Epistemological Disproof of the Existence of God

Great Debates
1

I don’t really believe the logic of this argument (I believe the conclusion, but not the logic), but I’ve been wondering for a while whether anyone has
a) seen it before
b) has a refutation.
Seeing as how word games are being used to “prove” God in another thread, I thought it would be appropiate to “disprove” God using the same tactics.

First some clarifications:
“God” refers to a being that is omniscient.
“Omniscient” is the property that if a statement is true, then the being in question knows that the statement is true.
“Know” refers to a state in which the statement in question is true.

Now, consider the following statement:
“when preceded by its quotation, forms a sentence which God does not know is true”, when preceded by its quotation, forms a sentence which God does not know is true.

Suppose this statement is false. For it to be false, God would have to know that it is true. But if God knows that it is true, then it is true. So it is true, which contradicts the assumption that it is false. So it can’t be false, so it must be true. So this is a statement that is true, but God does not know is true. Therefore God is not omniscient. But that contradicts one of the properties of God, so God can’t exist.

2

Your contradiction lies in the phrasing of the sentence itself.

Suppose this statement is false. For it to be false, God would have to know that it is true.

The statement is where the contradiction lies, therefore the statement is not a valid one to base a conclusion of whether or not God exists.

3

I think Willard Quine would have loved seeing this one. Pity he died just a few days ago.

4

The statement itself is a problem, and not just because it creates a self-referential paradox but because it says in it “which God does not know is true.” This doesn’t jive with the assumption that God is omnicient and in fact simply “declares” what it is supposed to “prove”. Instead it should be worded:

“when preceded by its quotation forms a sentence which is false” when preceded by its quotation forms a sentence which is false.

Now, with the existence of such a sentence, can God still be omniscient? Yes, but conditionally. If we posit (as is implicit for the “disproof”) that all things are either true or false, and omniscient means knowing true things are true and false things are false (and knowing all true and false things) then we haven’t disproved omnicience (or god) but the assumption that everything is true or false.
Now, instead we might say that things are either true, false, or impossible and omniscience is knowing what a particular thing is and knowing all things true, false, and impossible, then we can create an omniscient God which paradox doesn’t destroy (not that the original did anyway).
Wow.

5

This seems to be a form of Russell’s paradox and the solution to it comes out of 20th century set theory. The trouble is that your statement can neither be assigned a true nor false value - (to get mathematical, it lies outside the metalanguage in which you are trying to describe it.)

For those who are interested, Russell’s paradox involved sets of sets. In particular he considered power sets - those sets which include themselves. For example the set of spoons does not include itself, but the set of non-empty sets is itself non-empty, so does include itself. He then considered the set of sets that do not include themselves. (Pause for brains to catch up). If this were to contain itself, then it could not contain itself, yet if it does not contain itself then it must contain itself. Aargh!

Set theory did not come crashing down however. Instead some very intensive and serious work was done with the conclusion that the concept of sets containing themselves was bunkum - to be able to describe a system you must be outside of that system. Lots of clever paradoxes were then constructed to illustrate this - Lewis Carroll includes a few in Through the Looking Glass.

God, fortunately for Him, also falls into this category of being without the system He describes. As such, logical tricks do not work for Him.

S’fun though. Could God make a rock so heavy that He could not lift it?

pan

6

Can you explain that more thoroughly? Which statement is where the contradiction lies, and how does the contradiction make the arguemt invalid? Mathematicians routinely use contradictions to prove theorems. It’s called “indirect proof”.

Olentzero: Yes, his work inspired the “proof”.

aynrandlover

What’s wrong with that? First I present a statement which implies the nonexistence of God. Then I prove that statement is true. I see no lapse of logic there. It is no different from a mathematician starting a proof with the the phrase “Claim: The complement of every open set is closed” and then proceeding to prove that statement. As long as he avoids using the truth of the statement in his proof, there is no problem.

kabbes

Of course it can. It can be assigned the value “true”. Now, I may not be able to present a mathematically rigorous proof of the statement, but that doesn’t mean it isn’t true. The statement “The sun rises in the East” can’t be mathetacilly proven either.

7

Here is the problem.
Taking 1, 2, and 3 together one finds that, by definition, God knows everything. Therefore any statement which declares that God doesn’t know something is false outright before any resolution of any other part of the sentence meaning. By removing the “which God does not know is true” and simply replacing it with “which is false” you create a paradox, something which can neither be true nor false (or is both true and false, whichever you prefer) and thus shows that God cannot know everything and isn’t omnicient.
If that’s what the statement is for. :slight_smile:

8

“God does not know is true”

This statement implies that God is not omniscient. I have never before seen a statement which was a great example of begging the question … i think you just provided it for me. In other words, you first assume that God is not omniscient to prove that he is not omniscient.

9

The Ryan, I’ve only got one question for you. If I were to ask you to mail me $1,000, would your answer be the same as the answer to this question?

10

The contradiction is like saying, “The next sentence I will say is a lie. My previous sentence was the truth.”

11

No Ryan - in logic not all statements must be true or false. Some are provably unknowable from within the system being used to describe them. These statements do not have either truth value. Now you can insist until you are blue in the face that your statement must be true or that it must be false, but I’m afraid that you’d be arguing against modern mathematics and you’d be wrong.

pan

12

Thanks a lot, Tzel. You’ve crashed my brain.

13

Your construct is a paradox, and paradoxes are fun. Your statement holds up fine, but it doesn’t mean what I think you thought it might mean. God, in your construct, does not know the statement to be true. However, that is consistent with the statement not BEING true, and therefore does not contradict God’s omniscience.

The above statement cannot be reconciled as either true or false. You are correct in saying that it cannot be false, since if it were false it would be known to be false and would therefore fail to be false (which normally equates to being “true”). So you say at this point “So it is true”. But as aynrandlover points out, you’ve already established in your definition of “God” that God knows any truth to be true. Your statement therefore fails if we assume it to be true.

The statement, a paradox, is neither true nor false. God does not know it to be true. (Neither do I). You have failed to construct an epistemological disproof of the existence of God.

14

good question tzel :wink:

it would have to depend on the actual question, for it can be true for both yes and no.

but nomally you should just answer: “i would give you the same answer”.
its just like the game…dont say yes or no, black or white.

back on subject.

no, this line of logic is wrong.
assuming god as by your definition always knows what is true then he also knows when a statment lacks truth.

what you could have proved is that there is no such thing as omniscience. for if there is no omniscience there is no god.

but since omniscience is just a figure of speech, a word meaning exacly what was described in the OP it must exist, for we have a word for it, and supposedly only divine beings possess omniscience, so the existence of god is based on wheather or not he is omniscient.

we can of course not say if he is or not, we have no knowledge of that, we are not omniscient, yet we know that there is supposed to be a being that is.

one problem is: god can not know more than we do. we are the only ones that “know” god exists.
someone who does not belive in god does of course not know that god exists, therefore he does not know of any being that is omniscient and as such omniscience does not exist.

omniscience is basically an idea meant to grow to the size of our ignorance, everything we do not know omniscience knows, and while there is something we dont know there is a god there that does know it. so the second we know that there is no god there is no such thing as omniscience, for it will be obsolete, everybody will know everything.

lets pause at that; “everybody will know everything”.
if that is the point where omniscience is true then there can be no god, at least not a omniscient one.

why is that?

everybody can not know everything and god is not everybody, it is everywhere!
there is a great differance there. god supposedly gave us free will, but that is a paradox exacly like omniscience. how can you give something that is already there?

and more importantly, god does not know what free will is! therefore god does not know everything that is true and therefore omniscience is but an idea.

god might be a power, but he is not omniscient, he does not know what you are going to do.

bj0rn .

15

(a) nope
(b) IMHO, a word game is irrelevant to the question of God’s existence. I’ll also agree with the others who indicated that it seems like a bit of a false dichotomy.

16

Hey kabbes, any chance you want to add something to our epistemology discussion? By page 2 we are pretty much focused on the Ramified Theory of Types and Godel’s Incompleteness Theorems.

17

Huh? Why is that? Aren’t you assuming that God exists?

Monocracy:
I already dealt with that objection. I never assumed that God isn’t omniscient.

kabbes:

Just because the truth value is unknowable, that doesn’t mean it doesn’t exist.

AHunter3

I guess that would depend on what you think I thought it means.

No, it’s not. If the statement isn’t true, then God DOES know that it is true. Which is a contradiction.

18

Nope.
We are defining God to have {traits}. That is not to say God exists, merely that if God existed God would be something that {traits}.
Any statement about God, then, must follow the definition, and the statement “{stuff that}god does not know is true” does not.
We define God, as I stated earlier, to be omniscient; that is, God known all true things and all false things. If we are to then postulate that there is something God does not know is true we have violated our own definition, and it should come as no suprise that we then also invalidate God’s existence (this is, in poor terminology, setting up a strawgod ;)).
Again, the paradox only works if we posit that every statement is either true or false. As I mentioned earlier, however, the creation of a paradox serves not to undermine an omnicient being but our proposition itself, namely that everything is either true or false. It says nothing about God.
Now, if you then propose that the paradoxical statement is true or false, we just don’t know whether or not it is true or false, then again we haven’t accomplished anything because, by definition again, God does know. He’s just not telling us… :smiley:

19

no, god does not know!
god does not know what i am going to do in the next 5 minutes.
why?
because he supposedly gave us free will.
now, if he is capable of doing that, is he capable of taking this free will away from us?
i say no because if someone has the ability to take free will away from someone it cant be free will, it would be just like letting a dog out so he can play a little.

god can not have the ability to prevent our free will and because of that he can not know what we are going to do.
following the simple logic that if he knew what we are going to do we would not have free will.

bj0rn …

20

Being a big fan of determinism I really am touched by that last post. Almost had me convinced!
But, alas, the discussion is only about an omniscient being, not the Christian God per se. We defined god to be an omniscient being, not as a loving God, or a God that gave everyone free will, etc. :wink: