One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.

We are ... led to a somewhat vague distinction between what we may call "hard" data and "soft" data. This distinction is a matter of degree, and must not be pressed; but if not taken too seriously it may help to make the situation clear. I mean by "hard" data those which resist the solvent influence of critical reflection, and by "soft" data those which, under the operation of this process, become to our minds more or less doubtful.

When we look at a rock what we are seeing is not the rock, but the effect of the rock upon us.

As I grew up I became increasingly interested in philosophy, or which [his family] profoundly disapproved. Everytime the subject came up they repeated with unfailing regularity, "What is mind? No matter. What is matter? Never mind." After some fifty or sixty repititions, this remark ceased to amuse me.

Many people when they fall in love look for a little haven of refuge from the world, where they can be sure of being admired when they are not admirable, and praised when they are not praiseworthy.

What is new in our time is the increased power of the authorities to enforce their prejudices.

Self-respect will keep a man from being abject when he is in the power of enemies, and will enable him to feel that he may be in the right when the world is against him.