In considering irregular appearances, there are certain very natural mistakes which must be avoided.

Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians.

Zeno was concerned with three problems... These are the problem of the infinitesimal, the infinite, and continuity.

There may be no good reasons for very many opinions that are held with passion.

In regard to the past, where contemplation is not obscured by desire and the need for action, we see, more clearly than in the lives about us, the value for good and evil, of the aims men have pursued and the means they have adopted. It is good, from time to time, to view the present as already past, and to examine what elements it contains that will add to the world's store of permanent possessions, that will live and give life when we and all our generation have perished.

As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one can prove that there is not a God. On the other hand, if I am to convey the right impression to the ordinary man in the street I think that I ought to say that I am an Atheist, because, when I say that I cannot prove that there is not a God, I ought to add equally that I cannot prove that there are not the Homeric gods.

There are three ways of securing a society that shall be stable as regards population. The first is that of birth control, the second that of infanticide or really destructive wars, and the third that of general misery except for a powerful minority.