I was debating on whether or not to post something about this, because the reality is that any answer I give will be speculative. But I recently came across a few videos on youtube in which an atheist questioned how anyone could know himself to be omniscient. So, keeping in mind that speculation can be apologetically useful (link), I think I've found an appropriate context in which to give some thoughts on the title of this post.
I've spent quite a lot of time and written quite a few posts on how we can know God is omniscient. But this, of course, entails that God can and does know Himself to be omniscient. How? Well, the question itself might need some clarification. For instance, I don't believe God could have learned He is omniscient (link), but the distinction between discursive and intuitive knowledge is not what is at issue. What is at issue is the justification of knowledge [claims]. We can justify knowledge claims by divine revelation; according to what could God justify His knowledge claims in general and omniscience in particular? I think Gordon Clark provides the beginnings of a good answer:
The substantive point needing discussion is whether the law of contradiction is the one and only test of truth.
Ideally or for God this seems to be the case. Since there is nothing independent of God, he does not conform truth to an alleged reality beyond truth and beyond him. Since there is no possibility of “vertical” (to use Carnell’s terminology) coherence, the “horizontal” test, or, better the horizontal characteristic of logical consistency seems the only possible one.
Weaver correctly notes that I do not claim for human beings the ability to apply this test universally. In this sense it is a “negative” or, better, an incomplete test. For this reason it must be supplemented some way or other...
Undoubtedly I hold that truth is a consistent system of propositions. Most people would be willing to admit that two truths cannot be contradictories; and I would like to add that the complex of all truths cannot be a mere aggregate of unrelated assertions. Since God is rational, I do not see how any item of his knowledge can be unrelated to the rest. Weaver makes no comment on this fundamental characteristic of divine truth.
Rather, he questions whether this characteristic is of practical value, and whether it must be supplemented in some way. It is most strange that Weaver here says, “I must agree with Carnell,” as if he had convicted me of disagreeing with Carnell by providing no supplementation whatever. Now, I may disagree with the last named gentleman on many points, but since it is abundantly clear that I “supplement” consistency by an appeal to the Scripture for the determination of particular truths, it is most strange that Weaver ignores my supplementation. (Clark and His Critics, 2009, pgs. 287, 290)
That is, God can test His self-knowledge-claim for coherence. To expand, God could know Himself to be omniscient if it is the case that such is an epistemic necessity, a precondition for anyone to know anything. Or, if "God is omniscient" coheres with all other truths and "God is not omniscient" does not, then the former must be true.
[I don't want to complicate this post with references to the philosophy of time, necessitarianism vs. "free" knowledge, the metaphysics implied by a correspondence theory of truth, etc. Needless to say that I don't think any of them pose an incontrovertible obstacle to a modified coherentistic account of divine knowledge.]
Now, the atheist might ask what reason we have to think this is the case. But notice that that's a subtle change in the subject. If the atheist wants an account of how we can know that God can be omniscient, we are capable of providing a defense of our own knowledge-claims. But this is a question of what justification we have for believing God is omniscient, not what justification God could have for the same belief. There's a difference.
Our epistemic limitations and dependencies would obviously not pose a problem to an omniscient God. That we may not see the logical necessity would not imply there isn't one. That there necessarily is an omniscient God - whether we recognize or are even capable of recognizing such to be the case - does not appear contradictory, anyway, so as far as the burden of proof is concerned, the apologetic task that was set before us is complete.
At the same time, there is also no need to sell ourselves short. Of course, none of the above references to epistemic limitations is meant to imply we in fact can't see a logical necessity for an omniscient God. Actually, given the problem of partial knowledge and logical need for revelation from one who is omniscient, it is ironic that any argument against the possibility an omniscient mind presupposes revelation from such a mind. For as I mentioned above, this in turn presupposes that said mind can know himself to be omniscient, and that's what this was all about.