The fact that an opinion has been widely held is no evidence whatever that it is not utterly absurd.
If a man is offered a fact which goes against his instincts, he will scrutinize it closely, and unless the evidence is overwhelming, he will refuse to believe it. If, on the other hand, he is offered something which affords a reason for acting in accordance to his instincts, he will accept it even on the slightest evidence. The origin of myths is explained in this way.
When a man tells you that he knows the exact truth about anything you are safe in inferring that he is an inexact man.
Be scrupulously truthful, even if the truth is inconvenient, for it is more inconvenient when you try to conceal it.
One of the chief obstacles to intelligence is credulity, and credulity could be enormously diminished by instructions as to the prevalent forms of mendacity. Credulity is a greater evil in the present day than it ever was before, because, owing to the growth of education, it is much easier than it used to be to spread misinformation, and, owing to democracy, the spread of misinformation is more important than in former times to the holders of power.
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.
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. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
Education ought to foster the wish for truth, not the conviction that some particular creed is the truth.
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 inferring 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.
The argument against the persecution of opinion does not depend upon what the excuse for persecution may be. The argument is that we none of us know all truth, that the discovery of new truth is promoted by free discussion and rendered very difficult by suppression.
In the higher walks of politics the same sort of thing occurs. The statesman who has gradually concentrated all power within himself ... may have had anything but a public motive... The phrases which are customary on the platform and in the Party Press have gradually come to him to seem to express truths, and he mistakes the rhetoric of partisanship for a genuine analysis of motives... He retires from the world after the world has retired from him.
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.
There are infinite possibilities of error, and more cranks take up fashionable untruths than unfashionable truths.
Heretical views arise when the truth is uncertain, and it is only when the truth is uncertain that censorship is invoked.
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