There is Reason, asserting itself as above the world, and there is Reason as one of many factors within the world. The Greeks have bequeathed to us two figures, whose real or mystical lives conform to these two notions - Plato and Ulysses. The one shares Reason with the Gods, the other shares it with the foxes. (F.R. pp. 6-7)

Faith in reason is the trust that the ultimate natures of things lie together in a harmony which excludes mere arbitrariness. It is the faith that at the base of things we shall not find mere arbitrary mystery. (S.M.W. p. 27)

A clash of doctrines is not a disaster - it is an opportunity. (S.M.W. p. 266)

An attack upon systematic thought is treason to civilisation. (A.I. p. 208)

It requires a very unusual mind to under take the analysis of the obvious. (S.M.W. p. 6)

An unflinching determination to take the whole evidence into account is the only method of preservation against the fluctuating extremes of fashionable opinion. (S.M.W. p. 268)

Logic is the chosen resort of clear-headed people, severally convinced of the complete adequacy of their doctrines. It is such a pity that they cannot agree with each other. (Harvard p. 263)

In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions. (A.I. p. 91)

One source of vagueness is deficiency of language. We can see the variations of meaning; although we cannot verbalise them in any decisive, handy manner. Thus we cannot weave into a train of thought what we can apprehend in flashes.... For this reason, conventional English is the twin sister to barren thought. Plato had recourse to myth. (Phil. Rev. pp. 182-3)

We are told by logicians that a proposition must be either true or false, and that there is no middle term. But in practice, we may know that a proposition expresses an important truth, but that it is subject to limitations and qualifications which at present remain undiscovered. (S.M.W. p. 262).

The man with a method good for purposes of his dominant interests, is a pathological case in respect to his wider judgment on the co-ordination of this method with a more complete experience. Priests and scientists, statesmen and men of business, philosophers and mathematicians, are all alike in this respect. (F.R. p. 8)

No systematic thought has made progress apart from some adequately general working hypothesis, adapted to its special topic. Such a hypothesis directs observation, and decides upon the mutual relevance of various types of evidence. In short, it prescribes method. To venture upon productive thought without such an explicit theory is to abandon oneself to the doctrines derived from one's grandfather. (A.I. p. 286)

It is a profoundly erroneous truism, repeated by all copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilisation advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments. (Intro. Math. p. 61)

I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would he claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming - and a little mad. Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings. (S.M.W. p. 31)

The first use of 0 was to make the Arabic notation possible - no slight service. We can imagine that when it had been introduced for this purpose, practical men, of the sort who dislike fanciful ideas, deprecated the silly habit of identifying it with a number zero. But they were wrong as such men always are when they desert their proper function of masticating food which others have prepared. (Intro. Math. p. 65)

Traditional ideas are never static. They are either fading into meaningless formulae, or are gaining power by the new lights thrown by a more delicate apprehension. They are transformed by the urge of critical reason, by the vivid evidence of emotional experience, and by the cold certainties of scientific perception. One fact is certain, you cannot keep them still. (S.M.W. p. 269)

For, whereas you can make a replica of an ancient statue, there is no possible replica of an ancient state of mind. There can be no nearer approximation than that which a masquerade bears to real life. (S.M.W. p. 200)

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. "Necessity is the mother of invention" is a silly proverb. "Necessity is the mother of futile dodges" is much nearer to the truth. The basis of the growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity. (A.E. p. 69)