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The Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.
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While it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
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A stupid man's report of what a clever man says is never accurate, because he unconsciously translates what he hears into something that he can understand.
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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.
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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.
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What is new in our time is the increased power of the authorities to enforce their prejudices.
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New truth is often uncomfortable, especially to the holders of power; nevertheless, amid the long record of cruelty and bigotry, it is the most important achievement of our intelligent but wayward species. ''
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Democracy is the process by which people choose the man who'll get the blame.
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The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil.
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Modern physics... reduces matter to a set of events which proceed outward from a centre. If there is something further in the centre itself, we cannot know about it, and it is irrelevant to physics.
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I find that the whiter my hair becomes the more ready people are to believe what I say.
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Most people, at a crisis, feel more loyalty to their nation than to their class.
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It seems clear to me that marriage ought to be constituted by children, and relations not involving children ought to be ignored by the law and treated as indifferent by public opinion. It is only through children that relations cease to be a purely private matter.
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Philosophy seems to me on the whole a rather hopeless business.
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Our words tend to conceal what is private and particular in our impressions, and to make us believe that different people live in a common world to a greater extent than is in fact the case.
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Marriage is for women the commonest mode of livelihood, and the total amount of undesired sex endured by women is probably greater in marriage than in prostitution.
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I do not think it possible to get anywhere if we start from scepticism. We must start from a broad acceptance of whatever seems to be knowledge and is not rejected for some specific reason.
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To fear love is to fear life, and those who fear life are already three parts dead.
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The theoretical understanding of the world, which is the aim of philosophy, is not a matter of great practical importance to animals, or to savages, or even to most civilized men.
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It is a waste of energy to be angry with a man who behaves badly, just as it is to be angry with a car that won't go. The difference is that you can compel your car to go to a garage, but you cannot compel Hitler to go to a psychiatrist.
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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.
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The essence of the Liberal outlook lies not in what opinions are held, but in how they are held: instead of being held dogmatically, they are held tentatively, and with a consciousness that new evidence may at any moment lead to their abandonment.
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Wherever one finds oneself inclined to bitterness, it is a sign of emotional failure: a larger heart, and a greater self-restraint, would put a calm autumnal sadness in the place of the instinctive outcry of pain.
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Every man would like to be God, if it were possible; some few find it difficult to admit the impossibility.