PART 5 OF 5
It is probable that the majority of the Pythagoreans were anonymous, and remain unknown. But the following names are known and celebrated:
Of the Crotonians, Hippostratus, Dymas, Aegon, Aemon, Sillus, Cleosthenes, Agelas, Episylus, Phyciadas, Ecphantus, Timaeus, Buthius, Eratus, Itmaeus, Rhodippus, Bryas, Evandrus, Myllias, Antimedon, Ageas, Leophron, Agylus, Onatus, Hipposthenes, Cleophron, Alcmaeon, Damocles, Milon, and Menon.
At Metapontum resided Brontinus, Parmiseus, Orestadas, Leon, Damarmenus, Aeneas, Chilas, Melisias, Aristeas, Laphion, Evandrus, Agesidamus, Xenocades, Euryphemus, Aristomenes, Agesarchus, Alceas, Xenophantes, Thraseus, Arytus, Epiphron, Eiriscus, Megistias, Leocydes, Thrasymedes, Euphemus, Procles, Antimenes, Lacritus, Damotages, Pyrrho, Rhexibius, Alopecus, Astylus, Dacidas, Aliochus, Lacrates and Glycinus.
Of the Agrigentines was Empedocles.
Of the Eleatae, was Parmenides.
Of the Tarentines were Philolaus, Eurytus, Archytas, Theodorus, Aristippus, Lycon, Hestiaeus, Polemarchus, Asteas, Clinias, Cleon, Eurymedon, Arceas, Clinagoras, Archippus, Zopyrus, Euthynus, Dicaearchus, Philonidas, Phrontidas, Lysis, Lysibius, Dinocrates, Echecrates, Paction, Acusilidas, Icmus, Pisicrates, and Clearatus.
Of the Leontines were Phrynichus, Smichias, Aristoclidas, Clinias, Abroteles, Pisyrrhydus, Bryas, Evandrus, Archemachus, Mimnomachus, Achmonidas, Dicas and Carophantidas.
Of the Sybarites were Metopus, Hippasus, Proxenus, Evanor, Deanax, Menestor, Diocles, Empedus, Timasius, Polemaeus, Evaeus, and Tyrsenus.
Of the Carthaginians were Miltiades, Anthen, Odius and Leocritus.
Of the Parians, Aeetius, Phaenecles, Dexitheus, Alcimachus, Dinarchus, Meton, Timaeus, Timesianax, Amaerus, and Thymaridas.
Of the Locrians, Gyptius, Xenon, Philodamus, Evetes, Adicus, Sthenonidas, Sosistratus, Euthynus, Zaleucus, and Timares.
Of the Posidonians, Athamas, Simus, Proxenus, Cranous, Myes, Bathylaus, Phaedon.
Of the Lucani, Ocellus, and his brother Occillus, Oresandrus, Cerambus, Dardaneus, and Malion.
Of the Aegeans, Hippomedon, Timosthenes, Euelthon, Thrasydamus, Crito, and Polyctor.
Of the Lacones, Autocharidas, Cleanor, Eurycrates.
Of the Hyperboreans, Abaris.
Of the Rheginenses, Aristides, Demosthenes, Aristocrates, Phytius, Helicaon, Mnesibulus, Hipparchides, Athosion, Euthycles, Opsimus.
Of the Selinuntians, Calais.
Of the Syracusans, Leptines, Phintias, and Damon.
Of the Samians, Melissus, Lacon, Archippus, Glorippus, Heloris, Hippon.
Of the Caulonienses, Callibrotus, Dicon, Nastas, Drymon and Xentas.
Of the Phliasians, Diocles, Echecrates, Phanton and Polymnastus.
Of the Sicyonians, Poliades, Demon, Sostratius, and Sosthenes.
Of the Cyrenians, Prorus, Melanippus, Aristangelus and Theodorus.
Of the Cyziceni, Pythodorus, Hipposthenes, Butherus and Xenophilus.
Of the Catanaei, Charondas and Lysiades.
Of the Corinthians, Chrysippus.
Of the Tyrrhenians, Nausitheus.
Of the Athenians, Neocritus.
Of the Pontians, Lyramnus.
In all, two hundred and eighteen.
The most illustrious Pythagorean women include the following: Timycha, the wife of Myllias the Crotonian. Philtis, the daughter of Theophrius the Crotonian. Byndacis, the sister of Ocellus and Occillus, Lucanians. Chilonis, the daughter of Chilon the Lacedaemonian. Cratesiclea, the Lacedaemonian, the wife of the Lacedemonian Cleanor. Theano, the wife of Brontinus of Metapontum. Mya, the wife of Milon the Crotonian. Lasthenia the Arcadian. Abrotelia, the daughter of Abroteles the Tarentine. Echecratia the Phliasian. Tyrsenis the Sybarite. Pisirrhonde, the Tarentine. Nisleadusa, the Lacedaemonian. Byro, the Argive. Babelyma the Argive, and Cleaechmas, the sister of Autocharidas the Lacedaemonian. In all, seventeen.
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Notes:
1. That is, Moses.
2. Greek for "common life."
3. A form of Apollo as the physician of the Gods.
4. In Greek, pais - a child; paideia - education.
5. Hermes was the God of logos, reason or speech, the naming power. He was identified with the Egyptian deity Thoth, the lord of scribes, whose symbolic animals were the ibis and the ape, and who was said to have invented writing. Compare this passage with the early Christian writer Theodotus: "Pythagoras thought that he who gave things their names, ought to be regarded not only the most intelligent, but the oldest of the wise men..." He then goes on to discuss the investigation of names contained in scripture. Excerpts of Theodotus, 32.
6. "Reasons" = logoi, productive principles, ratios, patterns, etc.
7. Cf. Plato, Republic, 527e.
8. This chapter is based on the account given in Nichomachus' Manual of Harmonics. While the ratios given do indeed correspond to the musical intervals described, the method of obtaining them here related, using weights, is spurious. See Levin, The Harmonics of Nichomachus and the Pythagorean Tradition, chapter 6, for a discussion of this account.
9. The text here is confused.
10. The accounts about Damon and Phintias, Clinias and Prorus, are related by Iamblichus in chapter 33.
11. Zalmoxis was a deity of the Getae in Thrace, associated with a doctrine of the immortality of the soul. See Eliade, A History of Religiouis Ideas, II, p. 175 ff.
12. This section seems to be out of place in the received text.
The Pythagorean Sourcebook and Library
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THE LIFE OF PYTHAGORAS
PORPHYRY'S Life of Pythagoras is the only surviving fragment of his History of Philosophy in four books. Porphyry (c. 233-c. 305 C.E.), the brilliant student of Plotinus, was an important Neoplatonic philosopher who wrote over 70 works dealing with metaphysics, literary criticism, history, the allegorical interpretation of myth, and so on. Porphyry's biography of Pythagoras is short, enjoyable and informative, causing one to wish that his entire History of Philosophy had survived.
Kenneth Sylvan Guthrie was the first person to translate Prophyry's Life of Pythagoras into English. Since then the work has been translated by Morton Smith and appears in Hadas and Smith, Heroes and Gods: Spiritual Biographies in Antiquity, New York, 1965.
For an account of the life and work of Porphyry see the introduction to Porphyry's Letter to His Wife Marcella, Phanes Press, 1985. For a complete listing of his known writings see the appendix in Porphyry's Launching Points to the Realm of the Mind, Phanes Press, 1988.
THE LIFE OF PYTHAGORAS
MANY THINK THAT PYTHAGORAS was the son of Mnesarchus, but they differ as to the latter's race; some thinking him a Samian, while Neanthes, in the fifth book of his Fables states he was a Syrian, from the city of Tyre. As a famine had arisen in Samos, Mnesarchus went thither to trade, and was naturalized there. There also was born his son Pythagoras, who early manifested studiousness, but was later taken to Tyre, and there entrusted to the Chaldeans, whose doctrines he imbibed. Thence he returned to Ionia, where he first studied under the Syrian Pherecydes, then also under Hermodamas the Creophylian who at that time was an old man residing in Samos.
2. Neanthes says that others hold that his father was a Tyrrhenian, of those who inhabit Lemnos, and that while on a trading trip to Samos was there naturalized. On sailing to Italy, Mnesarchus took the youth Pythagoras with him. Just at this time this country was greatly flourishing. Neanthes adds that Pythagoras had two older brothers, Eunostus and Tyrrhenus. But Apollonius, in his book about Pythagoras, affirms that his mother was Pythais, a descendant, of Ancaeus, the founder of Samos. Apollonius adds that he was said to be the off-spring of Apollo and Pythais, on the authority of Mnesarchus; and a Samian poet sings:
Apollonius says that Pythagoras studied not only under Pherecydes and Hermodamas, but also under Anaximander.
3. Duris of Samos, in the second book of his Chronicles, writes that his son was Arimnestus, that he was the teacher of Democritus and that on returning from banishment, he suspended a brazen tablet in the temple of Hera, a pillar two cubits [three feet] in diameter, bearing this inscription:
This tablet was removed by Simus, a musician, who claimed the harmonic canon graven thereon, and published it as his own. Seven proportions were engraved, but when Simus took away one, the others were destroyed.
4. It is said that by Theano, a Cretan, the daughter of Pythonax, Pythagoras had a son, Telauges, and a daughter, Myia; to whom some add Arignota, whose Pythagorean writings are still extant. Timaeus relates that Pythagoras's daughter, while a maiden, took precedence among the maidens in Crotona, and when a wife, among married men. The Crotonians made Pythagoras' house a temple of Demeter, and the neighboring street they called Museum Street.
5. Lycus, in the fourth book of his Histories, noting different opinions about his country, says, "Unless you happen to know the country and the city which Pythagoras was a citizen, it will remain a mere matter of conjecture. Some say he was a Samian, others from Phlious [in the Peloponnesus], others from Metapontine [in southern Italy]."
6. As to his knowledge, it is said that he learned the mathematical sciences from the Egyptians, Chaldeans and Phoenicians; for of old the Egyptians excelled in geometry, the Phoenicians in numbers and proportions, and the Chaldeans of astronomical theorems, divine rites, and worship of the Gods; other secrets concerning the course of life he received and learned from the Magi.
7. These accomplishments are the more generally known, but the rest are less celebrated. Moreover Eudoxus, in the second book of his Description of the Earth, writes that Pythagoras practiced the greatest purity, and was shocked at all bloodshed and killing; that he not only abstained from animal food, but never in any way approached butchers or hunters. Antiphon, in his book On Illustrious Virtuous Men praises his perseverance while he was in Egypt, saying that Pythagoras, desiring to become acquainted with the institutions of Egyptian priests, and diligently endeavoring to participate therein, requested the Tyrant Polycrates [of Samos] to write to Amasis, the King of Egypt, his friend and former host, to procure him initiation. Coming to Amasis, he was given letters to the priests, but the priests of Heliopolis sent him on to those of Memphis, on the pretense that the were the more ancient. On the same pretense, he was sent on from Memphis to Diospolis [or ancient Thebes].
8. From fear of the King the latter priests dared not make excuses [to initiate Pythagoras], but thinking that he would desist from his purpose as a result of great difficulties, they enjoined on him very hard precepts, entirely different from the institutions of the Greeks. These he performed so readily that he won their admiration, and they permitted him to sacrifice to the Gods, and to acquaint himself with all their sciences, a favor never previously granted to a foreigner.
9. Returning to Ionia, he opened in his own country a school which is even now called Pythagoras's Semicircle, and in which the Samians meet to deliberate about matters of common interest. Outside the city he made a cave adapted to the study of his philosophy, in which he lived day and night, discoursing with a few of his associates. He was now forty years old, says Aristoxenus. Seeing that Polycrates's government was becoming so violent that soon a free man would become a victim of his tyranny, he journeyed towards Italy.
10. Diogenes, in his treatise On the Incredible Things Beyond Thule, has treated Pythagoras's affairs so carefully that I think his account should not be omitted. He says that Mnesarchus was of the race of the Etruscans who inhabited Lemnos, Imbros and Scyrus and that he departed thence to visit many cities and various lands. During his journeys he found an infant lying under a large, tall poplar tree. On approaching, he observed it lay on its back, looking steadily without winking at the sun. In its mouth was a little slender reed, like a pipe, through which the child was being nourished by the dew-drops that fell from the tree. This great wonder prevailed upon him to take the child, believing it to be of a divine origin. The child was fostered by a native of that country, named Androcles, who later on adopted him, and entrusted to him the management of affairs. On becoming wealthy, Mnesarchus educated the boy, naming him Astraeus, and rearing him with his own three sons, Eunostus, Tyrrhenus, and Pythagoras.
11. He sent the boy to a lyre-player, a gymnast and a painter. Later he sent him to Anaximander at Miletus, to learn geometry and astronomy. Then Pythagoras visited the Egyptians, the Arabians, the Chaldeans and the Hebrews, from whom he acquired expertise in the interpretation of dreams, and acquired the use of frankincense in the worship of divinities.
12. In Egypt he lived with the priests, and learned the language and wisdom of the Egyptians, and three kinds of letters, the epistolographic, the hieroglyphic, and symbolic, whereof one imitates the common way of speaking, while the others express the sense of allegory and parable. In Arabia he conferred with the King. In Babylon he associated with the other Chaldeans, especially attaching himself to Zaratus [= Zoroaster], by whom he was purified from the pollutions of this past life, and taught the things from which a virtuous man ought to be free. Likewise he heard lectures about Nature, and the principles of wholes. It was from his stay among these foreigners that Pythagoras acquired the greater part of his wisdom.
13. Astraeus was by Mnesarchus entrusted to Pythagoras, who received him, and after studying his physiognomy and the motions of his body, instructed him. He first accurately investigated the science about the nature of man, discerning the disposition of everyone he met. None was allowed to become his friend or associate without being examined in facial expression and disposition.
14. Pythagoras had another youthful disciple from Thrace. Zamolxis was his name because he was born wrapped in a bear's skin, in Thracian called zalmon. Pythagoras loved him, and instructed him in sublime speculations concerning sacred rites, and the worship of the Gods. Some say this youth was named Thales, and that the barbarians worshipped him as Hercules.
15. Dionysiphanes says that he was a servant of Pythagoras, who fell into the hands of thieves and by them was branded when Pythagoras was persecuted and banished, and bound up his forehead on account of the scars. Others say that the name Zalmoxis signifies a stranger or foreigner.
Pherecydes, in Delos fell sick; and Pythagoras attended him until he died, and performed his funeral rites. Pythagoras then, longing to be with Hermodamas the Creophylus, returned to Samos. After enjoying his society, Pythagoras trained the Samian athlete Eurymenes, who though he was of small stature, conquered at Olympia through his surpassing knowledge of Pythagoras' wisdom. While according to ancient custom the other athletes fed on cheese and figs, Eurymenes, by the advice of Pythagoras, fed daily on meat, which endued his body with great strength. Pythagoras gradually imbued him with his wisdom, exhorting him to go into the struggle not for the sake of victory, but for the exercise; that he should gain by the training, avoiding the envy resulting from victory. For the victors, are not always pure, though decked with leafy crowns, are not always pure.
16. Later, when the Samians were oppressed with the tyranny of Polycrates, Pythagoras saw that life in such a state was unsuitable for a philosopher, and so planned to travel to Italy. At Delphi he inscribed an elegy on the tomb of Apollo, declaring that Apollo was the son of Silenus, but was slain by Pytho, and buried in the place called "Tripod", so named from the local mourning for Apollo by the three daughters of Triopas.
17. Going to Crete, Pythagoras besought initiation from the priests of Morgos, one of the Idaean Dactyls, by whom he was purified with the meteoritic thunder-stone, during which he lay, at dawn, stretched upon his face by the seaside, and at night, beside a river, crowned with a black lamb's woolen wreath. Descending into the Idaean cave, wrapped in black wool, he stayed there tomb twenty-seven days, according to custom; he sacrificed to Zeus, and saw the couch which there is yearly made for him. On Zeus's tomb Pythagoras inscribed an epigram, "Pythagoras to Zeus," which begins: "Zan deceased here lies, whom men call Zeus."
18. When he reached Italy, he stopped at Croton. His presence was that of a free man, tall, graceful in speech and gesture, and in everything else. Dicaearchus relates that the arrival of this great traveler, endowed with all the advantages of nature, and prosperously guided by fortune, produced on the Crotonians so great an impression, that he won the esteem of the elder magistrates, by his many and excellent discourses. They ordered him to deliver exhortations to the young men, and then to the boys who flocked out of the school to hear him, and then to the women, who came together for this purpose.
19. Through this he achieved great reputation, and he drew great audiences from the city, not only of men, but also of women, among whom was a specially illustrious person named Theano. He also drew audiences from among the neighboring barbarians, among whom were magnates and kings. What he told his audiences cannot be said with certainty, for he enjoined silence upon his hearers. But the following is a matter of general information. He taught that the soul was immortal, and that after death it transmigrates into other animated bodies. After certain specified periods, he said, the same events occur again, for nothing was entirely new; all animated beings are kin, and should be considered as belonging to one great family. Pythagoras was the first one to introduce these teachings into Greece.
20. His speech was so persuasive that, according to Nicomachus, in one dress made on first landing in Italy, he made more than two thousand adherents. Out of desire to live with him, these built a large auditorium, to which both women and boys were admitted. [Foreign visitors were so many that] they built whole cities, settling that whole region of Italy now known as Magna Graecia. His ordinances and laws were by them received as divine precepts, and they would do nothing to transgress them. Indeed, they ranked him among the divinities and held all property in common; and whenever they communicated to each other some choice bit of his philosophy, from which physical truths could always be deduced, they would swear by the Tetraktys, adjuring Pythagoras as a divine witness, in the words,
21. During his travels in Italy and Sicily he found various cities subjected one to another, both of long standing and recently. By his disciples, some of whom were found in every city, he infused into them an aspiration for liberty, thus restoring to freedom Croton, Sybaris, Catana, Regium, Himera, Agrigentum, Tauromenium, and others, on whom he imposed laws through Charondas of Catana, and Zaleucus of Locri, which resulted in a long era of good government, emulated by all their neighbors. Simicus the tyrant of Centoripae, on hearing Pythagoras' discourse, abdicated his rule, and divided his property between his sister and the citizens.
22. According to Aristoxenus, some Lucanians, Messapians, Peucetians, and Romans came to him. He rooted out all dissensions, not only among his disciples and their successors, for many ages, but among all the cities of Italy and Sicily, both internally and externally. For he would continuously say, "We ought to the best of our ability avoid, and even with fire and sword eradicate from the body, sickness; from the soul, ignorance; from the belly, luxury; from a city, sedition; from a family, discord; and from all things, excess."
23. If we may credit what ancient and trustworthy writers have related of him, he exerted an influence even over irrational animals. The Daunian bear, who had committed extensive depredations in the neighborhood, he seized; and after having patted her for awhile, and given her barley and fruits, he made her swear never again to touch a living creature, and then released her. She immediately took herself into the woods and the hills, and from that time on never attacked any irrational animal.
24. At Tarentum, in a pasture, seeing an ox cropping beans, he went to the herdsman, and advised him to tell the ox to abstain from beans. The countryman mocked him, proclaiming his ignorance of the ox-language. So Pythagoras himself went and whispered in the ox's ear. Not only did the bovine at once desist from his diet of beans, but would never touch any thenceforward, though he survived many years near Hera's temple at Tarentum, until very old, being called the sacred ox, and eating any food given him.
25. While at the Olympic games, he was discoursing with his friends about auguries, omens, and divine signs, and how men of true piety do receive messages from the Gods. Flying over his head was an eagle, who stopped, and came down to Pythagoras. After stroking her awhile he released her.
Meeting with some fishermen who were drawing in their nets heavily laden with fishes from the deep, he predicted the exact number offish they had caught. The fishermen said that if his estimate was accurate they would do whatever he commanded. They counted them accurately, and found the number correct. He then bade them to return the fish alive into the sea; and, what is more wonderful, not one of them died, although they had been out of the water a considerable time.
26. Many of his associates he reminded of the lives lived by their souls before they were bound to their present body, and by irrefutable arguments demonstrated that he had been Euphorbus, the son of Panothus. He specially praised the following Homeric verses about himself, and sang them to the lyre most elegantly:
27. The stories about the shield of this Phrygian Euphorbus being at Mycenae dedicated to Hera of Argive, along with other Trojan spoils, shall here be omitted as being of too generally known a nature.
It is said that the river Caucasus, while he, with many of his associates was passing over it, said to him very clearly, "Hail, Pythagoras!"
Almost unanimous is the report that on one and the same day he was present at Metapontum in Italy, and at Tauromenium in Sicily, in each place conversing with his friends, though the places are separated by many miles, both at sea and land, demanding a journey of many days.
28. It is well known that he showed his golden thigh to Abatis the Hyperborean, to confirm him in the opinion that he was the Hyperborean Apollo, whose priest Abatis was.
A ship was coming into the harbor, and his friends expressed the wish to own the goods it contained. "Then," said Pythagoras, "you would own a corpse!" On the ship's arrival this was found to be the true state of affairs.
Of Pythagoras many other more wonderful and divine things are persistently and unanimously related, so that we have no hesitation in saying never was more attributed to any man, nor was any more eminent.
29. Verified predictions of earthquakes are handed down, also, that he immediately chased away a pestilence, suppressed violent winds and hail, calmed storms both on rivers and on seas, for the comfort and safe passage of his friends. As their poems attest, the like was often performed by Empedocles, Epimenides and Abaris, who had learned the art of doing these things from him. Empedocles, indeed, was surnamed Alexanemos, "the chaser of winds," Epimenides, Cathartes, "the purifyer," Abaris was called Aethrobates, the "air-walker," for he was carried in the air on an arrow of the Hyperborean Apollo, over rivers, seas, and inaccessible places. It is believed that this was the method employed by Pythagoras when on the same day he discoursed with his friends at Metapontum and Tauromenium.
30. He soothed the passions of the soul and body by rhythms, songs, and incantations. These he adapted and applied to his friends. He himself could hear the Harmony of the Universe, and understood the universal music of the spheres, and of the stars which move in concert with them, and which we cannot hear because of the limitations of our weak nature. This is testified to by these characteristic verses of Empedocles:
31. The words "sublimest things," and "he surveyed all existent things," and "the wealth of the mind," and the like, are indicative of Pythagoras' constitution of body, mind, seeing, hearing and understanding, which was exquisite, and surpassingly accurate.
Pythagoras affirmed that the Nine Muses were constituted by the sounds made by the seven planets, the sphere of the fixed stars, and that which is opposed to our earth, called the "counter-earth." [1] He called Mnemosyne, or Memory, the composition, symphony and connexion of them all, which is eternal and unbegotten as being composed of all of them.
32. Diogenes, setting forth his daily routine of living, relates that he advised all men to avoid ambition and vainglory, which chiefly excite envy, and to shun the presence of crowds. He himself held morning conferences at his residence, composing his soul with the music of the lyre, and singing certain ancient paeans of Thales. He also sang verses of Homer and Hesiod, which seemed to soothe the mind. He danced certain dances which he thought conferred on the body agility and health. Walks he took not too promiscuously, but only in company of one or two companions, in temples of sacred groves, selecting the most quiet and beautiful places.
33. His friends he loved exceedingly, being the first to declare that "The goods of friends are common," and that "A friend is another self." While they were in good health he always conversed with them; if they were sick, he nursed them; if they were afflicted in mind, he solaced them, some by incantations and magic charms, others by music. He had prepared songs for the diseases of the body, by singing which he cured the sick. He had also some that caused forgetfulness of sorrow, mitigation of anger, and destruction of lust.
34. As to food, his breakfast was chiefly of honey; at dinner he used bread made of millet, barley or herbs, raw and boiled. Only rarely did he eat the flesh of sacrificial victims, nor did he take this from every part of the anatomy. When he intended to sojourn in the sanctuaries of the divinities, he would eat no more than was necessary to still hunger and thirst. To quiet hunger he made a mixture of poppy seed and sesame, the skin of a sea-onion, well washed until entirely drained of the outward juices, of the flowers of the daffodil, and the leaves of mallows, of paste of barley and chick peas, taking an equal weight of which, and chopping it small, with honey of Hymettus he made it into a mass. Against thirst he took the seed of cucumbers, and the best dried raisins, extracting the seeds, and coriander flowers, and the seeds of mallows, purslane, scraped cheese, wheat meal and cream, all of which he mixed up with wild honey.
35. He claimed that this diet had, by Demeter, been taught to Hercules, when he was sent into the Libyan deserts. This preserved his body in an unchanging condition, not at one time well, and at another time sick, nor at one time fat, and at another lean. Pythagoras' countenance showed the same constancy that was also in his soul. For he was neither more elated by pleasure, nor dejected by grief, and no one ever saw him either rejoicing or mourning.
36.When Pythagoras sacrificed to the Gods, he did not use offensive profusion, but offered no more than barley bread, cakes and myrrh, least of all animals, unless perhaps cocks and pigs. When he discovered the proposition that the square of the hypotenuse of a right-angled triangle was equal to the squares on the sides containing the right angle, he is said to have sacrificed an ox, although the more accurate say that this ox was made of flour.
37. His utterances were of two kinds, plain or symbolical. His teaching was twofold: of his disciples some were called Students (mathematikoi), and others Hearers (akousmatikoi). The Students learned the fuller and more exactly elaborate reasons of science, while the Hearers heard only the summarized instructions of learning, without more detailed explanations.
38. He ordained that his disciples should speak well and think reverently of the Gods, daimons, and heroes, and likewise of parents and benefactors; that they should obey the laws; that they should not relegate the worship of the Gods to a secondary position, but should perform it eagerly, even at home; that to the celestial divinities they should sacrifice uncommon offerings, and ordinary ones to the inferior deities. [The world he divided into] opposite powers: the better is the Monad, light, right, equal, stable and straight; while the worse is an inferior Dyad, darkness, left, unequal, unstable and curved.
39. Moreover, he taught the following. A cultivated and fruit-bearing plant, harmless to man and beast, should be neither injured nor destroyed. A deposit of money or of teachings should be faithfully preserved by the trustee.
There are three kinds of things that deserve to be pursued and acquired: honorable and virtuous things, those that conduce to the use of life, and those that bring pleasures of the blameless, secure and solemn kind, and not the vulgar intoxicating kinds. Of pleasures there are two kinds: one that indulges the stomach and lusts by a profusion of wealth, which he compared to the murderous songs of the Sirens; the other kind consists of things honest, just, and necessary to life, which are just as sweet as the first, without being followed by repentance, and these pleasures he compared to the harmony of the Muses.
40. He advised that special regard should be given to two times of the day: the one when we go to sleep, and the other when we awake. At each of these we should consider our past actions, and those that are to come. We ought to require of ourselves an account of our past deeds, while of the future we should have a providential care. Therefore he advised everybody to repeat to himself the following verses before he fell asleep:
And on rising, the following:
41. Such things taught he, though advising above all things to speak the truth, for this alone deifies men. For as he had learned from the Magi, who call God Horomazda, God's body is like light, and his soul is like truth. He taught much else, which he claimed to have learned from Aristokleia at Delphi. Certain things he declared mystically, symbolically, most of which were collected by Aristotle, as when he called the sea a tear of Kronos, the Great and Little Bear the hands of Rhea, the Pleiades the lyre of the Muses, and the planets the dogs of Persephone. He called the sound caused by striking on brass the voice of a daimon enclosed in the brass.
42. He had also another kind of symbols, such as pass not over a balance, that is, shun avarice; poke not the fire with a sword, that is, we ought not to excite a man full of fire and answer with sharp language; pluck not a crown meant not to violate the laws, which are the crowns of cities.
Moreover, Eat not the heart signified not to afflict ourselves with sorrows. Do not sit upon a bushel basket meant not to live ignobly. On starting a journey, do not turn back, meant that this life should not be regretted when near its end. Do not walk in the public way meant to avoid the opinions of the multitude, adopting those of the learned and the few. Receive not swallows into your house meant not to admit under the same roof garrulous and intemperate men. Help a man to take up a burden, but not to lay it down, meant to encourage no one to be indolent, but to apply oneself to labor and virtue. Do not carry the images of the Gods in rings, signifies that one should not at once to the vulgar reveal one's opinions about the Gods, or discourse about them. Offer libations to the Gods, just to the ears of the cup, meant that we ought to worship and celebrate the Gods with music, for that penetrates through the ears. Do not eat those things that are unlawful -- beginning, increase, source nor end -- nor the first basis of all things.
43. He thereby taught abstention from the loins, testicles, genitals, brains, feet and heads of sacrificial victims. The loins he called a foundation, because on them as on foundations living beings are settled. Testicles and genitals he called beginning for no one is engendered without the help of these. The brain he called increase, as it is the cause of growth in living beings. The source was the feet, and the head the end, since it has the most power in the government of the body. He likewise advised abstention from beans, as if from human flesh.
44. Beans were forbidden, it is said, because the particular plants grow and individualize only after that which is the principle and origin of things is mixed together, so that many things underground are confused, and coalesce, after which everything rots together. Then living creatures were produced together with plants, so that both men and beans arose out of putrefaction, whereof he alleged many manifest arguments. For if anyone should chew a bean, and having ground it to a pulp with his teeth, and should expose that pulp to the warm sun, for a short while, and then return to it, he will perceive the scent of human blood. Moreover, if at the time when beans bloom, one should take a little of the flower, which is then black, and should put it into an earthen vessel, and cover it closely, and bury it in the ground for ninety days, and at the end thereof take it up, and uncover it, instead of the bean he will find that either the head of an infant or the vagina of a woman has developed.
45. He also wished men to abstain from other things, such as sea-wombs, red mullet, and a sea-fish called a "nettle" (anemone), and from nearly all other marine animals. He referred his origin to those of past ages, affirming that he was first Euphorbus, then Aethalides, then Hermotimus, then Pyrrhus, and last, Pythagoras. He showed to his disciples that the soul is immortal, and to those who were rightly purified he brought back the memory of the acts of their former lives.
46. He cultivated philosophy, the scope of which is to free the mind implanted within us from the impediments and fetters within which it is confined, without whose freedom none can learn anything sound or true, or perceive the unsoundness in the operation of sense. Pythagoras thought that mind alone sees and hears, while all the rest are blind and deaf. The purified mind should be applied to the discovery of beneficial things, which can be effected by certain arts, which by degrees induce it to the contemplation of eternal and incorporeal things which never vary. This orderliness of perception should begin from consideration of the most minute things, lest by any change the mind should be jarred and withdraw itself, through the failure of continuousness in its subject-matter.
47. That is the reason he made so much use of the mathematical disciplines and speculations, which are intermediate between the physical and the incorporeal realm, for the reason that, like bodies, they have a three-fold dimension, and yet share the impassibility of incorporeals. [These disciplines he used] as degrees of preparation to the contemplation of the really existent things, by an artistic principle diverting the eyes of the mind from corporeal things, whose manner and state never remain in the same condition, to a desire for true [spiritual] food. By means of these mathematical sciences therefore, Pythagoras rendered men truly happy, by this artistic introduction of truly existent things.
48. Among others, Moderatus of Gades, who learnedly treated of the qualities of numbers in eleven books, states that the Pythagoreans specialized in the study of numbers to explain their teachings symbolically, as do geometricians, inasmuch as the primary forms and principles are hard to understand and express otherwise in plain discourse. A similar case is the representation of sounds by letters, which are known by marks, which are called the first elements of learning; later, they inform us these are not the true elements, which they only signify.
49. As the geometricians cannot express incorporeal forms in words, and have recourse to the drawings of figures, saying "This is a triangle," and yet do not mean that the actually seen lines are the triangle, but only what they represent, the knowledge in the mind, so the Pythagoreans used the same objective method in respect to first reasons and forms. As these incorporeal forms and first principles could not be expressed in words, they had recourse to demonstration by numbers. Number One denoted to them the reason of Unity, Identity, Equality, the purpose of friendship, sympathy, and conservation of the Universe, which results from persistence in Sameness. For unity in the details harmonizes all the parts of a whole, as by the participation of the First Cause.
50. Number Two, or Dyad, signified the dual reason of diversity and inequality, of everything that is divisible, or mutable, existing at one time in one way, and at another time in another way. After all, these methods were not confined to the Pythagoreans, being used by other philosophers to denote unitive powers, which contain all things in the universe, among which are certain reasons of equality, dissimilitude and diversity. These reasons are what they meant by the terms Monad and Dyad, or by the words uniform, biform, or diversiform.
51. The same reasons apply to their use of other numbers, which were ranked according to certain powers. Things that had a beginning, middle and end they denoted by the number Three, saying that anything that has a middle is triform, which was applied to every perfect thing. They said that if anything was perfect it would make use of this principle, and be adorned according to it; and as they had no other name for it, they invented the form, Triad, and whenever they tried to bring us to the knowledge of what is perfect they led us to that by the form of this Triad. So also with the other numbers, where were ranked according to the same reasons.
52. All other things were comprehended under a single form and power, which they called Decad, explaining it by a pun, as dechada ("receptacle"), meaning comprehension. That is why they call Ten a perfect number, the most perfect of all, as comprehending all difference of numbers, reasons, species and proportions. For if the nature of the universe be defined according to the reasons (logoi) and proportions of numbers, and if that which is produced, increased and perfected, proceed according to the reason of numbers and since the Decad comprehends every reason [or ratio] of numbers, every proportion, and every species -- why should Nature herself not be denoted by the most perfect number, Ten? Such was the use of numbers among the Pythagoreans.
53. This primary philosophy of the Pythagoreans finally died out, first because it was enigmatical, and then because their commentaries were written in Doric [Greek], which dialect itself is somewhat obscure, so that Doric teachings were not fully understood, and they became misapprehended and finally suspect as spurious when later those who published them no longer were Pythagoreans. The Pythagoreans affirm that Plato, Aristotle, [and their followers] Speusippus, Aristoxenus and Xenocrates appropriated the best of them, making but minor changes, but later collected and delivered as characteristic Pythagorean doctrines whatever had been invented by envious and malicious persons, to cast contempt on Pythagoreanism.
54. Pythagoras and his associates were long held in such admiration in Italy. that many cities invited them to undertake their administration. At last, however, they incurred envy, and a conspiracy was formed against them as follows. Cylon, a Crotonian, who in race, nobility and wealth was the most preeminent, was of a severe, violent and tyrannical disposition, and did not hesitate to use the multitude of his followers to achieve his ends. As he esteemed himself worthy of whatever was best, he considered it his right to be admitted to Pythagorean fellowship. He therefore went to Pythagoras, extolled himself, and desired his conversation. Pythagoras, however, who was accustomed to read in the nature and manners of human bodies the disposition of the man, bade him to depart, and go about his business. Cylon, being of a rough and violent disposition, took it as a great affront, and became furious.
55. He therefore assembled his friends, began to accuse Pythagoras, and conspired against him and his disciples. Pythagoras then went to Delos, to visit the Syrian Pherecydes; formerly his teacher, who was dangerously sick, to nurse him. Pythagoras' friends than gathered together in the house of Milo the athlete, and were all stoned and burned when Cylon's followers set the house on fire. Only two escaped -- Archippus and Lysis -- according to the account of Neanthes. Lysis took refuge in Greece and settled in Thebes with Epaminodas, of whom he became the teacher.
56. But Dicaearchus and other more accurate historians relate that Pythagoras himself was present when this conspiracy bore fruit, for Pherecydes had died before he left Samos. Of his friends, forty who were gathered together in a house were slain; while others were gradually slain as they came to the city. As his friends were taken, Pythagoras himself first escaped to the harbor of Caulonia, and thence to Locri. Hearing of his coming, the Locrians sent some old men to their frontiers to intercept him. They said, "Pythagoras, you are wise and of great worth, but as our laws contain nothing reprehensible, we will preserve them intact. Go to some other place, and we will furnish you with any needed necessities of travel." Pythagoras turned back, and sailed to Tarentum, where, receiving the same treatment as at Croton, he went to Metapontum. Everywhere arose great mobs against him, of which even now the inhabitants make mention, calling them the Pythagorean riots, as his followers were called Pythagoreans.
57. Pythagoras fled to the temple of the Muses in Metapontum. There he abode forty days and, starving, died. Others, however, state that his death was due to grief at loss of all his friends who, when the house in which they were gathered was burned, in order to make a way for their master, threw themselves into the flames and made a bridge of safety for him with their own bodies, whereby indeed he escaped. When the Pythagoreans died, with them also died their knowledge, which till then they had kept secret, except for a few obscure things which were commonly repeated by those who did not understand them. Pythagoras himself left no book; but some little sparks of his philosophy, obscure and difficult to grasp, were preserved by the few who were preserved by being scattered, like Lysis and Archippus.
58. The Pythagoreans now avoided human society, being lonely, saddened and dispersed. Fearing nevertheless that among men the name of philosophy would be entirely extinguished, and that therefore the Gods would be angry with them, they made abstracts and commentaries. Each man made his own collection of written authorities and his own memories, leaving them wherever he happened to die, charging their wives, sons and daughters to preserve them within their families. This mandate of transmission within each family was obeyed for a long time.
59. Nicomachus says that this was the reason why the Pythagoreans studiously avoided friendship with strangers, preserving a constant friendship among each other.
Aristoxenus, in his book on The life of Pythagoras, says he heard many things from Dionysius, the tyrant of Sicily, who, after his abdication, taught letters at Corinth. Among these were that they abstained from lamentations and grieving, and tears; also from adulation, entreaty, supplication and the like.
60. It is said that Dionysius at one time wanted to test their mutual fidelity under imprisonment. He contrived this plan. Phintias was arrested, and taken before the tyrant, and charged with plotting against the tyrant, convicted, and condemned to death. Phintias, accepting the situation, asked to be given the rest of the day to arrange his own affairs, and those of Damon, his friend and associate, who now would have to assume the management. He therefore asked for a temporary release, leaving Damon as security for his appearance. Dionysius granted the request, and they sent for Damon, who agreed to remain until Phintias should return.
61. The novelty of this deed astonished Dionysius, but those who had first suggested the experiment scoffed at Damon, saying he was in danger of losing his life. But to the general surprise, near sunset Phintias came to die. Dionysius then expressed his admiration, embraced them both, and asked to be received as a third in their friendship. Though he earnestly besought this, they refused this, though assigning no reason therefore. Aristoxenus states that he heard this from Dionysius himself.
Hippobotus and Neanthes relate about Myllia and Timycha...
[Here the manuscript ends.]
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Notes:
1. According to the cosmology of the Pythagorean Philolaus, antichthon, the counter-earth, revolves in time with the earth opposite the central fire. Aristotle assumes that the counter-earth was introduced to bring the number of the celestial bodies up to ten, the Pythagorean perfect number.
For he would continuously say, "We ought to the best of our ability avoid, and even with fire and sword eradicate from the body, sickness; from the soul, ignorance; from the belly, luxury; from a city, sedition; from a family, discord; and from all things, excess."
He likewise advised abstention from beans, as if from human flesh. Beans were forbidden, it is said, because the particular plants grow and individualize only after that which is the principle and origin of things is mixed together, so that many things underground are confused, and coalesce, after which everything rots together. Then living creatures were produced together with plants, so that both men and beans arose out of putrefaction, whereof he alleged many manifest arguments. For if anyone should chew a bean, and having ground it to a pulp with his teeth, and should expose that pulp to the warm sun, for a short while, and then return to it, he will perceive the scent of human blood. Moreover, if at the time when beans bloom, one should take a little of the flower, which is then black, and should put it into an earthen vessel, and cover it closely, and bury it in the ground for ninety days, and at the end thereof take it up, and uncover it, instead of the bean he will find that either the head of an infant or the vagina of a woman has developed.
-- The Life of Pythagoras, by Porphyry
PORPHYRY'S Life of Pythagoras is the only surviving fragment of his History of Philosophy in four books. Porphyry (c. 233-c. 305 C.E.), the brilliant student of Plotinus, was an important Neoplatonic philosopher who wrote over 70 works dealing with metaphysics, literary criticism, history, the allegorical interpretation of myth, and so on. Porphyry's biography of Pythagoras is short, enjoyable and informative, causing one to wish that his entire History of Philosophy had survived.
Kenneth Sylvan Guthrie was the first person to translate Prophyry's Life of Pythagoras into English. Since then the work has been translated by Morton Smith and appears in Hadas and Smith, Heroes and Gods: Spiritual Biographies in Antiquity, New York, 1965.
For an account of the life and work of Porphyry see the introduction to Porphyry's Letter to His Wife Marcella, Phanes Press, 1985. For a complete listing of his known writings see the appendix in Porphyry's Launching Points to the Realm of the Mind, Phanes Press, 1988.
THE LIFE OF PYTHAGORAS
MANY THINK THAT PYTHAGORAS was the son of Mnesarchus, but they differ as to the latter's race; some thinking him a Samian, while Neanthes, in the fifth book of his Fables states he was a Syrian, from the city of Tyre. As a famine had arisen in Samos, Mnesarchus went thither to trade, and was naturalized there. There also was born his son Pythagoras, who early manifested studiousness, but was later taken to Tyre, and there entrusted to the Chaldeans, whose doctrines he imbibed. Thence he returned to Ionia, where he first studied under the Syrian Pherecydes, then also under Hermodamas the Creophylian who at that time was an old man residing in Samos.
2. Neanthes says that others hold that his father was a Tyrrhenian, of those who inhabit Lemnos, and that while on a trading trip to Samos was there naturalized. On sailing to Italy, Mnesarchus took the youth Pythagoras with him. Just at this time this country was greatly flourishing. Neanthes adds that Pythagoras had two older brothers, Eunostus and Tyrrhenus. But Apollonius, in his book about Pythagoras, affirms that his mother was Pythais, a descendant, of Ancaeus, the founder of Samos. Apollonius adds that he was said to be the off-spring of Apollo and Pythais, on the authority of Mnesarchus; and a Samian poet sings:
Pythais, of all Samians the most fair,
Jove-loved Pythagoras to Phoebus bare!
Apollonius says that Pythagoras studied not only under Pherecydes and Hermodamas, but also under Anaximander.
3. Duris of Samos, in the second book of his Chronicles, writes that his son was Arimnestus, that he was the teacher of Democritus and that on returning from banishment, he suspended a brazen tablet in the temple of Hera, a pillar two cubits [three feet] in diameter, bearing this inscription:
Me, Arimnestus, who many proportions traced,
Pythagoras's beloved son here placed.
This tablet was removed by Simus, a musician, who claimed the harmonic canon graven thereon, and published it as his own. Seven proportions were engraved, but when Simus took away one, the others were destroyed.
4. It is said that by Theano, a Cretan, the daughter of Pythonax, Pythagoras had a son, Telauges, and a daughter, Myia; to whom some add Arignota, whose Pythagorean writings are still extant. Timaeus relates that Pythagoras's daughter, while a maiden, took precedence among the maidens in Crotona, and when a wife, among married men. The Crotonians made Pythagoras' house a temple of Demeter, and the neighboring street they called Museum Street.
5. Lycus, in the fourth book of his Histories, noting different opinions about his country, says, "Unless you happen to know the country and the city which Pythagoras was a citizen, it will remain a mere matter of conjecture. Some say he was a Samian, others from Phlious [in the Peloponnesus], others from Metapontine [in southern Italy]."
6. As to his knowledge, it is said that he learned the mathematical sciences from the Egyptians, Chaldeans and Phoenicians; for of old the Egyptians excelled in geometry, the Phoenicians in numbers and proportions, and the Chaldeans of astronomical theorems, divine rites, and worship of the Gods; other secrets concerning the course of life he received and learned from the Magi.
7. These accomplishments are the more generally known, but the rest are less celebrated. Moreover Eudoxus, in the second book of his Description of the Earth, writes that Pythagoras practiced the greatest purity, and was shocked at all bloodshed and killing; that he not only abstained from animal food, but never in any way approached butchers or hunters. Antiphon, in his book On Illustrious Virtuous Men praises his perseverance while he was in Egypt, saying that Pythagoras, desiring to become acquainted with the institutions of Egyptian priests, and diligently endeavoring to participate therein, requested the Tyrant Polycrates [of Samos] to write to Amasis, the King of Egypt, his friend and former host, to procure him initiation. Coming to Amasis, he was given letters to the priests, but the priests of Heliopolis sent him on to those of Memphis, on the pretense that the were the more ancient. On the same pretense, he was sent on from Memphis to Diospolis [or ancient Thebes].
8. From fear of the King the latter priests dared not make excuses [to initiate Pythagoras], but thinking that he would desist from his purpose as a result of great difficulties, they enjoined on him very hard precepts, entirely different from the institutions of the Greeks. These he performed so readily that he won their admiration, and they permitted him to sacrifice to the Gods, and to acquaint himself with all their sciences, a favor never previously granted to a foreigner.
9. Returning to Ionia, he opened in his own country a school which is even now called Pythagoras's Semicircle, and in which the Samians meet to deliberate about matters of common interest. Outside the city he made a cave adapted to the study of his philosophy, in which he lived day and night, discoursing with a few of his associates. He was now forty years old, says Aristoxenus. Seeing that Polycrates's government was becoming so violent that soon a free man would become a victim of his tyranny, he journeyed towards Italy.
10. Diogenes, in his treatise On the Incredible Things Beyond Thule, has treated Pythagoras's affairs so carefully that I think his account should not be omitted. He says that Mnesarchus was of the race of the Etruscans who inhabited Lemnos, Imbros and Scyrus and that he departed thence to visit many cities and various lands. During his journeys he found an infant lying under a large, tall poplar tree. On approaching, he observed it lay on its back, looking steadily without winking at the sun. In its mouth was a little slender reed, like a pipe, through which the child was being nourished by the dew-drops that fell from the tree. This great wonder prevailed upon him to take the child, believing it to be of a divine origin. The child was fostered by a native of that country, named Androcles, who later on adopted him, and entrusted to him the management of affairs. On becoming wealthy, Mnesarchus educated the boy, naming him Astraeus, and rearing him with his own three sons, Eunostus, Tyrrhenus, and Pythagoras.
11. He sent the boy to a lyre-player, a gymnast and a painter. Later he sent him to Anaximander at Miletus, to learn geometry and astronomy. Then Pythagoras visited the Egyptians, the Arabians, the Chaldeans and the Hebrews, from whom he acquired expertise in the interpretation of dreams, and acquired the use of frankincense in the worship of divinities.
12. In Egypt he lived with the priests, and learned the language and wisdom of the Egyptians, and three kinds of letters, the epistolographic, the hieroglyphic, and symbolic, whereof one imitates the common way of speaking, while the others express the sense of allegory and parable. In Arabia he conferred with the King. In Babylon he associated with the other Chaldeans, especially attaching himself to Zaratus [= Zoroaster], by whom he was purified from the pollutions of this past life, and taught the things from which a virtuous man ought to be free. Likewise he heard lectures about Nature, and the principles of wholes. It was from his stay among these foreigners that Pythagoras acquired the greater part of his wisdom.
13. Astraeus was by Mnesarchus entrusted to Pythagoras, who received him, and after studying his physiognomy and the motions of his body, instructed him. He first accurately investigated the science about the nature of man, discerning the disposition of everyone he met. None was allowed to become his friend or associate without being examined in facial expression and disposition.
14. Pythagoras had another youthful disciple from Thrace. Zamolxis was his name because he was born wrapped in a bear's skin, in Thracian called zalmon. Pythagoras loved him, and instructed him in sublime speculations concerning sacred rites, and the worship of the Gods. Some say this youth was named Thales, and that the barbarians worshipped him as Hercules.
15. Dionysiphanes says that he was a servant of Pythagoras, who fell into the hands of thieves and by them was branded when Pythagoras was persecuted and banished, and bound up his forehead on account of the scars. Others say that the name Zalmoxis signifies a stranger or foreigner.
Pherecydes, in Delos fell sick; and Pythagoras attended him until he died, and performed his funeral rites. Pythagoras then, longing to be with Hermodamas the Creophylus, returned to Samos. After enjoying his society, Pythagoras trained the Samian athlete Eurymenes, who though he was of small stature, conquered at Olympia through his surpassing knowledge of Pythagoras' wisdom. While according to ancient custom the other athletes fed on cheese and figs, Eurymenes, by the advice of Pythagoras, fed daily on meat, which endued his body with great strength. Pythagoras gradually imbued him with his wisdom, exhorting him to go into the struggle not for the sake of victory, but for the exercise; that he should gain by the training, avoiding the envy resulting from victory. For the victors, are not always pure, though decked with leafy crowns, are not always pure.
16. Later, when the Samians were oppressed with the tyranny of Polycrates, Pythagoras saw that life in such a state was unsuitable for a philosopher, and so planned to travel to Italy. At Delphi he inscribed an elegy on the tomb of Apollo, declaring that Apollo was the son of Silenus, but was slain by Pytho, and buried in the place called "Tripod", so named from the local mourning for Apollo by the three daughters of Triopas.
17. Going to Crete, Pythagoras besought initiation from the priests of Morgos, one of the Idaean Dactyls, by whom he was purified with the meteoritic thunder-stone, during which he lay, at dawn, stretched upon his face by the seaside, and at night, beside a river, crowned with a black lamb's woolen wreath. Descending into the Idaean cave, wrapped in black wool, he stayed there tomb twenty-seven days, according to custom; he sacrificed to Zeus, and saw the couch which there is yearly made for him. On Zeus's tomb Pythagoras inscribed an epigram, "Pythagoras to Zeus," which begins: "Zan deceased here lies, whom men call Zeus."
18. When he reached Italy, he stopped at Croton. His presence was that of a free man, tall, graceful in speech and gesture, and in everything else. Dicaearchus relates that the arrival of this great traveler, endowed with all the advantages of nature, and prosperously guided by fortune, produced on the Crotonians so great an impression, that he won the esteem of the elder magistrates, by his many and excellent discourses. They ordered him to deliver exhortations to the young men, and then to the boys who flocked out of the school to hear him, and then to the women, who came together for this purpose.
19. Through this he achieved great reputation, and he drew great audiences from the city, not only of men, but also of women, among whom was a specially illustrious person named Theano. He also drew audiences from among the neighboring barbarians, among whom were magnates and kings. What he told his audiences cannot be said with certainty, for he enjoined silence upon his hearers. But the following is a matter of general information. He taught that the soul was immortal, and that after death it transmigrates into other animated bodies. After certain specified periods, he said, the same events occur again, for nothing was entirely new; all animated beings are kin, and should be considered as belonging to one great family. Pythagoras was the first one to introduce these teachings into Greece.
20. His speech was so persuasive that, according to Nicomachus, in one dress made on first landing in Italy, he made more than two thousand adherents. Out of desire to live with him, these built a large auditorium, to which both women and boys were admitted. [Foreign visitors were so many that] they built whole cities, settling that whole region of Italy now known as Magna Graecia. His ordinances and laws were by them received as divine precepts, and they would do nothing to transgress them. Indeed, they ranked him among the divinities and held all property in common; and whenever they communicated to each other some choice bit of his philosophy, from which physical truths could always be deduced, they would swear by the Tetraktys, adjuring Pythagoras as a divine witness, in the words,
I call to witness him who to our souls expressed the
Tetraktys, eternal Nature's fountain-spring.
21. During his travels in Italy and Sicily he found various cities subjected one to another, both of long standing and recently. By his disciples, some of whom were found in every city, he infused into them an aspiration for liberty, thus restoring to freedom Croton, Sybaris, Catana, Regium, Himera, Agrigentum, Tauromenium, and others, on whom he imposed laws through Charondas of Catana, and Zaleucus of Locri, which resulted in a long era of good government, emulated by all their neighbors. Simicus the tyrant of Centoripae, on hearing Pythagoras' discourse, abdicated his rule, and divided his property between his sister and the citizens.
22. According to Aristoxenus, some Lucanians, Messapians, Peucetians, and Romans came to him. He rooted out all dissensions, not only among his disciples and their successors, for many ages, but among all the cities of Italy and Sicily, both internally and externally. For he would continuously say, "We ought to the best of our ability avoid, and even with fire and sword eradicate from the body, sickness; from the soul, ignorance; from the belly, luxury; from a city, sedition; from a family, discord; and from all things, excess."
23. If we may credit what ancient and trustworthy writers have related of him, he exerted an influence even over irrational animals. The Daunian bear, who had committed extensive depredations in the neighborhood, he seized; and after having patted her for awhile, and given her barley and fruits, he made her swear never again to touch a living creature, and then released her. She immediately took herself into the woods and the hills, and from that time on never attacked any irrational animal.
24. At Tarentum, in a pasture, seeing an ox cropping beans, he went to the herdsman, and advised him to tell the ox to abstain from beans. The countryman mocked him, proclaiming his ignorance of the ox-language. So Pythagoras himself went and whispered in the ox's ear. Not only did the bovine at once desist from his diet of beans, but would never touch any thenceforward, though he survived many years near Hera's temple at Tarentum, until very old, being called the sacred ox, and eating any food given him.
25. While at the Olympic games, he was discoursing with his friends about auguries, omens, and divine signs, and how men of true piety do receive messages from the Gods. Flying over his head was an eagle, who stopped, and came down to Pythagoras. After stroking her awhile he released her.
Meeting with some fishermen who were drawing in their nets heavily laden with fishes from the deep, he predicted the exact number offish they had caught. The fishermen said that if his estimate was accurate they would do whatever he commanded. They counted them accurately, and found the number correct. He then bade them to return the fish alive into the sea; and, what is more wonderful, not one of them died, although they had been out of the water a considerable time.
26. Many of his associates he reminded of the lives lived by their souls before they were bound to their present body, and by irrefutable arguments demonstrated that he had been Euphorbus, the son of Panothus. He specially praised the following Homeric verses about himself, and sang them to the lyre most elegantly:
The shining circlets of his golden hair,
Which even the Graces might be proud to wear,
Instarred with gems and gold, bestrew the shore,
With dust dishonored, and deformed with gore,
As the young olive, in some sylvan scene,
Crowned by fresh fountains with celestial green,
Lifts the gay head in snowy flowerets fair,
And plays and dances to the gentle air,
When lo, a whirlwind from high heaven invades,
The tender plant, and withers all its shades;
It lies uprooted from its genial head,
A lovely ruin, now defaced and dead.
Thus young, the beautiful Euphorbus lay,
While the fierce Spartan tore his shield away.
(Iliad, 17.51-66.)
27. The stories about the shield of this Phrygian Euphorbus being at Mycenae dedicated to Hera of Argive, along with other Trojan spoils, shall here be omitted as being of too generally known a nature.
It is said that the river Caucasus, while he, with many of his associates was passing over it, said to him very clearly, "Hail, Pythagoras!"
Almost unanimous is the report that on one and the same day he was present at Metapontum in Italy, and at Tauromenium in Sicily, in each place conversing with his friends, though the places are separated by many miles, both at sea and land, demanding a journey of many days.
28. It is well known that he showed his golden thigh to Abatis the Hyperborean, to confirm him in the opinion that he was the Hyperborean Apollo, whose priest Abatis was.
A ship was coming into the harbor, and his friends expressed the wish to own the goods it contained. "Then," said Pythagoras, "you would own a corpse!" On the ship's arrival this was found to be the true state of affairs.
Of Pythagoras many other more wonderful and divine things are persistently and unanimously related, so that we have no hesitation in saying never was more attributed to any man, nor was any more eminent.
29. Verified predictions of earthquakes are handed down, also, that he immediately chased away a pestilence, suppressed violent winds and hail, calmed storms both on rivers and on seas, for the comfort and safe passage of his friends. As their poems attest, the like was often performed by Empedocles, Epimenides and Abaris, who had learned the art of doing these things from him. Empedocles, indeed, was surnamed Alexanemos, "the chaser of winds," Epimenides, Cathartes, "the purifyer," Abaris was called Aethrobates, the "air-walker," for he was carried in the air on an arrow of the Hyperborean Apollo, over rivers, seas, and inaccessible places. It is believed that this was the method employed by Pythagoras when on the same day he discoursed with his friends at Metapontum and Tauromenium.
30. He soothed the passions of the soul and body by rhythms, songs, and incantations. These he adapted and applied to his friends. He himself could hear the Harmony of the Universe, and understood the universal music of the spheres, and of the stars which move in concert with them, and which we cannot hear because of the limitations of our weak nature. This is testified to by these characteristic verses of Empedocles:
Amongst these was one in things sublimest skilled,
His mind with all the wealth of learning filled.
Whatever sages did invent, he sought;
And whilst his thoughts were on this work intent,
All things existent, easily he viewed,
Through ten or twenty ages making search.
31. The words "sublimest things," and "he surveyed all existent things," and "the wealth of the mind," and the like, are indicative of Pythagoras' constitution of body, mind, seeing, hearing and understanding, which was exquisite, and surpassingly accurate.
Pythagoras affirmed that the Nine Muses were constituted by the sounds made by the seven planets, the sphere of the fixed stars, and that which is opposed to our earth, called the "counter-earth." [1] He called Mnemosyne, or Memory, the composition, symphony and connexion of them all, which is eternal and unbegotten as being composed of all of them.
32. Diogenes, setting forth his daily routine of living, relates that he advised all men to avoid ambition and vainglory, which chiefly excite envy, and to shun the presence of crowds. He himself held morning conferences at his residence, composing his soul with the music of the lyre, and singing certain ancient paeans of Thales. He also sang verses of Homer and Hesiod, which seemed to soothe the mind. He danced certain dances which he thought conferred on the body agility and health. Walks he took not too promiscuously, but only in company of one or two companions, in temples of sacred groves, selecting the most quiet and beautiful places.
33. His friends he loved exceedingly, being the first to declare that "The goods of friends are common," and that "A friend is another self." While they were in good health he always conversed with them; if they were sick, he nursed them; if they were afflicted in mind, he solaced them, some by incantations and magic charms, others by music. He had prepared songs for the diseases of the body, by singing which he cured the sick. He had also some that caused forgetfulness of sorrow, mitigation of anger, and destruction of lust.
34. As to food, his breakfast was chiefly of honey; at dinner he used bread made of millet, barley or herbs, raw and boiled. Only rarely did he eat the flesh of sacrificial victims, nor did he take this from every part of the anatomy. When he intended to sojourn in the sanctuaries of the divinities, he would eat no more than was necessary to still hunger and thirst. To quiet hunger he made a mixture of poppy seed and sesame, the skin of a sea-onion, well washed until entirely drained of the outward juices, of the flowers of the daffodil, and the leaves of mallows, of paste of barley and chick peas, taking an equal weight of which, and chopping it small, with honey of Hymettus he made it into a mass. Against thirst he took the seed of cucumbers, and the best dried raisins, extracting the seeds, and coriander flowers, and the seeds of mallows, purslane, scraped cheese, wheat meal and cream, all of which he mixed up with wild honey.
35. He claimed that this diet had, by Demeter, been taught to Hercules, when he was sent into the Libyan deserts. This preserved his body in an unchanging condition, not at one time well, and at another time sick, nor at one time fat, and at another lean. Pythagoras' countenance showed the same constancy that was also in his soul. For he was neither more elated by pleasure, nor dejected by grief, and no one ever saw him either rejoicing or mourning.
36.When Pythagoras sacrificed to the Gods, he did not use offensive profusion, but offered no more than barley bread, cakes and myrrh, least of all animals, unless perhaps cocks and pigs. When he discovered the proposition that the square of the hypotenuse of a right-angled triangle was equal to the squares on the sides containing the right angle, he is said to have sacrificed an ox, although the more accurate say that this ox was made of flour.
37. His utterances were of two kinds, plain or symbolical. His teaching was twofold: of his disciples some were called Students (mathematikoi), and others Hearers (akousmatikoi). The Students learned the fuller and more exactly elaborate reasons of science, while the Hearers heard only the summarized instructions of learning, without more detailed explanations.
38. He ordained that his disciples should speak well and think reverently of the Gods, daimons, and heroes, and likewise of parents and benefactors; that they should obey the laws; that they should not relegate the worship of the Gods to a secondary position, but should perform it eagerly, even at home; that to the celestial divinities they should sacrifice uncommon offerings, and ordinary ones to the inferior deities. [The world he divided into] opposite powers: the better is the Monad, light, right, equal, stable and straight; while the worse is an inferior Dyad, darkness, left, unequal, unstable and curved.
39. Moreover, he taught the following. A cultivated and fruit-bearing plant, harmless to man and beast, should be neither injured nor destroyed. A deposit of money or of teachings should be faithfully preserved by the trustee.
There are three kinds of things that deserve to be pursued and acquired: honorable and virtuous things, those that conduce to the use of life, and those that bring pleasures of the blameless, secure and solemn kind, and not the vulgar intoxicating kinds. Of pleasures there are two kinds: one that indulges the stomach and lusts by a profusion of wealth, which he compared to the murderous songs of the Sirens; the other kind consists of things honest, just, and necessary to life, which are just as sweet as the first, without being followed by repentance, and these pleasures he compared to the harmony of the Muses.
40. He advised that special regard should be given to two times of the day: the one when we go to sleep, and the other when we awake. At each of these we should consider our past actions, and those that are to come. We ought to require of ourselves an account of our past deeds, while of the future we should have a providential care. Therefore he advised everybody to repeat to himself the following verses before he fell asleep:
Nor suffer sleep to close thine eyes
Till thrice thy acts that day thou has run o'er;
How slip? What deeds? What duty left undone?
And on rising, the following:
As soon as ere thou wakest, in order lay
The actions to be done that following day.
41. Such things taught he, though advising above all things to speak the truth, for this alone deifies men. For as he had learned from the Magi, who call God Horomazda, God's body is like light, and his soul is like truth. He taught much else, which he claimed to have learned from Aristokleia at Delphi. Certain things he declared mystically, symbolically, most of which were collected by Aristotle, as when he called the sea a tear of Kronos, the Great and Little Bear the hands of Rhea, the Pleiades the lyre of the Muses, and the planets the dogs of Persephone. He called the sound caused by striking on brass the voice of a daimon enclosed in the brass.
42. He had also another kind of symbols, such as pass not over a balance, that is, shun avarice; poke not the fire with a sword, that is, we ought not to excite a man full of fire and answer with sharp language; pluck not a crown meant not to violate the laws, which are the crowns of cities.
Moreover, Eat not the heart signified not to afflict ourselves with sorrows. Do not sit upon a bushel basket meant not to live ignobly. On starting a journey, do not turn back, meant that this life should not be regretted when near its end. Do not walk in the public way meant to avoid the opinions of the multitude, adopting those of the learned and the few. Receive not swallows into your house meant not to admit under the same roof garrulous and intemperate men. Help a man to take up a burden, but not to lay it down, meant to encourage no one to be indolent, but to apply oneself to labor and virtue. Do not carry the images of the Gods in rings, signifies that one should not at once to the vulgar reveal one's opinions about the Gods, or discourse about them. Offer libations to the Gods, just to the ears of the cup, meant that we ought to worship and celebrate the Gods with music, for that penetrates through the ears. Do not eat those things that are unlawful -- beginning, increase, source nor end -- nor the first basis of all things.
43. He thereby taught abstention from the loins, testicles, genitals, brains, feet and heads of sacrificial victims. The loins he called a foundation, because on them as on foundations living beings are settled. Testicles and genitals he called beginning for no one is engendered without the help of these. The brain he called increase, as it is the cause of growth in living beings. The source was the feet, and the head the end, since it has the most power in the government of the body. He likewise advised abstention from beans, as if from human flesh.
44. Beans were forbidden, it is said, because the particular plants grow and individualize only after that which is the principle and origin of things is mixed together, so that many things underground are confused, and coalesce, after which everything rots together. Then living creatures were produced together with plants, so that both men and beans arose out of putrefaction, whereof he alleged many manifest arguments. For if anyone should chew a bean, and having ground it to a pulp with his teeth, and should expose that pulp to the warm sun, for a short while, and then return to it, he will perceive the scent of human blood. Moreover, if at the time when beans bloom, one should take a little of the flower, which is then black, and should put it into an earthen vessel, and cover it closely, and bury it in the ground for ninety days, and at the end thereof take it up, and uncover it, instead of the bean he will find that either the head of an infant or the vagina of a woman has developed.
45. He also wished men to abstain from other things, such as sea-wombs, red mullet, and a sea-fish called a "nettle" (anemone), and from nearly all other marine animals. He referred his origin to those of past ages, affirming that he was first Euphorbus, then Aethalides, then Hermotimus, then Pyrrhus, and last, Pythagoras. He showed to his disciples that the soul is immortal, and to those who were rightly purified he brought back the memory of the acts of their former lives.
46. He cultivated philosophy, the scope of which is to free the mind implanted within us from the impediments and fetters within which it is confined, without whose freedom none can learn anything sound or true, or perceive the unsoundness in the operation of sense. Pythagoras thought that mind alone sees and hears, while all the rest are blind and deaf. The purified mind should be applied to the discovery of beneficial things, which can be effected by certain arts, which by degrees induce it to the contemplation of eternal and incorporeal things which never vary. This orderliness of perception should begin from consideration of the most minute things, lest by any change the mind should be jarred and withdraw itself, through the failure of continuousness in its subject-matter.
47. That is the reason he made so much use of the mathematical disciplines and speculations, which are intermediate between the physical and the incorporeal realm, for the reason that, like bodies, they have a three-fold dimension, and yet share the impassibility of incorporeals. [These disciplines he used] as degrees of preparation to the contemplation of the really existent things, by an artistic principle diverting the eyes of the mind from corporeal things, whose manner and state never remain in the same condition, to a desire for true [spiritual] food. By means of these mathematical sciences therefore, Pythagoras rendered men truly happy, by this artistic introduction of truly existent things.
48. Among others, Moderatus of Gades, who learnedly treated of the qualities of numbers in eleven books, states that the Pythagoreans specialized in the study of numbers to explain their teachings symbolically, as do geometricians, inasmuch as the primary forms and principles are hard to understand and express otherwise in plain discourse. A similar case is the representation of sounds by letters, which are known by marks, which are called the first elements of learning; later, they inform us these are not the true elements, which they only signify.
49. As the geometricians cannot express incorporeal forms in words, and have recourse to the drawings of figures, saying "This is a triangle," and yet do not mean that the actually seen lines are the triangle, but only what they represent, the knowledge in the mind, so the Pythagoreans used the same objective method in respect to first reasons and forms. As these incorporeal forms and first principles could not be expressed in words, they had recourse to demonstration by numbers. Number One denoted to them the reason of Unity, Identity, Equality, the purpose of friendship, sympathy, and conservation of the Universe, which results from persistence in Sameness. For unity in the details harmonizes all the parts of a whole, as by the participation of the First Cause.
50. Number Two, or Dyad, signified the dual reason of diversity and inequality, of everything that is divisible, or mutable, existing at one time in one way, and at another time in another way. After all, these methods were not confined to the Pythagoreans, being used by other philosophers to denote unitive powers, which contain all things in the universe, among which are certain reasons of equality, dissimilitude and diversity. These reasons are what they meant by the terms Monad and Dyad, or by the words uniform, biform, or diversiform.
51. The same reasons apply to their use of other numbers, which were ranked according to certain powers. Things that had a beginning, middle and end they denoted by the number Three, saying that anything that has a middle is triform, which was applied to every perfect thing. They said that if anything was perfect it would make use of this principle, and be adorned according to it; and as they had no other name for it, they invented the form, Triad, and whenever they tried to bring us to the knowledge of what is perfect they led us to that by the form of this Triad. So also with the other numbers, where were ranked according to the same reasons.
52. All other things were comprehended under a single form and power, which they called Decad, explaining it by a pun, as dechada ("receptacle"), meaning comprehension. That is why they call Ten a perfect number, the most perfect of all, as comprehending all difference of numbers, reasons, species and proportions. For if the nature of the universe be defined according to the reasons (logoi) and proportions of numbers, and if that which is produced, increased and perfected, proceed according to the reason of numbers and since the Decad comprehends every reason [or ratio] of numbers, every proportion, and every species -- why should Nature herself not be denoted by the most perfect number, Ten? Such was the use of numbers among the Pythagoreans.
53. This primary philosophy of the Pythagoreans finally died out, first because it was enigmatical, and then because their commentaries were written in Doric [Greek], which dialect itself is somewhat obscure, so that Doric teachings were not fully understood, and they became misapprehended and finally suspect as spurious when later those who published them no longer were Pythagoreans. The Pythagoreans affirm that Plato, Aristotle, [and their followers] Speusippus, Aristoxenus and Xenocrates appropriated the best of them, making but minor changes, but later collected and delivered as characteristic Pythagorean doctrines whatever had been invented by envious and malicious persons, to cast contempt on Pythagoreanism.
54. Pythagoras and his associates were long held in such admiration in Italy. that many cities invited them to undertake their administration. At last, however, they incurred envy, and a conspiracy was formed against them as follows. Cylon, a Crotonian, who in race, nobility and wealth was the most preeminent, was of a severe, violent and tyrannical disposition, and did not hesitate to use the multitude of his followers to achieve his ends. As he esteemed himself worthy of whatever was best, he considered it his right to be admitted to Pythagorean fellowship. He therefore went to Pythagoras, extolled himself, and desired his conversation. Pythagoras, however, who was accustomed to read in the nature and manners of human bodies the disposition of the man, bade him to depart, and go about his business. Cylon, being of a rough and violent disposition, took it as a great affront, and became furious.
55. He therefore assembled his friends, began to accuse Pythagoras, and conspired against him and his disciples. Pythagoras then went to Delos, to visit the Syrian Pherecydes; formerly his teacher, who was dangerously sick, to nurse him. Pythagoras' friends than gathered together in the house of Milo the athlete, and were all stoned and burned when Cylon's followers set the house on fire. Only two escaped -- Archippus and Lysis -- according to the account of Neanthes. Lysis took refuge in Greece and settled in Thebes with Epaminodas, of whom he became the teacher.
56. But Dicaearchus and other more accurate historians relate that Pythagoras himself was present when this conspiracy bore fruit, for Pherecydes had died before he left Samos. Of his friends, forty who were gathered together in a house were slain; while others were gradually slain as they came to the city. As his friends were taken, Pythagoras himself first escaped to the harbor of Caulonia, and thence to Locri. Hearing of his coming, the Locrians sent some old men to their frontiers to intercept him. They said, "Pythagoras, you are wise and of great worth, but as our laws contain nothing reprehensible, we will preserve them intact. Go to some other place, and we will furnish you with any needed necessities of travel." Pythagoras turned back, and sailed to Tarentum, where, receiving the same treatment as at Croton, he went to Metapontum. Everywhere arose great mobs against him, of which even now the inhabitants make mention, calling them the Pythagorean riots, as his followers were called Pythagoreans.
57. Pythagoras fled to the temple of the Muses in Metapontum. There he abode forty days and, starving, died. Others, however, state that his death was due to grief at loss of all his friends who, when the house in which they were gathered was burned, in order to make a way for their master, threw themselves into the flames and made a bridge of safety for him with their own bodies, whereby indeed he escaped. When the Pythagoreans died, with them also died their knowledge, which till then they had kept secret, except for a few obscure things which were commonly repeated by those who did not understand them. Pythagoras himself left no book; but some little sparks of his philosophy, obscure and difficult to grasp, were preserved by the few who were preserved by being scattered, like Lysis and Archippus.
58. The Pythagoreans now avoided human society, being lonely, saddened and dispersed. Fearing nevertheless that among men the name of philosophy would be entirely extinguished, and that therefore the Gods would be angry with them, they made abstracts and commentaries. Each man made his own collection of written authorities and his own memories, leaving them wherever he happened to die, charging their wives, sons and daughters to preserve them within their families. This mandate of transmission within each family was obeyed for a long time.
59. Nicomachus says that this was the reason why the Pythagoreans studiously avoided friendship with strangers, preserving a constant friendship among each other.
Aristoxenus, in his book on The life of Pythagoras, says he heard many things from Dionysius, the tyrant of Sicily, who, after his abdication, taught letters at Corinth. Among these were that they abstained from lamentations and grieving, and tears; also from adulation, entreaty, supplication and the like.
60. It is said that Dionysius at one time wanted to test their mutual fidelity under imprisonment. He contrived this plan. Phintias was arrested, and taken before the tyrant, and charged with plotting against the tyrant, convicted, and condemned to death. Phintias, accepting the situation, asked to be given the rest of the day to arrange his own affairs, and those of Damon, his friend and associate, who now would have to assume the management. He therefore asked for a temporary release, leaving Damon as security for his appearance. Dionysius granted the request, and they sent for Damon, who agreed to remain until Phintias should return.
61. The novelty of this deed astonished Dionysius, but those who had first suggested the experiment scoffed at Damon, saying he was in danger of losing his life. But to the general surprise, near sunset Phintias came to die. Dionysius then expressed his admiration, embraced them both, and asked to be received as a third in their friendship. Though he earnestly besought this, they refused this, though assigning no reason therefore. Aristoxenus states that he heard this from Dionysius himself.
Hippobotus and Neanthes relate about Myllia and Timycha...
[Here the manuscript ends.]
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Notes:
1. According to the cosmology of the Pythagorean Philolaus, antichthon, the counter-earth, revolves in time with the earth opposite the central fire. Aristotle assumes that the counter-earth was introduced to bring the number of the celestial bodies up to ten, the Pythagorean perfect number.
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Re: The Pythagorean Sourcebook and Library
by admin » Wed Nov 13, 2013 4:05 am
FIGURE 11. COIN FROM CROTON
ANONYMOUS:
THE LIFE OF PYTHAGORAS
PRESERVED BY PHOTIUS
THE ANONYMOUS BIOGRAPHY here reproduced was preserved in the writings of Photius (c. 820-891 C.E.), a Byzantine patriarch and professor of philosophy at the Imperial Academy in Constantinople. Little can be said about its unidentified author except that he, in turn, may preserve some parts of Aristotle's lost treatise On the Pythagoreans.
This work discusses briefly the family of Pythagoras and touches upon some elements of Pythagorean metaphysics and traditional cosmology. This tractate is particularly interesting in that it discusses the ancient Pythagorean idea that man is a microcosm, reflecting all of the elements that make up the universe.
Guthrie was the first translator to render this text into English.
THE LIFE OF PYTHAGORAS
PLATO WAS THE PUPIL of Archytas, and thus the ninth in succession from Pythagoras; the tenth was Aristotle. Those of Pythagoras' disciples that were devoted to contemplation were called sebastici. the reverend, while those who were engaged in business were called politicians (politikoi). Those who cultivated the disciplines of geometry and astronomy were called students (mathematikoi). Those who associated personally with Pythagoras were called Pythagoreans (Pythagorikoi), while those who merely imitated his teachings were called Pythagoristians (Pythagoristai). All these generally abstained from the flesh of animals; at a certain time they tasted the flesh of sacrificial animals only.
2. Pythagoras is said to have lived 104 years; and Mnesarchus, one of his sons, died a young man. Telauges was another son, and Sara and Myia were his daughters. Theano, it is said, was not only his disciple, but practically his daughter.
3. The Pythagoreans preach a difference between the Monad, and the One; the Monad dwells in the intelligible realm, while the One dwells among numbers. Likewise, the Two exists among numerable things, while the Dyad is indeterminate.
4. The Monad expresses equality and measure, the Dyad expresses excess and defect. Mean and measure cannot admit of more or less, while excess and defect, which proceed to infinity, admit it; that is why the Dyad is called indeterminate. Since, because of the all- inclusion of the Monad and Dyad, all things refer to number, they call all things numbers; and the number is perfected in the decad. Ten is reached by adding in order the first four figures; that is why the Ten is called the Quaternary [or Tetraktys].
5. They affirm that man may improve in three ways: first, by conversation with the Gods, for to them none can approach unless he abstain from all evil, imitating the divinity, even unto assimilation; second, by well-doing, which is a characteristic of the divinity; third by dying, for if the slight soul-separation from the body resulting from discipline improves the soul so that she begins to divine, in dreams -- and if the deliria of illness produces visions -- then the soul must surely improve far more when entirely separated from the body by death.
6. The Pythagoreans abstained from eating animals on account of their foolish belief in transmigration, and also because flesh-food engages digestion too much, and is too fattening. Beans they also avoided, because they produce flatulency, over-satiety, and for other reasons.
7. The Pythagoreans considered the Monad as the origin (arche) of all things, just as a point is the beginning of a line, a line of a surface, and a surface of a solid, which constitutes a body. A point implies a preceding Monad, so that it is really the principle of bodies, and all of them arise from the Monad.
8. The Pythagoreans are said to have predicted many things, and Pythagoras' predictions always came true.
9. Plato is said to have learned his speculative and physical doctrines from the Italian Pythagoreans, his ethics from Socrates, and his logic from Zeno, Pannenides and the Eleatics. But all of these teachings descended from Pythagoras.
10. According to Pythagoras, Plato and Aristotle, sight is the judge of the ten colors, white and black being the extremes of all others between: yellow, tawny, pale, red, blue, green, light blue, and grey. Hearing is the judge of the voice, sharp and flat. Smell is the judge of odors, good and bad, and putridity, humidity, liquidness and evaporation. Taste is the judge of tastes, sweet and bitter, and between them five: sharp, acid, fresh, salt and hot. Touch judges many things between the extremes of heaviness and lightness, such as heat and cold; and those between them, hardness and softness; and those between them, dryness and moistness, and those between them. While the four main senses are confined to their special senses in the head, touch is diffused throughout the head and the whole body, and is common to all the senses, but is specialized in the hands.
11. Pythagoras taught that in heaven there are twelve orders, the first and outermost being the fixed sphere where, according to Aristotle, dwelt the highest God, and the intelligible deities, and where Plato located his Ideas. Next are the seven planets: Saturn, Jupiter, Mars, Venus, Mercury, Sun and Moon. Then comes the sphere of Fire, that of Air, Water, and last, Earth. In the fixed sphere dwells the First Cause, and whatever is nearest thereto is the best organized, and most excellent; while that which is furthest therefrom is the worst. Constant order is preserved as low as the Moon, while all things sublunary are disorderly.
Evil, therefore, must necessarily exist in the neighborhood of the Earth, which has been arranged as the lowest, as a basis for the world, and as a receptacle for the lowest things. All superlunary things are governed in firm order, and Providentially by the decree of God, which they follow; while beneath the moon operate four causes: God, Fate, our election, and Fortune. For instance, to go aboard a ship, or not, is in our power; but the storms and tempests that may arise out of a calm, are the result of Fortune; and the preservation of the ship, sailing through the waters, is in the hands of Providence, of God. There are many different modes of Fate. There is a distinction to be made between Fate, which is determined, orderly and consequent, while Fortune is spontaneous and casual. For example, it is one mode of Fate that guides the growth of a boy through all the sequential ages to manhood.
12. Aristotle, who was a diligent investigator, agreed with the Pythagoreans that the Zodiac runs obliquely, on account of the generations of those earthly things which become complements to the universe. For if these moved evenly, there would be no change of seasons, of any kind. Now the passage of the sun and the other planets from one sign to another effect the four seasons of the year, which determine the growth of plants, and the generation of animals.
13. Others thought that the sun's size exceeded that of the earth by no more than thirty times; but Pythagoras, as I think correctly, taught it was more than a hundred times as great.
14.Pythagoras called the revolution of Saturn the great year, inasmuch as the other planets run their course in a shorter time; Saturn, thirty years, Jupiter, twelve, Mars, two; the Sun in one; Mercury and Venus the same as the Sun. The moon, being nearest to the Earth, has the smallest cycle, that of a month.
15. It was Pythagoras who first called heaven kosmos, because it is perfect, and "adorned" with infinite beauty and living beings.
With Pythagoras agreed Plato and Aristotle that the soul is immortal, although some who did not understand Aristotle claimed he thought the soul was mortal.
Pythagoras said that man was a microcosm, which means a compendium of the universe; not because, like other animals, even the least, he is constituted by the four elements, but because he contains all the powers of the cosmos. For the universe contains Gods, the four elements, animals and plants. All of these powers are contained in man. He has reason, which is a divine power; he has the nature of the elements, and the powers of moving, growing, and reproduction. However, in each of these he is inferior to the others. For example, an athlete who practices five kinds of sports, diverting his powers into five channels, is inferior to the athlete who practices a single sport well; so man, having all of the powers, is inferior in each. We have less reasoning powers than the Gods, and less of each of the elements than the elements themselves. Our anger and desire are inferior to those passions in the irrational animals, while our powers of nutrition and growth are inferior to those in plants. Constituted therefore of different powers, we have a difficult life to lead.
16. While all other things are ruled by one nature only, we are drawn by different powers; as for instance, when by God we are drawn to better things, or when we are drawn to evil courses by the prevailing of the lower powers. He who, like a vigilant and expert charioteer, [1] within himself cultivates the divine element, will be able to utilize the other powers by a mingling of the elements, by anger, desire and habit, just as far as may be necessary. Though it seems easy to know yourself, this is the most difficult of all things. This is said to derive from the Pythian Apollo, though it is also attributed to Chilo, one of the Seven Sages. Its message is, in any event, to discover our own power, which amounts to learning the nature of the whole extant world which, as God advises us, is impossible without philosophy.
17. There are eight organs of knowledge: sense, imagination, art, opinion, deliberation, science, wisdom and mind. Art, prudence, science and mind we share with the Gods; sense and imagination, with the irrational animals; while opinion alone is our characteristic. Sense is a fallacious knowledge derived through the body; imagination is a notion in the soul; art is a habit of cooperating with reason. The words "with reason" are here added, for even a spider operates, but it lacks reason. Deliberation is a habit selective of the rightness of planning deeds; science is a habit of those things which remain ever the same, with Sameness; wisdom is a knowledge of the first causes; while Mind is the principle and fountain of all good things.
18. Docility is divided into three parts: shrewdness, memory and acuteness. Memory guards the things which have been learned; acuteness is quickness of understanding, and shrewdness is the ability of deducing the unlearned from what one has learned to investigate.
19. Heaven may be interpreted in three ways: first, as the outermost sphere; second, the space from the fixed sphere to the moon; third, the whole world, heaven and earth. [2]
20. The extreme elements, the best and worst, operate constantly. There is no intermission in activity with God, and things near him in Mind and Reason; and plants are continuously nourished by day and night. But man is not always active, nor are irrational animals, which rest and sleep most of the time.
21. The Greeks always surpassed the Barbarians in manners and habits, on account of the mild climate in which" they live. The Scythians are troubled by cold, and the Aethiopians by heat, which determines a violent interior heat and moisture, resulting in violence and audacity. Analogously, those who live near the middle zone and the mountains participate in the mildness of the country they inhabit. [3] That is why, as Plato says, the Greeks, and especially the Athenians, improved the disciplines that they had derived from the Barbarians. [4]
22. [From them had come] stratagems, painting, mechanics, polemics, oratory, and physical culture. But the sciences of these were developed by the Athenians, owing to the favorable natural conditions of light, and purity of air, which had the double effect of not only drying out the earth, as it is in Attica, but also making subtle the minds of men. So a rarified atmosphere is unfavorable to the fertility of the earth, but is favorable to mental development.
_______________
Notes:
1. Cf. Plato, Phaedrus, for the myth of the charioteer.
2. From Aristotle, On the Heavens, 1. 9. 278b.
3. Cf. Aristotle, Politics, VII. 7. 1327b.
4. Plato, Epinomis, 987d.
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Re: The Pythagorean Sourcebook and Library
by admin » Wed Nov 13, 2013 4:08 am
DIOGENES LAERTIUS:
THE LIFE OF PYTHAGORAS
DIOGENES LAERTIUS, who flourished during the third century of the common era, is best known for his remarkable compilation, Lives of the Eminent Philosophers, in which this Life of Pythagoras appears.
In compiling his biographical encyclopedia of Greek philosophy, Diogenes drew on a great many sources of varying quality. His work is especially valuable because, like Iamblichus and Porphyry, he quotes many earlier writers, often verbatim.
A convenient edition of the entire Lives of the Eminent Philosophers appears in two volumes, in the Loeb Classical Library, published by Harvard University Press. The divisions of the following text are those of Guthrie.
THE LIFE OF PYTHAGORAS
1. Early Life
SINCE WE have now gone through the Ionian philosophy, which was derived from Thales, and the lives of the several illustrious men who were the chief ornaments of that school, we will now proceed to treat the Italian School, which was founded by Pythagoras, the son of Mnesarchus, a gem-engraver, as he is recorded to have been by Hermippus, a native of Samos, or, as Aristoxenus asserts, a Tyrrhenian, and a native of one of the islands which the Athenians, after they had driven out the Tyrrhenians, had occupied. But some authors say that he was the son of Marmacus, the son of Hippasus, the son of Euthyphron, the son of Cleonymus, who was an exile from Phlious; and that Marmacus settled in Samos, and that from this this circumstance Pythagoras was called a Samian. After that, he migrated to Lesbos, having come to Pherecydes, with letters from his uncle Zoilus. Then he made three silver goblets, and carried them to Egypt as a present for each of the three priests. He had brothers, the eldest of whom was named Eunomus, the second one Tyrrhenus, and a slave named Zalmoxis, to whom the Getae sacrifice, believing him to be the same as Kronos, according to the account of Herodotus (iv. 93).
2. Studies
HE WAS A PUPIL, as I have already mentioned, of Pherecydes the Syrian, and after his death he came to Samos, and became a pupil of Hermodamas, the descendant of Creophylus, who was already an old man now.
3. Initiations
AS HE WAS a youth devoted to learning, he left his country, and had himself initiated into the Grecian and barbarian sacred mysteries. Accordingly he went to Egypt, on which occasion Polycrates gave him a letter of introduction to Amasis; and he learned the Egyptian language as Antiphon tells us, in his treatise On Those Men Who Have Become Conspicuous for Virtue, and he also associated with the Chaldeans and Magi.
Afterwards he went to Crete, and in company with Epimenides, he descended into the Idaean cave -- and in Egypt too he had entered into the holiest parts of their temples, and learned all the most secret mysteries that relate to their Gods. Then he returned again to Samos, and finding his country under the absolute dominion of Polycrates, he set sail, and fled to Croton in Italy. Having given laws to the Italians, he there gained a very high reputation, together with his followers, who were about three hundred in number, and governed the republic in a most excellent manner, so that the constitution was very nearly an aristocracy.
4. Transmigration
HERACLEIDES OF PONTUS says that he was accustomed to speak of himself in this manner: that he had formerly been Aethalides, and had been accounted to be the son of Hennes, and that Hennes had desired him to select any gift he pleased except immortality. Accordingly, he had requested that, whether living or dead, he might preserve the memory of what had happened to him. While, therefore, he was alive, he recalled everything, and when he was dead he retained the same memory. At a subsequent period he passed into Euphorbus, and was wounded by Menelaus. While he was Euphorbus, he used to say that he had formerly been Aethalides; and that he had received as a gift from Hermes the perpetual transmigration of his soul, so that it was constantly transmigrating and passing into whatever plants or animals it pleased, and he had also received the gift of knowing and recollecting all that his soul had suffered in Hades, and what sufferings too are endured by the rest of the souls.
But after Euphorbus died, he said that his soul had passed into Hermotimus, and when he wished to convince people of this, he went into the territory of the Branchidae, and going into the temple of Apollo, he showed his shield which Menelaus had dedicated there as an offering. For he said that he, when he sailed from Troy, had offered up his shield which was already getting worn out, to Apollo, and that nothing remained but the ivory face which was on it. He said that when Hermotimus died he had become Pyrrhus, a fisherman of Delos, and that he still recollected everything, how he had formerly been Aethalides, then Euphorbus, then Hennotimus, and then Pyrrhus. When Pyrrhus died, he became Pythagoras, and still recollected all the circumstances I have been mentioning.
5. Works of Pythagoras
NOW THEY SAY that Pythagoras did not leave behind him a single book, but they talk foolishly for Heraclitus, the natural philosopher, speaks plainly enough of him saying, "Pythagoras, the son of Mnesarchus, practiced inquiry beyond all other men, and making selections from these writings he thus formed a wisdom of his own, an extensive learning, and cunning art." [1] Thus he speaks, because Pythagoras, in the beginning of his treatise On Nature, writes in the following manner: "By the air which I breathe, and by the water which I drink, I will not endure to be blamed on account of this discourse."
There are three volumes extant written by Pythagoras, one On Education, one On Politics, and one On Nature. The treatise which is now extant under the name of Pythagoras is the work of Lysis of Tarentum, a philosopher of the Pythagorean school, who fled to Thebes and became the teacher of Epaminondas. Heracleides, the son of Serapion, in his Abridgement of Sotion, says that he wrote a poem in epic verse On the Universe, and secondly the Sacred Poem which begins thus:
Thirdly he wrote On the Soul; fourthly On Piety; fifthly Helothales, the Father of Epicharmus of Cos; sixthly, Croton, and other works too. But the mystic discourse which is extant under his name, they say is really the work of Hippasus, having been composed with a view to bring Pythagoras into disrepute. There were also many other books composed by Aston of Croton, and attributed to Pythagoras.
Aristoxenus asserts that Pythagoras derived the greater part of his ethical doctrines from Themistoclea, the priestess at Delphi. Ion of Chios, in his Triagmi, says that he wrote some poems and attributed them to Orpheus. His also, it is said, is the poem called Scopiads, which begins thus:
6. General Views of Life
SOSICRATES, in his Successions of Philosophers, relates that when asked who he was by Leon, the tyrant of the Phliasians, Pythagoras replied, "A philosopher." He adds that Pythagoras used to compare life to the Greater Games where some people come to contend for the prizes, and others for the purposes of traffic, but the best as spectators. So also in life the men of slavish dispositions are born hunters after glory and covetousness, but philosophers are seekers after the truth. Thus he spoke on this subject.
But in the three treatises above mentioned, the following principles are laid down by Pythagoras. He forbids men to pray for anything in particular for themselves, because they do not know what is good for them. He terms drunkenness an expression identical with ruin, and rejects all superfluity, saying that no one ought to exceed the proper quantity of meat and drink. On the subject of venereal pleasures, he says, "One ought to sacrifice to Aphrodite in the winter, not in the summer, and in autumn and spring in a lesser degree. But the practice is pernicious at every season, and is never good for the health." And once, when he was asked when a man might indulge in the pleasures of love, he replied, "Whenever you wish to be weaker than yourself."
7. Ages of Life
THUS DOES HE divide the ages of life: "A boy for twenty years, a young man for twenty years, a middle aged man for twenty years, and an old man for twenty. These different ages correspond proportionately to the seasons; boyhood answers to the spring, youth to the summer, middle age to autumn, and old age to winter," meaning by youth one not yet grown, and by young man one of mature age.
8. Social Customs
TIMAEUS says that he was the first person to assert that "The property of friends is common," and that "Friendship is equality. " His disciples used to put all their possessions together into one store, and use them in common. For five years they kept silence, doing nothing but listening to discourses, and never once seeing Pythagoras, until they were approved; after that time they were admitted into his house and allowed to see him. They also abstained from the use of cypress coffins, because the sceptre of Zeus is made of that wood, as Hermippus tells us in the second book of his account On Pythagoras.
9. Distinguished Appearance
HE IS SAID to have been a man of the most dignified appearance, and his disciples adopted an opinion that he was Apollo who had come from the Hyperboreans. It is also said that once when he was stripped naked he was seen to have a golden thigh, and many people affirmed that when he was crossing the river Nessus it addressed him by name.
10. Women Deified by Marriage
TIMAEUS, in the tenth book of his Histories, tells us that he used to say that women who were married to men had the names of divinities, being successively called Virgins, Nymphs, and then Mothers.
11. Scientific Culture
ALSO it was Pythagoras who carried geometry to perfection, after Moeris had first found out the principles of the elements of that science, as Auticlides tells us in the second book of his History of Alexander, and that the part of that science to which Pythagoras applied himself above all others was arithmetic. He discovered the numerical relation of sounds on the monochord, and he also studied medicine. Apollodorus the logician says of him that he sacrificed a hecatomb, when he had discovered that the square of the hypotenuse of a right-angled triangle was equal to the squares of the sides containing the right angle. There is an epigram which is couched in the following terms:
12. Diet and Sacrifices
HE is also said to have been the first man who trained athletes on meat. Eurymenes was the first man, according to the statement of Favorinus, in the third book of his Commentaries, who ever did submit to this diet, as before that time men used to train themselves on dry figs, and moist cheese and wheaten bread, as the same Favorinus informs us in the eight book of his Miscellaneous History. But some authors state that a trainer of the name of Pythagoras certainly did train his athletes on this system, but that it was not our philosopher, for as he even forbade men to kill animals at all, much less would he have allowed his disciples to eat them, since they have a right to live in common with mankind. And this was his pretext, but in reality he prohibited the eating of animals because he wished to train and accustom men to simplicity of life, so that all their food should be easily procurable, as it would be if they ate only such things as required no fire to cook them, and if they drank plain water; for from this diet they would derive health of body and acuteness of intellect.
The only altar at which he worshipped was that of Apollo the Giver of Life, at Delos, which is at the back of the Altar of Horns, because wheat and barley, and cheese cakes are the only offerings laid upon it, as it is not dressed by fire, and no victim is ever slain there, as Aristotle tells us, in his Constitution of the Delians. It is also said that he was the first person who asserted that the soul, revolving around the circle of necessity, is transformed and confined at different times in different bodies.
13. Measures and Weights
HE was also the first person who introduced measures and weights among the Greeks, as Aristoxenus the musician informs us.
14. Hesperus as Phosphorus
PARMENIDES assures us too that he was the first person who asserted the identity of Hesperus and Phosphorus [the Evening and Morning Star].
15. Students and Reputation
HE was so greatly admired that it used to be said that his disciples looked on all his sayings as the oracles of God. In his writings he himself said that he had come among men after having spent two hundred and seven years among the shades below. Therefore the Lucanians, Peucetians, Messapians and Romans flocked around him, coming with eagerness to hear his discourses. But until the time of Philolaus no doctrines of Pythagoras were ever divulged, and he was the first person who published the three celebrated books which Plato wrote to have purchased from him for a hundred minas. The students who used to come to his nightly lectures were no less than six hundred. Whenever anyone of them was permitted to see him, he wrote of it to his friends, as if they had achieved something wonderful.
The people of Metapontum used to call his house the Temple of Demeter, and the street leading to it was called that of the Muses, as we are informed in the Miscellaneous History of Favorinus.
According to the account given by Aristoxenus in his tenth book of his Rules of Education, the rest of the Pythagoreans used to say that his precepts ought not to be divulged to all the world; and Xenophilus the Pythagorean, when he was asked what was the best way for a man to educate his son, said, "That he must first of all take care that he is born in a city which enjoys good laws."
Pythagoras formed many excellent men in Italy, by his precepts, and among them the lawgivers Zaleucus and Charondas.
16. Friendship Founded on Symbols
PYTHAGORAS was famous for his power of attracting friendships; and among other things, if he ever heard that anyone had adopted his symbolic precepts, he at once made him a companion and a friend.
17. Symbols and Maxims
NOW WHAT HE CALLED his symbols were such as these. Do not poke the fire with a sword. Do not violate the beam of a balance. Do not sit down on a bushel. Do not devour your heart. Do not aid men in discarding a burden, but in increasing one. Always have your bed packed up. Do not bear the image of God on a ring. Efface the traces of a pot in the ashes. Do not wipe a seat with a lamp. Do not urinate towards the sun. Do not walk in the main street. Do not offer your hand lightly. Do not cherish swallows under your roof. Do not cherish birds with crooked talons. Do not urinate or stand upon the parings of your nails, or the cuttings of your hair. Avoid a sharp sword. When travelling abroad, do not look back at your own borders.
Now the precept not to poke the fire with a sword meant not to provoke the anger or swelling pride of powerful men; do not violate the beam of the balance meant not to transgress fairness and justice; not to sit on a bushel is to have an equal care for the present and the future, for by the bushel is meant one's daily food. By not devouring one's heart, he intended to show that we ought not to waste away our souls with grief and sorrow. In the precept that a man when travelling abroad should not turn his eyes back, he recommended those who were departing this life not to be desirous to live, and not to be too much attracted by the pleasures here on earth. And the other symbols may be explained in a similar manner, that we may not be too long-winded here.
18. Personal Habits
ABOVE ALL THINGS, he used to prohibit the eating of the red mullet and the blacktail; also the hearts of animals, and beans. Aristotle informs us that to these prohibitions he sometimes added tripe and gurnard. Some authors assert that he himself used to be contented with honey, honey-eomb and bread, and that he never drank wine during the day. He usually ate vegetables, either boiled or raw, and he very rarely ate fish. His dress was white, very clean; his bed-clothes also were white, and woollen, for linen had not yet been introduced in that country. He was never known to have eaten too much, or to have drunk too much, or to indulge in the pleasures of love. He abstained wholly from laughter, and from all such indulgences as jests and idle stories. He never chastised anyone, whether slave or free man, while he was angry. Admonishing he used to call "feeding storks."
He used to practice divination, as far as auguries and auspices, but not by means of burnt offerings, except only the burning of frankincense. All the sacrifices which he offered consisted of inanimate things. But some, however, assert that he did sacrifice animals, limiting himself to cocks, and sucking kids, which are called apalioi, but that he never offered lambs. Aristoxenus, however, affirms that he permitted the eating of all other animals, and abstained only from oxen used in agriculture, and from rams.
19. Various Teachings
THE SAME AUTHOR tells us, as I have already mentioned, that he received his doctrines from Themistoclea, [the priestess] at Delphi. Hieronymus says, that when he descended into the shades below, he saw the soul of Hesiod bound to a brazen pillar, and gnashing its teeth, and that of Homer suspended from a tree, with snakes around it, as a punishment for the things that they said of the Gods. Those who refrained from commerce with their wives also were punished, and that on account of this he was greatly honored at Croton.
Aristippus of Cyrene, in his Account of Natural Philosophers, says that Pythagoras derived his name from the fact of his speaking (agoreuein) truth no less than the God at Delphi (tou Pythiou). [2]
He used to admonish his disciples to repeat these lines to themselves whenever they returned home to their houses:
He used to forbid them to offer sacrificial victims to the Gods, ordering them to worship only at those altars which were unstained with blood. He also forbade them to swear by the Gods, saying that every man ought so to exercise himself as to be worthy of belief without an oath. He also taught men that it behooves them to honor their elders, thinking that most honorable which is prior in time, just as in the world, the rising of the sun is more so than the setting, in life, the beginning more so than the end, and in animals, production more so than destruction.
Another of his rules was that men should honor the Gods above the daimons, and heroes above men, and that of all men, parents are those entitled to more honor. He held that people should associate with each other in such a way as not to make their friends enemies, but to render their enemies friends. Another rule was that they should not think anything exclusively their own. Another was to assist the law, and to make war upon lawlessness. He said not to destroy or to injure a cultivated tree, nor any animal which does not injure man. Modesty and decorum consist in never yielding to laughter, without looking stem. Men should avoid eating too much flesh, and in travelling should let rest and exertion alternate; that they should exercise memory, nor ever say or do anything in anger; to respect every kind of divination, to sing songs accompanied by the lyre, and to display a reasonable gratitude to the Gods and eminent men by hymns.
His disciples were forbidden to eat beans because, as they are flatulent, they greatly partake of animal properties; and besides, the stomach is kept in much better order by avoiding them, and such abstinence makes the visions that appear in one's sleep gentle and free from agitation.
Alexander, in his Successions of Philosophers, reports the following doctrines as contained in the Pythagorean memoirs. The Monad is the beginning of everything. From this proceeds the Indefinite Dyad, which is subordinate to the Monad, as to its cause. From the Monad and the Indefinite Dyad proceed numbers. From numbers proceed points. From these, lines, of which plane figures consist. From these plane figures are derived solid bodies. From solid bodies are derived sensible bodies, of which there are four elements, fire, water, earth, and air. The world, which is endued with life and intellect, and which is of a spherical figure, in its center containing the earth, which is also spherical, and inhabited allover, results from a combination of these elements, and from them derives its motion. There are also antipodes, and what to us is below, is to them above.
He also taught that light and darkness, cold and heat, dryness and moisture, are equally divided in the world; and that, while heat is predominant in summer, so when cold prevails, it is winter; when dryness prevails, it is spring; and when moisture preponderates, autumn. The loveliest season of the year is when all these qualities are equally balanced, of which the flourishing spring is the most wholesome, and the autumn the most pernicious. Of day, the most flourishing period is the morning, while the evening is the fading one, and the least healthy.
Another of his theories was that the air around the earth is immovable, and pregnant with disease, and that in it everything is mortal, while the upper air is in perpetual motion, and salubrious; and that in it everything is immortal, and on that account divine. The sun, moon and the stars are all Gods; for in them dominates the principle which is the cause of living things. The moon derives its light from the sun. There is a relationship between men and the Gods, because men partake of the divine principle, on which count, therefore, God exercises his providence for our advantage. Fate is the cause of the arrangement of the world, both in general and in particular. From the sun a ray penetrates both the cold aether, which is the air, aer, and the dense aether, pachun aithera, which is the sea and moisture. This ray descends into the depths and in this way vivifies all things. Everything which partakes of the principle of heat lives, by which account, also, plants are animated beings, but not all living beings necessarily have souls. The soul is something torn off from the aether, both warm and cold, for it partakes of the cold aether too. The soul is something different from life. It is immortal, because of the immortality of that from which it was torn.
Animals are born from one another by seeds [sperm], and it is impossible for there to be any spontaneous generation by the earth. Sperm is a drop from the brain which in itself contains a warm vapor, and when this is applied to the womb, it transmits moisture, virtue, and blood from the brain, from which flesh, sinews, bones and hair, and the whole body are produced. From the vapor is produced the soul and also sensation. The infant first becomes a solid being at the end of forty days, but, according to the principles of harmony, it is not perfect till seven, or perhaps nine, or at most ten months, and then it is brought forth. In itself it contains all the principles of life, which are all connected together, and by their union and combination form a harmonious whole, each of them developing itself at the appointed time.
In general the senses, and especially sight, are a vapor of intense heat, on which account a man is said to see through air, or through water. For the hot principle is opposed by the cold one; since, if the vapor in the eyes were cold, it would have the same temperature as the air, and so would be dissipated. As it is, in some passages he calls the eyes the gates of the sun. In a similar manner he speaks of hearing, and of the other senses.
He also says that the soul of man is divided into three parts: into intelligence, reason, and passion; and that the first and last divisions are found also in other animals, but that the middle one, reason, is found in man only. The chief abode of the soul is in those parts of the body which are between the heart and the brain. Passion abides in the heart, while intelligence and reason reside in the brain.
The senses are distillations of these, and the reasoning sense is immortal, while the others are mortal. The soul is nourished by the blood, and the faculties are the winds of the soul. The soul is invisible, and so are its faculties, inasmuch as the aether itself is invisible. The bonds of the soul are the arteries, veins and nerves. When the soul is vigorous, and is by itself in a quiescent state, then its bonds are words and actions. When it is cast forth upon the earth, it wanders about, resembling the body. Hermes is the steward of the souls, and that is the reason he is called Guide, Keeper of the Gate, and Subterranean, since it is he who conducts the souls from their bodies, and from earth, and sea. He conducts the pure souls to the highest region, and he does not allow the impure ones to approach them, nor to come near one another, committing them to be bound in indissoluble fetters by the Furies.
The Pythagoreans also assert that the whole air is full of souls, and that these are those that are accounted daimons or heroes. They are the ones that send down among men dreams, and tokens of disease and health; the latter not being reserved to human beings, but being sent also to sheep and cattle as well. They are concerned with purifications, expiations, and all kinds of divinations, oracular predictions, and the like.
Man's most important privilege is to be able to persuade his soul to be either good or bad. Men are happy when they have a good soul; yet [if bad] they are never quiet, never long retaining the same mind. An oath is justice; and on that account Zeus is God of Oaths. Virtue is harmony, health, universal good and God, on which account everything owes its existence and preservation to harmony. Friendship is a harmonious quality.
Honors to Gods and heroes should not be equal. The Gods should be honored at all times, extolling them with praises, clothed in white garments, and keeping one's body chaste; but, to the heroes, such honors should not be paid till after noon.
A state of purity is brought about by purifications, washings and lustrations, by a man's purifying himself from all deaths and births, or any kind of pollution, by abstaining from all animals that have died, from mullets, from gurnards, from eggs, from such animals as lay eggs, from beans, and from other things that are prohibited by those who have charge of the mysteries in the temples.
In his treatise On the Pythagoreans, Aristotle says that Pythagoras' reason for demanding abstention from beans on the part of his disciples, was that either they resemble genitals, or because they are like the gates of hell [... ] they are the only plants without parts, or because they dry up other plants, or because they are representative of universal nature, or because they are used in elections in oligarchical governments.
He also forbade his disciples to pick up what fell from the table, for the sake of accustoming them to eat moderately, or else because such things belong to the dead. Aristophanes, indeed, said that what fell belonged to the heroes, in his Heroes singing,
He also forbade his disciples to eat white poultry, because a cock of that color was sacred to the Month, and was also a suppliant. Now white is an indication of a good nature, and black of a bad one. He was also accounted a good animal and he was sacred to the Month, for he indicates the time.
The Pythagoreans were also forbidden to eat of all fish that were sacred, on the grounds that the same animals should not be served up before both Gods and men, just as the same things do not belong to both freemen and slaves.
Another of the precepts of Pythagoras was never to break bread because in ancient times friends used to gather around the same loaf, as they even now do among the barbarians. Nor would he allow men to divide bread which united them. Some think that he laid down this rule in reference to the judgment which takes place in Hades, some because this practice engenders timidity in war. According to others, the reference is to the union which presides over the government of the universe.
Another one of his doctrines was that, of all solid figures, the sphere is the most beautiful, and of all plane figures, the circle. He held that old age and all diminution is similar, as is all increase and youth. Health, he said, is the permanence of form, and disease, its destruction. He thought salt should be set before people as a reminder of things just, for salt preserves everything which it touches, and comes from the purest sources, the sun and the sea.
These are the doctrines which Alexander asserts that he discovered in the Pythagorean treatises; what follows is Aristotle's.
20. Poetic Testimonies
TIMON, in his Silli, has not left unnoticed the dignified appearance of Pythagoras, though he attacks him on other points. Thus he speaks of:
Referring to his having been different people at different times, Xenophanes says in an elegiac poem, that begins thus:
And later,
Cratinus also ridiculed him in his Pythagorean Woman, and in his Tarentines he speaks thus:
In his Alcmaeon, Mnesimachus says:
And Austophon says in his Pythagorean:
And:
And again in the same play he says,
21. The Death of Pythagoras
PYTHAGORAS died in this manner. When he was sitting with some of his companions in Milo's house, some of those whom he did not think worthy of admission into it, were by envy excited to set fire to it. But some say that the people of Croton themselves did this, being afraid lest he might aspire to the tyranny. Pythagoras was caught as he was trying to escape, and coming to a place full of beans, he stopped there, saying that it was better to be caught than to trample on the beans, and better to be slain than to speak; and so he was murdered by those who were pursuing him. In this way also, most of his companions were slain, being about forty in number, but a very few did escape, among whom were Archippus of Tarentum, and Lysis, whom I have mentioned before.
But Dicaearchus states that Pythagoras died later, having escaped as far as the temple of the Muses at Metapontum, where he died of [self-imposed] starvation after forty days. Heracleides, in his Epitome of the Lives of Satyrus, says that after he had buried Pherecydes at Delos, he returned to Italy, and there finding a superb banquet prepared at the house of Milo of Croton, he left that city, for Metapontum, where, not wishing any longer to live, he put an end to his life by starvation. But Hermippus says that when there was war between the Agrigentines and the Syracusans, Pythagoras, with his usual companions, joined the Agrigentine army, which was put to flight. Coming up against a field of beans, instead of crossing it, he ran around it, and so was slain by the Syracusans, and the rest, about thirty-five in number, were burned at the stake in Tarentum, where they were trying to set up a new government against the prevailing magistrates.
Hermippus also relates another story about Pythagoras. When in Italy, he made a subterranean apartment, and charged his mother to write an account of everything that took place, marking the time of each on a tablet, then sending them down to him until he should ascend. His mother did so. Then after a certain time Pythagoras came up again, lean, and looking like a skeleton, he came into the public assembly, and said that he had arrived from Hades below, and then he recited to them all that had happened to them in the meanwhile. Being charmed with what he told them, they believed that Pythagoras was a divine being, so they wept and lamented, and even entrusted to him their wives, as likely to learn some good from him, and they took upon themselves the name of Pythagorean women. Thus far Hermippus.
22. Pythagoras' Family
PYTHAGORAS had a wife whose name was Theano, the daughter of Brontinus of Croton. Some say that she was the wife of Brontinus, and only Pythagoras' pupil. As Lysis mentions in his letter to Hipparchus, he had a daughter named Damo. Lysis' letter speaks of Pythagoras thus: "And many say that you philosophize in public, as Pythagoras deemed unworthy; for, when he had entrusted his commentaries to his daughter Damo, he charged her not to divulge them to anyone outside of the house. Though she might have sold his discourses for much money, she did not abandon them; for she thought that obedience to her father's injunctions, even though this entailed poverty, was better than gold, and for all that she was a woman."
He had also a son, named Telauges, who was his father's successor in his school, and who, according to some authors, was the teacher of Empedocles. At least Hippobotus relates that Empedocles said,
There is no book extant which is the work of Telauges, though there are some extant that are attributed to his mother Theano. Of her is told a story, that once, when asked how long it was before a woman becomes pure after intercourse, she said, "The moment she leaves her own husband, she is pure; but she is never pure at all, after she leaves anyone else." A woman who was going to her husband was by her told to put off her modesty with her clothes, and when she left him, to resume it therewith. When she was asked, "What clothes?" she replied, "Those which cause you to be called a woman."
23. Jesting Epigrams
NOW PYTHAGORAS, according to Heracleides, the son of Serapion, died when he was eighty years of age, according to his own account; by that of others, he was over ninety. On him we have written a sportive epigram, as follows:
Another, which runs thus:
Another, which follows:
Another one follows:
24. The Last Pythagoreans
HE FLOURISHED about the sixtieth Olympiad (532-528 B.C.E.) and his system lasted for about nine or ten generations. The last Pythagoreans known to Aristoxenus were Xenophilus the Chalcidean, from Thrace, Phanton the Philiasian with his countrymen Echecrates, Diocles and Polymnastus, disciples of Philolaus and Eurytus of Tarentum.
25. Various Pythagorases
PYTHAGORAS was the name of four men, almost contemporaneous, and living close to each other. One was a native of Croton, a man with a tyrant's leanings; the second was a Phliasian, and as some say, a trainer of athletes. The third was a native of Zacynthus; the fourth was this our philosopher, to whom the mysteries of philosophy are said to belong, and in whose time the proverbial phrase, ipse dixit ("the Master said"), arose generally. Some also claim the existence of a fifth Pythagoras, a sculptor of Rhegium, who is believed to have been the first discoverer of rhythm and proportion. Another was a Samian sculptor. Another, an orator of small reputation. Another was a physician, who wrote a treatise on hernias, and some essays on Homer. Dionysius tells us there was another who wrote a history of the affairs of the Dorians.
Eratosthenes, quoted by Favorinus in the eighth book of his Miscellaneous History, tells us that this philosopher, of whom we are speaking, was the first man who ever practiced boxing in a scientific manner, in the forty-eighth Olympiad (588-584 B.C.E.), having long hair, and being robed in purple. From competition with boys he was rejected; but being ridiculed for his application for this, he immediately entered among the men, and was victorious. Among other things, this statement is confirmed by an epigram of Theaetetus:
Favorinus says that he employed definitions on account of the mathematical subjects to which he applied himself. Socrates and his pupils did still more, and in this they were later followed by Aristotle and the Stoics.
He too was the first man who applied to the universe the name kosmos, and who first called the earth round, though Theophrastus attributes this to Parmenides, and Zeno to Hesiod. It is also said that he had a constant adversary, named Cylon, as Socrates' was Antilochus. This epigram was formerly repeated concerning Pythagoras the athlete:
26. Pythagoras' Letter
EXTANT is a letter of our philosopher's, which follows:
But since we have now finished our account of Pythagoras, we must also speak of the most eminent of the Pythagoreans. After whom, we must mention those who are spoken of more promiscuously in connection with no particular school, and then we will connect the whole series of philosophers worth speaking of, till we arrive at Epicurus. Now Telauges and Theano we have mentioned, so we must now speak of Empedocles, in the first place, for according to some accounts, he was a pupil of Pythagoras.
27. Empedocles as a Pythagorean
[Guthrie has omitted some genealogical material here.]
TIMAEUS, in the ninth book of his Histories, relates that Empedocles was a pupil of Pythagoras, saying that he was afterwards convicted of having divulged his doctrines, in the same way as Plato was, and that he was therefore henceforth forbidden from attending his school. It is said that Empedocles had Pythagoras in mind when he said:
But some say the philosopher was here referring to Parmenides.
Neanthes relates that until the time of Philolaus and Empedocles the Pythagoreans used to admit all persons indiscriminately into their schools; but when Empedocles by means of his poems publicized the doctrines, then they made a law to admit no epic poet. They said that the same thing happened to Plato, for that he too was excluded from the school. Empedocles' Pythagorean teacher is not mentioned; and as for the letter of Telauges, in which he is stated to have been a pupil of Hippasus and Brontinus, that is not worthy of belief. But Theophrastus says that he was an imitator and rival of Parmenides in his poems, for that he too had delivered his opinions on natural philosophy in epic verse.
Hermippus, however, says that he was an imitator not of Parmenides, but of Xenophanes with whom he lived; and that he imitated his epic style, and that it was at a later period that he fell in with the Pythagoreans. But Alcimadas, in his Physics, says that Zeno and Empedocles were pupils of Pannenides, about the same time, and that they subsequently left him. Zeno was said to have adopted a philosophical system peculiar to himself, but Empedocles became a pupil of Anaxagoras and Pythagoras, and he imitated the demeanor and way of life and gestures of the latter, and the natural philosophy of the other...
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Notes:
1. Heraclitus didn't care very much for polymaths, hence his disapproval of Pythagoras.
2. Pythios is the name of Apollo at Delphi. Iamblichus also alludes in chapter 1 of his biography to the etymological connection between the name Pythagoras and the Delphic Apollo.
THE LIFE OF PYTHAGORAS
DIOGENES LAERTIUS, who flourished during the third century of the common era, is best known for his remarkable compilation, Lives of the Eminent Philosophers, in which this Life of Pythagoras appears.
In compiling his biographical encyclopedia of Greek philosophy, Diogenes drew on a great many sources of varying quality. His work is especially valuable because, like Iamblichus and Porphyry, he quotes many earlier writers, often verbatim.
A convenient edition of the entire Lives of the Eminent Philosophers appears in two volumes, in the Loeb Classical Library, published by Harvard University Press. The divisions of the following text are those of Guthrie.
THE LIFE OF PYTHAGORAS
1. Early Life
SINCE WE have now gone through the Ionian philosophy, which was derived from Thales, and the lives of the several illustrious men who were the chief ornaments of that school, we will now proceed to treat the Italian School, which was founded by Pythagoras, the son of Mnesarchus, a gem-engraver, as he is recorded to have been by Hermippus, a native of Samos, or, as Aristoxenus asserts, a Tyrrhenian, and a native of one of the islands which the Athenians, after they had driven out the Tyrrhenians, had occupied. But some authors say that he was the son of Marmacus, the son of Hippasus, the son of Euthyphron, the son of Cleonymus, who was an exile from Phlious; and that Marmacus settled in Samos, and that from this this circumstance Pythagoras was called a Samian. After that, he migrated to Lesbos, having come to Pherecydes, with letters from his uncle Zoilus. Then he made three silver goblets, and carried them to Egypt as a present for each of the three priests. He had brothers, the eldest of whom was named Eunomus, the second one Tyrrhenus, and a slave named Zalmoxis, to whom the Getae sacrifice, believing him to be the same as Kronos, according to the account of Herodotus (iv. 93).
2. Studies
HE WAS A PUPIL, as I have already mentioned, of Pherecydes the Syrian, and after his death he came to Samos, and became a pupil of Hermodamas, the descendant of Creophylus, who was already an old man now.
3. Initiations
AS HE WAS a youth devoted to learning, he left his country, and had himself initiated into the Grecian and barbarian sacred mysteries. Accordingly he went to Egypt, on which occasion Polycrates gave him a letter of introduction to Amasis; and he learned the Egyptian language as Antiphon tells us, in his treatise On Those Men Who Have Become Conspicuous for Virtue, and he also associated with the Chaldeans and Magi.
Afterwards he went to Crete, and in company with Epimenides, he descended into the Idaean cave -- and in Egypt too he had entered into the holiest parts of their temples, and learned all the most secret mysteries that relate to their Gods. Then he returned again to Samos, and finding his country under the absolute dominion of Polycrates, he set sail, and fled to Croton in Italy. Having given laws to the Italians, he there gained a very high reputation, together with his followers, who were about three hundred in number, and governed the republic in a most excellent manner, so that the constitution was very nearly an aristocracy.
4. Transmigration
HERACLEIDES OF PONTUS says that he was accustomed to speak of himself in this manner: that he had formerly been Aethalides, and had been accounted to be the son of Hennes, and that Hennes had desired him to select any gift he pleased except immortality. Accordingly, he had requested that, whether living or dead, he might preserve the memory of what had happened to him. While, therefore, he was alive, he recalled everything, and when he was dead he retained the same memory. At a subsequent period he passed into Euphorbus, and was wounded by Menelaus. While he was Euphorbus, he used to say that he had formerly been Aethalides; and that he had received as a gift from Hermes the perpetual transmigration of his soul, so that it was constantly transmigrating and passing into whatever plants or animals it pleased, and he had also received the gift of knowing and recollecting all that his soul had suffered in Hades, and what sufferings too are endured by the rest of the souls.
But after Euphorbus died, he said that his soul had passed into Hermotimus, and when he wished to convince people of this, he went into the territory of the Branchidae, and going into the temple of Apollo, he showed his shield which Menelaus had dedicated there as an offering. For he said that he, when he sailed from Troy, had offered up his shield which was already getting worn out, to Apollo, and that nothing remained but the ivory face which was on it. He said that when Hermotimus died he had become Pyrrhus, a fisherman of Delos, and that he still recollected everything, how he had formerly been Aethalides, then Euphorbus, then Hennotimus, and then Pyrrhus. When Pyrrhus died, he became Pythagoras, and still recollected all the circumstances I have been mentioning.
5. Works of Pythagoras
NOW THEY SAY that Pythagoras did not leave behind him a single book, but they talk foolishly for Heraclitus, the natural philosopher, speaks plainly enough of him saying, "Pythagoras, the son of Mnesarchus, practiced inquiry beyond all other men, and making selections from these writings he thus formed a wisdom of his own, an extensive learning, and cunning art." [1] Thus he speaks, because Pythagoras, in the beginning of his treatise On Nature, writes in the following manner: "By the air which I breathe, and by the water which I drink, I will not endure to be blamed on account of this discourse."
There are three volumes extant written by Pythagoras, one On Education, one On Politics, and one On Nature. The treatise which is now extant under the name of Pythagoras is the work of Lysis of Tarentum, a philosopher of the Pythagorean school, who fled to Thebes and became the teacher of Epaminondas. Heracleides, the son of Serapion, in his Abridgement of Sotion, says that he wrote a poem in epic verse On the Universe, and secondly the Sacred Poem which begins thus:
Dear youths, I warn you cherish peace divine,
And in your hearts lay deep these words of mine.
Thirdly he wrote On the Soul; fourthly On Piety; fifthly Helothales, the Father of Epicharmus of Cos; sixthly, Croton, and other works too. But the mystic discourse which is extant under his name, they say is really the work of Hippasus, having been composed with a view to bring Pythagoras into disrepute. There were also many other books composed by Aston of Croton, and attributed to Pythagoras.
Aristoxenus asserts that Pythagoras derived the greater part of his ethical doctrines from Themistoclea, the priestess at Delphi. Ion of Chios, in his Triagmi, says that he wrote some poems and attributed them to Orpheus. His also, it is said, is the poem called Scopiads, which begins thus:
Behave not shamelessly to anyone.
6. General Views of Life
SOSICRATES, in his Successions of Philosophers, relates that when asked who he was by Leon, the tyrant of the Phliasians, Pythagoras replied, "A philosopher." He adds that Pythagoras used to compare life to the Greater Games where some people come to contend for the prizes, and others for the purposes of traffic, but the best as spectators. So also in life the men of slavish dispositions are born hunters after glory and covetousness, but philosophers are seekers after the truth. Thus he spoke on this subject.
But in the three treatises above mentioned, the following principles are laid down by Pythagoras. He forbids men to pray for anything in particular for themselves, because they do not know what is good for them. He terms drunkenness an expression identical with ruin, and rejects all superfluity, saying that no one ought to exceed the proper quantity of meat and drink. On the subject of venereal pleasures, he says, "One ought to sacrifice to Aphrodite in the winter, not in the summer, and in autumn and spring in a lesser degree. But the practice is pernicious at every season, and is never good for the health." And once, when he was asked when a man might indulge in the pleasures of love, he replied, "Whenever you wish to be weaker than yourself."
7. Ages of Life
THUS DOES HE divide the ages of life: "A boy for twenty years, a young man for twenty years, a middle aged man for twenty years, and an old man for twenty. These different ages correspond proportionately to the seasons; boyhood answers to the spring, youth to the summer, middle age to autumn, and old age to winter," meaning by youth one not yet grown, and by young man one of mature age.
8. Social Customs
TIMAEUS says that he was the first person to assert that "The property of friends is common," and that "Friendship is equality. " His disciples used to put all their possessions together into one store, and use them in common. For five years they kept silence, doing nothing but listening to discourses, and never once seeing Pythagoras, until they were approved; after that time they were admitted into his house and allowed to see him. They also abstained from the use of cypress coffins, because the sceptre of Zeus is made of that wood, as Hermippus tells us in the second book of his account On Pythagoras.
9. Distinguished Appearance
HE IS SAID to have been a man of the most dignified appearance, and his disciples adopted an opinion that he was Apollo who had come from the Hyperboreans. It is also said that once when he was stripped naked he was seen to have a golden thigh, and many people affirmed that when he was crossing the river Nessus it addressed him by name.
10. Women Deified by Marriage
TIMAEUS, in the tenth book of his Histories, tells us that he used to say that women who were married to men had the names of divinities, being successively called Virgins, Nymphs, and then Mothers.
11. Scientific Culture
ALSO it was Pythagoras who carried geometry to perfection, after Moeris had first found out the principles of the elements of that science, as Auticlides tells us in the second book of his History of Alexander, and that the part of that science to which Pythagoras applied himself above all others was arithmetic. He discovered the numerical relation of sounds on the monochord, and he also studied medicine. Apollodorus the logician says of him that he sacrificed a hecatomb, when he had discovered that the square of the hypotenuse of a right-angled triangle was equal to the squares of the sides containing the right angle. There is an epigram which is couched in the following terms:
When the great Samian sage his noble problem found,
A hundred oxen with their life-blood dyed the ground.
12. Diet and Sacrifices
HE is also said to have been the first man who trained athletes on meat. Eurymenes was the first man, according to the statement of Favorinus, in the third book of his Commentaries, who ever did submit to this diet, as before that time men used to train themselves on dry figs, and moist cheese and wheaten bread, as the same Favorinus informs us in the eight book of his Miscellaneous History. But some authors state that a trainer of the name of Pythagoras certainly did train his athletes on this system, but that it was not our philosopher, for as he even forbade men to kill animals at all, much less would he have allowed his disciples to eat them, since they have a right to live in common with mankind. And this was his pretext, but in reality he prohibited the eating of animals because he wished to train and accustom men to simplicity of life, so that all their food should be easily procurable, as it would be if they ate only such things as required no fire to cook them, and if they drank plain water; for from this diet they would derive health of body and acuteness of intellect.
The only altar at which he worshipped was that of Apollo the Giver of Life, at Delos, which is at the back of the Altar of Horns, because wheat and barley, and cheese cakes are the only offerings laid upon it, as it is not dressed by fire, and no victim is ever slain there, as Aristotle tells us, in his Constitution of the Delians. It is also said that he was the first person who asserted that the soul, revolving around the circle of necessity, is transformed and confined at different times in different bodies.
13. Measures and Weights
HE was also the first person who introduced measures and weights among the Greeks, as Aristoxenus the musician informs us.
14. Hesperus as Phosphorus
PARMENIDES assures us too that he was the first person who asserted the identity of Hesperus and Phosphorus [the Evening and Morning Star].
15. Students and Reputation
HE was so greatly admired that it used to be said that his disciples looked on all his sayings as the oracles of God. In his writings he himself said that he had come among men after having spent two hundred and seven years among the shades below. Therefore the Lucanians, Peucetians, Messapians and Romans flocked around him, coming with eagerness to hear his discourses. But until the time of Philolaus no doctrines of Pythagoras were ever divulged, and he was the first person who published the three celebrated books which Plato wrote to have purchased from him for a hundred minas. The students who used to come to his nightly lectures were no less than six hundred. Whenever anyone of them was permitted to see him, he wrote of it to his friends, as if they had achieved something wonderful.
The people of Metapontum used to call his house the Temple of Demeter, and the street leading to it was called that of the Muses, as we are informed in the Miscellaneous History of Favorinus.
According to the account given by Aristoxenus in his tenth book of his Rules of Education, the rest of the Pythagoreans used to say that his precepts ought not to be divulged to all the world; and Xenophilus the Pythagorean, when he was asked what was the best way for a man to educate his son, said, "That he must first of all take care that he is born in a city which enjoys good laws."
Pythagoras formed many excellent men in Italy, by his precepts, and among them the lawgivers Zaleucus and Charondas.
16. Friendship Founded on Symbols
PYTHAGORAS was famous for his power of attracting friendships; and among other things, if he ever heard that anyone had adopted his symbolic precepts, he at once made him a companion and a friend.
17. Symbols and Maxims
NOW WHAT HE CALLED his symbols were such as these. Do not poke the fire with a sword. Do not violate the beam of a balance. Do not sit down on a bushel. Do not devour your heart. Do not aid men in discarding a burden, but in increasing one. Always have your bed packed up. Do not bear the image of God on a ring. Efface the traces of a pot in the ashes. Do not wipe a seat with a lamp. Do not urinate towards the sun. Do not walk in the main street. Do not offer your hand lightly. Do not cherish swallows under your roof. Do not cherish birds with crooked talons. Do not urinate or stand upon the parings of your nails, or the cuttings of your hair. Avoid a sharp sword. When travelling abroad, do not look back at your own borders.
Now the precept not to poke the fire with a sword meant not to provoke the anger or swelling pride of powerful men; do not violate the beam of the balance meant not to transgress fairness and justice; not to sit on a bushel is to have an equal care for the present and the future, for by the bushel is meant one's daily food. By not devouring one's heart, he intended to show that we ought not to waste away our souls with grief and sorrow. In the precept that a man when travelling abroad should not turn his eyes back, he recommended those who were departing this life not to be desirous to live, and not to be too much attracted by the pleasures here on earth. And the other symbols may be explained in a similar manner, that we may not be too long-winded here.
18. Personal Habits
ABOVE ALL THINGS, he used to prohibit the eating of the red mullet and the blacktail; also the hearts of animals, and beans. Aristotle informs us that to these prohibitions he sometimes added tripe and gurnard. Some authors assert that he himself used to be contented with honey, honey-eomb and bread, and that he never drank wine during the day. He usually ate vegetables, either boiled or raw, and he very rarely ate fish. His dress was white, very clean; his bed-clothes also were white, and woollen, for linen had not yet been introduced in that country. He was never known to have eaten too much, or to have drunk too much, or to indulge in the pleasures of love. He abstained wholly from laughter, and from all such indulgences as jests and idle stories. He never chastised anyone, whether slave or free man, while he was angry. Admonishing he used to call "feeding storks."
He used to practice divination, as far as auguries and auspices, but not by means of burnt offerings, except only the burning of frankincense. All the sacrifices which he offered consisted of inanimate things. But some, however, assert that he did sacrifice animals, limiting himself to cocks, and sucking kids, which are called apalioi, but that he never offered lambs. Aristoxenus, however, affirms that he permitted the eating of all other animals, and abstained only from oxen used in agriculture, and from rams.
19. Various Teachings
THE SAME AUTHOR tells us, as I have already mentioned, that he received his doctrines from Themistoclea, [the priestess] at Delphi. Hieronymus says, that when he descended into the shades below, he saw the soul of Hesiod bound to a brazen pillar, and gnashing its teeth, and that of Homer suspended from a tree, with snakes around it, as a punishment for the things that they said of the Gods. Those who refrained from commerce with their wives also were punished, and that on account of this he was greatly honored at Croton.
Aristippus of Cyrene, in his Account of Natural Philosophers, says that Pythagoras derived his name from the fact of his speaking (agoreuein) truth no less than the God at Delphi (tou Pythiou). [2]
He used to admonish his disciples to repeat these lines to themselves whenever they returned home to their houses:
In what have I transgressed? What have I done?
What that I should have done have I omitted?
He used to forbid them to offer sacrificial victims to the Gods, ordering them to worship only at those altars which were unstained with blood. He also forbade them to swear by the Gods, saying that every man ought so to exercise himself as to be worthy of belief without an oath. He also taught men that it behooves them to honor their elders, thinking that most honorable which is prior in time, just as in the world, the rising of the sun is more so than the setting, in life, the beginning more so than the end, and in animals, production more so than destruction.
Another of his rules was that men should honor the Gods above the daimons, and heroes above men, and that of all men, parents are those entitled to more honor. He held that people should associate with each other in such a way as not to make their friends enemies, but to render their enemies friends. Another rule was that they should not think anything exclusively their own. Another was to assist the law, and to make war upon lawlessness. He said not to destroy or to injure a cultivated tree, nor any animal which does not injure man. Modesty and decorum consist in never yielding to laughter, without looking stem. Men should avoid eating too much flesh, and in travelling should let rest and exertion alternate; that they should exercise memory, nor ever say or do anything in anger; to respect every kind of divination, to sing songs accompanied by the lyre, and to display a reasonable gratitude to the Gods and eminent men by hymns.
His disciples were forbidden to eat beans because, as they are flatulent, they greatly partake of animal properties; and besides, the stomach is kept in much better order by avoiding them, and such abstinence makes the visions that appear in one's sleep gentle and free from agitation.
Alexander, in his Successions of Philosophers, reports the following doctrines as contained in the Pythagorean memoirs. The Monad is the beginning of everything. From this proceeds the Indefinite Dyad, which is subordinate to the Monad, as to its cause. From the Monad and the Indefinite Dyad proceed numbers. From numbers proceed points. From these, lines, of which plane figures consist. From these plane figures are derived solid bodies. From solid bodies are derived sensible bodies, of which there are four elements, fire, water, earth, and air. The world, which is endued with life and intellect, and which is of a spherical figure, in its center containing the earth, which is also spherical, and inhabited allover, results from a combination of these elements, and from them derives its motion. There are also antipodes, and what to us is below, is to them above.
He also taught that light and darkness, cold and heat, dryness and moisture, are equally divided in the world; and that, while heat is predominant in summer, so when cold prevails, it is winter; when dryness prevails, it is spring; and when moisture preponderates, autumn. The loveliest season of the year is when all these qualities are equally balanced, of which the flourishing spring is the most wholesome, and the autumn the most pernicious. Of day, the most flourishing period is the morning, while the evening is the fading one, and the least healthy.
Another of his theories was that the air around the earth is immovable, and pregnant with disease, and that in it everything is mortal, while the upper air is in perpetual motion, and salubrious; and that in it everything is immortal, and on that account divine. The sun, moon and the stars are all Gods; for in them dominates the principle which is the cause of living things. The moon derives its light from the sun. There is a relationship between men and the Gods, because men partake of the divine principle, on which count, therefore, God exercises his providence for our advantage. Fate is the cause of the arrangement of the world, both in general and in particular. From the sun a ray penetrates both the cold aether, which is the air, aer, and the dense aether, pachun aithera, which is the sea and moisture. This ray descends into the depths and in this way vivifies all things. Everything which partakes of the principle of heat lives, by which account, also, plants are animated beings, but not all living beings necessarily have souls. The soul is something torn off from the aether, both warm and cold, for it partakes of the cold aether too. The soul is something different from life. It is immortal, because of the immortality of that from which it was torn.
Animals are born from one another by seeds [sperm], and it is impossible for there to be any spontaneous generation by the earth. Sperm is a drop from the brain which in itself contains a warm vapor, and when this is applied to the womb, it transmits moisture, virtue, and blood from the brain, from which flesh, sinews, bones and hair, and the whole body are produced. From the vapor is produced the soul and also sensation. The infant first becomes a solid being at the end of forty days, but, according to the principles of harmony, it is not perfect till seven, or perhaps nine, or at most ten months, and then it is brought forth. In itself it contains all the principles of life, which are all connected together, and by their union and combination form a harmonious whole, each of them developing itself at the appointed time.
In general the senses, and especially sight, are a vapor of intense heat, on which account a man is said to see through air, or through water. For the hot principle is opposed by the cold one; since, if the vapor in the eyes were cold, it would have the same temperature as the air, and so would be dissipated. As it is, in some passages he calls the eyes the gates of the sun. In a similar manner he speaks of hearing, and of the other senses.
He also says that the soul of man is divided into three parts: into intelligence, reason, and passion; and that the first and last divisions are found also in other animals, but that the middle one, reason, is found in man only. The chief abode of the soul is in those parts of the body which are between the heart and the brain. Passion abides in the heart, while intelligence and reason reside in the brain.
The senses are distillations of these, and the reasoning sense is immortal, while the others are mortal. The soul is nourished by the blood, and the faculties are the winds of the soul. The soul is invisible, and so are its faculties, inasmuch as the aether itself is invisible. The bonds of the soul are the arteries, veins and nerves. When the soul is vigorous, and is by itself in a quiescent state, then its bonds are words and actions. When it is cast forth upon the earth, it wanders about, resembling the body. Hermes is the steward of the souls, and that is the reason he is called Guide, Keeper of the Gate, and Subterranean, since it is he who conducts the souls from their bodies, and from earth, and sea. He conducts the pure souls to the highest region, and he does not allow the impure ones to approach them, nor to come near one another, committing them to be bound in indissoluble fetters by the Furies.
The Pythagoreans also assert that the whole air is full of souls, and that these are those that are accounted daimons or heroes. They are the ones that send down among men dreams, and tokens of disease and health; the latter not being reserved to human beings, but being sent also to sheep and cattle as well. They are concerned with purifications, expiations, and all kinds of divinations, oracular predictions, and the like.
Man's most important privilege is to be able to persuade his soul to be either good or bad. Men are happy when they have a good soul; yet [if bad] they are never quiet, never long retaining the same mind. An oath is justice; and on that account Zeus is God of Oaths. Virtue is harmony, health, universal good and God, on which account everything owes its existence and preservation to harmony. Friendship is a harmonious quality.
Honors to Gods and heroes should not be equal. The Gods should be honored at all times, extolling them with praises, clothed in white garments, and keeping one's body chaste; but, to the heroes, such honors should not be paid till after noon.
A state of purity is brought about by purifications, washings and lustrations, by a man's purifying himself from all deaths and births, or any kind of pollution, by abstaining from all animals that have died, from mullets, from gurnards, from eggs, from such animals as lay eggs, from beans, and from other things that are prohibited by those who have charge of the mysteries in the temples.
In his treatise On the Pythagoreans, Aristotle says that Pythagoras' reason for demanding abstention from beans on the part of his disciples, was that either they resemble genitals, or because they are like the gates of hell [... ] they are the only plants without parts, or because they dry up other plants, or because they are representative of universal nature, or because they are used in elections in oligarchical governments.
He also forbade his disciples to pick up what fell from the table, for the sake of accustoming them to eat moderately, or else because such things belong to the dead. Aristophanes, indeed, said that what fell belonged to the heroes, in his Heroes singing,
Never taste the things which fall.
From the table on the floor.
He also forbade his disciples to eat white poultry, because a cock of that color was sacred to the Month, and was also a suppliant. Now white is an indication of a good nature, and black of a bad one. He was also accounted a good animal and he was sacred to the Month, for he indicates the time.
The Pythagoreans were also forbidden to eat of all fish that were sacred, on the grounds that the same animals should not be served up before both Gods and men, just as the same things do not belong to both freemen and slaves.
Another of the precepts of Pythagoras was never to break bread because in ancient times friends used to gather around the same loaf, as they even now do among the barbarians. Nor would he allow men to divide bread which united them. Some think that he laid down this rule in reference to the judgment which takes place in Hades, some because this practice engenders timidity in war. According to others, the reference is to the union which presides over the government of the universe.
Another one of his doctrines was that, of all solid figures, the sphere is the most beautiful, and of all plane figures, the circle. He held that old age and all diminution is similar, as is all increase and youth. Health, he said, is the permanence of form, and disease, its destruction. He thought salt should be set before people as a reminder of things just, for salt preserves everything which it touches, and comes from the purest sources, the sun and the sea.
These are the doctrines which Alexander asserts that he discovered in the Pythagorean treatises; what follows is Aristotle's.
20. Poetic Testimonies
TIMON, in his Silli, has not left unnoticed the dignified appearance of Pythagoras, though he attacks him on other points. Thus he speaks of:
Pythagoras who often teaches
Precepts of magic, and with speeches
Of long high-sounding diction draws,
From gaping crowds, a vain applause.
Referring to his having been different people at different times, Xenophanes says in an elegiac poem, that begins thus:
Now will I upon another subject touch.
And lead the way
And later,
They say that once, as passing by he saw
A dog severely beaten, he did pity him;
And spoke as follows to the man who beat him:
"Stop now, and beat him not; since in his body
Abides the soul of a dear friend of mine,
Whose voice I recognized as he was crying."
Cratinus also ridiculed him in his Pythagorean Woman, and in his Tarentines he speaks thus:
They are accustomed, if by chance they see
A private individual abroad,
To try what powers of argument he has,
How he can speak and reason; and they bother him
With strange antitheses, and forced conclusions,
Errors, comparisons, and magnitudes,
Till they have filled, and quite perplexed his mind.
In his Alcmaeon, Mnesimachus says:
As we do sacrifice to the Phoebus whom
Pythagoras worships, never eating aught
Which has the breath of life.
And Austophon says in his Pythagorean:
He said that when he did descend below
Among the shades in Hell, he there beheld
All men who e'er had died; and there he saw,
That the Pythagoreans differed much
From all the rest; for that with them alone
Did Pluto deign to eat, much honoring
Their pious habits.
And:
He's a civil God,
If he likes eating with such dirty fellows.
And again in the same play he says,
They eat nothing but herbs and vegetables, and drink
Pure water only; but their lice are such,
Their cloaks so dirty, and their unwashed
So rank, that none of our younger men
Will for a moment bear them.
21. The Death of Pythagoras
PYTHAGORAS died in this manner. When he was sitting with some of his companions in Milo's house, some of those whom he did not think worthy of admission into it, were by envy excited to set fire to it. But some say that the people of Croton themselves did this, being afraid lest he might aspire to the tyranny. Pythagoras was caught as he was trying to escape, and coming to a place full of beans, he stopped there, saying that it was better to be caught than to trample on the beans, and better to be slain than to speak; and so he was murdered by those who were pursuing him. In this way also, most of his companions were slain, being about forty in number, but a very few did escape, among whom were Archippus of Tarentum, and Lysis, whom I have mentioned before.
But Dicaearchus states that Pythagoras died later, having escaped as far as the temple of the Muses at Metapontum, where he died of [self-imposed] starvation after forty days. Heracleides, in his Epitome of the Lives of Satyrus, says that after he had buried Pherecydes at Delos, he returned to Italy, and there finding a superb banquet prepared at the house of Milo of Croton, he left that city, for Metapontum, where, not wishing any longer to live, he put an end to his life by starvation. But Hermippus says that when there was war between the Agrigentines and the Syracusans, Pythagoras, with his usual companions, joined the Agrigentine army, which was put to flight. Coming up against a field of beans, instead of crossing it, he ran around it, and so was slain by the Syracusans, and the rest, about thirty-five in number, were burned at the stake in Tarentum, where they were trying to set up a new government against the prevailing magistrates.
Hermippus also relates another story about Pythagoras. When in Italy, he made a subterranean apartment, and charged his mother to write an account of everything that took place, marking the time of each on a tablet, then sending them down to him until he should ascend. His mother did so. Then after a certain time Pythagoras came up again, lean, and looking like a skeleton, he came into the public assembly, and said that he had arrived from Hades below, and then he recited to them all that had happened to them in the meanwhile. Being charmed with what he told them, they believed that Pythagoras was a divine being, so they wept and lamented, and even entrusted to him their wives, as likely to learn some good from him, and they took upon themselves the name of Pythagorean women. Thus far Hermippus.
22. Pythagoras' Family
PYTHAGORAS had a wife whose name was Theano, the daughter of Brontinus of Croton. Some say that she was the wife of Brontinus, and only Pythagoras' pupil. As Lysis mentions in his letter to Hipparchus, he had a daughter named Damo. Lysis' letter speaks of Pythagoras thus: "And many say that you philosophize in public, as Pythagoras deemed unworthy; for, when he had entrusted his commentaries to his daughter Damo, he charged her not to divulge them to anyone outside of the house. Though she might have sold his discourses for much money, she did not abandon them; for she thought that obedience to her father's injunctions, even though this entailed poverty, was better than gold, and for all that she was a woman."
He had also a son, named Telauges, who was his father's successor in his school, and who, according to some authors, was the teacher of Empedocles. At least Hippobotus relates that Empedocles said,
Telauges, noble youth, whom in due time
Theano bore, to wise Pythagoras.
There is no book extant which is the work of Telauges, though there are some extant that are attributed to his mother Theano. Of her is told a story, that once, when asked how long it was before a woman becomes pure after intercourse, she said, "The moment she leaves her own husband, she is pure; but she is never pure at all, after she leaves anyone else." A woman who was going to her husband was by her told to put off her modesty with her clothes, and when she left him, to resume it therewith. When she was asked, "What clothes?" she replied, "Those which cause you to be called a woman."
23. Jesting Epigrams
NOW PYTHAGORAS, according to Heracleides, the son of Serapion, died when he was eighty years of age, according to his own account; by that of others, he was over ninety. On him we have written a sportive epigram, as follows:
You are not the only man who has abstained
From living food; for so have we;
And who, I'd like to know, did ever taste
Food while alive, most sage Pythagoras?
When meat is boiled, or roasted well and salted,
I do not think it well can be called living.
Which, without scruple therefore then we eat it,
And call it no more living flesh, but meat.
Another, which runs thus:
Pythagoras was so wise a man, that he
Never ate meat himself, and called it sin.
Yet gave he good joints of beef to others;
So that I marvel at his principles;
Who others wronged, by teaching them to do
What he believed unholy for himself.
Another, which follows:
Should you Pythagoras' doctrine wish to know,
Look on the center of Euphorbus' shield.
For he asserts there lived a man of old,
And when he had no longer an existence,
He still could say that he had been alive,
Or else he would not still be living now.
Another one follows:
Alas! alas! why did Pythagoras hold
Beans in such wondrous honor? Why, besides,
Did he thus die among his choice companions?
There was a field of beans; and so the sage,
Died in the common road of Agrigentum,
Rather than trample down his favorite beans.
24. The Last Pythagoreans
HE FLOURISHED about the sixtieth Olympiad (532-528 B.C.E.) and his system lasted for about nine or ten generations. The last Pythagoreans known to Aristoxenus were Xenophilus the Chalcidean, from Thrace, Phanton the Philiasian with his countrymen Echecrates, Diocles and Polymnastus, disciples of Philolaus and Eurytus of Tarentum.
25. Various Pythagorases
PYTHAGORAS was the name of four men, almost contemporaneous, and living close to each other. One was a native of Croton, a man with a tyrant's leanings; the second was a Phliasian, and as some say, a trainer of athletes. The third was a native of Zacynthus; the fourth was this our philosopher, to whom the mysteries of philosophy are said to belong, and in whose time the proverbial phrase, ipse dixit ("the Master said"), arose generally. Some also claim the existence of a fifth Pythagoras, a sculptor of Rhegium, who is believed to have been the first discoverer of rhythm and proportion. Another was a Samian sculptor. Another, an orator of small reputation. Another was a physician, who wrote a treatise on hernias, and some essays on Homer. Dionysius tells us there was another who wrote a history of the affairs of the Dorians.
Eratosthenes, quoted by Favorinus in the eighth book of his Miscellaneous History, tells us that this philosopher, of whom we are speaking, was the first man who ever practiced boxing in a scientific manner, in the forty-eighth Olympiad (588-584 B.C.E.), having long hair, and being robed in purple. From competition with boys he was rejected; but being ridiculed for his application for this, he immediately entered among the men, and was victorious. Among other things, this statement is confirmed by an epigram of Theaetetus:
Stranger, if e'er you knew Pythagoras,
Pythagoras, the man with flowing hair,
The celebrated boxer, erst from Samos,
I am Pythagoras. And if you ask
A citizen of Elis of my deeds,
You will surely think he is relating fables.
Favorinus says that he employed definitions on account of the mathematical subjects to which he applied himself. Socrates and his pupils did still more, and in this they were later followed by Aristotle and the Stoics.
He too was the first man who applied to the universe the name kosmos, and who first called the earth round, though Theophrastus attributes this to Parmenides, and Zeno to Hesiod. It is also said that he had a constant adversary, named Cylon, as Socrates' was Antilochus. This epigram was formerly repeated concerning Pythagoras the athlete:
Pythagoras of Samos, son of Crates,
Came while a child to the Olympic games;
Eager to battle for the prize in boxing.
26. Pythagoras' Letter
EXTANT is a letter of our philosopher's, which follows:
Pythagoras to Anaximenes.
You too, most excellent friend, if you were not superior to Pythagoras in birth and reputation, would have migrated from Miletus, and gone elsewhere. But now the reputation of your father keeps you back, which perhaps would have restrained me too, if I had been like Anaximenes. But if you, who are the most eminent men, abandon the cities, all their ornaments will disappear, and the Median power will be the more dangerous to them. Nor is it always seasonable to be studying astronomy, but it is more honorable to exhibit a regard for one's country. I myself am not always occupied about speculations of my own fancy. but I am busied also with the wars which the Italians are waging one with another.
But since we have now finished our account of Pythagoras, we must also speak of the most eminent of the Pythagoreans. After whom, we must mention those who are spoken of more promiscuously in connection with no particular school, and then we will connect the whole series of philosophers worth speaking of, till we arrive at Epicurus. Now Telauges and Theano we have mentioned, so we must now speak of Empedocles, in the first place, for according to some accounts, he was a pupil of Pythagoras.
27. Empedocles as a Pythagorean
[Guthrie has omitted some genealogical material here.]
TIMAEUS, in the ninth book of his Histories, relates that Empedocles was a pupil of Pythagoras, saying that he was afterwards convicted of having divulged his doctrines, in the same way as Plato was, and that he was therefore henceforth forbidden from attending his school. It is said that Empedocles had Pythagoras in mind when he said:
And in that band there was a learned man
Of wondrous wisdom; one who of all men
Had the profoundest wealth of intellect.
But some say the philosopher was here referring to Parmenides.
Neanthes relates that until the time of Philolaus and Empedocles the Pythagoreans used to admit all persons indiscriminately into their schools; but when Empedocles by means of his poems publicized the doctrines, then they made a law to admit no epic poet. They said that the same thing happened to Plato, for that he too was excluded from the school. Empedocles' Pythagorean teacher is not mentioned; and as for the letter of Telauges, in which he is stated to have been a pupil of Hippasus and Brontinus, that is not worthy of belief. But Theophrastus says that he was an imitator and rival of Parmenides in his poems, for that he too had delivered his opinions on natural philosophy in epic verse.
Hermippus, however, says that he was an imitator not of Parmenides, but of Xenophanes with whom he lived; and that he imitated his epic style, and that it was at a later period that he fell in with the Pythagoreans. But Alcimadas, in his Physics, says that Zeno and Empedocles were pupils of Pannenides, about the same time, and that they subsequently left him. Zeno was said to have adopted a philosophical system peculiar to himself, but Empedocles became a pupil of Anaxagoras and Pythagoras, and he imitated the demeanor and way of life and gestures of the latter, and the natural philosophy of the other...
_______________
Notes:
1. Heraclitus didn't care very much for polymaths, hence his disapproval of Pythagoras.
2. Pythios is the name of Apollo at Delphi. Iamblichus also alludes in chapter 1 of his biography to the etymological connection between the name Pythagoras and the Delphic Apollo.
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Re: The Pythagorean Sourcebook and Library
by admin » Wed Nov 13, 2013 4:17 am
PART II: THE PYTHAGOREAN LIBRARY
FIGURE 12. THE PYTHAGOREAN Y
THE PYTHAGOREAN SYMBOLS OR MAXIMS
THE PYTHAGOREAN SYMBOLS are gnomic utterances whose meaning is not obvious on first glance. As Iamblichus observes, Pythagorean views were "not composed in popular or vulgar diction, or in a manner usual to all other writers, so as to be immediately understood, but in a way not easily apprehended by their readers."
"The result is that they who present these symbols without unfolding their meaning by a suitable exposition, run the danger of exposing them to the charge of being ridiculous and inane, trifling and garrulous. When, however, the meanings are expounded according to these symbols, and made clear and obvious even to the crowds, then they will be found analogous to prophetic sayings, such as the oracles of the Pythian Apollo. Their admirable meaning will inspire those who unite intellect and scholarliness."
The Pythagorean symbols are excellent examples of akousmata or "things heard," representing for the most part basic teachings on the proper conduct of life. A number of scholars have suggested that some of the Symbols represent archaic taboos to which Pythagoras gave spiritual or ethical interpretations.
In the following collection of 52 Symbols, many of the interpretations are traditional, but Guthrie has added some of his own. Most of the Symbols have more than one traditional interpretation. Iamblichus gives in-depth interpretations to 39 Pythagorean Symbols in his Exhortation to Philosophy, Phanes Press, 1988. Another good collection of Symbols, giving many variant interpretations and their sources, is the section on Pythagoras from Thomas Stanley's History of Philosophy, 1687, reprinted by the Philosophical Research Society, 1970.
THE PYTHAGOREAN SYMBOLS OR MAXIMS
1. Go not beyond the balance. (Transgress not Justice).
2. Sit not down on the bushel. (Do not loaf on your job).
3. Tear not to pieces the crown. (Do not be a joy-killer).
4. Eat not the heart. (Do not grieve over-much).
5. Do not poke the fire with a sword. (Do not further inflame the quarrelsome).
6. Having arrived at the frontiers, turn not back. (Do not wish to live your life over).
7. Go not by the public way. (Go not the broad popular way that leads to destruction).
8. Suffer no swallows around your house. (Associate not with those who chatter vainly).
9. Wear not the image of God on your ring. (Profane not the name of God).
10. Do not unload people, but load them up. (Encourage not idleness, but virtue).
11. Do not easily shake hands with a man. (Make no ill-considered friendship).
12. Leave not the least mark of the pot on the ashes. (After reconciliation, forget the disagreement).
13. Sow mallows, but never eat them. (Be mild to others, but not to yourself).
14. Wipe not out the place of the torch. (Let not all the lights of reason be extinguished).
15. Wear not a narrow ring. (Seek freedom, avoid slavery).
16. Feed not the animals that have crooked claws. (To your family admit no thief or traitor).
17. Abstain from beans. (Avoid food causing flatulence; avoid democratic voting).
18. Eat not fish whose tails are black. (Frequent not the company of men without reputation).
19. Never eat the gurnard. [1] (Avoid revenge).
20. Eat not the womb of animals. (Avoid that which leads to generation; avoid lust).
21. Abstain from flesh of animals that die of themselves. (Avoid decayed food).
22. Abstain from eating animals. (Have no conversation with unreasonable men).
23. Always put salt on the table. (Always use the principle of Justice to settle problems).
24. Never break the bread. (When giving charity, do not pare too close).
25. Do not spill oil upon the seat. (Do not flatter princes, praise God only).
26.Put not meat in a foul vessel. (Do not give good precepts to a vicious soul).
27. Feed the cock, but sacrifice him not; for he is sacred to the sun and the moon. (Cherish people who warn you, sacrifice them not to resentment).
28. Break not the teeth. (Do not revile bitterly; do not be sarcastic).
29. Keep far from you the vinegar-cruet. (Avoid malice and sarcasm).
30. Spit upon the parings of your nails, and on the clippings of your hair. (Abhor desires).
31. Do not urinate against the sun. (Be modest).
32. Speak not in the face of the sun. (Make not public the thoughts of your heart).
33. Do not sleep at noon. (Do not continue in darkness).
34. Stir up the bed as soon as you are risen; do not leave in it any print of the body. (When working, hanker not for luxurious ease).
35. Never sing without harp-accompaniment. (Make of life a whole).
36. Always keep your things packed up. (Always be prepared for all emergencies).
37. Quit not your post without your general's order. (Do not commit suicide).
38. Cut not wood on the public road. (Never turn to private use what belongs to the public).
39. Roast not what is boiled. (Never complicate that which is done in simplicity; mildness has no need of anger.)
40. Avoid the two-edged sword. (Have no conversation with slanderers).
41. Pick not up what is fallen from the table. (Always leave something for charity).
42. Abstain even from a cypress chest. (Avoid going to funerals).
43. To the celestial Gods sacrifice an odd number, but to the infernal, an even. (To God consecrate the indivisible soul; offer the body to hell).
44. Offer not to the Gods the wine of an unpruned vine. (Agriculture is a great piece of piety).
45. Never sacrifice without meal. (Encourage agriculture; offer bloodless offerings).
46. Adore the Gods, and sacrifice barefoot. (Pray and sacrifice in humility of heart).
47. Turn round when you worship. (Adore the immensity of God, who fills the universe).
48. Sit down when you worship. (Never worship in a hurry).
49. Pare not your nails during the sacrifice. (In the temple behave respectfully).
50. When it thunders, touch the ground. (Appease God by humility).
51. Do not primp by torch-light. (Look at things in the light of God).
52. One, Two. (God and Nature; all things are known in God).
53. Honor marks of dignity, the Throne, and the Ternary. (Worship magistrates, Kings, Heroes, Geniuses and God).
54. When the winds blow, adore echo. (During revolts, flee to deserts).
55. Eat not in the chariot. (Eat not in the midst of hurried, important business).
56. Put on your right shoe first, and wash your left foot first. (Prefer an active life, to one of ease and pleasure).
57. Eat not the brain. (Wear not out the brain; refresh yourself).
58. Plant not the Palm-tree. (Do nothing but what is good and useful).
59. Make thy libations to the Gods by the ear. (Beautify thy worship with music).
60. Never catch the cuttle-fish. (Undertake no dark, intricate affairs that will wound you).
61. Stop not at the threshold. (Be not wavering, but choose your side).
62. Give way to a flock that goes by. (Oppose not the multitude).
63. Avoid the weasel. (Avoid tale-tellers).
64. Refuse the weapons a woman offers you. (Reject all suggestions revenge inspires).
65. Kill not the serpent that chances to fall within your walls. (Harm no enemy who becomes your guest or suppliant).
66. It is a crime to throw stones into fountains. (It is a crime to persecute good men).
67. Feed not yourself with your left hand. (Support yourself by honest toil, not by robbery).
68. It is a horrible crime to wipe off the seat with iron. (It is criminal to deprive a man by force of what he earned by labor).
69. Stick not iron into the footsteps of a man. (Mangle not the memory of a man).
70. Sleep not on a grave. (Live not in idleness on the parents' inherited estates).
71. Lay not the whole faggot on the fire. (Live thriftily, spend not all at once).
72. Leap not from the chariot with your feet close together. (Do nothing inconsiderately).
73. Threaten not the stars. (Be not angry with your superiors).
74. Place not the candle against the wall. (Persist not in enlightening the stupid).
75. Write not in the snow. (Trust not your precepts to persons of an inconstant character).
_______________
Notes:
1. A type of fish.
FIGURE 12. THE PYTHAGOREAN Y
The Pythagoric Letter two ways spread,
Shows the two paths in which Man's life is led.
The right hand track to sacred Virtue tends,
Though steep and rough at first, in rest it ends;
The other broad and smooth, but from its Crown
On rocks the Traveller is tumbled down.
He who to Virtue by harsh toils aspires,
Subduing pains, worth and renown acquires:
But who seeks slothful luxury, and flies,
The labor of great acts, dishonor'd dies.
-Maximinus
THE PYTHAGOREAN SYMBOLS OR MAXIMS
THE PYTHAGOREAN SYMBOLS are gnomic utterances whose meaning is not obvious on first glance. As Iamblichus observes, Pythagorean views were "not composed in popular or vulgar diction, or in a manner usual to all other writers, so as to be immediately understood, but in a way not easily apprehended by their readers."
"The result is that they who present these symbols without unfolding their meaning by a suitable exposition, run the danger of exposing them to the charge of being ridiculous and inane, trifling and garrulous. When, however, the meanings are expounded according to these symbols, and made clear and obvious even to the crowds, then they will be found analogous to prophetic sayings, such as the oracles of the Pythian Apollo. Their admirable meaning will inspire those who unite intellect and scholarliness."
The Pythagorean symbols are excellent examples of akousmata or "things heard," representing for the most part basic teachings on the proper conduct of life. A number of scholars have suggested that some of the Symbols represent archaic taboos to which Pythagoras gave spiritual or ethical interpretations.
In the following collection of 52 Symbols, many of the interpretations are traditional, but Guthrie has added some of his own. Most of the Symbols have more than one traditional interpretation. Iamblichus gives in-depth interpretations to 39 Pythagorean Symbols in his Exhortation to Philosophy, Phanes Press, 1988. Another good collection of Symbols, giving many variant interpretations and their sources, is the section on Pythagoras from Thomas Stanley's History of Philosophy, 1687, reprinted by the Philosophical Research Society, 1970.
THE PYTHAGOREAN SYMBOLS OR MAXIMS
1. Go not beyond the balance. (Transgress not Justice).
2. Sit not down on the bushel. (Do not loaf on your job).
3. Tear not to pieces the crown. (Do not be a joy-killer).
4. Eat not the heart. (Do not grieve over-much).
5. Do not poke the fire with a sword. (Do not further inflame the quarrelsome).
6. Having arrived at the frontiers, turn not back. (Do not wish to live your life over).
7. Go not by the public way. (Go not the broad popular way that leads to destruction).
8. Suffer no swallows around your house. (Associate not with those who chatter vainly).
9. Wear not the image of God on your ring. (Profane not the name of God).
10. Do not unload people, but load them up. (Encourage not idleness, but virtue).
11. Do not easily shake hands with a man. (Make no ill-considered friendship).
12. Leave not the least mark of the pot on the ashes. (After reconciliation, forget the disagreement).
13. Sow mallows, but never eat them. (Be mild to others, but not to yourself).
14. Wipe not out the place of the torch. (Let not all the lights of reason be extinguished).
15. Wear not a narrow ring. (Seek freedom, avoid slavery).
16. Feed not the animals that have crooked claws. (To your family admit no thief or traitor).
17. Abstain from beans. (Avoid food causing flatulence; avoid democratic voting).
18. Eat not fish whose tails are black. (Frequent not the company of men without reputation).
19. Never eat the gurnard. [1] (Avoid revenge).
20. Eat not the womb of animals. (Avoid that which leads to generation; avoid lust).
21. Abstain from flesh of animals that die of themselves. (Avoid decayed food).
22. Abstain from eating animals. (Have no conversation with unreasonable men).
23. Always put salt on the table. (Always use the principle of Justice to settle problems).
24. Never break the bread. (When giving charity, do not pare too close).
25. Do not spill oil upon the seat. (Do not flatter princes, praise God only).
26.Put not meat in a foul vessel. (Do not give good precepts to a vicious soul).
27. Feed the cock, but sacrifice him not; for he is sacred to the sun and the moon. (Cherish people who warn you, sacrifice them not to resentment).
28. Break not the teeth. (Do not revile bitterly; do not be sarcastic).
29. Keep far from you the vinegar-cruet. (Avoid malice and sarcasm).
30. Spit upon the parings of your nails, and on the clippings of your hair. (Abhor desires).
31. Do not urinate against the sun. (Be modest).
32. Speak not in the face of the sun. (Make not public the thoughts of your heart).
33. Do not sleep at noon. (Do not continue in darkness).
34. Stir up the bed as soon as you are risen; do not leave in it any print of the body. (When working, hanker not for luxurious ease).
35. Never sing without harp-accompaniment. (Make of life a whole).
36. Always keep your things packed up. (Always be prepared for all emergencies).
37. Quit not your post without your general's order. (Do not commit suicide).
38. Cut not wood on the public road. (Never turn to private use what belongs to the public).
39. Roast not what is boiled. (Never complicate that which is done in simplicity; mildness has no need of anger.)
40. Avoid the two-edged sword. (Have no conversation with slanderers).
41. Pick not up what is fallen from the table. (Always leave something for charity).
42. Abstain even from a cypress chest. (Avoid going to funerals).
43. To the celestial Gods sacrifice an odd number, but to the infernal, an even. (To God consecrate the indivisible soul; offer the body to hell).
44. Offer not to the Gods the wine of an unpruned vine. (Agriculture is a great piece of piety).
45. Never sacrifice without meal. (Encourage agriculture; offer bloodless offerings).
46. Adore the Gods, and sacrifice barefoot. (Pray and sacrifice in humility of heart).
47. Turn round when you worship. (Adore the immensity of God, who fills the universe).
48. Sit down when you worship. (Never worship in a hurry).
49. Pare not your nails during the sacrifice. (In the temple behave respectfully).
50. When it thunders, touch the ground. (Appease God by humility).
51. Do not primp by torch-light. (Look at things in the light of God).
52. One, Two. (God and Nature; all things are known in God).
53. Honor marks of dignity, the Throne, and the Ternary. (Worship magistrates, Kings, Heroes, Geniuses and God).
54. When the winds blow, adore echo. (During revolts, flee to deserts).
55. Eat not in the chariot. (Eat not in the midst of hurried, important business).
56. Put on your right shoe first, and wash your left foot first. (Prefer an active life, to one of ease and pleasure).
57. Eat not the brain. (Wear not out the brain; refresh yourself).
58. Plant not the Palm-tree. (Do nothing but what is good and useful).
59. Make thy libations to the Gods by the ear. (Beautify thy worship with music).
60. Never catch the cuttle-fish. (Undertake no dark, intricate affairs that will wound you).
61. Stop not at the threshold. (Be not wavering, but choose your side).
62. Give way to a flock that goes by. (Oppose not the multitude).
63. Avoid the weasel. (Avoid tale-tellers).
64. Refuse the weapons a woman offers you. (Reject all suggestions revenge inspires).
65. Kill not the serpent that chances to fall within your walls. (Harm no enemy who becomes your guest or suppliant).
66. It is a crime to throw stones into fountains. (It is a crime to persecute good men).
67. Feed not yourself with your left hand. (Support yourself by honest toil, not by robbery).
68. It is a horrible crime to wipe off the seat with iron. (It is criminal to deprive a man by force of what he earned by labor).
69. Stick not iron into the footsteps of a man. (Mangle not the memory of a man).
70. Sleep not on a grave. (Live not in idleness on the parents' inherited estates).
71. Lay not the whole faggot on the fire. (Live thriftily, spend not all at once).
72. Leap not from the chariot with your feet close together. (Do nothing inconsiderately).
73. Threaten not the stars. (Be not angry with your superiors).
74. Place not the candle against the wall. (Persist not in enlightening the stupid).
75. Write not in the snow. (Trust not your precepts to persons of an inconstant character).
_______________
Notes:
1. A type of fish.
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Re: The Pythagorean Sourcebook and Library
by admin » Wed Nov 13, 2013 4:18 am
THE GOLDEN VERSES OF PYTHAGORAS
IN MANY WAYS the so-called Golden Verses of Pythagoras epitomize the Pythagorean way of life, outlining the principles of daily conduct leading to the divinization of the soul.
Concerning their authorship and date of composition there have been varying opinions. The French scholar Armand Delatte has argued in some depth that a large portion of the Golden Verses may go back in essence to an hexameter poem by Pythagoras, The Sacred Discourse, in which he set out a rule of life for members of his school. According to this theory the teaching was transmitted orally, only to be recorded when the few surviving Pythagoreans were expelled from Italy and threatened with extinction.
The Neoplatonic philosopher Hierocles of Alexandria was apparently the first to refer to these lines as the Golden Verses, explaining that as gold is the best and purest of metals, so are these the most divine of verses. The very interesting Commentaries of Hierocles on the Golden Verses of Pythagoras was first rendered into English in 1707 by N. Rowe and has been reprinted several times since.
THE GOLDEN VERSES OF PYTHAGORAS
FIRST HONOR THE IMMORTAL GODS, as the law demands;
Then reverence thy oath, and then the illustrious heroes;
Then venerate the divinities under the earth, due rites performing;
Then honor your parents, and all of your kindred.
Among others make the most virtuous thy friend!
Love to make use of his soft speeches, and learn from his deeds that are useful;
But alienate not the beloved comrade for trifling offences,
Bear all you can, what you can, for power is bound to necessity.
Take this well to heart: you must gain control of your habits;
First over stomach, then sleep, and then luxury, and anger.
What brings you shame, do not unto others, nor by yourself.
The highest of duties is honor of self.
Let justice be practiced in words as in deeds; |
Then make the habit, never inconsiderately to act;
Neither forget that death is appointed to all;
That possessions here gladly gathered, here must be left;
Whatever sorrow the fate of the Gods may here send us
Bear, whatever may strike you, with patience unmurmuring;
To relieve it, so far as you can, is permitted,
But reflect that not much misfortune has Fate given to the good.
The speech of the people is various, now good, and now evil;
So let them not frighten you, nor keep you from your purpose.
If false calumnies come to your ears, support it in patience;
Yet that which I now am declaring, fulfil it faithfully:
Let no one with speech or with deeds e'er deceive you
To do or to say what is not the best.
Think, before you act, that nothing stupid results;
To act inconsiderately is part of a fool;
Yet whatever later will not bring you repentance, that you should carry through.
Do nothing beyond what you know,
Yet learn what you may need: thus shall your life grow happy.
Do not neglect the health of the body;
Keep measure in eating and drinking, and every exercise of the body.
By measure, I mean what later will not induce pain.
Follow clean habits of life, but not the luxurious;
Avoid all things which will arouse envy.
At the wrong time, never be a prodigal, as if you did not know what was proper,
Nor show yourself stingy, for a due measure is ever the best.
Do only those things which will not harm thee, and deliberate before you act.
Never let slumber approach thy wearied eyelids,
Ere thrice you review what this day you did:
Wherein have I sinned? What did I? What duty is neglected?
All, from the first to the last, review; and if you have erred grieve in your spirit, rejoicing for all that was good.
With zeal and with industry, this, then, repeat; and learn to repeat it with joy.
Thus wilt thou tread on the paths of heavenly virtue.
Surely, I swear it by him who into our souls has transmitted the Sacred Quaternary, [1]
The spring of eternal Nature.
Never start on your task until you have implored the blessing of the Gods.
If this you hold fast, soon will you recognize of Gods and mortal men
The true nature of existence, how everything passes and returns.
Then will you see what is true, how Nature in all is most equal,
So that you hope not for what has no hope, nor that anything should escape you.
Men shall you find whose sorrows they themselves have created,
Wretches who see not the Good that is too near, nothing they hear;
Few know how to help themselve in misfortune.
That is the Fate that blinds humanity; in circles,
Hither and yon they run in endless sorrows;
For they are followed by a grim companion, disunion within themselves;
Unnoticed, ne'er rouse him, and fly from before him!
Father Zeus, 0 free them all from sufferings so great,
Or show unto each the Genius, who is their guide!
Yet, do not fear, for the mortals are divine by race,
To whom holy Nature everything will reveal and demonstrate;
Whereof if you have received, so keep what I teach you;
Healing your soul, you shall remain insured from manifold evil.
Avoid foods forbidden; reflect that this contributes to the cleanliness
And redemption of your soul. Consider all things well:
Let reason, the gift divine, be thy highest guide;
Then should you be separated from the body, and soar in the aether,
You will be imperishable, a divinity, a mortal no more.
_______________
Notes:
1. I.e., the Tetraktys.
IN MANY WAYS the so-called Golden Verses of Pythagoras epitomize the Pythagorean way of life, outlining the principles of daily conduct leading to the divinization of the soul.
Concerning their authorship and date of composition there have been varying opinions. The French scholar Armand Delatte has argued in some depth that a large portion of the Golden Verses may go back in essence to an hexameter poem by Pythagoras, The Sacred Discourse, in which he set out a rule of life for members of his school. According to this theory the teaching was transmitted orally, only to be recorded when the few surviving Pythagoreans were expelled from Italy and threatened with extinction.
The Neoplatonic philosopher Hierocles of Alexandria was apparently the first to refer to these lines as the Golden Verses, explaining that as gold is the best and purest of metals, so are these the most divine of verses. The very interesting Commentaries of Hierocles on the Golden Verses of Pythagoras was first rendered into English in 1707 by N. Rowe and has been reprinted several times since.
THE GOLDEN VERSES OF PYTHAGORAS
FIRST HONOR THE IMMORTAL GODS, as the law demands;
Then reverence thy oath, and then the illustrious heroes;
Then venerate the divinities under the earth, due rites performing;
Then honor your parents, and all of your kindred.
Among others make the most virtuous thy friend!
Love to make use of his soft speeches, and learn from his deeds that are useful;
But alienate not the beloved comrade for trifling offences,
Bear all you can, what you can, for power is bound to necessity.
Take this well to heart: you must gain control of your habits;
First over stomach, then sleep, and then luxury, and anger.
What brings you shame, do not unto others, nor by yourself.
The highest of duties is honor of self.
Let justice be practiced in words as in deeds; |
Then make the habit, never inconsiderately to act;
Neither forget that death is appointed to all;
That possessions here gladly gathered, here must be left;
Whatever sorrow the fate of the Gods may here send us
Bear, whatever may strike you, with patience unmurmuring;
To relieve it, so far as you can, is permitted,
But reflect that not much misfortune has Fate given to the good.
The speech of the people is various, now good, and now evil;
So let them not frighten you, nor keep you from your purpose.
If false calumnies come to your ears, support it in patience;
Yet that which I now am declaring, fulfil it faithfully:
Let no one with speech or with deeds e'er deceive you
To do or to say what is not the best.
Think, before you act, that nothing stupid results;
To act inconsiderately is part of a fool;
Yet whatever later will not bring you repentance, that you should carry through.
Do nothing beyond what you know,
Yet learn what you may need: thus shall your life grow happy.
Do not neglect the health of the body;
Keep measure in eating and drinking, and every exercise of the body.
By measure, I mean what later will not induce pain.
Follow clean habits of life, but not the luxurious;
Avoid all things which will arouse envy.
At the wrong time, never be a prodigal, as if you did not know what was proper,
Nor show yourself stingy, for a due measure is ever the best.
Do only those things which will not harm thee, and deliberate before you act.
Never let slumber approach thy wearied eyelids,
Ere thrice you review what this day you did:
Wherein have I sinned? What did I? What duty is neglected?
All, from the first to the last, review; and if you have erred grieve in your spirit, rejoicing for all that was good.
With zeal and with industry, this, then, repeat; and learn to repeat it with joy.
Thus wilt thou tread on the paths of heavenly virtue.
Surely, I swear it by him who into our souls has transmitted the Sacred Quaternary, [1]
The spring of eternal Nature.
Never start on your task until you have implored the blessing of the Gods.
If this you hold fast, soon will you recognize of Gods and mortal men
The true nature of existence, how everything passes and returns.
Then will you see what is true, how Nature in all is most equal,
So that you hope not for what has no hope, nor that anything should escape you.
Men shall you find whose sorrows they themselves have created,
Wretches who see not the Good that is too near, nothing they hear;
Few know how to help themselve in misfortune.
That is the Fate that blinds humanity; in circles,
Hither and yon they run in endless sorrows;
For they are followed by a grim companion, disunion within themselves;
Unnoticed, ne'er rouse him, and fly from before him!
Father Zeus, 0 free them all from sufferings so great,
Or show unto each the Genius, who is their guide!
Yet, do not fear, for the mortals are divine by race,
To whom holy Nature everything will reveal and demonstrate;
Whereof if you have received, so keep what I teach you;
Healing your soul, you shall remain insured from manifold evil.
Avoid foods forbidden; reflect that this contributes to the cleanliness
And redemption of your soul. Consider all things well:
Let reason, the gift divine, be thy highest guide;
Then should you be separated from the body, and soar in the aether,
You will be imperishable, a divinity, a mortal no more.
_______________
Notes:
1. I.e., the Tetraktys.
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Re: The Pythagorean Sourcebook and Library
by admin » Wed Nov 13, 2013 4:20 am
FIGURE 13. THE MUSIC OF THE SPHERES
THE FRAGMENTS OF PHILOLAUS
PHILOLAUS OF TARENTUM (latter half of fifth century B.C.E.) was educated by Lysis, one of the two Pythagoreans who escaped the persecution of the school at Croton. He was the first member of the school to record Pythagorean teachings in writing and it appears that these writings influenced the thought of Plato. Moreover, Plato's nephew Speusippus who took over the leadership of the Academy, drew on the work of Philolaus in compiling his treatise On Pythagorean Numbers, which dealt primarily with the properties of the Decad.
The fragments of Philolaus assembled here deal with the Pythagorean theory of the Limited and Unlimited, the principle of Harmonia through which they are conjoined, and the primacy of Number in the nature of Harmonia, and also the importance of Number in the pursuit of knowledge.
The Philolaic fragments are generally accepted as being authentic and their significance is not to be underestimated. This is because of all surviving Pythagorean writings the fragments of Philolaus are the earliest and most faithfully reflect the teachings of the original Pythagorean school.
For a good discussion of Philolaus see section 44 in Kathleen Freeman's Companion to the Presocratic Philosophers. The numbers following the fragments (e.g., DK 1) refer to the numeration in Diels-Kranz, Fragmente der Vorsokratieker, and are translated in Kathleen Freeman's Ancilla to the Pre-Socratic Philosophers.
THE LIFE OF PHILOLAUS
FROM DIOGENES LAERTIUS
PHILOLAUS OF CROTON, a Pythagorean, was he from whom Plato, in some of his Letters, begged Dion to purchase Pythagorean books. He (Dion) died under the accusation of having had designs on the tyranny. I have made about him the following epigram: "I advise everybody to take good care to avoid suspicion; even if you are not guilty but seem so, you are ruined. That is why Croton, the homeland of Philolaus, destroyed him, because he was suspected of wishing to establish autocracy."
Philolaus teaches that all things are produced by necessity and harmony, and he is the first who said that the earth has a circular movement; others, however, insist this was due to Hicetas of Syracuse. He had written a single book which the philosopher Plato, visiting Dionysius in Sicily, bought, according to Hermippus, from Philolaus' parents, for the sum of 40 Alexandrian minae, whence he drew his Timaeus. Others state that he received them as a present for having obtained the liberty of one Philolaus' disciples, whom Dionysius had imprisoned. In his Homonyms, Demetrius claims that he is the first of the Pythagorean philosophers who made a work On Nature public property. This book begins as follows: "The world's being is the harmonious compound of Unlimited and Limiting principles; such is the totality of the world and all it contains."
THE FRAGMENTS OF PHILOLAUS
1. (Stobaeus, 21. 7; Diogenes Laertius, 8. 85) The world's nature is a harmonious compound of Limited and Unlimited elements; similar is the totality of the world in itself, and of all it contains (DK 1).
B. All beings are necessarily Limited or Unlimited, or simultaneously Limited and Unlimited; but they could not all be Unlimited only.
2. Now, since it is clear that the beings cannot be formed either of elements that are all Unlimited, it is evident that the world in its totality, and its included beings are a harmonious compound of Limited and Unlimited elements. That can be seen in existing things. Those that are composed of Limiting elements, are Limited themselves; those that are composed of both Limiting and Unlimited elements, are both Limited and Unlimited; and those composed of Unlimited elements are Unlimited (DK 2).
B. All things, at least those we know, contain Number; for it is evident that nothing whatever can either be thought or known, without Number (DK 4). Number has two distinct kinds: the odd, and the even, and a third, derived from a mingling of the other two kinds, the even-odd. Each of its subspecies is susceptible of many very numerous varieties, which each manifests individually (DK 5).
3. (Nicomachus, Arith. Intr., 2. 509) Harmony is generally the result of contraries; for it is the unity of multiplicity, and the agreement of discordances (DK 10).
4. This is the state of affairs concerning Nature and Harmony. The Being of things is eternal; it is a unique and divine nature, the knowledge of which does not belong to man. Still it would not be possible that any of the things that exist, and that are known by us, should arrive to our knowledge if this Being was not the internal foundation of principles of which the world was founded-that is, of the Limited and Unlimited elements. Now since these principles are not mutually similar, nor of similar nature, it would be impossible that the order of the world should have been formed by them in any manner whatever unless harmony had intervened. Of course, the things that were similar, and of similar nature, did not need harmony; but the dissimilar things, which have neither a similar nature, nor an equivalent function, must be organized by the harmony, if they are to take their place in the connected totality of the world.
5. The extent of the Harmony [octave] is a fourth, plus a fifth. The fifth is greater than the fourth by 8:9; for from the lowest string to the second lowest there is a fourth; and from this to the higher a fifth; but from this to the next, or third string, a fourth; and from this third string to the lowest, a fifth. The interval between the second lowest and the third [from the bottom] is 8:9 [a tone]; the interval of the fourth is 3:4; that of the fifth, 2:3; that of the octave, 1:2. Thus the Harmony contains five whole tones plus two semitones; the fifth, three tones, plus one semitone; the fourth, two whole tones, plus one semitone (DK 6).
6. (Boethius, De. Inst. Mus., 3. 5). Nevertheless the Pythagorean Philolaus has tried to divide the tone otherwise; his tone's starting-point is the first uneven number which forms a cube, and you know that the first uneven number was an object of veneration among these Pythagoreans. Now the first odd number is three; thrice three is nine, and nine times three is 27, which differs from the number 24 by the interval of one tone, and differs from it by this very number 3. Indeed, 3 is one eight of 24, and this eighth part of 24, added to 24 itself, produces 27, the cube of 3. Philolaus divides this number 27 in two parts, the one greater than half, which he calls apotome the other one smaller than half he calls sharp, but which latterly has become known as minor half-tone. He supposes that this sharp contains thirteen unities, because 13 is the difference between 256 and 243, and that this same number is the sum of 9, 3, and unity, in which the unity plays the part of the point, 3 of the first odd line, and 9 of the first odd square. After having, for these reasons, expressed by 13 the sharp, which is called a semitone, out of 14 unities he forms the other part of the number 27, which he calls apotome, and as the difference between 13 and 14 is the unity, he insists that the unity forms the comma, and that 27 unities form an entire tone, because 27 is the difference between 216 and 243, which are distant by one tone. [1]
7. (Boethius, De. Inst. Mus., 3. 8). These are the definitions that Philolaus has given of these intervals, and of still smaller intervals. The comma, says he, is the interval whose eight-ninths relation exceeds the sum of two sharps, namely, the sum of two minor semitones. The schisma is half the comma, the diaschisma is half the sharp, namely, of the minor semitone.
8. (Claudianus Mamertus, De Statu Animae, 2. 3). Before treating of the substance of the soul, Philolaus, according to geometrical principles, treats of music, arithmetic, measures, weights, and numbers, insisting that these are the principles which support the existence of the universe.
9. (Nicomachus, Arithm. Intr., 2. p. 72). Some, in this following Philolaus, think that this kind of a proportion is called harmonic, because it has the greatest analogy with what is called geometrical harmony; which is the cube, because all its dimensions are mutually equal, and consequently in perfect harmony. Indeed this proportion is revealed in all kinds of cubes which always have 12 sides, 8 angles, and 6 surfaces. [2]
B. (Cassiodorus, Exp. in Ps., 9, p. 36). The number 8, which the arithmeticians call the first actual cube, has been given by the Pythagorean Philolaus the name of geometrical harmony, because he thinks he recognizes in it all the harmonic relations.
10 A. (Stobaeus, Eclog. Physic., 1. 15.7. p. 360). The world is single and it came into being from the center outwards. Starting from this center, the top is entirely identical to the base; still you might say that what is above the center is opposed to what is below it; for the base, lowest point would be the center, as for the top, the highest point would still be the center; and likewise for the other parts; in fact, in respect to the center, each one of the opposite points is identical, unless the whole be moved (DK 17).
B. (Stobaeus, Eclog. Physic., 1. 21. 1. p. 468). The prime composite, the One placed in the center of the sphere, is called Hestia (DK 7).
11. A. (Stobaeus, Eclog. Physic., 1. 22. 1. p. 488). Philolaus has located the fire in the middle, the center; he calls it Hestia, of the All, the Guardpost of Zeus, the Mother of the Gods, the Altar, the Link, and the Measure of Nature. Besides, he locates a second fire, quite at the top, surrounding the world. The center, says he, is by its nature the first; around it, the ten different bodies carry out their choral dance. These are: the heaven, the planets, lower the sun, and below it the moon; lower the earth, and beneath this, the counter-earth, then beneath these bodies the fire of Hestia, in the center, where it maintains order. The highest part of the Covering, in which he asserts that the elements exist in a perfectly pure condition, is called Olympus; the space beneath the revolution-circle of Olympus, and where in order are disposed the five planets, the sun and moon, forms the Cosmos; finally, beneath the latter is the sublunar region, which surrounds the earth, where are the generative things, susceptible to change. All that is the heaven. The order which manifests in the celestial phenomena is the object of science; the disorder which manifests in the things of becoming, is the object of virtue; the former is perfect, the latter is imperfect.
B. (ps.-Plutarch, Plac. Phil., 3. 11). The Pythagorean Philolaus locates the fire in the center -- it is the Hearth (Hestia) of the All -- then the counter-earth, then the earth we inhabit, placed opposite the other, and moving circularly, which is the reason that its inhabitants are not visible to ours.
C. (Stobaeus, Eclog. Physic., 1. 21. 6. p. 452). The directing fire, says Philolaus, is in the entirely central fire, which the Demiurge has placed as a sort of keel to serve as foundation to the sphere of the All.
12. (ps.-Plutarch, Plac. Phil., 2. 5). Philolaus explains destruction by two causes: one is the fire which descends from heaven, the other is the water of the moon, which is driven away therefrom by the circulation of the air; the exhalations of these two stars nourish the world.
13. A. (Diogenes Laertius, 8.85). Philolaus was the first who said that the world moves in a circle; others attribute it to Hicetas of Syracuse.
B. (ps.-Plutarch, Plac. Phil., 3. 7). Some insist that the earth is immovable; but the Pythagorean Philolaus says that it moves circularly around the central fire, in an oblique circle like the sun and moon.
14. (Stobaeus, Eclog. Physic., 1. 25. 3. p. 530). The Pythagorean Philolaus says that the sun is a vitrescent body which receives the light reflected by the fire of the Cosmos, and sends it back to us, having filtered them, light and heat; so that you might say that there are two suns, the body of the fire which is in the heaven, and the igneous light which emanates therefrom, and reflects itself in a kind of mirror. Perhaps we might consider as a third light that which, from the mirror in which it is reflected, falls back on us in dispersed rays.
15. (Stobaeus, Eclog. Physic., 1. 26. 1. p. 562). Some Pythagoreans, among whom is Philolaus, suggest that the moon's resemblance to the earth consists in its surface being inhabited, like our earth, but by animals and vegetation larger and more beautiful. For the lunar animals are fifteen times larger than ours, and do not evacuate excreta. The day is also fifteen times as long. Others say that the apparent form of the moon is only the reflection of the sea, which we inhabit and which passes beyond the circle of fire.
16. (Censorinus, De Die Natali, 18). According to the Pythagorean Philolaus there is a year composed of 59 years and 21 intercalary months; he considers that the natural year has 364 and a half days.
17. (Iamblichus, In. Nicom., 11). Philolaus says that Number is the sovereign and autogenic force which maintains the eternal permanence of cosmic things (DK 23).
18. A. (Stobaeus, 1. 3. 8). The power, efficacy and essence of Number is seen in the Decad; it is great, it realizes all its purposes, and it is the cause of all effects. The power of the Decad is the principle and guide of all life, divine, celestial, or human into which it is insinuated; without it everything is unlimited, obscure, and furtive. Indeed, it is the nature of Number which teaches us comprehension, which serves us as guide, and teaches us all things which would otherwise remain impenetrable and unknown to every man. For there is nobody who could get a clear notion about things in themselves, nor in their relations, if there was no Number or Number-essence. By means of sensation. Number instills a certain proportion. and thereby establishes among all things harmonic relations, analogous to the nature of the geometric figure called the gnomon; it incorporates intelligible reasons of things, separates them, individualizes them. both in limited and unlimited things. And it is not only in matters pertaining to daimons or Gods that you may see the force manifested by the nature and power of Number, but it is in all its works, in all human thoughts, everywhere indeed, and even in the productions of arts and music. The nature of Number and Harmony are numberless, for what is false has no part in their essence and the principle of error and envy is thoughtless, irrational, indefinite nature. Never could error slip into Number, for its nature is hostile thereto. Truth is the proper, innate character of Number (DK 11).
B. (ps.-Iamblichus, Theologumena Arithmeticae, 61). The Decad is also named Faith, because, according to Philolaus, it is by the Decad and its elements, if utilized energetically and without negligence, that we arrive at a solidly grounded faith about beings. It is also the source of memory, and that is why the Monad has been called Mnemosyne.
C. (Theon of Smyrna, Plat. Math., p. 49). The Decad determines every number, including the nature of everything, of the even and the odd, of the mobile and immobile, of good and evil. It has been the subject of long discussions by Archytas, and of Philolaus in his work On Nature.
D. (Lucian, Pro Lapsu Inter Salutandum, 5). Some called the Tetraktys the great oath of the Pythagoreans, because they considered it the perfect number, or even because it is the principle of Health; among them is Philolaus.
19. A. (Theon of Smyrna, Plat. Math., 4). Archytas and Philolaus use the terms Monad and Unity interchangeably.
B. (Syrianus, sub. init., Comment. in Arist. Met., 1. xiv). You must not suppose that the philosophers begin by principles supposed to be opposite; they know the principle above these two elements, as Philolaus acknowledges when saying that it is God who hypostasizes the Limited and Unlimited. He shows that it is by Limit that every coordinate series of things further approaches Unity, and that it is by the Unlimited that the lower series is produced. Thus even above these two principles they posited the unique and separate cause distinguished by all of its excellence. This is the cause which Archinetus called the cause before the cause, and which Philolaus vehemently insists is the principle of all, and of which Brontinus says that in power and dignity it surpasses all reason and essence.
C. (Iamblichus, In. Nicom., p. 109). In the formation of square numbers by addition, unity is as it were the starting-post from which one begins, and also the end whither one returns; for if one places the numbers in the form of a double procession, and you see them grow from unity to the root of the square, then the root is like the turning-point where the horses tum to go back through similar numbers to unity, as in the square of 5. For example:
It is not the same with rectangular numbers. If, just as in the gnomon, one adds to any number the sum of the even, then the number two will alone seem to receive and stand addition, and without the number two it will not be possible to produce rectangular numbers. Ifyou set out the naturally increasing series of numbers in the order of the double race-track, then unity, being the principle of everything, according to Philo1aus (for it is he who said, "unity, the principle of everything"), will indeed present itself as the barrier, the starting point which produces the rectangular numbers, but it will not be the goal or limit where the series returns and comes back; it is not unity, but the number 2, which will fulfill this function. Thus, 6 x 4:
D. (Philo, Mund. Opif., 24). Philolaus confirms what I have just said by the following words; "He who commands and governs everything is a God who is single, eternally existing, immutable, self-identical, and different from other things."
E. (Athenagoras, Legat. Pro Christ., 6). Philolaus says that all things are by God kept as in captivity, and thereby implies the he is single and superior to matter to matter.
20. (Proclus, In Eucl., I. 36). Even among the Pythagoreans we find different angles consecrated to the different divinities, as did Philolaus, who attributed to some the angle of the triangle, to others the angle of the rectangle, to others other angles, and sometimes the same to several.
The Pythagoreans say that the triangle is the absolute principle of generation of begotten things, and of their form; that is why Timaeus says that the reasons of physical being, and of the regular formation of the elements are triangular; indeed, they have the three dimensions, in unity they gather the elements which in themselves are absolutely divided and changing; they are filled with the infinity characteristic of matter, and above the material beings they form bonds that indeed are frail. That is why triangles are bounded by straight lines, and have angles which unite the lines, and are their bonds. Philo1aus was therefore right in devoting the angle of the triangle to four divinities, Kronos, Hades, Mars, and Bacchus, under these four names combining the fourfold disposition of the elements, which refers to the superior part of the universe, starting from the sky, or sections of the zodiac. Indeed, Kronos presides over everything humid and cold in essence; Mars, over everything fiery; Hades contains everything terrestrial, and Dionysius directs the generation of wet and warm things, represented by wine, which is liquid and warm. These four divinities divide their secondary operations, but they remain united; that is why Philolaus, by attributing to them one angle only, wished to express this power of unification.
The Pythagoreans also claim that, in preference to the quadrilateral, the tetragon bears the divine impress, and by it they express perfect order. For the property of being straight imitates the power of immutability, and equality represents that of permanence; for motion is the result of inequality, and rest, that of equality. Those are the causes of the organization of the being that is solid in its totality, and of its pure and immovable essences. They were therefore right to express it symbolically by the figure of the tetragon. Besides, Philolaus, with another stroke of genius, calls the angle of the tetragon that of Rhea, of Demeter, and of Hestia.... For considering the earth as a tetragon, and noting that this element possesses the property of continuousness, as we learned from Timaeus, and that the earth receives all that drips from the divinities, and also the generative powers that they contain, he was right in consecrating the angle of the tetragon to these divinities which procreate life. Indeed, some of them call the earth Hestia and Demeter, and claim that it partakes of Rhea, in its entirety, and that Rhea contains all the begotten cause. That is why, in obscure language, he says that the angle of the tetragon contains the single power which produces the unity of these divine creations.
And we must not forget that Philolaus assigns the angle of the triangle to four divinities, and the angle of the tetragon to three, thereby indicating their penetrative faculty, whereby they influence each other mutually, and showing how all things participate in all things, the odd things in the even and the even in the odd. The triad and the tetrad, participating in the generative and creative beings, contain the whole regular organization of begotten things. Their product is the dodecad, which ends in the single monad, the sovereign principle of Zeus, for Philolaus says that the angle of the dodecagon belongs to Zeus, because in unity Zeus contains the entire number of the dodecad.
21 A. (ps.-Iamblichus, Theologumena Arithmeticae, p. 56). After the mathematical magnitude which by its three dimensions or intervals realizes the number Four, Philolaus shows us the being manifesting in number Five quality and color; in the number Six, the soul and life; in the number Seven, reason, health, and what he calls light; then he adds that love, friendship, prudence and reflection are communicated to beings by the number Eight.
B. (ps.-Iamblichus, Theologumena Arithmeticae, p. 22). There are four principles of the reasonable animal, as Philolaus says in his work On Nature: the skull, the heart, the navel, and the sexual organs. The head is the seat of reason; the heart, that of the soul or life, and sensation; the navel, the principle of the faculty of striking roots and reproducing the first being; the sexual organs, of the faculty of projecting the sperma, and procreating. The skull contains the principle of man, the heart that of the animal, the navel that of the plant, the sexual organs that of all living beings, for these grow and produce offspring (DK 13).
C. (Stobaeus, Eclog. Physic., 1. 2. 3. p. 10). There are five bodies in the sphere: fire, water, earth, air, and the circle of the sphere which makes the fifth (DK 12). [3]
22. (Stobaeus, Eclog. Physic., 1. 20. 2. p. 418). This is from the Pythagorean Philolaus, drawn from his book On the Soul. He insists that the world is indestructible. Here is what he says in his book On the Soul:
That is why the world remains eternally, because it cannot be destroyed by any other, nor spontaneously destroy itself. Neither within it, nor without it can be found a force greater than itself, able to destroy it. The world has existed from all eternity, and will remain eternally, because it is One, governed by a principle whose nature is similar to its own, and whose force is omnipotent and sovereign. Besides, the single world is continuous, and endowed with a natural respiration, moving eternally in a circle, having the principle of motion and change; one of its parts is immovable, the other is changing. The immovable part extends from the soul, that embraces everything, to the moon; and the changing part from the moon to the earth; or, since the Mover has been acting since eternity, and continues his action eternally, and since the changeable part receives its manner of being from the Mover who acts thereon, it necessarily results thence that one of the parts of the world ever impresses motion, and that the other ever receives it passively. The one is entirely the domain of Mind and Soul, the other of Generation and Change; the one is anterior in power, and superior, the other is posterior and subordinate. The composite of these two things, the divine eternally in motion, and of generation ever changing, is the World. That is why one is right in saying that the world is the eternal energy of God, and of becoming which obeys the laws of changing nature. The one remains eternally in the same state, self-identical; the remainder constitutes the domain of plurality, which is born and perishes. But nevertheless, the things that perish transmit their essence and form, thanks to generation, which reproduces the identical form of the father who has begotten and fashioned them (DK 21).
23 A. (Claudianus Mamertus, De Statu Animae, 2. p. 7). The soul is introduced and associated with the body by Number, and by a harmony simultaneously immortal and incorporeal....the soul cherishes its body, because without it the soul cannot feel; but when death has separated the soul therefrom, the soul lives an incorporeal existence in the cosmos (DK 22).
B. (Macrobius, Commentariorum in Somnium Scipionis, 1. 14). Plato says that the soul is a self-moving essence; Xenocrates defines the soul as a self-moving number; Aristotle called it an entelechy; and Pythagoras and Philolaus, a harmony.
C. (Olympiodorus, In. Plat. Phaed., p. 150). Philolaus opposed suicide because it was a Pythagorean precept not to lay down the burden, but to help others carry theirs; namely, that you must assist, and not hinder it.
D. (Clement of Alexandria, Stromateis, 3. p. 433). It will help us to remember the Pythagorean Philolaus' utterance that the ancient theologians and divines claimed that the soul is bound to the body as a punishment, and is buried in it as in a tomb (DK 14).
24. A. (Aristotle, Eth. Eud., 2. 9). As Philolaus has said, there are some reasons (logoi) stronger than us (DK 16).
B. (Iamblichus, In Nicom., 1. 25). I shall later have a better opportunity to consider how, in raising a number to its square, by the position of the simple component unities, we arrive at very evident propositions, naturally, and not by any law, as says Philolaus.
25. (Sextus Empiricus, Adversus Mathematicos, 7. 92. p. 388). Anaxagoras has said how reason in general is the faculty of discerning and judging; the Pythagoreans also agree that it is Reason, not reason in general, but the Reason that develops in men by the study of mathematics, as Philolaus used to say, and they insist that if this Reason is capable of understanding All, it is only because its essence is kindred with this nature, for it is in the nature of things that the similar be understood by the similar.
26 A. (Laurentius Lydus, De Mens., p. 16; Cedrenus, 1. 169b). Philolaus was therefore right in calling it a Decad, because it receives (dechomai) the Infinite, and Orpheus was right in calling it the Branch, because it is the branch from which issue all the numbers, as so many branches.
B. (Cedrenus, 1. p. 72). Philolaus was therefore right to say that the number seven was motherless (DK 20).
C. (Cedrenus, 1. p. 208). Philolaus was therefore right to call the Dyad the spouse of Kronos (DK 20A).
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Notes:
1. This fragment concerns itself with musical intervals smaller than a whole tone. For a good discussion, which also relates to the next fragment, see McClain, The Pythagorean Plato. 159-62.
2. 8 is the harmonic mean between 6 and 12.
3. There is reason to believe that the "five bodies" referred to in this fragment are the so-called regular polyhedra or "Platonic solids" which are described for the first time in Plato's Timaeus. It is quite likely that the earlier Pythagoreans were aware of the regular solids. If this fragment is genuine, Plato followed their lead in associating these "molecular" forms with the "elements" of Greek physics, the latter of which actually represent slates of matter rather than specific substances.
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Re: The Pythagorean Sourcebook and Library
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PART 1 OF 2
THE FRAGMENTS OF ARCHYTAS
ARCHYTAS OF TARENTUM (first half of the fourth century B.C.E.) was a student of Philolaus and a personal friend of Plato, who came to visit him in 388 B.C.E. He made a major contribution to harmonic theory, was engaged in mathematical studies, and was the first to solve the geometrical problem of doubling the volume of the cube.
Like Pythagoras himself, Archytas was also involved in political affairs; he was quite well liked in this capacity, being elected chief magistrate of Tarentum for seven terms though the law, which was waived in his favor, allowed for a maximum of one term. Archytas also seems to have had a knack for practical inventions: he is said to have created a mechanical pigeon, made of wood, which flew, and Aristotle refers to another well-known invention, Archytas' rattle, "which they give to children so that by using it they may refrain from breaking things about the house; for young things cannot keep still."
With the exception of the mathematical fragments and a few others, the fragments of Archytas are not considered genuine. For example, "The Ten Categories of Archytas" are obviously indebted to Aristotelian thought rather than vice versa. Nonetheless, even though not written by Archytas himself, some of the other fragments are quite valuable, especially the ethical ones. The correspondence between Plato and Archytas, reproduced below in the biography from Diogenes Laertius, is thought to be spurious.
For more on Archytas see Freeman's Companion to the Pre-Socratic Philosophers, section 47, and Guthrie's History of Greek Philosophy, vol. 1, 333 ff.
THE LIFE OF ARCHYTAS
FROM DIOGENES LAERTIUS
ARCHYTAS OF TARENTUM, son of Mnesagoras, or of Hestius, according to Aristoxenus, also was a Pythagorean. It was he who, by a letter, saved Plato from the death threatened by Dionysius. He possessed all the virtues, so that, being the admiration of the crowd, he was seven times named general, in spite of the law which prohibited reelection after one year. Plato wrote him two letters, in response to this one of Archytas:
"Greetings. It is fortunate for you that you have recovered from your illness, for I have heard of it not only from you, but also from Lamiscus. I have busied myself about those notes, and took a trip into Lucania, where I met descendants of Ocellus. I have in my possession the treatises On Law and On Kingship, On Sanctity, and On the Origin of All Things, and I am sending them to you. The others could not be discovered. Should they be found, they will be sent to you."
Plato answered:
"Greetings. I am delighted to have received the works which you have sent me, and I acknowledge a great admiration for him who wrote them. He seems to be worthy of his ancient and glorious ancestors, who are said to be from Myra, and among the number of those Trojans who emigrated under the leadership of Laomedon, all worthy people, as the legend proves. Those works of mine about which you wrote me are not in a sufficient state of perfection, but I send them such as they are. Both of us are in perfect agreement on the subject of protecting them. No use to renew the request. May your health improve!"
Such are these two letters.
There were four Archytases: the first, of whom we have just spoken; the second, from Mytilene, was a musician; the third wrote On Agriculture; the fourth is an author of epigrams. Some mention a fifth, an architect, who left a treatise On Mechanics, beginning as follows: "This book contains what I have been taught by Teucer of Carthage. " The musician is said to have made this joke: on being reproached for not advertising himself more, he said "It is my instrument which speaks for me."
Aristoxenus claims that the philosopher Archytas was never defeated during his command. Once, overcome by envy, he had been obliged to resign his command, and his fellow-citizens were immediately conquered. He was the first who methodically applied the principles of mathematics to mechanics; who imparted an organic motion to a geometric figure, by the section of the semi-cylinder seeking two means that would be proportional, in order to double the cube. [1] He also first, by geometry, discovered the properties of the cube, as Plato records in the Republic (528 B).
THE FRAGMENTS OF ARCHYTAS
1. Metaphysical Fragments
1. There are necessarily two principles of beings: the one contains the series of beings organized, and finished; the other, contains unordered and unfinished beings. That one which is susceptible of being expressed, by speech, and which can be explained, embraces both beings, and determines and organizes the nonbeing.
For every time that it approaches the things of becoming, it orders them, and measures them, and makes them participate in the essence and form of the universal. On the contrary, the series of beings which escapes speech and reason, injures ordered things, and destroys those which aspire to essence and being; whenever it approaches them, it assimilates them to its own nature.
But since there are two principles of things of an opposite character, the one the principle of good, and the other the principle of evil, there are therefore also two reasons, the one of beneficent nature, the other of maleficent nature.
That is why the things that owe their existence to art, and also those which owe it to nature, must above all participate in these two principles: form and substance.
The form is the cause of essence; substance is the substrate which receives the form. Neither can substance alone participate in form, by itself; nor can form by itself apply itself to substance; there must therefore exist another cause which moves the substance of things, and forms them. This cause is primary, as regards substance, and the most excellent of all. Its most suitable name is God.
There are therefore three principles: God, the substance of things, and form. God is the artist, the mover; the substance is the matter, the moved; the essence is what you might call the art, and that to which the substance is brought by the mover. But since the mover contains forces which are self- contrary, those of simple bodies, and as the contraries are in need of a principle harmonizing and unifying them, it must necessarily receive its efficacious virtues and proportions from numbers, and all that is manifested in numbers and geometric forms, virtues and proportions capable of binding and uniting into form the contraries that exist in the substance of things. For, by itself, substance is formless; only after having been moved towards form does it become formed and receive the rational relations of order. Likewise, if movement exists, besides the thing moved, there must exist a prime mover; there must therefore be three principles: the substance of things, the form, and the principle that moves itself, and which by its power is the first; not only must this principle be an intelligence, it must be above intelligence, and we call it God.
Evidently the relation of equality applies to the being which can be defined by language and reason. The relation of inequality applies to the irrational being, and cannot be fixed by language; it is substance, and that is why all begetting and destruction take place in substance and do not occur without it.
2. In short, the philosophers began only by so to speak contrary principles; but above these elements they knew another superior one, as is testified to by Philolaus, who says that God has produced, and realized the Limited and Unlimited, and shown that at the Limit is attached the whole series which has a greater affinity with the One, and to the Unlimited, the series that is below. Thus, above these two principles they have posited a unifying cause, superior to everything; which, according to Archenetus, is the cause before the cause, and, according to Philolaus, the universal principle.
3. A. Which One are you referring to? The supreme One, or the infinitely small One that you can find in the parts? The Pythagoreans distinguish between the One and the Monad, as says Archytas: the One and the Monad have a natural affinity, yet they differ.
B. Archytas and Philolaus indiscriminately call the One a Monad, and Monad a One. The majority, however, add to the name Monad, the distinction of first Monad, for there is a Monad which is not the first, and which is posterior to the Monad in itself, and to the One.
C. Pythagoras said that the human soul was a tetragon with right angles. Archytas, on the contrary, instead of defining the soul by the tetragon, did so by a circle, because the soul is a self-mover, and consequently, the prime mover, and this is a circle or a sphere.
D. Plato and Archytas and the other Pythagoreans claim that there are three parts in the soul: reason, courage and desire.
4. The beginning of knowledge of beings is in the things that produce themselves. Of these some are intelligible, and others sensible; the former are immovable, the latter are moved. The criterion of intelligible things is the world; that of sensible things is sensation.
Of the things that do not manifest in things themselves, some are science, the others, opinion; science is immovable, opinion is movable.
We must, besides, admit these three things: the subject that judges, the object that is judged, and the rule by which that object is judged. What judges is the mind, or sensation; what is judged is the logos, or rational essence; the rule of judgement is the act itself which occurs in the being, whether intelligible or sensible. The mind is the judge of essence, whether it tends towards an intelligible being or a sensible one. When reason seeks intelligible things, it tends towards an intelligible element; when it seeks things of sense, it tends towards their element. Hence come those false graphic representations in figures and numbers seen in geometry, those researches in causes and probable ends, whose object are beings subject to becoming, and moral acts, in physiology or politics. It is while tending toward the intelligible element that reason recognizes that harmony is in the double relation [the octave] but sensation alone attests that this double relation is concordant. In mechanics, the object of science is figures, numbers, proportions -- namely, rational proportions; the effects are perceived by sensation, for you can neither study nor know them outside of the matter or movement. In short, it is impossible to know the reason of an individual thing, unless you have preliminarily by the mind grasped the essence of the individual thing; the knowledge of the existence, and of quality, belongs to reason and sensation: to reason, whenever we effect a thing's demonstration by a syllogism whose conclusion is inevitable; to sensation, when the latter is the criterion of a thing's essence.
5. Sensation occurs in the body, reason in the soul. The former is the principle of sensible things, the latter, of intelligible ones. Popular measures are number, length, the foot, weight, equilibrium, and the scales, while the rule and the measure of straightness in both vertical and longitudinal directions is the right angle.
Thus sensation is the principle and measure of the bodies; reason is the principle and measure of intelligible things. The latter is the principle of beings that are intelligible and naturally primary; the former is the principle of sense-objects, and is naturally secondary. Reason is the principle of our soul; sensation is the principle of our body. The mind is the judge of the noblest things; sensation is the judge of the most useful. Sensation was created in view of our bodies, and to serve them; reason was created in view of the soul, and to initiate wisdom therein. Reason is the principle of science; sensation is that of opinion. The latter derives its activity from sensible things; the former, from intelligible forms. Sensible objects participate in movement and change; intelligible objects participate in immutability and eternity. There is analogy between sensation and reason; for sensation's object is the sensible, which moves, changes, and never remains self-identical; therefore, as you can see, it improves or deteriorates. Reason's object is the intelligible, whose essence is immobility; wherefore in the intelligible we cannot conceive of either more or less, better or worse; and just as reason sees the primary being, and the [cosmic] model, so sensation sees the image, and the copied. Reason sees man in himself; sensation sees in them the circle of the sun, and the forms of artificial objects. Reason is perfectly simple and indivisible, as unity, and the point; it is the same with intelligible beings.
The idea is neither the limit nor the frontier of the body; it is only the figure of being, that by which the being exists, while sensation has parts, and is divisible.
Some beings are perceived by sensation, others by opinion, others by science, and others by reason.
The bodies that offer resistance are sensible; opinion knows those that participate in the ideas, and are its images, so to speak. Thus some particular man participates in the idea of man, and this triangle, in the triangle-idea. The objects of science are the necessary accidents of ideas; thus the object of geometry is the properties of the figures; reason knows the ideas themselves, and the principles of the sciences and of their objects, for example, the circle, the triangle, and the pure sphere in itself. Likewise, in us, in our souls, there are four kinds of knowledge: pure thought, science, opinion and sensation; two are principles of knowledge [thought and sensation], two are its purpose, science and opinion.
It is always the similar which is capable of knowing the similar: reason knows intelligible things; science understands knowable things; opinion knows conjecturable things; sensation knows sensible things.
That is why thought must rise from things that are sensible, to the conjecturable, and from these to the knowable, and on to the intelligible; and he who wishes to know the truth about these objects, must in a harmonious grouping combine all these means and objects of knowledge. This being established, you might represent them under the image of a line divided into two equal parts, each of which would be similarly divided; if we separate the sensible, dividing it into two parts, in the same proportion, the one will be clearer, the other obscurer. One of the sections of the sensible contains images of things, such as you see reflected in water, or mirrors; the second represents the plants and animals of which the former are images. Similarly dividing the intelligible, the different kinds of sciences will represent the images; for the students of geometry begin by establishing by hypothesis the odd and the even, figures, three kinds of angles, and from these hypotheses deduce their science. As to the things themselves, they leave them aside, as if they knew them, though they cannot account for them to themselves or to others; they employ sensible things as images, but these things are neither the object nor the end proposed in their researches and reasonings, which pursue only things in themselves, such as the diameter, or square. The second section is that of the intelligible, the object of dialectics. It really makes no hypotheses, positing principles whence it rises to arrive at the unconditioned, universal principle; then, by an inverse movement, grasping that principle, it descends to the end of the reasoning, without employing any sensible object, exclusively using pure ideas. By these four divisions, you can also analyze the soul-states, and give the highest the name of thought, reasoning to the second, faith to the third, and imagination to the fourth.
6. Archytas, at the beginning of his book On Wisdom gives this advice: in all human things, wisdom is as superior as sight is to all the other senses of the body, as mind is superior to soul, as the sun is superior to the stars. Of all the senses, sight is the one that extends furthest in its sphere of action, and gives us the most ideas. Mind, being supreme, accomplishes its legitimate operation by reason and reasoning; it is like sight, and is the power of the noblest objects. The sun is the eye and soul of natural things, for it is through it that they are all seen, begotten, and thought; through it the plants produced by root or seed are fed, developed, and endowed with sensation.
Of all beings, man is the wisest by far. For he is able to contemplate beings, and to acquire knowledge and understanding of all. That is why divinity has engraved in him, and has revealed to him the system of speech, which extends to everything, a system in which are classified all the beings, kinds of beings, and the meanings of nouns and verbs. For the specialized seats of the voice are the pharynx, the mouth and the nose. As man is naturally organized to produced sounds, through which nouns and verbs are expressed and formed, likewise he is naturally destined to contemplate the notions contained in visible objects. Such, in my view, is the purpose for which man has been created, and was born, and for which he received from God his organs and faculties.
Man is born and was created to know the essence of universal nature; and precisely the function of wisdom is to possess and contemplate the intelligence manifested in [all] beings.
The object of wisdom is no particular being, but all the beings, absolutely; and it should not begin to seek the principles of an individual being, but the principles common to all. The object of wisdom is all the beings, as the object of sight is all visible things. The function of wisdom is to see all the beings in their totality, and to know their universal attributes, and that is how wisdom discovers the principles of all beings.
He who is capable of analyzing all the species, and tracing and grouping them, by an inverse operation, into one single principle, seems to me the wisest, and the closest to the truth; he seems to have found that sublime observatory from the peak of which he may observe God, and all the things that belong to the series and order of divine things. Being master of this royal road, his mind will be able to rush forwards, and arrive at the end of the career, uniting principles to the purposes of things, and knowing that God is the principle, the middle and the end of all things made according to the rules of justice and right reason.
2. Physical and Mathematical Fragments
7. As Eudemus reports, Archytas used to ask this question: "If I was situated at the extreme and immovable limit of the world, could I, or could I not, extend a wand outside of it?" To say I could not, is absurd; but if I can, there must be something outside of the world, be it body or space; and in whatever manner we reason, by the same reasoning we will ever return to this limit. I will still place myself there, and ask, "Is there anything else on which I may place my wand?" Therefore, the Unlimited exists; if it is a body, our proposition is demonstrated; if it is space, place is that in which a body could be; and if it exists potentially, we will have to place it and classify it among the eternal things, and the Unlimited will then be a body and a place.
8. The essence of place is that all other things are in it, while itself is not in anything. For if it was in a place, there would be a place in a place, and that would continue to infinity. All other beings must therefore be in place, and place in nothing. Its relation to things is the same as Limit to limited things; for the place of the entire world is the Limit of all things.
9 A. Some say that time is the sphere of the world; such was the sentiment of the Pythagoreans, according to those who had heard Archytas give this general definition of time: "Time is the interval of the nature of all."
B. The divine Iamblichus, in the first book of his Commentaries on the Categories, said that Archytas thus defined time: "It is the number of movement, or in general the interval of the nature of all."
C. We must combine these two definitions, and recognize time as both continuous and discrete, though it is properly continuous. Iamblichus claims that Archytas taught the distinction of physical time, and psychic time. So at least Iamblichus interpreted Archytas, but we must recognize that there, and often elsewhere, he adds his own commentaries to explain matters.
10. The general proper essence of "when-ness" and time is to be indivisible and unsubstantial. For, being indivisible, the present time has passed, while expressing it and thinking of it; nothing remains of it, and so becoming continuously the same it never subsists numerically, but only specifically. In fact. the actually present time and the future are not identical with former time. For the one has past, and is no more; the other one passes while being produced and thought. Thus the present is never but a bond; it perpetually becomes, changes, and perishes, but nevertheless it remains identical in its own kind.
In fact, every present is without parts, and indivisible; it is the term of past time, the beginning of time to come; just as in a broken line, the point where the break occurs becomes the beginning of a line, and the end of the other. Time is continuous, and not discrete as are number, speech and harmony.
In speech, the syllables are parts, and distinct parts; in harmony, they are the sounds; in number, the unities. The line, place and space are continuous; if they are divided, their parts form common sections. For the line divides into points, the surface into lines, the solid into surfaces. Therefore time is continuous. In fact there was no time when time was not; and there was no moment when the present was not. But the present has always been, it will always be, and will never fail; it changes perpetually, and becomes another according to the number, but remains the same according to kind. The line differs from the other continua, in that if you divide the line, place, and space, its parts will subsist; but in time, the past has perished, and the future will. That is why either time does absolutely not exist, or it hardly exists, and has but an insensible existence. For of its parts one, the past, is no more, and the future is not yet; how then could the present, without parts and indivisible, possess true reality?
11. Plato says that the movement is the great and small, the non-being, the unusual, and all that reduces to these; like Archytas, we had better say that it is a cause.
12. Why do all natural bodies take the spherical form? Is it, as said Archytas, because in the natural movement is the proportion of equality? For everything moves in proportion; and this proportion of equality is the only one which, when it occurs, produces circles and spheres, because it returns on itself.
13. He who knows must have learned from another, or have found his knowledge by himself. The science that you learn from another, is as you might say, exterior; what you find by yourself, belongs to ourselves individually. To find without seeking is something difficult and rare; to find what one is seeking is commodious and easy; to ignore, and seek what you ignore, is impossible (DK 3).
14. The Pythagorean opinion about sciences to me seems correct, and they seem to show an exact judgment about each of them. Having known how to form a just idea of the nature of a ball, they should have likewise seen the essential nature of the parts. They have left us certain and evident theories about arithmetic, geometry and spherics, also about music, for all these sciences seem to be kindred. In fact, the first two kinds of being are indistinguishable.
15. A. First they have seen that it was not possible that noise should exist unless there was a shock of one body against another; they said there is a shock when moving bodies meet and strike each other. The bodies moved in the air in an opposite direction and those that are moved with an unequal swiftness-in the same direction-the first, when overtaken, makes a noise, because struck. Many of these noises are not susceptible of being perceived by our organs; some because of the slightness of the shock, the others because of their too great distance from us, some even because of the very excess of their intensity, for noises too great do not enter into our ears, as we cannot introduce anything into jars with too narrow an opening when one pours in too much at a time.
Of the sounds that fall within the range of our senses, some -- those that come quickly from the bodies struck -- seem shrill; those that arrive slowly and feebly, seem of low pitch. In fact, when one agitates some object slowly and feebly, the shock produces a low pitch; if the waving is done quickly, and with energy, the sound is shrill. This is not the only proof of the fact, which we can prove when we speak or sing; when we wish to speak loud and high, we use a great force of breath. So also with something thrown; if you throw them hard, they go far; if you throw them without energy, they fall near, for the air yields more to bodies moved with much force, than to those thrown with little. This phenomenon is also reproduced in the sound of the voice, for the sounds produced by an energetic breath are shrill, while those produced by a feeble breath are weak and low in pitch. This same observation can be seen in the force of a signal given from any place: if you pronounce it loud, it can be heard far; if you pronounce the same signal low, we do not hear it even when near. So also in flutes, the breath emitted by the mouth and which presents itself to the holes nearest the mouthpiece, produces a shriller sound, because the impulsive force is greater; farther [down], they are of lower pitch. It is therefore evident that the swiftness of the movement produces shrillness, and slowness, lower pitch. The same thing is seen in the bull roarers which are spun in the Mysteries; those that move slowly produce a low pitch, while those that move quickly with force make a shrill noise. Let us yet adduce the reed: if you close the lower opening, and blow into it, it will produce a certain sound; and if you stop it in the center, or in the front, the sound will be shrill. For the same breath traversing a long space weakens, while traversing a shorter, it remains of the same power. After having developed this opinion that the movement of the voice is measured by intervals, he resumes his discussion, saying, that the shrill sounds are the result of a swifter movement, the lower sounds, of a slower movement. This is a fact which numerous experiments demonstrate clearly.
B. Eudoxus and Archytas believed that the reasons of the agreement of the sounds was in the numbers; they agree in thinking that these reasons consist in the movements, the shrill movement being quick, because the agitation of the air is continuous, and the vibration more rapid; the low pitch movement being slow, because it is calmer.
16. Explaining himself about the means; Archytas writes: In music there are three means: the first is the arithmetical mean, the second is the geometrical, the third is the subcontrary mean, which is called harmonic. The mean is arithmetical, when the three terms are in a relation of analogical excess, that is to say, when the difference between the first and second is the same as between second and third; in this proportion, the relation of the greater terms is smaller, and the relation of the smaller is greater. The geometric mean exists when the first term is to the second as the second is to the third; here the relation of the greater is identical with the relation of the smaller terms. The subcontrary mean, which we call harmonic, exists when the first term exceeds the second by a fraction of itself, identically with the fraction [of the third] by which the second exceeds the third; in this proportion the relation of the greater terms is greater, and that of the smaller, smaller.
3. Ethical Fragments
17. A. We must first know that the good man is not thereby necessarily happy, but that the happy man is necessarily good; for the happy man is he who deserves praise and congratulations; the good man deserves only praise.
We praise a man because of his virtue, we congratulate him because of his success. The good man is such because of the goods that proceed from virtue; the happy man is such because of the goods that come from fortune. From the good man you cannot take his virtue; sometimes the happy man loses his good fortune. The power of virtue depends on nobody; that of happiness, on the contrary, is dependent. Long diseases, the loss of our senses, cause to fade the flower of our happiness.
B. God differs from the good man in that God not only possesses a perfect virtue, purified from all mortal affection, but enjoys a virtue whose power is faultless and independent, as suits the majesty and magnificence of his works.
Man, on the contrary, not only possesses an inferior virtue, because of the mortal constitution of his nature, but even sometimes by the very abundance of his goods, now by the force of habit, by the vice of nature, or from other causes, he is incapable of attaining the perfection of the good.
C. The good man, in my opinion, is he who knows how to act properly in serious circumstances and occasions. He will therefore know how to support good and bad fortune; in a brilliant and glorious condition, he will show himself worthy of it, and if fortune happens to change, he will know how to accept properly his actual fate. In short, the good man is he who, in every occasion, and according to the circumstances, well plays his part, and knows how to fit to it not only himself, but also those who have confidence in him, and are associated with his fortunes.
D. Since amidst the goods, some are desirable for themselves, and not for anything else, and others are desirable for something else, and not for themselves, there must necessarily exist a third kind of goods, which are desirable both for themselves and for other things. Which are the goods naturally desirable for themselves, and not for anything else? Evidently they include happiness, for it is the end on account of which we seek everything else, while we seek it only for itself, and not in view of anything else. Secondly, which are the goods chosen for something else, and not for themselves? Evidently those that are useful, and which are the means of procuring the real goods, which thus become the causes of the goods desirable for themselves; for instance: the bodily fatigues, the exercises, the tests which procure health; reading, meditation, the studies which procure virtues, and the quality of honesty. Finally, which are those goods which are both desirable for themselves, and for something else? The virtues, and the habitual possession of virtues, the resolutions of the soul, the actions, and in short anything pertaining to the possession of the beautiful. That which is to be considered for itself, and not for anything else, that is the only good.
Now what we seek for itself and for something else is divided into three classes: the one whose object is the soul, the body, and external goods. The first contains the virtues of the soul; the second contains the advantages of the body; the third consists in friends, glory, honor and wealth. Likewise with the goods that are desirable only for something else: one part of them procures goods for the soul, the other which regards the body, procures goods for it; the external goods furnish wealth, glory, honor and friendship.
We can prove that it is the characteristic of virtue to be desirable for itself, as follows: in fact, if the naturally inferior goods, I mean those of the body, are by us sought for themselves, and if the soul is better than the body, it is evident that we like the goods of the soul for themselves, and not for the result that they might produce.
E. In human life there are three circumstances: prosperity, adversity, and intermediary comfort. Since the good man who possesses virtue and practices it, practices it in these three circumstances -- either in adversity, or prosperity, or comfort, since besides in adversity he is unhappy, in prosperity he is happy, and in comfort he is not happy -- it is evident that happiness is nothing else than the use of virtue in prosperity. I speak here of human happiness. Man is not only a soul, he is also a body. The living being is a composite of both, and man also; for if the body is an instrument of the soul, it is as much a part of the man as the soul. That is why, among the goods, some belong to the man, and others belong to his component parts. The good of man is happiness amidst its integral parts. The soul's goods are prudence, courage, justice, and temperance; the body's are beauty, health, good disposition of its members, and the perfect condition of its senses. The external goods -- wealth, glory, honor, nobility -- are naturally superfluous advantages of man, and are naturally subordinate to the superior goods.
The inferior goods serve as satellites to the superior goods. Friendship, glory, and wealth are the satellites of the body and soul. Health, strength and sense-perfection are satellites of the body. Prudence, courage, justice and temperance are the satellites of the reason of the soul. Reason is the satellite of God; he is omnipotent, the supreme master. It is for these goods that the others must exist; for the army obeys the general, the sailors heed the pilot, the world obeys God, the soul heeds reason, the happy life is contingent on prudence. For prudence is nothing more than the science of the happy life, or the science of the goods which belong to human nature.
F. To God belongs happiness and the happy life; man cannot possess but a grouping of science, virtue and prosperity forming a single body. I call wisdom the science of the Gods and geniuses, and term prudence the science of human things, the science of life. For science should be the name of virtues which rest upon reasons and demonstrations, and moral virtue, the excellent habit of the irrational part of the soul, which makes you give the name of certain qualities corresponding to our habits, namely the names of liberal, just and temperate people. And I call prosperity this affluence of goods which we receive without reason being their cause. Then since virtue and science depend on us, and prosperity does not depend thereon, since happiness consists in the contemplation and practice of good things, and since contemplation and action when they meet obstacles, lend us a necessary support, when they go by an easy road, they bring us distraction and happiness. Since after all it is prosperity that gives us these benefits, it is evident that happiness is nothing else than the use of virtue in prosperity.
G. Man's relations with prosperity resemble a healthy and vigorous human body; he also can stand heat and cold, can raise a great burden, and can easily bear many other miseries.
H. Since happiness is the use of virtue in prosperity, let us speak of virtue and prosperity, the former first. Some goods, such as virtue, are not subject to excess; for excess is impossible in virtue, for one can never be too decent a man. Indeed, virtue's measure is duty, and is the habit of duty in practical life. But prosperity is subject to excess and lack, which excesses produce certain evils, disturbing man from his usual mood, so as to oppose him to virtue; this is not only the case with prosperity, but other more numerous causes also produce this effect. You need not be surprised at seeing in the hall certain impudent artists, who neglect true art, misleading the ignorant by a false picture; but do you suppose that this race does not exist as regards virtue? On the contrary, the greater and more beautiful virtue is, the more do people feign to adorn themselves with it. There are indeed many things which dishonor the appearance of virtue: first are the deceivers who simulate it, others are the natural passions which accompany it, and sometimes twist the dispositions of the soul into a contrary direction. Others are the bad habits which the body has rooted in us, or which have been ingrained in us by youth, age, prosperity, adversity, or by a thousand other circumstances. Wherefore we must not at all be surprised at entirely wrong judgments, because the true nature of our soul has been falsified within us. Just as we see an artist who is excellent make errors in works we are examining -- or the general, the pilot or the painter and like may make errors without our detracting from their talent -- so we must not call unworthy him who has had a moment of weakness, nor among the worthy a man who has done no more than a single action; but in respect to the evil, we must consider chance, and for the good, error, and to make an equitable and just judgment, and not regard a single circumstance, or a single period of time, but the whole life.
Just as the body suffers from both excess and lack, but as nevertheless the excess and so-called superfluities naturally produce the greatest diseases, so the soul suffers from both prosperity and adversity when they arrive at wrong times, and yet the greatest evils come from so-called absolute prosperity -- which is absolute because like wine it intoxicates the reason of the worthy.
I. That is why it is not adversity but prosperity which is the hardest to stand properly. All men, when they are in adversity, at least the greater part of them, seem moderate and modest; but in good fortune, ambitious, vain and proud. For adversity is apt to moderate the soul, and concentrate it, while on the contrary prosperity excites it and puffs it up. That is why wretches are docile to advice, and prudent in conduct, while the happy are bold and venturesome.
J. Thus there is a measure and limit of prosperity that the worthy man should desire to have as auxiliary in the accomplishment of his actions, just as there is a measure in the size of the ship, and in the length of the tiller, which permits the experienced pilot to traverse an immense extent of sea, and to carry through a great voyage.
The result of excess of prosperity, even among worthy people, is that the soul loses leadership to prosperity; just as too bright a light dazzles the eyes so too great a prosperity dazzles the reason of the soul. Enough about prosperity.
18. I insist that virtue is sufficient to preclude unhappiness, that badness precludes happiness, if we know how properly to judge of the genuine condition of the soul in these two conditions. For the evil reason is necessarily always unhappy, whether in abundance -- which he does not know how properly to judge or use -- or in poverty, just as a blind man is always wondering whether he is in brilliant light, or in darkness. But the worthy man is not always happy, for happiness does not consist in the possession of virtue, but in its use, just as a man who sees does not see all the time will not see without light.
Life is as it were divided into two roads: the rougher one, followed by patient Ulysses, and the more agreeable one followed by Nestor. I mean that virtue desires the one, but can also follow the other. But nature cries aloud that happiness is life desirable in itself, whose state is assured, because one can realize one's purposes in it, so that if life is traversed by things one has not desired, one is not happy, without however being absolutely unhappy. Therefore be not so bold as to insist that the worthy man is exempt from sickness, and suffering; dare not to say that he does not know pain, for if the body is allow some causes of pain, the soul should also be allowed some. The griefs of the insane lack reason and measure, while those of the wise are contained within the measure which reason gives to everything. But this so advertised insensitivity to sorrow enervates the character of generosity of virtue, when it stands trials, great sorrows, when it is exposed to death, suffering, and poverty, for it is easy to support small sorrows. You must therefore practice metriopathy or sorrow -- standardization so as to avoid the insensitivity just as much as the over-sensibility of pain, and not in words to boast about our strength above the measure of our human nature.
19. We might define philosophy as the desire of knowing and understanding things in themselves, joined with practical virtue, inspired and realized by the love of science. The beginning of philosophy is the science of nature, the middle, practical life, and the end, science itself. It is fortunate to have been well born, to have received a good education, to have been accustomed to obey a just rule, and to have habits conformable to nature. One must also have been exercised in virtue, and have been educated by wise parents, governors and masters. It is fine to impose the rule of duty on oneself, to have no need of constraint, to be docile to those who give us good advice about life and science. For a fortunate disposition of nature, and a good education are often more powerful than lessons to bring us to the good; its only lack would be the efficacious light of reason, which science gives us. Two rival directions of life contend for mastery, these being practical and philosophical life. By far the most perfect life unites them both, and in each different path adapts itself to circumstances. We are born for rational activity, which we call practical. Practical reason leads us to politics; the theoretical reason, to the contemplation of the universality of things. Mind itself, which is universal, embraces these two powers necessary to happiness, which we define as the activity of virtue in prosperity; it is not exclusively either a practical life which would exclude science, nor a speculative life which would exclude the practical. Perfect reason inclines towards these two omnipotent principles for which man is born, the principles of society and science. For if these opposite principles seem mutually to interfere in their development, the political principles turning us away from speculation, and the speculative principles turning us from politics, to persuade us to live at rest, nevertheless nature, uniting the ends of these two movements, shows them fused; for virtues are not contradictory and mutually antipathetic. Indeed, no harmony is more constant than the harmony of virtues. If from his youth man has subjected himself to the principles of virtues, and to the divine law of the world harmony, he will lead an easy life; and if, by his own inclination, he inclines towards evil and has the luck of meeting better guides, he will, by rectifying his course, arrive at happiness, like passengers favored by chance, finishing a fortunate sea-passage -- thanks to the pilot -- and the fortunate passage of life is happiness. But if by himself he cannot know his real interests, and if he does not have the luck of meeting prudent directors, what benefit would it be if he did have immense treasures? For the fool, even if he had for himself all the other elements of luck, is eternally unhappy. And since, in everything, you must first consider the end -- for that is what is done by the pilots ever meditating over the harbor whither they are to land the ship, by the drivers who keep their eye on the goal of their trip, and by the archers and slingers who consider their objective, for it is the objective towards which all their efforts must tend-virtue must necessarily undertake an objective, which should become the art of living, and that is the name I give it in both directions it can take. For practical life this objective is improvement; for the philosophical life, the perfect good, which, in their human affairs the sages call happiness. Those who are in misery are not capable of judging of happiness according to exact ideas, and those who do not see it clearly would not know how to choose it. Those who consider that pleasure is the sovereign good are punished therefore by foolishness; those who above all seek the absence of pain, also receive their punishment. In summary: to define life-happiness as the enjoyment of the body, in an unreflective state of soul, is to expose oneself to all the whirlwinds of the tempest. Those who suppress moral beauty, by avoiding all discussion, all reflection about the matter, and seeking pleasure, absence of pain, simple and primitive physical enjoyments, and the irreflective inclinations of body and soul, are not more fortunate, for they commit a double fault by reducing the good of the soul and its superior functions to the level of that of the body, and in raising the good of the body to the high level due to the good of the soul. For an exact discernment of these goods, we should outline its proper part for the divine element, and for nature; yet some do not observe this relation of dignity from the better to the worse. But we do so when we say that if the body is the organ of the soul, then reason is the guide of the entire soul, the mistress of the body, this tent of the soul, and that all the other physical advantages should serve only as instruments to the intellectual activity, if you wish it to be perfect in power, duration and wealth.
20. These are the most important conditions to become a sage: first, you must have received from fate a mind endowed with facility to understand, memory, and industry. You must then from youth on exercise your intelligence by the practice of argumentation, by mathematical studies, and by the exact sciences. Then you must study healthful philosophy, after which you may undertake the knowledge of the Gods, of laws, and of human life. For there are two means of arriving at this state known as wisdom. The first is to acquire the habit of work that is intellectual, and the taste for knowledge; the other is to seek to see many things, to undertake business frequently, and to know them, either directly at first hand, or indirectly. For he who from youth on has exercised reason by dialectic reasonings, mathematical studies, and exact sciences, is not yet ready for wisdom, any more than he who has neglected these labors, and has only listened to others, and has immersed himself in business. The one has become blind, when the business is to judge particular facts; the other, when he is to judge of general deductions. Just as in calculations you obtain the total by combining the parts, so also, in business practice, reason can vaguely sketch the general formula, but experience alone can enable us to grasp the details and individual facts.
21. Age is in the same relation to youth. Youth makes men energetic, age makes them prudent. Never by imprudence does it let a thought escape. It reflects on what it has done, it considers maturely what it ought to do, in order that this comparison of the future with the present, and of the present with the future lead it to good conduct. To the past it applies memory, to the present, sensation, and to the future, foresight; for our memory has always as object the past, foresight the future, and sensation the present. He who therefore wishes to lead an honest and beautiful life must not only have senses and memory, but foresight.
THE FRAGMENTS OF ARCHYTAS
ARCHYTAS OF TARENTUM (first half of the fourth century B.C.E.) was a student of Philolaus and a personal friend of Plato, who came to visit him in 388 B.C.E. He made a major contribution to harmonic theory, was engaged in mathematical studies, and was the first to solve the geometrical problem of doubling the volume of the cube.
Like Pythagoras himself, Archytas was also involved in political affairs; he was quite well liked in this capacity, being elected chief magistrate of Tarentum for seven terms though the law, which was waived in his favor, allowed for a maximum of one term. Archytas also seems to have had a knack for practical inventions: he is said to have created a mechanical pigeon, made of wood, which flew, and Aristotle refers to another well-known invention, Archytas' rattle, "which they give to children so that by using it they may refrain from breaking things about the house; for young things cannot keep still."
With the exception of the mathematical fragments and a few others, the fragments of Archytas are not considered genuine. For example, "The Ten Categories of Archytas" are obviously indebted to Aristotelian thought rather than vice versa. Nonetheless, even though not written by Archytas himself, some of the other fragments are quite valuable, especially the ethical ones. The correspondence between Plato and Archytas, reproduced below in the biography from Diogenes Laertius, is thought to be spurious.
For more on Archytas see Freeman's Companion to the Pre-Socratic Philosophers, section 47, and Guthrie's History of Greek Philosophy, vol. 1, 333 ff.
THE LIFE OF ARCHYTAS
FROM DIOGENES LAERTIUS
ARCHYTAS OF TARENTUM, son of Mnesagoras, or of Hestius, according to Aristoxenus, also was a Pythagorean. It was he who, by a letter, saved Plato from the death threatened by Dionysius. He possessed all the virtues, so that, being the admiration of the crowd, he was seven times named general, in spite of the law which prohibited reelection after one year. Plato wrote him two letters, in response to this one of Archytas:
"Greetings. It is fortunate for you that you have recovered from your illness, for I have heard of it not only from you, but also from Lamiscus. I have busied myself about those notes, and took a trip into Lucania, where I met descendants of Ocellus. I have in my possession the treatises On Law and On Kingship, On Sanctity, and On the Origin of All Things, and I am sending them to you. The others could not be discovered. Should they be found, they will be sent to you."
Plato answered:
"Greetings. I am delighted to have received the works which you have sent me, and I acknowledge a great admiration for him who wrote them. He seems to be worthy of his ancient and glorious ancestors, who are said to be from Myra, and among the number of those Trojans who emigrated under the leadership of Laomedon, all worthy people, as the legend proves. Those works of mine about which you wrote me are not in a sufficient state of perfection, but I send them such as they are. Both of us are in perfect agreement on the subject of protecting them. No use to renew the request. May your health improve!"
Such are these two letters.
There were four Archytases: the first, of whom we have just spoken; the second, from Mytilene, was a musician; the third wrote On Agriculture; the fourth is an author of epigrams. Some mention a fifth, an architect, who left a treatise On Mechanics, beginning as follows: "This book contains what I have been taught by Teucer of Carthage. " The musician is said to have made this joke: on being reproached for not advertising himself more, he said "It is my instrument which speaks for me."
Aristoxenus claims that the philosopher Archytas was never defeated during his command. Once, overcome by envy, he had been obliged to resign his command, and his fellow-citizens were immediately conquered. He was the first who methodically applied the principles of mathematics to mechanics; who imparted an organic motion to a geometric figure, by the section of the semi-cylinder seeking two means that would be proportional, in order to double the cube. [1] He also first, by geometry, discovered the properties of the cube, as Plato records in the Republic (528 B).
THE FRAGMENTS OF ARCHYTAS
1. Metaphysical Fragments
1. There are necessarily two principles of beings: the one contains the series of beings organized, and finished; the other, contains unordered and unfinished beings. That one which is susceptible of being expressed, by speech, and which can be explained, embraces both beings, and determines and organizes the nonbeing.
For every time that it approaches the things of becoming, it orders them, and measures them, and makes them participate in the essence and form of the universal. On the contrary, the series of beings which escapes speech and reason, injures ordered things, and destroys those which aspire to essence and being; whenever it approaches them, it assimilates them to its own nature.
But since there are two principles of things of an opposite character, the one the principle of good, and the other the principle of evil, there are therefore also two reasons, the one of beneficent nature, the other of maleficent nature.
That is why the things that owe their existence to art, and also those which owe it to nature, must above all participate in these two principles: form and substance.
The form is the cause of essence; substance is the substrate which receives the form. Neither can substance alone participate in form, by itself; nor can form by itself apply itself to substance; there must therefore exist another cause which moves the substance of things, and forms them. This cause is primary, as regards substance, and the most excellent of all. Its most suitable name is God.
There are therefore three principles: God, the substance of things, and form. God is the artist, the mover; the substance is the matter, the moved; the essence is what you might call the art, and that to which the substance is brought by the mover. But since the mover contains forces which are self- contrary, those of simple bodies, and as the contraries are in need of a principle harmonizing and unifying them, it must necessarily receive its efficacious virtues and proportions from numbers, and all that is manifested in numbers and geometric forms, virtues and proportions capable of binding and uniting into form the contraries that exist in the substance of things. For, by itself, substance is formless; only after having been moved towards form does it become formed and receive the rational relations of order. Likewise, if movement exists, besides the thing moved, there must exist a prime mover; there must therefore be three principles: the substance of things, the form, and the principle that moves itself, and which by its power is the first; not only must this principle be an intelligence, it must be above intelligence, and we call it God.
Evidently the relation of equality applies to the being which can be defined by language and reason. The relation of inequality applies to the irrational being, and cannot be fixed by language; it is substance, and that is why all begetting and destruction take place in substance and do not occur without it.
2. In short, the philosophers began only by so to speak contrary principles; but above these elements they knew another superior one, as is testified to by Philolaus, who says that God has produced, and realized the Limited and Unlimited, and shown that at the Limit is attached the whole series which has a greater affinity with the One, and to the Unlimited, the series that is below. Thus, above these two principles they have posited a unifying cause, superior to everything; which, according to Archenetus, is the cause before the cause, and, according to Philolaus, the universal principle.
3. A. Which One are you referring to? The supreme One, or the infinitely small One that you can find in the parts? The Pythagoreans distinguish between the One and the Monad, as says Archytas: the One and the Monad have a natural affinity, yet they differ.
B. Archytas and Philolaus indiscriminately call the One a Monad, and Monad a One. The majority, however, add to the name Monad, the distinction of first Monad, for there is a Monad which is not the first, and which is posterior to the Monad in itself, and to the One.
C. Pythagoras said that the human soul was a tetragon with right angles. Archytas, on the contrary, instead of defining the soul by the tetragon, did so by a circle, because the soul is a self-mover, and consequently, the prime mover, and this is a circle or a sphere.
D. Plato and Archytas and the other Pythagoreans claim that there are three parts in the soul: reason, courage and desire.
4. The beginning of knowledge of beings is in the things that produce themselves. Of these some are intelligible, and others sensible; the former are immovable, the latter are moved. The criterion of intelligible things is the world; that of sensible things is sensation.
Of the things that do not manifest in things themselves, some are science, the others, opinion; science is immovable, opinion is movable.
We must, besides, admit these three things: the subject that judges, the object that is judged, and the rule by which that object is judged. What judges is the mind, or sensation; what is judged is the logos, or rational essence; the rule of judgement is the act itself which occurs in the being, whether intelligible or sensible. The mind is the judge of essence, whether it tends towards an intelligible being or a sensible one. When reason seeks intelligible things, it tends towards an intelligible element; when it seeks things of sense, it tends towards their element. Hence come those false graphic representations in figures and numbers seen in geometry, those researches in causes and probable ends, whose object are beings subject to becoming, and moral acts, in physiology or politics. It is while tending toward the intelligible element that reason recognizes that harmony is in the double relation [the octave] but sensation alone attests that this double relation is concordant. In mechanics, the object of science is figures, numbers, proportions -- namely, rational proportions; the effects are perceived by sensation, for you can neither study nor know them outside of the matter or movement. In short, it is impossible to know the reason of an individual thing, unless you have preliminarily by the mind grasped the essence of the individual thing; the knowledge of the existence, and of quality, belongs to reason and sensation: to reason, whenever we effect a thing's demonstration by a syllogism whose conclusion is inevitable; to sensation, when the latter is the criterion of a thing's essence.
5. Sensation occurs in the body, reason in the soul. The former is the principle of sensible things, the latter, of intelligible ones. Popular measures are number, length, the foot, weight, equilibrium, and the scales, while the rule and the measure of straightness in both vertical and longitudinal directions is the right angle.
Thus sensation is the principle and measure of the bodies; reason is the principle and measure of intelligible things. The latter is the principle of beings that are intelligible and naturally primary; the former is the principle of sense-objects, and is naturally secondary. Reason is the principle of our soul; sensation is the principle of our body. The mind is the judge of the noblest things; sensation is the judge of the most useful. Sensation was created in view of our bodies, and to serve them; reason was created in view of the soul, and to initiate wisdom therein. Reason is the principle of science; sensation is that of opinion. The latter derives its activity from sensible things; the former, from intelligible forms. Sensible objects participate in movement and change; intelligible objects participate in immutability and eternity. There is analogy between sensation and reason; for sensation's object is the sensible, which moves, changes, and never remains self-identical; therefore, as you can see, it improves or deteriorates. Reason's object is the intelligible, whose essence is immobility; wherefore in the intelligible we cannot conceive of either more or less, better or worse; and just as reason sees the primary being, and the [cosmic] model, so sensation sees the image, and the copied. Reason sees man in himself; sensation sees in them the circle of the sun, and the forms of artificial objects. Reason is perfectly simple and indivisible, as unity, and the point; it is the same with intelligible beings.
The idea is neither the limit nor the frontier of the body; it is only the figure of being, that by which the being exists, while sensation has parts, and is divisible.
Some beings are perceived by sensation, others by opinion, others by science, and others by reason.
The bodies that offer resistance are sensible; opinion knows those that participate in the ideas, and are its images, so to speak. Thus some particular man participates in the idea of man, and this triangle, in the triangle-idea. The objects of science are the necessary accidents of ideas; thus the object of geometry is the properties of the figures; reason knows the ideas themselves, and the principles of the sciences and of their objects, for example, the circle, the triangle, and the pure sphere in itself. Likewise, in us, in our souls, there are four kinds of knowledge: pure thought, science, opinion and sensation; two are principles of knowledge [thought and sensation], two are its purpose, science and opinion.
It is always the similar which is capable of knowing the similar: reason knows intelligible things; science understands knowable things; opinion knows conjecturable things; sensation knows sensible things.
That is why thought must rise from things that are sensible, to the conjecturable, and from these to the knowable, and on to the intelligible; and he who wishes to know the truth about these objects, must in a harmonious grouping combine all these means and objects of knowledge. This being established, you might represent them under the image of a line divided into two equal parts, each of which would be similarly divided; if we separate the sensible, dividing it into two parts, in the same proportion, the one will be clearer, the other obscurer. One of the sections of the sensible contains images of things, such as you see reflected in water, or mirrors; the second represents the plants and animals of which the former are images. Similarly dividing the intelligible, the different kinds of sciences will represent the images; for the students of geometry begin by establishing by hypothesis the odd and the even, figures, three kinds of angles, and from these hypotheses deduce their science. As to the things themselves, they leave them aside, as if they knew them, though they cannot account for them to themselves or to others; they employ sensible things as images, but these things are neither the object nor the end proposed in their researches and reasonings, which pursue only things in themselves, such as the diameter, or square. The second section is that of the intelligible, the object of dialectics. It really makes no hypotheses, positing principles whence it rises to arrive at the unconditioned, universal principle; then, by an inverse movement, grasping that principle, it descends to the end of the reasoning, without employing any sensible object, exclusively using pure ideas. By these four divisions, you can also analyze the soul-states, and give the highest the name of thought, reasoning to the second, faith to the third, and imagination to the fourth.
6. Archytas, at the beginning of his book On Wisdom gives this advice: in all human things, wisdom is as superior as sight is to all the other senses of the body, as mind is superior to soul, as the sun is superior to the stars. Of all the senses, sight is the one that extends furthest in its sphere of action, and gives us the most ideas. Mind, being supreme, accomplishes its legitimate operation by reason and reasoning; it is like sight, and is the power of the noblest objects. The sun is the eye and soul of natural things, for it is through it that they are all seen, begotten, and thought; through it the plants produced by root or seed are fed, developed, and endowed with sensation.
Of all beings, man is the wisest by far. For he is able to contemplate beings, and to acquire knowledge and understanding of all. That is why divinity has engraved in him, and has revealed to him the system of speech, which extends to everything, a system in which are classified all the beings, kinds of beings, and the meanings of nouns and verbs. For the specialized seats of the voice are the pharynx, the mouth and the nose. As man is naturally organized to produced sounds, through which nouns and verbs are expressed and formed, likewise he is naturally destined to contemplate the notions contained in visible objects. Such, in my view, is the purpose for which man has been created, and was born, and for which he received from God his organs and faculties.
Man is born and was created to know the essence of universal nature; and precisely the function of wisdom is to possess and contemplate the intelligence manifested in [all] beings.
The object of wisdom is no particular being, but all the beings, absolutely; and it should not begin to seek the principles of an individual being, but the principles common to all. The object of wisdom is all the beings, as the object of sight is all visible things. The function of wisdom is to see all the beings in their totality, and to know their universal attributes, and that is how wisdom discovers the principles of all beings.
He who is capable of analyzing all the species, and tracing and grouping them, by an inverse operation, into one single principle, seems to me the wisest, and the closest to the truth; he seems to have found that sublime observatory from the peak of which he may observe God, and all the things that belong to the series and order of divine things. Being master of this royal road, his mind will be able to rush forwards, and arrive at the end of the career, uniting principles to the purposes of things, and knowing that God is the principle, the middle and the end of all things made according to the rules of justice and right reason.
2. Physical and Mathematical Fragments
7. As Eudemus reports, Archytas used to ask this question: "If I was situated at the extreme and immovable limit of the world, could I, or could I not, extend a wand outside of it?" To say I could not, is absurd; but if I can, there must be something outside of the world, be it body or space; and in whatever manner we reason, by the same reasoning we will ever return to this limit. I will still place myself there, and ask, "Is there anything else on which I may place my wand?" Therefore, the Unlimited exists; if it is a body, our proposition is demonstrated; if it is space, place is that in which a body could be; and if it exists potentially, we will have to place it and classify it among the eternal things, and the Unlimited will then be a body and a place.
8. The essence of place is that all other things are in it, while itself is not in anything. For if it was in a place, there would be a place in a place, and that would continue to infinity. All other beings must therefore be in place, and place in nothing. Its relation to things is the same as Limit to limited things; for the place of the entire world is the Limit of all things.
9 A. Some say that time is the sphere of the world; such was the sentiment of the Pythagoreans, according to those who had heard Archytas give this general definition of time: "Time is the interval of the nature of all."
B. The divine Iamblichus, in the first book of his Commentaries on the Categories, said that Archytas thus defined time: "It is the number of movement, or in general the interval of the nature of all."
C. We must combine these two definitions, and recognize time as both continuous and discrete, though it is properly continuous. Iamblichus claims that Archytas taught the distinction of physical time, and psychic time. So at least Iamblichus interpreted Archytas, but we must recognize that there, and often elsewhere, he adds his own commentaries to explain matters.
10. The general proper essence of "when-ness" and time is to be indivisible and unsubstantial. For, being indivisible, the present time has passed, while expressing it and thinking of it; nothing remains of it, and so becoming continuously the same it never subsists numerically, but only specifically. In fact. the actually present time and the future are not identical with former time. For the one has past, and is no more; the other one passes while being produced and thought. Thus the present is never but a bond; it perpetually becomes, changes, and perishes, but nevertheless it remains identical in its own kind.
In fact, every present is without parts, and indivisible; it is the term of past time, the beginning of time to come; just as in a broken line, the point where the break occurs becomes the beginning of a line, and the end of the other. Time is continuous, and not discrete as are number, speech and harmony.
In speech, the syllables are parts, and distinct parts; in harmony, they are the sounds; in number, the unities. The line, place and space are continuous; if they are divided, their parts form common sections. For the line divides into points, the surface into lines, the solid into surfaces. Therefore time is continuous. In fact there was no time when time was not; and there was no moment when the present was not. But the present has always been, it will always be, and will never fail; it changes perpetually, and becomes another according to the number, but remains the same according to kind. The line differs from the other continua, in that if you divide the line, place, and space, its parts will subsist; but in time, the past has perished, and the future will. That is why either time does absolutely not exist, or it hardly exists, and has but an insensible existence. For of its parts one, the past, is no more, and the future is not yet; how then could the present, without parts and indivisible, possess true reality?
11. Plato says that the movement is the great and small, the non-being, the unusual, and all that reduces to these; like Archytas, we had better say that it is a cause.
12. Why do all natural bodies take the spherical form? Is it, as said Archytas, because in the natural movement is the proportion of equality? For everything moves in proportion; and this proportion of equality is the only one which, when it occurs, produces circles and spheres, because it returns on itself.
13. He who knows must have learned from another, or have found his knowledge by himself. The science that you learn from another, is as you might say, exterior; what you find by yourself, belongs to ourselves individually. To find without seeking is something difficult and rare; to find what one is seeking is commodious and easy; to ignore, and seek what you ignore, is impossible (DK 3).
14. The Pythagorean opinion about sciences to me seems correct, and they seem to show an exact judgment about each of them. Having known how to form a just idea of the nature of a ball, they should have likewise seen the essential nature of the parts. They have left us certain and evident theories about arithmetic, geometry and spherics, also about music, for all these sciences seem to be kindred. In fact, the first two kinds of being are indistinguishable.
15. A. First they have seen that it was not possible that noise should exist unless there was a shock of one body against another; they said there is a shock when moving bodies meet and strike each other. The bodies moved in the air in an opposite direction and those that are moved with an unequal swiftness-in the same direction-the first, when overtaken, makes a noise, because struck. Many of these noises are not susceptible of being perceived by our organs; some because of the slightness of the shock, the others because of their too great distance from us, some even because of the very excess of their intensity, for noises too great do not enter into our ears, as we cannot introduce anything into jars with too narrow an opening when one pours in too much at a time.
Of the sounds that fall within the range of our senses, some -- those that come quickly from the bodies struck -- seem shrill; those that arrive slowly and feebly, seem of low pitch. In fact, when one agitates some object slowly and feebly, the shock produces a low pitch; if the waving is done quickly, and with energy, the sound is shrill. This is not the only proof of the fact, which we can prove when we speak or sing; when we wish to speak loud and high, we use a great force of breath. So also with something thrown; if you throw them hard, they go far; if you throw them without energy, they fall near, for the air yields more to bodies moved with much force, than to those thrown with little. This phenomenon is also reproduced in the sound of the voice, for the sounds produced by an energetic breath are shrill, while those produced by a feeble breath are weak and low in pitch. This same observation can be seen in the force of a signal given from any place: if you pronounce it loud, it can be heard far; if you pronounce the same signal low, we do not hear it even when near. So also in flutes, the breath emitted by the mouth and which presents itself to the holes nearest the mouthpiece, produces a shriller sound, because the impulsive force is greater; farther [down], they are of lower pitch. It is therefore evident that the swiftness of the movement produces shrillness, and slowness, lower pitch. The same thing is seen in the bull roarers which are spun in the Mysteries; those that move slowly produce a low pitch, while those that move quickly with force make a shrill noise. Let us yet adduce the reed: if you close the lower opening, and blow into it, it will produce a certain sound; and if you stop it in the center, or in the front, the sound will be shrill. For the same breath traversing a long space weakens, while traversing a shorter, it remains of the same power. After having developed this opinion that the movement of the voice is measured by intervals, he resumes his discussion, saying, that the shrill sounds are the result of a swifter movement, the lower sounds, of a slower movement. This is a fact which numerous experiments demonstrate clearly.
B. Eudoxus and Archytas believed that the reasons of the agreement of the sounds was in the numbers; they agree in thinking that these reasons consist in the movements, the shrill movement being quick, because the agitation of the air is continuous, and the vibration more rapid; the low pitch movement being slow, because it is calmer.
16. Explaining himself about the means; Archytas writes: In music there are three means: the first is the arithmetical mean, the second is the geometrical, the third is the subcontrary mean, which is called harmonic. The mean is arithmetical, when the three terms are in a relation of analogical excess, that is to say, when the difference between the first and second is the same as between second and third; in this proportion, the relation of the greater terms is smaller, and the relation of the smaller is greater. The geometric mean exists when the first term is to the second as the second is to the third; here the relation of the greater is identical with the relation of the smaller terms. The subcontrary mean, which we call harmonic, exists when the first term exceeds the second by a fraction of itself, identically with the fraction [of the third] by which the second exceeds the third; in this proportion the relation of the greater terms is greater, and that of the smaller, smaller.
3. Ethical Fragments
17. A. We must first know that the good man is not thereby necessarily happy, but that the happy man is necessarily good; for the happy man is he who deserves praise and congratulations; the good man deserves only praise.
We praise a man because of his virtue, we congratulate him because of his success. The good man is such because of the goods that proceed from virtue; the happy man is such because of the goods that come from fortune. From the good man you cannot take his virtue; sometimes the happy man loses his good fortune. The power of virtue depends on nobody; that of happiness, on the contrary, is dependent. Long diseases, the loss of our senses, cause to fade the flower of our happiness.
B. God differs from the good man in that God not only possesses a perfect virtue, purified from all mortal affection, but enjoys a virtue whose power is faultless and independent, as suits the majesty and magnificence of his works.
Man, on the contrary, not only possesses an inferior virtue, because of the mortal constitution of his nature, but even sometimes by the very abundance of his goods, now by the force of habit, by the vice of nature, or from other causes, he is incapable of attaining the perfection of the good.
C. The good man, in my opinion, is he who knows how to act properly in serious circumstances and occasions. He will therefore know how to support good and bad fortune; in a brilliant and glorious condition, he will show himself worthy of it, and if fortune happens to change, he will know how to accept properly his actual fate. In short, the good man is he who, in every occasion, and according to the circumstances, well plays his part, and knows how to fit to it not only himself, but also those who have confidence in him, and are associated with his fortunes.
D. Since amidst the goods, some are desirable for themselves, and not for anything else, and others are desirable for something else, and not for themselves, there must necessarily exist a third kind of goods, which are desirable both for themselves and for other things. Which are the goods naturally desirable for themselves, and not for anything else? Evidently they include happiness, for it is the end on account of which we seek everything else, while we seek it only for itself, and not in view of anything else. Secondly, which are the goods chosen for something else, and not for themselves? Evidently those that are useful, and which are the means of procuring the real goods, which thus become the causes of the goods desirable for themselves; for instance: the bodily fatigues, the exercises, the tests which procure health; reading, meditation, the studies which procure virtues, and the quality of honesty. Finally, which are those goods which are both desirable for themselves, and for something else? The virtues, and the habitual possession of virtues, the resolutions of the soul, the actions, and in short anything pertaining to the possession of the beautiful. That which is to be considered for itself, and not for anything else, that is the only good.
Now what we seek for itself and for something else is divided into three classes: the one whose object is the soul, the body, and external goods. The first contains the virtues of the soul; the second contains the advantages of the body; the third consists in friends, glory, honor and wealth. Likewise with the goods that are desirable only for something else: one part of them procures goods for the soul, the other which regards the body, procures goods for it; the external goods furnish wealth, glory, honor and friendship.
We can prove that it is the characteristic of virtue to be desirable for itself, as follows: in fact, if the naturally inferior goods, I mean those of the body, are by us sought for themselves, and if the soul is better than the body, it is evident that we like the goods of the soul for themselves, and not for the result that they might produce.
E. In human life there are three circumstances: prosperity, adversity, and intermediary comfort. Since the good man who possesses virtue and practices it, practices it in these three circumstances -- either in adversity, or prosperity, or comfort, since besides in adversity he is unhappy, in prosperity he is happy, and in comfort he is not happy -- it is evident that happiness is nothing else than the use of virtue in prosperity. I speak here of human happiness. Man is not only a soul, he is also a body. The living being is a composite of both, and man also; for if the body is an instrument of the soul, it is as much a part of the man as the soul. That is why, among the goods, some belong to the man, and others belong to his component parts. The good of man is happiness amidst its integral parts. The soul's goods are prudence, courage, justice, and temperance; the body's are beauty, health, good disposition of its members, and the perfect condition of its senses. The external goods -- wealth, glory, honor, nobility -- are naturally superfluous advantages of man, and are naturally subordinate to the superior goods.
The inferior goods serve as satellites to the superior goods. Friendship, glory, and wealth are the satellites of the body and soul. Health, strength and sense-perfection are satellites of the body. Prudence, courage, justice and temperance are the satellites of the reason of the soul. Reason is the satellite of God; he is omnipotent, the supreme master. It is for these goods that the others must exist; for the army obeys the general, the sailors heed the pilot, the world obeys God, the soul heeds reason, the happy life is contingent on prudence. For prudence is nothing more than the science of the happy life, or the science of the goods which belong to human nature.
F. To God belongs happiness and the happy life; man cannot possess but a grouping of science, virtue and prosperity forming a single body. I call wisdom the science of the Gods and geniuses, and term prudence the science of human things, the science of life. For science should be the name of virtues which rest upon reasons and demonstrations, and moral virtue, the excellent habit of the irrational part of the soul, which makes you give the name of certain qualities corresponding to our habits, namely the names of liberal, just and temperate people. And I call prosperity this affluence of goods which we receive without reason being their cause. Then since virtue and science depend on us, and prosperity does not depend thereon, since happiness consists in the contemplation and practice of good things, and since contemplation and action when they meet obstacles, lend us a necessary support, when they go by an easy road, they bring us distraction and happiness. Since after all it is prosperity that gives us these benefits, it is evident that happiness is nothing else than the use of virtue in prosperity.
G. Man's relations with prosperity resemble a healthy and vigorous human body; he also can stand heat and cold, can raise a great burden, and can easily bear many other miseries.
H. Since happiness is the use of virtue in prosperity, let us speak of virtue and prosperity, the former first. Some goods, such as virtue, are not subject to excess; for excess is impossible in virtue, for one can never be too decent a man. Indeed, virtue's measure is duty, and is the habit of duty in practical life. But prosperity is subject to excess and lack, which excesses produce certain evils, disturbing man from his usual mood, so as to oppose him to virtue; this is not only the case with prosperity, but other more numerous causes also produce this effect. You need not be surprised at seeing in the hall certain impudent artists, who neglect true art, misleading the ignorant by a false picture; but do you suppose that this race does not exist as regards virtue? On the contrary, the greater and more beautiful virtue is, the more do people feign to adorn themselves with it. There are indeed many things which dishonor the appearance of virtue: first are the deceivers who simulate it, others are the natural passions which accompany it, and sometimes twist the dispositions of the soul into a contrary direction. Others are the bad habits which the body has rooted in us, or which have been ingrained in us by youth, age, prosperity, adversity, or by a thousand other circumstances. Wherefore we must not at all be surprised at entirely wrong judgments, because the true nature of our soul has been falsified within us. Just as we see an artist who is excellent make errors in works we are examining -- or the general, the pilot or the painter and like may make errors without our detracting from their talent -- so we must not call unworthy him who has had a moment of weakness, nor among the worthy a man who has done no more than a single action; but in respect to the evil, we must consider chance, and for the good, error, and to make an equitable and just judgment, and not regard a single circumstance, or a single period of time, but the whole life.
Just as the body suffers from both excess and lack, but as nevertheless the excess and so-called superfluities naturally produce the greatest diseases, so the soul suffers from both prosperity and adversity when they arrive at wrong times, and yet the greatest evils come from so-called absolute prosperity -- which is absolute because like wine it intoxicates the reason of the worthy.
I. That is why it is not adversity but prosperity which is the hardest to stand properly. All men, when they are in adversity, at least the greater part of them, seem moderate and modest; but in good fortune, ambitious, vain and proud. For adversity is apt to moderate the soul, and concentrate it, while on the contrary prosperity excites it and puffs it up. That is why wretches are docile to advice, and prudent in conduct, while the happy are bold and venturesome.
J. Thus there is a measure and limit of prosperity that the worthy man should desire to have as auxiliary in the accomplishment of his actions, just as there is a measure in the size of the ship, and in the length of the tiller, which permits the experienced pilot to traverse an immense extent of sea, and to carry through a great voyage.
The result of excess of prosperity, even among worthy people, is that the soul loses leadership to prosperity; just as too bright a light dazzles the eyes so too great a prosperity dazzles the reason of the soul. Enough about prosperity.
18. I insist that virtue is sufficient to preclude unhappiness, that badness precludes happiness, if we know how properly to judge of the genuine condition of the soul in these two conditions. For the evil reason is necessarily always unhappy, whether in abundance -- which he does not know how properly to judge or use -- or in poverty, just as a blind man is always wondering whether he is in brilliant light, or in darkness. But the worthy man is not always happy, for happiness does not consist in the possession of virtue, but in its use, just as a man who sees does not see all the time will not see without light.
Life is as it were divided into two roads: the rougher one, followed by patient Ulysses, and the more agreeable one followed by Nestor. I mean that virtue desires the one, but can also follow the other. But nature cries aloud that happiness is life desirable in itself, whose state is assured, because one can realize one's purposes in it, so that if life is traversed by things one has not desired, one is not happy, without however being absolutely unhappy. Therefore be not so bold as to insist that the worthy man is exempt from sickness, and suffering; dare not to say that he does not know pain, for if the body is allow some causes of pain, the soul should also be allowed some. The griefs of the insane lack reason and measure, while those of the wise are contained within the measure which reason gives to everything. But this so advertised insensitivity to sorrow enervates the character of generosity of virtue, when it stands trials, great sorrows, when it is exposed to death, suffering, and poverty, for it is easy to support small sorrows. You must therefore practice metriopathy or sorrow -- standardization so as to avoid the insensitivity just as much as the over-sensibility of pain, and not in words to boast about our strength above the measure of our human nature.
19. We might define philosophy as the desire of knowing and understanding things in themselves, joined with practical virtue, inspired and realized by the love of science. The beginning of philosophy is the science of nature, the middle, practical life, and the end, science itself. It is fortunate to have been well born, to have received a good education, to have been accustomed to obey a just rule, and to have habits conformable to nature. One must also have been exercised in virtue, and have been educated by wise parents, governors and masters. It is fine to impose the rule of duty on oneself, to have no need of constraint, to be docile to those who give us good advice about life and science. For a fortunate disposition of nature, and a good education are often more powerful than lessons to bring us to the good; its only lack would be the efficacious light of reason, which science gives us. Two rival directions of life contend for mastery, these being practical and philosophical life. By far the most perfect life unites them both, and in each different path adapts itself to circumstances. We are born for rational activity, which we call practical. Practical reason leads us to politics; the theoretical reason, to the contemplation of the universality of things. Mind itself, which is universal, embraces these two powers necessary to happiness, which we define as the activity of virtue in prosperity; it is not exclusively either a practical life which would exclude science, nor a speculative life which would exclude the practical. Perfect reason inclines towards these two omnipotent principles for which man is born, the principles of society and science. For if these opposite principles seem mutually to interfere in their development, the political principles turning us away from speculation, and the speculative principles turning us from politics, to persuade us to live at rest, nevertheless nature, uniting the ends of these two movements, shows them fused; for virtues are not contradictory and mutually antipathetic. Indeed, no harmony is more constant than the harmony of virtues. If from his youth man has subjected himself to the principles of virtues, and to the divine law of the world harmony, he will lead an easy life; and if, by his own inclination, he inclines towards evil and has the luck of meeting better guides, he will, by rectifying his course, arrive at happiness, like passengers favored by chance, finishing a fortunate sea-passage -- thanks to the pilot -- and the fortunate passage of life is happiness. But if by himself he cannot know his real interests, and if he does not have the luck of meeting prudent directors, what benefit would it be if he did have immense treasures? For the fool, even if he had for himself all the other elements of luck, is eternally unhappy. And since, in everything, you must first consider the end -- for that is what is done by the pilots ever meditating over the harbor whither they are to land the ship, by the drivers who keep their eye on the goal of their trip, and by the archers and slingers who consider their objective, for it is the objective towards which all their efforts must tend-virtue must necessarily undertake an objective, which should become the art of living, and that is the name I give it in both directions it can take. For practical life this objective is improvement; for the philosophical life, the perfect good, which, in their human affairs the sages call happiness. Those who are in misery are not capable of judging of happiness according to exact ideas, and those who do not see it clearly would not know how to choose it. Those who consider that pleasure is the sovereign good are punished therefore by foolishness; those who above all seek the absence of pain, also receive their punishment. In summary: to define life-happiness as the enjoyment of the body, in an unreflective state of soul, is to expose oneself to all the whirlwinds of the tempest. Those who suppress moral beauty, by avoiding all discussion, all reflection about the matter, and seeking pleasure, absence of pain, simple and primitive physical enjoyments, and the irreflective inclinations of body and soul, are not more fortunate, for they commit a double fault by reducing the good of the soul and its superior functions to the level of that of the body, and in raising the good of the body to the high level due to the good of the soul. For an exact discernment of these goods, we should outline its proper part for the divine element, and for nature; yet some do not observe this relation of dignity from the better to the worse. But we do so when we say that if the body is the organ of the soul, then reason is the guide of the entire soul, the mistress of the body, this tent of the soul, and that all the other physical advantages should serve only as instruments to the intellectual activity, if you wish it to be perfect in power, duration and wealth.
20. These are the most important conditions to become a sage: first, you must have received from fate a mind endowed with facility to understand, memory, and industry. You must then from youth on exercise your intelligence by the practice of argumentation, by mathematical studies, and by the exact sciences. Then you must study healthful philosophy, after which you may undertake the knowledge of the Gods, of laws, and of human life. For there are two means of arriving at this state known as wisdom. The first is to acquire the habit of work that is intellectual, and the taste for knowledge; the other is to seek to see many things, to undertake business frequently, and to know them, either directly at first hand, or indirectly. For he who from youth on has exercised reason by dialectic reasonings, mathematical studies, and exact sciences, is not yet ready for wisdom, any more than he who has neglected these labors, and has only listened to others, and has immersed himself in business. The one has become blind, when the business is to judge particular facts; the other, when he is to judge of general deductions. Just as in calculations you obtain the total by combining the parts, so also, in business practice, reason can vaguely sketch the general formula, but experience alone can enable us to grasp the details and individual facts.
21. Age is in the same relation to youth. Youth makes men energetic, age makes them prudent. Never by imprudence does it let a thought escape. It reflects on what it has done, it considers maturely what it ought to do, in order that this comparison of the future with the present, and of the present with the future lead it to good conduct. To the past it applies memory, to the present, sensation, and to the future, foresight; for our memory has always as object the past, foresight the future, and sensation the present. He who therefore wishes to lead an honest and beautiful life must not only have senses and memory, but foresight.
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Re: The Pythagorean Sourcebook and Library
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PART 2 OF 2
4. Political Fragments
22 A. The laws of the wicked and atheists are opposed by the unwritten laws of the Gods, who inflict evils and terrible punishments on the disobedient. It is these divine laws which have developed and directed the laws and written maxims given to men.
B. The relation of law to the soul and human life is identical to that of harmony to the sense of hearing, and the voice; for the law instructs the soul, and thereby, the life, as harmony regulates the voice through education of the ear. In my opinion, every society is composed of the commander, the commanded, and the laws. Among the latter, one is living, namely the king, and the other is inanimate, this being the written letter. The law is therefore the most essential; only through it is the king legitimate, the magistrate regularly instituted, the commanded free, and the whole community happy. When it is violated, the king is no more than a tyrant, the magistrate is illegitimate, the commanded becomes a slave, and the whole community becomes unhappy. Human acts are like a mingled tissue, formed of command, duty, obedience, and force sufficient to overcome resistance. Essentially, the command belongs to the better, being commanded to the inferior, and force belongs to both. For the reasonable part of the soul commands, and the irrational part is commanded. Both have the force to conquer the passions. Virtue is born from the harmonious cooperation of both and leads the soul to rest and indifference by turning it away from pleasures and sorrows.
C. Law must conform to nature, and exercise an efficient power over things, and be useful to the social community; for if it lacks one, two, or all of these characteristics, it is no longer a law, or at least it is no longer a perfect law. It conforms to nature if it is the image of natural right, which fits itself, and distributes to each according to his deserts. It prevails if it harmonizes with the men who are to be subject thereto; for there are many people who are not apt to receive what by nature is the first of goods, and who are fitted to practice only the good which is in relation with them, and possible for them, for that is how the sick and the suffering have to be nursed. Law is useful to the political society if it is not monarchical, if it does not constitute privileged classes, if it is made in the interest of all, and is equally imposed on all. Law must also regard the country and the lands, for not all soils can yield the same returns, neither all human souls the same virtues. That is why some establish the aristocratic constitution, While others prefer the democratic or oligarchic. The aristocratic constitution is founded on the subcontrary proportion, [2] and is the most just, for this proportion attributes the greatest results to the greatest terms, and the smallest to the smallest. The democratic constitution is founded on the geometrical proportion, in which the results of the great and small are equal [in ratio]. The oligarchic and tyrannic constitutions are founded on the arithmetical proportion, which, being the opposite of the subcontrary, attributes to the smallest terms the greatest results, and vice versa.
Such are the kinds of proportions, and you can observe their image in families and political constitutions; for either the honors, punishments and virtues are equally attributed to the great and small, or they are so attributed unequally, according to superiority, in virtue, wealth or power. Equal distribution is the characteristic of democracy; and the unequal, that of aristocracy and oligarchy.
D. The best law and constitution must be a composite of all other constitutions, and contain something democratic, oligarchic, monarchic and aristocratic, as in Lacedaemon; for in it the kings formed the monarchic element, the elders the aristocracy, the magistrates the oligarchy, while the cavalry generals and the youths formed the democracy. Law must therefore not only be beautiful and good, but its different parts must mutually compensate. This will give it power and durability, and by this mutual opposition I mean that the same magistracy command and be commanded, as in the wise laws of Lacedaemon. For the power of its kings is balanced by the magistrates, this by the elders, and between these two powers are the cavalry generals and the youths, who, as soon as they see anyone party acquire the preponderance, throw themselves on the other side.
The law's first duty is to decide about the Gods, the geniuses, the parents -- in short, on all that is estimable and worthy -- and later decide about utility. It is proper that the secondary regulations should follow the best, and that the laws be inscribed, not on the houses and doors, but in the depths of the souls of the citizens. Even in Lacedaemon, which has excellent laws, the State is not administered by manifold written ordinances. Law is useful to the political community, if it is not monarchical, and does not serve private interests, if it is useful to all, if it extends its obligation to all, and if it aims its punishments to shame the guilty, and to brand him with infamy, rather than to deprive him of his wealth. If, indeed, you are seeking to punish the guilty by ignominy, the citizens will try to lead a wiser and more honest life, so as to avoid the law's punishment; if it is only by money fines, they will rate above everything wealth, understanding that it is their best means to repair their faults. The best would be that the State should be organized in a manner such that it would need nothing from strangers, neither for virtue, power, or anything else. In the same way the right constitution of a body, a house, or an army is to contain, and not to depend on outside sources for the principle of its safety; for in that way the body is more vigorous, the house better ordered, and the anny will be neither mercenary nor badly drilled.
Beings that are thus organized are superior to others; they are free and liberated from servitude unless, for their conservation, they need many things, but have only few needs easily satisfied. In that way the vigorous man becomes able to bear heavy burdens, and the athlete, to resist cold, for men are exercised by events and misfortunes. The temperate man, who has tested his body and soul, finds any food, drink, even a bed of leaves, delectable. He who has preferred to live like a Sybarite among delights, would finally scorn and reject the magnificence of the great [Persian] king. Law must therefore deeply penetrate into the souls and habits of the citizens; it will make them satisfied with their fate, and distribute to each his deserts. Thus the sun, in traversing the zodiac, distributes to everything on the earth growth, food, life, in the proper measure, and institutes this wise legislation which regulates the succession of the seasons. That is why we call Zeus nomios, law-giver, from Nomeios, and we call nomeus he who distributes their food to the sheep; that is why we call the verses sung by the lyre players nomoi, [3] for these verses impart order to the soul because they are sung according to the laws of harmony, rhythm, and measure.
23. The true chief must not only possess the science and power of commanding well, but he must also love men; for it is absurd that a shepherd should hate his flock, and feel hostile towards those he is educating. Besides, he must be legitimate; only thus can he sustain a chiefs dignity. His science will permit him to discern well, his power to punish, his kindness to be beneficent, and the law to do everything according to reason. The best chief would be he who would closest approach the law, for he would never act in his own interest, and always in that of others, since the law does not exist for itself, but for its subjects.
24. See 21 A.
25. When the art of reflection was discovered, dissension diminished and concord increased; those who possess it feel the pride of predominance yielding to the sentiment of equality. It is by reflection that we succeed in adjusting our affairs in a friendly fashion; through it the poor receive riches, and the rich give to the poor, each possessing the confidence that he possesses the equality of rights.
26. Reflection is like a rule which hinders and turns aside the people who know how to reflect from committing injustices, for it convinces them that they cannot remain hidden if they carry out their purposes, and the punishment which has overtaken those who have not known how to abstain makes them reflect and not become back-sliders.
5. Logical Fragments
27. Logic, compared with the other sciences, is by far the most successful and succeeds in demonstrating its objectives even better than geometry. Where geometric demonstration fails, logic succeeds; and logic deals not only with general classes, but also with their exceptions.
28. In my opinion it is a complete error to insist that about every subject there are two contrary opinions which are equally true. To begin with, I consider it impossible that, if both opinions are true, they should contradict each other, and that beauty should contradict beauty, and whiteness whiteness. It cannot be so, for beauty and ugliness, whiteness and blackness are contraries. Likewise, the true is contrary to the false, and you cannot produce two contrary opinions either true or false; the one must be true, at the expense of the falseness of the other. For instance, he who praises the soul of man and accuses his body is not speaking of the same object, unless you claim that speaking exclusively of the heaven you are speaking exclusively of the earth. Why no -- they are not one, but two propositions. What am I trying to demonstrate? That he who says that the Athenians are skillful and witty and he who says they are not grateful, are not supporting contradictory propositions, for contradictories are opposed to each other on the same points, and here the two points are different.
29. Archytas' Ten Universal Categories. First, all kinds of arts deal with five things: the matter, the instrument, the part, the definition, the end. The first notion, the substance, is something self-existent and self-subsistent. It needs nothing else for its essence, though it is subject to growth if it happens to be something that is born, for only the divine is uncreated, and veritably self-subsistent. The other notions are considered in relation to substance when the latter by opposition to them is termed self- subsisting, but such is not the case in relation to the divine. The nine notions appear and disappear without implying the ruin of the subject, the substrate, and that is what is called the universal accident. For the same subject does not lose its identity by being increased or diminished in quantity. Thus, excessive feeding creates excessive size and stoutness; sobriety and abstinence make men lean, but it is always the same body, the same substrate. Thus also human beings passing from childhood to youth remain the same substance, differing only in quantity. Without changing essence, the identical object may become white or black, changing only as regards quality. Again, without changing essence, the identical man may change disposition and relation, as he is friend or enemy, but being today in Thebes, and tomorrow in Athens changes nothing in his substantial nature. Without changing essence, we remain the same today that we were yesterday; the change affected only time. The man standing is the same as the man sitting; he has changed only in situation. Being armed or unarmed is a difference only of possession; the striker and the cutter are the same man in essence, though not in action. He who is cut or struck -- which belongs to the category of suffering -- still retains his essence.
The differences of the other categories are clearer. Those of quality, possession, and suffering present some difficulties in the differences, for we hesitate about the question of knowing if having fever, shivering or rejoicing belong to the category of quality, possession or suffering. We must distinguish: if we say it is fever, it is shivering, it is joy, it is quality; if we say he has fever, he shivers, he rejoices, it is possession. Possession again differs from suffering, in that the latter can be conceived without the agent. Suffering is a relation to the agent, and is understood only by him who produces it. If we say he is cut, he is beaten, we express the patient; if we say he suffers, we express possession.
We say that Archytas has ten, and no more universal notions, of which we may convince ourselves by the following division: the being is in a subject [a substance], or is not in a subject. That which is not in a subject, forms the substance. That which is in a subject is conceived by itself, or is not conceived by itself. That which is not conceived by itself constitutes relation, for relative beings, which are not conceived by themselves, but which forcibly import the idea of another being, are what is called scheseis, conditions; thus the term son is associated with the term father, that of slave, master. Thus all relative beings are conceived in a necessary bond together with something else, and not by themselves. The self-conceivable being is either divisible -- when it is quantity -- or indivisible, when it constitutes quality. The six other notions are produced by combination of the former. Substance mingled with quantity, if seen in space, constitutes the category of where; if seen in time, constitutes that of when. Mingled with quality, substance is either active, and forms the category of action, or when passive, forms that of suffering or passivity. Combined with relation, it is either posited in another, and that is what is called situation, or it is attributed to somebody else, and then it is possession.
As to the order of the categories, quantity follows substance and precedes quality because, by a natural law, everything that receives quality also receives mass, and that it is only by means of something so determinate that quality can be so affirmed and expressed. Again, quality precedes relation, because the former is self-sufficient, and the latter [subsists] through a relation; we first have to conceive and express something by itself before in a relation.
After these universal categories follow the others. Action precedes passivity, because its force is greater; the category of situation precedes that of possession, because being situated is something simpler than being possessed, and you cannot conceive something attributed to another, without conceiving the former as situated somewhere. That which is situated is also in a position, such as standing, seated, or lying. The characteristic of substance is more-or-lessness; for we say that a man is no more of an animal than a horse, by substance, and do not admit the contraries. The characteristic of quality is to admit more or less; for we say, more or less white, or black. The characteristic of quantity is to admit equality or inequality; for a square foot is not equal to an acre, and 144 square inches equals a square foot; five is not equal to ten, and twice five is equal to ten. The characteristic of relation is to join contraries; for if there is a father, there is a son, and if there is a master, there is a slave. The characteristic of whereness is to include, and of whenness not to remain, of situation to be located, and of possession to be attributed. The composite of substance and quantity is anterior to the composite of quality; the composite of substance and quality in its turn precedes that of substance and relation. Whereness precedes whenness because whereness presupposes the place that is fixed and permanent; whenness relates to time, and time, ever in movement, has no fixity, and rest is anterior to movement. Action is anterior to passivity, and situation to possession.
A. Category of Substance. Substance is divided into corporeal and incorporeal; the corporeal may be divided into bodies animate and inanimate. Animated bodies are divisible into those endowed with sensation, and without sensation. Sense-bodies can be divided into animals and zoophytes, which do not further divide into opposite distinctions. The animal is divided into rational and irrational; the rational is divisible into mortal and immortal; the mortal can be divided into differences of genus, such as man, ox, horse, and the rest. The species are divided into individuals who have no abiding value. Each of the sections that we obtained above by opposite divisions is susceptible of being in turn divided equally, until we arrive at the indivisible individuals who are of no value.
B. Category of Quantity. This is divided into seven parts: the line, surface, the body, the place, the time, the number, and language. Quantity is either continuous or discrete: of continuous quantities there are five; of the discrete, number and language. In quantity, you may distinguish that which is composed of parts having position relative to each other, such as line, surface, body, and space; and of those whose parts have no position, such as number, language, and time. For although time is a continuous quantity, nevertheless its parts have no position because it is not permanent, and that which has no permanence could not have any position. Quantity has produced four sciences: immovable continuous quantity, geometry; movable continuous quantity, astronomy; immovable discrete quantity, arithmetic; and the movable discrete, music.
C. Category of Quality. This is divided into hexis, or habit, and diathesis, or affection, passive quality and passivity, power and impotence, figure and form. Habit is affection in a state of energetic tension. It is the permanence and fixity derived from continuity and the energy of affection; it is affection become [second] nature, a second enriched nature. Another explanation of habit is the qualities given us by nature, and which are derived neither from affection, nor from the natural progress of the being; as sight and the other senses; both passive quality and passivity are increase, intensity, and weakening. To both of these are attributed anger, hate, intemperance, the other vicious passions, the affections of sickness, heat and cold; but these are classified at will under habit and affection, or under passive quality and passivity. You might say that so far as affection is communicable it might be called habit; so far as it causes a passion, it might be called a passive quality, which refers both to its permanence and fixity. For a modification contained in the measure is called passion. Thus from the one to whom it is communicated, heat may be called a habit. From the cause which produces the modification, we may say that it is either the passive quality, or the power of the passion; as when we say of a child that he is potentially a runner or a philosopher, and, in short, when at a given moment the being does not have the power to act, but it is possible that after the lapse of a certain period of time this power may belong to him. Impotence is when nature refuses itself to the possibility of accomplishing certain actions, as when the man is impotent to fly, the horse to speak, the eagle to live in water, and all the natural impossibilities.
Figure is a conformation of a determined character. Form is the quality showing itself exteriorly by color, or beauty or ugliness showing itself on the surface by color, and in short any form that is apparent, determinate, and striking. Some limit figure to inanimate things reserving form to living beings. Some say that the word figure gives the idea of the dimension of depth, and that the word form is applied only to the superficial appearance; but you have been taught all of that.
D. Category of Relation. Generally the relatives are divided into four classes: nature, art, chance and will. The relation of father to son is natural; that of master to disciple, that of art; that of master to slave, that of chance; and that of friend to friend, and enemy to enemy, that of will, although you might say that these are all natural relations.
E. Category of Whereness. The simplest division is into six: up, down, forwards, backwards, right and left. Each of these subdivisions contains varieties. There are many differences in upness: in the air, in the stars, to the pole, or beyond the pole, and such differences are repeated below. The infinitely divided spaces themselves are further subject to an infinity of differences, but this very ambiguous point will be explained later.
F. Category of Whenness. This is divided into present, past and future. The present is indivisible, the past is divided into nine subdivisions, the future into five. We have already spoken of them.
G. Category of Action. This is divided into action, discourse and thought. Action is in work of the hands, with tools, and with the feet, and each of these divisions is subdivided into technical divisions which also have their parts. Language is divided into Greek or barbarian, and each of these divisions has its varieties, namely, its dialects. Thought is divided into an infinite world of thoughts, whose objects are the world, other people, and the hypercosmic. Language and thought really belong to action, for they are acts of the reasonable nature; in fact, if we are asked, "What is Mr. X doing?" we answer that he is chatting, conversing, thinking, reflecting, and so on.
H. Category of Passivity. Passivity is divided into suffering of the soul and of the body. Each of these is subdivided into passions which result from actions of somebody else, as for instance, when somebody is struck, and passions which arise without the active intervention of someone else which occur in a thousand different forms.
I. Category of Situation. This is divided into three: standing, sitting, and lying, and each of these is subdivided by differences of location. We may stand on our feet, or on the tips of our fingers, with the leg unflexed, or the knee bent. Further differences are equal or unequal steps or walking on one or two feet. Being seated has the same differences: one may be straight, bent, reversed; the knees may form an acute or obtuse angle; the feet may be placed over each other, or in some other way. Likewise with lying down prone or head forwards, or to the side, the body extended, in a circle, or angularly. Far from uniform are these divisions; they are quite various. Position is also subject to other divisions: for instance, an object may be spread out like corn, sand, oil, and like all the other solids that are susceptible to position, and like all the liquids that we know. Nevertheless, being extended belongs to position, as with cloth and nets.
J. Category of Possession. "Having" signifies things that we put on, such as shoes, arms, coverings; things which are put on others, such as a basket, a bottle, and other vases, for we say that the basket has oats, that the bottle has wine. The same is true also of wealth and estates; we say, he has a fortune, fields, cattle, and other similar things.
30. The order of the categories is the following: in the first rank is substance, because it alone serves as substrate to all the others. We can conceive it alone, and by itself, but the others cannot be conceived without it, for all attributes' subjects reside therein, or are affirmed thereof. The second is quality, for it is impossible for a thing to have a quality without an essence.
31. Every naturally physical and sensible substance must, to be conceived by man, be either classified within the categories, or be determined by them, and cannot be conceived without them.
32. Substance has three differences: the one consists in matter, the other in form, and the third in the mixture of both.
33. These notions, these categories, have characteristics that are common and individual. I say that they are characteristics common to substance, not to receive more-or-lessness; for it is not possible to be more or less man, God, or plant. The characteristics have no contraries, for man is not the contrary of man, neither God of a God; neither is it contrary to other substances, to exist by oneself, and not to be in another, as green or blue color is the characteristic of the eye, since all substance depends on itself. All the things that belong to it intimately, or the accidents in it, cannot exist without it; quality is suited by several characteristics of substance, for example, not to be subject to more-or-lessness.
34. It is the property to remain self-identical, one in number, and to be susceptible of the contraries. Waking is the contrary of sleep; slowness is contrary to swiftness, sickness to health, and the same man is susceptible of all these differences. For he awakes, sleeps, moves slowly or quickly, is well or sick, and in short is able to receive all similar contraries, so long as they be not simultaneous.
35. Quantity has three differences: one consists in weight, like bullion; the other in size, as the yard; the other in multitude, as ten.
36. Including its accidents, substance is necessarily primary; that is how they [the categories] are in relation to something else. After the substance come the relations of accidental qualities.
37. A common property which must be added to quality is to admit certain contraries and privation. The relation is subject to more-or-lessness. For though a being remains ever the same, to be greater or smaller than anything else is moreness. But all the relations are not susceptible thereto, for you cannot be more or less father, brother, or son. I do not mean to express the sentiments of both parents, nor the degree of tenderness held mutually by beings of the same blood, and the sons of the same parents; I only mean the tenderness which is in the nature of these relations.
38. Quality has certain common characteristics: for example, of receiving the contraries and privation, which more or less affect the passions. That is why the passions are marked by the characteristics of indetermination, because they are in a greater or less indeterminate measure.
39. Relation is susceptible to conversion, and this conversion is founded either on resemblance, as the equal, and the brother, or on lack of resemblance, the large and the small. There are relatives which are not converted, for instance, science and sensation; for we may speak of the science of the intelligible, and of the sensation of the sensible, and the reason is that the intelligible and the sensible can exist independently of science and sensation while science and sensation cannot exist without the intelligible and the sensible [...] The characteristic of relatives is to exist simultaneously in each other, for if we grant the existence of doubleness, the half must necessarily exist; and if the half exists necessarily must the double exist, as it is the cause of the half, as the half is the cause of the double.
40. Since every moved thing moves in a place, since action and passivity are actualized movements, it is clear that there must be a primary space in which exist the acting and the passive objects.
41. The characteristic of the agent is to contain the cause of the motion, while the characteristic of the thing done, which is passive, is to have it in some other. For the sculptor contains the cause of the making of the statue, the bronze possesses the cause of the modification it undergoes, both in itself and in the sculptor. So also with the passions of the soul, for it is in the nature of anger to be aroused as the result of something else -- that it be excited by some other external thing, as for example by scorn, dishonor, and outrage -- and he who acts thus towards another, contains the cause of his action.
42. The highest degree of the action is the act which contains three differences: it may be accomplished in the contemplation of the stars, or in doing, such as healing or constructing, or in action, as in commanding an army, or administering the affairs of state. An act may occur even without reasoning, as in irrational animals. Those are the most general contraries.
43. Passion differs from the passive state, for passion is accompanied by sensation, like anger, pleasure and fear, while one can undergo something without sensation, such as the wax that melts, or the mud that dries. Then also the deed done differs also from the passive state, for the deed done has undergone a certain action, while everything that has undergone a certain action is not a deed done; for a thing may be in a passive state as a result of lack or privation.
44. On one side there is the agent, on the other the patient; for example, in nature, God is the being who acts, matter the being which undergoes, and the elements are neither the one nor the other.
45. The characteristic of possession is to be something adventitious, something corporeal, separated from essence. Thus a veil or shoes are distinct from the possessor; they are not natural characteristics, nor essential accidents, like the blue color of the eyes, and rarefaction. The latter are two incorporeal characteristics while possession relates to something corporeal and adventitious.
46. Since the signs and the things signified have a purpose, and because man uses these signs and signified things is to fulfill the perfect function of speech, let us finish what we have said by proving that the harmonious grouping of all these categories does not belong to man in general, but to a certain definite individual. Necessarily it must be a definite man existing somewhere who possesses quality, quantity, relation, action, passivity, location and possession, who is in a place and time. The man in himself receives only the first of these expressions, I mean essence and form. But he has no quality, no age, he is not old, neither does he suffer anything, he has no location, he possesses nothing, he exists neither in place nor time. All those are only accidents of the physical and corporeal being, but not of the intelligible, immovable, and indivisible being.
47. Among contraries, some are said to be mutually opposed by convention and nature, as good to evil, the sick to the well man, truth to error; the others, as possession is opposed to privation, such as life and death, sight and blindness, science and ignorance; others as relatives, as the double and the half, the commander and the commanded, the master and the slave; others, like affirmation and negation, as being man and not a man, being honest and not.
48. The relatives arise and disappear necessarily simultaneously; the existence of the double is impossible without implying that of the half and vice versa. If something becomes double, the half must arise, and if the double is destroyed, the half passes away with it.
49. Of the relatives, some respond to each other in two senses, as the greater, the smaller, the brother, the relative. Others again respond, but not in the two senses, for we say equally, the science of the intelligible, and the science of the sensible, but we do not say the reciprocal, the intelligible of science, and the sensible of sensation. The reason is that the object of judgment can exist independently of him who judges, for instance, the sensible can exist without sensation, and the intelligible without science, while it is not possible that the subject which bears a judgment exists without the object which he judges. For example, there can be no sensation without sensible object, nor science without intelligible object. Relatives which respond reciprocally are of two kinds: these are those that respond indifferently, as the relative, the brother, the equal, for they are mutually similar and equal. Some respond reciprocally, but not indifferently, for this one is greater than that one, and that one is smaller than this one, and this one is the father of that one, and that one the son of this one.
50. These opposites divide into kinds which band together; for of the contraries some are without a middle term and the others have one. There is no middle term between sickness and health, rest and movement, waking and sleep, straightness and curvedness, and other such contraries. But between the much and the little, there is a just medium; between the shrill and the low, there is the unison; between the rapid and slow, there is the equality of movement; between the greatest and the smallest, the equality of measure. Of universal contraries there must be one that belongs to what receives them, for they do not admit any medium term. Thus there is no medium term between health and sickness, for every living being is necessarily sick or well; neither between waking and sleeping, for every living being is either awake or asleep; nor between rest and movement, for every human being is either at rest or moving. [Concerning the opposites of which neither belong to the subject which may receive them,] between black and white there is the fawn, and it is not necessary that an animal be black or white. Between the great and the small there is the equal, and it is not necessary that a living being be either great or small; between the rough and soft there is the gentle, and it is not necessary that a living being be either rough or soft. In the opposites there are three differences: some are opposed, as the good is to evil, for instance, or health to sickness; the others, like evil to evil, as for instance, avarice to lechery; the others, as being neither the one or the other, for instance, as white is opposed to black, and the heavy to the light. Of the opposites, some occur in genus or genera, for the good is opposed to evil, and the good is the genus of virtues, and evil that of the evils. Other occur in the genera of species; virtue is the opposite of vice, and virtue is the genus of prudence and temperance, and vice is the genus of foolishness and debauch. Others occur in the species: courage is opposed to cowardliness, justice to injustice, and justice and excellence are species of virtue, injustice and debauch species of vice. The primary genera, which we call genera of genera, can be divided; the last species, which are the immediate nearest to the object, that is sensible, could no longer be genera, and are only species. For the triangle is the genus of the rectangle, of the equilateral and of the scalene [...] the species of good [...]
51. The opposites differ from each other in that for some -- the contraries -- it is not necessary that they arise at the same time, and disappear simultaneously. For health is the contrary of sickness, and rest that of movement; nevertheless neither of them arises or perishes at the same time as its opposite. Possession and privation of production differ in this, that it is in the nature of contraries that one passes from one to the other, for instance, from sickness to health and vice versa. It is not so with possession and privation; you do indeed pass from possession to privation, but the privation does not return to possession: the living die, but the dead never return to life. In short, possession is the persistence of what is according to nature, while privation is its lack and decay. Relatives necessarily arise and disappear simultaneously; for it is impossible for the double to exist without half, or vice versa. If some double happens to arise, it is impossible that the half should not arise, or if some double be destroyed, that the half be not destroyed. Affirmation and negation are forms of proposition, and they eminently express the true and the false. Being a man is a true proposition, if the thing exists, and false if it does not exist. You could say as much of negation: it is true or false according to the thing expressed.
Moreover, between good and evil there is a medium which is neither good nor evil; between much and little, the just measure; between the slow and the fast, the equality of speed; between possession and privation there is no medium. For there is nothing between life and death, and sight and blindness, unless indeed you say that the living who is not yet born, but who is being born, is between life and death, and that the puppy who does not yet see is between blindness and sight. In such an expression we are using an accidental medium and not one according to the true and proper definition of contraries.
Relatives have middle terms, for between the master and the slave there is the free man, and between the greatest and the smallest there is equality; between the wide and the narrow there is the proper width. One might likewise find between the other contraries a medium, whether or not it has a name.
Between affirmation [and negation] there are no contraries, for instance, between being a man and not being a man, being a musician and not being a musician. In short, we have to affirm or deny. Affirming is showing of something that it is a man, for instance, or a horse, or an attribute of these beings, as of the man that he is a musician, and of the horse that he is warlike. We call it denying when we show of something that it is not something, not man, not horse, or that it lacks an attribute of these beings, for instance, that the man is not a musician and that the horse is not warlike; and between this affirmation and this negation there is nothing.
52. Privation and being deprived is taken in three senses: one does not at all have the thing, as the blind man does not have sight, the mute does not have voice, and the ignorant does not have science; or that one does not have it but partially, as the man hard of hearing has hearing, and that the man with sore eyes has sight; or one can say that partially he does not have it, as one says that a man whose legs are [so] crooked that he has no legs, and of a man who has [such] a bad voice that he has no voice.
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Notes:
1. See Heath, A History of Greek Mathematics, vol. 1. 246-49.
2. I.e., the harmonic mean.
2. Nomoi, in addition to meaning "laws," is also the term used for the various modes of Greek music. Each Greek mode or "scale" was associated with a distinctive style of playing and affect.
4. Political Fragments
22 A. The laws of the wicked and atheists are opposed by the unwritten laws of the Gods, who inflict evils and terrible punishments on the disobedient. It is these divine laws which have developed and directed the laws and written maxims given to men.
B. The relation of law to the soul and human life is identical to that of harmony to the sense of hearing, and the voice; for the law instructs the soul, and thereby, the life, as harmony regulates the voice through education of the ear. In my opinion, every society is composed of the commander, the commanded, and the laws. Among the latter, one is living, namely the king, and the other is inanimate, this being the written letter. The law is therefore the most essential; only through it is the king legitimate, the magistrate regularly instituted, the commanded free, and the whole community happy. When it is violated, the king is no more than a tyrant, the magistrate is illegitimate, the commanded becomes a slave, and the whole community becomes unhappy. Human acts are like a mingled tissue, formed of command, duty, obedience, and force sufficient to overcome resistance. Essentially, the command belongs to the better, being commanded to the inferior, and force belongs to both. For the reasonable part of the soul commands, and the irrational part is commanded. Both have the force to conquer the passions. Virtue is born from the harmonious cooperation of both and leads the soul to rest and indifference by turning it away from pleasures and sorrows.
C. Law must conform to nature, and exercise an efficient power over things, and be useful to the social community; for if it lacks one, two, or all of these characteristics, it is no longer a law, or at least it is no longer a perfect law. It conforms to nature if it is the image of natural right, which fits itself, and distributes to each according to his deserts. It prevails if it harmonizes with the men who are to be subject thereto; for there are many people who are not apt to receive what by nature is the first of goods, and who are fitted to practice only the good which is in relation with them, and possible for them, for that is how the sick and the suffering have to be nursed. Law is useful to the political society if it is not monarchical, if it does not constitute privileged classes, if it is made in the interest of all, and is equally imposed on all. Law must also regard the country and the lands, for not all soils can yield the same returns, neither all human souls the same virtues. That is why some establish the aristocratic constitution, While others prefer the democratic or oligarchic. The aristocratic constitution is founded on the subcontrary proportion, [2] and is the most just, for this proportion attributes the greatest results to the greatest terms, and the smallest to the smallest. The democratic constitution is founded on the geometrical proportion, in which the results of the great and small are equal [in ratio]. The oligarchic and tyrannic constitutions are founded on the arithmetical proportion, which, being the opposite of the subcontrary, attributes to the smallest terms the greatest results, and vice versa.
Such are the kinds of proportions, and you can observe their image in families and political constitutions; for either the honors, punishments and virtues are equally attributed to the great and small, or they are so attributed unequally, according to superiority, in virtue, wealth or power. Equal distribution is the characteristic of democracy; and the unequal, that of aristocracy and oligarchy.
D. The best law and constitution must be a composite of all other constitutions, and contain something democratic, oligarchic, monarchic and aristocratic, as in Lacedaemon; for in it the kings formed the monarchic element, the elders the aristocracy, the magistrates the oligarchy, while the cavalry generals and the youths formed the democracy. Law must therefore not only be beautiful and good, but its different parts must mutually compensate. This will give it power and durability, and by this mutual opposition I mean that the same magistracy command and be commanded, as in the wise laws of Lacedaemon. For the power of its kings is balanced by the magistrates, this by the elders, and between these two powers are the cavalry generals and the youths, who, as soon as they see anyone party acquire the preponderance, throw themselves on the other side.
The law's first duty is to decide about the Gods, the geniuses, the parents -- in short, on all that is estimable and worthy -- and later decide about utility. It is proper that the secondary regulations should follow the best, and that the laws be inscribed, not on the houses and doors, but in the depths of the souls of the citizens. Even in Lacedaemon, which has excellent laws, the State is not administered by manifold written ordinances. Law is useful to the political community, if it is not monarchical, and does not serve private interests, if it is useful to all, if it extends its obligation to all, and if it aims its punishments to shame the guilty, and to brand him with infamy, rather than to deprive him of his wealth. If, indeed, you are seeking to punish the guilty by ignominy, the citizens will try to lead a wiser and more honest life, so as to avoid the law's punishment; if it is only by money fines, they will rate above everything wealth, understanding that it is their best means to repair their faults. The best would be that the State should be organized in a manner such that it would need nothing from strangers, neither for virtue, power, or anything else. In the same way the right constitution of a body, a house, or an army is to contain, and not to depend on outside sources for the principle of its safety; for in that way the body is more vigorous, the house better ordered, and the anny will be neither mercenary nor badly drilled.
Beings that are thus organized are superior to others; they are free and liberated from servitude unless, for their conservation, they need many things, but have only few needs easily satisfied. In that way the vigorous man becomes able to bear heavy burdens, and the athlete, to resist cold, for men are exercised by events and misfortunes. The temperate man, who has tested his body and soul, finds any food, drink, even a bed of leaves, delectable. He who has preferred to live like a Sybarite among delights, would finally scorn and reject the magnificence of the great [Persian] king. Law must therefore deeply penetrate into the souls and habits of the citizens; it will make them satisfied with their fate, and distribute to each his deserts. Thus the sun, in traversing the zodiac, distributes to everything on the earth growth, food, life, in the proper measure, and institutes this wise legislation which regulates the succession of the seasons. That is why we call Zeus nomios, law-giver, from Nomeios, and we call nomeus he who distributes their food to the sheep; that is why we call the verses sung by the lyre players nomoi, [3] for these verses impart order to the soul because they are sung according to the laws of harmony, rhythm, and measure.
23. The true chief must not only possess the science and power of commanding well, but he must also love men; for it is absurd that a shepherd should hate his flock, and feel hostile towards those he is educating. Besides, he must be legitimate; only thus can he sustain a chiefs dignity. His science will permit him to discern well, his power to punish, his kindness to be beneficent, and the law to do everything according to reason. The best chief would be he who would closest approach the law, for he would never act in his own interest, and always in that of others, since the law does not exist for itself, but for its subjects.
24. See 21 A.
25. When the art of reflection was discovered, dissension diminished and concord increased; those who possess it feel the pride of predominance yielding to the sentiment of equality. It is by reflection that we succeed in adjusting our affairs in a friendly fashion; through it the poor receive riches, and the rich give to the poor, each possessing the confidence that he possesses the equality of rights.
26. Reflection is like a rule which hinders and turns aside the people who know how to reflect from committing injustices, for it convinces them that they cannot remain hidden if they carry out their purposes, and the punishment which has overtaken those who have not known how to abstain makes them reflect and not become back-sliders.
5. Logical Fragments
27. Logic, compared with the other sciences, is by far the most successful and succeeds in demonstrating its objectives even better than geometry. Where geometric demonstration fails, logic succeeds; and logic deals not only with general classes, but also with their exceptions.
28. In my opinion it is a complete error to insist that about every subject there are two contrary opinions which are equally true. To begin with, I consider it impossible that, if both opinions are true, they should contradict each other, and that beauty should contradict beauty, and whiteness whiteness. It cannot be so, for beauty and ugliness, whiteness and blackness are contraries. Likewise, the true is contrary to the false, and you cannot produce two contrary opinions either true or false; the one must be true, at the expense of the falseness of the other. For instance, he who praises the soul of man and accuses his body is not speaking of the same object, unless you claim that speaking exclusively of the heaven you are speaking exclusively of the earth. Why no -- they are not one, but two propositions. What am I trying to demonstrate? That he who says that the Athenians are skillful and witty and he who says they are not grateful, are not supporting contradictory propositions, for contradictories are opposed to each other on the same points, and here the two points are different.
29. Archytas' Ten Universal Categories. First, all kinds of arts deal with five things: the matter, the instrument, the part, the definition, the end. The first notion, the substance, is something self-existent and self-subsistent. It needs nothing else for its essence, though it is subject to growth if it happens to be something that is born, for only the divine is uncreated, and veritably self-subsistent. The other notions are considered in relation to substance when the latter by opposition to them is termed self- subsisting, but such is not the case in relation to the divine. The nine notions appear and disappear without implying the ruin of the subject, the substrate, and that is what is called the universal accident. For the same subject does not lose its identity by being increased or diminished in quantity. Thus, excessive feeding creates excessive size and stoutness; sobriety and abstinence make men lean, but it is always the same body, the same substrate. Thus also human beings passing from childhood to youth remain the same substance, differing only in quantity. Without changing essence, the identical object may become white or black, changing only as regards quality. Again, without changing essence, the identical man may change disposition and relation, as he is friend or enemy, but being today in Thebes, and tomorrow in Athens changes nothing in his substantial nature. Without changing essence, we remain the same today that we were yesterday; the change affected only time. The man standing is the same as the man sitting; he has changed only in situation. Being armed or unarmed is a difference only of possession; the striker and the cutter are the same man in essence, though not in action. He who is cut or struck -- which belongs to the category of suffering -- still retains his essence.
The differences of the other categories are clearer. Those of quality, possession, and suffering present some difficulties in the differences, for we hesitate about the question of knowing if having fever, shivering or rejoicing belong to the category of quality, possession or suffering. We must distinguish: if we say it is fever, it is shivering, it is joy, it is quality; if we say he has fever, he shivers, he rejoices, it is possession. Possession again differs from suffering, in that the latter can be conceived without the agent. Suffering is a relation to the agent, and is understood only by him who produces it. If we say he is cut, he is beaten, we express the patient; if we say he suffers, we express possession.
We say that Archytas has ten, and no more universal notions, of which we may convince ourselves by the following division: the being is in a subject [a substance], or is not in a subject. That which is not in a subject, forms the substance. That which is in a subject is conceived by itself, or is not conceived by itself. That which is not conceived by itself constitutes relation, for relative beings, which are not conceived by themselves, but which forcibly import the idea of another being, are what is called scheseis, conditions; thus the term son is associated with the term father, that of slave, master. Thus all relative beings are conceived in a necessary bond together with something else, and not by themselves. The self-conceivable being is either divisible -- when it is quantity -- or indivisible, when it constitutes quality. The six other notions are produced by combination of the former. Substance mingled with quantity, if seen in space, constitutes the category of where; if seen in time, constitutes that of when. Mingled with quality, substance is either active, and forms the category of action, or when passive, forms that of suffering or passivity. Combined with relation, it is either posited in another, and that is what is called situation, or it is attributed to somebody else, and then it is possession.
As to the order of the categories, quantity follows substance and precedes quality because, by a natural law, everything that receives quality also receives mass, and that it is only by means of something so determinate that quality can be so affirmed and expressed. Again, quality precedes relation, because the former is self-sufficient, and the latter [subsists] through a relation; we first have to conceive and express something by itself before in a relation.
After these universal categories follow the others. Action precedes passivity, because its force is greater; the category of situation precedes that of possession, because being situated is something simpler than being possessed, and you cannot conceive something attributed to another, without conceiving the former as situated somewhere. That which is situated is also in a position, such as standing, seated, or lying. The characteristic of substance is more-or-lessness; for we say that a man is no more of an animal than a horse, by substance, and do not admit the contraries. The characteristic of quality is to admit more or less; for we say, more or less white, or black. The characteristic of quantity is to admit equality or inequality; for a square foot is not equal to an acre, and 144 square inches equals a square foot; five is not equal to ten, and twice five is equal to ten. The characteristic of relation is to join contraries; for if there is a father, there is a son, and if there is a master, there is a slave. The characteristic of whereness is to include, and of whenness not to remain, of situation to be located, and of possession to be attributed. The composite of substance and quantity is anterior to the composite of quality; the composite of substance and quality in its turn precedes that of substance and relation. Whereness precedes whenness because whereness presupposes the place that is fixed and permanent; whenness relates to time, and time, ever in movement, has no fixity, and rest is anterior to movement. Action is anterior to passivity, and situation to possession.
A. Category of Substance. Substance is divided into corporeal and incorporeal; the corporeal may be divided into bodies animate and inanimate. Animated bodies are divisible into those endowed with sensation, and without sensation. Sense-bodies can be divided into animals and zoophytes, which do not further divide into opposite distinctions. The animal is divided into rational and irrational; the rational is divisible into mortal and immortal; the mortal can be divided into differences of genus, such as man, ox, horse, and the rest. The species are divided into individuals who have no abiding value. Each of the sections that we obtained above by opposite divisions is susceptible of being in turn divided equally, until we arrive at the indivisible individuals who are of no value.
B. Category of Quantity. This is divided into seven parts: the line, surface, the body, the place, the time, the number, and language. Quantity is either continuous or discrete: of continuous quantities there are five; of the discrete, number and language. In quantity, you may distinguish that which is composed of parts having position relative to each other, such as line, surface, body, and space; and of those whose parts have no position, such as number, language, and time. For although time is a continuous quantity, nevertheless its parts have no position because it is not permanent, and that which has no permanence could not have any position. Quantity has produced four sciences: immovable continuous quantity, geometry; movable continuous quantity, astronomy; immovable discrete quantity, arithmetic; and the movable discrete, music.
C. Category of Quality. This is divided into hexis, or habit, and diathesis, or affection, passive quality and passivity, power and impotence, figure and form. Habit is affection in a state of energetic tension. It is the permanence and fixity derived from continuity and the energy of affection; it is affection become [second] nature, a second enriched nature. Another explanation of habit is the qualities given us by nature, and which are derived neither from affection, nor from the natural progress of the being; as sight and the other senses; both passive quality and passivity are increase, intensity, and weakening. To both of these are attributed anger, hate, intemperance, the other vicious passions, the affections of sickness, heat and cold; but these are classified at will under habit and affection, or under passive quality and passivity. You might say that so far as affection is communicable it might be called habit; so far as it causes a passion, it might be called a passive quality, which refers both to its permanence and fixity. For a modification contained in the measure is called passion. Thus from the one to whom it is communicated, heat may be called a habit. From the cause which produces the modification, we may say that it is either the passive quality, or the power of the passion; as when we say of a child that he is potentially a runner or a philosopher, and, in short, when at a given moment the being does not have the power to act, but it is possible that after the lapse of a certain period of time this power may belong to him. Impotence is when nature refuses itself to the possibility of accomplishing certain actions, as when the man is impotent to fly, the horse to speak, the eagle to live in water, and all the natural impossibilities.
Figure is a conformation of a determined character. Form is the quality showing itself exteriorly by color, or beauty or ugliness showing itself on the surface by color, and in short any form that is apparent, determinate, and striking. Some limit figure to inanimate things reserving form to living beings. Some say that the word figure gives the idea of the dimension of depth, and that the word form is applied only to the superficial appearance; but you have been taught all of that.
D. Category of Relation. Generally the relatives are divided into four classes: nature, art, chance and will. The relation of father to son is natural; that of master to disciple, that of art; that of master to slave, that of chance; and that of friend to friend, and enemy to enemy, that of will, although you might say that these are all natural relations.
E. Category of Whereness. The simplest division is into six: up, down, forwards, backwards, right and left. Each of these subdivisions contains varieties. There are many differences in upness: in the air, in the stars, to the pole, or beyond the pole, and such differences are repeated below. The infinitely divided spaces themselves are further subject to an infinity of differences, but this very ambiguous point will be explained later.
F. Category of Whenness. This is divided into present, past and future. The present is indivisible, the past is divided into nine subdivisions, the future into five. We have already spoken of them.
G. Category of Action. This is divided into action, discourse and thought. Action is in work of the hands, with tools, and with the feet, and each of these divisions is subdivided into technical divisions which also have their parts. Language is divided into Greek or barbarian, and each of these divisions has its varieties, namely, its dialects. Thought is divided into an infinite world of thoughts, whose objects are the world, other people, and the hypercosmic. Language and thought really belong to action, for they are acts of the reasonable nature; in fact, if we are asked, "What is Mr. X doing?" we answer that he is chatting, conversing, thinking, reflecting, and so on.
H. Category of Passivity. Passivity is divided into suffering of the soul and of the body. Each of these is subdivided into passions which result from actions of somebody else, as for instance, when somebody is struck, and passions which arise without the active intervention of someone else which occur in a thousand different forms.
I. Category of Situation. This is divided into three: standing, sitting, and lying, and each of these is subdivided by differences of location. We may stand on our feet, or on the tips of our fingers, with the leg unflexed, or the knee bent. Further differences are equal or unequal steps or walking on one or two feet. Being seated has the same differences: one may be straight, bent, reversed; the knees may form an acute or obtuse angle; the feet may be placed over each other, or in some other way. Likewise with lying down prone or head forwards, or to the side, the body extended, in a circle, or angularly. Far from uniform are these divisions; they are quite various. Position is also subject to other divisions: for instance, an object may be spread out like corn, sand, oil, and like all the other solids that are susceptible to position, and like all the liquids that we know. Nevertheless, being extended belongs to position, as with cloth and nets.
J. Category of Possession. "Having" signifies things that we put on, such as shoes, arms, coverings; things which are put on others, such as a basket, a bottle, and other vases, for we say that the basket has oats, that the bottle has wine. The same is true also of wealth and estates; we say, he has a fortune, fields, cattle, and other similar things.
30. The order of the categories is the following: in the first rank is substance, because it alone serves as substrate to all the others. We can conceive it alone, and by itself, but the others cannot be conceived without it, for all attributes' subjects reside therein, or are affirmed thereof. The second is quality, for it is impossible for a thing to have a quality without an essence.
31. Every naturally physical and sensible substance must, to be conceived by man, be either classified within the categories, or be determined by them, and cannot be conceived without them.
32. Substance has three differences: the one consists in matter, the other in form, and the third in the mixture of both.
33. These notions, these categories, have characteristics that are common and individual. I say that they are characteristics common to substance, not to receive more-or-lessness; for it is not possible to be more or less man, God, or plant. The characteristics have no contraries, for man is not the contrary of man, neither God of a God; neither is it contrary to other substances, to exist by oneself, and not to be in another, as green or blue color is the characteristic of the eye, since all substance depends on itself. All the things that belong to it intimately, or the accidents in it, cannot exist without it; quality is suited by several characteristics of substance, for example, not to be subject to more-or-lessness.
34. It is the property to remain self-identical, one in number, and to be susceptible of the contraries. Waking is the contrary of sleep; slowness is contrary to swiftness, sickness to health, and the same man is susceptible of all these differences. For he awakes, sleeps, moves slowly or quickly, is well or sick, and in short is able to receive all similar contraries, so long as they be not simultaneous.
35. Quantity has three differences: one consists in weight, like bullion; the other in size, as the yard; the other in multitude, as ten.
36. Including its accidents, substance is necessarily primary; that is how they [the categories] are in relation to something else. After the substance come the relations of accidental qualities.
37. A common property which must be added to quality is to admit certain contraries and privation. The relation is subject to more-or-lessness. For though a being remains ever the same, to be greater or smaller than anything else is moreness. But all the relations are not susceptible thereto, for you cannot be more or less father, brother, or son. I do not mean to express the sentiments of both parents, nor the degree of tenderness held mutually by beings of the same blood, and the sons of the same parents; I only mean the tenderness which is in the nature of these relations.
38. Quality has certain common characteristics: for example, of receiving the contraries and privation, which more or less affect the passions. That is why the passions are marked by the characteristics of indetermination, because they are in a greater or less indeterminate measure.
39. Relation is susceptible to conversion, and this conversion is founded either on resemblance, as the equal, and the brother, or on lack of resemblance, the large and the small. There are relatives which are not converted, for instance, science and sensation; for we may speak of the science of the intelligible, and of the sensation of the sensible, and the reason is that the intelligible and the sensible can exist independently of science and sensation while science and sensation cannot exist without the intelligible and the sensible [...] The characteristic of relatives is to exist simultaneously in each other, for if we grant the existence of doubleness, the half must necessarily exist; and if the half exists necessarily must the double exist, as it is the cause of the half, as the half is the cause of the double.
40. Since every moved thing moves in a place, since action and passivity are actualized movements, it is clear that there must be a primary space in which exist the acting and the passive objects.
41. The characteristic of the agent is to contain the cause of the motion, while the characteristic of the thing done, which is passive, is to have it in some other. For the sculptor contains the cause of the making of the statue, the bronze possesses the cause of the modification it undergoes, both in itself and in the sculptor. So also with the passions of the soul, for it is in the nature of anger to be aroused as the result of something else -- that it be excited by some other external thing, as for example by scorn, dishonor, and outrage -- and he who acts thus towards another, contains the cause of his action.
42. The highest degree of the action is the act which contains three differences: it may be accomplished in the contemplation of the stars, or in doing, such as healing or constructing, or in action, as in commanding an army, or administering the affairs of state. An act may occur even without reasoning, as in irrational animals. Those are the most general contraries.
43. Passion differs from the passive state, for passion is accompanied by sensation, like anger, pleasure and fear, while one can undergo something without sensation, such as the wax that melts, or the mud that dries. Then also the deed done differs also from the passive state, for the deed done has undergone a certain action, while everything that has undergone a certain action is not a deed done; for a thing may be in a passive state as a result of lack or privation.
44. On one side there is the agent, on the other the patient; for example, in nature, God is the being who acts, matter the being which undergoes, and the elements are neither the one nor the other.
45. The characteristic of possession is to be something adventitious, something corporeal, separated from essence. Thus a veil or shoes are distinct from the possessor; they are not natural characteristics, nor essential accidents, like the blue color of the eyes, and rarefaction. The latter are two incorporeal characteristics while possession relates to something corporeal and adventitious.
46. Since the signs and the things signified have a purpose, and because man uses these signs and signified things is to fulfill the perfect function of speech, let us finish what we have said by proving that the harmonious grouping of all these categories does not belong to man in general, but to a certain definite individual. Necessarily it must be a definite man existing somewhere who possesses quality, quantity, relation, action, passivity, location and possession, who is in a place and time. The man in himself receives only the first of these expressions, I mean essence and form. But he has no quality, no age, he is not old, neither does he suffer anything, he has no location, he possesses nothing, he exists neither in place nor time. All those are only accidents of the physical and corporeal being, but not of the intelligible, immovable, and indivisible being.
47. Among contraries, some are said to be mutually opposed by convention and nature, as good to evil, the sick to the well man, truth to error; the others, as possession is opposed to privation, such as life and death, sight and blindness, science and ignorance; others as relatives, as the double and the half, the commander and the commanded, the master and the slave; others, like affirmation and negation, as being man and not a man, being honest and not.
48. The relatives arise and disappear necessarily simultaneously; the existence of the double is impossible without implying that of the half and vice versa. If something becomes double, the half must arise, and if the double is destroyed, the half passes away with it.
49. Of the relatives, some respond to each other in two senses, as the greater, the smaller, the brother, the relative. Others again respond, but not in the two senses, for we say equally, the science of the intelligible, and the science of the sensible, but we do not say the reciprocal, the intelligible of science, and the sensible of sensation. The reason is that the object of judgment can exist independently of him who judges, for instance, the sensible can exist without sensation, and the intelligible without science, while it is not possible that the subject which bears a judgment exists without the object which he judges. For example, there can be no sensation without sensible object, nor science without intelligible object. Relatives which respond reciprocally are of two kinds: these are those that respond indifferently, as the relative, the brother, the equal, for they are mutually similar and equal. Some respond reciprocally, but not indifferently, for this one is greater than that one, and that one is smaller than this one, and this one is the father of that one, and that one the son of this one.
50. These opposites divide into kinds which band together; for of the contraries some are without a middle term and the others have one. There is no middle term between sickness and health, rest and movement, waking and sleep, straightness and curvedness, and other such contraries. But between the much and the little, there is a just medium; between the shrill and the low, there is the unison; between the rapid and slow, there is the equality of movement; between the greatest and the smallest, the equality of measure. Of universal contraries there must be one that belongs to what receives them, for they do not admit any medium term. Thus there is no medium term between health and sickness, for every living being is necessarily sick or well; neither between waking and sleeping, for every living being is either awake or asleep; nor between rest and movement, for every human being is either at rest or moving. [Concerning the opposites of which neither belong to the subject which may receive them,] between black and white there is the fawn, and it is not necessary that an animal be black or white. Between the great and the small there is the equal, and it is not necessary that a living being be either great or small; between the rough and soft there is the gentle, and it is not necessary that a living being be either rough or soft. In the opposites there are three differences: some are opposed, as the good is to evil, for instance, or health to sickness; the others, like evil to evil, as for instance, avarice to lechery; the others, as being neither the one or the other, for instance, as white is opposed to black, and the heavy to the light. Of the opposites, some occur in genus or genera, for the good is opposed to evil, and the good is the genus of virtues, and evil that of the evils. Other occur in the genera of species; virtue is the opposite of vice, and virtue is the genus of prudence and temperance, and vice is the genus of foolishness and debauch. Others occur in the species: courage is opposed to cowardliness, justice to injustice, and justice and excellence are species of virtue, injustice and debauch species of vice. The primary genera, which we call genera of genera, can be divided; the last species, which are the immediate nearest to the object, that is sensible, could no longer be genera, and are only species. For the triangle is the genus of the rectangle, of the equilateral and of the scalene [...] the species of good [...]
51. The opposites differ from each other in that for some -- the contraries -- it is not necessary that they arise at the same time, and disappear simultaneously. For health is the contrary of sickness, and rest that of movement; nevertheless neither of them arises or perishes at the same time as its opposite. Possession and privation of production differ in this, that it is in the nature of contraries that one passes from one to the other, for instance, from sickness to health and vice versa. It is not so with possession and privation; you do indeed pass from possession to privation, but the privation does not return to possession: the living die, but the dead never return to life. In short, possession is the persistence of what is according to nature, while privation is its lack and decay. Relatives necessarily arise and disappear simultaneously; for it is impossible for the double to exist without half, or vice versa. If some double happens to arise, it is impossible that the half should not arise, or if some double be destroyed, that the half be not destroyed. Affirmation and negation are forms of proposition, and they eminently express the true and the false. Being a man is a true proposition, if the thing exists, and false if it does not exist. You could say as much of negation: it is true or false according to the thing expressed.
Moreover, between good and evil there is a medium which is neither good nor evil; between much and little, the just measure; between the slow and the fast, the equality of speed; between possession and privation there is no medium. For there is nothing between life and death, and sight and blindness, unless indeed you say that the living who is not yet born, but who is being born, is between life and death, and that the puppy who does not yet see is between blindness and sight. In such an expression we are using an accidental medium and not one according to the true and proper definition of contraries.
Relatives have middle terms, for between the master and the slave there is the free man, and between the greatest and the smallest there is equality; between the wide and the narrow there is the proper width. One might likewise find between the other contraries a medium, whether or not it has a name.
Between affirmation [and negation] there are no contraries, for instance, between being a man and not being a man, being a musician and not being a musician. In short, we have to affirm or deny. Affirming is showing of something that it is a man, for instance, or a horse, or an attribute of these beings, as of the man that he is a musician, and of the horse that he is warlike. We call it denying when we show of something that it is not something, not man, not horse, or that it lacks an attribute of these beings, for instance, that the man is not a musician and that the horse is not warlike; and between this affirmation and this negation there is nothing.
52. Privation and being deprived is taken in three senses: one does not at all have the thing, as the blind man does not have sight, the mute does not have voice, and the ignorant does not have science; or that one does not have it but partially, as the man hard of hearing has hearing, and that the man with sore eyes has sight; or one can say that partially he does not have it, as one says that a man whose legs are [so] crooked that he has no legs, and of a man who has [such] a bad voice that he has no voice.
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Notes:
1. See Heath, A History of Greek Mathematics, vol. 1. 246-49.
2. I.e., the harmonic mean.
2. Nomoi, in addition to meaning "laws," is also the term used for the various modes of Greek music. Each Greek mode or "scale" was associated with a distinctive style of playing and affect.
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Re: The Pythagorean Sourcebook and Library
by admin » Wed Nov 13, 2013 4:32 am
COCELLUS LUCANUS:
ON THE NATURE OF THE UNIVERSE
OCELLUS LUCANUS was an early Pythagorean as were other members of his family. This writing seems to be post-Aristotelian. As Holger Thesleff observes in his Introduction to the Pythagorean Writings of the Hellenistic Period, the work seems to be influenced by Peripatetic conceptions and demonstrations concerning the nature of generation and destruction; and the ending. on the generation of good offspring. may derive from Aristoxenus.
ON THE NATURE OF THE UNIVERSE
1. On the Eternity and Indestructibility of the Universe
OCELLUS LUCANUS HAS WRITTEN what follows concerning the nature of the universe, having learnt some things through clear arguments from Nature herself, but others from opinion in conjunction with reason, it being his intention [here] to derive what is probable from intellectual perception.
Therefore it appears to me that the universe is indestructible and unbegotten, since it always was and always will be; for if it had a temporal beginning, it would not always have existed. Thus therefore the universe is unbegotten and indestructible. For if some one should claim that it was once generated, he would not be able to find anything into which it can be corrupted and dissolved, since that from which it was generated would be the first part of the universe; and again, that into which it would be dissolved would be the last part of it.
But if the universe was generated, it was generated together with all things; and if it should be corrupted, it would be corrupted together with all things. This however is impossible. This universe is therefore without a beginning, and without an end; nor is it possible that it can have any other mode of subsistence.
It may be added that everything which has received a beginning of generation, and which ought also to participate in dissolution, receives two mutations. The first, indeed, proceeds from the less to the greater, and from the worse to the better; and that from which it begins to change is denominated generation, but that which at length it arrives is called climax. The other mutation, however, proceeds from the great to the less, and from the better to the worse; but the end of this mutation is called corruption and dissolution.
If therefore the whole and the universe were generated, and are corruptible, they must, when generated, have been changed from the less to the greater, and from the worse to the better; but when corrupted, they must be changed from the greater to the less, and from the better to the worse. Hence, if the world was generated, it would receive increase, and would arrive at its consummation; and again, it would afterwards decrease and end. For every thing which has a progression possesses three boundaries and two intervals: the three boundaries are generation, consummation and end, and the intervals are progression from generation to consummation, and from consummation to end.
The whole, however, and the universe affords as from itself no indication of anything of this kind; for neither do we perceive it rising into existence, or becoming to be, nor changing to the better and the greater, nor changing to worse or less, but it always continues to subsist in the identical manner, and perpetually remains self-identical.
Clear signs and indications of this are the orders of things, their symmetry, figurations, positions, intervals, powers, swiftness and slowness in respect to each other; and besides these, their numbers and temporal periods are clear signs and indications. For all such things as these change and diminish conformably to the course of generation; for things that are greater and better tend towards consummation through power, but those that are less and worse decay through the inherent weakness of nature.
The whole world is what I call the whole universe; for this word "cosmos" was given it as a result of its being adorned with all things. From itself it is a consummate and perfect system of all things, for there is nothing external to the universe, since whatever exists is contained in the universe, and the universe subsists together with this, comprehending in itself all things, both parts and superfluities.
The things contained in the world are naturally congruous with it; but the world harmonizes with nothing else, symphonizing with itself. Other things do not possess self-subsistence, but require adjustment with their environment. Thus animals require conjunction with air for the purpose of respiration, and with light in order to see, and similarly the other senses with other environments to function satisfactorily. A conjunction with earth is necessary for the germination of plants. The sun, moon, planets and fixed stars likewise integrate with the world, as part of its general arrangement. The world, however, has no conjunction with anything outside of itself.
The above is supported by the following. Fire which imparts heat to others is self-hot; honey which is sweet to the taste is self-sweet. The principles of demonstrations, which conclude to things unapparent, are self-evident. Therefore the cause of the perfection of other things is itself perfect. That which preserves and renders permanent other things must itself be preserved and permanent. What harmonizes must itself be self-harmonic. Now as the world is the cause of the existence, preservation and perfection of other things, the world must itself be perpetual and perfect; and because its duration is everlasting, it becomes the cause of the permanence of all other things.
In short, if the universe should be dissolved, it would be dissolved either into the existent or non-existent. It could not be dissolved into existence, for in this case the dissolution would not be a corruption, as being either the universe or some part of it. Nor can it be dissolved into non-entity, since being cannot possibly arise from non-being, or be dissolved into non-entity. Therefore the universe is incorruptible and never can be destroyed.
If, however, somebody should think that it can be corrupted, it must be corrupted either from something external to or contained in the universe; but it cannot be corrupted by anything external to it, for nothing such exists, since all other things are comprehended in the universe, and the world is the whole and the all. Nor can it be corrupted by the things it contains, which would imply their greater power. This however is impossible, for all things are led and governed by the universe, and thereby are preserved and adjusted, possessing life and soul. But if the universe can neither be corrupted by anything external to it, nor by anything contained within it, the world must therefore be incorruptible and indestructible, for we consider the world identical with the universe.
Further, the whole of nature surveyed through its own totality, will be found to derive continuity from the first and most honorable bodies, proportionally attenuating this continuity, introducing it to everything mortal, and receiving the progression of its peculiar subsistence; for the first (and most honorable) bodies in the universe revolve according to the Same, [1] and similarly. The progression of the whole of nature, however, is not successive and continuous, nor yet local, but is subject to mutation.
When condensed, fire generates air, air water, and water earth. A return circuit of transformation extends backward from earth to fire, whence it originated. Likewise, fruits and most rooted plants, originate from seeds. When however they fruit and mature, they are again resolved into seed, nature producing a complete circular progression.
In a subordinate manner men and other animals change the universal boundary of nature, for in these there is no periodical return to the first age; nor is there a transfusion, such as between fire and air, and water and earth, but the mutations of their ages being accomplished in a four-cycled circle, they are dissolved and reformed.
These therefore are the signs and indications that the universe which comprehends [all things) will always endure and be preserved, but that its parts and its nonessential additions are corrupted and dissolved.
Further, it is credible that the universe is without a beginning, and without end, from its figure, motion, time and essence; and therefore it may be concluded that the world is unbegotten and incorruptible, for its figure is circular, and as a circular figure is similar and equal on all sides, it is therefore without a beginning or end. Circular is also the motion of the universe, but this motion is stable and without transition. Time, likewise, in which motion exists, is infinite, for neither had this a beginning, nor will it have an end of its revolution. The universe's essence also does not waste elsewhere, and is immutable, because it is not naturally adapted to change, either from worse to better, or from better to worse. From all these arguments, therefore, it is obviously credible that the world is unbegotten and incorruptible. So much about the world and the universe.
2. Creation of the Elements
SINCE, HOWEVER, IN THE UNIVERSE there is a difference between generation and the generated, and since generation occurs where there is a mutation and egress from things which rank as subjects, then must the cause of generation subsist as long as the generated matter. The cause of generation must be both efficient and motive, while the recipient must be passive and moved.
The Fates themselves distinguish and separate the impassive part of the world from that which is perpetually in motion. For the course of the moon is the meeting-line of generation and immortality. The region above the moon, as well as the lunar domain, is the residence of divinities, while the sublunar regions are the abodes of strife and nature, for in this place there is a mutation of things that are generated and a regeneration of things which have perished.
In that part of the world, however, in which nature and generation predominate, it is necessary that the three following things be present. In the first place, there is the body which yields to the touch, and which is the subject of all generated natures. But this will be an universal recipient, and a characteristic of generation itself, having the same relation to the things that are generated from it, as water to taste, silence to sound, darkness to light, and the matter of artificial forms to the forms themselves. For water is tasteless and devoid of quality, yet is capable of receiving the sweet and the bitter, the tart and the salty. Air also, which is formless as regards sound, is the recipient of words and melody. Darkness, which is without color, and without form, becomes the recipient of splendor, and of the yellow color, and the white; but white pertains to the statuary's art and to the wax-sculptor's art. Matter's relation, however, is different from the sculptor's art, for in matter, prior to generation, all things exist in potential, but they exist in perfection when they are generated, and receive their proper nature. Hence matter [or universal recipient] is necessary to the existence of generation.
The second necessity is the existence of contrarieties, in order to effect mutations and changes in quality, matter for this purpose receiving passive qualities and an aptitude to the participations of form. Contrariety is also necessary in order that powers which are naturally mutually repugnant may not finally conquer or vanquish each other. These powers are hot and cold, dryness and moistness.
In the third place rank essences, and these are fire and water, air and earth, of which heat and cold, dryness and moistness, are powers. Yet essences differ from powers, for essences are locally corrupted by each power, but powers are neither corrupted nor generated, as their reasons [or forms] are incorporeal.
Of these four powers, however, heat and cold subsist as causes and things of an effective nature, but the dry and the moist rank as matter and things that are passive, though matter is the first recipient of things, for it is that which is spread under all things in common. Hence the body, whose capacity is the object of sense, and ranks as a principle, is the first thing; while contraries, such as heat and cold, moistness and dryness, rank as primary differences, and heaviness and lightness, density and rarity, are related as things produced from primary differences. All of them, however, amount to sixteen: heat and cold, moistness and dryness, heaviness and lightness, rarity and density, smoothness and roughness, hardness and softness, thinness and thickness, acuteness and obtuseness. Knowledge of all of these is had by touch, which forms a judgement; hence also any body whatever which contains capacity for these can be apprehended by touch.
Heat and dryness, rarity and sharpness are the powers of fire; coldness and moistness, density and obtuseness are those of water; those of air are softness, smoothness, light, and the quality of being attenuated; while those of earth are hardness and roughness, heaviness and thickness.
Of these four bodies, however, fire and earth are the intensities of contraries. Fire is the intensity of heat, as ice is of cold; and if ice is a concretion of moisture and frigidity, fire will be the fervor of dryness and heat. That is why neither fire nor ice generate anything.
Fire and earth, therefore, are the extremities of the elements, while water and air are the media, for they have a mixed corporeal nature. Nor is it possible that there could be only one of the extremes, a contrary thereto being necessary. Nor could there only be two, for it is necessary to have a medium, as media oppose extremes.
Fire therefore is hot and dry, but air is hot and moist; water is moist and cold, and earth is cold and dry. Hence heat is common to air and fire; cold is common to water and earth; dryness to earth and fire, and moisture to water and air. But with respect to the peculiarities of each, heat is the peculiarity of fire, dryness of earth, moisture of air, and frigidity of water. These essences remain permanent, through the possession of common properties, but they change through such as are peculiar, when one contrary overcomes another.
Hence, when the moisture in air overcomes the dryness in fire, or when water's frigidity overcomes air's heat, and earth's dryness overcomes water's moistness, and vice versa, then are effected the mutual mutations and generations of the elements.
The body, however, which is the subject and recipient of mutations, is a universal receptacle, and is in capacity the first tangible substance.
But the mutations of the elements are effected either from a change of earth into fire, or from fire into air, or from air into water, or from water into earth. Mutation is also effected in the third place, when each element's contrariness is corrupted, simultaneously with the preservation of everything kindred and coeval. Generation therefore is effected when one contrary quality is corrupted. For fire, indeed, is hot and dry, but air is hot and moist, and heat is common to both; and the peculiarity of fire is dryness, and of air, moisture. Hence when the moisture in air overcomes the dryness in fire, then fire is changed into air.
Again, since water is moist and cold, but air is moist and hot, moisture is common to both. Water's peculiarity is coldness, and that of air, heat. When therefore the coldness in water overcomes the heat in air, air is altered into water.
Further, earth is cold and dry, and water cold and moist, coldness being common to both. But earth's peculiarity is dryness, and water's moisture. When therefore earth's dryness overcome water's moisture, water is altered into earth.
Earth's mutation in the ascending alteration occurs in a contrary way. One alternate mutation is effected when one whole vanquishes another, and two contrary powers are corrupted, nothing being common to them, at the same time. For since fire is hot and dry, while water is cold and moist, when the moisture in water overcomes the dryness in fire, and water's coldness overcomes fire's heat, then fire is altered into water.
Again, earth is cold and dry, while air is hot and moist. When therefore earth's coldness overcomes air's heat, and earth's dryness overcomes air's moisture, then air is altered into earth.
When air's moisture corrupts fire's heat, then from both of them will be generated fire; for air's heat, and fire's dryness will remain, fire being hot and dry.
When earth's coldness is corrupted, and also water's moisture, then from both of them will be generated earth. For earth's dryness and water's coldness will be left, as earth is cold and dry.
But when air's heat and fire's heat are corrupted, no element will be generated; for in both of these will remain contraries, air's moisture and fire's dryness. Moisture is however contrary to dryness.
Again, when earth's coldness, and that of water are corrupted, neither thus will any generation occur, for earth's dryness, and water's moisture will remain. But dryness is contrary to moisture.
Thus we have briefly discussed the generation of the first bodies, and how and from what subjects it is effected.
Since, however, the world is indestructible and unbegotten, and neither had a beginning of generation, nor will have an end, it is necessary that the nature which produces generation in another thing, and also that which generates in itself, should be simultaneously present. That which produces generation in another thing is the whole superlunary region, though the more proximate cause is the sun, who by his comings and goings continually changes the air, from hot to cold, which again changes the earth, and alters all its contents.
The obliquity of the zodiac, also, is well placed in respect to the sun's motion, for it likewise is the cause of generation. This is universally accomplished by the universe's proper order, wherein some things are active, and others passive. Different therefore is the generator, which is superlunary, while that which is generated is sublunary; and that which consists of both of these -- namely, an ever- running body, and an ever-mutable generated nature -- is the world itself.
3. The Perpetuity of the World
MAN'S GENERATION did not originate from the earth, other animals, or plants, but the world's proper order being perpetual, the aptly arranged natures it contains should share with it never-failing subsistence. As primarily the world existed always, its parts must coexist with it, and by these I mean the heavens, the earth, and what is contained between them, and that which is on high and is called aerial, for the world does not exist without these, but with and from these.
As the world's parts are co-subsistent, their comprehended natures must coexist with them; with the heavens, indeed, the sun, moon, fixed stars and planets; with the earth, animals and plants, gold and silver; with the aerial region, pneumatic substances and wind, heating and cooling; for it is the property of the heavens to subsist in conjunction with the natures which it comprehends, of the earth to support its native plants and animals, and of the aerial regions to be co-subsistent with the natures it has generated.
Since therefore in each division of the world there is arranged a certain genus of animals which surpasses its fellows, the heavens are the habitat of the Gods, on the earth men, and in the space between, the geniuses. Therefore the race of men must be perpetual, since reason convinces us that not only are the world's parts co-subsistent with it, but so also are their comprehended natures.
Sudden destruction and mutations, however, take place in the parts of the earth; the sea overflows on to the land, or the earth shakes and splits through the unobserved entrance of wind or water. But an entire destruction of the earth's whole arrangement never took place nor ever will.
Hence the story that Grecian history began with Inachus of Argos is false, if understood to be a first principle, but true as some mutation of Greek politics; for Greece has frequently been and will again be barbarous, not only from the influx of foreigners, but from Nature herself, which, although she does not become greater or less, yet is always younger, and has a beginning in reference to us.
So much about the whole, and the universe, the generation and corruption of natures generated in it, of how they subsist, and forever, one part of the universe consisting of a nature which is perpetually moved, and another part being passive; and of how the former governs and how the latter is ever governed.
4. The Generation of Men
LAW, TEMPERANCE AND PIETY conspire in explaining as follows the generation of men from each other, after what manner, from what particulars, and how it is effected. The first postulate is that sexual association should occur never for pleasure, but only for procreation of children.
Those powers and instruments and appetites ministering to copulation were implanted in men by divinity, not for the sake of voluptuousness, but for the perpetuation of the race. Since it was impossible that man, who is born mortal, should participate in a divine life were his race not immortal, divinity operated this immortality through individuals, and lent continuity to mankind's generation. This is the first essential, that cohabitation should not be effected for mere pleasure.
Next, man should be considered in connection with the social organism, a house or city, and especially that each human progeny should work at the completion of the world, unless he plans to be a deserter of either the domestic, political or divine Vestal hearth.
For those who are not entirely connected with each other for the sake of begetting children injure the most honorable system of convention. But if persons of this description procreate with libidinous insolence and intemperance, their offspring will be miserable and flagitious, and will be execrated by God and divinities, by men, families and cities.
Those therefore who deliberately consider these things ought not, in a way similar to irrational animals, to engage in venereal connection, but should think copulation a necessary good. For it is the opinion of worthy men that it is necessary and beautiful not only to fill houses with large families, and also the greater part of the earth, for man is the most mild and the best of all animals, and it is a thing of the greatest consequence to cause them to abound with the most excellent men.
For on this account men inhabit cities governed by the best laws, rightly manage their domestic affairs, and if they are able, impart to their friends such political employments as are conformable to the polities in which they live, since they not only provide for the multitude at large, but especially for worthy men.
Hence many men err who enter into the connubial state without regarding the magnitude of the power of fortune, or of public utility, but direct their attention to wealth, or to dignity of birth. For in consequence of this, instead of uniting with females who are young and in the flower of their age, they become connected with extremely old women; and instead of having wives with a disposition according with, and most similar to their own, they marry those who are of an illustrious family, or are extremely rich. On this account they procure for themselves discord instead of concord; and instead of unanimity, dissension, contending with each other for the mastery. For the wife who surpasses her husband in wealth, in birth, or in friends, is desirous of ruling over him, contrary to the law of nature. But the husband justly resisting this desire of superiority in his wife, and wishing not to be the second, but the first in domestic sway, is unable in the management of his family to take the lead.
This being the case, it happens that not only families, but cities become miserable. For families are parts of cities, while the composition of the whole and the universe derives its subsistence from its parts. It is therefore reasonable to admit that such as are the parts, such likewise will be the whole and the all which consists of things of this kind.
As in fabrics of a primary nature the first structures cooperate greatly to the good or bad completion of the whole work-as for instance the manner in which the foundation is laid in house-building, the structure of a keel in ship-building, and the utterance and closing of the voice in musical modulation-so the concordant condition of families greatly contributes to the well or ill establishment of a polity.
Those therefore who direct their attention to the propagation of the human species ought to guard against everything which is dissimilar and imperfect; for neither plants nor animals when imperfect are prolific, but their fructification demands a certain amount of time, so that when the bodies are strong and perfect they may produce seeds and fruits.
Hence it is necessary that boys and girls while they are virgin should be trained up in exercises and proper endurance, and that they be nourished with that kind of food which is adapted to a laborious, temperate and patient life.
Moreover, in human life there are many things of such a kind that it is better for the knowledge of them to be deferred for a certain time. Hence a boy should be so tutored as not to seek after venereal pleasures before he is twenty years of age, and then should rarely engage in them. This however will take place if he conceives that a good habit of body and continence are beautiful and honorable.
The following laws should be taught in Grecian cities: that connection with a mother, or a daughter, or a sister should not be permitted Whether in temples or in a public place, for it would be well to employ numerous impediments to this energy.
All unnatural connections should be prevented, especially those attended with wanton insolence. But such as harmonize with nature should be encouraged, such as are effected with temperance for the purpose of producing a temperate and legitimate offspring.
Again, those who intend to beget children should providentially attend to the welfare of their future offspring. A temperate and salutary diet therefore is the first and greatest thing to be considered by the would-be begetter, so that he should neither be filled with unseasonable food, nor become intoxicated, nor subject himself to any other perturbation which may injure the body-habits. But above all things he should be careful that the mind, in the act of copulation, should remain in a tranquil state, for bad seed is produced from depraved, discordant and turbulent habits.
With all possible earnestness and attention we should endeavor that children be born elegant and graceful, and that when born they should be well educated. For it is foolish that those who rear horses, birds or dogs should with the utmost diligence render the breed perfect, doing what is proper when it is proper, and likewise consider how they ought to be disposed when they copulate with each other, that the offspring be not the result of chance-while men are inattentive to their progeny, begetting them by chance; and having begotten offspring, should neglect both their food and education. It is the disregard of these things that causes all vice and depravity, since those born will resemble cattle, and will be ignoble and vile.
A FRAGMENT ON LAWS
AS LIFE CONTAINS BODIES, whose cause is the soul, so harmony, connectedly, comprehends the world, whose cause is God. Likewise concord unites families, whose cause is the law. Therefore there is a certain cause and nature which perpetually adapts to each other the parts of the world, hindering their being disordered and unconnected. However, cities and families continue only for a short time, as the formers' constituent matter, and the latters' progeny -- being causes of dissolution-derive their subsistence from a mutable and perpetually passive nature. For the destruction of things which are generated is the salvation of the matter from which they are generated. That nature, however, which is perpetually moved [the celestial region] governs, while that which is always passive [the sublunary region] is governed, the capacity of the former being prior, and of the latter posterior. The former is divine, possessing reason and intellect, the latter being generated, irrational and mutable.
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Notes:
1. The Same and the Other are Platonic terms for Limit and Unlimited.
ON THE NATURE OF THE UNIVERSE
OCELLUS LUCANUS was an early Pythagorean as were other members of his family. This writing seems to be post-Aristotelian. As Holger Thesleff observes in his Introduction to the Pythagorean Writings of the Hellenistic Period, the work seems to be influenced by Peripatetic conceptions and demonstrations concerning the nature of generation and destruction; and the ending. on the generation of good offspring. may derive from Aristoxenus.
ON THE NATURE OF THE UNIVERSE
1. On the Eternity and Indestructibility of the Universe
OCELLUS LUCANUS HAS WRITTEN what follows concerning the nature of the universe, having learnt some things through clear arguments from Nature herself, but others from opinion in conjunction with reason, it being his intention [here] to derive what is probable from intellectual perception.
Therefore it appears to me that the universe is indestructible and unbegotten, since it always was and always will be; for if it had a temporal beginning, it would not always have existed. Thus therefore the universe is unbegotten and indestructible. For if some one should claim that it was once generated, he would not be able to find anything into which it can be corrupted and dissolved, since that from which it was generated would be the first part of the universe; and again, that into which it would be dissolved would be the last part of it.
But if the universe was generated, it was generated together with all things; and if it should be corrupted, it would be corrupted together with all things. This however is impossible. This universe is therefore without a beginning, and without an end; nor is it possible that it can have any other mode of subsistence.
It may be added that everything which has received a beginning of generation, and which ought also to participate in dissolution, receives two mutations. The first, indeed, proceeds from the less to the greater, and from the worse to the better; and that from which it begins to change is denominated generation, but that which at length it arrives is called climax. The other mutation, however, proceeds from the great to the less, and from the better to the worse; but the end of this mutation is called corruption and dissolution.
If therefore the whole and the universe were generated, and are corruptible, they must, when generated, have been changed from the less to the greater, and from the worse to the better; but when corrupted, they must be changed from the greater to the less, and from the better to the worse. Hence, if the world was generated, it would receive increase, and would arrive at its consummation; and again, it would afterwards decrease and end. For every thing which has a progression possesses three boundaries and two intervals: the three boundaries are generation, consummation and end, and the intervals are progression from generation to consummation, and from consummation to end.
The whole, however, and the universe affords as from itself no indication of anything of this kind; for neither do we perceive it rising into existence, or becoming to be, nor changing to the better and the greater, nor changing to worse or less, but it always continues to subsist in the identical manner, and perpetually remains self-identical.
Clear signs and indications of this are the orders of things, their symmetry, figurations, positions, intervals, powers, swiftness and slowness in respect to each other; and besides these, their numbers and temporal periods are clear signs and indications. For all such things as these change and diminish conformably to the course of generation; for things that are greater and better tend towards consummation through power, but those that are less and worse decay through the inherent weakness of nature.
The whole world is what I call the whole universe; for this word "cosmos" was given it as a result of its being adorned with all things. From itself it is a consummate and perfect system of all things, for there is nothing external to the universe, since whatever exists is contained in the universe, and the universe subsists together with this, comprehending in itself all things, both parts and superfluities.
The things contained in the world are naturally congruous with it; but the world harmonizes with nothing else, symphonizing with itself. Other things do not possess self-subsistence, but require adjustment with their environment. Thus animals require conjunction with air for the purpose of respiration, and with light in order to see, and similarly the other senses with other environments to function satisfactorily. A conjunction with earth is necessary for the germination of plants. The sun, moon, planets and fixed stars likewise integrate with the world, as part of its general arrangement. The world, however, has no conjunction with anything outside of itself.
The above is supported by the following. Fire which imparts heat to others is self-hot; honey which is sweet to the taste is self-sweet. The principles of demonstrations, which conclude to things unapparent, are self-evident. Therefore the cause of the perfection of other things is itself perfect. That which preserves and renders permanent other things must itself be preserved and permanent. What harmonizes must itself be self-harmonic. Now as the world is the cause of the existence, preservation and perfection of other things, the world must itself be perpetual and perfect; and because its duration is everlasting, it becomes the cause of the permanence of all other things.
In short, if the universe should be dissolved, it would be dissolved either into the existent or non-existent. It could not be dissolved into existence, for in this case the dissolution would not be a corruption, as being either the universe or some part of it. Nor can it be dissolved into non-entity, since being cannot possibly arise from non-being, or be dissolved into non-entity. Therefore the universe is incorruptible and never can be destroyed.
If, however, somebody should think that it can be corrupted, it must be corrupted either from something external to or contained in the universe; but it cannot be corrupted by anything external to it, for nothing such exists, since all other things are comprehended in the universe, and the world is the whole and the all. Nor can it be corrupted by the things it contains, which would imply their greater power. This however is impossible, for all things are led and governed by the universe, and thereby are preserved and adjusted, possessing life and soul. But if the universe can neither be corrupted by anything external to it, nor by anything contained within it, the world must therefore be incorruptible and indestructible, for we consider the world identical with the universe.
Further, the whole of nature surveyed through its own totality, will be found to derive continuity from the first and most honorable bodies, proportionally attenuating this continuity, introducing it to everything mortal, and receiving the progression of its peculiar subsistence; for the first (and most honorable) bodies in the universe revolve according to the Same, [1] and similarly. The progression of the whole of nature, however, is not successive and continuous, nor yet local, but is subject to mutation.
When condensed, fire generates air, air water, and water earth. A return circuit of transformation extends backward from earth to fire, whence it originated. Likewise, fruits and most rooted plants, originate from seeds. When however they fruit and mature, they are again resolved into seed, nature producing a complete circular progression.
In a subordinate manner men and other animals change the universal boundary of nature, for in these there is no periodical return to the first age; nor is there a transfusion, such as between fire and air, and water and earth, but the mutations of their ages being accomplished in a four-cycled circle, they are dissolved and reformed.
These therefore are the signs and indications that the universe which comprehends [all things) will always endure and be preserved, but that its parts and its nonessential additions are corrupted and dissolved.
Further, it is credible that the universe is without a beginning, and without end, from its figure, motion, time and essence; and therefore it may be concluded that the world is unbegotten and incorruptible, for its figure is circular, and as a circular figure is similar and equal on all sides, it is therefore without a beginning or end. Circular is also the motion of the universe, but this motion is stable and without transition. Time, likewise, in which motion exists, is infinite, for neither had this a beginning, nor will it have an end of its revolution. The universe's essence also does not waste elsewhere, and is immutable, because it is not naturally adapted to change, either from worse to better, or from better to worse. From all these arguments, therefore, it is obviously credible that the world is unbegotten and incorruptible. So much about the world and the universe.
2. Creation of the Elements
SINCE, HOWEVER, IN THE UNIVERSE there is a difference between generation and the generated, and since generation occurs where there is a mutation and egress from things which rank as subjects, then must the cause of generation subsist as long as the generated matter. The cause of generation must be both efficient and motive, while the recipient must be passive and moved.
The Fates themselves distinguish and separate the impassive part of the world from that which is perpetually in motion. For the course of the moon is the meeting-line of generation and immortality. The region above the moon, as well as the lunar domain, is the residence of divinities, while the sublunar regions are the abodes of strife and nature, for in this place there is a mutation of things that are generated and a regeneration of things which have perished.
In that part of the world, however, in which nature and generation predominate, it is necessary that the three following things be present. In the first place, there is the body which yields to the touch, and which is the subject of all generated natures. But this will be an universal recipient, and a characteristic of generation itself, having the same relation to the things that are generated from it, as water to taste, silence to sound, darkness to light, and the matter of artificial forms to the forms themselves. For water is tasteless and devoid of quality, yet is capable of receiving the sweet and the bitter, the tart and the salty. Air also, which is formless as regards sound, is the recipient of words and melody. Darkness, which is without color, and without form, becomes the recipient of splendor, and of the yellow color, and the white; but white pertains to the statuary's art and to the wax-sculptor's art. Matter's relation, however, is different from the sculptor's art, for in matter, prior to generation, all things exist in potential, but they exist in perfection when they are generated, and receive their proper nature. Hence matter [or universal recipient] is necessary to the existence of generation.
The second necessity is the existence of contrarieties, in order to effect mutations and changes in quality, matter for this purpose receiving passive qualities and an aptitude to the participations of form. Contrariety is also necessary in order that powers which are naturally mutually repugnant may not finally conquer or vanquish each other. These powers are hot and cold, dryness and moistness.
In the third place rank essences, and these are fire and water, air and earth, of which heat and cold, dryness and moistness, are powers. Yet essences differ from powers, for essences are locally corrupted by each power, but powers are neither corrupted nor generated, as their reasons [or forms] are incorporeal.
Of these four powers, however, heat and cold subsist as causes and things of an effective nature, but the dry and the moist rank as matter and things that are passive, though matter is the first recipient of things, for it is that which is spread under all things in common. Hence the body, whose capacity is the object of sense, and ranks as a principle, is the first thing; while contraries, such as heat and cold, moistness and dryness, rank as primary differences, and heaviness and lightness, density and rarity, are related as things produced from primary differences. All of them, however, amount to sixteen: heat and cold, moistness and dryness, heaviness and lightness, rarity and density, smoothness and roughness, hardness and softness, thinness and thickness, acuteness and obtuseness. Knowledge of all of these is had by touch, which forms a judgement; hence also any body whatever which contains capacity for these can be apprehended by touch.
Heat and dryness, rarity and sharpness are the powers of fire; coldness and moistness, density and obtuseness are those of water; those of air are softness, smoothness, light, and the quality of being attenuated; while those of earth are hardness and roughness, heaviness and thickness.
Of these four bodies, however, fire and earth are the intensities of contraries. Fire is the intensity of heat, as ice is of cold; and if ice is a concretion of moisture and frigidity, fire will be the fervor of dryness and heat. That is why neither fire nor ice generate anything.
Fire and earth, therefore, are the extremities of the elements, while water and air are the media, for they have a mixed corporeal nature. Nor is it possible that there could be only one of the extremes, a contrary thereto being necessary. Nor could there only be two, for it is necessary to have a medium, as media oppose extremes.
Fire therefore is hot and dry, but air is hot and moist; water is moist and cold, and earth is cold and dry. Hence heat is common to air and fire; cold is common to water and earth; dryness to earth and fire, and moisture to water and air. But with respect to the peculiarities of each, heat is the peculiarity of fire, dryness of earth, moisture of air, and frigidity of water. These essences remain permanent, through the possession of common properties, but they change through such as are peculiar, when one contrary overcomes another.
Hence, when the moisture in air overcomes the dryness in fire, or when water's frigidity overcomes air's heat, and earth's dryness overcomes water's moistness, and vice versa, then are effected the mutual mutations and generations of the elements.
The body, however, which is the subject and recipient of mutations, is a universal receptacle, and is in capacity the first tangible substance.
But the mutations of the elements are effected either from a change of earth into fire, or from fire into air, or from air into water, or from water into earth. Mutation is also effected in the third place, when each element's contrariness is corrupted, simultaneously with the preservation of everything kindred and coeval. Generation therefore is effected when one contrary quality is corrupted. For fire, indeed, is hot and dry, but air is hot and moist, and heat is common to both; and the peculiarity of fire is dryness, and of air, moisture. Hence when the moisture in air overcomes the dryness in fire, then fire is changed into air.
Again, since water is moist and cold, but air is moist and hot, moisture is common to both. Water's peculiarity is coldness, and that of air, heat. When therefore the coldness in water overcomes the heat in air, air is altered into water.
Further, earth is cold and dry, and water cold and moist, coldness being common to both. But earth's peculiarity is dryness, and water's moisture. When therefore earth's dryness overcome water's moisture, water is altered into earth.
Earth's mutation in the ascending alteration occurs in a contrary way. One alternate mutation is effected when one whole vanquishes another, and two contrary powers are corrupted, nothing being common to them, at the same time. For since fire is hot and dry, while water is cold and moist, when the moisture in water overcomes the dryness in fire, and water's coldness overcomes fire's heat, then fire is altered into water.
Again, earth is cold and dry, while air is hot and moist. When therefore earth's coldness overcomes air's heat, and earth's dryness overcomes air's moisture, then air is altered into earth.
When air's moisture corrupts fire's heat, then from both of them will be generated fire; for air's heat, and fire's dryness will remain, fire being hot and dry.
When earth's coldness is corrupted, and also water's moisture, then from both of them will be generated earth. For earth's dryness and water's coldness will be left, as earth is cold and dry.
But when air's heat and fire's heat are corrupted, no element will be generated; for in both of these will remain contraries, air's moisture and fire's dryness. Moisture is however contrary to dryness.
Again, when earth's coldness, and that of water are corrupted, neither thus will any generation occur, for earth's dryness, and water's moisture will remain. But dryness is contrary to moisture.
Thus we have briefly discussed the generation of the first bodies, and how and from what subjects it is effected.
Since, however, the world is indestructible and unbegotten, and neither had a beginning of generation, nor will have an end, it is necessary that the nature which produces generation in another thing, and also that which generates in itself, should be simultaneously present. That which produces generation in another thing is the whole superlunary region, though the more proximate cause is the sun, who by his comings and goings continually changes the air, from hot to cold, which again changes the earth, and alters all its contents.
The obliquity of the zodiac, also, is well placed in respect to the sun's motion, for it likewise is the cause of generation. This is universally accomplished by the universe's proper order, wherein some things are active, and others passive. Different therefore is the generator, which is superlunary, while that which is generated is sublunary; and that which consists of both of these -- namely, an ever- running body, and an ever-mutable generated nature -- is the world itself.
3. The Perpetuity of the World
MAN'S GENERATION did not originate from the earth, other animals, or plants, but the world's proper order being perpetual, the aptly arranged natures it contains should share with it never-failing subsistence. As primarily the world existed always, its parts must coexist with it, and by these I mean the heavens, the earth, and what is contained between them, and that which is on high and is called aerial, for the world does not exist without these, but with and from these.
As the world's parts are co-subsistent, their comprehended natures must coexist with them; with the heavens, indeed, the sun, moon, fixed stars and planets; with the earth, animals and plants, gold and silver; with the aerial region, pneumatic substances and wind, heating and cooling; for it is the property of the heavens to subsist in conjunction with the natures which it comprehends, of the earth to support its native plants and animals, and of the aerial regions to be co-subsistent with the natures it has generated.
Since therefore in each division of the world there is arranged a certain genus of animals which surpasses its fellows, the heavens are the habitat of the Gods, on the earth men, and in the space between, the geniuses. Therefore the race of men must be perpetual, since reason convinces us that not only are the world's parts co-subsistent with it, but so also are their comprehended natures.
Sudden destruction and mutations, however, take place in the parts of the earth; the sea overflows on to the land, or the earth shakes and splits through the unobserved entrance of wind or water. But an entire destruction of the earth's whole arrangement never took place nor ever will.
Hence the story that Grecian history began with Inachus of Argos is false, if understood to be a first principle, but true as some mutation of Greek politics; for Greece has frequently been and will again be barbarous, not only from the influx of foreigners, but from Nature herself, which, although she does not become greater or less, yet is always younger, and has a beginning in reference to us.
So much about the whole, and the universe, the generation and corruption of natures generated in it, of how they subsist, and forever, one part of the universe consisting of a nature which is perpetually moved, and another part being passive; and of how the former governs and how the latter is ever governed.
4. The Generation of Men
LAW, TEMPERANCE AND PIETY conspire in explaining as follows the generation of men from each other, after what manner, from what particulars, and how it is effected. The first postulate is that sexual association should occur never for pleasure, but only for procreation of children.
Those powers and instruments and appetites ministering to copulation were implanted in men by divinity, not for the sake of voluptuousness, but for the perpetuation of the race. Since it was impossible that man, who is born mortal, should participate in a divine life were his race not immortal, divinity operated this immortality through individuals, and lent continuity to mankind's generation. This is the first essential, that cohabitation should not be effected for mere pleasure.
Next, man should be considered in connection with the social organism, a house or city, and especially that each human progeny should work at the completion of the world, unless he plans to be a deserter of either the domestic, political or divine Vestal hearth.
For those who are not entirely connected with each other for the sake of begetting children injure the most honorable system of convention. But if persons of this description procreate with libidinous insolence and intemperance, their offspring will be miserable and flagitious, and will be execrated by God and divinities, by men, families and cities.
Those therefore who deliberately consider these things ought not, in a way similar to irrational animals, to engage in venereal connection, but should think copulation a necessary good. For it is the opinion of worthy men that it is necessary and beautiful not only to fill houses with large families, and also the greater part of the earth, for man is the most mild and the best of all animals, and it is a thing of the greatest consequence to cause them to abound with the most excellent men.
For on this account men inhabit cities governed by the best laws, rightly manage their domestic affairs, and if they are able, impart to their friends such political employments as are conformable to the polities in which they live, since they not only provide for the multitude at large, but especially for worthy men.
Hence many men err who enter into the connubial state without regarding the magnitude of the power of fortune, or of public utility, but direct their attention to wealth, or to dignity of birth. For in consequence of this, instead of uniting with females who are young and in the flower of their age, they become connected with extremely old women; and instead of having wives with a disposition according with, and most similar to their own, they marry those who are of an illustrious family, or are extremely rich. On this account they procure for themselves discord instead of concord; and instead of unanimity, dissension, contending with each other for the mastery. For the wife who surpasses her husband in wealth, in birth, or in friends, is desirous of ruling over him, contrary to the law of nature. But the husband justly resisting this desire of superiority in his wife, and wishing not to be the second, but the first in domestic sway, is unable in the management of his family to take the lead.
This being the case, it happens that not only families, but cities become miserable. For families are parts of cities, while the composition of the whole and the universe derives its subsistence from its parts. It is therefore reasonable to admit that such as are the parts, such likewise will be the whole and the all which consists of things of this kind.
As in fabrics of a primary nature the first structures cooperate greatly to the good or bad completion of the whole work-as for instance the manner in which the foundation is laid in house-building, the structure of a keel in ship-building, and the utterance and closing of the voice in musical modulation-so the concordant condition of families greatly contributes to the well or ill establishment of a polity.
Those therefore who direct their attention to the propagation of the human species ought to guard against everything which is dissimilar and imperfect; for neither plants nor animals when imperfect are prolific, but their fructification demands a certain amount of time, so that when the bodies are strong and perfect they may produce seeds and fruits.
Hence it is necessary that boys and girls while they are virgin should be trained up in exercises and proper endurance, and that they be nourished with that kind of food which is adapted to a laborious, temperate and patient life.
Moreover, in human life there are many things of such a kind that it is better for the knowledge of them to be deferred for a certain time. Hence a boy should be so tutored as not to seek after venereal pleasures before he is twenty years of age, and then should rarely engage in them. This however will take place if he conceives that a good habit of body and continence are beautiful and honorable.
The following laws should be taught in Grecian cities: that connection with a mother, or a daughter, or a sister should not be permitted Whether in temples or in a public place, for it would be well to employ numerous impediments to this energy.
All unnatural connections should be prevented, especially those attended with wanton insolence. But such as harmonize with nature should be encouraged, such as are effected with temperance for the purpose of producing a temperate and legitimate offspring.
Again, those who intend to beget children should providentially attend to the welfare of their future offspring. A temperate and salutary diet therefore is the first and greatest thing to be considered by the would-be begetter, so that he should neither be filled with unseasonable food, nor become intoxicated, nor subject himself to any other perturbation which may injure the body-habits. But above all things he should be careful that the mind, in the act of copulation, should remain in a tranquil state, for bad seed is produced from depraved, discordant and turbulent habits.
With all possible earnestness and attention we should endeavor that children be born elegant and graceful, and that when born they should be well educated. For it is foolish that those who rear horses, birds or dogs should with the utmost diligence render the breed perfect, doing what is proper when it is proper, and likewise consider how they ought to be disposed when they copulate with each other, that the offspring be not the result of chance-while men are inattentive to their progeny, begetting them by chance; and having begotten offspring, should neglect both their food and education. It is the disregard of these things that causes all vice and depravity, since those born will resemble cattle, and will be ignoble and vile.
A FRAGMENT ON LAWS
AS LIFE CONTAINS BODIES, whose cause is the soul, so harmony, connectedly, comprehends the world, whose cause is God. Likewise concord unites families, whose cause is the law. Therefore there is a certain cause and nature which perpetually adapts to each other the parts of the world, hindering their being disordered and unconnected. However, cities and families continue only for a short time, as the formers' constituent matter, and the latters' progeny -- being causes of dissolution-derive their subsistence from a mutable and perpetually passive nature. For the destruction of things which are generated is the salvation of the matter from which they are generated. That nature, however, which is perpetually moved [the celestial region] governs, while that which is always passive [the sublunary region] is governed, the capacity of the former being prior, and of the latter posterior. The former is divine, possessing reason and intellect, the latter being generated, irrational and mutable.
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Notes:
1. The Same and the Other are Platonic terms for Limit and Unlimited.
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