Oracles and the Halting Problem

[Angrboda]

In order for the list to be searched, it must first exist. The list may be generated algorithmically or non-algorithmically. The halting problem says the list cannot be generated algorithmically. Therefore, for the list to be generated, it has to be generated non-algorithmically, which removes it from the purview of the halting problem.

Moreover, it raises the specter of the question of correctness. In computer science, we're taught how to mathematically analyze an algorithm or program for correctness. Correctness being the property that the given algorithm or program will yield the correct result, tautologically. The proof of the correctness of an algorithm, assuming it exists, rests on those mathematical and logical assumptions that underpin the proof. Especially, the belief that such methods are robustly deterministic. If not, then correctness seems to lose all meaning. Let's suppose God provides you with this list. How do you determine its correctness? Verify one entry? A random sampling? The majority? All of them? Suppose you check all of them and God comes back and tells you he gave you the wrong list, that the list he gave you was for some other question, which just happened to be exactly the same list as the one he gave you for the halting problem. Is that list, the wrong list, a 'correct' solution to the halting problem?