[jsprogrammer]

If an AI is an algorithm, then it will be unable to produce "answers" to what we observe. That is the relevance. One would need to show a contradictory example to the theorem to ignore it.

>There is nothing whatsoever in the paper that stops an AI from having whatever ability to choose freely humans have.

There is if an AI is dependent on deterministic methods. I agree that AI is not a well-defined term, but all proposals I have seen are algorithms, which are entirely deterministic. This is entirely at odds with the human conception of free choice. An algorithm will always produce the same choice given the same input. Any other behavior is an error.

The SFWT says that observations can be made that cannot be replicated through deterministic means, which would seem (I agree there is a very slight leap in logic here) to rule out any AI from ever being able to understand at least some aspects of our reality (and also reveals them to be simple, logical machines, with no choice).

[bllguo]

Algorithms are not by definition deterministic, which seems to be one of your key points. Probabilistic algorithms exist. They may or may not be used in machine learning currently, but they do exist.

[jsprogrammer]

Can you provide an example? All probabilistic algorithms I have seen rely on a pseudo-random generator a rely on an external source if numbers. I have argued elsewhere in these comments that both cases my be considered deterministic.