eal 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 themselves,
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 element 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 object 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 exhaustive and systematic.

Plato's actual performance of the supreme task of dialectic, the
classification and arrangement of all Ideas, is not great.