2 ms·
Oh this is interesting, I didn't know about this historical detail. It makes sense, Godel's first could be mostly seen as a version of the halting problem, whi
by qsort 3y ago
Oh this is interesting, I didn't know about this historical detail.
It makes sense, Godel's first could be mostly seen as a version of the halting problem, while the second is "game over" for a Hilbert-like foundation program.
p.s. Just wanted to point out that it's funny how we wrote two mostly identical sets of comments. Great minds think alike? :)
- Tainnor 3y ago> Oh this is interesting, I didn't know about this historical detail. That's the characterisation I got from Peter Smith's book about Gödel's theorems. I didn't verify original sources or anything, but it sounds very plausible to me. And it also kind of answers the question about why we should care: if a system can't prove its own consistency, well that's not terribly interesting (even if it could, we would have to believe the system a priori to trust its own consistency proof). But if it also can't prove a stronger system consistent, then that's much more interesting. > Great minds think alike? That would be a bit too self-aggrandizing for me. :D I'm very curious about logic (and maths in general), that's why I know some stuff about it, but I'm no maths genius.