Axioms in philosophy are not axioms until they are proved upon our pulses: we read fine things but never feel them to the full until we have gone the same steps as the author.

For axioms in philosophy are not axioms until they are proved upon our pulses.

No collection of facts is ever complete, because the universe is without bounds. And no synthesis or interpretation is ever final, because there are always fresh facts to be found after the first collection has been provisionally arranged.

How empty is theory in the presence of fact!

It always seems to me absurd to speak of a complete proof of a theorem being rigorously demonstrated. An incomplete proof is no proof and a mathematical truth not rigorously demonstrated is not demonstrated at all. I do not mean to deny that there are mathematical truths, morally certain, which defy and will probably to the end of time to defy proof, as, e.g. that every indecomposable integer polynomial function must represent an infinitude of primes. I have sometimes thought that the profound mystery which envelops our conceptions relative to prime numbers depends upon the limitation of our faculties in regard to time, which like space may be in its essence poly-dimensional, and that this and such sort of truths would become self-evident to a being whose mode of perception is according to superficially as distinguished from our own limitation to linearly extended time.

"Even facts become fictions without adequate ways of seeing "the facts". We do not need theories so much as the experience that is the source of the theory. We are not satisfied with faith, in the sense of an implausible hypothesis irrationally held: we demand to experience the "evidence"."

Though the theory is worthless without the well-observed facts, the facts are useless without the frame of the theory to receive them.

Proof must be solid break walls of facts.