No, we're talking abot God's omniscience. The word "God", however, is used by different people to mean different things, so talking about God's omniscience might be talk about different things. However, since the target for debunking is what (most) theist philosophers call "God", going by their concept(s) seems proper.
Now, even among Christian philosophers (who make up the vast majority of theist philosophers), there are different usages of "God". But the usage of nearly all of them does seem to have some things in common. In particular, they all require that for a person to be God, he must know all truths - including all necessary truths.
So, the target is fine.
If you want to use the word "God" to mean something else, that's fine too. But that would not affect Ipetrich's argument. It's his argument, and so it's his choice what to target (which he did not specify, but I reckon it's implicit in the context: he's trying to debunk the existence of God, using "God" in a way that covers what nearly all theist philosophers, not what you might mean by that word).
Speakpigeon said:
It depends on what kind of knowledge God has. The ridiculous mistake is to project the prevailing theory of human knowledge on to God, as if it was anything but a non-starter. But that's not how God knows things. God has an intimate knowledge of things, what Russell called acquaintance knowledge. And it's not propositional so any notions of 'set' just won't ever apply. It's a bit like ants disputing that it's impossible for human beings to visit Mars because that would require an intelligence inconceivably greater than what ants are familiar with.
Actually, different theists have different beliefs about whether God's knowledge is propositional (I already pointed that out), and sometimes even define "God" in a way that implies propositional knowledge.
But regardless, the concept of set might still apply to non-propositional knowledge, as long as it weren't so big.
After all, if it were not for size constraints, if one is justified in saying that if A is God, then A knows what you had for breakfast, that 2+2=4, etc. (which is implicit in the way theist philosophers talk), then whether there is some sophisticated way in which the knowledge can be called "not propositional", an argument would succeed: one would just use another word instead of "proposition".
Speakpigeon said:
Yeah, Ok, human beings do possess acquaintance knowledge and, well, it's the only knowledge they possess, that's true, but, still, God does it better. Always.
But as long as it's coherent and justified to talk about God knowing that such-and-such, etc., whether there is some sophisticated objection to the claim that God's knowledge is propositional is immaterial: one can make an argument as if it were. Now, a theist might say it's justified to talk about God knowing that such-and-such, etc., in some cases, but not in the case in which one is making an argument against omniscience. But that would be blatant special pleading, unless the theist can give some reason to make the distinction.