The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilised of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.

The only use of a knowledge of the past is to equip us for the present. The present contains all that there is. It is holy ground; for it is the past, and it is the future.

Error is the price we pay for progress.

Vigorous societies harbor a certain extravagance of objectives, so that men wander beyond the safe provision of personal gratifications.

The fixed person for the fixed duties who in older societies was such a godsend, in future will be a public danger.

The Universe is vast. Nothing is more curious than the self-satisfied dogmatism with which mankind at each period of its history cherishes the delusion of the finality of existing modes of knowledge. Skeptics and believers are alike. At this moment scientists and skeptics are the leading dogmatists. Advance in detail is admitted; fundamental novelty is barred. This dogmatic common sense is the death of philosophic adventure.

An open mind is all very well in its way, but it ought not to be so open that there is no keeping anything in or out of it.