in one supreme Idea, which is the highest expression of its
unity. Moreover, each separate Idea is, in the same way, a
many in one. It is one in regard to itself. That is to say, if
we ignore its relations to other Ideas, it is, in itself, single.
But as it has also many relations to other Ideas, it is, in
this way, a multiplicity.
Every Idea is likewise a Being which contains not-being.
For each Idea combines with some Ideas and not with oth-
ers. Thus the Idea of corporeal body combines both with
the Idea of rest and that of motion. {199} But the Ideas
of rest and motion will not combine with each other. The
Idea of rest, therefore, is Being in regard to itself, not-being
in regard to the Idea of motion, for the being of rest is the
not-being of motion. All Ideas are Being in regard to them-
selves, and not-being in regard to all those other Ideas with
which they do not combine.
In this way there arises a science of Ideas which is called
dialectic. This word is sometimes used as identical with
the phrase, “theory of Ideas.” But it is also used, in a
narrower sense, to mean the science which has to do with
the knowledge of which Ideas will combine and which not.
Dialectic is the correct joining and disjoining of Ideas. It
is the knowledge of the relations of all the Ideas to each
other.
The attainment of this knowledge is, in Plato’s opinion, the
chief problem of philosophy. To know all the Ideas, each
in itself and in its relations to other Ideas, is the supreme
task. This involves two steps. The first is the formation of
concepts. Its object is to know each Idea separately, and its
procedure is by inductive reason to find the common ele-
ment in which the many individual objects participate. The
second step consists in the knowledge of the inter-relation
of Ideas, and involves the two processes of classification and
division. Classification and division both have for their ob-
ject to arrange the lower Ideas under the proper higher
Ideas, but they do this in opposite ways. One may begin
with the lower Ideas, such as redness, whiteness,etc., and
range them under their higher Idea, that of colour. This
is classification. Or one may begin with the higher Idea,
colour, and divide it into the lower Ideas, red, white, {200}
etc. Classification proceeds from below upwards. Division
proceeds from above downwards. Most of the examples
of division which Plato gives are divisions by dichotomy.
We may either divide colour straight away into red, blue,
white,etc.; or we may divide each class into two sub-classes.
Thus colour will be divided into red and not-red, not-red
into white and not-white, not-white into blue and not-blue,
and so on. This latter process is division by dichotomy, and
Plato prefers it because, though it is tedious, it is very ex-
haustive and systematic.Plato’s actual performance of the supreme task of dialectic,
the classification and arrangement of all Ideas, is not great.
He has made no attempt to complete it. All he has done
is to give us numerous examples. And this is, in reality, all
that can be expected, for the number of Ideas is obviously
infinite, and therefore the task of arranging them cannot
be completed. There is, however, one important defect in
the dialectic, which Plato ought certainly to have remedied.
The supreme Idea, he tells us, is the Good. This, as being