Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the … - Bertrand Russell

The first thing to realize, if you wish to become a philosopher, is that most people go through life with a whole world of beliefs that have no sort of rational justification, and that one man's world of beliefs is apt to be incompatible with another man's, so that they cannot both be right. People's opinions are mainly designed to make them feel comfortable; truth, for most people is a secondary consideration.

Knowledge is not so precise a concept as is commonly thought. Instead of saying "I know this," we ought to say "I more or less know something more or less like this." It is true that this proviso is hardly necessary as regards the multiplication table, but knowledge in practical affairs has not the certainty or the precision of arithmetic. Suppose I say "democracy is a good thing": I must admit, first, that I am less sure of this than I am that two and two are four, and secondly, that "democracy" is a somewhat vague term which I cannot define precisely. We ought to say, therefore: "I am fairly certain that it is a good thing if a government has something of the characteristics that are common to the British and American Constitutions," or something of this sort. And one of the aims of education ought to be to make such a statement more effective from a platform than the usual type of political slogan.

I am sure that university life would be better, both intellectually and morally, if most university students had temporary childless marriages. This would afford a solution to the sexual urge neither restless nor surreptitious, neither mercenary nor casual, and of such a nature that it need not take up time which ought to be given to work.