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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
System
Means
Formalized
Mean
Inference
Modes
Consistency
Carried
Math
Proof

More quotes by Kurt Gödel

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All generalizations, with the possible exception of this one, are false.
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The physical laws, in their observable consequences, have a finite limit of precision.
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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 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.
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The axiomatic method is very powerful
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Said to physicist John Bahcall. I don't believe in natural science.
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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 don't believe in natural science.
Kurt Gödel
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I like Islam, it is a consistent idea of religion and open-minded.
Kurt Gödel
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Nothing new had been done in Logic since Aristotle!
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But every error is due to extraneous factors (such as emotion and education) reason itself does not err.
Kurt Gödel
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The meaning of world is the separation of wish and fact.
Kurt Gödel
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I don't believe in empirical science. I only believe in a priori truth.
Kurt Gödel