Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Nine-tenths of the activities of a modern Government are harmful; therefore the worse they are performed, the better.

What will be the good of the conquest of leisure and health, if no one remembers how to use them?

More cranks take up unfashionable errors than unfashionable truths.

Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.

The fundamental principle in the analysis of propositions containing descriptions is this: Every proposition which we can understand must be composed wholly of constituents with which we are acquainted.

The opposition of instinct and reason is mainly illusory. Instinct, intuition, or insight is what first leads to the beliefs which subsequent reason confirms or confutes; but the confirmation, where it is possible, consists, in the last analysis, of agreement with other beliefs no less instinctive. Reason is a harmonizing, controlling force rather than a creative one. Even in the most purely logical realms, it is insight that first arrives at what is new.