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A comment on 1931: Kurt Gödel shows limits of math, logic, computing, AI. Parent comment

Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by kaba0 on Thursday June 17, 2021 @07:32AM (#27538465)
I’m not too knowledgeable on the topic, but Gödel’s proof uses a smaller logic system — on which a meta-language can be used to prove consistency/completeness. It is precisely about not being able to prove these properties “from within”.
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Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by ProfHewitt on Monday June 21, 2021 @10:47AM (#27579690)
As explicitly stated in the title [Gödel 1931] for a system

for the foundation of mathematics.

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Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by erichahn on Thursday June 17, 2021 @07:46AM (#27538539)
Which one? I don't think so tbh because his proof uses PA.
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Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by ProfHewitt on Monday June 21, 2021 @10:50AM (#27579713)
The reason that [Gödel 1931] was influential was that it

claimed to prove incompleteness for a system for the

foundations of mathematics.

1st-order systems such a PA were introduced later and

quickly shown to be inadequate for the foundations of mathematics.

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Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by kyberias on Thursday June 17, 2021 @07:54AM (#27538588)
It's very easy for you to check this from his 1931 article.
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Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by ProfHewitt on Monday June 21, 2021 @10:51AM (#27579729)
Yes, it is very easy to check that [Gödel 1931] was for a

system for the foundation of mathematics.

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Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by erichahn on Thursday June 17, 2021 @08:16AM (#27538768)
If you figure this out correctly you can claim the third incompleteness theorem. (If I am right)
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Re:1931: Kurt Gödel shows limits of math, logic, computing, AI by ProfHewitt on Monday June 21, 2021 @12:00PM (#27580448)
Results in [Gödel 1931] depend on existence of proposition

I'mUnprovable. Since, the proposition doesn't exist in

foundations, the results in [Gödel 1931] do not hold for foundations.

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