If we are to define science, ... it does not consist so much in knowing, nor even in "organized knowledge," as it does in diligent inquiry into truth for truth's sake, without any sort of axe to grind, nor for the sake of the delight of contemplating it, but from an impulse to penetrate into the reason of things.

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

Generality is, indeed, an indispensable ingredient of reality; for mere individual existence or actuality without any regularity whatever is a nullity. Chaos is pure nothing.

The essence of belief is the establishment of a habit.

Whenever a man acts purposively, he acts under a belief in some experimental phenomenon. Consequently, the sum of the experimental phenomena that a proposition implies makes up its entire bearing upon human conduct.

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

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