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.

The pragmatist knows that doubt is an art which hs to be acquired with difficulty.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

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.

The a priori method is distinguished for its comfortable conclusions. It is the nature of the process to adopt whatever belief weare inclined to, and there are certain flatteries to the vanity of man which we all believe by nature, until we are awakened from our pleasing dream by rough facts.

We do not really think, we are barely conscious, until something goes wrong.

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