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

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

It is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.

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

True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.

Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler-such penetrating minds as Descartes and Pascal-were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.

It is the man of science, eager to have his every opinion regenerated, his every idea rationalized, by drinking at the fountain of fact, and devoting all the energies of his life to the cult of truth, not as he understands it, but as he does not yet understand it, that ought properly to be called a philosopher.