Thesis: If Open Theism is true, then either possibly there are some things some humans know that God doesn't know or possibly God has some false beliefs. The conclusion is absurd, hence we should reject Open Theism.
For simplicity I will abbreviate "x does not fulfill the promise P and nothing prevents x from keeping P, nor does x conclude a defeater arises, nor does x forget" as "x violates P".
- Let x and y be humans. Often when x knows y's character to be solid and knows y to have promised to do something for x, x is not only justified in believing y will not violate the promise, but x knows it.
- If Open Theism holds, there is no possible divine doxastic policy such that, necessarily: (In every case like the one described in (1), God believes y will not violate the promise, and God has no false beliefs).
- Therefore, whatever possible divine doxastic policy is adopted, either in some worlds there will be a situation like that described in (1) where x knows y will not violate the promise, but God doesn't believe it and hence doesn't know it, or in some worlds God will have a false belief.
- This is absurd, and so Open Theism should be rejected.
Moreover, it is very likely that in the actual world either there are going to be cases of (1) where God doesn't know y will not violate the promise, or cases where God has some false belief. For there are so many cases of (1) in the actual world, that it is highly likely that any divine doxastic policy that doesn't involve foreknowledge of free actions will either miss some cases of (1) or will lead to belief in some cases where y in fact violates the promise.
To fill out the argument, I need to argue for (1) and (2). I think (1) is true. We certainly say things like: "I knew you wouldn't let me down." I think we should take them at face value. If we don't because we're worried about the fact that y might still freely choose to do the wrong thing, then likewise we should deny that the testimony of a reliable witness of solid character gives knowledge, because we should likewise be worries that such a witness still might have freely chosen to lie.
What about (2)? Well, the intuition here is this. If God doesn't have foreknowledge of future free events, his policy will be based on his evaluating evidence. When the evidence that y will not violate the promise is strong enough, God will believe it; when not, he won't. Now the bar for strength of evidence is either higher than that which we use when coming to believe that someone's character is solid enough that we can count on her not violating the promise or not higher. If it is not higher, then just we sometimes judge falsely based on the evidence, so, too, God will sometimes judge falsely based on the evidence. But if the evidential bar is higher, there will surely be at least some logically possible, and probably some actual, cases like (1) where we will be more epistemically bold than God, and where we'll nonetheless get it right and have knowledge. So then sometimes we'll know something God doesn't know.
The argument works best against Open Theisms that allow for non-trivial truth-values of future tensed contingent propositions, but I think a variant of it may work in general.