gödel in A Sentence

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He was a winner of the Gödel Prize in 2001.

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2

Kurt Gödel, the genius mathematician and philosopher, was obsessively afraid of being poisoned;

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When Adele fell ill and was hospitalized for six months, Gödel starved to death.

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4

It's been broken since 1931, when the logician Kurt Gödel published his famous incompleteness theorems.

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Another open question is to start from this notion to find an extension of Gödel's theorems to fuzzy logic.

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Russell and Norvig note that Gödel's argument only applies to what can theoretically be proved, given an infinite amount of memory and time.

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Gödel's Incompleteness Theorem: any logical model of reality is incomplete(and possibly inconsistent) and must be continuously refined/adapted in the face of new observations.

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Gödel and Cohen showed that it's impossible to prove that the continuum hypothesis is right, but also it's impossible to prove that it's wrong.

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9

Kurt Gödel described a model that satisfies the axioms of set theory, which does not allow for an infinite set to exist whose size is between the natural numbers and the real numbers.

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10

The first of these was proposed by Kurt Gödel, a solution known as the Gödel metric, but his(and many others') example requires the universe to have physical characteristics that it does not appear to have.

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More speculatively, Gödel conjectured that the human mind can correctly eventually determine the truth or falsity of any well-grounded mathematical statement(including any possible Gödel statement), and that therefore the human mind's power is not reducible to a mechanism.

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12

A consequence of Gödel's two incompleteness theorems is that in any mathematical system that includes Peano arithmetic(including all of analysis and geometry), truth necessarily outruns proof, i.e. there are true statements that cannot be proved within the system.

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13

Gödelian anti-mechanist arguments tend to rely on the innocuous-seeming claim that a system of human mathematicians(or some idealization of human mathematicians) is both consistent(completely free of error) and believes fully in its own consistency(and can make all logical inferences that follow from its own consistency, including belief in its Gödel statement).

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