Indexicality and Omniscience

Patrick Grim gives something like the following argument for the impossibility of divine omniscience. 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. 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 omniscient₂ =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.  Logical: God cannot actualize (create) an internally contradictory state of affairs. Non-logical: God cannot restore a virgin.  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.'

Comments

[Krzysztof]

What about the following line of reasoning?

1.[P] There is a fact that "I am hungry."
2.[P] God is sufficient reason (cause, ground, etc.) for every fact.
3. God is sufficient reason for the fact that "I am hungry."
4.[P] If God is sufficient reason for x, then God knows x.
5. God knows the fact that "I am hungry."
6.[P/df?] If x is indexical fact, then only the subject P, who utters the indexical sentence can know the fact which makes this sentence true [alternatively (maybe better for God's case): If x is indexical fact, then only the subject P, who entertain the proposition made true by fact x can know this fact.]
7.[P] Fact that "I crave for coffee" is indexical fact.
8. I am the only subject, who knows that "I crave for coffee."
9.[P] And I'm pretty sure I'm not God

And so we have a contradiction.

We also need justification for 4.:

1. God is sufficient reason for x iff range of God's power include bringing about x.
2. God knows x iff range of God's knowledge include x.
3. If capabilities (/power[/attribute?]) x and y are identical, then they have the same range.
4. God is simple.
5. So God's power is identical to God's knowledge.
6. So God's power and God's knowledge have the same range.
7. So if God is sufficient reason for x, then God knows x.

This argument is not much convincing for me, because it includes too many uncertainties, but probably it is a fate of metaphysician. We can also try the following argument:

1. Let's assume that it's false that if God is sufficient reason for x, the God knows x.
2. So it's possible that God is sufficient reason for x and God does not know that x.
3. We can substitute x for a class of considered indexical facts, so: It's possible that God is sufficient reason for the facts connected with usage of first-person pronouns and does not know them.
4. Knowledge of facts connected with the usage of first-person pronouns is necessary for certain knowledge that one is a subject. (possibility of Cartesian machines, zombies etc.)
5. So it's possible that God is sufficient reason for a subject, but does not know with certainty that the effect of his being reason is a subject.

Well, if the argument is correct, then we have a bit unpleasant consequence, particularly if we have religious intuitions that world somehow exists for persons. But again, I did not inspect premises thoroughly, so I may be wrong (God's knows best).

[David Gudeman]

Is an indexical fact even a distinct fact? Doesn't "I am making a mess" represent the same fact as "David is making a mess"?

It seems to me that there is some conflation going on here between subjective perception of a fact vs. the fact itself.

[BV]

David,

Your point is well taken. If a fact is a truth-maker, then 'Dave is making a mess' and 'I am making a mess' (uttered by Dave) would seem to have the same truth-maker. A fact in this sense is a concrete state of affairs having a concrete infinitely-properties thing as a subject constituent.

The abstract propositions expressed by the two sentences would seem to be different however.

Dave could have a de re belief about himself without realizing that the man about whom he has the belief is himself. Suppose Dave sees a man in a mirror making a mess, and that man is himself, but Dave doesn't realize that the man is himself. So Dave believes that the man in the mirror is making a mess, and the man = Dave, but Dave does not believe the proposition expressed by 'I am making a mess' as uttered by Dave.

[David Gudeman]

Hm. You seem to have uncovered an inconsistency in my collection of beliefs about propositions, states of affairs, and intensional logic. I'll have to think about it.

Thank you, I guess? :)

[BV]

If a being is omniscient just in case it knows every true proposition, then it would appear that no one knower could be omniscient assuming that there is more than one knower.

Suppose there are just two knowers, God and Socrates. Socrates is not omniscient for obvious reasons. But neither is God. For there is one proposition that God does not know, namely, the proposition that Socrates knows when he knows that he himself is Socrates. This is the proposition expresed by 'I am Socrates' when assertively uttered by Socrates.

[Casey]

I presume that no property, had in actuality by any thing whatsoever, ever involves the obtaining of the impossible (logical or non-logical, as per your distinction), and that few will want to claim God has such properties (though some, somewhere, no doubt have). So mustn't any argument, such as Grim's about omniscience, claiming that God cannot have property X because no being can have it (logically or non-logically), only ever end up leading to the clarification of the nature of the divine attributes -- refining them so that they don't involve the obtaining of the impossible -- rather than showing God doesn't exist? It seems to me like this approach must always be only an exercise in clarification (not without value) rather than any demonstration of fact, just as some would say of the ontological argument's potential and limitations. I'm wondering in general to what extent the theistic tradition contains any descriptions of God that an atheist could ever legitimately leverage into an a priori argument against God (e.g. Normal Malcolm's argument against any being being necessary, which you've discussed before), as opposed to just leading to the refining of our definitions. Is the a priori approach, sometimes pursued to prove God, doomed to be a non-starter as far as disproving God?

[BV]

Casey,

I agree with you. God cannot be proved a priori not to exist since to do that the atheist has to begin with a definition of God, one that the theist is free to modify or reject.

At most, the atheists can demonstrate a priori that a certain concept of God cannot be instantiated, say a concept of God according to which God can do absolutely anything; but the theist is under no obligation to accept that concept.

For example, it is provable a priori that nothing can be both a necessary being and capable of doing absolutely anything. For if God can do absolutely anything, then he can commit suicide/deicide; but if he could do that he would not be a necessary being.

The theist response will be that there are limits on divine power.