In fleshing out the traditional definition of omniscience, William Lane Craig distinguishes between propositional knowledge and non-propositional knowledge, claiming that to be omniscient is to know every true proposition and not believe any false ones. He goes on to explain that God also possesses all appropriate self-knowledge, but that being non-propositional in nature, this is a bonus which is not essential to omniscience.
To illustrate this distinction, he compares the sentence "I have been treed by a moose" with "Bill has been treed by a moose," concluding that although they express the same proposition, the latter sentence must be conjoined with "I am Bill" in order for it to play the same role as the former sentence in influencing behavior. The claim is that the sentence "I am Bill" is not propositional knowledge, but a sort of non-propositional self-knowledge. This is the part I don't understand.
Firstly, I don't even understand why this distinction is helpful in its context. Dr. Craig's goal appears to be clarifying that omniscience is normally understood in terms of propositional knowledge, and that therefore God does not need to possess all self-knowledge in order to be omniscient, thus deflecting any objection to omniscience based on the incoherence of God possessing the knowledge, i.e., "I am Napoleon." The problem is that even without this distinction, I can't see how "I am Napoleon" would be anything more than a false proposition when expressed from the perspective of God, which shouldn't do anything to scratch Craig's picture of God's omniscience, despite his claim, "But God doesn’t have the self-knowledge that, say, Napoleon does, in that God doesn’t believe that he is Napoleon. God doesn’t believe that he is Ronald Reagan. God knows that he is God. That is why I said that what God possesses is appropriate self-knowledge. To have all self-knowledge would be a cognitive dysfunction, not an excellence. God would be literally schizophrenic and would hold false beliefs if God thought that he were Ronald Reagan or Napoleon." If this self-knowledge was propositional in nature, God would simply not believe such propositions (and believe their negations), since they're false. Why should this be any different from God knowing "the average lifespan of a human is 5000 years" to be false? Furthermore, even if "I am Napoleon" is not a proposition, surely "I am Napoleon or married bachelors exist" is a proposition, so wouldn't this self-knowledge still turn out to be implicitly essential to omniscience?
But the deeper question is how saying this self-knowledge is non-propositional even makes sense. "I am Bill" has a truth value, when expressed from some perspective that satisfies the indexical, just as the uncontroversially propositional sentence, "I have been treed by a moose" does. Granting that "God [...] would hold false beliefs if God thought that he were Ronald Reagan or Napoleon" makes it clear that "I am Ronald Reagan" and "I am Napoleon" have truth values, and isn't that sufficient for their being propositions?
I was able to find some information on non-propositional knowledge under the label "knowledge-how," but this seems to be quite a different animal.
Knowledge-how refers to experiential knowledge proposed to be "irreducibly complex." Perhaps how to play the flute cannot be broken down into propositions, but this type of knowledge isn't true or false. This seems quite different from self-knowledge, instances of which actually make sense to associate with truth values. What is the correct way to conceive of self-knowledge in relation to propositions/propositional knowledge?