I think the following yields a pretty good formulation of the argument for incompatibility of foreknowledge and free will. Start with the principles:
- If x freely chooses A at t, and p is a truth solely about what happened prior to t, then p does not entail that x freely chose A at t.
- <God believes at t* that x freely chooses A at t> entails <x freely chooses A at t>.
- <God believes at t* that x freely chooses A at t> is solely about what happens at t*.
But here is a criticism of (1) that I don't remember seeing, though it's obvious enough that I expect it's there somewhere. Claim (1) is supposed to capture our intuition about alternate possibilities. But it fails to capture these intuitions. Consider this case. Suppose the laws of nature are necessary, and you simultaneously deterministically cause me to have an irresistible desire to do a Hitler salute and push me into a time machine so that it is nomically necessary that I perform the Hitler salute in the year 3000 BC. Next thing I see, it's the first moment of the year 3000 BC, and I am doing a Hitler salute. Intuitively, here is a violation of alternate possibilities. But (1) does not indicate this. Let p be a complete description of the universe at the time you push me into the time machine. Then p entails that I do a Hitler salute in the year 3000 BC. But p is not a proposition about what happened prior to the year 3000 BC. Hence, (1) does not rule out my freedom, even though it is surely meant to.
Here's a second, less weird case. Simultaneous causation is at least imaginable. Imagine the laws are necessary, and there is some state of the world that deterministically causes me to simultaneously raise my arm in a Hitler salute. Again, (1) does not tell me that the action is unfree, even though the alternate-possibilities intuitions that led to (1) surely do. So (1) does not capture these intuitions.
So what went wrong in (1)? I know two suggestions. The first one is that "prior to t" in (1), which was originally meant to be "objectively temporally prior" should be understood: "temporally prior in x's subjective time." I think this is unsatisfactory. For instance, x's subjective time only runs when x exists. But surely (1) is meant to rule out a necessitating manipulator of a free agent even when the necessitating manipulator acted before x's conception. The second suggestion is that "prior to t" should become: "explanatorily prior to the agent's freely choosing A." This gives the correct result in time travel case. For while your pushing me in the time machine is not temporally prior to my arriving at 3000 BC, it is explanatorily prior. And it gives the right answer in the simultaneous causation case.
But now note that if we replace "prior to t" in (1) with "explanatorily prior to the agent's freely choosing A", then the argument against foreknowledge fails. For the defender of libertarian free will and foreknowledge can simply deny that God's belief that I will freely do something is explanatorily prior to my doing it.
Now, granted, we might try to capture the intuitions by replacing "prior to t" with "temporally prior to t or explanatorily prior to the free action". But that's too messy.