CHAPTER III

THE PYTHAGOREANS

Not much is known of the life of Pythagoras. Three so-called biographies have come down to us from antiquity, but they were written hundreds of years after the event, and are filled with a tissue of extravagant fancies, and with stories of miracles and wonders worked by Pythagoras. All sorts of fantastic legends seem to have gathered very early around his life, obscuring from us the actual historical details. A few definite facts, however, are known. He was born somewhere between 580 and 570 B.C. at Samos, and about middle age he migrated to Crotona in South Italy. According to legend, before he arrived in South Italy he had travelled extensively in Egypt and other countries of the East. There is, however, no historical evidence of this. There is nothing in itself improbable in the belief that Pythagoras made these travels, but it cannot be accepted as proved for lack of evidence. The legend is really founded simply upon the oriental flavour of his doctrines. In middle age he arrived in South Italy and settled at Crotona. There he founded the Pythagorean Society and lived for many years at the head of it. His later life, the date and manner of his death, are not certainly known.

Now it is important to note that the Pythagorean {32} Society was not primarily a school of philosophy at all. It was really a religious and moral Order, a Society of religious reformers. The Pythagoreans were closely associated with the Orphic Sect, and took from it the belief in the transmigration of souls, including transmigration of human souls into animals. They also taught the doctrine of the "wheel of things," and the necessity of obtaining "release" from it, by which one could escape from the weary round of reincarnate lives. Thus they shared with the Orphic religious Sect the principle of reincarnation. The Orphic Sect believed that "release" from the wheel of life was to be obtained by religious ceremonial and ritual. The Pythagoreans had a similar ritual, but they added to this the belief that intellectual pursuits, the cultivation of science and philosophy, and, in general, the intellectual contemplation of the ultimate things of the universe would be of great help towards the "release" of the soul. From this arose the tendency to develop science and philosophy. Gradually their philosophy attained a semi-independence from their religious rites which justifies us in regarding it definitely as philosophy.

The Pythagorean ethical views were rigorous and ascetic in character. They insisted upon the utmost purity of life in the members of the Order. Abstinence from flesh was insisted upon, although this was apparently a late development. We know that Pythagoras himself was not a total abstainer from flesh. They forbade the eating of beans. They wore a garb peculiar to themselves. The body, they taught, is the prison or tomb of the soul. They thought that one must not attempt to obtain "release" by suicide, because "man is the {33} property of God," the chattel of God. They were not politicians in the modern sense, but their procedure in practice amounted to the greatest possible interference in politics. It appears that the Pythagoreans attempted to impose their ordinances upon the ordinary citizens of Crotona. They aimed at the supersession of the State by their own Order and they did actually capture the government of Crotona for a short period. This led to attacks on the Order, and the persecution of its members. When the plain citizen of Crotona was told not to eat beans, and that under no circumstances could he eat his own dog, this was too much. A general persecution occurred. The meeting place of the Pythagoreans was burnt to the ground, the Society was scattered, and its members killed or driven away. This occurred between the years 440 and 430 B.C. Some years later the Society revived and continued its activities, but we do not hear much of it after the fourth century B.C.

It was largely a mystical society. The Pythagoreans developed their own ritual, ceremonial and mysteries. This love of mystery, and their general character as miracle-mongers, largely account for the legends which grew up around the life of Pythagoras himself. Their scientific activities were also considerable. They enforced moral self-control. They cultivated the arts and crafts, gymnastics, music, medicine, and mathematics. The development of mathematics in early Greece was largely the work of the Pythagoreans. Pythagoras is said to have discovered the 47th Proposition of Euclid, and to have sacrificed an ox in honour thereof. And there is good reason to believe that practically the whole of the substance of the First Book of Euclid is the work of Pythagoras.

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Turning now to their philosophical teaching, the first thing that we have to understand is that we cannot speak of the philosophy of Pythagoras, but only of the philosophy of the Pythagoreans. For it is not known what share Pythagoras had in this philosophy or what share was contributed by his successors. Now we recognize objects in the universe by means of their qualities. But the majority of these qualities are not universal in their scope; some things possess some qualities; others possess others. A leaf, for example, is green, but not all things are green. Some things have no colour at all. The same is true of tastes and smells. Some things are sweet; some bitter. But there is one quality in things which is absolutely universal in its scope, which applies to everything in the universe--corporeal or incorporeal. All things are _numerable_, and can be counted. Moreover, it is impossible to conceive a universe in which number is not to be found. You could easily imagine a universe in which there is no colour, or no sweet taste, or a universe in which nothing possesses weight. But you cannot imagine a universe in which there is no number. This is an inconceivable thought. Upon these grounds we should be justified in concluding that number is an extremely important aspect of things, and forms a fundamental pad of the framework of the world. And it is upon this aspect of things that the Pythagoreans laid emphasis.

They drew attention to proportion, order, and harmony as the dominant notes of the universe. Now when we examine the ideas of proportion, order, and harmony, we shall see that they are closely connected with number. Proportion, for example, must necessarily {35} be expressible by the relation of one number to another. Similarly order is measurable by numbers. When we say that the ranks of a regiment exhibit order, we mean that they are arranged in such a way that the soldiers stand at certain regular distances from each other, and these distances are measurable by numbers of feet or inches. Lastly, consider the idea of harmony. If, in modern times, we were to say that the universe is a harmonious whole, we should understand that we are merely using a metaphor from music. But the Pythagoreans lived in an age when men were not practised in thought, and they confused cosmical harmony with musical harmony. They thought that the two things were the same. Now musical harmony is founded upon numbers, and the Pythagoreans were the first to discover this. The difference of notes is due to the different numbers of vibrations of the sounding instrument. The musical intervals are likewise based upon numerical proportions. So that since, for the Pythagoreans, the universe is a musical harmony, it follows that the essential character of the universe is number. The study of mathematics confirmed the Pythagoreans in this idea. Arithmetic is the science of numbers, and all other mathematical sciences are ultimately reducible to numbers. For instance, in geometry, angles are measured by the number of degrees.

Now, as already pointed out, considering all these facts, we might well be justified in concluding that number is a very important aspect of the universe, and is fundamental in it. But the Pythagoreans went much further than this. They drew what seems to us the extraordinary conclusion that the world is _made of_ {36} numbers. At this point, then, we reach the heart of the Pythagorean philosophy. Just as Thales had said that the ultimate reality, the first principle of which things are composed, is water, so now the Pythagoreans teach that the first principle of things is number. Number is the world-ground, the stuff out of which the universe is made.

In the detailed application of this principle to the world of things we have a conglomeration of extraordinary fancies and extravagances. In the first place, all numbers arise out of the unit. This is the prime number, every other number being simply so many units. The unit then is the first in the order of things in the universe. Again, numbers are divided into odd and even. The universe, said the Pythagoreans, is composed of pairs of opposites and contradictories, and the fundamental character of these opposites is that they are composed of the odd and even. The odd and even, moreover, they identified with the limited and the unlimited respectively. How this identification was made seems somewhat doubtful. But it is clearly connected with the theory of bipartition. An even number can be divided by two and therefore it does not set a limit to bipartition. Hence it is unlimited. An odd number cannot be divided by two, and therefore it sets a limit to bipartition. The limited and the unlimited become therefore the ultimate principles of the universe. The Limit is identified with the unit, and this again with the central fire of the universe. The Limit is first formed and proceeds to draw more and more of the unlimited towards itself, and to limit it. Becoming limited, it becomes a definite "something," a thing. So the formation of the {37} world of things proceeds. The Pythagoreans drew up a list of ten opposites of which the universe is composed. They are (1) Limited and unlimited, (2) odd and even, (3) one and many, (4) right and left, (5) masculine and feminine, (6) rest and motion, (7) straight and crooked, (8) light and darkness, (9) good and evil, (10) square and oblong.

With the further development of the number-theory Pythagoreanism becomes entirely arbitrary and without principle. We hear, for example, that 1 is the point, 2 is the line, 3 is the plane, 4 is the solid, 5 physical qualities, 6 animation, 7 intelligence, health, love, wisdom. There is no principle in all this. Identification of the different numbers with different things can only be left to the whim and fancy of the individual. The Pythagoreans disagreed among themselves as to what number is to be assigned to what thing. For example, justice, they said, is that which returns equal for equal. If I do a man an injury, justice ordains that injury should be done to me, thus giving equal for equal. Justice must, therefore, be a number which returns equal for equal. Now the only numbers which do this are square numbers. Four equals two into two, and so returns equal for equal. Four, then, must be justice. But nine is equally the square of three. Hence other Pythagoreans identified justice with nine.

According to Philolaus, one of the most prominent Pythagoreans, the quality of matter depends upon the number of sides of its smallest particles. Of the five regular solids, three were known to the Pythagoreans. That matter whose smallest particles are regular tetrahedra, said Philolaus, is fire. Similarly earth is composed {38} of cubes, and the universe is identified with the dodecahedron. This idea was developed further by Plato in the "Timaeus," where we find all the five regular solids brought into the theory.

The central fire, already mentioned as identified with the unit, is a characteristic doctrine of the Pythagoreans. Up to this time it had been believed that the earth is the centre of the universe, and that everything revolves round it. But with the Pythagoreans the earth revolves round the central fire. One feels inclined at once to identify this with the sun. But this is not correct. The sun, like the earth, revolves round the central fire. We do not see the central fire because that side of the earth on which we live is perpetually turned away from it. This involves the theory that the earth revolves round the central fire in the same period that it takes to rotate upon its axis. The Pythagoreans were the first to see that the earth is itself one of the planets, and to shake themselves free from the geocentric hypothesis. Round the central fire, sometimes mystically called "the Hearth of the Universe," revolve ten bodies. First is the "counter-earth," a non-existent body invented by the Pythagoreans, next comes the earth, then the sun, the moon, the five planets, and lastly the heaven of the fixed stars. This curious system might have borne fruit in astronomy. That it did not do so was largely due to the influence of Aristotle, who discountenanced the theory, and insisted that the earth is the centre of the universe. But in the end the Pythagorean view won the day. We know that Copernicus derived the suggestion of his heliocentric hypothesis from the Pythagoreans.

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The Pythagoreans also taught "The Great Year," probably a period of 10,000 years, in which the world comes into being and passes away, going in each such period through the same evolution down to the smallest details.

There is little to be said by way of criticism of the Pythagorean system. It is entirely crude philosophy. The application of the number theory issues in a barren and futile arithmetical mysticism. Hegel's words in this connection are instructive:--

"We may certainly," he says, "feel ourselves prompted to associate the most general characteristics of thought with the first numbers: saying one is the simple and immediate, two is difference and mediation, and three the unity of both these. Such associations however are purely external; there is nothing in the mere numbers to make them express these definite thoughts. With every step in this method, the more arbitrary grows the association of definite numbers with definite thoughts ... To attach, as do some secret societies of modern times, importance to all sorts of numbers and figures is, to some extent an innocent amusement, but it is also a sign of deficiency of intellectual resource. These numbers, it is said, conceal a profound meaning, and suggest a deal to think about. But the point in philosophy is not what you may think but what you do think; and the genuine air of thought is to be sought in thought itself and not in arbitrarily selected symbols." [Footnote 3]

[Footnote 3: Hegel's _Smaller Logic_, translated by Wallace, second edition, page 198.]

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