GREEK PHILOSOPHY - I.
§ 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
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
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
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
"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
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).
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
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.
(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.
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
(5) Ueberweg's Hist. of Phil. (trans.) Vol. I. p. 49.