Omniscience: A thought experiment

[Hatshepsut]

Now let Q be the proposition that the Being can  determine whether it is in Scenario A or B, regardless of how it does so. Does Q have a truth value? (See OP)

I suspect that Q does have a truth value and that value is untrue. If that's the case, the SEP definition for omniscience is paradoxical (which is my original point: omniscience, if you impose a very strict definition such as the SEP, is an impossible standard). It results in paradox because whether or not the Being is in Scenario A or B also has a truth value, and so an omniscient being would have to know something that it knows it cannot know (it reminds me of the Liar Paradox e.g. "this sentence is false"). However, if I'm incorrect and it turns out Q is true, then omniscience is preserved - but I know of no proposed solution to the problem that results in Q being true.

I think your bolded part is a premise in the OP which we have to grant, or the whole OP setup would be pointless. Good. That clearly implies the Being cannot be in both A and B. Now we can dispense with Q = true. Suppose the Being is in scenario B. Then the Being thinks that it is in A, because it's wrong. In this case, the Being fails to determine its scenario, so Q cannot be true. We haven't yet shown that Q = false, because while it's false provided the Being is in B, we still need to show it is false if the Being is in A. I haven't been able to do that.

Your theorem that Q = false ---> The SEP definition is paradoxical ...?? I'm stumped. One half of it is easy, like you said. Let Being satisfy the SEP. Then it knows that Q = false. Therefore it doesn't know if it's in A or B. Therefore it doesn't satisfy the SEP.

But to finish paradox, we must let Being not satisfy SEP and show this implies that it does satisfy SEP. If we have only the first half, it's possible the class of Beings which satisfy SEP is empty.

Omniscience and omnipotence are such childish claims.

Kind of like angels dancing on a pinhead.