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.

Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.

The one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.

The essence of belief is the establishment of a habit; and different beliefs are distinguished by the different modes of action to which they give rise.

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

The essence of belief is the establishment of a habit.

It is... easy to be certain. One has only to be sufficiently vague.