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Introductory Paragraph

Early Ionic Natural Philosophers

The Pythagoreans

The Eleatics


Later Natural Philosophers

General Character of the First Period in the History of Greek Philosophy

The Sophist


The Followers of Socrates

The Lesser Socratics

Plato. Life. Works

Plato. Philosophy

The Disciples of Plato

The Old Academy

Aristotle: Life and works

Aristotle: Theory of Knowledge

Aristotle: Metaphysics

Aristotle: Physics

Aristotle: Psychology

Aristotle: Practical Philosophy

Aristotle: Rhetoric and Poetic

Aristotle: Sources

Aristotle: Unity of Plato and Aristotle

Aristotle: result

The Peripatetic School

Three Leading Post-Aristotelian Schools

The Stoics and Stoicism

The Epicureans and Epicureanism

The Sceptics

The Common Ground of the Stoics, Epicureans, and Sceptics

Philosophy in Rome: Eclecticism

The Later Peripatetics

The Later Academics

The Later Stoics

General Character of the Second Period

Standpoint and Schools of the Third and Latest Period of Greek Philosophy

Jewish-Alexandrian School


The Eclectic Platonist

Neo-Platonism. Plotinus

Neo-Platonism. Porphyry. Jamblichus

Neo-Platonism. Proclus




B. C. BURT (1852-1915) - Table of contents                        




§ 2. The Pythagoreans

The next step in Greek speculation was taken by Pythagoras and his followers, regarding whom and the theories of whom it is difficult to arrive at clear, consistent, unquestionable views (1).

Pythagoras and the Pythagorean Order

Pythagoras was born on the island of Samos, near the coast of  Asia Minor, about the year 580 B.C., dying at Metapontum in Lower Italy about the year 510 B.C. Possibly he was a pupil of Anaximander, and familiar with his scientific and philosophical views. Possibly, also, he travelled in Egypt, making additions to the store of his scientific knowledge, and receiving a new religious and ethical impulse through contact with the learned priesthood there. He was regarded by Heraclitus, a philosopher of the next century, as very learned, but not very profound. He either founded or contemplated founding an ethico-religious order in his native place. Such an order he did found in Crotona, Lower Italy, whither some of his countrymen had migrated and he himself went in 529 B.C. This order was, it may be conjectured, such an embodiment as was possible to be made by a Grecian on Grecian soil, of the idea of monasticism which Pythagoras, if he visited Egypt, had brought from that country. The discipline of the society was, particularly in the later period of its existence, of the rigid, aristocratic sort, out of harmony, as Hegel remarks, with the democratic spirit of Greece. Habitual silence, implicit obedience to the authority of the master, fidelity to friends, abstinence, self-scrutiny, non-proselytism, were required of all its members. Physical, as well as intellectual, moral, and religious, culture was aimed at. Pythagoras professed to be, not σοφός, wise, but φιλόσοφος, lover of wisdom; and we may regard the society he founded as an organization intended to furnish the conditions for a philosophic life. He was, it appears, a man capable of leading such a life and of inspiring others to do so. He was looked upon as a very Apollo in his appearance, character, and gift of inspiration; and fabulous stories gathered about his name. By his personal dignity and worth, and by his teachings, he was able to show —and was perhaps the first among the Greek philosophers who did show— that wisdom is an affair of character and life as well as of knowledge. The maxims of the so-called "Wise Men" savor of a moral utilitarianism not to be found in the doctrine and practice of Pythagoras and his followers.


  But the ideal of Pythagoras was not that of pure asceticism; nor was the society, at least in the earlier part of its existence, narrowly monastic: the earlier Pythagoreans were, says Grote, men of "practical efficiency of body and mind". The society became large, and strong, not merely by its influence upon the lives of its members, but also by its influence in the political affairs of Lower Italy. It was the prototype of many societies in other cities in Lower Italy. It existed for more than a century; having been finally broken up by the opposition it aroused in the democratic element of the population because of its too decided espousal of the principles of the aristocratic party.

The Pythagorean Philosophy

We come now to the Pythagorean philosophy, the speculations, that is to say, of Pythagoras and his followers. It has been found impossible to distinguish those of Pythagoras from those of his followers.

The Number-Theory and the Doctrine of' "Contraries''

According to Aristotle (2), the Pythagoreans, having especially cultivated the mathematical sciences, fancied that they discovered the patterns, or archetypes, of things, not in any sensible thing, as fire, earth, or water, but in number, and asserted that the principles of number were the principles of being, and that the "whole heaven was a harmony and number". They did not distinguish between the affirmation that the principles or laws of number are the principles or laws of things, and the affirmation that numbers themselves are things or the substances of things; between number as a "formal cause," and number as a "material cause," of all things. Now number is odd or even, one being both odd and even. The odd is finite; the even infinite. The number ten was held to be perfect. Some of the Pythagoreans, Aristotle states, asserted that the first principles were ten in number —ten pairs of "contraries": the finite and infinite, the odd and the even, unity and plurality, right and left, male and female, rest and motion, straight and crooked, light and darkness, good and bad, square and oblong. There seems at first to be no direct connection between this crude table of "categories" and the number-theory. The uniting link between them may, however, be the thought that the truth is the union of a contrariety of elements, i.e., a harmony. Such seem to be the main features of the Pythagorean theory in its earlier form.

Theories not purely Pythagorean

Other theories have been, though to some extent wrongly (3), attributed to the Pythagoreans. In one of these the number one represents the Deity, and, again, the principle of unity or continuity in things, two represents the principle of variety or difference, three the union of the two, four (as the square of two) the "perfection" of mere difference, and ten, "the perfect number" (the sum of one, two, three, and four), the complete organic unity and harmony of the world. Again: "The author of a work ascribed to Philolaus [a Pythagorean of the fifth century B.C] sees in the principles of number the principles of things. These principles are "the limiting" and "'illimitation". They converge to harmony, which is unity in multiplicity and agreement in heterogeneity. Thus they generate in succession, first, unity, then the series of arithmetical or monadic numbers, then "geometrical" numbers or "magnitudes," i.e., the forms of space: point, line, surface, solid; next material objects, then life, sensuous consciousness, and the higher psychical forces, as love, friendship, mind, and intelligence. Like is known by like, but it is by number that things are brought into harmonious relations to the soul. The understanding, developed by mathematical study, is the organ of knowledge. Musical harmony depends on a certain numerical proportion in the lengths of musical strings. The octave, in particular, or harmony in the narrow sense, depends on the ratio 1:2, which includes the two ratios of the fourth (3: 4) and the fifth (2:3 or 4:6). [This fact was discovered by Pythagoras himself.] The five regular solids —the cube, the tetrahedron, the octahedron, icosahedron, the dodecahedron— are respectively the fundamental forms of earth, fire, air, water, and the fifth element, which encompasses all the rest. The soul is united by number and harmony with the body, which is its organ, and at the same time its prison. From the Hestia, i.e., from the central fire around which the earth and counter-earth (4) daily revolve, the soul of the world spreads through the spheres of the counter-earth, the earth, the moon, the sun, the planets Mercury, Venus, Mars, Jupiter, Saturn, and the fixed stars to "Olympus," the last sphere, which includes all the others. The world is eternal and ruled by the One, who is akin to it, and has supreme might and excellence. The director and ruler of all things is God; he is one and eternal, enduring and immovable, ever like himself and different from all things beside him. He compasses and guards the universe (5).

Miscellaneous Theories

Certain other discoveries and theories of Pythagoras and the Pythagoreans may be here mentioned for interest's sake; some of them bear relation to the number-theory, others do not. Pythagoras is said to have discovered two important truths in geometry: one relating to the triangle inscribed within a semicircle, and another to the square of the hypothenuse of a right-angled triangle. The discovery of the latter is said to have elated him so much that he sacrificed a hundred oxen and made a great feast. Some of the Pythagoreans, if not Pythagoras himself, fancied that the supposed celestial spheres were arranged at intervals corresponding mathematically to the intervals of the octave. Some of the Pythagoreans believed that the earth rotated upon an axis. Pythagoras held the doctrine of the transmigration of souls, —believed that his own soul had inhabited the body of Euphorbus, a Trojan hero. The noblest education for a youth he thought to be that which would fit him to be the citizen of a well-regulated state.


From the foregoing it appears that though the Pythagorean order was primarily religious and ethical, the Pythagorean philosophy was cosmical, a philosophy not of conduct and of God but of the sensible universe; it appears, also, that, as Aristotle pointed out, the first principle, the άρχή, of the Pythagorean theory is not "material" but "formal" or primarily so. The subject of the Pythagorean speculation was, that is to say, not the original world-stuff or material source of things but the order stamped upon phenomena. These speculations must be regarded as a step in advance of those of the Hylicists. The Pythagorean theories, we shall hereafter see, largely influenced subsequent speculation, particularly that of Plato and the Platonists.


(1) See Zeller's Pre-Socratic Philosophy (a translation by S. F. Alleyne of a portion of Zeller's Geschichte der Philosophie der Griechen), Vol. I. pp. 306-308.

(2) Metaphysics, Bk. I., ch. 5.

(3) Zeller's Pre-Socratic Phil, Vol. I. pp. 386 and fol.

(4) Supposed to be under the earth and moving around the central fire with it. Ten being the perfect number, there must, it was thought, be ten bodies "borne through the heaven". There being, says Aristotle, only nine apparent, the Pythagoreans assumed a tenth, calling it Counter-Earth (άντίχθων).

(5) Ueberweg's Hist. of Phil. (trans.) Vol. I. p. 49.



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