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

The third physical philosopher produced by Miletus, seemingly before the time of her terrible disasters suffered from the Persians after the Ionic revolt between 500-494 B.C., was Anaximenes, who struck out a third hypothesis. He assumed, as the primordial substance, and as the source of all generation or transmutation, Air, eternal in duration, infinite in extent. He thus returned to the principle of the Thaletian theory, selecting for his beginning a known substance, though not the same substance as Thales. To explain how generation of new products was possible (as Anaximander had tried to explain by his theory of evolution of latent contraries), Anaximenes adverted to the facts of condensation and rarefaction, which he connected respectively with cold and heat.17 The Infinite Air, possessing and exercising an inherent generative and developing power, perpetually in motion, passing from dense to rare or from rare to dense, became in its utmost rarefaction, Fire and Æther; when passing through successive stages of increased condensation it became first cloud, next water, then earth, and, lastly, in its utmost density, stone.18 Surrounding, embracing, and pervading the Kosmos, it also embodied and carried with it a vital principle, which animals obtained from it by inspiration, and which they lost as soon as they ceased to breathe.19 Anaximenes included in his treatise (which was written in a clear Ionic dialect) many speculations on astronomy and meteorology, differing widely from those of Anaximander.

He conceived the Earth as a broad, flat, round plate, resting on the air.20 Earth, Sun, and Moon were in his view condensed air, the Sun acquiring heat by the extreme and incessant velocity with which he moved. The Heaven was not an entire hollow sphere encompassing the Earth below as well as above, but a hemisphere covering the Earth above, and revolving laterally round it like a cap round the head.21

The general principle of cosmogony, involved in the hypothesis of these three Milesians — one primordial substance or Something endued with motive and transmutative force, so as to generate all the variety of products, each successive and transient, which our senses witness — was taken up with more or less modification by others, especially by Diogenes of Apollonia, of whom I shall speak presently. But there were three other men who struck out different veins of thought — Pythagoras, Xenophanes, and Herakleitus: the two former seemingly contemporary with Anaximenes (550-490 B.C.), the latter somewhat later.

Of Pythagoras I have spoken at some length in the thirty-seventh chapter of my History of Greece. Speculative originality was only one among many remarkable features in his character. He was an inquisitive traveller, a religious reformer or innovator, and the founder of a powerful and active brotherhood, partly ascetic, partly political, which stands without parallel in Grecian history. The immortality of the soul, with its transmigration (metempsychosis) after death into other bodies, either of men or of other animals — the universal kindred thus recognised between men and other animals, and the prohibition which he founded thereupon against the use of animals for food or sacrifice — are among his most remarkable doctrines: said to have been borrowed (together with various ceremonial observances) from the Egyptians.22 After acquiring much celebrity in his native island of Samos and throughout Ionia, Pythagoras emigrated (seemingly about 530 B.C.) to Kroton and Metapontum in Lower Italy, where the Pythagorean brotherhood gradually acquired great political ascendancy: and from whence it even extended itself in like manner over the neighbouring Greco-Italian cities. At length it excited so much political antipathy among the body of the citizens,23 that its rule was violently put down, and its members dispersed about 509 B.C. Pythagoras died at Metapontum.

Though thus stripped of power, however, the Pythagoreans still maintained themselves for several generations as a social, religious, and philosophical brotherhood. They continued and extended the vein of speculation first opened by the founder himself. So little of proclaimed individuality was there among them, that Aristotle, in criticising their doctrine, alludes to them usually under the collective name Pythagoreans. Epicharmus, in his comedies at Syracuse (470 B.C.) gave occasional utterance to various doctrines of the sect; but the earliest of them who is known to have composed a book, was Philolaus,24 the contemporary of Sokrates. Most of the opinions ascribed to the Pythagoreans originated probably among the successors of Pythagoras; but the basis and principle upon which they proceed seems undoubtedly his.

The problem of physical philosophy, as then conceived, was to find some primordial and fundamental nature, by and out of which the sensible universe was built up and produced; something which co-existed always underlying it, supplying fresh matter and force for generation of successive products. The hypotheses of Thales, Anaximander, and Anaximenes, to solve this problem, have been already noticed: Pythagoras solved it by saying, That the essence of things consisted in Number. By this he did not mean simply that all things were numerable, or that number belonged to them as a predicate. Numbers were not merely predicates inseparable from subjects, but subjects in themselves: substances or magnitudes, endowed with active force, and establishing the fundamental essences or types according to which things were constituted. About water,25 air, or fire, Pythagoras said nothing.26 He conceived that sensible phenomena had greater resemblance to numbers than to any one of these substrata assigned by the Ionic philosophers. Number was (in his doctrine) the self-existent reality — the fundamental material and in-dwelling force pervading the universe. Numbers were not separate from things27 (like the Platonic Ideas), but fundamenta of things — their essences or determining principles: they were moreover conceived as having magnitude and active force.28 In the movements of the celestial bodies, in works of human art, in musical harmony — measure and number are the producing and directing agencies.

According to the Pythagorean Philolaus, “the Dekad, the full and perfect number, was of supreme and universal efficacy as the guide and principle of life, both to the Kosmos and to man. The nature of number was imperative and lawgiving, affording the only solution of all that was perplexing or unknown; without number all would be indeterminate and unknowable.”29

The first principle or beginning of Number, was the One or Monas — which the Pythagoreans conceived as including both the two fundamental contraries — the Determining and the Indeterminate.30 All particular numbers, and through them all things, were compounded from the harmonious junction and admixture of these two fundamental contraries.31 All numbers being either odd or even, the odd numbers were considered as analogous to the Determining, the even numbers to the Indeterminate. In One or the Monad, the Odd and Even were supposed to be both contained, not yet separated: Two was the first indeterminate even number; Three, the first odd and the first determinate number, because it included beginning, middle, and end. The sum of the first four numbers — One, Two, Three, Four = Ten (1 + 2 + 3 + 4) was the most perfect number of all.32 To these numbers, one, two, three, four, were understood as corresponding the fundamental conceptions of Geometry — Point, Line, Plane, Solid. Five represented colour and visible appearance: Six, the phenomenon of Life: Seven, Health, Light, Intelligence, &c.: Eight, Love or Friendship.33 Man, Horse, Justice and Injustice, had their representative numbers: that corresponding to Justice was a square number, as giving equal for equal.34