We shall do better to abandon the whole attempt to learn the truthunless we can trust to the human mind's having such a powerof guessing right that before very many hypotheses shall have been tried, intelligent guessing may be expected to lead us to one which will support all tests, leaving the vast majority of possible hypotheses unexamined.

All the progress we have made in philosophy ... is the result of that methodical skepticism which is the element of human freedom.

Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus "theoretically," is to uselanguage in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.

A true proposition is a proposition belief which would never lead to such disappointment so long as the proposition is not understood otherwise than it was intended.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.

And what, then, is belief? It is the demi-cadence which closes a musical phrase in the symphony of our intellectual life.