From Chapter II., Science and Religion
It was this, no doubt, that led Pythagoras to say all
things were numbers. We shall see that, at a later date, the
Pythagoreans identified these numbers with geometrical
figures; but the mere fact that they called them "numbers,"
taken in connexion with what we are told about the method of
Eurytos, is sufficient to show this was not the original sense
of the doctrine. It is enough to suppose that Pythagoras
reasoned somewhat as follows. If musical sounds can be reduced
to numbers, why not everything else? There are many likenesses
to number in things, and it may well be that a lucky
experiment, like that by which the octave was discovered, will
reveal their true numerical nature. The Neopythagorean
writers, going back in this as in other matters to the
earliest tradition of the school, indulge their fancy in
tracing out analogies between things and numbers in endless
variety; but we are fortunately dispensed from following them
in these vagaries. Aristotle tells us distinctly that the
Pythagoreans explained only a few things by means of numbers,91
which means that Pythagoras himself left no developed doctrine
on the subject, while the Pythagoreans of the fifth century
did not care to add anything of the sort to the tradition.
Aristotle does imply, however, that according to them the
"right time" (καιρός) was seven, justice was four, and
marriage three. These identifications, with a few others like
them, we may safely refer to Pythagoras or his immediate
successors; but we must not attach too much importance to
them. We must start, not from them, but from any statements we
can find that present points of contact with the teaching of
the Milesian school. These, we may fairly infer, belong to the
system in its most primitive form.
91. Arist. Met. M, 4. 1078 b 21 (R. P. 78). The Theologumena Arithmetica is full of such fancies
(R. P. 78 a). Alexander, in Met. p. 38, 8, gives a few definitions which may be old (R. P. 78 c).