Certain characteristics of the subject are clear. To begin with, we do not in this subject deal with particular things or particular properties: we deal formally with what can be said about any thing or any property. We are prepared to say that one and one are two, but not that Socrates and Plato are two.

The fact that an opinion has been widely held is no evidence whatever that it is not utterly absurd.

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 have sought love, first, because it brings ecstasy – ecstasy so great that I would often have sacrificed all the rest of life for a few hours of that joy. ... I have sought it, finally, because in the union of love I have seen, in a mystic miniature, the prefiguring vision of the heaven that saints and poets have imagined.

It is in our hearts that evil lies, and it is from our hearts that it must be plucked out.

Liberty is the right to do what I like; licence, the right to do what you like.

He will see himself and life and the world as truly as our human limitations will permit; realizing the brevity and minuteness of human life, he will realize also that in individual minds is concentrated whatever of value the known universe contains. And he will see that the man whose mind mirrors the world becomes in a sense as great as the world. In emancipation from the fears that beset the slave of circumstance he will experience a profound joy, and through all the vicissitudes of his outward life he will remain in the depths of his being a happy man.