You assume that a human cannot be described with something less powerful than a Turing machine. There is no reason to believe that knowing what a human will do in this instance is equal to decidability of computer programs.
I almost objected, but you're right. The human has finite time with which to calculate. The predictor can easily be assumed to have more time. There's no problem calculating if a program will halt in finite time.
I assume nothing of the sort. I merely assume that humans, like computers, are capable of evaluating the truth of something and then deliberately reporting the opposite. That is all that is required.
