prisoners

"People are said to believe in God, or to disbelieve in Adam and Eve. But in such cases what is believed or disbelieved is that there is an entity answering a certain description. This, which can be believed or disbelieved is quite different from the actual entity (if any) which does answer the description. Thus the matter of belief is, in all cases, different in kind from the matter of sensation or presentation, and error is in no way analogous to hallucination. A hallucination is a fact, not an error; what is erroneous is a judgment based upon it."

"When people begin to philosophize they seem to think it necessary to make themselves artificially stupid."

"The above proposition is occasionally useful."

"Life seems to me essentially passion, conflict, rage... It is only intellect that keeps me sane; perhaps this makes me overvalue intellect against feeling."

"I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza's God, it won't love us in return."

"The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111, 777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. This contradiction was suggested to us by Mr. G. G. Berry of the Bodleian Library."

"Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform."

"The rules of logic are to mathematics what those of structure are to architecture."

"Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world."

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement."

"To those who inquire as to the purpose of mathematics, the usual answer will be that it facilitates the making of machines, the travelling from place to place, and the victory over foreign nations, whether in war or commerce. ... The reasoning faculty itself is generally conceived, by those who urge its cultivation, as merely a means for the avoidance of pitfalls and a help in the discovery of rules for the guidance of practical life."

"Brief and powerless is Man's life; on him and all his race the slow, sure doom falls pitiless and dark."

"The life of man is a long march through the night, surrounded by invisible foes, tortured by weariness and pain, towards a goal that few can hope to reach, and where none may tarry long."

"The slave is doomed to worship time and fate and death, because they are greater than anything he finds in himself, and because all his thoughts are of things which they devour."

"Freedom comes only to those who no longer ask of life that it shall yield them any of those personal goods that are subject to the mutations of time."

"Indignation is a submission of our thoughts, but not of our desires."

"In action, in desire, we must submit perpetually to the tyranny of outside forces; but in thought, in aspiration, we are free, free from our fellowmen, free from the petty planet on which our bodies impotently crawl, free even, while we live, from the tyranny of death."

"In spite of Death, the mark and seal of the parental control, Man is yet free, during his brief years, to examine, to criticise, to know, and in imagination to create. To him alone, in the world with which he is acquainted, this freedom belongs; and in this lies his superiority to the resistless forces that control his outward life."

"That Man is the product of causes that had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve individual life beyond the grave; that all the labors of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins – all these things, if not quite beyond dispute, are yet so nearly certain that no philosophy which rejects them can hope to stand. Only within the scaffolding of these truths, only on the firm foundation of unyielding despair, can the soul's habitation henceforth be safely built."

"Ironclads and Maxim guns must be the ultimate arbiters of metaphysical truth."

"Take the question whether other people exist. ...It is plain that it makes for happiness to believe that they exist – for even the greatest misanthropist would not wish to be deprived of the objects of his hate. Hence the belief that other people exist is, pragmatically, a true belief. But if I am troubled by solipsism, the discovery that a belief in the existence of others is 'true' in the pragmatist's sense is not enough to allay my sense of loneliness: the perception that I should profit by rejecting solipsism is not alone sufficient to make me reject it. For what I desire is not that the belief in solipsism should be false in the pragmatic sense, but that other people should in fact exist. And with the pragmatist's meaning of truth, these two do not necessarily go together. The belief in solipsism might be false even if I were the only person or thing in the universe."

"We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science."

"All's well that ends well; which is the epitaph I should put on my tombstone if I were the last man left alive."

"A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science."

"The past alone is truly real: the present is but a painful, struggling birth into the immutable being of what is no longer. Only the dead exist fully. The lives of the living are fragmentary, doubtful, and subject to change; but the lives of the dead are complete, free from the sway of Time, the all but omnipotent lord of the world. Their failures and successes, their hopes and fears, their joys and pains, have become eternal—our efforts cannot now abate one jot of them. Sorrows long buried in the grave, tragedies of which only a fading memory remains, loves immortalized by Death's hallowing touch these have a power, a magic, an untroubled calm, to which no present can attain. ...On the banks of the river of Time, the sad procession of human generations is marching slowly to the grave; in the quiet country of the Past, the march is ended, the tired wanderers rest, and the weeping is hushed."

"It is true that numerous instances are not always necessary to establish a law, provided the essential and relevant circumstances can easily be disentangled. But, in history, so many circumstances of a small and accidental nature are relevant, that no broad and simple uniformities are possible. Where our main endeavour is to discover general laws, we regard these as intrinsically more valuable than any of the facts which they inter-connect. In astronomy, the law of gravitation is plainly better worth knowing than the position of a particular planet on a particular night, or even on every night throughout a year. There are in the law a splendour and simplicity and sense of mastery which illuminate a mass of otherwise uninteresting details... But in history the matter is far otherwise... Historical facts, many of them, have an intrinsic value, a profound interest on their own account, which makes them worthy of study, quite apart from any possibility of linking them together by means of causal laws."

"I have been merely oppressed by the weariness and tedium and vanity of things lately: nothing stirs me, nothing seems worth doing or worth having done: the only thing that I strongly feel worth while would be to murder as many people as possible so as to diminish the amount of consciousness in the world. These times have to be lived through: there is nothing to be done with them."

"Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians."

"What does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being, as that which belongs even to the non-existent."

"I may as well say at once that I do not distinguish between inference and deduction. What is called induction appears to me to be either disguised deduction or a mere method of making plausible guesses."

"The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself."

"Pure Mathematics is the class of all propositions of the form "p implies q," where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth."

"Philosophy seems to me on the whole a rather hopeless business."

"Only in thought is man a God; in action and desire we are the slaves of circumstance."

"What a monstrous thing that a University should teach journalism! I thought that was only done at Oxford. This respect for the filthy multitude is ruining civilisation."

"Again, in regard to actual human existence, I have found myself giving honour to those who feel its tragedy, who think truly about Death, who are oppressed by ignoble things even when they are inevitable; yet these qualities appear to me to militate against happiness, not only to the possessors, but to all whom they affect. And, generally, the best life seems to me one which thinks truly and feels greatly about human things, and which, in addition, contemplates the world of beauty and of abstract truths. This last is, perhaps, my most anti-utilitarian opinion: I hold all knowledge that is concerned with things that actually exist – all that is commonly called Science – to be of very slight value compared to the knowledge which, like philosophy and mathematics, is concerned with ideal and eternal objects, and is freed from this miserable world which God has made. [Utilitarians] have been strangely anxious to prove that the life of the pig is not happier than that of the philosopher – a most dubious proposition..."

"It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true."

"[Unlike the] utilitarian... I judge pleasure and pain to be of small importance compared to knowledge, the appreciation and contemplation of beauty, and a certain intrinsic excellence of mind which, apart from its practical effects, appears to me to deserve the name of virtue. [For] many years it seemed to me perfectly self-evident that pleasure is the only good and pain the only evil. Now, however, the opposite seems to me self-evident. What first turned me away from utilitarianism was the persuasion that I myself ought to pursue philosophy, although I had (and have still) no doubt that by doing economics and the theory of politics I could add more to human happiness. It appeared to me that the dignity of which human existence is capable is not attainable by devotion to the mechanism of life, and that unless the contemplation of eternal things is preserved, mankind will become no better than well-fed pigs. But I do not believe that such contemplation on the whole tends to happiness. It gives moments of delight, but these are outweighed by years of effort and depression."

"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. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. 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."

"Thee might observe incidentally that if the state paid for child-bearing it might and ought to require a medical certificate that the parents were such as to give a reasonable result of a healthy child – this would afford a very good inducement to some sort of care for the race, and gradually as public opinion became educated by the law, it might react on the law and make that more stringent, until one got to some state of things in which there would be a little genuine care for the race, instead of the present haphazard higgledy-piggledy ways."

"Thee will find out in time that I have a great love of professing vile sentiments, I don't know why, unless it springs from long efforts to avoid priggery."

"The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt."

"I am looking forward very much to getting back to Cambridge, and being able to say what I think and not to mean what I say: two things which at home are impossible. Cambridge is one of the few places where one can talk unlimited nonsense and generalities without anyone pulling one up or confronting one with them when one says just the opposite the next day."