Patrick Grim gives something like the following argument. What I know when I know that
1. I am making a mess
is an indexical fact that no one else can know. At most, what someone else can know is that
2. BV is making a mess
or perhaps, pointing to BV, that
3. He is making a mess.
Just as no one except BV can refer to BV by tokening the first-person singular pronoun, no one except BV has access to the indexical fact that, as BV would put it to himself, I am BV. Only BV is privy to this fact; only BV knows himself in the first-person way. Now an omniscient being knows everything that can be known. But although I am not omniscient, there is at least one proposition that I know -- namely (1) -- that is not known by any other knower, including an omniscient knower. So an omnisicent being is impossible: by its very definition it must know every fact that can be known, but there are indexical facts that it cannot know. God can know that BV is making a mess but he cannot know what I know when I know that I am making a mess. For any subject S distinct from God, the first-person facts appertinent to S are inaccessible to every mind distinct from S, including God's mind. That is what I take to be Grim's argument.
I suppose one could counter the argument by denying that there are indexical facts. But since I hold that there are both indexical propositions and indexical facts, that response route is not available to me. Let me see if I can respond by making a distinction between two senses of 'omniscience.'
A. X is omniscient1=df X knows every fact knowable by some subject or other.
B. X is omniscient[2] =df X knows every fact knowable by some one subject.
What indexical facts show is that no being is or can be omniscient in the first sense. No being knows every indexical and non-indexical fact. But a failure to know what cannot be known does not count against a being's being omniscient in a defensible sense of this term any more than a failure to do what cannot be done counts against a being's being omnipotent. A defensible sense of 'omniscience' is supplied by (B). In this second sense, God is omniscient: he knows every fact that one subject can know, namely, every non-indexical fact, plus all facts pertaining to the divine subjectivity. What more could one want?
Since no being could possibly satisfy (A), (A) is not the appropriate sense of 'omniscience.' Compare omnipotence. An omnipotent being cannot be one who can do just anything, since there are both logical and non-logical limits on what any agent can do. So from the fact that it is impossible for God to know what is impossible for any one being to know, it does not follow that God is not omniscient.
To sum up. There are irreducible first-personal facts that show that no being can be omniscient in the (A)-sense: Patrick Grim's argument is sound. But the existence of irreducible first-personal facts is consistent with the truth of standard theism since the latter is committed only to a being omniscient in the (B)-sense of 'omniscience.'
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