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

Do you call it doubting to write down on a piece of paper that you doubt? If so, doubt has nothing to do with any serious business. But do not make believe; if pedantry has not eaten all the reality out of you, recognize, as you must, that there is much that you do not doubt, in the least. Now that which you do not at all doubt, you must and do regard as infallible, absolute truth.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

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

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

One will meet, for example, the virtual assumption that what is relative to thought cannot be real. But why not, exactly? Red is relative to sight, but the fact that this or that is in that relation to vision that we call being red is not itself relative to sight; it is a real fact.

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.