While, in a sense, then, even the indefinite has number, inasmuch as it is
capable of having number or order imposed upon it (and only in so far as it
has this imposed upon it, does it become knowable or intelligible), yet, as
a positive factor, Number belongs only to the first class; as such it is the
source of all knowledge and of all good. In reality the Pythagoreans had not
got any further by this representation of nature than was reached, for
example, by Anaximander,
and still more definitely by Heraclitus, when they posited an Indefinite or Infinite principle in
nature which by the clash of innate antagonisms developed into a knowable
universe. But one can easily imagine that once the idea of Number became
associated with that of the knowable in things, a wide field of detailed
development and experiment, so to speak, in the arcana of nature, seemed to
be opened. Every arithmetical or geometrical theorem became in this view
another window giving light into the secret heart of things. Number became a
kind of god, a revealer; and the philosophy of number a kind of religion or
mystery. And this is why the second grade of disciples were called
Mathematicians; mathematics was the essential preparation for and initiation
into philosophy.
Whether that which truly exists was actually identical with Number or
Numbers, or whether it was something different from Number, but had a
certain relation to Number; whether if there were such a relation, this was
merely a relation of analogy or of conformability, or whether Number were
something actually embodied in that which truly exists—these were
speculative questions which were variously answered by various teachers, and
which probably interested the later more than the earlier leaders of the
school.
A History of Greek Philosophy /
PYTHAGORAS AND THE PYTHAGOREANS
