“The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.”

“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.”

“Some care is needed in using Descartes' argument. "I think, therefore I am" says rather more than is strictly certain. It might seem as though we are quite sure of being the same person to-day as we were yesterday, and this is no doubt true in some sense. But the real Self is as hard to arrive at as the real table, and does not seem to have that absolute, convincing certainty that belongs to particular experiences.”

“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.”

“Noone has yet succeeded in inventing a philosophy at once credible and self-consistent. Locke aimed at credibility, and achieved it at the expense of consistency. Most of the great philosophers have done the opposite. A philosophy which is not self-consistent cannot be wholly true, but a philosophy which is self-consistent can very well be wholly false. The most fruitful philosophies have contained glaring inconsistencies, but for that very reason have been partially true. There is no reason to suppose that a self-consistent system contains more truth than one which, like Locke’s, is more or less wrong.”

“The true function of logic ... as applied to matters of experience ... is analytic rather than constructive; taken a priori, it shows the possibility of hitherto unsuspected alternatives more often than the impossibility of alternatives which seemed prima facie possible. Thus, while it liberates imagination as to what the world may be, it refuses to legislate as to what the world is”

“Our great democracies still tend to think that a stupid man is more likely to be honest than a clever man, and our politicians take advantage of this prejudice by pretending to be even more stupid than nature made them.”