l, and was developed by successive leaders
of the school. The doctrine, therefore, is generally spoken of as
that, not of Pythagoras, but of the Pythagoreans. Nor can we fix for
certain on one fundamental conception, upon which the whole structure
of their doctrine was built.

[52]

One dictum we may start with because of its analogies with what has
been said of the earlier {24} philosophies. The universe, said the
Pythagoreans, was constituted of _indefinites_ and _definers_, _i.e._
of that which has no character, but has infinite capacities of taking a
character; and secondly, of things or forces which impose a character
upon this. Out of the combination of these two elements or principles
all knowable [53] existences come into being. "All things," they said,
"as known have _Number_; and this number has two natures, the Odd and
the Even; the known thing is the Odd-Even or union of the two."

[66]

By a curious and somewhat fanciful development of this conception the
Pythagoreans drew up two parallel columns of antithetical principles in
nature, ten in each, thus:--

Definite Indefinite
Odd Even
One Many
Right Left
Male Female
Steadfast Moving
Straight Bent
Light Dark
Good Evil
Four Square Irregular

Looking down these two lists we shall see that the first covers various
aspects of what is conceived as the ordering, defining, formative
principle in nature; and that the second in like manner comprises
various {25} aspects of the unordered, neutral, passive, or
disorganised element or principle; the first, to adopt a later method
of expression, is _Form_, the second _Matter_. How this antithesis was
worked out by Plato and Aristotle we shall see later on.

[54]

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