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

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

We feel much happier and more secure when we think we know precisely what to do, no matter what happens, then when we have lost our way and do not know where to turn.

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.

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.

No simplicity of mind, no obscurity of station, can escape the universal duty of questioning all that we believe.

There is no scientific discoverer, no poet, no painter, no musician, who will not tell you that he found ready made his discovery or poem or picture — that it came to him from outside, and that he did not consciously create it from within.