The ultimate metaphysical ground is the creative advance into novelty.

Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.

I regret that it has been necessary for me in this lecture to administer a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are.

Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are cavalry charges in a battle - they are limited in number, they require fresh horses, and must only be made at decisive moments.

There will be some fundamental assumptions which adherents of all the variant systems within the epoch unconsciously presuppose. Such assumptions appear so obvious that people do not know what they are assuming because no other way of putting things has ever occurred to them. With these assumptions a certain limited number of types of philosophic systems are possible, and this group of systems constitutes the philosophy of the epoch.

No reason can be given for the nature of God, because that nature is the ground of rationality.

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