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 necessarily 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 include 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 likewise excludes all the Ideas of the
other particular colours. So too the highest Idea of all contains only
what all the Ideas agree in, but all the rest falls outside it. Thus
the Idea of whiteness is perfect in its kind. And as all Ideas are
likewise perfect, the highest Idea is that in which they all agree,
namely, perfection itself. But this means that the perfection of the
Idea of whiteness is contained in the supreme Idea, but its specific
character in which it differs from other Ideas is excluded. Its
specific character is just its whiteness. Thus the perfection of
whiteness is contained in the Good, but its whiteness is not.
Conse