Logic Quote by John von Neumann

““When we talk mathematics, we may be discussing a secondary language, built on the primary language truly used by the central nervous system. Thus the outward forms of our mathematics are not absolutely relevant from the point of view of evaluating what the mathematical or logical language truly used by the central nervous system is. However, the above remarks about reliability and logical and arithmetical depth prove that whatever the system is, it cannot fail to differ considerably from what we consciously and explicitly consider as mathematics.””

John von Neumann

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Logic Mathematics Nervous system Point of view

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Truth is much too complicated to allow anything but approximations.

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Problems are often stated in vague terms... because it is quite uncertain what the problems really are.

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It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful…

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I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore.

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There is no point in being precise if you do not even know what you are talking about.

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If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.

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The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than…

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The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical…

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Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will…

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If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.

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Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.

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