“We shall be compelled to renounce the hope of finding philosophical proofs of religious beliefs. ...Hence, once more, the value of philosophy must not depend upon any supposed body of definitely ascertainable knowledge to be acquired by those who study it.”

“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.”

“Since all terms that are defined are defined by means of other terms, it is clear that human knowledge must always be content to accept some terms as intelligible without definition, in order to have a starting point for its definitions...[and] since human powers are finite, the definitions known to us must always begin somewhere, with terms undefined for the moment, though perhaps not permanently." - Introduction to Mathematical Philosophy”

“The extent to which beliefs are based upon evidence is very much less than believers suppose. Take the kind of action which is most nearly rational: the investment of money by a rich City man. You will often find that his view (say) on the question whether the French franc will go up or down depends upon his political sympathies, and yet is so strongly held that he is prepared to risk money on it.”

“To teach how to live without certainty, and yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy, in our age, can still do for those who study it.”

“The methods of increasing the degree of truth in our beliefs are well known; they consist in hearing all sides, trying to ascertain all the relevant facts, controlling our own bias by discussion with people who have the opposite bias, and cultivating a readiness to discard any hypothesis which has proved inadequate.”

“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.”