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.
For knowing is spoken of in three ways: it may be either universal knowledge or knowledge proper to the matter in hand or actualising such knowledge; consequently three kinds of error also are possible.
The only thing that one really knows about human nature is that it changes. Change is the one quality we can predicate of it. The systems that fail are those that rely on the permanency of human nature, and not on its growth and development. The error of Louis XIV was that he thought human nature would always be the same. The result of his error was the French Revolution. It was an admirable result.
What is this self-inside us, this silent observer, severe and speechless critic, who can terrorize us, and urge us onto futile activity, and in the end, judge us still more severely for the errors into which his own reproaches drove us?
There is nothing grand or noble in having the use of a slave, in so far as he is a slave; or in issuing commands about necessary things. But it is an error to suppose that every sort of rule is despotic like that of a master over slaves, for there is as great a difference between the rule over freemen and the rule over slaves as there is between slavery by nature and freedom by nature . .
A collection of errors does not make a truth: quality cannot stem from quantity – a value is not a weight. The reasons of the majority cannot be taken as good reasons.