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 as-
sert 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 as-
serted 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 means that the lower Ideas must find
their necessity in the highest Idea. If we could see that
the Idea of the Good necessarily involves the other Ideas,
then these other Ideas would be really explained. In other
words, we ought to be able to deduce all the other Ideas
from this one Idea. It ought to be possible to show that,
granted the Idea of the Good, all the other Ideas neces-
sarily follow, that to assume the Good and deny the other
Ideas would be self-contradictory and unthinkable. There
are examples in Plato of the kind of deduction we require.
For example, in the “Parmenides” he showed that the Idea
of the one necessarily involves the Idea of the many, and
vice versa. You cannot think the one without also thinking
the many. This means that the many is deduced from the
one, and the one from the many. Just in the same way, we
ought to be able to deduce the Idea of whiteness from the
Idea of the Good. But this is clearly not possible. You may
analyse the Good as long as you like, you may turn it in
every conceivable direction, but you cannot get whiteness
out of it. The two Ideas do not involve each other. They
are thinkable apart. It is quite possible to think the Good
without thinking whiteness. And it is the same with all the
other Ideas. None of them can be deduced from the Good.And the reason of this is very obvious. Just as the lower
Ideas contain only what is common among the things of a
class, and exclude their differences, so the higher Ideas in-
clude what is common to the Ideas that come under them,
but exclude what is not common. For example, the Idea
of colour contains what white, blue, red, and green, have
in common. But all colours {245} have not whiteness in
common. Green, for example, is not white. Hence the
Idea of colour excludes the Idea of whiteness, and it like-
wise excludes all the Ideas of the other particular colours.
So too the highest Idea of all contains only what all the