Philip's Πυθ.

Philip, James A. 1966. Pythagoras and Early Pythagoreanism. Toronto: University of Toronto Press. [De Gruyter]

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1. The Problem [3-7]

I embarked on an inquiry into Pythagoreanism in order to discover what was the nature and extent of Pythagorean influence on Plato, an influence to which all commentators allude. I found that the pre-Platonic evidence was slight, and that it was greatly inflated by a literature of interpretation and conjecture in which both early and late sources were used. (Philip 1966)

Mõned uurivad pütaagorlasi, et mõista Platonit; mõned loevad Platonit, et uurida pütaagorlasi.

Pythagoras casts a long shadow in the history of Greek thought, but whan we attempt to discern the person casting that shadow, when we look for a figure of history and a body of doctrine, then Pythagoras eludes us. Ancient sources provide us material ampler than that for any other Greek thinker, but it is only as they become more distant in time from Pythagoras that the accounts grow more precise and more detailed; after a millenium they tell us the composition of the cakes that were his principal sustenance. (Philip 1966: 3)

"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." (Zeller 1881: 308-309)

So there emerges a multifarious Pythagoras who can be depicted, and has indeed been depicted, as anything from a Greek shaman to the first mathematical physicist, and whose doctrines become anything from elaborate para-mathematical system to religious mumbo-jumbo. (Philip 1966: 3)

Huvitav kas Esmasust, Teisesust ja Kolmasust võiks ka nimetada paramatemaatiliseks?

The questions he [the inquirer] asks are vague and general ones, such as: How did the speculations about physis of the earliest natural philosophers move from the physical towards the conceptual? Who first saw physical problems quantitatively, and put physical thought on the road to quantitative abstraction? How did the notions of identity and contrariety, of unity and plurality, acquire their role? And above all how and why does philosophy become a way of life as well as a mode of inquiry? Pythagoras is the deus ex machina who provides us with the answers to these questions. He not only formulates the problems; with the aid of a Pythagorean "brotherhood" he develops his answers, and defends them against attack, until they can be delivered safely into the hands of Plato. (Philip 1966: 4)

Mõned näited mõtteloolistest küsimustest, mille alguspunktis seisab Pythagoras oma koolkonnaga.

I have sought to establish elsewhere that he [Aristotle] had adequate sources of information, that he is a principal source for subsequent writers, and that there is no esoteric tradition deriving from a Pythagorean "brotherhood" and subsequently debouching in the Neopythagorean writings. (Philip 1966: 6)

See, et pärast pütaagorlaste Krotoonast väljapeksmist mõned liikmed panid kirja mida nad mäletasid ja pärandasid oma lastele, et need hoiaksid seda salaõpetust elus, läheneb küll juba Dan Browni loomingule.

But I have used the material of this tradition only when it throws light on the Aristotelian account. What little testimony we have that is earlier than Aristotle I have of course considered, except for hints and allusions in the Platonic dialogues. (Philip 1966: 6)

Philip seega võtab Aristotelesest säilinud katkendeid tõsiselt ja võtab eelsokraatilisi allikaid arvesse kui nad toetavad Aristotelest. Platoni dialoogidest kõigi pütaagorlike vihjete ja näpunäidete väljaotsimine on aga märksa keerulisem ettevõtmine.

2. The Tradition [8-23]

Each succeeding revival has a contemporary colouring, and the persons then calling themselves Pythagoreans feel themselves licensed to great latitude in interpreting the thought of Pythagoras, so long as they preserve in their interpretation something of the religious aura surrounding the person and something of the arithmological character of the doctrines. Such revivals occurred repeatedly in antiquity, and have since occurred. Even in our own times, in the year 1955, a World Congress of Pythagorean Societies, having the characteristic of a revival, was held in Athens. (Philip 1966: 8)

Parafraseerides Huffmanni: See Pythagoras, kellest meie räägime, ei ole enam sinu vanaema Pythagoras.

Both of them [Xenophanes & Heraclitus] were exponents of the Ionian enlightenment and could not but repudiate his departure from that tradition. In the same spirit of protest Herodotus, writing half a century later, tells us the tale of Salmoxis (Hdt. 4, 95) and though he himself migrated to Magna Graecia and knew of the Pythagoreans there (Hdt. 2, 123) he chose to pass over their history in silence. He tells us nothing of the role of Pythagoras and the Pythagoreans in Magna Graecia. (Philip 1966: 9)

Kaasaegsed ütlevad pütaagorlaste kohta selle autori arvates vähe, sest Pythagoras ajas oma asja, mis eraldus Joonia traditsioonist.

The "pro-Pythagorean" oral tradition is reflected only once in the early fragments, in a passage in which Empedocles (Vors. 31 B 129) makes reference to Pythagoras, though not by name, with a respect bordering on reverence, and in which it is plain that if Pythagoras is not already invested in the whole heroic panoply he enjoys a more than mortal status. (Philip 1966: 10)

Empedoklese filosoofial on päris kummalised kokkulangevused pütagorismiga, sh reinkarnatsioon, taimetoitlus, armastus (ja kaos), harmoonia, jne. Väga huvitav tegelane. Osad arvavad, et Empedoklese luule sisaldab pütaagorlikke õpetusi: "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).

The written tradition begins at a time critical not only for Greek but for all philosophy. In Plato's youth there were professing Pythagoreans in mainland Greece whose views were known, but the younger Plato appears to have been little influenced by them. The only plausible explanation of the radical change in his thought that later produced the Timaeus and the Philebus in his encounter with Archytas in Tarentum. Even then his writings do not reveal the extent of that influence. He refers to Pythagoras once, and to the Pythagoreans once. What we believe to be the distinguishing mark of Pythagoreanism, a doctrine of the mathematical structure of reality and of the soul that comprehends reality, is explicit only in the agrapha dogmata, or "unwritten doctrines." (Philip 1966: 10)

Platoni nooruses uitas veel elavaid pütaagorlasi Kreekas ringi. Timaios on väidetavalt tema kõige pütaagorlikum dialoog ja põhiline, mida loeti keskajal Euroopas. Philebus on üks tema hilisemaisematest/viimastest dialoogidest ja käsitleb naudingut vs teadmisi, sh piiratud vs piiritu.

Xenocrates (fr. 39 Heinze) may not have equated the One with the point - for Plato the first generated number was two - but in his treatise on Pythagorean numbers (Theol. Ar. 82-85 = Speus. fr. 4 Lang = Vors. 44 A 13) Speusippus equated point and one, line and two, plane surface and three, solid and four. (Philip 1966: 11)

"The philosophy of the "so-called Pythagoreans," however, the number theory, was dependent on the late Plato, and was basically a creation of Speusippus, who had also himself forged the book attributed to Philolaus." (Burkert 1972: 7)

Some ten years older than Aristotle and for thirty years a member of the Academy, Heraclides played an important role in the Platonic circle. He was a man of noble birth, wealthy, and of great personal dignity. The consideration he enjoyed is shown by the fact that Plato left him as the acting head of the Academy during his third voyage to Sicily, and that he was a candidate for the headship on Speusippus' death. (Philip 1966: 13)

So: (1) wealthy; (2) of great personal dignity; and (3) of noble birth. (cf. also Iamblichus 1989: 104)

As a philosopher Heraclides displayed remarkable insights and made some inspired conjectures, especially in the field of astronomy. But his principal interest was the life of the soul, the supernatural, the miraculous, the occult - an interest that appears to derive rather from the intellectual's reaction against excessive rationalism than from any recrudescence of superstition or reversion to traditional faith. The legend of Pythagoras was as if made for his purpose. He fastened on it and reshaped it. His Pythagoras emerged as a sage possessed of occult wisdom, capable of performing miracles, aware of his soul's past; as the author of an ethical rule or discipline for an austere Pythagorean way of life. His friend Speusippus sought to adapt and give expression to the more scientific aspects of Pythagoreanism. Heraclides sought to revive the Pythagorean way of life. His writings gave new life to a legend that was destined to have great influence in later antiquity and the early Christian centuries. (Philip 1966: 13)

"All of Heraclides' writings have been lost; only a few fragments remain. Like the Pythagoreans Hicetas and Ecphantus, Heraclides proposed that the apparent daily motion of the stars was created by the rotation of the Earth on its axis once a day. [...] Heraclides also seems to have had an interest in the occult. In particular he focused on explaining trances, visions and prophecies in terms of the retribution of the gods, and reincarnation. [...] [He] refers with much admiration that Pythagoras would remember having been Pirro and before Euphorbus and before some other mortal." (Wikipedia)

He [Aristoxenus], however, contributed to [|] the reshaping of the Pythagoras legend even more than did Heraclides. He appears to have been an aggressive and disgruntled man, hostile to the philosophical and intellectual tendencies of his time and in particular to the contemporary Academy. In his published Lives - he was immensely prolific - he attacked the memory of Socrates, recounting scandalous tales of his matrimonial misadventures. He attacked Plato for plagiarizing the Republic from Protagoras. As he maintained contacts with the Pythagorean group in Phlius (Wehrli, fr. 19) he may be the source for the suggestion of Timon of Phlius (Gell. 3.17.4 = Vors. 1, 399) that Plato plagiarized an early Pythagorean source also in his Timaeus. (Philip 1966: 13-14)

"Among the later Pythagoreans there are also mentioned Xenophilus of the Thracian Chalcis, Echecrates, Diocles, and Polymnastus, the common birth-place of which three was the little town of Phlius: with these it has been asserted that Aristoxenus, the disciple of Aristotle, was acquainted." (Ritter 1836: 352) - "The well-known story of Heracleides of Pontus, and of Sosicrates [...] 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)

He [Aristoxenus] did not confine himself to protest but went on to write three books on Pythagoreanism, the first a life of Pythagoras, the second a description of the Pythagorean way of life or discipline, the third on Pythagorean maxims. In these books he reinterpreted both the legend and the scientific tradition. The Pythagoras of legend was divested of many of his backward traits, such as abstinence from meat and beans, and became an enlightened sage who had taught all the doctrines Aristoxenus chose to attribute to him. The Pythagorean way of life became a discipline acceptable to the fourth-century intellectual - emphatically not the way practised by the poor, dirty, unshodden, vegetarian "Pythagorists" of his time. (Philip 1966: 14)

See seletab nii mõndagi. A la "Aristoxenus asserted a personal acquaintance between Pythagoras and Zoroaster" ja "Aristoxenus expressly contradicts" [...] "the story about Pythagoras' prohibition of beans" (Zeller 1881: 329, fn3). Selle tüübi kohta tuleb lähemalt lugeda.

When Athens grasped that a fundamental and permanent change had occurred the philosophical reaction was significant. At the turn of the century both Academy and Peripatos were tending to specialization or to literary rather than philosophical effort. They reacted to a changed world by becoming "academic" and for the time being lost their influence. Two new schools arose, the Stoic with its doctrine of total commitment and the Epicurean with its doctrine of total detachment. Stoicism was well adapted to become a religion of empire, Epicureanism to dispel the fears and anxieties of those for whom the world had become too wide, too complex, too foreign. (Philip 1966: 15)

Jutt käib kreeklaste reaktsioonist Aleksander Suure vallutustele: "Alexander's conquests in Asia and in Africa had opened up a new world of experience in that they made the Greek a citizen of a state or empire the boundaries of which were practically costerminous with those of his world, and had extended Greek culture to all that world" (samas, 15). Sotsiopoliitiline kontekst stoikute ja epikuurlaste esilekerkimisele.

But we know that in Magna Graecia scientific writings subsequent to Archytas were collected into a Pythagorean corpus during the second century B.C. (Thesleff, An Introduction, 120). In Alexandria pseudepigrapha of the same period indicate an interest in the legend rather than the science. The Pythagorean treatise excerpted by Alexander Polyhistor (D.L. 8, 24-36) about the first century B.C. testifies to the fact that during the period of Stoic influence someone chose to write a treatise on Pythagoreanism in sympathetic vein. But these are straws in the wind. Pythagoreanism if not extinct was clearly dormant. (Philip 1966: 16)

Teisel sajandil eKr valitses pütagorismi teemal peaaegu, et vaikus.

In the first century B.C. there occurred a revival of Pythagoreanism at Rome and in Alexandria that was to be of the greatest consequence for thought in the ancient world. The origins of the revival had long been disputed (see Thesleff [1961] 46-71 for a summary). Scholars have asked whether it is to be imputed to a tradition continuing underground, or to some external and non-Greek source, such as Zeller's Essenes, or simply to a contemporary initiative of scholars. They have asked whether the revival originated at Rome with Nigidius Figulus, as asserted by Cicero (Tim. 1), or in Alexandria with Eudorus and Arius Didymus. The questions that interest us here are rather - Why did the revival, occurring at the time it did, encounter such immediate success? And what changes did it provoke in the tradition? (Philip 1966: 16)

Mul ei ole sõnu millega kirjeldada, kuidas see katkend kõditab minu vandenõuteooriat, et kristlus leiutati Aleksandria intelligentsia poolt 1. sajandil eKr ja 1. sajandil pKr ning võttis põhiliseks (aga mitte ainsaks) mudeliks (neo)pütagorismi. Kahjuks ei ole meil nt Arius Didymus'e kohta palju infomatsiooni - tema elulugu Diogenes Laertiuse teoses ei ole meieni säilinud.

Greece had always been tolerant in matters of belief. From the time of Antiochus, the Hellenistic world became increasingly eclectic and increasingly tolerant in questions of philosophical doctrine. The differences between stoicizing Platonists and platonizing Stoics were negligible. The Neopythagoreans felt no compunction in adopting or adapting any doctrine that seemed to fit into their general scheme of thought. (Philip 1966: 16)

Arvata võib. Neopütaagorlased panid sinna väikese remiksi sisse.

The first stirrings of Neopythagoreanism were followed, probably in the second half of the first century A.D., by an attempt to state the teaching of Pythagoras. Moderatus of Gades interpreted the earlier [|] number theory in a metaphysical sense and symbolically. His writings, very influential at the time, are lost to us, but we have a substantial part of the writings of Nicomachus of Gerasa (fl. ca. 100 A.D.) - his Introduction to Arithmetic, Manual of Harmony, and Inquiry into the Divine Nature of Number. They are a sober restatement of Pythagorean number theory and number mysticism. Neither Moderatus nor Nicomachus by the character of their writings prepare us for their somewhat older and much more colourful contemporary, Apollonius of Tyana. He was a philosopher of some pretensions, an itinerant preacher and teacher, celibate, ascetic, a miracle-worker. He laid claim to semi-divine status and after his death was the object of a cult. (Philip 1966: 16-17)

Nimed on ammu tuttavad, aga nüüd siis tean, et Moderatus of Gades, Nicomachus of Gerasa ja Apollonius of Typana olid kaasaegsed. Vandenõuteooria osas tuleb välja osutada, et esimese sajandi pKr teisel poolel hakati kirjutama ka allegoorilisi jutustusi ühest juudi imetegijast, kelle ajaloolisest olemasolust ei ole meil 1. sajandist ühtegi usaldusväärset jälge.

Though the revival of Pythagoreanism may have been the work of scholars we see in Apollonius of Tyana that in practice it produced the salvationist doctrines characteristic of the times. Apollonius claimed to be a reincarnation of Pythagoras, and he wrote a Life of Pythagoras in which the legend was presented in conformity with his own ideals. Modern scholarship suggests that this Life was the source for the more extravagant tales in Iamblichus, but Apollonius may have been less extreme than we imagine. (Philip 1966: 17)

Peaks Philostratust lugema.

The further history of Neopythagoreanism and of its eventual fusion with Neoplatonism through Numenius (H. Dörrie, "Ammonios der Lehrer Plotins," Hermes 83 [1955] 444. n. 3), the predecessors of Plotinus, and Plotinus himself, is a part of the general history of philosophy of the period and a natural development. It is only at the end of this development that we find the life and doctrines of Pythagoras treated again. (Philip 1966: 17)

Jälle see Plotinus.

3. The Pythagoreans in the Fifth Century [24-43]

In the many discussions of Pythagorean doctrine in his treatises, Aristotle refers infrequently and only incidentally to individual Pythagoreans, and never to Pythagoras. As a rule he refers collectively to "the Pythagoreans." To what collectivity are we to suppose him to refer? To this troublesome question there are as many answers as there are historians of philosophy. The simplest solution is to say that "the Pythagoreans" are a brotherhood or religious society or sect having a body of doctrine to which the "brothers" subscribe. (Philip 1966: 24)

Igal uurijal on oma arusaam nii Pythagorasest kui ka pütaagorlastest. Selle küsimuse üle, kes on või ei ole pütaagorlane, on päris teravaid akadeemilisi lahinguid peetud (vt nt L. Zhmud).

From the fourth century onwards the lacunae in the history of Pythagoreanism began to be filled by tendentious writers. When the Neopythagoreans annexed the mathematical disciplines as their province they equipped early Pythagoreans with mathematical achievements, and Pan-Pythagoreans like Iamblichus simply swept everything they could into the Pythagorean net, as is evidenced by his all too catholic list of Pythagoreans (VP 265-267). (Philip 1966: 24-25)

Panpütaagorlased?

A few exiles collected around Lysis and Philolaus in Thebes, and there was a small group, not of [|] Italiot origin and of no great consequence philosophically, in Phlius. At about the end of the century Philolaus appears to have returned to Tarentum where political circumstances had again become favourable. The so-called Pythagorists were expelled from other parts of Magna Graecia about 390 B.C., but Tarentum continued to offer Pythagoreans a haven. It became a centre of importance for them when Archytas, a professing Pythagorean, became its strategos. (Philip 1966: 25-26)

Jällegi, kõik on tuttav, aga nüüd ilusti kokku võetud.

Hippasus is a puzzling figure concerning whom our most trustworthy source is Aristotle, and he tells us very little. The only reference occurs in his account of early opinions on first principles and causes. There he says that "Hippasus of Metapontum and Heraclitus of Ephesus make the first principle fire" (984a 7). But, Simplicius (Phys. 23.33 = Dox. Gr. 475 = Vors. 18.7) obviously alluding to the Metaphysics, tells us that "Hippasus of Metapontum and Heraclitus of Ephesus make the first principle one, in motion, limited; but for them it is fire, and they assert that existing things come to be from fire by condensation and rarefaction, and are again broken up or dissolved into fire, that being the only substrate of the physical world." (Philip 1966: 26)

Talletan küsitavuse pärast, kas tuli, üks, liikumine ja "piiratud" moodustavad mingi seotud ahela.

Aristoxenus was no doubt aware of the crass contrast between the ideal of the Pythagorean sage he was seeking to depict and the dirty, barefoot, vegetarian Pythagorists of the Middle Comedy (Vors. 1.479-480). He could not deny that they "belonged," but somehow he must present them as second-class Pythagoreans. He will have felt no compunction in inventing a suitable tale around a nebulous Hippasus. (Diels, Elementum. 63, remarks that "the confusion of Hippon, Hipponax, Hippys, and Hippasus in our tradition is an almost inextricable one.") This Hippasus, in that he held fire to be the first principle, was already stamped as deviant if not dissident. Aristoxenus may himself have added the betraying of mathematical secrets. He was not inclined to the excessive mathematical emphasis of the Academy. In any case he must have had some hand in creating this early, and disreputable, forerunner of the acusmatici, though he himself did not use the terms mathematici and acusmatici. (Philip 1966: 29)

On võimalik, et Aristoxenus leiutas Hippasuse ja loo sellest, kuidas Hippasus reetis pütaagorlaste matemaatilisi saladusi ("irrational numbers and incommensurability"), et eristada oma ideaali Pythagorasest kui õpetajast neist räpastest, paljasjalgsetest taimetoitlastest, keda tunti samuti pütaagorlastena (vähemalt Theophrastose komöödias). On võimalik, et Iamblichus omakorda leiutas selle eristuse põhjal matemaatikud ja akusmaatikud.

The view that commands widest acceptance is that, towards the end of the fourth century, when many [|] Pythagorean pseudepigrapha were written, someone set himself the task of writing a book purporting to be a treatise On Nature by Philolaus. This forger may have used genuine writings of Philolaus, but he has one eye on the Academy, whose curiosity about things Pythagorean was intense. He has produced a brilliant and convincing document, telling the fourth-century Platonist (as it also tells us) precisely what he would most wish to know, with that hierophantic concision that Plato had taught them to regard as archaic. But even if we could regard the fragments as genuine, in whole or in part, they would not enable us to solve our problems. For they reveal a thinker of no great stature, whose interests are peripheral. (Philip 1966: 31-32)

On võimalik, et Philolause raamat, mida Aristoteles kasutab, on võltsing kirjutatud ajal mil selliseid võltsinguid kirjutati rohkesti, sest Aristotelese Akadeemias oldi kõigest, mis puudutas pütagorismi, väga huvitatud.

If we are surprised to find intuition used as a tool of inquiry in the last half of the fifth century, we need only remind ourselves of the success it encountered in the fourth, in the person of Heraclides Ponticus. (Philip 1966: 33)

Üllatunud peaksime olema tõesti, sest "intuitsioon" on poolteist tuhat aastat hilisem mõiste.

Aristotle (1092b 9) uses the same illustration in asking: Are numbers causes in the sense that points are causes of solids? Eurythus, he says, used to specify the number of man or horse, representing by pebbles the shapes of animals and plants as do those who represent triangles [|] and rectancles. Alexander (826-828) explains in detail how, given the number of man, Eurythus would create a sort of mosaic portrait by the use of coloured pebbles. He would probably do so in outline, after the manner of mythical figures seen in constellations, and the original number would be arrived at arithmologically (985b 23 - 986a 12). (Philip 1966: 33-34)

Eurythus on järjekordne hämar tegelane, kelle kohta teame ainult üksikuid kuulujutte, mis ei sobitu väga hästi ka meie arusaamadesse pütaagorlastest: "A striking fact about the examples that Aristotle gives for the Pythagoren equation of numbers and things is that it is never a question of the relation of individual things and individual number - aside from the isolated fooleries of Eurythus - but of the correspondence of a plurality of things to the system of numbers, and in particular the correspondence of alterations in things to alterations in the number series." (Burkert 1972: 48)

Aristotle was well able to distinguish between the Pythagoreans and Archytas, on whom he wrote a monograph, fragments of which remain. What we know of the thought and the mathematics of Archytas bears little or no relation to Aristotle's account of Pythagoreanism in general character, themes of discussion, or methodological approach. Archytas was a mathematician who dealt with the mathematical problems of his times. He was not an antiquarian and did not archaize. But the Pythagoreans of Aristotle'saccount propounded a cosmology. The problems they faced, and the attitudes they assumed to these problems, were not those of the early fourth century but of a much earlier time. (Philip 1966: 34)

Kosmoloogia on võib-olla see, mis jääb järele, kui kõik paremad palad endale võtta: "what was essential, or "fruitful," in their doctrines agrees with Plato and Aristotle, and that they could make no good use of what historical tradition had to offer as the ἴδια of Pythagoreanism" (Burkert 1972: 95).

They key figure is Parmenides. Parmenides was born, according to Apollodorus, about 540 B.C. or, if we take the date to be inferred from Plato's Parmenides, about 515 B.C. He is said to have "heard" Xenophanes, a critic of Pythagoras, but then, departing from him and his teachings, to have "followed" Ameinias, a Pythagorean to whom he dedicated a tomb. What we may take as certain is that Parmenides could not have been born and have lived his life in Magna Graecia without being familiar with Pythagorean doctrines. (Philip 1966: 35)

Lühidalt, "the Eleatic system seems to presuppose Pythagoreanism" (Zeller 1881: 512).

The origins of the Atomists theories can be explained without recourse to a hypothesis of Pythagorean influence. But that they may have had reference to the doctrines of Pythagoras, such as those mentioned by Aristotle, is rendered plausible not only by the obvious and admitted similarities of monad and atom, but also because our tradition tells us of an interest shown by Democritus in Pythagorean doctrine, and indeed of a book of his having the title Pythagoras. So it is possible that Pythagorean doctrine was present and working as a leaven in Atomist theories. It need not surprise us that it did not produce mathematical inquiry in the strict sense. It could produce only curious number speculation until the development of mathematical method, and mathematical method was not evolved by the Pythagoreans. (Philip 1966: 37)

"We have the testimony of a contemporary that Democritus studied with a Pythagorean" (Burkert 1972: 259).

Aristotle (987a 29-31) tells us that Plato's thought, though it had its own peculiar characterestics, was in most respects based on the theories of the Pythagoreans; and by Pythagorean theories he must mean those theories he himself has described in passages immediately preceding, principally theories having to do with number. But every theme that Plato uses undergoes a sea-change, a process of re-thinking and re-imagining that makes it impossible to distinguish between tradition and innovation. (Philip 1966: 37)

Nii konkreetselt siis ütlebki. Metafüüsika 1. peatükk. (Siin kahjuks vahele jäetud.)

Perhaps the clearest reference is in the Philebus (16c): "This is the technê I mean. To my mind it is a gift of the gods which somehow they sent us down by means of a Prometheus, with a kind of clearest fire; and the ancients, being better men than we and not so far removed from the gods, have bequeathed us the tradition that things that are said to be proceed from a one and a many, and that they have as original constituent [|] a Limit and an Unlimited." In the theory Plato here presents, the Prometheus is likely to be Pythagoras - though not all scholars agree - and the contrariety peras/apeiron must be Pythagorean. (Philip 1966: 37-38)

Konkreetne katkend Philebus-est. See on see "philosophy of Limit and Unlimited, of number and harmony, to which Plato alludes in the Philebus and which Aristotle ascribes to the Pythagoreans" (Burkert 1972: 276-277).

4. The Opposites [44-59]

Anaximander (12 B 1) spoke of the elements "making reparation" to one another, and so preserving the order or balance of the universe while admitting cyclical process. He was compelled to recognize, however dimly, that there must be not only a substrate but also some form of causation. The solution of Alcmaeon of Croton (Vors. 24) is a similar one, but for him the cosmic forces were in isonomia or balance rather than in conflict. His opposites were the homely ones of the physician - wet and dry, hot and cold, bitter and sweet - and between these the balance which is health must be kept. This balance must be maintained not only for physical well-being but also in the isonomia of states and in the process of the cosmos. (Philip 1966: 46)

Kosmilised jõud on võrdõiguslikud.

But opposites were no peculiar mark of early Pythagorean thought. Indeed it would appear that they were less concerned with contrariety than other thinkers of their own time, except in one important respect. The idea of Limit/Unlimited appears to have been fundamental. From that one pair of contraries they generated both the universe and number. (Philip 1966: 47)

"The Pythagoreans described the origination of the world as a union which came to pass between the opposite principles of the unlimited and the limiting, the even and the odd." (Ritter 1836: 285)

Aristotle then continues 968a 22:

Other Pythagoreans say the first principles are ten, each of them a pair of opposites, arranged in a so-called Table:

Limit	Unlimited
Odd	Even
Unity	Plurality
Right	Left
Male	Female
At Rest	In Motion
Straight	Curved
Light	Darkness
Good	Evil
Square	Oblong

[.|.] The list itself exhibits no logical sequence nor structure. We have first the primary oppositions (pairs 1 and 2). There follow unity and plurality (3), four pairs that may be cosmological (4-8), an ethical pair (9), and a geometrical pair (10). The table would appear to have been padded out to the perfect number of the tetractys. It is significant because of the ethical character that has been given to contrariety, all those subsumed under Limit having an obviously "good" colouring, those under Unlimited "bad." That the opposites were so interpreted in the Pythagoreanism of the fourth century we need no doubt. It is improbable that the original pairs were all so qualified. (Philip 1966: 47-48)

"Naissoost" ja "meessoost" on kosmoloogiline vastandus? Kõige selgemõistuslikuim tõlgendus, mida ma praegu oskan anda, on tabeli kokkulangevus numbritega. Naine ja mees on tabelis viiendal kohal; 5 sümboliseerib abielu (2 - naine; 3 - mees). (vt Zeller 1881: 411 ja Burkert 1972: 33, fn27)

What he [Aristotle] himself understands by Limit emerges from his definition of peras (1022a 4-13) as (1) the limit or boundary of a given thing, (2) its form or figure (eidos), (3) its extreme limits - terminus ad quem or a quo, (4) its essence or being. Aristotle adds that it has as many meanings as arche (first principle) with which it is often synonymous. Of the meanings here given, form or figure (eidos) suggests the Pythagorean term chroia, and chroia appears to be equated with peras in one of Aristotle's few discussions of Pythagorean cosmology (1091a 12-18):

It is absurd and indeed impossible to erect a theory ascribing coming-to-be (genesis) to eternal things. Yet without a doubt the Pythagoreans do so. They say that when the One has come into existence, by being put together from plane surfaces or surface limits (chroia) or seeds or some unspecified constituent, at once Limit draws in to itself and limits the nearest parts of the Unlimited.

This theory that Aristotle summarily dismisses is a cosmological one, and as such not immediately relevant to our inquiry into the nature of the primary opposition. What we may note is that Limit is conceived of as an active force operating on (a passive) Unlimited to produce the One, our physical world. Then, the One having come to be, Limit persists in its active role, drawing in to itself the nearest part of the Unlimited, elsewhere (1048b 10) equated with the Void. At the same time, under the guise of chroia, Limit has the further role of surface or limit of things. It is at once a cosmological first principle, a principle creating discrete quantities (Burnet EGP 108) and the exterior surface of these quantities. (Philip 1966: 50)

"As Ross remarks on De Sensu 439a 30, the original meaning of χροιά is skin. By it the Pythagoreans mean surface, and were not identifying surface nad colour, colour being a later meaning of the word. Cf. 1028b 16." (ibid, 58, note 10)

He [Aristotle] says that (15-16) Limit (peperasmenon - that which has been limited) and Unlimited, a pair that has no other "matter" constituting it is the Pythagorean material cause. But immediately thereafter (18) the pair is referred to as the One and the Unlimited. So "that which has been limited" is the One. (Philip 1966: 51)

Apeiron, peras, peperasmenon.

Earlier (987a 17-21) when the procession of Pythagorean archai was described, the following order emerged:

Limit - Unlimited
Odd (Limited - Even (Unlimited)
The One (even-odd)
Numbers that are things

In the present passage the One (as limited) is paired with the Unlimited. We infer that Aristotle distinguished between the primary cosmological opposites peras and apeiron and the opposites that are material cause in our physical world. (Philip 1966: 51)

Siin jääb mulje, et piir ja piiramatu ühendus annab kas paaris (piiratud) või paaritu (piiramatu), mille ühendus omakorda annab Ühe (mis on korraga paaris-paaritu), millele juurde lisamine-liitmine annab kõik ülejaäänud asjad (elu, taimed, loomad, inimesed, kangelased ja jumalad). Koos tabeliga: (1) piir ja piiramatu; (2) paaris või paaritu; (3) ühtsus (mis on paaris-paaritu) või paljusus; - ja siis ülejäänud asjad - (4) vasak/parem; (5) meheline ja naiseline; (6) paigalolek ja liikumine; (7) sirge ja kõver; (8) valgus ja pimedus; (9) hea ja halb; (10) ruut ja ristkülik. Mul on aimdus, et neid kõiki ühendab mingi üleminek, mis ühendab või lahutab, ja mida tuleks mõtestada piiramise võtmes.

It may be further urged that there is no conflict with the peras/apeiron theme as developed in the Philebus, nor with the theory vaguely outlined in the Philolaus fragment (infra 112-117). Nor is there any Platonic contamination of One and indefinite dyad, or of point, line, surface, solid. (Philip 1966: 53)

Hackforthi tõlge.

5. Pythagorean Cosmology [60-75]

They fail to explain to us how, if they assume only Limit/Unlimited and Odd/Even, motion is to occur, and how, without motion and change, generation and destruction can take place and the movements of the heavenly bodies. Further, even if one were to grant them that spatial magnitude proceeds from these first principles, or if this were proven, how would some bodies be light, others heavy? For to judge by their assumptions and explanations, what they say applies equally to mathematicals and sensibles. The reason why they have nothing to say of fire or earth or such (physical) bodies is, I suppose, that none of their teachings is peculiarly applicable to sensibles.
Further, how are we to understand the thesis that number and the modifications of number are the cause of the things that come to be and are in the universe, both in the beginning and at the present, and yet that there exists no number other than the number out of which the universe was framed? In one part they situate opinion and opportunity, then a little closer to or farther from the centre of the universe injustice and decision or mixture. They allege as a proof that each of these is a number, but it so happens that there are already in this place many composite magnitudes, because such modifications of number occur in each and every region. Are we to take it that this self-same number which constitutes things in the physical universe also constitutes the things mentioned? Or is it not this but some other number? Plato says it is another number. He too considers physical magnitudes and their causes to be numbers, but he considers the magnitudes to be perceptible, and the intelligible numbers to be causes. (Aristotle 990a, in Philip 1966: 62)

Arvamus (2), võimalus (7), ebaõiglus, otsustamine (vt Ritter 1836: 400). Ebaselge, kas ebaõiglus ja otsustamine/segunemine on ka sümboolsed arvud või kuskil arvamuse ja võimaluse vahepeal. Võib-olla on see üleüldse bunk: "See also [Alexander's] remarks 74.3-75.23, where, however, his equation of dyad and doxa is not Pythagorean." (ibid, 71, note 2)

In this passage Aristotle is not as sharply critical as he later becomes of Platonic number theories and of the Pythagorean theories which he holds to be allied to them. He has failed to appreciate the possibilities of mathematical physics, which we may consider to have been intuited by the Pythagoreans and adumbrated by the Plato of the Timaeus, but the criticisms he makes are justified. (Philip 1966: 63)

"For a discussion, from the point of view of the physicist, of Aristotle's account of Pythagoreanism, and of his failure to see its potentialities see Sambursky [pp.] 45-48." (ibid, 71, note 3)

He [Aristotle] goes on to say (1066a 7-16 = Phys. 201b 16-26):

That this is a sound definition is clear from what other thinkers have to say about motion, and from the fact that it is difficult to define it otherwise. One cannot put it in another genus than that in which we have put it, as is clear if it is considered how some define it when they say that motion is otherness, or inequality, or non-being. None of these is necessarily in motion. The process of change does not originate nor terminate in them, any more than it does from their opposites. Motion is thus defined because it appears to be an Unlimited, and the first principles in the one column of the table of opposites are all unlimiteds because they are privatives.

Here the Pythagoreans are not mentioned by name, but the "table of opposites" is held by commentators, both ancient and modern, to refer to that mentioned earlier (986a 25) or to some similar Pythagorean table, where the primary opposition is Limited/Unlimited, and where under Unlimited are subsumed terms that in Aristotle's terminology are privatives, matter, form, and privation being the factors involved in his theory of motion and change. But though At Rest/In Motion appears in the table Same/Other, Equal/Unequal, Being/Non-Being do not. These pairs are more reminiscent of Plato in the Sophist. (Philip 1966: 63)

Paigalolek on liikumise puudumine, sirgus on kõveruse puudumine ja headus on halbuse puudumine, aga kas mehelikkus on naiselikkuse puudumine või kas valgus on pimeduse puudumine või kas ruut on ristküliku(likkuse?) puudumine?

The Pythagoreans too assert the existence of a void, and that it enters the universe as it were breathed in from the infinite breath. This void delimits existents [physeis], it being a sort of separation and delimiting of things adjacent to one another. It is also primary in the case of numbers, the void delimiting their nature.

(Fr. Sel. p. 137): In the first book of his monograph on Pythagorean philosophy [Aristotle] writes that the universe is one, and that it draws in to itself from the infinite [apeiron] time and breath and the void, which has the function of delimiting the space occupied by individual existents.

In his long discussion of the term "apeiron" in the Physics, Aristotle first points out the difficulties inherent in the concept "infinity." (Philip 1966: 64)

"Burkert seems to suggest that this notion of time (as breathed in at the constitution of the universe?) is prior to and implied in Plato Tim. 37d. [...] Aristotle makes no reference to any other Pythagorean time doctrine." (ibid, 71, note 4)

Both cosmology and first principles are again subjected to an exhaustive critique at the end of the Metaphysics, and there Aristotle again allows his theme to dictate his approach. Pythagorean theories interest him chiefly because he considers them to have been an important source for Platonic theory, and it is Plato's theory of idea-numbers that is here as elsewhere the principal butt of his attack. (Philip 1966: 65)

Ma ikka veel ei väsi kogumast selliseid üldisi väiteid.

So from the first the Pythagorean peras and apeiron were mathematically conditioned or coloured. Not only were Odd and Even subsumed under Limit and Unlimited. They were in some functions, identical with them. The first peperasmenon, the One, which is "even-odd", is a product of both pairs. (Philip 1966: 68)

Üks mu tühine-spekulatiivne küsimus on, kas ei ole võimalik, et ka ülejäänud tabelis toimib samasugune ühendumine?

The key role in Pythagorean thought that Aristotle ascribes to the apeiron is in itself remarkable. For the apeiron is central only in the thought of Anaximander, and in that of no other Presocratic thinker. Pythagoras was a younger contemporary of Anaximander, by whose thought he was probably influenced during his formative years and his maturity in Samos. Its two features most likely to have acted as stimuli are the notion of apeiron and that of structure capable of numerical expression. Both of these doctrines are reflected in Aristotle's report. (Philip 1966: 69)

An endnote recommends Solmsen, Friedrich 1962. Anaximander's Infinite: Traces and Influences. Archiv für Geschichte der Philosophie 44(2): 109-131. DOI:10.1515/agph.1962.44.2.109 [De Gruyter]

If we are to deny the possibility that the thought Artistotle reports as Pythagorean is in substance the thought of Pythagoras himself, then we must deny to Pythagoras, as many have done, any status as a thinker. We must deny that he, though an Ionian of the sixth century, can have been deeply influenced by the intellectual tendencies and speculations of his day. And we must explain the long shadow he cast as the shadow of a subsequent construct rather than that of the historical person. (Philip 1966: 70)

Karm.

6. Pythagorean Number Theory [76-109]

Regarding the internal mechanism of our world in Pythagorean theory he isprodical of hints, but the implications of these hints is for ancient as for modern commentators a matter of dispute. One of the recurring themes of the treatises, a theme Aristotle pursued compulsively, was Plato's Theory of Ideas. He never appears to feel that he has refuted it once and for all. In contexts where the theory is relevant he sometimes offers merely an allusive, pro-forma refutation, but often devised a new one appropriate to the question under discussion. He [|] argues, not against a standard version of the Theory of Ideas but against every variation of it, from the early statements in the Phaedo to the agrapha dogmata, and to the modifications introduced by his own contemporaries in the Academy. In this context he makes frequent reference to the Pythagoreans. He does so in part because to his mind their number theories anticipate the Theory of Ideas but chiefly because he is persuaded (an assertion we still have not succeeded in swallowing) that (987a 29) "On the philosophical systems I have mentioned there followed Plato's school and thought. In most respects Plato followed the Pythagoreans, but some features were peculiar to his own system and non-Pythagorean." (Philip 1966: 76-77)

Aristoteles vastandus ikka väga tõsiselt Platoni ideedeõpetusele.

The Neopythagoreans and Neoplatonists, however, deal with it at great length. Their views are known to us from the extant mathematical treatises of Nicomachus of Gerasa (2nd cent. A.D.) and Iamblichus (3rd-4th cent. A.D.) and from numerous incidental references, especially in Plutarch and Sextus Empiricus. The picture they present of Pythagorean number theory is, in many respects, remarkably similar to that of Aristotle. They are not concerned with mathematical science proper but with speculations about number itself as a first principle, and about particular numbers as having special significance. (Philip 1966: 77)

E.g. "the number 729 has for Plato also [...] an especial significance" (Zeller 1881: 459, fn2).

We note here that reference is to the decad and not to the tetractys, which is neither tetrad nor decad. The tetractys does not designate any one number, but is a summation of numbers, being 1 + 2 + 3 + 4 = 10. It gets its name from τέτραχα (Plato Gorgias 464c) formed on the analogy of δίχα τριχα, and so has as its basic meaning "in four parts or ways." According to the Commentary of Hierocles (FPG 1, 408) on the Carmen Aureum (48), this is the meaning implied in the Pythagorean oath - "by him who brought our kind the tetractys, in which is the source and root of everlasting nature." The oath is often regarded as a document of early Pythagoreanism attesting the tetractys as a central doctrine. But it has been pointed out that the oath cannot be earlier than Empedocles whose term rhizoma - root is used, and if by γενέα we are to understand "Pythagorean sect" rather than "human kind" then it is likely to be much later. (Philip 1966: 97, note 5)

464c esitab neli valdkonda "medicine and gymnastic, justice and legislation", aga seos tetraktiga on (veel) arusaamatu. Vt ka: Heninger, S. K. 1961. Some Renaissance Versions of the Pythagorean Tetrad. Studies in the Renaissance 8: 7-35. DOI: 10.2307/2856986 [JSTOR]

His account does not reflect an interest on the part of the Pythagoreans in arithmetic or geometry, the two branches of mathematical science which they are generally supposed to have advanced. It does indicate an interest in number speculation, or arithmology or, if we are disposed to deprecate their pursuits, in number mysticism. An interest in the arcane significance of the cardinal numerals is characteristic of most peoples, and not only in a primitive period of their culture. Such an interest is reflected in the epic (G. Germain), and when mathematical knowledge began to reach the Ionians from Babylon it must have given new life to such speculations. Anaximander explained the relation of our earth to the sun and moon in terms of number relations and mathematical symmetry. Pythagoras went further. He maintained that the cosmos was not only expressible in terms of number, but was number. But there were neither means nor methods of quantitative observation. (Philip 1966: 79)

"We can define arithmology as a literary genre of popular philosophy, originated in the framework of Neopythagoreanism, that systematized various speculations on the generation, properties and extra-mathematical significance of the first ten numbers in their relations to each other." (Zhmud 2021: 347)

Ad 1083b 8 [Alexander] 767.9-21 describes their operations as being very simple. They say, for instance, that water is the number nine. Nine is the square of a prime number which, being odd, lies between (and so limits) two even numbers. These characteristics of nine are the characteristics they seek in water. The particular operations Alexander describes may be Neopythagorean, but similar procedures characterized Pythagorean arithmology in all periods. (Philip 1966: 101, note 9)

See kivikestega mängimine on juba natuke tuttav (vt Burkert 1972: 435, fn 49).

The second thesis is that the Way of Truth itself is a reaction to Pythagorean cosmology. Raven (KR 272-277) argues that "each of his [Parmenides'] affirmations involves a corresponding denial" (273) and that the predicates of the One which he is rejecting are Pythagorean predicates of their One. If we may take it that the Pythagorean cosmology against which [|] Parmenides was reacting was the cosmology described by Aristotle, and that Parmenides was denying a generation of the cosmos, a surrounding void, and a procession of number from the One, then the thesis that the Way of Truth was a direct reaction to Pythagoreanism seems to me to gain weight. The proem describes a journey to the source of truth, undertaken to discover or learn truth. It seems both probable and credible (though incapable of proof) that what Parmenides describes is a wrestling with the philosophical system that, in his youth, had most authority in Magna Graecia - Pythagoreanism. (Philip 1966: 89-90)

Põnev lugu.

The notion of apeiron is Anaximander's. Pythagoras is the only succeeding thinker who adopts it in the sense in which it was propounded (74. n.12), and it seems more likely that Pythagoras should have adopted it before his departure from Ionia than that some [|] subsequent western thinkers should have revived it. If we try to impute the paternity of the idea to a successor of Pythagoras in the first half of the 5th century we are forced to postulate an X (Hippasus will not do), living in the year "Pythagoras-minus-30," as the father of Pythagorean doctrine. On the other hand, we suppose that this X lived in the second half of the century (and Philolaus will not do) he is curiously untouched by post-Parmenidean speculation and the critique of Zeno. (Philip 1966: 93-94)

Pythagoras oli Anaximanderi ainus siiras järgija?

If the Pythagoreanism of Aristotle's report is to be attributed to Pythagoras himself, how can he have arrived at those theories? We may assume that Pythagoras either "heard" Anaximander or read his writings, and that the companion notions of a Boundless and of mathematical determination will have made particular impression on [|] him. Further, Babylonian mathematics, when they became familiar to the Ionians of the sixth century, may have provided the stimulus and excitement that the opening up of a new world of ideas often gives to its epoch. As, a century earlier, Ionia had come under orientalizing influences in art, so in the sixth century Thales, Anaximander, and Pythagoras may have come under the influence of Babylonian mathematics as a revelation of a new idiom in which the mind could express its thought. (Philip 1966: 94-95)

"We may imagine this to have occurred much as the ideas of Darwinism, Freudian psychology, relativity, however much garbled and watered down, took possession of imaginations for a few decades." (ibid, 109, note 18)

7. Astronomy and Harmonia [110-122]

The nature of our tradition creates further major difficulties. Here, as in mathematics, we find all astronomical thinkers whose allegiance is at all doubtful being dubbed Pythagoreans. This myth of Pythagorean science is generally accepted by the later doxography and the commentators, who can be used to supplement or to verify Aristotle's account only with caution. (Philip 1966: 110)

Tüüpiline ebakindlus.

There are some who assert that there is a left and a right in the universe, as do the Pythagoreans - (for this thesis is theirs). Let us inquire whether there is a right and left as they describe them or if some other description would be more appropriate if we are going to apply these terms at all to the physical universe. [...]

So, Aristotle goes on to say (285a 1-13, 25-27), we quarrel with the Pythagoreans because they recognize only one of the three pairs of translatory motions and that not the most important pair, and because they think that that pair, right/left, applies to all existents equally. (Philip 1966: 111)

Meikib senssi kui nad seavad kivikesi kahele poole ja "üks" on nende vahel/keskel, eraldab paremat ja vasakut.

It is true that we may properly apply right/left as well as the prior pair up/down to the universe because it is a living creature. But the "up" part of the living creature must be the southern hemisphere because only so will the heavenly bodies rise from its right. This is the opposite of what the Pythagoreans assert (285b 25-28). For them we are in the upper part of the universe and the heavenly bodies rise on our right. (That is, the Pythagoreans imagined themselves in the position assumed by soothsayers and diviners, facing north.) (Philip 1966: 111)

Pütaagorlased vaatavad põhja poole.

Alexander (38.8-39.19 = Ross, Fr. Sel. 138-139), commenting on the passage in the Metaphysics (985b 27) where things are said to be numbers, remarks: "As the sun is the cause of seasons they assert that it has its place where the seventh number (which they call 'due season') is located. For the sun occupies the seventh place from the periphery among the ten heavenly bodies moving around the hearth at the centre. Its orbit comes after the fixed stars and the five planets. After the sun comes the moon as eigth, next the earth as ninth, and then the counter-earth." (Philip 1966: 113)

7 - päike, 8 - kuu, 9 - Maa.

Philolaus wrote a book, probably a short one, that treated of most aspects of Pythagorean doctrine including first principles, cosmology, numbers, astronomy, music. Its emphasis may have been on music. This book was perhaps a product of Pythagorean piety, an effort to state the doctrines of Pythagoras because they seemed to be threatened by oblivion, but what Philolaus can have recollected from instrution in his youth or have learned from hearsay in the course of his years in exile would have been scanty and vague, its tendency being towards ethical paideia.
What knowledge of this book can be derived from the fragments or inferred from Aristotle suggests that it was unscientific and without real philosophical understanding of the doctrines it reports. It was, however, the earliest written document of Pythagoreanism. Though Plato, Speusippus, and Aristotle will have known, from their contacts with the circle of Archytas, that it could not have any canonical status and that its doctrines had a larger background, nevertheless, it existed as written word. So it served as a basis for the interpretation of Pythagoreanism, the first generation of the Academy either using it cautiously or reinterpreting it, the doxography using it as an authoritative source. So Philolaus' vague, airy, poetical speculation on Pythagorean themes, neither philosophy nor astronomy, probably furnished a background for the ethical paideia of Pythagoreans in mainland Greece during the last half of the fifth century. It was for this ethical paideia that they were held in singular respect and esteem. (Philip 1966: 116)

Ilus kokkuvõte.

8. The Harmony of the Spheres [123-133]

Only in a secondary and occasional instances does άρμονία mean concord, the musical attunement which we observe as present in musical sounds. In origin and usually it is a "fitting together," primarily of things, that is imposed by a craftsman or maker. In the Iliad (5.60) Phereclus, the builder of the ships in which Paris carried off Helen, and a favourite of the artisans' patron Athene, is the son of Tekton (or carpenter-builder) who in his turn is the son of Harmon (or joiner). Odysseus (Od. 5.248) fits together his raft with άρμονίησιν (joints) and dowels. Anything apparently that is fashioned with joints such that they make the original pieces part of a unified structure is a άρμονία.
In the Presocratics (Vors. vol. 3 - Wortindex) we find the word used first by Heraclitus largely in a musical sense of an accord or fitting-together of sounds in a melody, each note "fitting" that which precedes it (and not as what we call harmony, part-singing or polyphonic music). But Heraclitus also refers to the άρμονία of the bow and the lyre. In Empedocles we encounter the word, personified and deified, as a fitting-together or union. Sphairos is established in the secret place of Harmonia (B 27). Bones are fitted together by the strong glues of Harmonia (B 96).
Though we find that the Pythagorean usage is predominantly musical - either as a concord or as a concordant musical scale - the earlier sense of a fitting-together-into-one imposed by a craftsman is often also present. (Philip 1966: 128, note 1)

So, "the limiting and illimination [...] converge to harmony, which is unity in multiplicity and agreement in heterogeneity" (Ueberweg 1889: 49); "It is not things that are alike and of the same kind that need harmony, but things unlike and different and of unequal speed; such things must be bonded together by harmony, if they are to be held together in a cosmos" (Philolaus, in Burkert 1972: 252).

Lasos of Hermione is said by Theon of Smyrna (59.4 = Vors. 18.13), to have discovered the musical intervals. Agathocles, Pindar's instructor in music, was also th eteacher of Damon (Plato, Laches 180d = Vors. 37 A 2) who was undoubtedly a theorist, probably not only in prosody. This Agathocles is said to have been the pupil of Pythoclides, a Pythagorean (?), and according to both Plato (Alcib. 1.118c) and Aristotle (Plut. Peric 4 = Vors. 37 A 4), Pythoclides taught music to Pericles. (Philip 1966: 126)

Pythoclidese nime kohtan vististi esmakordselt. Tal ei ole isegi vikipeedia-artiklit ja Google otsing annab ainult 98 tulemust (vs nt Agathocles annab 513,000). Vb huvitav lugemine: Else, Gerald F. 1958. "Imitation" in the Fifth Century. Classical Philology 53(2): 73-90. [JSTOR]

In Plato's Myth of Er (Rep. 617a-b) we have, for the first time, an exposition of the "music of the spheres," and musical and astronomical components are full-fledged. Eight Sirens are seated on the eight whorls [|] of the spindle of Necessity. They represent the sphere of the fixed stars, sun, moon, and the five planets. Each of the Sirens sings one note, and the succession of notes corresponds to the musical scale (Heath, Aristarch. 108-110). We are not told why these notes sounded together should produce a harmonia and there is no need to speculate, for the Platonic theory arises not in music but in astronomy. We believe that Plato had an earlier source for his myth. (Philip 1966: 126-127)

Myth of Er (Wiki) - äärmiselt huvitav lugu, aga täitsa raamatu lõpus, kuhu ma praeguses tempos niipea ei jõua.

As all these theories have some astronomical and musical background, and as the Myth of Er seems not much more advanced, although Plato's theories in the Timaeus do, it seems probable that they should all be referred to some time about the end of the fifth century. (Philip 1966: 127)

Timaios näib üsna keeruline.

9. The Pythagorean Symbola [134-150]

Aristotle's account of Pythagoreanism falls into two distinct parts. In the treatises he reports and discusses Pythagorean theories having a scientific or para-scientific character. In his monograph On the Pythagoreans he transmits a collection of material relating to Pythagorean religious practice and to legend. He makes little or no attempt to relate these two aspects of Pythagoreanism. (Philip 1966: 134)

One could say that in Aristotle's accounts of pythagoreanism, their lore and science do not meet.

The Pythagorean Symbola or Acusmata exercised the same sort of fascination on the Greek mind that they do on our own. They were felt to be curious and somehow significant, but to be altogether incongruous with the scientific character of Pythagoreanism. So we find them allegorically interpreted, explained away, sometimes repudiated. (Philip 1966: 134)

Boehm, F. 1905. De symbolis Pythagoreis. Berlin: Diss. Friedrich-Wilhelms-Universität. [Internet Archive] - Ladina keeles. "F. Boehm classifies them [symbola] according to subject, cites their occurrences in the literature, and gives parallel instances for each precept or veto from Greek or other cultures. His study was an important step towards an understanding of the symbola as a cultural phenomenon which was only incidentally Pythagorean." (ibid, 148, note 1)

There follows a list of what we would call superstitious rules and observances. All are short and imperative. Most of them have following them a brief statement of the reason for the injunction or veto. Iamblichus (VP 86) denies that these explanations are Pythagorean, and in some cases he is certainly right. He is obviously troubled by the ridiculous nature of some of the symbola (VP 105) and insists (VP 227) on the value of their arcane significations. (Philip 1966: 135)

Mõned neist on tõepoolest naeruväärsed.

We know that by the sixth century Onomacritus was engaged in a collection and editing of oracles. We know from Euripides (Alc. 967-68, Hippol. 954) that in his time Orphic writings were widely current. Plato (Rep. 364e) can speak of a mountain of Orphic writings. It seems highly probable that in Orphic or in Pythagorean circles a record would be made of the Pythagorean symbola, particularly as they may have been, at least in part, common to the Orphics. (Philip 1966: 136)

Platoni nooruses kondas pütaagorlasi Kreekas ringi (ülal) ja seal oli mägede kaupa orfistlikke kirjutisi.

We know of one such collection, made by Anaximander of Miletus (Vors. 58 C 6) who wrote an "exegesis of Pythagorean symbola" in the reign of Artaxerxes Memnon (405-359 B.C.). His work is therefore earlier than Aristotle's monograph if Aristotle entered the Academy in 368-67 at the age of seventeen. If at least one collection of symbola existed before the time of Aristotle, there may have been others. Certainly the tradition was still vigorous enough in the time of Aristoxenus for him to combat it (Wehrli, Aristoxenos fr. 25), and apparently it retained its vigour because we have knowledge of two further collections, that of Alexander Polyhistor and that of "Androkydes," before the beginning of the Christian era. (Philip 1966: 136)

Kolm sümbolikogujat.

Most of the symbola are ancient usages or superstitions that long antedate the sixth century and many of them have an almost world-wide diffusion. As has been frequently pointed out, there are parallels for them not only in primitive practice but also in Homer, Hesiod, Delphic precept, and the practices of the mysteries (Nilsson [|] 705). The conclusion is inescapable that the symbola are not Pythagorean in origin but were adopted and systematized by them as congenial and appropriate to their way of life. The question then arises whether they were common to Orphics and Pythagoreans - a question to which, as there are no Orphic documents of the period, no positive answer can be given. (Philip 1966: 136-137)

"Of all men, Pythagoras, the son of Mnesarchus, most practiced inquiry; his own wisdom was eclectic and nothing better than polymathy and perverted art" (Heracleitus, in Ueberweg 1889: 44-45).

What precisely were the relation between Orphism and Pythagoreanism in the sixth century we have no means of determining, but we may assume that they had much common ground in doctrine of the soul, demand for ritual purity, and allied notions. For our purposes however it is more important to know what their differences were, and we may infer something of these differences from the direction their respective adherents took. Plato, in a famous passage of the Republic (364b-365a), depicts the Orphics of his day as hawkers of pardons from [|] door to door, and all his references to them are contemptuous (Vors. 1 B 1-8) as are those of other contemporaries. However revolutionary their religious innovations may have been in an earlier age, by the fourth century they had degenerated into practitioners of formal rites of purification, and their writings were a chaotic mythology. (Philip 1966: 137-138)

Naljakas, et samal ajal kui Theophrastuse komöödias käivad Kreekas ringi vaesed, räpased, paljasjalgsed taimetoitlastest "Pütagoristid" (vt ülal), käivad mingid mandunud orfistid lunastuskirju müümas.

Before we attempt to answer that question we must ask ourselves whether there was a Pythagorean brotherhood, and if so what its nature was. It is generally assumed, and often unhesitatingly affirmed, that there was such a brotherhood, and that it was something like the community described by Iamblichus, with a superior, postulants, a novitiate, and at least two orders of adepts, the mathematici and the acusmatici. Any such institution would be unique in the Greek world before the Christian era. The hetaireiai and the thiasoi were familiar institutions, but they never had the characteristics of a brotherhood with a rule. (Philip 1966: 138)

Autor on läbivalt peibutanud, et tema arvates ei olnud mingit pütaagorlaste vennaskonda, millest üldse rääkida. Olulisim osa on tema teooria, et Aristoxenus leiutas matemaatikute ja akusmaatikute eristuse, et võõrandada noid vaeseid, räpaseid paljasjalgseid taimetoitlasi.

Festugière has shown (La révélation 2.33-47) that Iamblichus' picture reflects patterns of the third and fourth centuries of our era. Missionary enterprise, conversion, the establishment of ascetic communities - no unusual occurrences especially among Syrian Christians (Vööbus, History of Asceticism in the Syrian Orient I, iv-ix and 136-150) - will have been familiar to Iamblichus, himself a Syrian. Eunapius (V. Soph. Iambl. 485-460; Loeb ed. 362-372) tells us that Iamblichus gathered around him a large number of disciples, that he performed miracles, and that while in prayer he was seen to be lifted from the ground, a halo about his head. If he himself was surrounded by this atmosphere it need not surprise us that he credits Pythagoras with success on a yet grander scale in Croton, and we would probably dismiss his account (cf. ZM 2.403, n.1) if it were not that Porphyry gives us an account in substance very similar, alleging the authority of Dicaearchus (Porph. VP 18 = Wehrli, Dikaiarchos 33). (Philip 1966: 139)

Haakub Iamblichuse tõlkija Clarke'i seletusega, et Iamblichuse ülesanne (keiser Juliani antud) oli kirjutada 10 raamatut paganlikust filosoofiast, mis võiks piibliga võistelda (vt Clark 1989: xii-xiii).

As this account of the arrival in Croton is the primary source for all accounts of the Pythagorean "brotherhood" I give a translation in extenso:

Pythagoras, when he disembarked in Italy and reached Croton, was a much-travelled and an exceptional man, endowed by fortune with great natural gifts. He was tall and of noble aspect, having grace and beauty of voice, of manner, and of every other kind. On his arrival the effect he produced in Croton was immense. With a long and eloquent discourse he so moved the magistracy of elders that they bade him pronounce an exhortation suitable to that age to the young men, and then to all the boys assembled from their schools. Then an assembly of women was arranged for him.

[...]

As a result of these meetings his reputation rapidly grew, and he gained many disciples in that city, men and women as well - the name of one of the women, [|] Theano, has come down to us - and many princes and rulers from the neighbouring non-Greek country. There is no certain account of what he used to say to those frequenting him, for they preserved an extraordinary secrecy. But it became known, and is commonly known, that he declared the soul to be immortal, that it transmigrates into creatures of other species, and furthermore that there are cycles in which events recur and nothing is absolutely new, and again that we must consider all animate creatures to be of one genus or kind. Pythagoras is said to have been the first to bring these beliefs to Greece. [end of Diels' quotation] He so converted everyone to his way of thinking, as Nicomachus asserts, that with one single lesson which he gave on disembarking in Magna Graecia he gained two thousand adherents by his discourse. They did not return to their homes, but together with their wives and children set up a great school [or lecture-hall] and created the state generally called Magna Graecia. They received laws and regulations from him, and respected them as if they were divine covenants. These disciples pooled their goods and counted Pythagoras to the gods.

(Philip 1966: 139-140)

Porphyry kirjutatud Pythagorase elulugu ma ei olegi veel näppinud. Siin on iva selles, et Porphyry on parafraseerinud Dicaerchust, kellel Philipi arvates ei saa olla asjast täpseid teadmisi:

For our purposes, however, what is really important is to observe that Nicomachus, and not Dicaerchus, is alleged as his source for the founding of a community. It is prima facie unlikely that Dicaerchus (born ca. 360-340) should be the source for such a notion. We know of political and other associations (hetaireiai) in the fourth century, but none of them are religious communities of the kind here described, having their goods in common and living a communal life. Such communities however are common in the time of Nicomachus (c. 100 A.D.), and when Apollonius of Tyana (Iambl. VP 254) describes a brotherhood of 300 members as the foundation of Pythagoras, he is speaking of an institution with which he is familiar. (Philip 1966: 140)

St Philipi hot take on, et pütaagorlaste kogukond on tagantjärgi leiutatud varakristlike kogukondade põhjal.

Porphyry (VP 21) continues his account of the initial period in Magna Graecia with another tale, at least in part ascribed to Aristoxenus, to whom Wehrli (Aristoxenus fr. 17 and comment) ascribes the whole context. In this account we learn that on coming to Italy and Sicily he stirred up the spirit of freedom and procured the liberation of subject states, that he legislated for them by the agency of Zaleucas [|] and Charondas, and that he persuaded the tyrant of Centuripe to abdicate and distribute his patrimony. His influence extended to the nearby non-Greek tribes and to the Romans. Aristoxenus' prophet of freedom and concord who travels through Italy and Sicily preaching his gospel, is very different from the philosopher-statesman of Dicaerchus who settles in Croton and establishes an ascendency there.
We need not seek to reconcile the two pictures. The Peripatetic Bios-biography is a tract in which an ethical, political, or philosophical ideal is outlined under the name of a person, in this case Pythagoras. The events of the actual life are interpreted according to the tendency of the author, and suitable events are freely invented. Diraerchus is depicting a hero of the "active life," in protest against the Aristotelian ideal of the contemplative life. Aristoxenus is depicting the Pythagorean Sage, as distinct from the philosopher of Academy or Lyceum. (Philip 1966: 140-141)

Aristoxenus kujutab Pythagorast, kes tuleb vabastab Lõuna-Itaalia türannidest, nö vabaduse prohvetit, pütaagorlikku mõttetarka (püha õpetajat), kes erineks nii Platoni Akadeemia ettekujutusest, milles Pythagoras elas aktiivset poliitilist elu (vita activa) kui ka Aristotelese Lütseumi ettekujutusest, milles Pythagoras elas askeetlikku, mõtlikku elu (vita contemplativa) ja viljeles mitte-kõige-paremat filosoofiat, aga ikkagi filosoofiat. Siin on kolm erinevat Pythagorast, kelle panpütaagorlik Iamblichus justkui põimib üheks isikuks kokku.

Is it not possible that Aristoxenus and Dicaerchus had in mind an idealized Academy, and perhaps also the institutions of Plato's Republic? Such a solution is excluded by the fact that the guardians of Plato's Republic were all philosophers with a lifelong training, and that they were equals among themselves, governing by consent. Their community of property is not ascetic in intention but is a political device. And as for Plato's role in the Academy, he neither played nor aspired to that of a master speaking inspired truth. So, in the fourth century, the notion of a community or brotherhood could not have been the casual product of Peripatetic imagination, suggested by contemporary institutions. We must conclude that there is no evidence for the idea, nor any likelihood that it arose before Nicomachus of Gerasa and Apollonius. (Philip 1966: 141)

Huvitav küsimus ja väga nõrgad vastuargumendid. Kas pütaagorlaste kogukonnas ei olnud liikmed üksteisega võrdsed? Kas nende ühisvara oli rangelt võttes askeetlik kui nad osalesid linna poliitikas? Kas Platon ei võinud ette kujutada ideaalset ühiskonda pütaagorlaste kogukonna eeskujul, aga ilma Pythagoraseta, kes elas võib-olla kauem kui tema kogukond?

There are obvious similarities between Pythagoras and Empedocles, a kinship that Empedocles appears to recognize (Vors. 31 B 129), The parallels have been brought out forcibly by Rohde (378 ff.). and by Dodds (144-147) regarding common "shamanistic aspects.' [|] But the analogy can be misleading. It is not for nothing that Aristotle calls Empedocles the father of rhetoric (Dl 8.57) and we can readily imagine him as a wandering poet-philosopher addressing throngs. As for Pythagoras, there is nothing but the suppositious Croton discourses to suggest that he gained adherents by preaching. The whole Pythagorean tradition is non-rhetorical until we come down to Apollonius of Tyana, who himself was an itinerant preaching prophet. Earlier Pythagoreans seem to have been sparing of their words and to have sought disciples rather by instruction than by emotional conversion. (Philip 1966: 141-142)

Salaõpetust ei röögita seebikasti otsast.

A further argument for the existence of a Pythagorean community or brotherhood hinges on the saying κοινὰ τὰ φίλον or κοινά τὰ τῶν φίλον. The critical passage (Schol. T Plat. Phaedr. 279c = Jacoby FGrH 566 F. 13a) reads:

κοινὰ τὰ τῶν φίλον: Applied to things shared well. They say the proverb first became current in Magna Graecia, in the period in which Pythagoras persuaded the inhabitants to have all goods in common. Timaeus in Book 9 says: "When the young men approached him, desiring to join his community, he did not accede to the request at once but replied that they must have property in common." And subsequently Timaeus continues: "It was through them that the saying spread in Magna Graecia κοινά τὰ τῶν φίλον."

Diogenes Laertios (8.10 cf. Porph. VP 33) on the same authority, expands this somewhat:

Timaeus asserts that Pythagoras was the first to say κοινὰ τὰ φίλον and "friendship is equality." His disciples paid their substance into a common pool and observed silence for five years, never seeing Pythagoras, but only hearing his discourses, until they passed the test. Then they became members of his household and shared in (the privilege of) seeing him.

[.|.] Aristotle, who quotes it, adds as a gloss that friendship implies a community of interest - that is, that not only one's substance and one's effort, but one's personal involvement are at the disposal of a friend for him to draw on. That it was so understood by the Pythagoreans is shown by the tales of Damon and Phintias, Kleinias and Proros, and other anecdotes, and by accounts of ready generosity. The point of these tales is that a friend may count on his friend to the last farthing and the last bretah, not that friends must have their property in common. (Philip 1966: 142-143)

Aristoteles kirjutas ise päris palju sõprusest (nt Nicomachose Eetika 9. peatükk) niiet siin võib täitsa vabalt olla keiss, et ta ratsionaliseerib seda ütlust/sümbolit. (Ei saa jätta märkamata, et Minar on bibliograafias, aga temale viidatakse ainult seoses võimalusega, et Cylon võis olla müütiline/väljamõeldud tegelan.)

Timaeus (ca. 356 - ca. 260 B.C.) came to Athens some time between 317 and 312, after the death of Aristotle. He had Peripatetic connections and must have known Aristoxenus and Diraechus, though they were probably of an older generation and certainly senior in the Peripatos. In his chapters on Pythagoras he will have used their writings but, as we have seen, there is no ground for believing that they spoke of a Pythagorean community. If that idea arises with Timaeus, how did he come by it? Von Fritz (68-69; cf. Jacoby FGrH 3b 550-552) has argued, in the main convincingly, that Timaeus has projected into the sixth century and the times of Pythagoras, events that occurred only in the mid-fifth century. That there then existed Pythagorean political associations appears to be beyond doubt. Timaeus saw them as religious-political associations founded by Pythagoras and operative in his lifetime. (Philip 1966: 143)

Ajaloolane Timaeus ei ole pütaagorlane Timaeus of Locri, kelle järgi on nimetatud see kõige keerulisem Platoni dialoog ja põhiline, mida keskaegses Euroopas loeti (ja kes omakorda, Diogenes Laertiose järgi, võis olla varjunimi Philolaosele).

In his account Timaeus sought to explain both the religious and the political aspects of the association he assumed to have existed, but if we had the complete account we might find that the political aspects predominated, as they do in the summary account of Justinus (20.4) which is said to be based on Timaeus and which I translate: (discussed von Fritz, 33-67)

[...] After all this study he arrived in Croton, and by his authority recalled to a frugal way of life the people of that city who had lapsed into soft living. Daily he praised virtue and told of the vices ensuing on soft and wanton living, and of the many states whose downfall had been so caused. He stirred up among the citizens such a zeal for frugality of life that it seemed incredible any of them had ever been soft or wanton. [...] But three hundred of the young men bound themselves by oath to a fraternal association, and lived (together with their comrades) apart from the rest of the citizens, as if they were the assembly of a secret conspiracy. This association achieved control of the state, and the other citizens determined, when they were assembled in one house, to burn down [house and] brotherhood within it. In that fire sixty members perished and the rest went into exile. At that time Pythagoras, after having spent twenty years in Croton, moved to Metapontum and died there. The veneration for him was so great that they made a temple of his home and treated him as a god.

[|] In this passage there is first the familiar theme of tryphe developed in connection with the coming of Pythagoras and then, without explanation of how the transition is made, we are told of a political association of young men, of which it is not said either that it was founded by Pythagoras or that it was headed by him. It looks as if the well-worn topos had come from one context and the tale of political action from another and that Timaeus, in his narrative, connected them. (Philip 1966: 144-145)

Ainult, et kui see kokkuvõte tõesti põhineb Timaeusel ja ta kirjutas 3. sajandil eKr 300-st noormehest, kes astusid vennaskonda, siis ei saa see olla neopütaagorlaste väljamõeldis nagu ta soovitas ennist (ülal). Also, üsna disrespektaabel lugeja suhtes öelda, et tryphe on juba tuttav teema kui see mõiste esineb raamatus esimest korda ja sellele ei anta seletust (autor eeldab, et lugeja juba tunneb seda mõistet).

A division into classes within a community might be also assumed from the various references to Pythagorean "silence," (quoted ZM 2.404, n. 4), of which we must distinguish two kinds - continence in speech, and the silentium of an ascetic discipline mentioned by Iamblichus but not in earlier accounts. Isocrates (Bus 29, cf. Iambl. VP 94) is the first to mention continence in speech or taciturnity, saying that the Pythagoreans gained more respect by saying little than did others by saying much. This silence is rather a virtue than an ascetic practice. It is virtue commonly recognized, characterizing the "dignity" of Plato (e.g. Rep. 388d and by implication in references to adoleschia) and the magnanimous man of Aristotle (EN 1125a 13), its contrary vice being satirized by Theophrastus (Char. 3, 7). (Philip 1966: 146)

Vaatasin Republic-us katkendi järgi - Sokrates jälle jahub midagi kohatult naermisest.

10. Transmigration [151-171]

Aristotle attributes a doctrine of the soul to the Pythagoreans only in the De Anima, where they are mentioned among those believing the soul to be the cause of motion, and are grouped together with the Atomists. Democritus is first cited as holding that soul consists in spherical particles, "like the motes we see in a sunbeam falling through a window" (De An. 404a 2-4). These particles are breathed in and maintain life as long as respiration continues. "Pythagorean doctrine" Aristotle continues (404a 16-20), "appears to be very similar. For some of them assert that soul is the motes in the air, others that it is what moves these motes. They observe that these are in constant motion, even in a complete windstill." (Philip 1966: 151)

"It is obviously the Pythagoreans who inspired the atomists to see in the motes in a sunbeam an indication of the nature of the soul-atoms" (Burkert 1972: 259).

J. S. Pearce, Collected Papers 1.88-90, using the example of the Pythagorean tradition and the golden thigh, argues that the historian must not disregard or arbitrarily reinterpret the facts of which he cannot make sense. "We have no right at all to say that supernal powers had not put a physical mask upon him as extraordinary as was his personality." For the life of St. Francis the Fioretti are more significance than are local archives. (Philip 1966: 165, note 3)

This is the most wrong I have ever seen someone get C. S. Peirce's name. "But we never can conclude with any probability that the ratio is strictly zero; and even if we knew that the proportion of men with golden thighs is exactly zero, that would be no argument at all against Pythagoras having had a golden thigh." (CP 1.88)

When Pythagoras left Samos for Magna Graecia he was a man of mature years and of a wide range of intellectual interests. Whatever the meaning of Heraclitus' polymathia (22B 129 may be, and however derogatory its sense, it must imply intellectual curiosity, wide inquiry, [|] and reading. It is clear from the authority he acquired in the world into which he migrated that there he found scope for his gifts and an audience for his teachings. In many respects it must have been very different from Ionia, then the centre of the Greek would politically, intellectually, and artistically. Whereas the Ionians were in contact with Eastern nations from whom they accepted cultural stimulus, in Magna Graecia the Greeks were in contact, often hostile, with the lesser cultures of Southern Italy, Etrusria, Sicily, to whom they owed commercial wealth rather than ideas. But it was a world of wider horizons and greater possibilities, a world in social and political ferment. Its cults were Greek and if there was any religious emphasis characteristic of the area it was on the Apollo of Delphi, the promoter of colonization and, in predominantly agricultural states, on the cult of the agrarian divinities, Demeter and Persephone. (Philip 1966: 153-154)

Paljuõppimine. Vb (1) artistically, (2) politically, ja (3) intellectually. Järjekordne asi, mida Apollo kohta varem ei teadnud.

"Pythagoras used to teach that he was of higher than mortal origin" (Aelian VH 4.17 = Fr. Sel. 131). "Aristotle says that Pythagoras was hailed by the people of Croton as Hyperborean Apollo" (Aelian VH 2.26 = Fr. Sel. 130). "He is said to have been an awesome person, and it was the opinion of his disciples that he was Apollo, come from the Hyperboreans" (D.L. 8.11 = Fr. Sel.. 131). "One of the acusmata was 'Who are you, Pythagoras?' For they say he is the Hyperborean Apollo" (Iambl. VP 30 = Fr. Sel. 131). (Philip 1966: 156)

Njah, "his appearance was such as to strike awe into those who saw him, and made them aware of his true nature" (Iamblichus 1989: 15).

Nor does the division of the species "rational creature" into gods, men, and an intermediate class sound either Aristotelian or primitive. In the foregoing passage Iamblichus has in mind daimon status. Pythagoras is "a good daimon, kindly disposed to mankind," or "one of the daimones that inhabit the moon." That Pythagoras was said by his early followers to have been a sort of Agathos Daimon or an astral divinity is improbable. (Philip 1966: 157)

Jutt käib ütlusest, mille Iamblichus väidetavalt laenas Aristoteleselt, et On kolme tüüpi mõistusega olendeid: jumalad, inimesed, ja olendid nagu Pythagoras. Või siis, "some said he was one of the spirits who live in the moon" (Iamblichus 1989: 12).

He has the gift of bilocation and of prophetic foresigt. He has power over animals. He strokes the head of an eagle, need not fear poisonous snakes, tames a bear, and, according to Iamblichus (VP 61) whispers in the ear of a bull to keep him out of a field of beans. These latter tales may imply transmigration. Pythagoras may be able to speak to the souls inhabiting animals. He calls down th eeagle and speaks to the bear. But power over animals is a trait of godhead. (Philip 1966: 158)

Võib-olla Pythagorasel oli õnnestunud endale napsata sõnajalaõis? "Mitte ainult kõiknägewaks ei saanud sõnajala õie omanik, waid niisamutigi kõikteadjaks ja kõikmõistjaks. Ei mõistnud ainult inimeste keeli, waid mõistis ka lindude, loomade ja putukate keeli. Sai koguni sellestki aru, mis puud oma kohisemisega kõnelewad." (Eisen 1899: 54)

That the aura of miracle and supernatural occurrence could attach to events other than those occurring in a context of religion or philosophy is shown by the legend of the Battle of the Sagra. Before that battle, the Locrians sent to Sparta for help. The Spartans' hands were full, but they solemnly sent the Dioscuri, in a ship, with envoys and crew. The Dioscuri disembarked at Locri, fought on the side of the Locrians - on white horses, in scarlet cloaks - and were instrumental in defeating the greatly superior forces of Croton. That they were in fact [|] present at the battle was proven when one of the Crotoniate wounded was sent by an oracle to the temple of the Dioscuri in SParta, was healed there and then miraculously returned to his home. (Dunbabin, The Western Greeks 358; Strabo 261; cf. FGrH 115 F 392). (Philip 1966: 161-162)

Nomisasiseenüüdsiison?

11. Conclusion [172-182]

What he found reported as Pythagorean theory posed a curious and difficult problem for him. He could not simply brush it aside. It was held to be of great importance by all the persons having most authority within the Academy. They considered (and Aristotle agrees) that Pythagorean number theory was not merely a formative influence but the real foundation of their own theories of the constitution of the cosmos and of the derivation of physical body. Thes etheories, both in [|] their simpler Pythagorean form and in their later Academic elaborations, Aristotle considered an aberration, and an aberration that it was one of the chief aims of the treatises to combat. (Philip 1966: 172-173)

Ikka veel ei väsi kogumast väiteid selle kohta, kui tähtis oli pütagorism Platoni Akadeemia jaoks.

Of later fifth-century Pythagoreans he alluded to Philolaus and mentions Eurytus. Otherwise he always speaks of "the Pythagoreans." This practice has contributed in no small measure to the myth of a "society" or "brotherhood" but we have seen reason to believe that it is simply a locution of Aristotle's to express his non liquet. He could feel no certainty that the divine person of the legend, the worker of miracles, the man of the golden thigh, was also the thinker. He knew of no other Pythagorean to whom the thought could be ascribed. A collective name served his polemical purpose just as well, and the manner of transmission of the doctrines made a collective name more plausible. We have seen reason to believe that the doctrines he ascribes to "the Pythagoreans" may in substance be imputed to Pythagoras himself. (Philip 1966: 173)

Lisanduseks autori arvamusele, et pütaagorlaste koolkonda kui sellist ei eksisteerinud, pakub ta, et nende eksistentsi võidi eeldada sellest, et Aristoteles räägib "pütaagorlastest" üldiselt. Ja seda tegi ta ehk seetõttu, et pütaagorlaste õpetusi vahendas suusõnaline (oraalne) traditsioon.

Pythagoras was about twenty-five years of age when Sardis fell. His native Samos was spared foreign domination and reached a modus vivendi with the Persians, under the tyranny enjoying such power and prospecity as it had not known before. "I have dwelt at some length on the affairs of Samos" says Herodotus (3.60), "because they built three of the greatest public works constructed by any Greek state." All three of these were built in the lifetime of Pythagoras. The first was a tunnel nearly a mile long, cut through a hill in order to bring water to the island's chief city - a feat that testifies to the skill of its engineers. The second was the improvement of the harbour by the construction of great sea-walls, still in part extant. The third was the rebuilding of the temple of Hera, the largest of all Greek temples, begun by Polycrates and still unfinished at the time of his downfall. (Philip 1966: 174)

Olin aktiivselt teadlik ainult tunnelist, millest on Wikipeedias ilusad pildid: (1) Tunnel of Eupalinos; (2) sadam on vb see, mis kannab nime Pythagoreion; ja (3) tempel on Heraion of Samos.

Polycrates further enriched it by expanding the semipiratical rule of the seas into a virtual blockade of Aegean commerce. He showed his concern for its cultural life by attracting to it Democedes of Croton, the greatest physician of his day (Hdt. 3.125; 3.131) and two of the greatest contemporary poets, Anacreon (Hdt. 3.121) and Ibycus (Suid. s.v.). In the second half of the sixth century Samos was, briefly, the principal power of Ionia and centre of its culture. And in [|] this Samos Pythagoras passed his mature years. Even if he never visited Miletus - and it is more than likely that he did, as it was only a few sailing hours away - he will have had occasion to familiarize himself with the thought of the Milesians and to read, among others, Anaximander's book. (Philip 1966: 174-175)

Democedesest on mul kogunenud ainult nii palju, et Zelleri (1881: 343, fn1) järgi tõi ta Zoroastrianistliku dualismi Krotoonasse (meh) ja Morrison (1956: 150) kirjutab, et pärast Sybarise võitmist lahkus Democedes linnast.

To two of their gods they had such access. Apollo was accessible to the healer, the soothsayer, the poet, and the musician, to the sick and the polluted. Dionysus took possession of his devotees rather than awaiting their intercession. It is perhaps somewhere [|] in the cult of these two divinities that we should look for an interest in the after-like. Both of them have an existence apart from the divine family of Olympus. Both have if not their origin at least important areas of cult outside the Greek world. The two are associated in the religion of Delphi. The ecstatic cult of Dionysus provides favourable soil for the growth of a belief that the soul which leaves the body in ecstasy may be capable of surviving the body. In the religion of Apollo the power of the god is exercised not on the physical person but on some faculty within the person that is enabled to sing, prophesy, heal. (Philip 1966: 176-177)

Alles sain teada, et need kaks olid vennad (Burkert 1972: 132). Nüüd tuleb välja, et nad seisid kogu Kreeka panteonist eraldi.

Heraclitus was a generation younger than Pythagoras and, if Pythagoras emigrated from Samos about 532 B.C., can have known him only by repute. But he came from the neighbouring city of Ephesus, where he would have occasion to hear any accounts of Pythagoras still current [|] Ionia in the decades following his departure. Pythagoras, he tells us (22 B 129), practised inquiry more thna any other man. He took what he could use from writings in that kind, and fashioned himself from them a learning derived from many sources, a polymathy that was mistaken in method. Heraclitus calls him (B 81) a logic-chopper or misleader, and argues (B 40) that much learning does not teach a mas wisdom. If it did it would have taught Hesiod and Pythagoras, Xenophanes and Hecateus. (Philip 1966: 177-178)

Tsiteerisin juba Ueberwegi versiooni ülal. Pmst kogun versioone.

For Pythagoras the knowledge at which he aimed was a knowledge of the structure of the universe as determined by number. His cosmos, like the cosmos of Anaximander, was symmetrical, the relations of its parts being expressible in number. Its first principles were the apeiron - the apeiron of Anaximander - and the peras implied by that apeiron. Under these two first principles were subsumed Odd and Even. From the interaction of these two pairs of opposites was produced the One, our Cosmos. From the One and its surrounding apeiron or void were generated the number-things of our physical world. We do not know whether Pythagoras explained the manner of their generation. It seems improbable that he did. We do know that he thought the "correspondences" between disparate things, produced by their common numerical components, could be perceived. (Philip 1966: 179)

Võib-olla olulisim take-away sellest raamatust on rõhk Anaximandrose mõjul Pythagorasele. Varasemad autorid, keda ma olen lugenud, räägivad Thalesest, Pherekydesest ja Anaximandrosest võrdselt kui võimalikest õpetajatest.

Appendix I: Biography and Chronology [185-199]

Aristoxenus, however, makes him a Tyrrhenian "from one of the islands from which the Athenians ejected the Tyrrhenians" (D.L. 8.1 = Wehrli, Aristoxenus 11a = Vors. 14.8) and we are told that Theopompus (FGrH 115 F 72) and Aristarchus concur. This Aristarchus may have been the grammarian or the astronomer or some other. (There are no grounds for Preller's emendation to ARistoteles.) The tale of Tyrrhenian paternity is meant to explain, as Wehrli (comment ad loc.) suggests, how Pythagoras came to be in possession of religious secrets. (Wehrli cites Hdt. 2.51 and PLato, Laws 738c). This story is known to Neanthes (or Kleanthes, Porph. VP 1-2; cf. GFrH 84 F 29) who specifies Lemnos as the island referred to. But Neanthes states that Pythagoras was a Syrian from Tyre, and Porphyry, himself a Syrian from Tyre (Porph. V. Plot. 21), seems to lean to this version. (Philip 1966: 185)

Väga huvitav alternatiivne narratiiv. Türseenid (dno kes nad eesti keeles peaksid olema) olid Kreeka autorite keelekasutuses üleüldiselt mitte-Kreeklased. Pakutakse, et nad võisid olla ka etruskid. Mingisugune piraadi-rahvas, kes asustasid Egeuse meres ühte saart - Lemnos. Huvitav kokkusattumus küll, et Lemnos ei ole Samosest vaga kaugel ja Krooton ei ole etruskitest väga kaugel, aga üksteisest on nad ikka väga kaugel.

Diogenes Laertius has also preserved for us what appears to be another independent tradition (D.L. 8.1): "Some say that he was a son of Marmacus, son of Hippasus, son of Euthyphro, son of Cleonymus; and that Marmacus was an exile from Phlius resident in Samos." Pausanias (2.13.2) has a story - possibly related - of an Hippasus who was the leader of an anti-Dorian party in Phlius and fled to Samos. In his account the descent is Hippasus-Euphranor-Mnesarchus-Pythagoras. It looks as if Diogenes' source had confused the generations and corrupted the names (for Mnesarchus is correct). (Philip 1966: 186)

Jälle see Phlius, mingi täiesti tühine koht 20km Korintosest.

Pythagoras is connected with Phlius also in the anecdote deriving from Heraclides Ponticus (D.L. 1.12 = Wehrli, Her. Pont. 87) that Pythagoras was the first to use the term "philosopher," in his reply to Leon, tyrant of Sicyon or Phlius, that God alone is wise. We recall that in Plato's Phaedo the other person of the dialogue is Echecrates, a Pythagorean of Phlius, where the dialogue is set; and that most of "the last Pythagoreans" whom Aristoxenus claims to have known (D.L. 8.46) are from Phlius. It would appear that there was a Phliasian legend, at least partly independent, from which these tales came. (Philip 1966: 186)

Isegi mu lemmikanekdoodil on midagi pistmist Phliusega.

Duris of Samos (Porph. V.P. 3; FGrH 76 fr. 23 = Vors. 14.6 and 56.2) tells us that, in Samos, Pythagoras had a son, Arimnestus, who was exiled, instructed Democritus (in Abdera?), returned to Samos, and erected in the temple of Hera there a bronze votive offering with an inscription citing his own paternity, "son of Pythagoras." Duris is a Samian of the early third century (CR 12.3 [1962] 189-192), has apparently seen the inscription, and accepts the association with our Pythagoras. In form the inscription is a possible one. One is led to suspect, however, the fabrication of a Samian background for Pythagoras by local patriotism. It is connected (Porph. V.P. 3) (see comment ad Vors. 56.2) with a curious epilogue in which one Simos steals one of the seven skills (?) from the epigram (!) and so destroys the other six, all of them apparently connected with musical theory and some form of scales (Wilamovitz, Platon [Berlin 1920] 2.94). This tale still awaits a satisfactory explanation. It seems unlikely to be genuine in any part. (Philip 1966: 187)

Tõepoolest ongi kohe 3. punkt Porphyry kirjutatud Pythagorase eluloos sellest Durisest, kes kirjutab oma raamatus, et Pythagorasel oli poeg nimega Arimnestus, kes oli Demokritose õpetaja ning kes pagendusest naasedes riputas Hera templisse ~60x60cm pronksist plaadi, mille keegi muusik nimega Simus varastas? Arusaamatu värk ja ma ei tea veel kas keegi peale Guthrie on seda (arusaadavamalt) tõlkinud. Igal juhul jääb tõepoolest mulje, et vb ei olnud Pythagoras üldse Samoselt pärit ja selle jõuka saare asukad paigutasid Pythagorase meelevaldselt sinna.

But it would be rash to argue from what he [Timaeus] tells us of Pythagoras' family, to a definite civil status, and all other accounts have an air of romance. The very names, except for Mnesarchus, a son named after the grandfather, have obvious derivations; Telauges, an attribute of light or Apollo, Myia, a woman busy as a fly or bee, Arignote, "known far and wide." Even the name Theano may have suggestions of divinity, but it appears to have a surer place in the legend than the rest. (Philip 1966: 187)

Esimest korda kohtan informatsiooni, et Pythagorase väidetavate laste nimed võivad olla sõnamängud.

Two masters are assigned to Pythagoras in the tradition, Pherecydes of Syros and Hermodamas. The reasons for associating Pherecydes and Pythagoras are suggested in Suidas (s.v. Pherecydes = Vors. 7 A 2): "It is said that Pythagoras was instructed by him, but that Pherecydes himself had no teacher. He acquired secret books of the Phoenicians and taught himself. [...] Pherecydes was the first to introduce the doctrine of metempsychosis." The fact that Pherecydes taught doctrines best explainable as foreign and esoteric, involving the soul, made him a suitable teacher to attribute to Pythagoras. (Philip 1966: 188)

Väga ei imesta. Pherekydes ajas mingit päris hullu kosmogooniat sellest, kuidas Elu abiellub Maaga ja siis Aeg läheb puhkusele ja Elu võtab Aja käest valitseja rolli üle vms. Hermodamas on loetud autorite hulgas läbi käinud 1 korra, kõige vanimal (vt Ritter 1836: 332) ja märkimisväärseim asi tema juures on see, et tal ei ole inglisekeelset Vikipeedia-lehekülge.

The voyages of Pythagoras were favourite theme of the biographical tradition. In early times philosophers and sophists, as they shared the name of "sophist," shared also the characteristic of travelling from city to city and from country to country. In that he remained all his life in Athens, Socrates was an exception to the rule. His pupil Plato, however, in his first voyage to Sicily undertook what was a voyage of instruction in the strict sense, and thereafter it was common for philosophers to embark on a journey abroad to learn what there was to be learned in foreign lands. They naturally imagined their predecessors to have made similar journeys, and when it came to writing the life of Pythagoras they credited him not only with migration from Ionia and Magna Graecia but also with preceding voyages of instruction. They did so the more readily because, in the Academy of Plato's later years, a lively interest in the East developed, and the tendency arose to seek the origins of Greek religious and philosophical doctrines there (Jaeger, Aristotle [1948] 131-137). That this tendency was not restricted to the Academy is shown by the fact that Isocrates (Bus. 28 = Vors. 14.4) alludes to a journey made by Pythagoras to Egypt. (Philip 1966: 189)

"He [Pythagoras] realised that [...] all the earlier philosophers had continued their careers abroad" (Iamblichus 1989: 11).

I have not attempted to discuss anecdotes of more obviously legendary character. The legend in all its aspects is discussed by I. Lévy (Sources; Légende). Lévy's studies leave considerations of historical fact on one side and sometimes overstate their thesis, especially in suggesting that Pythagoras is the prototype of Jesus. He perhaps overestimates the role played by Heraclides Ponticus, and underestimates that of Neopythagorean elaboration. Nevertheless he has contributed greatly to our understanding of the character of the legend. (Philip 1966: 196)

Lévy, Isidore 1926. Recherches sur les sources de la légende de Pythagore. Paris: Leroux. - Väga kahju, et keelebarjääri taga. Tema mahukam teos - 1927. La légende de Pythagore de Grèce en Palestine. Paris: Édouard Champion. - on isegi kättesaadav. [Internet Archive]

The two principal, alternative accounts - death in the uprising or withdrawal in the face of it - are those given by Dicaerchus and Aristoxenus respectively, and are the earliest accounts we have. Diraearchus was portraying Pythagoras as the exemplar as the exemplar of the active life. His hero must be a leader in the affairs of his state, and must refuse to survive débâcle or at least not appear to flee in the face of it. Aristoxenus was portraying the sage whose first concern was his doctrine and way of life, an apostle of freedom but also of political harmony. It was appropriate that his Pythagoras should withdraw in the face of opposition and threatened violence, just as, when confronted with the tyranny of Polycrates, he had left Samos. (Philip 1966: 192)

Sama kamm mis eelpool. Pythagorase elu ja surm on sõltub sellest, kumb peripateetiline filosoof seda omatahtsi jutustab.

Some authorities, Diogenes Laertius (8.6) asserts, maintain (wrongly) that Pythagoras left behind him no writings. We have, he says, the emphatic statement [|] of Heraclitus (Vors. 22 B 129) that "Pythagoras more than all other men was given to the practice of systematic inquiry and the pursuit of knowledge; he picked and chose among the writings (he used) and set up as a philosopher with what was in fact merely a mass of information organized on mistaken and misleading lines." Diogenes misunderstood the language of Heraclitus to imply that Pythagoras himself was the author of "writings." He cites a work in three parts - on education, politics, physics - and, on the authority of Heraclides Lembus (ca 170 B.C.), a further six works. (Philip 1966: 192-193)

Ma võiksin vanduda, et iga kord kui ma seda Herakleitose tsitaati kohtan, on see eelnevatest natuke erinev.

The incuse coinage of Magna Graecia, which began to be struc at about the middle of the sixth century - that is, roughly, at the time of Pythagoras' arrival there - has been connected with his coming. If this connection could be made probable it would offer a basis for our chronological independent of the Pythagoras tradition. The Duc de Luynes (Nouvelles Annalse de l' Arch. de Rome [1836] 388 ff.) was the first to suggest that the coinage was Pythagoras' invention. [...] It has had a recent and enthusiastic propagandist in C. J. Seltman, "The Problem of the First Italote Coins," Num. Chron. 6 (1949) 1-21; Greek Coins (London 1955) 77-79; "Pythagoras: Artist, Statesman, Philosopher," History Today (1956) 522-27 and 592-97. Seltman argues that Pythagoras belonged to a family of artisans, he, like his father Mnesarchus, being a gem-engraver or, in Seltman's term, a "celator." (Philip 1966: 197, note 5)

Seltman's History Today articles are online (pt 1 and pt 2) but behind a paywall and thus useless. Celator is naturally "concealer, hider".

Appendix II: Irrationals and Incommensurability [200-207]

This theorem is true for the triangle having sides 3, 4, and 5 (3² + 4² = 5²); the triangle which, it is alleged, first suggested the theorem to Pythagoras. However, when this theorem began to be tested for other right-angled triangles the discovery soon was made that the length of the diagonal was not always expressible as an integer. This was the case most obviously for the diagonal of the square, the length of which proved to be √2, or irrational ἄλογος. Some historians suggest that the term alogos expresses the horror of the early Pythagoreans at the discovery and that it is to be translated as "unutterable," a meaning that the word has once, in Sophocles. Otherwise it means, as one would expect, without logos or ratio and so irrational. (Philip 1966: 200)

3-4-5 külgedega kolmnurk on ainus tõeline kolmnurk.

It is suggested that a form of arithmetic (and of geometry) called psephoi-arithmetic was practised by the Pythagoreans in the fifth century. This suggestion is developed in great detail and with much ingenuity by O. Becker (Das Mathematische (40-52) and K. von Fritz (Gnomon [1958] 82), though not believing the practise to go back to the sixth century, would accept it as early. Though its physical means are not described, for there is no record of any such method, it is apparently thought of as practised on a sand table with pebbles not as counters but as representing units. Now in the treatises of Nicomachus of Gerasa and of Theon of Smyrna we find number theories illustrated in a similar manner, by means of unit patterns, but they use alphas to represent the unit, alpha being "one" in alphabetical notation. This shows that Neopythagoreans of the second century A.D. practised something like psephoi-arithmetic, and their use of the alphabetical symbol may derive from an earlier use of pebbles on a sand-table. (Philip 1966: 202)

a + a = aa

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