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When the training in music and gymnastic is completed, there

follows the first stage of active and public life. But soon

education is to begin again from a new point of view. In the

interval between the Fourth and Seventh Books we have discussed

the nature of knowledge, and have thence been led to form a

higher conception of what was required of us. For true knowledge,

according to Plato, is of abstractions, and has to do, not with

particulars or individuals, but with universals only; not with

the beauties of poetry, but with the ideas of philosophy. And the

great aim of education is the cultivation of the habit of

abstraction. This is to be acquired through the study of the

mathematical sciences. They alone are capable of giving ideas of

relation, and of arousing the dormant energies of thought.