It is certain that the only hope of retroductive reasoning ever reaching the truth is that there may be some natural tendency toward an agreement between the ideas which suggest themselves to the human mind and those which are concerned in the laws of nature.

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

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

When an image is said to be singular, it is meant that it is absolutely determinate in all respects. Every possible character, or the negative thereof, must be true of such an image.

There is not a single truth of science upon which we ought to bet more than about a million of millions to one.

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

The a priori method is distinguished for its comfortable conclusions. It is the nature of the process to adopt whatever belief weare inclined to, and there are certain flatteries to the vanity of man which we all believe by nature, until we are awakened from our pleasing dream by rough facts.