Oracles and the Halting Problem

[Tiberius]

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.

It does? Where?

The list you mentioned was one that God had which had every possible algorithm on it, and whether or not it halted. Such a list is cannot be generated (nor can it even exist) since it would violate the entire proof that Alan Turing set about in 1936:

"Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist."

If such a list could exist, then as you said before, there would be an algorithm for determining whether any given program halted (simply search the list until you find the algorithm). However, this determination algorithm would clearly meet the criteria for being the general algorithm that Alan Turing proved cannot exist. Therefore, the list cannot exist either (since all lists are searchable).