Omniscience and self-knowledge

Reposted from comments here.

a. Bits of knowledge are differentiated at the level of sense (or description if you like), while objects of knowledge are differentiated at the level of reference. There's a nice bit in Aquinas (at least, I think its Aquinas) where he points out that knowledge of the road from Thebes to Athens is different from knowledge of the road from Athens to Thebes, even though the object of knowledge is, of course, identical to itself.

b. There are bits of knowledge that can be known only by their knower. Consider the sentence I am married to N, where N is some proper name. The only person who can truthfully assent to the statement usually expressed by that sentence is the spouse of the person named by N. Probably, God knows this as So-and-so is married to N. Plainly, the two bits of knowledge have the same object (the marriage relation between So-and-so and the referent of N). Equally plainly, they're distinct bits of knowledge. That's basically all that's required to get the case off the ground. It's easy to produce a bit of self-knowledge that a knower once had which he now lacks and can't regain.

To borrow John Perry’s example, suppose I’m walking around a supermarket shelf following a sugar trail, when suddenly I realise that the sugar-trail I’m following is my sugar trail. The truth that it is my sugar trail I’m following is a truth that only I can know. (everyone else knows something like: Cirdan is following his sugar trail.) If I then became amnesiac, then for as long as I was an amnesiac, there would be a truth nobody could know.

If that case, or a similar one, survives, then there are unknowable truths in a strongr-than-usual sense. This is not particularly a problem for omniscience, for omniscience is knowledege of everything that can be known - if it's impossible to know something, then omniscience doesn't require that it be known.