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...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.

Kurt Gödel

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Kurt Gödel
Age: 71 †
Born: 1906
Born: April 28
Died: 1978
Died: January 14
Computer Scientist
Logician
Mathematician
Philosopher
Physicist
University Teacher
Brünn
Kurt Friedrich Gödel
Mean
Inference
Modes
Consistency
Carried
Math
Proof
System
Means
Formalized

More quotes by Kurt Gödel

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I don't believe in natural science.
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The physical laws, in their observable consequences, have a finite limit of precision.
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I don't believe in empirical science. I only believe in a priori truth.
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Nothing new had been done in Logic since Aristotle!
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Ninety percent of [contemporary philosophers] see their principle task as that of beating religion out of men's heads. ... We are far from being able to provide scientific basis for the theological world view.
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I like Islam, it is a consistent idea of religion and open-minded.
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Said to physicist John Bahcall. I don't believe in natural science.
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But every error is due to extraneous factors (such as emotion and education) reason itself does not err.
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All generalizations, with the possible exception of this one, are false.
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The meaning of world is the separation of wish and fact.
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Either mathematics is too big for the human mind or the human mind is more than a machine.
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The axiomatic method is very powerful
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The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.
Kurt Gödel