James Andrix: an AI would be perfectly capable of understanding a proof that it was deterministic, assuming that it in fact was deterministic.
Despite this, it would not be capable of understanding a proof that at some future time, it will take action X, some given action, and will not take action Y, some other given action.
This is clear for the reason stated. It sees both X and Y as possibilities which it has not yet decided between, and as long as it has not yet decided, it cannot already believe that it is impossible for it to take one of the choices. So if you present a “proof” of this fact, it will not accept it, and this is a very strong argument that your proof is invalid.
The fact is clear enough. The reason for it is not quite clear simply because the nature of intelligence and consciousness is not clear. A clear understanding of these things would show in detail the reason for the fact, namely that understanding the causes that determine which actions will be taken and which ones will be not, takes more “power of understanding” than possessed by the being that makes the choice. So the superintelligent AI might very well know that you will do X, and will not do Y. But it will not know this about itself, nor will you know this about the AI, because in order to know this about the AI, you would require a greater power of understanding than that possessed by the AI (which by hypothesis is superintelligent while you are not.)