THE PYTHAGOREANS
Not much is known of the life of Pythagoras. Three so-called
biographies have come down to us from antiquity, but they were written
hundreds of years after the event, and are filled with a tissue of
extravagant fancies, and with stories of miracles and wonders worked
by Pythagoras. All sorts of fantastic legends seem to have gathered
very early around his life, obscuring from us the actual historical
details. A few definite facts, however, are known. He was born
somewhere between 580 and 570 B.C. at Samos, and about middle age he
migrated to Crotona in South Italy. According to legend, before he
arrived in South Italy he had travelled extensively in Egypt and other
countries of the East. There is, however, no historical evidence of
this. There is nothing in itself improbable in the belief that
Pythagoras made these travels, but it cannot be accepted as proved for
lack of evidence. The legend is really founded simply upon the
oriental flavour of his doctrines. In middle age he arrived in South
Italy and settled at Crotona. There he founded the Pythagorean Society
and lived for many years at the head of it. His later life, the date
and manner of his death, are not certainly known.
Now it is important to note that the Pythagorean {32} Society was not
primarily a school of philosophy at all. It was really a religious and
moral Order, a Society of religious reformers. The Pythagoreans were
closely associated with the Orphic Sect, and took from it the belief
in the transmigration of souls, including transmigration of human
souls into animals. They also taught the doctrine of the "wheel of
things," and the necessity of obtaining "release" from it, by which
one could escape from the weary round of reincarnate lives. Thus they
shared with the Orphic religious Sect the principle of reincarnation.
The Orphic Sect believed that "release" from the wheel of life was to
be obtained by religious ceremonial and ritual. The Pythagoreans had a
similar ritual, but they added to this the belief that intellectual
pursuits, the cultivation of science and philosophy, and, in general,
the intellectual contemplation of the ultimate things of the universe
would be of great help towards the "release" of the soul. From this
arose the tendency to develop science and philosophy. Gradually their
philosophy attained a semi-independence from their religious rites
which justifies us in regarding it definitely as philosophy.
The Pythagorean ethical views were rigorous and ascetic in character.
They insisted upon the utmost purity of life in the members of the
Order. Abstinence from flesh was insisted upon, although this was
apparently a late development. We know that Pythagoras himself was not
a total abstainer from flesh. They forbade the eating of beans. They
wore a garb peculiar to themselves. The body, they taught, is the
prison or tomb of the soul. They thought that one must not attempt to
obtain "release" by suicide, because "man is the {33} property of
God," the chattel of God. They were not politicians in the modern
sense, but their procedure in practice amounted to the greatest
possible interference in politics. It appears that the Pythagoreans
attempted to impose their ordinances upon the ordinary citizens of
Crotona. They aimed at the supersession of the State by their own
Order and they did actually capture the government of Crotona for a
short period. This led to attacks on the Order, and the persecution of
its members. When the plain citizen of Crotona was told not to eat
beans, and that under no circumstances could he eat his own dog, this
was too much. A general persecution occurred. The meeting place of the
Pythagoreans was burnt to the ground, the Society was scattered, and
its members killed or driven away. This occurred between the years 440
and 430 B.C. Some years later the Society revived and continued its
activities, but we do not hear much of it after the fourth century
B.C.
It was largely a mystical society. The Pythagoreans developed their
own ritual, ceremonial and mysteries. This love of mystery, and their
general character as miracle-mongers, largely account for the legends
which grew up around the life of Pythagoras himself. Their scientific
activities were also considerable. They enforced moral self-control.
They cultivated the arts and crafts, gymnastics, music, medicine, and
mathematics. The development of mathematics in early Greece was
largely the work of the Pythagoreans. Pythagoras is said to have
discovered the 47th Proposition of Euclid, and to have sacrificed an
ox in honour thereof. And there is good reason to believe that
practically the whole of the substance of the First Book of Euclid is
the work of Pythagoras.
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Turning now to their philosophical teaching, the first thing that we
have to understand is that we cannot speak of the philosophy of
Pythagoras, but only of the philosophy of the Pythagoreans. For it is
not known what share Pythagoras had in this philosophy or what share
was contributed by his successors. Now we recognize objects in the
universe by means of their qualities. But the majority of these
qualities are not universal in their scope; some things possess some
qualities; others possess others. A leaf, for example, is green, but
not all things are green. Some things have no colour at all. The same
is true of tastes and smells. Some things are sweet; some bitter. But
there is one quality in things which is absolutely universal in its
scope, which applies to everything in the universe--corporeal or
incorporeal. All things are _numerable_, and can be counted. Moreover,
it is impossible to conceive a universe in which number is not to be
found. You could easily imagine a universe in which there is no
colour, or no sweet taste, or a universe in which nothing possesses
weight. But you cannot imagine a universe in which there is no number.
This is an inconceivable thought. Upon these grounds we should be
justified in concluding that number is an extremely important aspect
of things, and forms a fundamental pad of the framework of the world.
And it is upon this aspect of things that the Pythagoreans laid
emphasis.
They drew attention to proportion, order, and harmony as the dominant
notes of the universe. Now when we examine the ideas of proportion,
order, and harmony, we shall see that they are closely connected with
number. Proportion, for example, must necessarily {35} be expressible
by the relation of one number to another. Similarly order is
measurable by numbers. When we say that the ranks of a regiment
exhibit order, we mean that they are arranged in such a way that the
soldiers stand at certain regular distances from each other, and these
distances are measurable by numbers of feet or inches. Lastly,
consider the idea of harmony. If, in modern times, we were to say that
the universe is a harmonious whole, we should understand that we are
merely using a metaphor from music. But the Pythagoreans lived in an
age when men were not practised in thought, and they confused cosmical
harmony with musical harmony. They thought that the two things were
the same. Now musical harmony is founded upon numbers, and the
Pythagoreans were the first to discover this. The difference of notes
is due to the different numbers of vibrations of the sounding
instrument. The musical intervals are likewise based upon numerical
proportions. So that since, for the Pythagoreans, the universe is a
musical harmony, it follows that the essential character of the
universe is number. The study of mathematics confirmed the
Pythagoreans in this idea. Arithmetic is the science of numbers, and
all other mathematical sciences are ultimately reducible to numbers.
For instance, in geometry, angles are measured by the number of
degrees.
Now, as already pointed out, considering all these facts, we might
well be justified in concluding that number is a very important aspect
of the universe, and is fundamental in it. But the Pythagoreans went
much further than this. They drew what seems to us the extraordinary
conclusion that the world is _made of_ {36} numbers. At this point,
then, we reach the heart of the Pythagorean philosophy. Just as Thales
had said that the ultimate reality, the first principle of which
things are composed, is water, so now the Pythagoreans teach that the
first principle of things is number. Number is the world-ground, the
stuff out of which the universe is made.
In the detailed application of this principle to the world of things
we have a conglomeration of extraordinary fancies and extravagances.
In the first place, all numbers arise out of the unit. This is the
prime number, every other number being simply so many units. The unit
then is the first in the order of things in the universe. Again,
numbers are divided into odd and even. The universe, said the
Pythagoreans, is composed of pairs of opposites and contradictories,
and the fundamental character of these opposites is that they are
composed of the odd and even. The odd and even, moreover, they
identified with the limited and the unlimited respectively. How this
identification was made seems somewhat doubtful. But it is clearly
connected with the theory of bipartition. An even number can be
divided by two and therefore it does not set a limit to bipartition.
Hence it is unlimited. An odd number cannot be divided by two, and
therefore it sets a limit to bipartition. The limited and the
unlimited become therefore the ultimate principles of the universe.
The Limit is identified with the unit, and this again with the central
fire of the universe. The Limit is first formed and proceeds to draw
more and more of the unlimited towards itself, and to limit it.
Becoming limited, it becomes a definite "something," a thing. So the
formation of the {37} world of things proceeds. The Pythagoreans drew
up a list of ten opposites of which the universe is composed. They are
(1) Limited and unlimited, (2) odd and even, (3) one and many, (4)
right and left, (5) masculine and feminine, (6) rest and motion, (7)
straight and crooked, (8) light and darkness, (9) good and evil, (10)
square and oblong.
With the further development of the number-theory Pythagoreanism
becomes entirely arbitrary and without principle. We hear, for
example, that 1 is the point, 2 is the line, 3 is the plane, 4 is the
solid, 5 physical qualities, 6 animation, 7 intelligence, health,
love, wisdom. There is no principle in all this. Identification of the
different numbers with different things can only be left to the whim
and fancy of the individual. The Pythagoreans disagreed among
themselves as to what number is to be assigned to what thing. For
example, justice, they said, is that which returns equal for equal. If
I do a man an injury, justice ordains that injury should be done to
me, thus giving equal for equal. Justice must, therefore, be a number
which returns equal for equal. Now the only numbers which do this are
square numbers. Four equals two into two, and so returns equal for
equal. Four, then, must be justice. But nine is equally the square of
three. Hence other Pythagoreans identified justice with nine.
According to Philolaus, one of the most prominent Pythagoreans, the
quality of matter depends upon the number of sides of its smallest
particles. Of the five regular solids, three were known to the
Pythagoreans. That matter whose smallest particles are regular
tetrahedra, said Philolaus, is fire. Similarly earth is composed {38}
of cubes, and the universe is identified with the dodecahedron. This
idea was developed further by Plato in the "Timaeus," where we find
all the five regular solids brought into the theory.
The central fire, already mentioned as identified with the unit, is a
characteristic doctrine of the Pythagoreans. Up to this time it had
been believed that the earth is the centre of the universe, and that
everything revolves round it. But with the Pythagoreans the earth
revolves round the central fire. One feels inclined at once to
identify this with the sun. But this is not correct. The sun, like the
earth, revolves round the central fire. We do not see the central fire
because that side of the earth on which we live is perpetually turned
away from it. This involves the theory that the earth revolves round
the central fire in the same period that it takes to rotate upon its
axis. The Pythagoreans were the first to see that the earth is itself
one of the planets, and to shake themselves free from the geocentric
hypothesis. Round the central fire, sometimes mystically called "the
Hearth of the Universe," revolve ten bodies. First is the
"counter-earth," a non-existent body invented by the Pythagoreans,
next comes the earth, then the sun, the moon, the five planets, and
lastly the heaven of the fixed stars. This curious system might have
borne fruit in astronomy. That it did not do so was largely due to the
influence of Aristotle, who discountenanced the theory, and insisted
that the earth is the centre of the universe. But in the end the
Pythagorean view won the day. We know that Copernicus derived the
suggestion of his heliocentric hypothesis from the Pythagoreans.
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The Pythagoreans also taught "The Great Year," probably a period of
10,000 years, in which the world comes into being and passes away,
going in each such period through the same evolution down to the
smallest details.
There is little to be said by way of criticism of the Pythagorean
system. It is entirely crude philosophy. The application of the number
theory issues in a barren and futile arithmetical mysticism. Hegel's
words in this connection are instructive:--
"We may certainly," he says, "feel ourselves prompted to associate the
most general characteristics of thought with the first numbers: saying
one is the simple and immediate, two is difference and mediation, and
three the unity of both these. Such associations however are purely
external; there is nothing in the mere numbers to make them express
these definite thoughts. With every step in this method, the more
arbitrary grows the association of definite numbers with definite
thoughts ... To attach, as do some secret societies of modern times,
importance to all sorts of numbers and figures is, to some extent an
innocent amusement, but it is also a sign of deficiency of
intellectual resource. These numbers, it is said, conceal a profound
meaning, and suggest a deal to think about. But the point in
philosophy is not what you may think but what you do think; and the
genuine air of thought is to be sought in thought itself and not in
arbitrarily selected symbols." [Footnote 3]
[Footnote 3: Hegel's _Smaller Logic_, translated by Wallace, second
edition, page 198.]
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