5 ms·
“semi” rigurously is what spooked me. The thing with Gödel’s proof is that it is very hard to do rigurously...
by pfortuny 7y ago
“semi” rigurously is what spooked me. The thing with Gödel’s proof is that it is very hard to do rigurously...
- QuesnayJr 7y agoIt's not that hard. There are several computer-checked proofs of it. It's hard to explain, because the idea of encoding statements about a system in terms of the system itself is weird if you haven't seen it before.
- thethirdone 7y agoThere are a lot of details that are needed in the proof. You need to define a first order logic and prove arithmetic theorems on top of PA to even start a rigorous proof. That said it can be fully covered in a single semester of undergraduate study, so its not that hard. There are many theorems that couldn't be fully proved in a semester.
- mensetmanusman 7y agoThere are many true theorems that couldn’t be fully proved ;)
- caleb-allen 7y agoProve it!
- cellular 7y agoOk: "this sentence is unprovably true".
- mensetmanusman 7y agoOr Pinocchio saying: “My nose will get longer”
- adz_6891 7y agoI went through it the first time by reading over Computability & Logic (5th edition) [1]. I'd love to go over it again, and would recommend it to anyone interested who has a few weekends to invest. [1] https://www.goodreads.com/book/show/1556746.Computability_and_Logic https://www.goodreads.com/book/show/1556746.Computability_an...