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

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Religion is what a person does in his solitariness.

The worth of men consists in their liability to persuasion. They can persuade and can be persuaded by the disclosure of alternatives, the better and the worse. Civilization is the maintenance of social order, by its own inherent persuasiveness as embodying the nobler alternative. The recourse to force, however, unavoidable, is a disclosure of the failure of civilization, either in the general society or in a remnant of individuals. Thus in a live civilization there is always an element of unrest.

Art is the imposing of a pattern on experience.

Thus the negative perception is the triumph of consciousness.

It is a profoundly erroneous truism, repeated by all copy books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.