Pythagorean Kosmos and Astronomy — geometrical and harmonic laws guiding the movements of the cosmical bodies.

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

Music of the Spheres.

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

Pythagorean list of fundamental Contraries — Ten opposing pairs.

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.

Eleatic philosophy — Xenophanes.

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.

His censures upon the received Theogony and religious rites.

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

His doctrine of Pankosmism, or Pantheism — The whole Kosmos is Ens Unum or God — Ἓν καὶ Πᾶν. Non-Ens inadmissible.

Though Xenophanes thus appears (like Pythagoras) mainly as a religious dogmatist, yet theogony and cosmogony were so intimately connected in the sixth century B.C., that he at the same time struck out a new philosophical theory. His negation of theogony was tantamount to a negation of cosmogony. In substituting one God for many, he set aside all distinct agencies in the universe, to recognise only one agent, single, all-pervading, indivisible. He repudiated all genesis of a new reality, all actual existence of parts, succession, change, beginning, end, etc., in reference to the universe, as well as in reference to God. “Wherever I turned my mind (he exclaimed) everything resolved itself into One and the same: all things existing came back always and everywhere into one similar and permanent nature.”52 The fundamental tenet of Xenophanes was partly religious, partly philosophical, Pantheism, or Pankosmism: looking upon the universe as one real all-comprehensive Ens, which he would not call either finite or infinite, either in motion or at rest.53 Non-Ens he pronounced to be an absurdity — an inadmissible and unmeaning phrase.

Scepticism of Xenophanes — complaint of philosophy as unsatisfactory.

It was thus from Xenophanes that the doctrine of Pankosmism obtained introduction into Greek philosophy, recognising nothing real except the universe as an indivisible and unchangeable whole. Such a creed was altogether at variance with common perception, which apprehends the universe as a plurality of substances, distinguishable, divisible, changeable, &c. And Xenophanes could not represent his One and All, which excluded all change, to be the substratum out of which phenomenal variety was generated — as Water, Air, the Infinite, had been represented by the Ionic philosophers. The sense of this contradiction, without knowing how to resolve it, appears to have occasioned the mournful complaints of irremediable doubt and uncertainty, preserved as fragments from his poems. “No man (he exclaims) knows clearly about the Gods or the universe: even if he speak what is perfectly true, he himself does not know it to be true: all is matter of opinion.”54

Nevertheless while denying all real variety or division in the universe, Xenophanes did not deny the variety of human perceptions and beliefs. But he allowed them as facts belonging to man, not to the universe — as subjective or relative, not as objective or absolute. He even promulgated opinions of his own respecting many of the physical and cosmological subjects treated by the Ionic philosophers.

His conjectures on physics and astronomy.

Without attempting to define the figure of the Earth, he considered it to be of vast extent and of infinite depth;55 including, in its interior cavities, prodigious reservoirs both of fire and water. He thought that it had at one time been covered with water, in proof of which he noticed the numerous shells found inland and on mountain tops, together with the prints of various fish which he had observed in the quarries of Syracuse, in the island of Paros, and elsewhere. From these facts he inferred that the earth had once been covered with water, and even that it would again be so covered at some future time, to the destruction of animal and human life.56 He supposed that the sun, moon, and stars were condensations of vapours exhaled from the Earth, collected into clouds, and alternately inflamed and extinguished.57

Parmenides continues the doctrine of Xenophanes — Ens Parmenideum, self-existent, eternal, unchangeable, extended, — Non-Ens, an unmeaning phrase.

Parmenides, of Elea, followed up and gave celebrity to the Xenophanean hypothesis in a poem, of which the striking exordium is yet preserved. The two veins of thought, which Xenophanes had recognised and lamented his inability to reconcile, were proclaimed by Parmenides as a sort of inherent contradiction in the human mind — Reason or Cogitation declaring one way, Sense (together with the remembrances and comparisons of sense) suggesting a faith altogether opposite. Dropping that controversy with the popular religion which had been raised by Xenophanes, Parmenides spoke of many different Gods or Goddesses, and insisted on the universe as one, without regarding it as one God. He distinguished Truth from matter of Opinion.58 Truth was knowable only by pure mental contemplation or cogitation, the object of which was Ens or Being, the Real or Absolute: here the Cogitans and the Cogitatum were identical, one and the same.59 Parmenides conceived Ens not simply as existent, but as self-existent, without beginning or end,60 as extended, continuous, indivisible, and unchangeable. The Ens Parmenideum comprised the two notions of Extension and Duration:61 it was something Enduring and Extended; Extension including both space, and matter so far forth as filling space. Neither the contrary of Ens (Non-Ens), nor anything intermediate between Ens and Non-Ens, could be conceived, or named, or reasoned about. Ens comprehended all that was Real, without beginning or end, without parts or difference, without motion or change, perfect and uniform like a well-turned sphere.62

He recognises a region of opinion, phenomenal and relative, apart from Ens.

In this subject Ens, with its few predicates, chiefly negative, consisted all that Parmenides called Truth. Everything else belonged to the region of Opinion, which embraced all that was phenomenal, relative, and transient: all that involved a reference to man’s senses, apprehension, and appreciation, all the indefinite diversity of observed facts and inferences. Plurality, succession, change, motion, generation, destruction, division of parts, &c., belonged to this category. Parmenides did not deny that he and other men had perceptions and beliefs corresponding to these terms, but he denied their application to the Ens or the self-existent. We are conscious of succession, but the self-existent has no succession: we perceive change of colour and other sensible qualities, and change of place or motion, but Ens neither changes nor moves. We talk of things generated or destroyed — things coming into being or going out of being — but this phrase can have no application to the self-existent Ens, which is always and cannot properly be called either past or future.63 Nothing is really generated or destroyed, but only in appearance to us, or relatively to our apprehension.64 In like manner we perceive plurality of objects, and divide objects into parts. But Ens is essentially One, and cannot be divided.65 Though you may divide a piece of matter you cannot divide the extension of which that matter forms part: you cannot (to use the expression of Hobbes66) pull asunder the first mile from the second, or the first hour from the second. The milestone, or the striking of the clock, serve as marks to assist you in making a mental division, and in considering or describing one hour and one mile apart from the next. This, however, is your own act, relative to yourself: there is no real division of extension into miles, or of duration into hours. You may consider the same space or time as one or as many, according to your convenience: as one hour or as sixty minutes, as one mile or eight furlongs. But all this is a process of your own mind and thoughts; another man may divide the same total in a way different from you. Your division noway modifies the reality without you, whatever that may be — the Extended and Enduring Ens — which remains still a continuous one, undivided and unchanged.