If you presuppose that the universe is not “mathematically possible”, you can’t really prove that it is possible for anyone to ask it that question. For that matter, it might just say “it halts” and be right. (It’s a mathematically impossible world, and you’re using math both when you’re deciding what the algorithm will do and what the box should answer.)
By the way, the usual statement for the halting problem is that you can’t make an algorithm that solves it, and by algorithm it usually means something a Turing machine, i.e. everything the algorithm does can be done by a Turing machine. In this case, assuming it makes sense to use math to reason about it, “Feed this algorithm to the magic box” is not actually something a Turing machine can do (it only has heads and tapes, no magic boxes). If you also give it the magic box it’s no longer just a Turing machine, it’s a [Turing machine + Turing oracle], which is something a bit different.
Imagine the magic box accepts algorithms expressed in Lisp (which theoretically allows unlimited memory). How do you express “feed something to the magic box” in Lisp?
By the way, does anyone know if it’s proven impossible (or even if discussed) to build a limited halting-problem solving algorithm that works for all algorithms except those that contain (complete or limited) halting solver algorithms as subroutines, in which case they also halt but say something like “don’t be an ass”?
If you presuppose that the universe is not “mathematically possible”, you can’t really prove that it is possible for anyone to ask it that question. For that matter, it might just say “it halts” and be right. (It’s a mathematically impossible world, and you’re using math both when you’re deciding what the algorithm will do and what the box should answer.)
By the way, the usual statement for the halting problem is that you can’t make an algorithm that solves it, and by algorithm it usually means something a Turing machine, i.e. everything the algorithm does can be done by a Turing machine. In this case, assuming it makes sense to use math to reason about it, “Feed this algorithm to the magic box” is not actually something a Turing machine can do (it only has heads and tapes, no magic boxes). If you also give it the magic box it’s no longer just a Turing machine, it’s a [Turing machine + Turing oracle], which is something a bit different.
Imagine the magic box accepts algorithms expressed in Lisp (which theoretically allows unlimited memory). How do you express “feed something to the magic box” in Lisp?
By the way, does anyone know if it’s proven impossible (or even if discussed) to build a limited halting-problem solving algorithm that works for all algorithms except those that contain (complete or limited) halting solver algorithms as subroutines, in which case they also halt but say something like “don’t be an ass”?