Only if God exists. Supposse I were to say “all unicorns are pink”, then say “no unicorns are pink”. If there exists a non-pink unicorn, my first statement is false, and if there is a pink unicorn then my second statement is false. The only way both statements can be true is if there are no unicorns. Similarly, the only way the statements “all members of the category “God” know everything” and “there is something which God does not know” can be true is if God does not exist.
I haven’t said that we don’t know. I just said that it is theoretically possible for us to not know. I have presented an argument supporting the claim that we do know.
“…only if god exists.”
No, either way. The number “1” does not exist (unless your a Platonist or nominalist or something) but that does not mean we may take any liberties we want with it. Once something is defined we must stick to that definition or anything we say is meaningless in context.
If you define a unicorn to be pink and then find a purple unicorn one of two things must happen (logically). One, you redefine “unicorn” to include a non-pink variety. Two, you state that this must not be a unicorn by definition. “what we have here is a unhorn, though I admit the similarities are breathtaking.”
So in the OP’s context, we are discussing a God not defined in 1,2, or 3 and so, in context given, it is a meaningless statement. In fact, it is not even paradoxical because no part of the sentence has any truth value to be in conflict with.
You are attempting a reducto ad absurdum here which has its own merits, but is following incorrectly. What must be done is something must be assumed and then it is shown that, in assuming this, one reaches a contradiction showing that the original assumption cannot be true. The paradoxical statement does not do this, it assumes the opposite.
1 does exist. If it did, we could take whatever liberties with it that we want.
Suppose I wanted to disprove the existence of a round triangle. So I say “A round triangle is something that has no corners. Suppose there is a round triangle. Then, since it a triangle, it has corners. Therefore, it is not a round triangle. Therefore, there are no round triangles.” According to your logic, this argument is flawed beacuse my assumption that there is such a thing as a round triangle is false.
I’m not quite sure what you’re saying here. Why does the fact that the object under discussion doesn’t fulfill the requirements of being God mean that the statement is meaningless? I can see how it makes it false but I don’t see how it makes it meaningless.
Well, Ryan, you’re talking epistemology here so you’ll have to define things and stick to those definitions. The round triangle example is flawed because it doesn’t say “round triangles” are triangles in the classical sense, so if we define it to have no corners than it surely has no corners by definition.
You may assume whatever you want so long as it doesn’t contradict existing definitions. The God sentence does…it postulates something which God doesn’t know. This, by definition, is impossible (since god, by definition, is omniscient).
What’s wrong with contradicting a previously existing definition? It’s kind of hard to have a proof by contradiction without contradicting something.
Yes, exactly. It’s impossible. Therefore, one of the assumptions (e.g., that God exists) must be false. Proofs by contradiction depend on reaching a situation whichi s impossible. That’s how they work.
I’m afraid that I can only repeat - you are wrong. For some statements a truth value does not exist (kind of like the value of zero divided by zero doesn’t exist). I admit that I am using an argument of authority here, because I’ve studied the relevant maths and I’d guess that you have not, but I’m not sure how else to argue this one, short of telling you to delve into the works of Godel, Russell et al.
Actually, probably the best way of explaining it is the approach by Aynrandlover. I think I’ll leave it to him.
Spiritus - I’ve been following that other thread with great enjoyment. Actually since it got a bit much for me to read it at work I even printed it out for a little bedtime reading. All I can say is that it seems to me that the almost Socratean conversation going on between you and Aynrandlover would be spoilt by the inteference of a third party. Rest assured though that others are reading it!
Exactly, reaching a situation which is impossible. This “epistemological” disproof of God doesn’t reach a contradiction, it declares it right at the bat. Sorry, but that’s what you’re supposed to prove.
Proof by contradiction entails the following.
We want to prove A.
We assume ~A.
~A implies B.
B is patently false.
Therefore ~A must be incorrect, and A is true.
The proof would have to take the following form for our purposes.
We want to prove (god does not exist)
We assume (god does exist)
If God existed it would imply (something impossible)
Therefore god does not exist.
Our proof uses an off-track method that is only similar to the above. Because we define god to be omniscient, our proof looks like
We want to prove god (an omniscient being by definition) doesn’t exist.
Assume that there is something god does not know.
uhhh
It doesn’t work for a number of reasons. One, we contradict our definition or specifically, the properties we define our object to have. Because of this, we no longer are talking about the same object we defined. We have proven something maybe, but nothing about our originally defined being. Two, we can dispense with “god” and achieve the same effect: disproving omniscience. Three, depending on how we look at such a proof, we might just conclude that we’ve completed the larget proof-by-contradiction in history in “finding out” that we were wrong: things can be true, false, or indeterminite. So much for the excluded middle.
the problem is that if free will is used to utter a statement, that statement can not be nothing but the truth, even if someone else views it or even knows it to be false.
so if i say; “7up is good”.
and you say; “7up is not good”.
both statements are true, but they do not apply for all. thus an omniscient being has to know alot of truths, some of which oppose to each other…and that is not possible, no one both likes and dislikes something. even if the person in question holds no specific affection to a given soda drink it still does not make the other statments false.
Actually, I am familiar with Godel, etc. I know that Godel showed that some statements can neither be proved nor disproved. However, that if very different from neither being true nor false.
aynrandlover:
Would you agree with the following argument:
“Santa is defined as a being which brings toys to children. If Santa does not exist, then Santa can’t bring toys to children, which would contradict the definition of Santa. Therefore, Santa must exist”?
I consider, implicit in the statement “X does Y”, to be the statement “X exists”. Since you apparently do not, I’ll make it explicit.
Suppose I reworded it thusly:
“when preceded by its quotation, forms a sentence which, if God exists, God does not know is true”, when preceded by its quotation, forms a sentence which, if God exists, God does not know is true.
Suppose this statement is false. For it to be false, God must exist, and know that it is true. But if God knows that it is true, then it is true. If it is true, that 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, if God exists, God does not know is true. It is not poosible for God to not know that a true statement is true, therefore God does not exist.
Yes, but it’s still very possible for a statement to be neither true nor false. As has been posted earlier, take the following pair of statements:
The following statement is true. The preceding statement is false.
Neither statement can be true or false. It is impossible. This kind of situation arises quite readily with self-referential statements (like yours) or statements that refer to each other, like the set above.
**
This is just nonsense. It doesn’t follow the logical form outlines by aynrandlover. It doesn’t “contradict the definition of Santa,” it denies the existence of Santa, which precludes Santa from exhibiting any of his Santa-like properties, not existing and all. It doesn’t affect the definition of Santa. If you will recall, the second statement has to prove that something impossible follows from the negation of what you are attempting to prove. “Santa not bringing toys to children,” is not impossible. It’s indeed quite possible. It happens (or rather, doesn’t happen) every Christmas. Hell, every day.
If one wanted to get really picky, we could just go after your first statement. Santa is not a being which brings toys to children, he is a mythical figure who is imagined to bring toys to children.
**
So, looking at your Santa argument, your first statement contains the implicit assumption that Santa exists. If this is your definition of Santa, then your parents have a long overdue bit of news for you.
Basically, then, your argument, boiled down to its core assumptions, looks like this: “Santa is defined as a being who exists. If Santa did not exist, this would contradict the definition of Santa. Therefore, Santa exists.” This is very, very different from the sound bit of logic presented by aynrandlover.
**
OR, for it to be false, God could exist and know that that silly sentence indeed does not form a sentence which, if God exists God does not know is true.
No offense, but your epistomelogical disproof does a good job of making St. Anselm’s argument look like a brilliant piece of logic.
