hthly, the Ideas are outside space and time. That they are outside
space is obvious. If they were in space, they would have to be in some
particular place. We ought to be able to find them somewhere. A
telescope or microscope might reveal them. And this would mean that
they are individual and particular things, and not universals at all.
They are also outside time. For they are unchangeable and eternal; and
this does not mean that they are the same at all times. If that were
so, their immutability would be a matter of experience, and not of
reason. We should, so to speak, have to look at them from time to time
to see that they had not really changed. But their immutability is not
a matter of experience, but is known to thought. It is not merely that
they are always the same in time, but that time is irrelevant to them.
They are timeless. In the "Timaeus" eternity is distinguished from
infinite time. The latter is described as a mere copy of eternity.

Ninthly, the Ideas are rational, that is to say, they are apprehended
through reason. The finding of the common element in the manifold is
the work of inductive {191} reason, and through this alone is
knowledge of the Ideas possible. This should be noted by those persons
who imagine that Plato was some sort of benevolent mystic. The
imperishable One, the absolute reality, is apprehended, not by
intuition, or in any kind of mystic ecstasy, but only by rational
cognition and laborious thought.

Lastly, towards the end of his life, Plato identified the Ideas with
the Pythagorean numbers. We know this from Aristotle, but it is not
mentioned in the dialogues of Plato himself. It appears to have been a
theory adopted in old age, and set forth in the lectures which
Aristotle attended. It is a retrograde step, and tends to degrade the
great and lucid idealism of Plato into a mathematical mysticism. In
this, as in other respects, the influence of the Pythagoreans upon
Plato was harmful.

It results from this whole theory of Ideas that there are two sources
of human experience, sense-perception and reason. Sense-perception has
for its object the world of sense; reason has for its object the
Ideas. The world of sense has all the opposite characteristics to the
Ideas. The Ideas are absolute reality, absolute Being. Objects of
sense are absolute unreality, not-being, except in so far as the Ideas
are in them. Whatever reality they have they owe to the Ideas. There
is in Plato's syst