinks this too ordinary a reason to be held by a school, the founder of which had himself heard the harmony of the spheres, and gives this sublimer reason (also indicated by Cicero, Somn. c. 5, together with that of Aristotle) that the [|] music of the heavenly bodies is not perceptible to the ears of ordinary mortals. Porphyry expresses this idea in a physical manner (in Ptol. Harm. p. 257) when he says that our ears are too narrow to perceive these powerful sounds. Archytas seems to have anticipated him in this, vide the fragment quoted in Porph. 1. c. and supra, p. 306 sq. (Zeller 1881: 463-464, fn1)
The sources for the various claims: (1) Pythagoras himself "he heard the harmony of the spheres" (Ritter 1836: 330); (2) "or perhaps because the harmony of the universe, from the grandeur of its tones, surpasses our faculty of hearing" (Ritter 1836: 396-397).
The chief function of the fire of the circumference, in the Pythagorean theory, was to hold the cosmos together as a covering embracing the whole, and on this account they seem to have called it necessity. It [|] is not improbable also that they derived the light of the stars from it, and in a certain degree that of the sun; there are reasons too for supposing that they believed that this fire, or a radiation from it, was seen in the milky way. [...] Necessity seems rather to mean, with them, to bond of the universe; and when they say that it embraces the world, we think most naturally of the fire of the periphery. (Zeller 1881: 465-466)
Perhaps a hint towards what "Power [being] a near neighbour to necessity" (GV 9) might mean.
The statement of the treatise on the heavens, on the contrary, refers to the opposition of the superior and inferior hemispheres of the earth; in regard to this, the Pythagoreans maintain, in opposition to Aristotle, that our hemisphere is turned towards the periphery of the world, and is in ordinary language the superior hemisphere. Aristotle, from his standpoint, called it the right; the Pythagoreans must have called it the left. (Zeller 1881: 471, fn1)
This obscure cosmology goes far above my head but the portion I highlighted may have something to do with Aristotle placing "Right" in his account of the table of opposites on the left.
They also held the upper portions of the universe to be the most perfect, and distinguished the outermost circle of fire from the circles of the stars, dividing these again into the circles above and below the moon; so that the universe was divided into three regions, Olympus, Cosmos, and Uranos. Olympus contained [|] the elements in their purity; Cosmos was the place of ordered and uniform motion, Uranos that of Becoming and Change. (Zeller 1881: 471-472)
To me this sounds like the triad in reverse: (1) Becoming and Change - Motivity; (2) ordered and uniform motion - Spontaneity; (3) the elements in their purity - Reason.
This astronomical theory of the universe is connected, as we have seen, with the idea of the respiration of the world and of its right and left sides. In this we see the favourite ancient comparison of the world with a living creature; but, after our previous enquiries concerning the world-soul, we cannot allow that this thought had any important influence on the Pythagorean system. (Zeller 1881: 473)
Calls to mind a long-forgotten memory of a visualization of the universe as a sphere composed of unequal hemispheres, almost the shape of the human brain, but one side being larger and the other one smaller - in some sense even and uneven - though I may have just as well hallucinated this image instead of remembering it from obscure physics video.
It therefore relates only to the destruction of individual things: in regard to the [|] universe generally, it would appear that the Pythagoreans did not believe in any destruction of the world; what the Pseudo-Plutarch tells us on the subject is no doubt merely derived from Timœus the Locrian, or other similar sources. It is clear on the contrary, from Eudemus, that they thought, as the Stoics did afterwards, not only that the same persons who had lived in the world would re-enter it at a later period; but thta they would again do the same actions and live in the same circumstances; this is confirmed by a passage in Porphyry, not in itself of much weight. This theory was no doubt connected with the doctrine of Transmigration and of the gerat year of the world: if the heavenly bodies were to occupy the same place as before, everything else would return to the same condition, and consequently the same persons would be present under the same circumstances. But it is a question whether this doctrine belonged to the whole school, or only to a portion of it. (Zeller 1881: 473-474)
I was not aware that the Stoics, too, believed in this. From this discourse it would appear that every 729 years, everything repeats exactly the same way.
In the fragment of his Physics ap. Simpl. Phys. 173 a, he enquires whether the same time which has been, shall be again, or not? and the answer is: that which comes after is only qualitatively the same as that which has gone before: [...] (Zeller 1881: 474, fn2)
Not exactly the same - the sizes will be different (e.g. there will be more people in the world); in other words, every 729 will rhyme.
In regard to Philolaus, we are told that in the same way that he derived geometrical determinations (the point, the line, the surface, the solid) from the first four numbers, so he derived physical qualities from five, the soul from six; reason, health, and light from seven; love, friendship, prudence, and inventive faculty from eight. Herein (apart from the number schematism) is contained the thought that things represent a graduated scale of increasing perfection; but we hear nothing of any attempt to prove this in detail, or to seek out the characteristics proper to each particular region. (Zeller 1881: 475)
Wow, much more thorough than Ritter's exposition: (5) physical qualities; (6) soul; (7) reason, health, and light; (8) love, friendship, prudence, and inventive faculty.
ποιότητα καὶ χοῶσιν. The colour no doubt describes in a general manner the external nature [...] (Zeller 1881: 475, fn2)
"Physical qualities" (5) specifically includes colour?
Τὸ ὑπ' αὐτοῦ λεγόμενον φῶς, therefore not light in the ordinary sense, but some quality or state of man; or in general, health, well-being. (Zeller 1881: 475, fn3)
Helgus (7).
Concerning the parts of the soul, various theories are ascribed to the Pythagoreans by more recent writers which I cannot admit them to have originally held. According to some, they were acquainted with the Platonic distinction of a rational and an irrational soul, and the analogous distinction of Reason, Courage, and Desire [Posidonius ap. Galen. De Hipp. et Plat. iv. 7]; together with the Platonic division of the intellectual faculty into νοῦς, ἐπιστήμη, δόξα, and αἴσθησις [The Pseudo-Archytas ap Stob. Ecl. i. 722. 784, 790]; we are told by another writer [Alex. Polyhistor ap. Diog. viii. 30] that they divided the soul into Reason, Mind, and Courage (νοῦς, φρένες, θυμὸς); Reason and Courage being in men and [|] beasts, Mild in men only; Courage having its seat in the heart, the two other faculties in the brain. There is more warrant for supposing that Philolaus placed the seat of Reason in the brain; of life and sensation in the heart; of seed and germination in the navel; of generation in the sexual parts: in the first of these regions, he said, lay the germ of men; in the second, that of beasts; in the third, that of plants; in the fourth, that of all creatures. With this, our knowledge of the philosophic anthropology of the Pythagoreans is exhausted. (Zeller 1881: 479-480)
Philolaus's system appears here even more extensive than it did in Ritter. The exposition here is confusing. Presumably, the four forms of life - (1) in general, (2) plants, (3) beasts, and (4) men - should somehow correspond to a series I can't exactly identify: seed and germination? Men reproduce with seed, but so do beasts; plants via germination, perhaps other life (mushrooms, bacteria, viruses), too. But what are "the third" and "the fourth" here? - that the tripartite divisions may be spurious, we've already seen: "It has already been shown, pp. 393, 3; 447, 2, that this exposition is not authentic. The whole division is confused, and contains many Stoical definitions, for example, that the senses are emanations from the soul, that the soul is nourished by the blood, &c." (ibid, 479, fn3). - This evidently concerns the question of "the Stoic and Aristotelian distinction of matter and efficient cause" (p. 393, fn3); and that "the soul [...] should be regarded as the eternally moved and the eternally moving" (p. 448, fn2) - neither of which I would personally connect (yet) with the parts of the soul (though Plato's Timaeus may change this).
We can only discuss in a supplementary manner certain theories which have been omitted in the preceding exposition as not forming an integral part of the physical system of the Pythagoreans, but which were either incorporated by later writers from other sources into their own doctrine, or stand isolated without philosophical foundation, and are based merely on observation. (Zeller 1881: 480, fn2)
Some pythagorean stuff is less frequently treated because it has little to do with their philosophy or other relevant categories. Such as:
We may also instance what is said about colours: Placita, i. 15, 2 (cf. Stob. i. 362; Anon. Phot. Cod. 249, p. 439 a, cf. Porph. in Ptol. Harm. c, 3, p. 213; Arist. De Sensu, c. 3, 439, a. 30); on the five zones of heaven and earth, Plac. ii. 12, 1; iii. 14 (Galen. H. ph. c. 12, 21. cf. Theo in Arat. ii. 359): on sight, and the reflections of the mirror, Plac. iv. 14, 3 (Stob. Ecl. i. 502, and in the extracts of Joh. Damasc. Parall. p. 1, 17, 15; Stob. Floril. ed. Mein. iv. 174; Galen, c. 21, p. 296); on the voice, Plac. iv. 20, 1 (G. c. 26); on seed, Plac. v. 3, 2, 4, 2, 5, 1 (G. c. 31); on the five senses, Stob. Ecl. i. 1104; Phot. 1. c.; on the rainbow. Ælian, V. H. iv. 17; on the nutrition of animals by smell, Arist. De Sensu, 5 (vide supra, p. 475, 4); on the origin of maladies, Galen. c. 39. If even these notices really reproduce the doctrines of the ancient Pythagoreans (which can only be supposed in regard to a portion of them), they have no connection with the Pythagorean philosophy. Similarly the definitions of the calm of the air and of the sea, given by Arist. Metaph. viii. 2, ad fin., as those of Archytas, all of small importance; and the statement according to which (Arist. Probl. xvi. 9) this philosopher showed that the round form of certain organs in animals and plants was the result of the law of equality which governs natural movement, stands entirely alone. As to the pretended logic and philosophy of language of the Pythagoreans, vide infra, § vi. (Zeller 1881: 481, fn2)
Only some of these ring familiar (the five zones and the round form). I'm particularly interested in the calm of the air and sea, given that this was a remarkable instance in Iamblichus' biography of Pythagoras, and of course their logic and philosophy of language, of which I know nothing yet, I guess.
5. Religious and ethical doctrines of the Pythagoreans [p. 481-496]
Of all the Pythagorean doctrines, none is better known, and none can be traced with greater certainty to the founder of the school, than that of the Transmigration of souls. It is mentioned by Xenophanes, and later by Io of Chios; Philolaus speaks of it, Aristotle describes it as a Pythagorean fable, and Plato unmistakably [|] copied his mythical descriptions of the conditions of the condition of the soul after death from the Pythagoreans. As Philolaus says, and Plato repeats, the soul is confined in the body and buried in it, as a punishment for faults. The body is a prison in which it has been placed by God as a penalty, and from which it consequently has no right [|] to free itself by a presumptuous act. So long as the soul is in the body it requires the body; for through the body alone can it feel and perceive; separated from the body it leads an incorporeal life in a higher world. (Zeller 1881: 481-483)
How unmistakable it is, I will surely find out at some point.
The veins are called, ap. Diog. viii. 31, the bonds of the soul. The rest does not seem to belong to the ancient Pythagoreans. (Zeller 1881: 482, fn1)
Veresooned on hingepaelad.
Plut. Plac. v. 20, 4 (Galen, c. 35) interprets this to mean that the souls of animals are indeed rational in themselves, but are incapable, on account of their bodies, of acting rationally. Plut. Plac. 1. 4; Galen. c. 28; Theodoret, Cur. gr. aff. v. 123, represent only the rational part of the soul as existing after death; but these, like the assertions of the equality of the spirit in men and animals (Sext. M. ix. 127; vide sup. p. 417, 3) are subsequent inferences. (Zeller 1881: 484, fn2)
This makes sense, and is one way to interpret Aristotle (in the first book of Nicomachean Ethics) writing that animals possess the rational principle but humans exercise it.
The belief in subterranean abodes of the departed was undoubtedly maintained by the Pythagoreans. What was their precise conception of the future state, whether like Plato they supposed that some of the souls underwent refining punishments in Hades, and that a definite interval must elapse between the departure from one body and the entrance into another; [...] (Zeller 1881: 485)
Familiar: "venerate the divinities under the earth, due rites performing" (GV 4).
If the soul originally floats in the air, and enters the body of the newly-born with the first breath, it escapes equally from the body of the dying with the last; and if it does not ascend to a superior abode, or sink to an inferior place, it must float about in the air until it enters another body. This Orphic conception itself seems to be connected with an ancient popular belief: the invocation in use at Athens of the Tritopatores, or gods of the wind, to make marriages fruitful (Suid. πριτοπ.; cf. Lobeck. Aglaoph. 754), presupposes that the soul of the child was brought by the wind, cf. p. 73, 2. (Zeller 1881: 485, fn2)
Give birth in a windy place, then?
The belief in dæmons, to which the ancient Pythagoreans were much addicted, must also be included [|] among their mystic doctrines. As far as we know on the subject, they thought that dæmons were bodiless souls which dwell, some of them under the earth, and some in the air, and which from time to time appear to men; but spirits of nature as well as the souls of the dead seem to have been called by this name. The Pythagoreans derived revelations and soothsaying from the dæmons, and connected them with purifications and expiations: the high estimation in which they held soothsaying is frequently attested. To the class of dæmons belonged also the heroes, but there appears to have been nothing particular in the worship accorded [|] to them. The opinion that dæmons occupied an intermediate place between gods and men already existed in the more ancient popular faith. (Zeller 1881: 487-489)
Congruous with the ufological tenet that some extraterrestials live in underground (and underwater) compounds where they seal themselves off from the unhygienic life on Earth.
If we turn from the dæmons to the gods, we find, as has already been observed, that the Pythagoreans, in all probability, brought their theology into no scientific connection with their philosophical principle. That the conception of God as a religious idea was of the highest significance to them, is indubitable; nevertheless, apart from the untrustworthy statements of later writers, of which we have before spoken, very little has been handed down to us about their peculiar theological tenets. Philolaus says that everything is enclosed in the divinity as in a prison; he is also said to have called God the beginning of all things; and in a fragment the authenticity of which is not certain, he describes him in the manner of Xenophanes as the one, eternal, unchangeable, unmoved, self-consistent ruler of all things. (Zeller 1881: 489)
God = universe. In my own recent speculations: central fire = the center of the galaxy; counter-earth = the earth's core, which can become loose from the thin crust.
The religious belief of the Pythagoreans stood in close connection with their moral prescripts. Human life, they were convinced, was not only, like everything [|] else, in a general manner under the Divine care and protection; but was also in a particular sense the road which leads to the purification of the soul, from which no one, therefore, has any right to depart on his own choice. The essential problem of man's life, consequently, is his moral purification and perfection; and if during his earthly life, he is condemned to imperfect effort; if, instead of wisdom, virtue merely, or a struggle for wisdom, is possible, the only inference is that in this struggle man cannot do without the support which the relation to the Deity offers to him. The Pythagorean ethical doctrine therefore has a thoroughly religious character: to follow God and to become like Him is its highest principle. (Zeller 1881: 490-491)
A familiar song and dance. That is, it is nothing to merely believe in a figure like Christ, the point is to become Christ-like.
The statement that Pythagoras was the first to speak of virtue seems to have arisen from the passage quoted, p. 420, 2, from Metaph. xiii. 4. (Zeller 1881: 492, fn1)
Is there any truth to this?
The Pythagoreans, according to Aristoxenus, required before all things adoration of the gods and of dæmons, and in the second place reverence to parents and to the laws of one's country, which ought not to be lightly exchanged for foreign laws. They regarded lawlessness as the greatest evil; for without authority they believed the human race could not subsist. Rulers and the ruled should be united together by love; every citizen should have his special place assigned to him in the whole; boys and youths are to be educated for the state, adults and old men are to be active in its service. Loyalty, fidelity, and long-suffering in friendship, subordination of the young to the old, gratitude to parents and benefactors are strictly enjoined. (Zeller 1881: 493)
It is not indeed difficult to imagine that such views could have inspired Plato's Republic. E.g. "According to Aristotle, Hippodamus was the first private citizen who undertook to say any thing respecting the best form of constitution for the state. The territory of the state, he taught, should be divided into three portions: a sacred portion for the service of the gods, a common domain for the support of the military order, and a third portion to be held as private property" (Ueberweg 1889: 48).
He who possesses true love for the beautiful will not devote himself to outward show, but to moral activity and science; conversely, science can only succeed when it is pursued with love and desire. In many things man is dependent on Fortune, but in many he is himself the lord of his fate. (Zeller 1881: 494)
A view I can identify with.
In the same spirit are the moral prescripts of the Golden Poem. Reverence towards the gods and to parents, loyalty to friends, justice and gentleness to all men, temperance, self-command, discretion, purity of life, resignation to fate, regular self-examination, prayer, observance of consecrating rites, abstinence from impure food, - such are the duties for the performance of which the Pythagorean book of precepts promises a happy lot after death. These, and similar virtues, Pythagoras is said to have enforced, in those parabolic maxims, of which so many specimens are given us, but the origin of which is in individual instances as obscure as their meaning. (Zeller 1881: 494)
A brief break-down of the Golden Verses.
He taught, as we are elsewhere informed, [|] reverence to parents and the aged, respect for the laws, faithfulness and disinterestedness in friendship, friendliness to all, moderation and decorum; commanded that the gods should be approached in pure garments and with a pure mind; that men should seldom wear, and never break their oaths, keep what is entrusted to them, avoid wanton desire, and not injure useful plants and animals. (Zeller 1881: 494-495)
Also congruous with ufological stereotypes: the "visitors" are germophobes, and, being telepathic, don't come to face-to-face with humanity often because we are full of negative emotions (don't have a pure mind), i.e. full of fear and quick to anger and violence, also very sad, melancholic creatures. To the forbidding of injuring useful plants and animals we may today add forbidding to blow our planet up with atomic weapons or destroy it with climate change and pollution.
E.g. the famous κοινὰ τὰ τῶν φίλων (supra, p. 345, 2); the saying that man should be one. ap. Clem. Strom. iv. 535 C; cf. Proclus in Alcib. iii. 72; Conv. in Parm. iv. 78, 112 (the end of life is, according to the Pythagoreans, the ἑνότης and φιλία); [...] (Zeller 1881: 495)
This is commonly interpreted differently - everything is common between friends. Here it sounds like the typical esoteric tenet about the "oneness" of humanity.
But, according to the unanimous testimony [|] of our authorities, and to what has already been said on the political character of the Pythagorean association, we may consider it proved that the school of Pythagoras, believing in the almighty power of the gods, and in future retribution, enforced purity of life, moderation and justice, minute self-examination and discretion in all actions, and especially discouraged self-conceit; that it also required unconditional observance of moral order in the family, in the state, in friendship, and in general intercourse. (Zeller 1881: 495-496)
The rare occasion when pythagoreanism links up with the topic of phaticity.
6. Retrospective summary: character, origin, and antiquity of the Pythagorean philosophy [p. 496-521]
This is not to treat physics ethically, but ethics physically. Schleiermacher, indeed, would have us regard their mathematics as the technical part of their ethics. He thinks that all virtues and all ethical relations were expressed by particular numbers; he sees [|] an evidently ethical tendency underlying the table of opposites. But as these assertions are devoid of all foundation, it is unnecessary to refute them; how arbitrary they are, must have already appeared from our previous exposition. Ritter observes, more correctly, that the mathematics of the Pythagoreans were connected with their ethics by the general idea of order, which is expressed in the concept of harmony. (Zeller 1881: 500-501)
More often than not, Zeller speaks ill of Schleiermacher's interpretations of pythagoreanism, so I do not know what to make of this.
Of this, however, there is no trace; for the incidental remark of Philolaus, that the sensuous perception is only possible by means of the body, even if genuine, cannot be regarded as a fragment of a theory of knowledge, and what later writers have related as Pythagorean, on the distinction between reason, science, opinion, and sensation, is as untrustworthy as the statement of Sextus, that [|] the Pythagorean declared mathematical reason to be the criterion. (Zeller 1881: 504-505)
E.g. "And intellectual knowledge indeed, as being contracted according to impartible union, they referred to the monad; but scientific knowledge, as being evolved, and as proceeding from cause to the thing caused, yet through the inerratic, and always through the same thing, they referred to the duad; and opinion to the triad, because the power of it is not always directed to the same thing, but at one time inclines to the true, and at another to the false" (Taylor 1818: 220).
This system is therefore, as it stands, the work of various men and various periods; its authors did not consciously attempt from the beginning to gain a whole of scientific propositions mutually supporting and explaining one another, but as each philosopher was led by his observation, his calculations, or his imagination, so the fundamental conceptions of the Pythagorean theory of the universe were developed, sometimes in one direction, sometimes in another. The traces of such an origin are not entirely obliterated even in our imperfect traditions of the doctrine of the Pythagoreans. That their principle was apprehended [|] in many different ways in the school we cannot indeed admit; but the development of it was certainly not from the same type. The table of the ten opposites belonged, according to Aristotle, only to some, who were, it would seem, later Pythagoreans. (Zeller 1881: 508-509)
Eclectic.
The geometric construction of the elements, and the discrimination of four organs and of four vital functions in man, were introduced by Philolaus; the doctrine of the ten moving heavenly bodies seems to have been less ancient than the poetical conception of the spheral harmony; as to the relation of particular numbers to concrete phenomena, little agreement is to be found. (Zeller 1881: 509)
I'm probably going to have to deal with Philolaus much much more, what with both Plato and Aristotle so frequently hanging on him.
Heracleitus mentions him as a man who laboured beyond all others to amass knowledge, and who by his evil arts, as he calls them, gained the reputation of wisdom; but whether this wisdom consisted in philosophic theories, or in empirical knowledge, or in theological doctrines, or in practical efforts, cannot be gathered from his words. (Zeller 1881: 510)
"Of all men, Pythagoras, the son of Mnesarchus, most practiced inquiry; his own wisdom was eclectic and nothing better than polymathy and perverted art" (in Ueberweg 1889: 44-45).
The words ἱστορία and πολυμάθεια describe the man who enquires from others, and seeks to learn, in opposition to the man who forms his opinions himself by his own reflection. (Zeller 1881: 510, fn5)
Kompileerija, mitte mõtleja.
But though direct evidence fails us yet on general grounds, it is probable that at any rate the fundamental thoughts of the system emanated from Pythagoras himself. In the first place this furnishes the best explanation of the fact that the system, so far as we know, was confined to the adherents of Pythagoras, and, among them, was universally disseminated; and moreover, that all that we are told of the Pythagorean philosophy, in spite of the differences on minor points, agrees in the main traits. (Zeller 1881: 511)
We are told that "the Pythagoreans were scrupulous to preserve the purity of their doctrine" (Ritter 1836: 354), and "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" (Ritter 1836: 342).
Secondly, the internal relation of the Pythagorean theory to other systems gives us reason to suppose that it originated previously to the beginning of the fifth century. Among all the later systems, there is none in which the influence of the Eleatic doubt concerning the possibility of Becoming does not manifest itself. Leucippus, Empedocles, and Anaxagoras, however their views may differ in other respects, are all at one in admitting the first proposition of Parmenides, viz., [|] the impossibility of Becoming, and consequently in reducing birth and decay to mere change. The Pythagoreans might be supposed to be especially open to the influence of these profound doctrines of their Eleatic neighbours; but not a trace of this influence is to be found. Empedocles, who alone, while adhering to the Pythagorean life and theology, is as a philosopher allied to Parmenides, on this very account departs from the Pythagorean school, and becomes the author of an independent theory. This tends to prove that the Pythagorean philosophy not only did not arise out of an attempt to reconcile the Heracleitean and Eleatic doctrines, but that it was not even formed under the influence of the Eleatic system. On the other hand, the Eleatic system seems to presuppose Pythagoreanism; for the abstraction of reducing the multitudinous mass of phenomena to the one concept of being, is so bold that we cannot avoid seeking for some historical preparation for it; and no system adapts itself better to this purpose, as has already been shown (p. 204), than the Pythagorean, the principle of which is exactly intermediate between the sensible intuition of the ancient Ionians, and the pure thought of the Eleatics. (Zeller 1881: 511-512)
This is indeed not impossible: "we are informed by a statement by no means improbable, that he [Parmenides] was less a disciple of Xenophanes than of Ameinias and Diochætes, of whom the latter is styled a Pythagorean" (Ritter 1836: 445).
7. Pythagoreanism in combination with other elements: Alcmæon, Hippasus, Ecphantus, Epicharmus [p. 521-533]
He [Alcmæon] explained sleep by the repletion of the blood-vessels, and waking by the emptying of them (Plut. Pl. v. 23, 1). (Zeller 1881: 522, fn2)
Kui seda tõlgendada aju jääkainete väljutamise mõttes, siis väga ei eksigi.
The leading point of view in these theories [of Alcmæon] is, on the one hand, the opposition between the perfect or celestial, and the imperfect or terrestial; and on the other, the spiritual affinity of man with the eternal. The heavens and the heavenly bodies are divine, because they uninterruptedly revolve in a motion that returns into itself; the race of man, on the contrary, is [|] transitory, because we are not in a position to unite the beginning with the end - to begin a new course after the expiration of our period of life. Our soul, however, is exempt from this transitoriness: it moves eternally, like the stars, and is therefore immortal. (Zeller 1881: 523-524)
It is once again somewhat difficult for me not to read this ufologically: the celestial is "perfect" and the terrestial "imperfect" in the sense that the rest of the galaxy is ruled by a federation of telepathic races, whereas our planet is a kind of wild zoo, like a national park in a sense. We are "transitory" in the sense that our planet is not for long - it is threatened by too many cosmic dangers (we are too close the center of the galaxy to be eternal).
So also its knowledge is not limited to the sense-perception - but it has also understanding and consciousness. But everything human is on this account imperfect. The gods know what is hidden, we can only conjecture it: they enjoy a uniform existence; our life moves between contraries, and its healthfulness depends on the equilibrium [|] of opposite forces; when, on the contrary, one of its elements gains a preponderance over the others, sickness and death are the result. (Zeller 1881: 524-525)
(1) sense-perception - Motivity; (2) understanding - Spontaneity; (3) consciousness - Rationality. Our contraries - opinions.
Respecting Hippasus and Ecphantus our information is still more scanty. As to the former, the ancient writers themselves seem to have known no more than is to be found in Aristotle - namely, that, like Heracleitus, he held fire to be the primitive matter. The farther statements, that he declared fire to be the Deity; that he made derived things arise out of fire by rarefaction and condensation; that he thought the soul was of a fiery nature; that the world was limited and eternally moved, and subject to a periodic transformation: all these must be mere inferences from the comparison of him with Heracleitus, since even the scholars of the Alexandrian epoch possessed no writing of his. It was perhaps this approximation to the Heracleitean doctrine which made later writers call him a spurious Pythagorean, and the head of the so-called [|] Acusmatics; elsewhere he is spoken of purely and simply as a Pythagorean, and fragments of writings are adduced which were falsely attributed to him on this supposition. If we enquire by what means he could have been led, as a Pythagorean, to the theory ascribed to him, it is most obvious to think of the doctrine of the central fire. According to the Pythagoreans, this fire was the germ of the universe, to which everything else had reference; and Hippasus seems for this reason to have regarded it as the matter of which all things consist. There is every probability, however, that he was also influenced by the example of Heracleitus, and that his theory thus resulted from a combination of the Pythagorean and Heracleitean doctrine. (Zeller 1881: 526-527)
This I once again read as support for the arbitrary thesis that the central fire is the center of the galaxy.
