The universe ought to be presumed too vast to have any character.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

The woof and warp of all thought and all research is symbols, and the life of thought and science is the life inherent in symbols; so that it is wrong to say that a good language is important to good thought, merely; for it is the essence of it.

Over against any cognition, there is an unknown but knowable reality; but over against all possible cognition, there is only the self-contradictory. In short, cognizability (in its widest sense) and being are not merely metaphysically the same, but are synonymous terms.

There is not a single truth of science upon which we ought to bet more than about a million of millions to one.

It is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.

All the evolution we know of proceeds from the vague to the definite.