is on the level of sensation, and not of thought. He was aware that
there was a distinction between the infinitely great and the infinitely
small, but he would have equally denied the claim of either to true
existence. Of that positive infinity, or infinite reality, which we
attribute to God, he had no conception.

The Greek conception of the infinite would be more truly described, in
our way of speaking, as the indefinite. To us, the notion of infinity
is subsequent rather than prior to the finite, expressing not absolute
vacancy or negation, but only the removal of limit or restraint, which
we suppose to exist not before but after we have already set bounds to
thought and matter, and divided them after their kinds. From different
points of view, either the finite or infinite may be looked upon
respectively both as positive and negative (compare 'Omnis determinatio
est negatio')' and the conception of the one determines that of the
other. The Greeks and the moderns seem to be nearly at the opposite
poles in their manner of regarding them. And both are surprised when
they make the discovery, as Plato has done in the Sophist, how large an
element negation forms in the framework of their thoughts.

2, 3. The finite element which mingles with and regulates the infinite
is best expressed to us by the word 'law.' It is that which measures all
things and assigns to them their limit; which preserves them in their
natural state, and brings them within the sphere of human cognition.
This is described by the terms harmony, health, order, perfection, and
the like. All things, in as far as they are good, even pleasures, which
are for the most part indefinite, partake of this element. We should be
wrong in attributing to Plato the conception of laws of nature derived
from observation and experiment. And yet he has as intense a conviction
as any modern philosopher that nature does not proceed by chance. But
observing that the wonderful construction of number and figure, which he
had within himself, and which seemed to be prior to himself, explained
a part of the phenomena of the external world, he extended their
principles to the whole, finding in them the true type both of human
life and of the order of nature.

Two other points may be noticed respecting the third class. First, that
Plato seems to be unconscious of any interval or chasm which separates
the finite from the infinite. The one is in various ways and degrees
working i