If an opinion can eventually go to the determination of a practical belief, it, in so far, becomes itself a practical belief; and every proposition that is not pure metaphysical jargon and chatter must have some possible bearing upon practice.

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

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.

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

...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.

The universe ought to be presumed too vast to have any character.

This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.