For any finite subset of Turing machines, there exists a program that will act as a halting oracle on that subset. For example, the alien box might be a Giant Look-Up Table that has the right answer for every Turing Machine up to some really, really big number. (Would we be able to tell the difference between a true halting oracle and one that has an upper bound on the size of a Turing machine that it can analyze accurately?)
For any finite subset of Turing machines, there exists a program that will act as a halting oracle on that subset. For example, the alien box might be a Giant Look-Up Table that has the right answer for every Turing Machine up to some really, really big number. (Would we be able to tell the difference between a true halting oracle and one that has an upper bound on the size of a Turing machine that it can analyze accurately?)