All the followers of science are fully persuaded that the processes of investigation, if only pushed far enough, will give one certain solution to each question to which they can be applied.... This great law is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate is what we mean by the truth, and the object represented in this opinion is the real.

No general description of the mode of advance of human knowledge can be just which leaves out of account the social aspect of knowledge. That is of its very essence. What a thing society is! The workingman, with his trade union, knows that. Men and women moving in polite society understand it, still better. But Bohemians, like me, whose work is done in solitude, are apt to forget that not only is a man as a whole little better than a brute in solitude, but also that everything that bears any important meaning to him must receive its interpretation from social considerations.

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.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

For example, there are numbers of chemists who occupy themselves exclusively with the study of dyestuffs. They discover facts that are useful to scientific chemistry; but they do not rank as genuine scientific men. The genuine scientific chemist cares just as much to learn about erbium-the extreme rarity of which renders it commercially unimportant-as he does about iron. He is more eager to learn about erbium if the knowledge of it would do more to complete his conception of the Periodic Law, which expresses the mutual relations of the elements.

The a priori method is distinguished for its comfortable conclusions. It is the nature of the process to adopt whatever belief weare inclined to, and there are certain flatteries to the vanity of man which we all believe by nature, until we are awakened from our pleasing dream by rough facts.

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.