> Your reversing of the relationship between the Halting Problem and the Incompleteness theorem ...
Here's what I said: "Even something as trivial as the Turing halting problem is known to be insoluble because of its connection to the incompleteness theorems."
That doesn't reverse the relationship between the two, it identifies that there is a relationship. That's not controversial.
> It's not that the Incompleteness Theorem tells us about the Halting Problem, but rather, that the Halting Problem tells us about the Incompleteness theorem.
The Turing halting problem and the incompleteness theorems are related. Without the GIT, we would not be aware that the Turing halting problem is insoluble, a statement that can be made about any number of similar issues.
> Also, we have no reason to think that the universe satisfies some of the requirements of the Incompleteness Theorem (or even things like the Halting Problem).
You mean, apart from the fact that the question is whether the universe is a vast computer simulation, by definition subject to the halting problem, which lacks a solution because of the GIT?
> Both require some kind of unbounded or self-referential behavior, which we might not have in the universe.
We're not discussing the universe's behavior, we're discussing the feasibility of establishing whether or not it is a simulation, and do this from within the universe. That is the very definition of self-referential.
Here's what I said: "Even something as trivial as the Turing halting problem is known to be insoluble because of its connection to the incompleteness theorems."
That doesn't reverse the relationship between the two, it identifies that there is a relationship. That's not controversial.
> It's not that the Incompleteness Theorem tells us about the Halting Problem, but rather, that the Halting Problem tells us about the Incompleteness theorem.
The Turing halting problem and the incompleteness theorems are related. Without the GIT, we would not be aware that the Turing halting problem is insoluble, a statement that can be made about any number of similar issues.
> Also, we have no reason to think that the universe satisfies some of the requirements of the Incompleteness Theorem (or even things like the Halting Problem).
You mean, apart from the fact that the question is whether the universe is a vast computer simulation, by definition subject to the halting problem, which lacks a solution because of the GIT?
> Both require some kind of unbounded or self-referential behavior, which we might not have in the universe.
We're not discussing the universe's behavior, we're discussing the feasibility of establishing whether or not it is a simulation, and do this from within the universe. That is the very definition of self-referential.