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.
There is more evidence to prove that saltness [of the sea] is due to the admixture of some substance, besides that which we have adduced. Make a vessel of wax and put it in the sea, fastening its mouth in such a way as to prevent any water getting in. Then the water that percolates through the wax sides of the vessel is sweet, the earthy stuff, the admixture of which makes the water salt, being separated off as it were by a filter.
When we look at the matter from another point of view, great caution would seem to be required. For the habit of lightly changing the laws is an evil, and, when the advantage is small, some errors both of lawgivers and rulers had better be left; the citizen will not gain so much by making the change as he will lose by the habit of disobedience.
The soul of animals is characterized by two faculties, (a) the faculty of discrimination which is the work of thought and sense, and (b) the faculty of originating local movement.
Once more: there are three offices according to whose directions the highest magistrates are chosen in certain states - guardians of the law, probuli, councilors - of these, the guardians of the law are an aristocratical, the probuli an oligarchical, the council a democratical institution.
Again, it is possible to fail in many ways (for evil belongs to the class of the unlimited and good to that of the limited), while to succeed is possible only in one way (for which reason also one is easy and the other difficult—to miss the mark easy, to hit it difficult); for these reasons also, then, excess and defect are characteristic of vice, and the mean of virtue; For men are good in but one way, but bad in many.
In the case of some people, not even if we had the most accurate scientific knowledge, would it be easy to persuade them were we to address them through the medium of that knowledge; for a scientific discourse, it is the privilege of education to appreciate, and it is impossible that this should extend to the multitude.