“[Ideas] are like shadows — substantial enough until we try to grasp them.”
— Samuel Butler
— Samuel Butler
“The chief danger to philosophy is narrowness in the selection of evidence.”
— Alfred North Whitehead
— Alfred North Whitehead
“There is much pleasure to be gained from useless knowledge.”
— Bertrand Russell
— Bertrand Russell
“So in all human affairs one notices, if one examines them closely, that it is impossible to remove one inconvenience without another emerging.”
— Niccolò Machiavelli
— Niccolò Machiavelli
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“In every science, after having analysed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that cannot be reduced among them, and that one can define no further. These are the primitive ideas of the science; it is necessary to acquire them through experience, or through induction; it is impossible to explain them by deduction.”
— Giuseppe Peano
— Giuseppe Peano
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“Intuitionistic mathematics consists in mental constructions; a mathematical theorem expresses a purely empirical fact, namely the success of a certain construction.”
— Arend Heyting
— Arend Heyting
“Mathematics is not a deductive science — that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does. Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared.”
— Paul Halmos
— Paul Halmos
“When a measure becomes a target, it ceases to be a good measure.”
— Goodhart's law
— Goodhart's law
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“You can’t use up creativity. The more you use, the more you have.”
— Maya Angelou
— Maya Angelou
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“Art does not imitate, but interpret. It searches out the idea lying dormant in the symbol, in order to present the symbol to men in such form as to enable them to penetrate through it to the idea.”
— Giuseppe Mazzini
— Giuseppe Mazzini
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“The world neither ever saw, nor ever will see, a perfectly fair lottery.”
— Adam Smith
— Adam Smith
“[M]an's words, for good or ill, can now so easily reach the millions.”
— Lester B. Pearson, 1957
— Lester B. Pearson, 1957
“I am conscious of my inability to grasp, in all its details and positive developments, any very large portion of human knowledge. The greatest intelligence would not be equal to a comprehension of the whole.”
— Mikhail Bakunin, 1871
— Mikhail Bakunin, 1871
“The great difference between magic and the scientific imitation of life is that where the former is content to copy external appearance, the latter is concerned more with performance and behavior.”
— William Grey Walter
— William Grey Walter
“Today war..., [is] not a war of human beings but a technical struggle of machines one against another and all against the non–combatant population.”
— Karl Jaspers, 1933
— Karl Jaspers, 1933