we
must surely first show that reason itself is rational, or rather, to
be more accurate, that _our conception_ of reason is rational. There
must not be any mere inexplicable facts, any mysteries, any dark
places, in our notion of reason. It must be penetrated through and
through by the light of reason. It must be absolutely transparent,
crystalline. How can we hope to explain the world, if our very first
principle itself contains irrationalities?

Each concept then must prove itself rational. And this means that it
must be a necessary concept. A necessary proposition, we saw, is one,
such as that two and two equal four, the opposite of which is
unthinkable. So for Plato's Ideas to be really necessary it ought to
be logically impossible for us to deny their {243} reality. It ought
to be impossible to think the world at all without these concepts. To
attempt to deny them ought to be shown to be self-contradictory. They
ought to be so necessarily involved in reason that thought without
them becomes impossible. Clearly this is the same as saying that the
Ideas must not be mere ultimate inexplicable facts. Of such a fact we
assert merely that it is so, but we cannot see any reason for it. To
see a reason for it is the same as seeing its necessity, seeing not
merely that it is so, but that it must be so.

Now Plato's Ideas are not of this necessary kind. There is, we are
told, an Idea of whiteness. But why should there be such an Idea? It
is a mere fact. It is not a necessity. We can think the world quite
well without the Idea of whiteness. The world, so far as we can see,
could get on perfectly well without either white objects or the Idea
of whiteness. To deny its reality leads to no self-contradictions. Put
it in another way. There are certainly white objects in the world. We
demand that these, among other things, be explained. Plato tells us,
by way of explanation, that there are white objects because there is
an Idea of whiteness. But in that case why is there an Idea of
whiteness? We cannot see. There is no reason. There is no necessity in
this. The same thing applies to all the other Ideas. They are not
rational concepts. They are not a part of the system of reason.

But at this point, perhaps, a glimmer of hope dawns upon us. We ask
the reason for these Ideas. Has not Plato asserted that the ultimate
reason and ground of all the lower Ideas will be found in the supreme
Idea of {244} the Good? Now if this is so, it