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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
by fiatjaf 5y ago
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.
- denton-scratch 5y ago> 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.
- fiatjaf 5y agoYes, 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.