“I wish to propose for the reader's favourable consideration a doctrine which may, I fear, appear wildly paradoxical and subversive. The doctrine in question is this: that it is undesirable to believe a proposition when there is no ground whatever for supposing it true.”

“Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] 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. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.”

“Moreover, the attitude that one ought to believe such and such a proposition, independently of the question whether there is evidence in its favor, is an attitude which produces hostility to evidence and causes us to close our minds to every fact that does not suit our prejudices.”

“My desire and wish is that the things I start with should be so obvious that you wonder why I spend my time stating them. This is what I aim at because the point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.”

“I do not think there can be any defense for the view that knowledge is ever undesirable.”

“Every isolated passion, is, in isolation, insane; sanity may be defined as synthesis of insanities. Every dominant passion generates a dominant fear, the fear of its non-fulfillment. Every dominant fear generates a nightmare, sometimes in form of explicit and conscious fanaticism, sometimes in paralyzing timidity, sometimes in an unconscious or subconscious terror which finds expression only in dreams. The man who wishes to preserve sanity in a dangerous world should summon in his own mind a parliament of fears, in which each in turn is voted absurd by all the others.”

“What we firmly believe, if it is true, is called knowledge, provided it is either intuitive or inferred (logically or psychologically) from intuitive knowledge from which it follows logically. What we firmly believe, if it is not true, is called error. What we firmly believe, if it is neither knowledge nor error, and also what we believe hesitatingly, because it is, or is derived from, something which has not the highest degree of self-evidence, may be called probable opinion. Thus the greater part of what would commonly pass as knowledge is more or less probable opinion.”