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“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.”

Bertrand Russell

Letter to Alys Pearsall Smith (1894); published in The Selected Letters of Bertrand Russell, Volume 1: The Private Years (1884–1914), edited by Nicholas Griffin. It should be noted that in his talk of "the race", he is referring to "the human race". Smith married Russell in December 1894; they divorced in 1921.
1890s

“Man differs from other animals in one very important respect, and that is that he has some desires which are, so to speak, infinite, which can never be fully gratified, and which would keep him restless even in Paradise. The boa constrictor, when he has had an adequate meal, goes to sleep, and does not wake until he needs another meal. Human beings, for the most part, are not like this.”

Bertrand Russell

1950s, What Desires Are Politically Important? (1950)

“If human nature were unchangeable, as ignorant people still suppose it to be, the situation would indeed be hopeless.”

Bertrand Russell

Source: 1920s, Sceptical Essays (1928), Ch. 17: Some Prospects: Cheerful and Otherwise

“It is not by prayer and humility that you cause things to go as you wish, but by acquiring a knowledge of natural laws.”

Bertrand Russell

1950s, The Impact of Science on Society (1952)

“Of course not. After all, I may be wrong.”

Bertrand Russell

When asked asked if he was willing to die for his beliefs.
The Times book of quotations (2000), p. 84
Disputed
Variant: "I would never die for my beliefs because I might be wrong."

“The typical Westerner wishes to be the cause of as many changes as possible in his environment; the typical Chinaman wishes to enjoy as much and as delicately as possible.”

Bertrand Russell

The Problem of China (1922), Ch. XII: The Chinese Character
1920s

“No man who believes that all is for the best in this suffering world can keep his ethical values unimpaired, since he is always having to find excuses for pain and misery.”

Bertrand Russell

The Collected Papers of Bertrand Russell: A fresh look at empiricism, 1927-42 (G. Allen & Unwin, 1996), p. 217
Attributed from posthumous publications

“There are three forces on the side of life which require no exceptional mental endowment, which are not very rare at present, and might be very common under better social institutions. They are love, the instinct of constructiveness, and the joy of life. All three are checked and enfeebled at present by the conditions under which men live—not only the less outwardly fortunate, but also the majority of the well-to-do. Our institutions rest upon injustice and authority: it is only by closing our hearts against sympathy and our minds against truth that we can endure the oppressions and unfairnesses by which we profit. The conventional conception of what constitutes success leads most men to live a life in which their most vital impulses are sacrificed, and the joy of life is lost in listless weariness. Our economic system compels almost all men to carry out the purposes of others rather than their own, making them feel impotent in action and only able to secure a certain modicum of passive pleasure. All these things destroy the vigor of the community, the expansive affections of individuals, and the power of viewing the world generously. All these things are unnecessary and can be ended by wisdom and courage. If they were ended, the impulsive life of men would become wholly different, and the human race might travel towards a new happiness and a new vigor.”

Bertrand Russell

Source: 1910s, Why Men Fight https://en.wikisource.org/wiki/Why_Men_Fight (1917), pp. 18-19

“My objections to Marx are of two sorts: one, that he was muddle-headed; and the other, that his thinking was almost entirely inspired by hatred. The doctrine of surplus value, which is supposed to demonstrate the exploitation of wage-earners under capitalism, is arrived at: (a) by surreptitiously accepting Malthus's doctrine of population, which Marx and all his disciples explicitly repudiate; (b) by applying Ricardo's theory of value to wages, but not to the prices of manufactured articles. He is entirely satisfied with the result, not because it is in accordance with the facts or because it is logically coherent, but because it is calculated to rouse fury in wage-earners. Marx's doctrine that all historical events have been motivated by class conflicts is a rash and untrue extension to world history of certain features prominent in England and France a hundred years ago. His belief that there is a cosmic force called Dialectical Materialism which governs human history independently of human volitions, is mere mythology. His theoretical errors, however, would not have mattered so much but for the fact that, like Tertullian and Carlyle, his chief desire was to see his enemies punished, and he cared little what happened to his friends in the process.”

Bertrand Russell

Source: 1950s, Portraits from Memory and Other Essays (1956), p. 211

“The State is a collection of officials, different for difference purposes, drawing comfortable incomes so long as the status quo is preserved. The only alteration they are likely to desire in the status quo is an increase of bureaucracy and the power of bureaucrats.”

Bertrand Russell

Source: 1920s, Sceptical Essays (1928), Ch. 12: Free Thought and Official Propaganda http://books.google.com/books?id=9tQsg5ITfHsC&q=%22The+State+is+a+collection+of+officials+different+for+different+purposes+drawing+comfortable+incomes+so+long+as+the+status+quo+is+preserved+The+only+alteration+they+are+likely+to+desire+in+the+status+quo+is+an+increase+of+bureaucracy+and+the+power+of+bureaucrats%22&pg=PA134#v=onepage

“The criminal law has, from the point of view of thwarted virtue, the merit of allowing an outlet for those impulses of aggression which cowardice, disguised as morality, restrains in their more spontaneous forms. War has the same merit. You must not kill you neighbor, whom perhaps you genuinely hate, but by a little propaganda this hate can be transferred to some foreign nation, against whom all your murderous impulses become patriotic heroism.”

Bertrand Russell

Part III: Man and Himself, Ch. 17: Fear, p. 175
1950s, New Hopes for a Changing World (1951)

“The pursuit of knowledge is, I think, mainly actuated by love of power. And so are all advances in scientific technique. In politics, also, a reformer may have just as strong a love of power as a despot. It would be a complete mistake to decry love of power altogether as a motive. Whether you will be led by this motive to actions which are useful, or to actions which are pernicious, depends upon the social system, and upon your capacities.”

Bertrand Russell

1950s, What Desires Are Politically Important? (1950)

“I have been accused of a habit of changing my opinions … I am not myself in any degree ashamed of having changed my opinions. What physicist who was already active in 1900 would dream of boasting that his opinions had not changed during the last half century? In science men change their opinions when new knowledge becomes available; but philosophy in the minds of many is assimilated rather to theology than to science. … The kind of philosophy that I value and have endeavoured to pursue is scientific, in the sense that there is some definite knowledge to be obtained and that new discoveries can make the admission of former error inevitable to any candid mind. For what I have said, whether early or late, I do not claim the kind of truth which theologians claim for their creeds. I claim only, at best, that the opinion expressed was a sensible one to hold at the time when it was expressed. I should be much surprised if subsequent research did not show that it needed to be modified. I hope, therefore, that whoever uses this dictionary will not suppose the remarks which it quotes to be intended as pontifical pronouncements, but only as the best I could do at the time towards the promotion of clear and accurate thinking. Clarity, above all, has been my aim.”

Bertrand Russell

Preface to The Bertrand Russell Dictionary of Mind, Matter and Morals (1952) edited by Lester E. Denonn
1950s

“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.”

Bertrand Russell

Source: 1910s, Our Knowledge of the External World (1914), p. 8

“It is said (I do not know with what truth) that a certain Hindu thinker believed the earth to rest upon an elephant. When asked what the elephant rested upon, he replied that it rested upon a tortoise. When asked what the tortoise rested upon, he said, "I am tired of this. Suppose we change the subject."”

Bertrand Russell

This illustrates the unsatisfactory character of the First-Cause argument.
"Is There a God?" (1952)
1950s

“[Messrs Ogden and Richards] will reply that they are considering the meaning of a "thought," not of a word. A "thought" is not a social phenomenon, like speech, and therefore does not have the two sides, active and passive, which can be distinguished in speech. I should urge, however, that all the reasons which led our authors to avoid introducing images in explaining meaning should have also led them to avoid introducing "thoughts." If a theory of meaning is to be fitted into natural science as they desire, it is necessary to define the meaning of words without introducing anything "mental" in the sense in which what is "mental" is not subject to the laws of physics. Therefore, for the same reasons for which I now hold that the meaning of words should be explained without introducing images – which I argued to be possible in the above-quoted passage – I also hold that meaning in general should be treated without introducing "thoughts," and should be regarded as a property of words considered as physical phenomena. Let us therefore amend their theory. They say: "'I am thinking of A' is the same thing as 'My thought is being caused by A.'" Let us substitute: "'I am speaking of A' is the same thing as 'My speech is being caused by A.'" Can this theory be true?”

Bertrand Russell

1920s, Review of The Meaning of Meaning (1926)

“To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.”

Bertrand Russell

As quoted in Williams' Weighing the Odds: A Course in Probability and Statistics (2001), p. 498
Attributed from posthumous publications

“I think modern educational theorists are inclined to attach too much importance to the negative virtue of not interfering with children, and too little to the positive merit of enjoying their company.”

Bertrand Russell

Source: 1930s, In Praise of Idleness and Other Essays (1935), Ch. 12: Education and Discipline

“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.”

Bertrand Russell

1900s, "The Study of Mathematics" (November 1907)

“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.”

Bertrand Russell

Principles of Mathematics (1903), p. 451
1900s