4 ms·
No; halting would be a proof of inconsistency. We expect it never to halt because we believe ZFC to be consistent.
by tromp 10y ago
No; halting would be a proof of inconsistency.
We expect it never to halt because we believe ZFC to be consistent.
- rrobukef 10y agoBelief has nothing to do with it. I can believe ZFC is inconsistent and the world will not change a bit. You can't prove me wrong. (It's almost a religious argument) If I believe the inconsistency of ZFC then I believe the machine must halt. I can't ever observe it since I can't know the number of steps needed. There's almost a paradox but not quite.
- Grue3 10y agoNo, if ZFC is inconsistent, then you can know the number of steps needed. Every statement, true or false, is derivable from ZFC if it is inconsistent. If there's contradiction in ZFC, it can be found in finite time by enumerating all the theorems.