one of the world's greatest persons, but he wrote nothing, and it is
hard to say how much of the doctrine we know as Pythagorean is due to
the founder of the society and how much is later development. It is
also hard to say how much of what we are told about the life of
Pythagoras is trustworthy; for a mass of legend gathered around his
name at an early date. Sometimes he is represented as a man of
science, and sometimes as a preacher of mystic doctrines, and we might
be tempted to regard one or other of those characters as alone
historical. The truth is that there is no need to reject either of the
traditional views. The union of mathematical genius and mysticism is
common enough. Originally from Samos, Pythagoras founded at Kroton (in
southern Italy) a society which was at once a religious community and
a scientific school. Such a body was bound to excite jealousy and
mistrust, and we hear of many struggles. Pythagoras himself had to
flee from Kroton to Metapontion, where he died.
It is stated that he was a disciple of Anaximander, his astronomy was
the natural development of Anaximander's. Also, the way in which the
Pythagorean geometry developed also bears witness to its descent from
that of Miletos. The great problem at this date was the duplication of
the square, a problem which gave rise to the theorem of the square on
the hypotenuse, commonly known still as the Pythagorean proposition
(Euclid, I. 47). If we were right in assuming that Thales worked with
the old 3:4:5 triangle, the connection is obvious.
Pythagoras argued that there are three kinds of men, just as there are
three classes of strangers who come to the Olympic Games. The lowest
consists of those who come to buy and sell, and next above them are
those who come to compete. Best of all are those who simply come to
look on. Men may be classified accordingly as lovers of wisdom, lovers
of honor, and lovers of gain. That seems to imply the doctrine of the
tripartite soul, which is also attributed to the early Pythagoreans on
good authority, though it is common now to ascribe it to Plato. There
are, however, clear references to it before his time, and it agrees
much better with the general outlook of the Pythagoreans. The
comparison of human life to a gathering like the Games was often
repeated in later days. Pythagoras also taught the doctrine of Rebirth
or transmigration, which we may have learned from the contemporary
Orphics. Xenophanes made fun of him for pretending to recognize the
voice of a departed friend in the howls of a beaten dog. Empedocles
seems to be referring to him when he speaks of a man who could
remember what happened ten or twenty generations before. It was on
this that the doctrine of Recollection, which plays so great a part in
Plato, was based. The things we perceive with the senses, Plato
argues, remind us of things we knew when the soul was out of the body
and could perceive reality directly.
There is more difficulty about the cosmology of Pythagoras. Hardly any
school ever professed such reverence for its founder's authority as
the Pythagoreans. 'The Master said so' was their watchword. On the
other hand, few schools have shown so much capacity for progress and
for adapting themselves to new conditions. Pythagoras started from the
cosmical system of Anaximenes. Aristotle tells us that the
Pythagoreans represented the world as inhaling 'air' form the
boundless mass outside it, and this 'air' is identified with 'the
unlimited'. When, however, we come to the process by which things are
developed out of the 'unlimited', we observe a great change. We hear
nothing more of 'separating out' or even of rarefaction and
condensation. Instead of that we have the theory that what gives form
to the Unlimited is the Limit. That is the great contribution of
Pythagoras to philosophy, and we must try to understand it. Now the
function of the Limit is usually illustrated from the arts of music
and medicine, and we have seen how important these two arts were for
Pythagoreans, so it is natural to infer that the key to its meaning is
to be found in them.
It may be taken as certain that Pythagoras himself discovered the
numerical ratios which determine the concordant intervals of the
musical scale. Similar to musical intervals, in medicine there are
opposites, such as the hot and the cold, the wet and the dry, and it
is the business of the physician to produce a proper 'blend' of these
in the human body. In a well-known passage of Plato's Phaedo (86 b) we
are told by Simmias that the Pythagoreans held the body to be strung
like an instrument to a certain pitch, hot and cold, wet and dry
taking the place of high and low in music. Musical tuning and health
are alike means arising from the application of Limit to the
Unlimited. It was natural for Pythagoras to look for something of the
same kind in the world at large. Briefly stated, the doctrine of
Pythagoras was that all things are numbers. In certain fundamental
cases, the early Pythagoreans represented numbers and explained their
properties by means of dots arranged in certain 'figures' or patterns.
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