The Pythagorean School

Article 2. The Pythagorean School

a) Pythagoras; b) Notable Pythagoreans. While the cosmological inquiry was developing in Ionia, a different School of Greek philosophers made its appearance in Crotona, a Greek city in southern Italy. This was the School of the Pythagoreans. Like the Ionians, the Pythagoreans tried to discover the nature of all the world, but the particular point of their inquiry was the order, unity, and proportion observable in the world. The Pythagoreans also sought a rule of life and conduct, and the School of Crotona was a religio-philosophical society which followed a community life under strict discipline. Members of the School were required to hold their goods in common, to practise simplicity of dress and diet, and to preserve chastity. The connection between the philosophy of the Pythagoreans and their moral-religious code was slight, if it existed at all.

a) Pythagoras (about 582-497 b. c.)

Life: Pythagoras was born on the island of Samos, a part of Ionia. Though Ionian by birth, it is said that he was of Dorian ancestry. Legendary accounts say that Pythagoras travelled extensively in Egypt and in Asia, where he became acquainted with Oriental learning. He was particularly given to mathematical study. About 530 b. c. he went to Italy and founded the Crotona establishment, a “school” which lasted about twenty years, and was then dispersed because of its increasing political influence. After the breaking up of the Crotona school, Pythagoras retired to Metapontum, in southern Italy, and died there about 497 b. c.

Works: We have no writings of Pythagoras. The work called his “Golden Sayings” is a forgery. What we know of this philosopher is taken largely from Philolaus, a prominent Pythagorean of the latter 5 century b. c., and from Aristotle (4 century b. c.).

Doctrine: The doctrine here given is that of the Pythagoreans. There is no means of discerning the special tenets of Pythagoras from those of the school at large—and there was no such means even as early as the 4 century b. c. when Aristotle wrote. The Pythagoreans were men of decided mathematical bent, and the order, unity, and proportion in the world appealed to them as a thing capable of expression in mathematical formulas, and, indeed, as mathematical in nature. They taught that all things are numbers. It is well to remember when taking up the study of this unusual theory that the Pythagoreans were men of unpractised thought who made no nice distinction between numbers and things arranged according to number. Numbers appealed to these philosophers by their exactness. Stated movements, capable of being numbered, appeared in the heavenly bodies, and were observable in the succession of seasons, of days and nights, of births and deaths. And everywhere the accompaniment, if not the result, of regular, proportioned, numbered existence was observed to be harmonious, or simply harmony. Number and harmony are the two notes that characterize the Pythagorean philosophy.

There are two series of numbers—odd and even, and these come from the unit. The unit is both odd and even, for units make up every possible number of either series, and a unit added to an odd number makes it even, and added to an even number makes it odd. The unit thus contains all numbers in itself potentially, i. e., all numbers can be developed from the unit. Now the contrariety of the odd-even series of numbers has its counterpart in nine other contrarieties. Altogether, then, there are ten contrarieties in the universe; and ten, for some mystical reason, was a Magic Number to the Pythagoreans. Totaling to the Magic Number appeared to these philosophers a proof of value in the process so resulting. The ten contrarieties are:

odd…even

the limited …the unlimited

singularity …plurality right …left male …female rest…motion

straight …crooked (curved or bent)

good …evil light …darkness square…oblong

These lists are not mutually exclusive in their entirety; they are not an odd list and an even list respectively. The analogy to the odd-even relation is found in each pair of contrarieties taken alone and without respect to the other pairs. The bodily universe is expressed in numbers, and is actually made of numbers. The universe is expressed in numbers. Let a block of wood represent the bodily world. The block has ends or limits ; these are points : the unit is the point. Each dimension of the block is measured by two termini or points, and is conceived as a line running between the two points : the number two is the line. The smallest number of lines that meet to form an enclosed surface is three (the triangle) : the number three is thus surface. The solid with the smallest number of surfaces is the triangular pyramid which has four points and four faces : the number four is the solid. Adding the numbers one to four we find that they total ten, and ten is the Magic Number. The universe is actually made of numbers. Numbers are the essence of things. We have seen that points, lines, surfaces, and solids are properly expressed in numbers. It remains to be shown that the bulk or mass or bodiliness of things enclosed and limited by points, lines, and surfaces, is also number. Points, lines, and surfaces are the limiting element in bodies; the mass or bulk of bodies which these limiting things enclose is called the unlimited element, or simply the Unlimited. Different numbered combinations of the Unlimited and the limiting element constitute the variety of things that exists in the universe. In the beginning there was a primordial mass of points (the limiting) and intervals of a substance (the Unlimited), all mingled together. Then the limiting drew off from the Unlimited, and the two came together again in such wise that five fundamental essences emerged. The Unlimited in definite numerical intervals met with and joined the limiting to form these essences, which are so many geometrical figures. The five essences are: the pyramid (fire) ; the cube (earth) ; the octohedron (air) ; the icosahedron (water) ; and the dode-kahedron (ether). Of these five essences all bodily things are made; these are the elements of all things. Fire is the noblest of the elements. It occupies the centre of the universe. About the central fire ten great bodies or planets swing in regular, numbered movement. These bodies are : the earth, the counter earth, the sun, the moon, the firmament of fixed stars, the planets, Jupiter, Mars, Mercury, Venus, and Saturn. The “counter earth” is an invention to fill out the Magic Number of worldly spheres. In their movement about the central fire these bodies produce a most wonderful harmony of sound; but our ears do not perceive this “music of the spheres,” either because it is too subtle for human hearing, or because it is ceaseless, and sound is noticed only by contrast with preceding or subsequent silence. The Pythagoreans believed in God—and in one God. Their theology, however, is very obscure. They taught that God permeates all, yet transcends all. In external practice they accepted the current mythology. It was a positive doctrine of Pythagoreanism that man has a soul, and that his soul is a number. It is the principle of motion in man; nay, more: it is the principle of motion in anything, and anything that can move has a soul. Man’s soul is imprisoned in the body by reason of some sin. The soul must purify itself from sin by virtuous living, else it will pass, after death, into another body (metempsychosis or transmigration) and then into another and another, until purification is achieved or found utterly impossible of achievement. The hopelessly vile soul will be banished to Tartarus, while purified souls will enter a world of happiness, where they will continue to live without being rejoined to their bodies. Besides souls, the Pythagoreans admitted the existence of an unseen world of demons which lived under the earth or in the air. Some of the demons were good and helped men, others were evil and wrought harm to mankind.

Remarks: Pythagoreanism was a step forward in the development of philosophy. The Earlier Ionians taught that all things in the world have a single basic nature and a common source, that different things are but different forms or manifestations of the world-stuff—granted that the forms are essentially different in their present being. The Pythagoreans taught that all things are made of numbers. The idea of number is a more abstract idea than that of a bodily worldstuff. The Earlier Ionians achieved a physical idea ; the Pythagoreans attained to a mathematical idea. Before philosophy could reach its proper character, it had to develop a still higher and more abstract idea—a metaphysical idea—and to consider all things in the unifying light of the idea of being.

b) Notable Pythagoreans. The most notable members of the Pythagorean School were:

1— Timæus of Locris;

2— Archytas of Tarentum;

3— Ocellus the Lucanian ;

4— Hippodamus of Miletus;

5— Philolaus of Crotona.