I think the puzzle ultimately fails.
We say that God is His will, and at the same time we say that God could have willed a different universe instead of this one. As I see it, the problem is that we're equating the "faculty" (so to speak), which is identical to God, with its relationship to other things, which is not identical to God. So perhaps we can say God is identical to His act of willing (the "faculty"), but not with the content of His will (the "relation"). This same answer, I think, applies to God's knowledge--God is identical to His act of knowing, but not with the content, although that assumes that I've given something coherent, instead of just a confused mess. (I'm not even sure right now whether this entails that God has accidental properties, which I suppose is a no-no.)
Since I'm offering this, I'll say I believe it's consistent with Dr. Vallicella's premise (1) (and therefore Divine Simplicity itself) because the content of God's knowledge is internal to Him in a different sense than is used when we talk about His attributes proper.

Anyhow, if both theism and atheism are incoherent, then what are the remaining options? I figure Emanationism is one...

Grace and Rust wrote:

We say that God is His will, and at the same time we say that God could have willed a different universe instead of this one. As I see it, the problem is that we're equating the "faculty" (so to speak), which is identical to God, with its relationship to other things, which is not identical to God. So perhaps we can say God is identical to His act of willing (the "faculty"), but not with the content of His will (the "relation"). This same answer, I think, applies to God's knowledge--God is identical to His act of knowing, but not with the content, although that assumes that I've given something coherent, instead of just a confused mess. (I'm not even sure right now whether this entails that God has accidental properties, which I suppose is a no-no.)

Vallicella sidesteps any problems the distinction between God's act of knowing and knowledge might cause by putting his argument entirely in terms of the latter. (I actually had this distinction in mind when I chose Vallicella's version of the argument.)

John West wrote:

But then God's Nature in worlds he knows the proposition p would differ from God's Nature in worlds he knows ~p. And by immutability, God's Nature can't differ between worlds.*

(Plus, if God knows anything, and knowledge requires true belief, then the original problem.)

*God's Nature is strictly identical across all possible worlds.

​But does this rely on possible worlds talk? Would the objection still apply if the theist had some other framework for understanding modality (for example, because possible worlds seem to make contingency problematic by implying the existence of all contingent or possible worlds)? If something could have been different but isn't, then, absent possible worlds talk, does that require a change in an atemporal God's nature?

​Interestingly, I believe Ibn Sina and some of the other Masha'iyya seem to believe God did not have knowledge of particulars.
 

John West wrote:

There are none. If theism is the affirmation of “God exists”, atheism is its denial, and both are incoherent, then theism is both false and not false, and there is a contradiction in reality.

But there are no contradictions in reality. So, I say “both positions appear to have contradictions in them”, and neither affirm nor deny “God exists”.

​Technically, if you are correct, couldn't it be the case the contradiction is in our (discursive) reason? It wouldn't have to be reality per se.
 

Technically, if you are correct, couldn't it be the case the contradiction is in our (discursive) reason? It wouldn't have to be reality per se.

I'm not sure. I don't think the mystics—this has been turned into a dirty word, but it shouldn't be one—would be bothered by anything I've said here, though, no.  

(I could have done a much better job with the paragraphs you're replying to, hah.)