PYTHAGOREANISM.
1. ITS RELATIVE POSITION.—The development of the Ionic philosophy
discloses the tendency to abstract matter from all else; though they
directed this process solely to the determined _quality_ of matter. It
is this abstraction carried to a higher step, when we look away from the
sensible concretions of matter, and no more regard its _qualitative_
determinateness as water, air, &c., but only direct our attention to its
_quantitative_ determinateness,—to its space-filling property. But the
determinateness of quantity is number, and this is the principle and
standpoint of Pythagoreanism.
2. HISTORICAL AND CHRONOLOGICAL.—The Pythagorean doctrine of numbers is
referred to Pythagoras of Samos, who is said to have flourished between
540 and 500 B. C. He dwelt in the latter part of his life at Crotonia,
in Magna Grecia, where he founded a society, or, more properly, an
order, for the moral and political regeneration of the lower Italian
cities. Through this society, this new direction of philosophy seems to
have been introduced,—though more as a mode of life than in the form of
a scientific theory. What is related concerning the life of Pythagoras,
his journeys, the new order which he founded, his political influence
upon the lower Italian cities, &c., is so thoroughly interwoven with
traditions, legends, and palpable fabrications, that we can be certain
at no point that we stand upon a historical basis. Not only the old
Pythagoreans, who have spoken of him, delighted in the mysterious and
esoteric, but even his new-Platonistic biographers, Porphyry and
Jamblichus, have treated his life as a historico-philosophical romance.
We have the same uncertainty in reference to his doctrines, _i. e._ in
reference to his share in the number-theory. Aristotle, _e. g._ does not
ascribe this to Pythagoras himself, but only to the Pythagoreans
generally, _i. e._ to their school. The accounts which are given
respecting his school have no certainty till the time of Socrates, a
hundred years after Pythagoras. Among the few sources of light which we
have upon this subject, are the mention made in Plato’s Phædon of the
Pythagorean Philolaus and his doctrines, and the writings of Archytas, a
cotemporary of Plato. We possess in fact the Pythagorean doctrine only
in the manner in which it was taken up by Philolaus, Eurytas and
Archytas, since its earlier adherents left nothing in a written form.
3. THE PYTHAGOREAN PRINCIPLE.—The ancients are united in affirming that
the principle of the Pythagorean philosophy was number. But in what
sense was this their principle—in a material or a formal sense? Did they
hold number as the material of things, _i. e._ did they believe that
things had their origin in numbers, or did they regard it as the
archetype of things, _i. e._ did they believe that things were made as
the copy or the representation of numbers? From this very point the
accounts given by the ancients diverge, and even the expressions of
Aristotle seem to contradict each other. At one time he speaks of
Pythagoreanism in the former, and at another in the latter sense. From
this circumstance modern scholars have concluded that the Pythagorean
doctrine of numbers had different forms of development; that some of the
Pythagoreans regarded numbers as the substances and others as the
archetypes of things. Aristotle, however, gives an intimation how the
two statements may be reconciled with each other. Originally, without
doubt, the Pythagoreans regarded number as the material, as the inherent
essence of things, and therefore Aristotle places them together with the
Hylics (the Ionic natural philosophers), and says of them that “they
held things for numbers” (_Metaph._ I., 5, 6). But as the Hylics did not
identify their matter, _e. g._ water, immediately with the sensuous
thing, but only gave it out as the fundamental element, as the original
form of the individual thing, so, on the other side, numbers also might
be regarded as similar fundamental types, and therefore Aristotle might
say of the Pythagoreans, that “they held numbers to be the corresponding
original forms of being, as water, air, &c.” But if there still remains
a degree of uncertainty in the expressions of Aristotle respecting the
sense of the Pythagorean doctrine of numbers, it can only have its
ground in the fact that the Pythagoreans did not make any distinction
between a formal and material principle, but contented themselves with
the undeveloped view, that, “number is the essence of things, every
thing is number.”
4. THE CARRYING-OUT OF THIS PRINCIPLE.—From the very nature of the
“number-principle,” it follows that its complete application to the
province of the real, can only lead to a fruitless and empty symbolism.
If we take numbers as even and odd, and still farther as finite and
infinite, and apply them as such to astronomy, music, psychology,
ethics, &c., there arise combinations like the following, viz.: one is
the point, two are the line, three are the superficies, four are the
extension of a body, five are the condition (_beschaffenheit_),
&c.—still farther, the soul is a musical harmony, as is also virtue, the
soul of the world, &c. Not only the philosophical, but even the
historical interest here ceases, since the ancients themselves—as was
unavoidable from the arbitrary nature of such combinations—have given
the most contradictory account, some affirming that the Pythagoreans
reduced righteousness to the number three, others, that they reduced it
to the number four, others again to five, and still others to nine.
Naturally, from such a vague and arbitrary philosophizing, there would
early arise, in this, more than in other schools, a great diversity of
views, one ascribing this signification to a certain mathematical form,
and another that. In this mysticism of numbers, that which alone has
truth and value, is the thought, which lies at the ground of it all,
that there prevails in the phenomena of nature a rational order, harmony
and conformity to law, and that these laws of nature can be represented
in measure and number. But this truth has the Pythagorean school hid
under extravagant fancies, as vapid as they are unbridled.
The physics of the Pythagoreans possesses little scientific value, with
the exception of the doctrine taught by Philolaus respecting the
circular motion of the earth. Their ethics is also defective. What we
have remaining of it relates more to the Pythagorean life, _i. e._ to
the practice and discipline of their order than to their philosophy. The
whole tendency of Pythagoreanism was in a practical respect ascetic, and
directed to a strict culture of the character. As showing this, we need
only to cite their doctrines concerning the transmigration of the soul,
or, as it has been called, their “immortality doctrine,” their notion in
respect of the lower world, their opposition to suicide, and their view
of the body as the prison of the soul—all of which ideas are referred to
in Plato’s Phædon, and the last two of which are indicated as belonging
to Philolaus.