So, I have been thinking a lot about Free Will and Omniscience, and though it has been rewarding I am less than happy with the results because I have been convinced that the proof I gave is only valid if one accepts metaphysical ssumptions that I do not accept…drat! I suppose there is some solice in knowing that it can be used to attack people who do hold those metaphysical views…but in the course of thinking about this stuff I came to realize that there are some problems with the claim that God is omnicient…for instance consider (1),
1. God knows that this sentence is false.
If (1) is true then God knows that the sentence is false, but if he knows that it is false then it is false and if it is false He doesn’t know it and so is not omniscient. So if this sentence is true then God is not omniscient. However if the sentence is false then God doesn’t know that the sentence is false and so he is not omnicient.
So God can’t know everything. But one may think that this is only due to the fact that (1) is contradictory and no one can know contradictions…but what about (2),
2.God can’t know that there is something that He doesn’t know
If (2) is true then there is something that God doesn’t know, namely that He doesn’t know something. If the sentence is false, then he can know that there is something that He doesn’t know, and since he knows this, that means that there is something that He doesn’t know and so can’t be omniscient.
hmmm…..
Richard Brown 
Hi Richard,
I think we should, in general, be suspicious of attempts to prove something substantive about the world using liar-like paradoxes, because they can be used to prove too much. Consider
(a) Richard Brown does not believe this statement is true.
Do you believe (a) or not? Or consider
(b) If Richard Brown believes this statement is true, Richard Brown believes every statement is true.
Do you believe every statement is true? If you think you don’t, considering (b) may give you pause.
So what can we infer from these and like examples? I think they show that *something* screwy is going on in our conceptual scheme, but what exactly it is is hard to pin down. I would counsel that untill we have a unified theory of what goes wrong in the Liar and related paradoxes the best course is probably to remain agnostic.
Also, I think your example (2) is ambiguous. We could either read it as:
(2′) It cannot be the case that: God does not know that p and God knows that God does not know that p
or we could read it as:
(2”) God does not know that p and it cannot be the case that: God knows that p
If I have things right, it seems that only (2”) entails that there is something God doesn’t know. All you can get from (2′) is that *if* there were something that God didn’t know, *then* He couldn’t know that He didn’t know it. But that is perfectly compatible with God’s *actually* knowing everything, including the conditional proposition that *if* there were something God didn’t know *then* He couldn’t know that He didn’t know it.
You should check out Peter Milne’s little note in the last issue of Analysis, where he argues using a similar case. It’s called ‘Omniscient Beings are Dialetheists’.
I think more importantly the problem with this claim is what God’s eye is fixed upon (to use religious sounding language). Should we believe the sentences’ first case that exists in your argument or the second case. Let me explain these distinct cases and thus better clarify your argument.
Your argument has two claims. First you have the first case:
(1) God knows that this sentence is false.
Where this sentence’s truth claim signifies the sentence. And than you have the second case:
(2) God knows that the sentence “God knows this sentence is false” is true or false.
Where this sentences truth claim is signified by the mind of God. There is a subtle distinction we can clear up if we go with the second case. In the second case we are talking about the mind of God and its reflection upon the sentence. I think in this instance God would know that if he were to believe the first case than he would be caught in a paradox. However, it is not the case that if he believes it is false than he does not know all things. This is clear if we continue to work with the distinction between the first and second case as reflecting upon the sentential meaning and the mind of God as distinct entities.
It is important to point out that this is incomprehensible unless we clarify between truth and knowledge. I think, for instance, that all true things, including sentences, can be known. However, all things that can be known are not true. I know, in a closed system, that 5+5=8 is false. And that, in this argument, I am making the same move previously made with the mind of God. My knowledge is not about the truth claim itself but about the truth and falsity of the truth claim.
If we share this kind of understanding with God, which I believe is the case, than God can have the second order knowledge about the truth and falsity of the claim. A move that is inherent in the argument itself, thus God is safe from contradiction if and only if he believes that the truth claim in sentence (1) is false like he does in sentence (2). Now the sentential meaning of (1) is empty (meaningless) if we want to confer some theory of substance that classical minds do upon God.
In my argument, God preempted the bind by believing that the sentence is false because of the nature of non-contradiction. He thus, is not lacking knowledge but knows that the sentential meaning is false in itself while his knowing it still prevails and along with it his knowing all things.
I think a more frightening concept is ‘God knows the expression, “I do not exist.”‘ I will say that, I’m content to just say that God does not know all things, and that we only have a proof that suggests he does not know things that contradict themselves. And what value do those kinds of things have? None in my book.
Hi Richard, I notice that you and I’ve posted on the same subject on the same day, what could such synchronicity say about God’s being?! Regarding your argument, I agree with Jason, since I take the view that the Liar-style sentences are nonsense (disguised as, well, contradictions that are disguised as just one of the conjuncts, more or less:)
…I also agree with Jason’s second point. E.g. with God defined to be omniscient, then it is false that there is something that He doesn’t know, and since God can’t know that because it’s false, (2) would be true unproblematically (while with my God (2) would be false:)
Hi Jason, thanks for the comments!!
I am not the one that is supposed to omniscient…so it is clearly going to be the case that there will be differences between me and God, so I am not too worried about those kinds of sentences…but even if I should be notice that is perfectly consistent to say that I do not in fact believe that the statement is true…people believe all kinds of things, even false and contradictory things! and the second sentence is eaisly false because it can be true that I believe that the statement is true but false that I believe every statement…so I don’t see what the problem is suppose to be…
What I want to bring out is that there is something problematic about an omniscient being and I think that these kinds of sentences show that there is…what does that show ‘about the world’? I don’t know, maybe nothing…but it does show that there is something screwy about the idea of a being that knows everything…
Sorry Jason, I forgot to reply to the rest of your comments!
Yor 2′ is even more problematic that 2”…the reason of course is that there is LOTS of stuf that God doesn’t know…for instance He doesn’t know that 2+2=5, since that is false….but 2′ says that He can’t know that He doesn’t know this…so 2′ is NOt compatible with God’s knowing everything…He will now know that He doesn’t know all of the false things…
Hi Aidan,
Mucho thanks for the reference…I am going to read that ASAP!
Hi Daniel,
Thanks for the comment!
….I am going to have to think about what you say for a bit and get back to you…
Hi Enigman,
oooo…..spoooky….
🙂
I don’t quite see how 2 is supposed to be true ‘unproblematically’…if He doesn’t know something, then He should be able to know that He doesn’t know it…but 2 says that He can’t…
Hi Danial, sorry for the delay in getting back to you!
I am not sure that I am following everything that you say, but I take it that the general point that you are trying to make is that to say that there is something that God doesn’t know is perfectly acceptable if what we mean is that there is some false thing and that God doesn’t know it (because it’s false), but that won’t be a problem because God will know that it is false and so still knows everything….is this right?
If so, I take the point but I don’t see how it is supposed to avoid the difficulty…
By the way, if anyone is interested, I just read the Milne paper that Aidan recomended, his example is
S: No omniscient being knows that which the sentence S expresses
from this we can derive theconclusion that the omniscient being both knows what sentence S expresses and does not know what sentence S expresses, so the omniscient being knows that (p & ~p)…Milne himself doesn’t draw any further conclusions from this…but it occurs to me that this would be a nice way to get the proof I gave a couple of posts back to be valid in all frames. Because, if God can know things of the form ~p, then He can know falsehoods and so He should know everything in all possible worlds…this is what step 7 in the proof says…nice!
Hi Richard, from S being true we could immediately derive that omniscient beings don’t exist, but why would S be true? Regarding your earlier question, why would an omniscient being need to know falsehoods? (Prima facie an omniscient being would know all and only the truths:)
Why would we derive that instead of that Dialethiesm is true?
Sentence S shows that there is at least one falsehood that an omniscient being must know…also I have just found out about something called ‘middle knowledge’ which, according to Plantinga, is the kind of knowledge that God has about what happens in other possible worlds, so this view requires that God knows things that are false in the actual world, or that He knows falsehoods…
“I have just found out about something called ‘middle knowledge’ which, according to Plantinga, is the kind of knowledge that God has about what happens in other possible worlds, so this view requires that God knows things that are false in the actual world, or that He knows falsehoods…”
Um, no. Knowledge of “what happens in other possible worlds” (and I think Plantinga would say the same thing) is just knowledge of what *would have been the case* if those possible worlds were actual. To give an example, suppose there is some possible world w_1 in which Socrates, and not Aristotle, was the tutor of Alexander the Great. Now consider the conditional (which I will call C): “If w_1 had been actual, Socrates would have been the tutor of Alexander the Great.” C is true, and thus true in the actual world. Indeed, C is necessarily true, because no matter what had been the case, Socrates *would have taught* Alexander *if* w_1 had been actual. And given His omniscience, God (assuming for the sake of argument that He exists) knows this. What isn’t true (“in the actual world”, if you prefer that addition), and what God doesn’t know, is that Socrates *was* the tutor of Alexander. And this is just as it should be, because he wasn’t. So does God know falsehoods? Maybe, if the case for dialetheism can be made out, but I don’t think middle knowledge will get you there.
Actually, I am afraid so. 🙂
But seriously Jason, how does he know that it’s true?
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