We cannot begin with complete doubt.

There is a kink in my damned brain that prevents me from thinking as other people think.

Three elements go to make up an idea. The first is its intrinsic quality as a feeling. The second is the energy with which it affects other ideas, an energy which is infinite in the here-and-nowness of immediate sensation, finite and relative in the recency of the past. The third element is the tendency of an idea to bring along other ideas with it.

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.

It is a common observation that those who dwell continually upon their expectations are apt to become oblivious to the requirements of their actual situation.

Third, consider the insistency of an idea. The insistency of a past idea with reference to the present is a quantity which is less, the further back that past idea is, and rises to infinity as the past idea is brought up into coincidence with the present.

Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus "theoretically," is to uselanguage in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.