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

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

We may say that feelings have two kinds of intensity. One is the intensity of the feeling itself, by which loud sounds are distinguished from faint ones, luminous colors from dark ones, highly chromatic colors from almost neutral tints, etc. The other is the intensity of consciousness that lays hold of the feeling, which makes the ticking of a watch actually heard infinitely more vivid than a cannon shot remembered to have been heard a few minutes ago.

I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way.But in this water there are countless objects at different depths; and certain influences will give certain kinds of those objects an upward influence which may be intense enough and continue long enough to bring them into the upper visible layer. After the impulse ceases they commence to sink downwards.

Notwithstanding all that has been discovered since Newton's time, his saying that we are little children picking up pretty pebbles on the beach while the whole ocean lies before us unexplored remains substantially as true as ever, and will do so though we shovel up the pebbles by steam shovels and carry them off in carloads.

Some think to avoid the influence of metaphysical errors, by paying no attention to metaphysics; but experience shows that these men beyond all others are held in an iron vice of metaphysical theory, because by theories that they have never called in question.

All the progress we have made in philosophy ... is the result of that methodical skepticism which is the element of human freedom.