Plato and the Other Companions of Sokrates, 3rd ed. Volume 1

The Pythagoreans conceived the Kosmos, or the universe, as one single system, generated out of numbers.35 Of this system the central point — the determining or limiting One — was first in order of time, and in order of philosophical conception. By the determining influence of this central constituted One, portions of the surrounding Infinite were successively attracted and brought into system: numbers, geometrical figures, solid substances, were generated. But as the Kosmos thus constituted was composed of numbers, there could be no continuum: each numerical unit was distinct and separated from the rest by a portion of vacant space, which was imbibed, by a sort of inhalation, from the infinite space or spirit without.36 The central point was fire, called by the Pythagoreans the Hearth of the Universe (like the public hearth or perpetual fire maintained in the prytaneum of a Grecian city), or the watch-tower of Zeus. Around it revolved, from West to East, ten divine bodies, with unequal velocities, but in symmetrical movement or regular dance.37 Outermost was the circle of the fixed stars, called by the Pythagoreans Olympus, and composed of fire like the centre. Within this came successively, — with orbits more and more approximating to the centre, — the five planets, Saturn, Jupiter, Mars, Venus, Mercury: next, the Sun, the Moon, and the Earth.

Lastly, between the Earth and the central fire, an hypothetical body, called the Antichthon or Counter-Earth, was imagined for the purpose of making up a total represented by the sacred number Ten, the symbol of perfection and totality. The Antichthon was analogous to a separated half of the Earth; simultaneous with the Earth in its revolutions, and corresponding with it on the opposite side of the central fire.

The inhabited portion of the Earth was supposed to be that which was turned away from the central fire and towards the Sun, from which it received light. But the Sun itself was not self-luminous: it was conceived as a glassy disk, receiving and concentrating light from the central fire, and reflecting it upon the Earth, so long as the two were on the same side of the central fire. The Earth revolved, in an orbit obliquely intersecting that of the Sun, and in twenty-four hours, round the central fire, always turning the same side towards that fire. The alternation of day and night was occasioned by the Earth being during a part of such revolution on the same side of the central fire with the Sun, and thus receiving light reflected from him: and during the remaining part of her revolution on the side opposite to him, so that she received no light at all from him. The Earth, with the Antichthon, made this revolution in one day: the Moon, in one month:38 the Sun, with the planets, Mercury and Venus, in one year: the planets, Mars, Jupiter, and Saturn, in longer periods respectively, according to their distances from the centre: lastly, the outermost circle of the fixed stars (the Olympus, or the Aplanes), in some unknown period of very long duration.39

The revolutions of such grand bodies could not take place, in the opinion of the Pythagoreans, without producing a loud and powerful sound; and as their distances from the central fire were supposed to be arranged in musical ratios,40 so the result of all these separate sounds was full and perfect harmony. To the objection — Why were not these sounds heard by us? — they replied, that we had heard them constantly and without intermission from the hour of our birth; hence they had become imperceptible by habit.41

Ten was, in the opinion of the Pythagoreans, the perfection and consummation of number. The numbers from One to Ten were all that they recognised as primary, original, generative. Numbers greater than ten were compounds and derivatives from the decad. They employed this perfect number not only as a basis on which to erect a bold astronomical hypothesis, but also as a sum total for their list of contraries. Many Hellenic philosophers42 recognised pairs of opposing attributes as pervading nature, and as the fundamental categories to which the actual varieties of the sensible world might be reduced. While others laid down Hot and Cold, Wet and Dry, as the fundamental contraries, the Pythagoreans adopted a list of ten pairs. 1. Limit and Unlimited; 2. Odd and Even; 3. One and Many; 4. Right and Left; 5. Male and Female; 6. Rest and Motion; 7. Straight and Curve; 8. Light and Darkness; 9. Good and Evil; 10. Square and Oblong.43 Of these ten pairs, five belong to arithmetic or to geometry, one to mechanics, one to physics, and three to anthropology or ethics. Good and Evil, Regularity and Irregularity, were recognised as alike primordial and indestructible.44

The arithmetical and geometrical view of nature, to which such exclusive supremacy is here given by the Pythagoreans, is one of the most interesting features of Grecian philosophy. They were the earliest cultivators of mathematical science,45 and are to be recognised as having paved the way for Euclid and Archimedes, notwithstanding the symbolical and mystical fancies with which they so largely perverted what are now regarded as the clearest and most rigorous processes of the human intellect. The important theorem which forms the forty-seventh Proposition of Euclid’s first book, is affirmed to have been discovered by Pythagoras himself: but how much progress was made by him and his followers in the legitimate province of arithmetic and geometry, as well as in the applications of these sciences to harmonics,46 which they seem to have diligently cultivated, we have not sufficient information to determine with certainty.

Contemporary with Pythagoras, and like him an emigrant from Ionia to Italy, was Xenophanes of Kolophon. He settled at the Phokæan colony of Elea, on the Gulf of Poseidonia; his life was very long, but his period of eminence appears to belong (as far as we can make out amidst conflicting testimony) to the last thirty years of the sixth century B.C. (530-500 B.C.). He was thus contemporary with Anaximander and Anaximenes, as well as with Pythagoras, the last of whom he may have personally known.47 He composed, and recited in person, poems — epic, elegiac, and iambic — of which a very few fragments remain.

Xenophanes takes his point of departure, not from Thales or Anaximander, but from the same ancient theogonies which they had forsaken. But he follows a very different road. The most prominent feature in his poems (so far as they remain), is the directness and asperity with which he attacks the received opinions respecting the Gods — and the poets Hesiod and Homer, the popular exponents of those opinions. Xenophanes not only condemns these poets for having ascribed to the Gods discreditable exploits, but even calls in question the existence of the Gods, and ridicules the anthropomorphic conception which pervaded the Hellenic faith. “If horses or lions could paint, they would delineate their Gods in form like themselves. The Ethiopians conceive their Gods as black, the Thracians conceive theirs as fair and with reddish hair.”48 Dissatisfied with much of the customary worship and festivals, Xenophanes repudiated divination altogether, and condemned the extravagant respect shown to victors in Olympic contests,49 not less than the lugubrious ceremonies in honour of Leukothea. He discountenanced all Theogony, or assertion of the birth of Gods, as impious, and as inconsistent with the prominent attribute of immortality ascribed to them.50 He maintained that there was but one God, identical with, or a personification of, the whole Uranus. “The whole Kosmos, or the whole God, sees, hears, and thinks.” The divine nature (he said) did not admit of the conception of separate persons one governing the other, or of want and imperfection in any way.51