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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.

http://www.reasonablefaith.org/defenders-2-podcast/transcript/s3-13

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.

http://plato.stanford.edu/entries/knowledge-how/

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?

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    This is really long, so I haven't read it super carefully, but the feature that is probably being highlighted to make "I am Bill" non-propositional is the "I". I don't think you need to go to knowledge-how and don't think it helps in this case. – virmaior Jul 31 '16 at 23:17
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    The problem with stopping there is that other sentences containing indexicals, including "I," are indeed propositions, i.e., "I have been treed by a moose." – user20658 Jul 31 '16 at 23:20
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    @virmaior is definitely right - this goes into something I recall Dilip Ninan presenting about once, on de se (?) attitudes. It's essentially the puzzle that people with identical attitudes (which may include pronouns like "I") react differently. This, of course, is not what the article you've linked is arguing. I think the argument there is flawed in that somehow "non-propositional" is being injected without cause. If I can I'll think about this a bit to try and pull it apart. – commando Jul 31 '16 at 23:21
  • Where would it end? If I say "Ahab is captain of the Pequod" is that true? Or have I forgotten to specify, "In the novel Moby Dick, and not in the fan fiction version where Ahab is cabin boy and Pip is the captain?" "I am up a tree" is true if I happen to be up a tree. – user4894 Aug 1 '16 at 0:26
  • @user4894 fictional worlds are a whole different problem for semantics. Perhaps the most common account is that your first sentence is true under the contextual (pragmatic) assumption that you're talking about the novel, while the second is true, period. – commando Aug 1 '16 at 1:18
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Simply put, the speaker begs the question. Their argument seems to be structured like this:

  1. The propositional content of the two characters' knowledge can be exhaustively expressed by "Bill has been treed by a moose"
  2. The two characters respond differently to their equivalent propositional knowledge.
  3. Therefore there is such a thing as non-propositional "self-knowledge" e.g. "I am Bill"

The problem, of course, is that "I am Bill" is a proposition (and, in the related literature I mentioned in my comment, is treated as such), and should have been included up in premise 1. Why is it not? The speaker glosses over that completely and takes it for granted, then seems to pull some sort of sleight of hand, arguing (vaguely) "because these two people responded differently to the same propositional knowledge, they must have some non-propositional knowledge. Here it is!" That itself begs another question: why must two people have non-propositional knowledge, if they act differently in response to propositional knowledge? They may have different temperaments, beliefs, et cetera.

My answer to your title question is thus that "I am Bill" is a proposition - one which indicates that two senses ("I" and "Bill") point to the same referent (the individual named Bill). The transcript you've linked simply asserts that it's not a proposition, without arguing for that position.

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  • Full disclosure: I get a little miffed by people who claim to rationalize either atheism or theism, since in my experience they do a good job of producing deplorable pseudo-philosophy. If I seemed uncharitable in my answer, that's why. – commando Aug 1 '16 at 0:19
  • Try applying the model-theoretic interpretation of validity to it. It fails to be true in all models (e.g. if is not true when I do not exist) and it is definitely true in some models (e.g. when I am, in fact, the Bill in question). So, if you want to consider it a proposition, it is neither true nor false. This is not in the spirit of propositional logic, but of some more refined version of logic. – user9166 Aug 2 '16 at 2:09
  • @jobermark I don't think propositions are exclusive to propositional logic? All more complex/higher-order logics still use propositions. – commando Aug 2 '16 at 3:27
  • But they wrap other mechanisms around them. A quantified statement, a formula of set theory, or a modal assertion is not a proposition, it is something less basic, made up of a proposition, and some context. If you are just arguing for a less technical definition of 'proposition', the original author is just as right to use the technical one. – user9166 Aug 2 '16 at 3:47
  • @jobermark the "technical" definition is not one that's in question when talking about propositional vs. non-propositional knowledge. But moreover, under the "technical" definition of "proposition", you run into the same problems with "Bill has been treed by a bear": it's not true if Bill or the bear doesn't exist, for example. And if you suggest that "Bill" and "bear" are not distinct subformulas in the proposition, then I can say the same of "I am Bill" - it's equivalent to the basic proposition "the sense of 'I' as spoken by this individual refers to the same individual as 'Bill'". – commando Aug 2 '16 at 3:59

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