The doctrine (of) maintaining that the language of daily life, with words used in their ordinary meanings, suffices for philosophy . . . I find myself totally unable to accept . . . . Because it makes almost inevitable the perpetuation amongst philosophers of the muddle-headedness they have taken over from common sense.

A drop of water is not immortal; it can be resolved into oxygen and hydrogen. If, therefore, a drop of water were to maintain that it had a quality of aqueousness which would survive its dissolution we should be inclined to be skeptical. In like manner we know that the brain is not immortal.

It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible.

Any philosophy worth taking seriously would have to be built upon a firm foundation of unyielding despair.

The power of thought, the vast regions it can master.

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.

But courage in fighting is by no means the only form, nor perhaps even the most important. There is courage in facing poverty, courage in facing derision, courage in facing the hostility of one's own herd. In these, the bravest soldiers are often lamentably deficient. And above all there is the courage to think calmly and rationally in the face of danger, and to control the impulse of panic fear or panic rage.