Gödel's Incompleteness Theorem in Bash

Re:Gödel's Incompleteness Theorem in Bash by fiatjaf on Friday February 25, 2022 @05:54AM (#30465875)

They are definitely distinct. The key insight of Godel's incompleteness theorem is that there is a statement that can't be proved as true but is indeed true and can be perceived as true by an observer outside of the mechanical-logical realm inside of which that statement lives.

It says there are something non-mechanical about intelligence.

Apparently people think it is just a paradox or some other boring idea.

See "Emperor's New Mind" from Roger Penrose.

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Re:Gödel's Incompleteness Theorem in Bash by denton-scratch on Friday February 25, 2022 @07:00AM (#30466341)

> It says there are something non-mechanical about intelligence.

I don't think Gödel drew that conclusion; that's Roger Penrose's reasoning. He uses Gödel's Theorem as an example of correct reasoning that can't be algorithmic (i.e. Gödel's mind cannot be replaced by an algorithm). It's not a proof, and it's controversial. I find it convincing; but then I'm biased - I'm predisposed to the view that the mind is not algorithmic.

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Re:Gödel's Incompleteness Theorem in Bash by fiatjaf on Monday February 28, 2022 @03:00PM (#30504359)

Yes, I just used this opportunity to raise this point. I don't know what Gödel himself thought of it.

But I find it very disheartening when such an interesting find is presented as simply "a paradox" akin to the phrase "this is a lie". That would be the most uninteresting thing ever.

Many articles on the internet thus describe Gödel's theorem, and also that famous book from Douglas Hofstadter.

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