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.

If a man is offered a fact which goes against his instincts, he will scrutinize it closely, and unless the evidence is overwhelming, he will refuse to believe it. If, on the other hand, he is offered something which affords a reason for acting in accordance to his instincts, he will accept it even on the slightest evidence. The origin of myths is explained in this way.

Love should be a tree whose roots are deep in the earth, but whose branches extend into heaven.

Philosophy arises from an unusually obstinate attempt to arrive at real knowledge. What passes for knowledge in ordinary life suffers from three defects: it is cocksure, vague and self-contradictory. The first step towards philosophy consists in becoming aware of these defects, not in order to rest content with a lazy scepticism, but in order to substitute an amended kind of knowledge which shall be tentative, precise and self-consistent.

The Church no longer contends that knowledge is in itself sinful, though it did so in its palmy days; but the acquisition of knowledge, even though not sinful, is dangerous, since it may lead to pride of intellect, and hence to a questioning of the Christian dogma.

Science tells us what we can know but what we can know is little and if we forget how much we cannot know we become insensitive of many things of very great importance. Theology, on the other hand induces a dogmatic belief that we have knowledge where in fact we have ignorance and by doing so generates a kind of impertinent insolence towards the universe. Uncertainty in the presence of vivid hopes and fears is painful, but must be endured if we wish to live without the support of comforting fairy tales.

Moral indignation is one of the most harmful forces in the modern world, the more so as it can always be diverted to sinister uses by those who control propaganda.