... the most essential characteristic of mind is memory, using this word in its broadest sense to include every influence of past experience on present reactions...

A hallucination is a fact, not an error; what is erroneous is a judgment based upon it.

A process which led from the amoeba to man appeared to the philosophers to be obviously a progress -- though whether the amoeba would agree with this opinion is not known.

A truer image of the world, I think, is obtained by picturing things as entering into the stream of time from an eternal world outside, than from a view which regards time as the devouring tyrant of all that is.

Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in infering that he is an inexact man. Every careful measurement in science is always given with the probable error... every observer admits that he is likely wrong, and knows about how much wrong he is likely to be.

An extra-terrestrial philosopher, who had watched a single youth up to the age of twenty-one and had never come across any other human being, might conclude that it is the nature of human beings to grow continually taller and wiser in an indefinite progress towards perfection; and this generalization would be just as well founded as the generalization which evolutionists base upon the previous history of this planet.

Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.

At the age of eleven, I began Euclid, with my brother as my tutor.... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.

Broadly speaking, we are in the middle of a race between human skill as a means and human folly as an end.

But it is just this characteristic of simplicity in the laws of nature hitherto discovered which it would be fallacious to generalize, for it is obvious that simplicity has been a part cause of their discovery, and can, therefore, give no ground for the supposition that other undiscovered laws are equally simple

Can a society in which thought and technique are scientific persist for a long period, as, for example, ancient Egypt persisted, or does it necessarily contain within itself forces which must bring either decay or explosion?

Even if the open windows of science at first make us shiver after the cozy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigor, and the great spaces have a splendor of their own.

Fear is the main source of superstition, and one of the main sources of cruelty. To conquer fear is the beginning of wisdom, in the pursuit of truth as in the endeavour after a worthy manner of life.?

If the matter is one that can be settled by observation, make the observation yourself. Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted.

In attempting to understand the elements out of which mental phenomena are compounded, it is of the greatest importance to remember that from the protozoa to man there is nowhere a very wide gap either in structure or in behaviour. From this fact it is a highly probable inference that there is also nowhere a very wide mental gap..

It is a curious and painful fact that almost all the completely futile treatments that have been believed in during the long history of medical folly have been such as caused acute suffering to the patient. When anesthetics were discovered, pious people considered them an attempt to evade the will of God. It was pointed out, however, that when God extracted Adam's rib He put him into a deep sleep. This proved that anesthetics are all right for men; women, however, ought to suffer, because of the curse of Eve.

John Locke invented common sense, and only Englishmen have had it ever since!

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 georgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. (1902)

Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.

One must expect a war between U.S.A. and U.S.S.R. which will begin with the total destruction of London. I think the war will last 30 years, and leave a world without civilised people, from which everything will have to build afresh—a process taking (say) 500 years.
Stated just one month after the Hiroshima atomic explosion. Russell became one of the best-known antinuclear activists of his era.

One of the chiefest triumphs of modern mathematics consists in having discovered what mathematics really is.

One of the symptoms of approaching nervous breakdown is the belief that one's work is terribly important.

Only mathematics and mathematical logic can say as little as the physicist means to say. (1931)

Organic life, we are told, has developed gradually from the protozoan to the philosopher, and this development, we are assured, is indubitably an advance. Unfortunately it is the philosopher, not the protozoon, who gives us this assurance.

People are born ignorant, not stupid; they are made stupid by education.

Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion. So whenever you find yourself getting angry about a difference of opinion, be on your guard, you will probably find, on examination, that your belief is going beyond what the evidence warrants.?

Philosophy is that part of science which at present people chose to have opinions about, but which they have no knowledge about. Therefore every advance in knowledge robs philosophy of some problems which formerly it had …and will belong to science.

Physics, owing to the simplicity of its subject matter, has reached a higher state of devlopment than any other science. (1931)

Pure mathematics consists entirely of such asseverations as 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. ... 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.

Pure mathematics consists entirely of such asseverations as that, if such and such is a proposition is true of anything, then such and such another propositions 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. ... If our hypothesis is about anything and not about some one or more particular things, then our deductions constititute mathematics. Thus mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true.

Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home...

Science is what you more or less know and philosophy is what you do not know.

Scientific method, although in its more refined forms it may seem complicated, is in essence remarkably simply. It consists in observing such facts as will enable the observer to discover general laws governing facts of the kind in question. The two stages, first of observation, and second of inference to a law, are both essential, and each is susceptible of almost indefinite refinement. (1931)

The examination system, and the fact that instruction is treated mainly as a training for a livelihood, leads the young to regard knowledge from a purely utilitarian point of view as the road to money, not as the gateway to wisdom.

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 of the analysis of Symbolic Logic itself.

The first man who said 'fire burns' was employing scientific method, at any rate if he had allowed himself to b e burnt several times. This man had already passed through the two stages of observation and generalization. He had not, however, what scientific technique demands—a careful choice of significant facts on the one hand, and, on the other hand, various means of arriving at laws otherwise than my mere generalization. (1931)

The human race may well become extinct before the end of the century. Speaking as a mathematician, I should say the odds are about three to one against survival.

The more we realize our minuteness and our impotence in the face of cosmic forces, the more amazing becomes what human beings have achieved.

The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic.

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

The scientific attitude of mind involves a sweeping away of all other desires in the interest of the desire to know.

The trouble with the world is that the stupid are cocksure and the intelligent full of doubt.

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.

The universe may have a purpose, but nothing we know suggests that, if so, this purpose has any similarity to ours.

There are infinite possibilities of error, and more cranks take up fashionable untruths than unfashionable truths.

Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.

To a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal. (1959)

To be able to fill leisure intelligently is the last product of civilization.

What Galileo and Newton were to the seventeenth century, Darwin was to the nineteenth.

What is best in mathematics deserves not merely to be learnt as a task, but to assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

When Benjamin Franklin invented the lightning-rod, the clergy, both in England and America, with the enthusiastic support of George III, condemned it as an impious attempt to defeat the will of God. For, as all right-thinking people were aware, lightning is sent by God to punish impiety or some other grave sin—the virtuous are never struck by lightning. Therefore if God wants to strike any one, Benjamin Franklin [and his lightening-rod] ought not to defeat His design; indeed, to do so is helping criminals to escape. But God was equal to the occasion, if we are to believe the eminent Dr. Price, one of the leading divines of Boston. Lightning having been rendered ineffectual by the 'iron points invented by the sagacious Dr. Franklin,' Massachusetts was shaken by earthquakes, which Dr. Price perceived to be due to God's wrath at the 'iron points.' In a sermon on the subject he said,' In Boston are more erected than elsewhere in New England, and Boston seems to be more dreadfully shaken. Oh! there is no getting out of the mighty hand of God.' Apparently, however, Providence gave up all hope of curing Boston of its wickedness, for, though lightning-rods became more and more common, earthquakes in Massachusetts have remained rare.

William James used to preach the 'will to believe'. For my part, I should wish to preach the 'will to doubt.' … What is wanted is not the will to believe, but the wish to find out, which is the exact opposite.

William James used to preach the 'will to believe.' For my part, I should wish to preach the 'will to doubt' ... what is wanted is not the will to believe, but the wish to find out, which is the exact opposite.

Work is of two kinds: first, altering the position of matter at or near the earth's surface relative to other such matter; second, telling other people to do so. The first kind is unpleasant and ill paid; the second is pleasant and highly paid.

[Man] ... 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 an individual life beyond the grave; that all the labour 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...

The difference between myth and science is the difference between divine inspiration of 'unaided reason' (as Bertrand Russell put it) on the one hand and theories developed in observational contact with the real world on the other. It is the difference between the belief in prophets and critical thinking, between Credo quia absurdum (I believe because it is absurd–Tertullian) and De omnibus est dubitandum (Everything should be questioned–Descartes). To try to write a grand cosmical drama leads necessarily to myth. To try to let knowledge substitute ignorance in increasingly large regions of space and time is science.