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.

In the first place a philosophical proposition must be general. It must not deal specially with things on the surface of the earth, or within the solar system, or with any other portion of space and time. . . . This brings us to a second characteristic of philosophical propositions, namely that they must be a priori. A philosophical proposition must be such as can neither be proved nor disproved by empirical evidence. . . . Philosophy, if what has been said is correct, becomes indistinguishable from logic as that word has now come to be used.

Few people can be happy unless they hate some other person, nation, or creed.

When all experts agree, you need to watch out.

To avoid the various foolish opinions to which mankind are prone, no superhuman genius is required. A few simple rules will keep you, not from all error, but from silly error.

A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.

Science can teach us, and I think our hearts can teach us, no longer to look around for imaginary supporters, no longer to invent allies in the sky, but rather to look to our own efforts here below to make the world a fit place to live.