Dogmatism and skepticism are both, in a sense, absolute philosophies; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or ignorance.

The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.

Only mathematics and mathematical logic can say as little as the physicist means to say.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

I must, before I die, find some way to say the essential thing that is in me, that I have never said yet -- a thing that is not love or hate or pity or scorn, but the very breath of life, fierce and coming from far away, bringing into human life the vastness and the fearful passionless force of non-human things.

Scientific method, although in its more refined forms it may seem complicated, is in essence remarkably simply. It consists in observing such facts as will enable the observer to discover general laws governing facts of the kind in question. The two stages, first of observation, and second of inference to a law, are both essential, and each is susceptible of almost indefinite refinement. (1931)

It's coexistence or no existence.