A Critical History of Greek Philosophy by W. T. Stace (short story to read txt) 📖

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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CHAPTER IV

THE ELEATICS

The Eleatics are so called because the seat of their school was at Elea, a town in South Italy, and Parmenides and Zeno, the two chief representatives of the school, were both citizens of Elea. So far we have been dealing with crude systems of thought in which only the germs of philosophic thinking can be dimly discerned. Now, however, with the Eleatics we step out definitely for the first time upon the platform of philosophy. Eleaticism is the first true philosophy. In it there emerges the first factor of the truth, however poor, meagre, and inadequate. For philosophy is not, as many persons suppose, simply a collection of freak speculations, which we may study in historical order, but at the end of which, God alone knows which we ought to believe. On the contrary, the history of philosophy presents a definite line of evolution. The truth unfolds itself gradually in time.

Xenophanes

The reputed founder of the Eleatic School was Xenophanes. It is, however, doubtful whether Xenophanes ever went to Elea. Moreover, he belongs more properly {41} to the history of religion than to the history of philosophy. The real creator of the Eleatic School was Parmenides. But Parmenides seized upon certain germs of thought latent in Xenophanes and transmuted them into philosophic principles. We have, therefore, in the first instance, to say something of Xenophanes. He was born about the year 576 B.C., at Colophon in Ionia. His long life was spent in wandering up and down the cities of Hellas, as a poet and minstrel, singing songs at banquets and festivals. Whether, as sometimes stated; he finally settled at Elea is a matter of doubt, but we know definitely that at the advanced age of ninety-two he was still wandering about Greece. His philosophy, such as it is, is expressed in poems. He did not, however, write philosophical poems, but rather elegies and satires upon various subjects, only incidentally expressing his religious views therein. Fragments of these poems have come down to us.

Xenophanes is the originator of the quarrel between philosophy and religion. He attacked the popular religious notions of the Greeks with a view to founding a purer and nobler conception of Deity. Popular Greek religion consisted of a belief in a number of gods who were conceived very much as in the form of human beings. Xenophanes attacks this conception of God as possessing human form. It is absurd, he says, to suppose that the gods wander about from place to place, as represented in the Greek legends. It is absurd to suppose that the gods had a beginning. It is disgraceful to impute to them stories of fraud, adultery, theft and deceit. And Xenophanes inveighs against Homer and Hesiod for disseminating these degrading conceptions {42} of the Deity. He argues, too, against the polytheistic notion of a plurality of gods. That which is divine can only be one. There can only be one best. Therefore, God is to be conceived as one. And this God is comparable to mortals neither in bodily form nor understanding. He is "all eye, all ear, all thought." It is he "who, without trouble, by his thought governs all things." But it would be a mistake to suppose that Xenophanes thought of this God as a being external to the world, governing it from the outside, as a general governs his soldiers. On