asunder and was becoming transparent. From
this brief notice of the Ionic philosophy, sufficient for our purpose,
let us return to the Pythagorean school, in which, although the faculty
at work is essentially objective, there is a closer consideration of the
analogies between thought and the world, and the ground is more often
retraced, so that theory assumes a more intellectual form.

The Pythagoreans represented the origin of the world as the union of the
two opposite principles of the illimitable and the limited, of the equal
and the unequal. Yet they conceive this to be a primitive union, since
they formulated the supreme principle as equal--unequal (Arist. _Met_.
xii. 7.) They held the infinite to be _the place of the one_. There was
an attraction between the two principles, which was termed the _act of
breathing_; hence the void entered into the world and separated things
from each other. Thus their conception of the world was that of a
concourse of opposite principles. They represented its limits as a unity
and as the true beginning of multiplicity. They regarded the development
of the world as a process of life regulated by the primitive principles
contained in the world; its breath or life depended on the breaking
forth of the infinite void in Uranus, and the time which is termed the
_interval_ of all nature penetrates at once and with the breath into the
world. All therefore emanates from one, and all is at the same time
governed by one supreme power. Number is everything, and is the essence
of things, but the _triad_ includes all number, since it contains the
beginning, middle, and end. Everything is derived from the primitive
_one_ and from the principal number; and since this number in breathing
its vital evolution into the void is divided into many units, everything
is derived from the multiplicity of these units or numbers.

Since, by his idea of the source of universal order, Pythagoras partly
accepted the theocosmic monad as the final and necessary root of all
life, and of all that is knowable, he could not fail to see the
convertibility of the unit into the Being. But if the unit must always
precede the manifold, there is a first unit from which all the others
proceed; if this first and eternal unit is at the same time the absolute
being, it follows that number and the world have a common origin and a
common essence, and that the intrinsic causes and possible combinations
of number are virtually accom