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.