Error is the price we pay for progress.

The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.

In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.

There is no nature at an instant.

To come very near to a true theory, and to grasp its precise application, are two different things, as the history of science teaches us. Everything of importance has been said before by someone who did not discover it.

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

The importance of an individual thinker owes something to chance. For it depends upon the fate of his ideas in the minds of his successors.