I was going to say “Congratulations, you just proved the halting theorem.”—but actually I think the paradox you’re gesturing at fails to “work” for shallower reasons (e.g., the reals not being well-ordered—trivially not by the usual ordering, and less trivially not by anything computable, because it’s consistent with ZF for there to be no well-ordering of the reals).
I was going to say “Congratulations, you just proved the halting theorem.”—but actually I think the paradox you’re gesturing at fails to “work” for shallower reasons (e.g., the reals not being well-ordered—trivially not by the usual ordering, and less trivially not by anything computable, because it’s consistent with ZF for there to be no well-ordering of the reals).