Yet a strong AI should be able to construct any string mapping whatsoever.
Why? I do not see why a strong AI must be able to construct any string mapping whatsoever. And for the reason that conversations have lengths that are bounded (as per the quote) we can know that the AI's string look up table will be finite.
"We do not know whether human programming is enumerable; thus, we cannot draw the analogy you attempted to draw."
My argument is only that there is an abstraction where you can view humans as a black box that takes a string and outputs a string. But I see the problem now, you are right in that I treat the CTT as true so I don't even notice when I am assuming the human black box is not something like a hypercomputer. But it is simpler to believe that humans are not something exotic like a hypercomputer than to believe they are.
> "we can know that the AI's string look up table will be finite."
If the AI's lookup table is finite, then we can just feed it its whole lookup table and ask it to say something that hasn't already been said. (This will take considerably less time than if its lookup table is infinite ;) )
Granted, many humans would probably just tell you where to stick it, so perhaps an AI could be programmed with that response and be indistinguishable from the average human. But in principle, whether the AI's lookup table is finite or not, it's possible to construct a query that requires it to go outside of its lookup table.
Why? I do not see why a strong AI must be able to construct any string mapping whatsoever. And for the reason that conversations have lengths that are bounded (as per the quote) we can know that the AI's string look up table will be finite.
"We do not know whether human programming is enumerable; thus, we cannot draw the analogy you attempted to draw."
My argument is only that there is an abstraction where you can view humans as a black box that takes a string and outputs a string. But I see the problem now, you are right in that I treat the CTT as true so I don't even notice when I am assuming the human black box is not something like a hypercomputer. But it is simpler to believe that humans are not something exotic like a hypercomputer than to believe they are.