I didn't mean that the two aren't related, just that they aren't as strongly related as the group seemed to be implying. They were saying that Ethereum being turing complete made it inconsistent in some way.
But yes, the two definitely are connected.
For example:
A program which could solve the halting problem would be able to determine whether a given system is consistent.
So, as a result, if a system could prove that a program solved the halting problem, and it could simulate programs running, then it could simulate the program that solves the halting problem being applied to a program that searches for inconsistencies in the system. This would allow it to prove whether it is itself consistent.
Therefore, by Godel's second incompleteness theorem, a system which can simulate programs for any number of steps, and which is consistent, and which can do arithmetic and such, cannot prove that any particular program solves the halting problem.
Admittedly, this is a lot weaker than "no program solves the halting problem", but I think it is a fairly clear connection.
So, yes, I agree that they are related.
But Ethereum's Turing completeness (or, Turing completeness except being limited by gas costs), does not mean that Ethereum is "inconsistent", because that is, uh, pretty much a nonsense claim. And that is the claim that I think the other group was making (Though they may have stopped making it since.)
Also, btw, wrt that blogpost, they got the number of states for a machine which ZFC cannot prove does not halt, but which does not halt, down to, iirc, like 2030 ? But you probably knew that already because it is the next blogpost on there.
But yes, the two definitely are connected.
For example:
A program which could solve the halting problem would be able to determine whether a given system is consistent.
So, as a result, if a system could prove that a program solved the halting problem, and it could simulate programs running, then it could simulate the program that solves the halting problem being applied to a program that searches for inconsistencies in the system. This would allow it to prove whether it is itself consistent.
Therefore, by Godel's second incompleteness theorem, a system which can simulate programs for any number of steps, and which is consistent, and which can do arithmetic and such, cannot prove that any particular program solves the halting problem.
Admittedly, this is a lot weaker than "no program solves the halting problem", but I think it is a fairly clear connection.
So, yes, I agree that they are related.
But Ethereum's Turing completeness (or, Turing completeness except being limited by gas costs), does not mean that Ethereum is "inconsistent", because that is, uh, pretty much a nonsense claim. And that is the claim that I think the other group was making (Though they may have stopped making it since.)
Also, btw, wrt that blogpost, they got the number of states for a machine which ZFC cannot prove does not halt, but which does not halt, down to, iirc, like 2030 ? But you probably knew that already because it is the next blogpost on there.
But yeah that is a cool result!