One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.

What hunger is in relation to food, zest is in relation to life.

Philosophy, from the earliest times, has made greater claims, and achieved fewer results, than any other branch of learning.

The world in which we live can be understood as a result of muddle and accident; but if it is the outcome of deliberate purpose, the purpose must have been that of a fiend. For my part, I find accident a less painful and more plausible hypothesis.

There have been poverty, pestilence, and famine, which were due to man's inadequate mastery of nature. There have been wars, oppressions and tortures which have been due to men's hostility to their fellow men.

Philosophy seems to me on the whole a rather hopeless business.

Men have physical needs, and they have emotions. While physical needs are unsatisfied, they take first place; but when they are satisfied, emotions unconnected with them become important in deciding whether a man is to be happy or unhappy.