- #1
gsingh2011
- 115
- 1
So Godel's Incompleteness Theorem states that we cannot prove all facts about the natural numbers. Are we still able to prove that those proofs are impossible? Or are we stuck not knowing whether it is possible to prove something?
The second part of the theorem says that any system that can prove certain facts about the natural numbers cannot proved to be consistent. I got this from wikipedia and the wording confuses me. What certain facts? Does inconsistent mean that any theorem you prove may not be true?
Thanks in advance.
The second part of the theorem says that any system that can prove certain facts about the natural numbers cannot proved to be consistent. I got this from wikipedia and the wording confuses me. What certain facts? Does inconsistent mean that any theorem you prove may not be true?
Thanks in advance.