We, one and all of us, have an instinct to pray; and this fact constitutes an invitation from God to pray.

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

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

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

Mathematics is purely hypothetical: it produces nothing but conditional propositions.

In all the works on pedagogy that ever I read — and they have been many, big, and heavy — I don't remember that any one has advocated a system of teaching by practical jokes, mostly cruel. That, however, describes the method of our great teacher, Experience.

A quality is something capable of being completely embodied. A law never can be embodied in its character as a law except by determining a habit. A quality is how something may or might have been. A law is how an endless future must continue to be.