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Humphrey Bogart
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Date Joined Jun 2003
Total Posts : 205
| Posted 5/24/2004 1:35 AM (GMT -6) |   |
Hello everyone! I have a tricky problem which an atheist came up with, and I'd be interested to know if anyone has a good answer.
The argument is that omniscience (that God knows all true propositions) is logically incoherent. The argument is, consider the following statement:
God does not know this statement is true.
Now if God knows the statement is true, then the statement is false, and since you can't know something that is false, he doesn't know it.
On the other hand, if he doesn't know it is true, then it is true, and there's something he doesn't know.
What do you think?
(What I think is that the problem relates to the whole concept of omniscience as propositional knowledge).
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Humphrey Bogart
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Date Joined Jun 2003
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| Posted 5/24/2004 2:31 AM (GMT -6) | | The statement seems perfectly meaningful, and indeed if God doesn't know it then it seems to be true.
I think at the very least you're going to have to modify the standard version of omniscience from "God knows all true propositions" to something like "God knows all true propositions which it is logically possible for him to know".
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Humphrey Bogart
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Date Joined Jun 2003
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| Posted 5/24/2004 2:40 AM (GMT -6) | |
Hey Kingsaint,
I think you mistyped the URL. I just tried the link you posted and got this message:
The requested URL /research/iep/p/par-liar.htm. was not found on this server.
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Humphrey Bogart
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Date Joined Jun 2003
Total Posts : 205
| Posted 5/24/2004 2:58 AM (GMT -6) | | Kingsaint, saw your link, very interesting, but can't figure out at the moment how it might help solve the problem. Maybe some kind of demarcation of whether a proposition is "allowable" or not might rule the statement "God does not know this statement is true" out. But I don't know what that criterion would be.
Anyone else have any ideas?
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Starkman
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Date Joined Oct 2001
Total Posts : 1747
| Posted 5/24/2004 4:07 AM (GMT -6) | | Quote:quote:
"God does not know this statement is true."
What statement is it at issue? The one quoted above or the previous statement (in your post), which would then be the antecedent: The argument is that omniscience (that God knows all true propositions) is logically incoherent. The argument is, consider the following statement:
If I understand your post correctly, I don't think the statement in question is the latter, but the former. And if so, what is it in the statement that can be true or false? Statements like "Go, right now" are not a true or false proposition or premise and, therefore, cannot be deduced to a true or false conclusion.
So to say, "God does not know that this statement is true" is the same thing as saying "God does not know that there is no true or false premise in the statement to deduce a conclusion." (At this point it is now true that God does know that there is nothing of a true or false nature in the statement to conclude a true or false deduction. Further, the atheist's argument just went out the door, because the argument is not based on sound reasoning.)
quote:
The argument is that omniscience (that God knows all true propositions) is logically incoherent. The argument is, consider the following statement:
This isn't a complete statement about God's omniscience. It should read like this: God knows all true propositions and believes no false propositions. God can and does know what is false; he does not, however, believe what is false.
quote:
Now if God knows the statement is true, then the statement is false, and since you can't know something that is false, he doesn't know it.
Here, then, based upon a complete statement of God's omniscience, the initial argument falls apart even more.
Starkman
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Humphrey Bogart
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| Posted 5/24/2004 1:50 PM (GMT -6) | | Starkman: Statements like "Go, right now" are not a true or false proposition or premise and, therefore, cannot be deduced to a true or false conclusion.
Albert: Yes, but that's an imperative, not an indicative. The statement "God does not know this statement is true" is an indicative.
Starkman: So to say, "God does not know that this statement is true" is the same thing as saying "God does not know that there is no true or false premise in the statement to deduce a conclusion."
Albert: I'm not quite sure what you're getting at here ("premise" seems to resolve down to just another proposition, which would be circular). We don't have to deduce conclusions from statements for them to be meaningful. For that matter, statements that are completely vacuous can still be true (e.g. "a cat is a cat").
Starkman: This isn't a complete statement about God's omniscience. It should read like this: God knows all true propositions and believes no false propositions. God can and does know what is false; he does not, however, believe what is false.
Albert: OK, but this extended definition makes the problem worse, not better. It means the standard definition fails on two counts instead of just one. God still can't know the statement is true, because otherwise it would be false. But if he doesn't know it's true, then whatever he believes about it (that it's false, that it's meaningless, whatever), the statement is true.
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Humphrey Bogart
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| Posted 5/24/2004 3:25 PM (GMT -6) | | hi John!
The problem is that your statement "God doesn't know that I'm a female", if God doesn't know it, is still false. So there's no problem.
But the statement "God does not know this statement is true", if God doesn't know it, is then TRUE. Hence the problem.
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John Earp
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Total Posts : 1715
| Posted 5/24/2004 3:29 PM (GMT -6) | | quote:
Originally posted by albert
hi John!
The problem is that your statement "God doesn't know that I'm a female", if God doesn't know it, is still false. So there's no problem.
But the statement "God does not know this statement is true", if God doesn't know it, is then TRUE. Hence the problem.
God can know the statement, "God does not know this statement is true" is true or false. If it is true, one would have to further define precisely what it is the sentence is referring to.
On further reflection, it seems to me that this objection is no different than the old, "Can God make a rock so big He can't lift it?" question. The fatal flaw in such a question is that God is not able to do many things. For instance, He cannot will himself to not exist. He cannot make right wrong, up down, left right, or something both exist and not exist at the same time.
Since the question your friend has formulated does not correspond to reality and really says nothing substantive that would include an object for God to know or not know, it seems to me that this is really not a meaningful statement at all. It's not unlike Dr. Boyd's favorite example of Calvinism's logical inconsistencies: "God loves all married bachelors whom He hates."
"The Discovery of new truth will modify old views and opinions, and there is perhaps no end to this process with finite minds in any world." Charles G. Finney, Systematic Theology.
revivaltheology.net
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John Earp
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Total Posts : 1715
| Posted 5/24/2004 4:38 PM (GMT -6) | | quote:
Originally posted by jefscott
Why do I see John Earp as the last poster but don't see his post? I've seen this once before - is it a bug in the forum software?
I think it's because I edited my post after you posted after me. | | Back to Top | | |
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Humphrey Bogart
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Date Joined Jun 2003
Total Posts : 205
| Posted 5/24/2004 7:15 PM (GMT -6) | | John: On further reflection, it seems to me that this objection is no different than the old, "Can God make a rock so big He can't lift it?" question. The fatal flaw in such a question is that God is not able to do many things. For instance, He cannot will himself to not exist. He cannot make right wrong, up down, left right, or something both exist and not exist at the same time.
Albert: Ah, that response has been tried. The difference is that such a rock doesn't exist. If someone could find a rock bigger than God could lift, and demonstrate it, then that would certainly disprove God's omnipotence. But until said rock is found and demonstrated, we can't be sure that such a rock is possible.
However, in the case of a statement God (apparently) can't know, we DO know that such a statement exists. Its specified as "God does not know this statement is true". So this statement is actual. It is not imaginary like the rock. Unless we can find a way around it, we have a problem.
John: Since the question your friend has formulated does not correspond to reality and really says nothing substantive
Albert: But it does appear to say something substantive. It seems to say that God doesn't know it to be true. That makes sense. Where's the problem?
Jefscott: Since the phrase "this statement" equals "God does not know this statement is true," when we plug that value in, we get:
God doesn't know that God doesn't know that this statement is true is true.
We could plug it in again and derive:
God doesn't know that God doesn't know that God doesn't know that this statement is true is true is true.
Jefscott: Seems like an infinite loop to me.
Albert: Yes, but that's true of any statement. E.g. "the cat is on the mat", "the statement that the cat is on the mat is true", "the statement that the statement that the cat is on the mat is true is true" and so forth are all equivalent.
Jefscott: BTW, Albert, not to get off topic but I would still like to hear your thoughts on the Holy Spirit that you alluded to in "Fullness of the Godhead Bodily" thread. You really gave me some food for thought.
Albert: Can't remember specifically what they were. Can you jog my memory?
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Starkman
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Total Posts : 1747
| Posted 5/25/2004 3:55 AM (GMT -6) | | In other words...
"God does not know this statement is true."
There is nothing true or false about the statement; what is "this statement"? It's nothing. There's nothing there to be true or false. Kind of like, "The Cat in the Hat." Is there a true or false conclusion to this? No, there isn't.
Mind you, just because a sentence contains words like "God," "statement" and "true" in a sentence does not mean that the sentence conveys a complete thought or that it can logically and sufficiently be used to prove a point, anymore than a sentence without those words can do so. It's simple trickery to argue against omniscience using these loaded words and incoherent sentences, such as "God does not know this statement is true."
Albert:
quote:
OK, but this extended definition makes the problem worse, not better. It means the standard definition fails on two counts instead of just one. God still can't know the statement is true, because otherwise it would be false. But if he doesn't know it's true, then whatever he believes about it (that it's false, that it's meaningless, whatever), the statement is true.
We really need to be clear about something here. God DOES know falsehoods, if by "know" we mean that He is completely aware of them. In other words, God knows it to be true that the falsehood is, in fact, false. And God does not believe the falsehood.
So, as our man John pointed out in regard to the definition of ominiscience, that God knows all truths and believes no falsehoods stands fine as it is.
Got to run...
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Alan Rhoda
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Total Posts : 680
| Posted 5/25/2004 5:14 AM (GMT -6) | | quote:
Originally posted by albert:
Consider the following statement:
God does not know this statement is true.
Now if God knows the statement is true, then the statement is false, and since you can't know something that is false, he doesn't know it.
On the other hand, if he doesn't know it is true, then it is true, and there's something he doesn't know.
Interesting question, you pose, Albert, but it doesn't point to any fundamental difficulty with omniscience. Rather, it points to a semantic difficulty that has to be faced by any theory of truth. As kingsaint pointed out, the issue here is essentially the same as that in the Liar's Paradox. It has to do with the difficulty of assigning truth values in a consistent manner to self-referential statements.
Your atheist associate's objection against omniscience misses the mark because it is not omniscience per se that gives rise to the problem. We know this because we can formulate an exactly parallel problem (a la the Liar's Paradox) that makes no reference to God or omniscience. Thus consider the self-referential statement:
This statement is false.
If the statement is true then it is false that it is false, so it is false. But if it is false then it is true that it is false, so it is true. The exact same problem arises as with "God does not know this statement is true." So the problem has nothing to do with God or omniscience, as such, and everything to do with the semantics of self-referential statements. Getting rid of omniscience does nothing to solve the fundamental problem, so the atheist's argument doesn't refute omniscience. It only refutes semantic theories that cannot handle the Liar's Paradox.
quote:
Jefscott: Since the phrase "this statement" equals "God does not know this statement is true," when we plug that value in, we get:
God doesn't know that God doesn't know that this statement is true is true.
We could plug it in again and derive:
God doesn't know that God doesn't know that God doesn't know that this statement is true is true is true.
Jefscott: Seems like an infinite loop to me.
Albert: Yes, but that's true of any statement. E.g. "the cat is on the mat", "the statement that the cat is on the mat is true", "the statement that the statement that the cat is on the mat is true is true" and so forth are all equivalent.
Jefscott: In the statement "the cat is on the mat," each word is explicable in terms of it's grammatical role in the sentence. The statement you are using has a reference ("this statement") which can only be understood by FINISHING the sentence and then RE-thinking it in an irregular manner to understand the WHOLE meaning of the reference. This is circular. The fact that our mind can do this process almost instantaneously is irrelevant; there IS a difference in the sequence of the logical apprehension of it's meaning. The proposition, "the cat is on the mat" is not like that.
I think jefscott has put his finger on something here. Self-referential statements like "this statement is false" contain an indexical reference that cannot, in principle, be made fully explicit. When you try to spell out what the indexical phrase "this statement" refers to, you generate another statement containing the same indexical, which just defers the explication that was sought, generating a vicious regress. Statements like "the cat is on the mat" don't suffer from this malady simply because they are not self-referential.
Now a statement's being self-referential does not generate the paradox all by itself, for there are examples of self-referential statements that are unproblematic. For instance, "This statement contains six English words" is self-referential but unambiguously true. Moreover, no vicious regress is generated because there is no further need for explication after ""This statement contains six English words" contains six English words". If we could get to the heart of the difference between problematic self-referential statements like "This statement is false" and unproblematic ones like "This statement contains six English words", then we would be able to explain just how "God does not know this statement is true" goes semantically awry. Unfortunately, I don't have time to explore that issue right now.
God bless,
Alan | | Back to Top | | |
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Starkman
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| Posted 5/25/2004 5:32 AM (GMT -6) | | | | |
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Humphrey Bogart
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Date Joined Jun 2003
Total Posts : 205
| Posted 5/26/2004 1:01 AM (GMT -6) | | Alan Rhoda: It has to do with the difficulty of assigning truth values in a consistent manner to self-referential statements.
Albert: Absolutely. The trouble is, how do you come up with a clear, non-arbitrary, explanation for why statements like this one and the liar paradox are non-statements.
Alan: Getting rid of omniscience does nothing to solve the fundamental problem, so the atheist's argument doesn't refute omniscience. It only refutes semantic theories that cannot handle the Liar's Paradox.
Albert: It does refute omniscience unless you can answer the question above, how to show that it is a non-statement. A semantic theory that handle's the Liar's Paradox may well solve the problem, provided that that theory was evidently true, and not an ad hoc dodge.
Alan: Unfortunately, I don't have time to explore that issue right now.
Albert: Fair enough!
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Alan Rhoda
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Total Posts : 680
| Posted 5/26/2004 1:09 PM (GMT -6) | | quote:
Alan: Getting rid of omniscience does nothing to solve the fundamental problem, so the atheist's argument doesn't refute omniscience. It only refutes semantic theories that cannot handle the Liar's Paradox.
Albert: It does refute omniscience unless you can answer the question above, how to show that it is a non-statement. A semantic theory that handles the Liar's Paradox may well solve the problem, provided that that theory was evidently true, and not an ad hoc dodge.
It seems to me that the Liar's Paradox (and the "Strengthened Liar's Paradox") ought to be regarded as supplying a priori constraints on semantic theories. In other words, any semantic theory that cannot handle those paradoxes is ipso facto not an adequate semantic theory. Since it is the job of a semantic theory to account for the meaningfulness of meaningful statements and the meaninglessness of meaningless statements and thereby to enable us to distinguish which is which (i.e., which apparently meaningful statements really are meaningful and which are not), and since we we already know that we make meaningful statements (indeed, the claim that there are no meaningful statements is self-refuting), there must, therefore, be a correct semantics, even if we haven't come up with it yet, and even if it is beyond our ken to develop it fully. As far as semantics goes, the doctrine of omniscience only requires that there be a correct semantics. Since we know there is one, semantic paradoxes cannot refute omniscience. All they can do is spur us on to develop a better semantic theory.
Regards,
Alan
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