Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Between friends there is no need for justice, but people who are just still need the quality of friendship; and indeed friendliness is considered to be justice in the fullest sense.
What we know is not capable of being otherwise; of things capable of being otherwise we do not know, when they have passed outsideour observation, whether they exist or not. Therefore the object of knowledge is of necessity. Therefore it is eternal; for things that are of necessity in the unqualified sense are all eternal; and things that are eternal are ungenerated and imperishable.
In the many forms of government which have sprung up there has always been an acknowledgement of justice and proportionate equality, although mankind fail in attaining them, as indeed I have already explained. Democracy, for example, arises out of the notion that those who are equal in any respect are equal in all respects; because men are equally free, they claim to be absolutely equal.
The attainment of truth is then the function of both the intellectual parts of the soul. Therefore their respective virtues are those dispositions which will best qualify them to attain truth.
There are three qualifications required in those who have to fill the highest offices, - (1) first of all, loyalty to the established constitution; (2) the greatest administrative capacity; (3) virtue and justice of the kind proper to each form of government.