Pythagoras; (3) the unquestioning submission with which the dicta of the master were received by his disciples, as shown by the famous avròs epa, ipse dixit, which was to them an end of all controversy. The brotherhood, first established at Crotona, soon gained great influence with the wealthier class in that and the neighbouring cities; but after some twenty years of prosperity they seem to have provoked the opposition of the democratic party by their arrogance and exclusiveness. Pythagoras himself is Isaid to have been banished from Crotona and taken refuge at Metapontum. A worse fate overtook his followers about a hundred years later, when their church at Crotona was burnt down, and they themselves massacred with the exception of two. The school appears to have died out altogether about the middle of the 4th century B.C., but revived in the time of Cicero. The new and startling feature in the Pythagorean philosophy, as opposed to the Ionic systems, was that it found its axý, its key of the universe, not in any known substance, but in number and proportion. This might naturally have occurred to one who had listened to the teaching of Thales and Anaximander. After all it makes no difference, he might say, what we take as our original matter, it is the law of development, the measure of condensation, which determines the nature of each thing. Number rules the harmonies of music, the proportions of sculpture and architecture, the movements of the heavenly bodies'. It is Number which makes the universe into a 1 He believed that the intervals between the heavenly bodies corresponded exactly to those of the octave, and that hence arose the Harmony of the Spheres, which mortals were unable to hear, either because it was too powerful for their organs of hearing or be Kóσμos', and is the secret of a virtuous and orderly life. Then, by a confusion similar to that which led Heraclitus to identify the law of movement with Fire, the Pythagoreans went on to identify number with form, substance and quality. One, the Monad, evolved out of itself Limit (order), exhibited in the series of odd numbers, and the Unlimited (freedom, expansiveness), the Dyad, exhibited in the series of even numbers, especially of the powers of Two; out of the harmonious mixture of these contraries all particular substances were produced. Again, One was the point, Two the line, Three the plane, Four the concrete solid (but from another point of view, as being the first square number, equal into equal, it was conceived to be Justice). Yet once more, One was the central fire, the hearth of the universe, the throne of Zeus. Around this revolved in regular dance ten spheres; on the outside that of the fixed stars, within this the five planets in their order, then the Sun, the Moon, the Earth, between which and the central fire was interposed the imaginary Anti-Chthon or Counter-Earth, cutting off our view of the central fire and leaving us dependent on the reflection of its light by the Sun, which was not in itself luminous. The separation of the Earth into its two hemispheres was for the purpose of making up the Decad, the symbol of totality. As the Decad was the sum of the first four numbers (1 + 2 + 3 + 4 = 10), special sacredness attached to this group, known under the name Tetractys3. cause they had never experienced absolute silence. Arist. Cael. II. 9, Plin. N. II. II. 22. 1 Pythagoras is said to have been the first who called the universe by this name. 2 Compare the Pythagorean oath contained in the Golden Verses, The number Ten was also the number of the Pythagorean categories, or list of contraries, thus given by Aristotle (Met. I. v. 986), Limit and Unlimited, Odd and Even, One and Many, Right and Left, Male and Female, Rest and Motion, Straight and Curved, Light and Darkness, Good and Bad, Square and Oblong. These mystical extravagances appear to have been the necessary introduction to the sciences of Arithmetic and Geometry, just as Astrology and Alchemy were the introduction to Astronomy and Chemistry. Indeed we find that men like Copernicus and Kepler were to some extent influenced and guided in their investigations by the ideas of Pythagoras. Nor was he himself deficient in knowledge of a more exact kind, if it is true that he was the discoverer of the theorem which we know as the 47th in the first book of Euclid, and was also acquainted with such properties of numbers as are mentioned by Zeller (1. p. 322*). The Pythagorean doctrine of the soul and of God is variously reported. If we may trust the oldest accounts, there does not seem to have been any close connexion between the religious and philosophical opinions of οὐ μὰ τὸν ἡμετέρᾳ γενεᾷ παραδόντα τετρακτύν, παγὰν ἀενάου φύσιος ῥιζώματ ̓ ἔχουσαν. There was of course no end to the fancies which might be connected with numbers. Thus, One was reason, as being unchangeable; Two was opinion, and the earth as the region of opinion; Three was perfection, as comprising in itself beginning, middle, and end; Five was marriage, the union of odd and even, Later Pythagoreans made the Monad God, the Dyad Matter, the Triad the World. For other interpretations, see Zeller I. p. 359* foll. The five regular solids were supposed to be the ultimate forms of the five elements, the cube of earth, pyramid of fire, octahedron of air, icosahedron of water, dodecahedron of the etherial element which encompassed the universe on the outside. Pythagoras. We are told that he believed in One God eternal, unchangeable, ruling and upholding all things, that the soul was a 'harmony',' that the body was its prison, in which it was punished for past sin and disciplined for a divine life after death, that those who failed to profit by this discipline would pass into lower forms of life, or suffer severer penalties in Hades. Heraclides Ponticus reports (Diog. L. Proem. 12, Cic. Tusc. v. 3) that Pythagoras was the first to call himself pióropos, a lover of wisdom, saying that the name σopós, used by the older sages, properly belonged to God alone. He compared human life to the gathering at the Olympic games, where some came to win glory, others to make gain, others to watch the spectacle: the philosopher, he said, resembled these last in despising honour and gain, and caring only for knowledge. Other sayings attributed to Pythagoras are the following: 'man is at his best when he visits the temples of the Gods3.' 'Choose the best life; use will make it pleasant,' (Stob. Flor. 1. 29). 'Do not speak few things in many words, but many things in few words,' (Stob. Flor. xxxv. 8). 'Either be silent, or speak words better than silence,' (Stob. Flor. XXXIV. 7). 'Be sleepless in the things of the 1 The statement of Cicero and others that Pythagoras held the human soul to be a portion of the Divine soul (Cato M. 78) is not confirmed by the earlier authorities. 2 So Philolaus (R. and P. § 124) διά τινας τιμωρίας ἡ ψυχὰ τῷ σώματι συνέζευκται καὶ καθάπερ ἐν σάματι τούτῳ τέθαπται. Plato adds that he condemned suicide as desertion of our post, ev TIVI φρουρᾷ ἐσμεν οἱ ἄνθρωποι, καὶ οὐ δεῖ δὴ ἑαυτὸν ἐκ ταύτης λύειν οὐδ ̓ ἀποδιδράσκειν. 3 Βέλτιστοι ἑαυτῶν γίνονται ἄνθρωποι ὅταν πρὸς τοὺς θεοὺς Badiswow, Plut. Def. Or. 183, see Cic. Leg. II. II. spirit; for sleep in them is akin to death,” (Stob. Flor. I. 19). 'It is hard to take many paths in life at the same time,' (Stob. Flor. 1. 27). 'It is the part of a fool to attend to every opinion of every man, above all to that of the mob,' (Iambl. V. P. 31). The second of the Italic schools was the Eleatic, founded by Xenophanes of Colophon in Asia Minor (b. 569 B.C.), who migrated to Elea in Italy about 540 B.C. While the Pythagoreans strove to explain nature mathematically and symbolically, the Eleatics in their later developments did the same by their metaphysical abstractions. Xenophanes himself seems to have received his first philosophical impulse in the revulsion from the popular mythology. In his philosophical poem he condemns anthropomorphism and polytheism altogether, and charges Homer and Hesiod with attributing to the Gods conduct which would have been disgraceful in men. 'If animals had had hands they would have depicted Gods each in their own form, just as men have done'. is God one, all eye, all ear, all understanding; he is for ever unmoved, unchangeable, a vast all-embracing sphere.' 1 Πάντα θεοῖς ἀνέθηκαν Ὅμηρος θ' Ησίοδός τε |