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.

Mathematics is purely hypothetical: it produces nothing but conditional propositions.

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

Fate then is that necessity by which a certain result will surely be brought to pass according to the natural course of events however we may vary the particular circumstances which precede the event.

It is... easy to be certain. One has only to be sufficiently vague.

Bad reasoning as well as good reasoning is possible; and this fact is the foundation of the practical side of logic.

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.