Because I am interested in coherence of theism issues, I think I’ll tackle these arguments. They come from this YouTube video here. The arguments supposedly support two contentions, in order: A. God cannot know that he knows everything, and B. God cannot act contrary to his own predictions. What follows is first the argument for (A), then some comments, and then the argument from (B), followed by comments. It was difficult to represent these syllogistically in a valid manner. I did try to represent the argument fairly, however.
1. God cannot know that there isn’t a God higher than God, which places him in a deceptive simulation (Cartesian demon idea).
2. This works as an infinite regress.
3. Therefore, there is some amount of doubt, for God, to the claim that God knows everything.
4. Therefore, God cannot know that he knows everything.
Now, technically speaking, (4) doesn’t follow from (3) unless we also add that it’s a truth that God must know with certainty in order to satisfy omniscience. That premise I am willing to grant. Now what is omniscience? It seems to be that a naïve but generally functional view is to say that omniscience is that God knows all truths and believes no false ones. It’s important, in fact vital, to note that the above criticism is supposed to be an internal issue of coherency. Internal criticisms will grant, for the sake of argument, the issue under contention, and then try to show that either it is incoherent (hence, a coherency objection), or otherwise factually false (entails some fact which we are more likely to reject than we are to accept the issue under contention as true).
Why, given omniscience, should we think (1) is true? If omniscience entails that God knows all truths and believes no false ones, and if there is a truth of the conditions of (1), then God would know it. So God would know “I am not being deceived about omniscience.” The reason Cartesian doubt works is precisely because Descartes (and other humans) are not omniscient. If omniscience is true, it is not so much as logically possible that God is being deceived by an evil being. You can’t assume omniscience is true, posit the above claim, and then ask, “How does God know that?” By omniscience, of course! There is also the further fact that, if Perfect Being Theology (or something very much like it) is a correct representation of what God would be like, then God would be both omniscient and the Greatest Conceivable Being. But from these two it follows: “There is no other God so construed” and “God knows that there is no other God so construed,” which renders the objection doubly moot.
Argument against Predictions
1. If there is a true prediction, then the event must occur.
2. God supposedly makes true predictions.
3. Therefore, the events God predicts must come true.
4. If this is so, then even God cannot bring it about that what he has predicted will not come true.
5. This includes events that God predicts involving himself.
6. Therefore, God does not have free will with respect to his predictions.
The idea trades on a modal fallacy that is all-too-easy to commit. The argument boils down to this scenario: God is infallible, he predicts he will do X at T, T comes, and God decides to do not-X at T, this falsifies his prediction. God’s prediction cannot be falsified; therefore, God cannot decide to do not-X at T given that he has predicted he will do X at T.
The modal fallacy occurs when the necessity of some whole is distributed to the parts of the scenario. All that is necessarily false is the complete idea that “God makes a prediction about free actions and that prediction fails to come true.” For a quick example, the following proposition, as a whole, is necessarily false: “Diane planted exactly six rosebushes at T and Diane planted exactly ten rosebushes at T,” where we take all of the terms to be univocal and T to describe both time and place. Yet it would be fallacious then to infer that one of these was logically impossible. Surely either of them could have been true; what’s logically impossible is that they both are.
So it is with the argument above. All that’s impossible is that God makes a prediction and the prediction fails to come true. So how could this be resolved? God doesn’t make the prediction at all, God makes it about himself on the basis of what he knows he will choose, etc. After all, if God is omniscient, then he would know that, if he made some prediction X, that when the time came, he would do X or not-X, and so would predict that accordingly. Seen as such, these arguments should not be very persuasive.
 For Descartes, the logical possibility of the evil demon was an epistemic possibility (i.e., “For all I know, I am being deceived by an evil demon”). But, given omniscience, this epistemic possibility evaporates, by definition.
 This example was adapted from the Internet Encyclopedia of Philosophy < http://www.iep.utm.edu/foreknow/#H6>, accessed March 25, 2014.