The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.
The whole of theology, in regard to hell no less than to heaven, takes it for granted that Man is what is of most importance in the Universe of created beings. Since all theologians are men, this postulate has met with little opposition.
The very best proof that something can be done is that someone has already done it.
3 is prime, 5 is prime, 7 is prime, 9 is a paradox; as is a paradox why the number 1 is not prime if it has no other divisors besides himself.
Science is at no moment quite right, but it is seldom quite wrong, and has, as a rule, a better chance of being right than the theories of the unscientific. It is, therefore, rational to accept it hypothetically.
In considering irregular appearances, there are certain very natural mistakes which must be avoided.
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.
Work is of two kinds: first, altering the position of matter at or near the earth’s surface relative to other matter; second, telling other people to do so.
A sense of duty is useful in work but offensive in personal relations. People wish to be liked, not to be endured with patient resignation.
The degree of one’s emotions varies inversely with one’s knowledge of the facts.
Ethics is in origin the art of recommending to others the sacrifices required for cooperation with oneself.
The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice.
Men who are unhappy, like men who sleep badly, are always proud of the fact.
The place of the father in the modern suburban family is a very small one, particularly if he plays golf.
None but a coward dares to boast that he has never known fear.
Those who forget good and evil and seek only to know the facts are more likely to achieve good than those who view the world through the distorting medium of their own desires.
Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
I’ve made an odd discovery. Every time I talk to a savant I feel quite sure that happiness is no longer a possibility. Yet when I talk with my gardener, I’m convinced of the opposite.
Liberty is the right to do what I like; license, the right to do what you like.
It seems to be the fate of idealists to obtain what they have struggled for in a form which destroys their ideals.