We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.

The aim of scientific thought, then, is to apply past experience to new circumstances; the instrument is an observed uniformity in the course of events. By the use of this instrument it gives us information transcending our experience, it enables us to infer things that we have not seen from things that we have seen; and the evidence for the truth of that information depends on our supposing that the uniformity holds good beyond our experience.

Thought is powerless, except it make something outside of itself: the thought which conquers the world is not contemplative but active.

Namely, we have no right to believe a thing true because everybody says so unless there are good grounds for believing that some one person at least has the means of knowing what is true, and is speaking the truth so far as he knows it.

If a man, holding a belief which he was taught in childhood or persuaded of afterwards, keeps down and pushes away any doubts which arise about it in his mind, purposely avoids the reading of books and the company of men that call in question or discuss it, and regards as impious those questions which cannot easily be asked without disturbing it - the life of that man is one long sin against mankind.

He who truly believes that which prompts him to an action has looked upon the action to lust after it, he has committed it already in his heart.

We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.