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.

Every new concept first comes to the mind in a judgment.

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

The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. That is the way I would explain reality.

It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty.

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

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.