The essence of belief is the establishment of a habit.

There is not a single truth of science upon which we ought to bet more than about a million of millions to one.

It is not knowing, but the love of learning, that characterizes the scientific man.

True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.

Do you call it doubting to write down on a piece of paper that you doubt? If so, doubt has nothing to do with any serious business. But do not make believe; if pedantry has not eaten all the reality out of you, recognize, as you must, that there is much that you do not doubt, in the least. Now that which you do not at all doubt, you must and do regard as infallible, absolute truth.

We shall do better to abandon the whole attempt to learn the truthunless we can trust to the human mind's having such a powerof guessing right that before very many hypotheses shall have been tried, intelligent guessing may be expected to lead us to one which will support all tests, leaving the vast majority of possible hypotheses unexamined.

Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus "theoretically," is to uselanguage in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.