A Beginner's History of Philosophy, Vol. 1: Ancient and Mediæval Philosophy

by Herbert Ernest Cushman

The Later Pythagoreans. Had the Pythagorean band remained what Pythagoras had designed it, had it not had its political aspirations crushed at the battle of Crotona and the members scattered far and wide, it would probably have for the historian of to-day only the importance of a local band of political and religious reformers. The adversity at Crotona was, however, a blessing in disguise for the Pythagoreans and for Greece, for it turned the Pythagoreans from religious politics to science and metaphysics. In the first place, they became the authors of an important metaphysical theory.This was the theory of numbers, which influenced Plato, became the foundation of a vigorous school in Alexandria in the Hellenic-Roman Period, flourished during the Middle Ages, and united with the doctrines of the Jews in what is called the Cabala. To-day the magic numbers persist in our superstitions. In the second place, the Pythagoreans turned to science,—especially to mathematics and astronomy,—and in these two branches became very celebrated in ancient times. Their astronomical theory had a most extraordinary history. With modifications it was preserved by Plato and Aristotle, and later became the basis of the Ptolemaic system of astronomy. This system was the scientifically accepted system for fifteen hundred years, when it was supplanted by the Newtonian theory. It is a most singular fact that the cosmological background of the Epics of Dante and Milton is the astronomical system of the Pythagoreans as expressed in the Ptolemaic system.

The Pythagoreans, be it remarked, were “Reconcilers,” but they were more. The original ethical motive of Pythagoras influenced them as scientists. They did not attempt to formulate a science of ethics, but the ethical motive was always back of their mathematics and astronomy.

1. The Pythagorean Conception of Being. The Pythagorean conception of reality is the most advanced of any cosmological theory in this period. The Pythagoreans were hylozoists, but they come the nearest to transcending the hylozoism of their time. The influence of the later Pythagoreans, whom Plato met in Italy, upon Plato shows that Pythagorean philosophy forms a link between the cosmology of the colonies and the following comprehensive systems of thought.

The important position in the evolution of Greek thought occupied by the Pythagoreans depends upon their conception of that Being that abides amid all change. Pythagoreanism is usually spoken of as “the number theory.” This is, however, only a suggestion of its import. For numbers are not to the Pythagoreans what the different kinds of cosmic matter were to the early monists, or what the several elements were to the pluralists,—Empedocles, Anaxagoras, and the atomists. Neither are they abstractions merely, such as we use in scientific reckoning. The Pythagoreans were pluralists and hylozoists whose plural numbers look beyond hylozoism.

There are two kinds of reality in the Pythagorean teaching: (1) numbers, and (2) unlimited space. The essential nature of things, the Being that abides, consists in the shaping of this unlimited space into mathematical forms. The numbers or the forms are the limited aspect of Being; space is the unlimited aspect of Being. Actual Being consists in the union of the two aspects. Being therefore has two roots, each being necessary to the other. The later Pythagoreans, indeed, called attention to the fact that their numbers were not the same as the different kinds of matter out of which the other Cosmologists conceived the world to be fashioned. Numbers are not the stuff out of which the world of nature-objects have arisen, but rather are forms of nature-objects. Numbers are the patterns or models of things; things are the copies or imitations of numbers. Unlimited space furnishes the material; numbers or mathematical forms furnish the mould; the result is a material thing. Here we find the early basis of Plato’s doctrine of Ideas, and the correlation in Aristotle of Form and matter. If we were to draw an analogybetween the Pythagorean conception of numbers and any part of the preceding cosmological teaching, we should find the similarity between the numbers and the earlier efficient causes and not between the numbers and the elements. For example, Pythagorean numbers have a function more nearly like Love and Hate than like the four elements in Empedocles’ teaching. On the other hand, Pythagorean unlimited space is analogous to the Empedoclean elements.

2. The Pythagorean Dualistic World.[13] The Pythagoreans carried out their conception of this twofold reality both in their mathematical studies and in their conceptions of natural objects. It was from such investigations that they were impressed by the dualism in everything and so reached their principle. They observed in mathematics that the number-series consists of alternate odd and even numbers. The odd numbers are limited and the even unlimited (because they could be divided). They explained the elements as determined by mathematical forms: fire has the form of a tetrahedron; earth, of the cube; air, of the octohedron; water, of the icosahedron; and an additional fifth element, the æther, of the dodecahedron. They carried this dualism further by identifying the limited form with the odd, with the perfect, and with the good; while the unlimited was identified with the even, the imperfect, and the bad. Some of the Pythagoreans even sought to trace out this dualism in the many realms of experience, and they originated a table of ten pairs of opposites: limited and unlimited; odd and even; one and many; right and left; male and female; rest and motion;straight and crooked; light and dark; good and bad; square and oblong.

There is a system in the Pythagorean theory not to be found in the teaching of the other reconcilers. Although all the numbers, and with them all the world, are divided into two opposing classes, these are, nevertheless, united in a harmony. The harmony of a dualism reminds us of Heracleitus’ harmony of antitheses. All series of numbers have their unity and harmony in the odd-even number, One. To the Pythagorean the opposites of life—the good and the bad, the limited and unlimited, the perfect and imperfect, the odd and even—exist in an harmonious whole.

As the Pythagorean school grew in years, the realms to which it applied its theory increased. While we have stated its metaphysical theory first in order to give it prominence, the school came to the formulation of its theory through its investigations in mathematics, music, and astronomy. Then it applied the theory to geometrical structures and to other fields with a procedure that was arbitrary and unmethodical. Yet so universal was the application of the theory that it lived to have superstitious authority for the human mind in the Middle Ages.

3. Pythagorean Astronomy. The formation of the world-all began from the One, or central fire, which attracted and limited the nearest portions of the unlimited. This fire became the centre of the world-all, which had the shape of a hollow globe. Around the central fire the celestial bodies move in globular transparent shells. Their movements are concentric to the fire. This is the beginning of the astronomical theory of the crystalline spheres. The world-all is divided into threeconcentric portions. The periphery or outer rim is Olympus, where all is perfection and where the gods dwell. Between Olympus and the moon is Cosmos, where all is orderly and all movements are in circles. Between the moon and the central fire is the region called Uranus, where all is disorderly and the movements are up and down. The earth is in this lower section of disorder, and moves in a transparent globular shell like the celestial bodies around the central fire. The number of the heavenly bodies is the perfect number, ten. The world-all is conceived as a heavenly heptachord, with the orbits of the seven planets as the sounding strings. Upon this notion was founded the harmony of the spheres, which harmony is not heard by man because it is constant. In modifying this astronomical theory and then accepting it, the most important change that Aristotle made was to conceive the earth as at the centre of the world-all with the sun revolving about it. This was the form in which the Ptolemaic astronomers received it.

Historical Retrospect. In these many searchings of the Cosmologists for a reality amid the changes of nature, what result can be found significant for the Cosmological Period and valuable as a bequest for the following periods? Are these crude scientific speculations of the early Greeks to be looked upon as out of connection with their own age and the age to come? The Cosmological philosophy had two definite results. In the first place, with reference to its own century and a half, it saved the intellectual world of Greece from the slavery of a mystic religion. When we started with Thales in 625 B. C., we saw Greece confronted with two perils. One was political, and consisted of internecinetroubles and of danger from its warlike neighbors. This peril grew still greater, until at the very end of the period it was averted at the battle of Salamis. Greek arms banished this political peril. But the other peril was subjective and therefore more menacing. The mysteries of the Orphic religion would have quenched the Greek genius had not its rational philosophy given the Greek intellectual life new conceptions. In the next place, it bequeathed to the succeeding period a fairly well-drawn contrast between a world of intellectual order and a world of sensuous disorder. The thought of an order in nature in conformity to law was developed into clearness in the Cosmological Period. The order was obtained from the astronomical studies of these scientists. Reasoning from the order that they saw, to an ordering principle, Anaxagoras and the Pythagoreans almost, but not quite, gave to that principle a teleological meaning. The principle of permanence that these nature scientists sought was found in the great and simple relations of the stars, whose revolutions are the expression of order and constancy. Impregnated as they were with their elemental hylozoism, the Greek Cosmologists were as yet not quite able to find an orderly permanence in the terrestrial world with its manifold and intersecting motions. Yet Greek thought was looking forward. The Cosmologist had already contrasted the terrestrial as the imperfect with the celestial as the perfect peace and permanence. The step was but a short one from the contrast of the two realms to the effort to bring them into a unity. Thus in this astronomical and concrete form a distinction of value was obtained that had lasting ethical and æsthetical significance, not only upon Plato and Aristotle, but upon modern thought.