Re:An intutive counterexample to the axiom of choice
by 6gvONxR4sf7o on Monday January 23, 2023 @11:58AM
(#34491503)
It seems like the validity of what you're saying is intertwined with the axiom itself. You're going from a comment about the domain (the domain includes indescribable elements) to a comment about specific arguments (arguments may be indescribable).
Ultimately, you're saying that if we have an indescribable x, then x+1 is conditionally describable (to abuse terminology). But I think that just sidesteps the question. Even then, if we're taking a computability lens, then indescribable(x) implies indescribable(x+1), which would seem to imply that applying your function to indescribable x's is a moot point.
The fact that your function is finitely describable even though we can't describe each of its applications is admittedly a mindfuck.
Ultimately, you're saying that if we have an indescribable x, then x+1 is conditionally describable (to abuse terminology). But I think that just sidesteps the question. Even then, if we're taking a computability lens, then indescribable(x) implies indescribable(x+1), which would seem to imply that applying your function to indescribable x's is a moot point.
The fact that your function is finitely describable even though we can't describe each of its applications is admittedly a mindfuck.