Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

For the learning of every virtue there is an appropriate discipline, and for the learning of suspended judgment the best discipline is philosophy.

Science, by itself, cannot supply us with an ethic. It can show us how to achieve a given end, and it may show us that some ends cannot be achieved.

The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.

Truth is a shining goddess, always veiled, always distant, never wholly approachable, but worthy of all the devotion of which the human spirit is capable.

Happiness, as is evident, depends partly upon external circumstances and partly upon oneself.

In the ordinary business of life punctuality is . . . necessary.