TheJesusConspiracy

Assume, for the sake of argument, the existence of an omnipotent being. Such a being would be capable of doing anything. Additionally, this entails that the being would be capable of doing anything I am capable of doing. Let's call this being 'God'.

I can prove not only that there is something God cannot do, but that I can do it.

Take the statement, G: "God will never soundly prove G."

1. Assume not-G.
2. If not-G, then God will at some point soundly prove G.
3. If God soundly proves G, then G.
4. From 1-3, G and not-G.
5. Therefore, by indirect proof 1-4, our assumption is necessarily false, and it is the case that G.

Q.E.D.

So G is true, and God will never prove G.
Therefore there is something God cannot do, that I just did.

God sucks!

So, I have proven that

Jesus Tap-Dancin' Christ

Of course, that does involve a circular statement...

echidna

Heh, that might be part of why very few intellectual atheists even bother attempting dis-proofs of God.

TheJesusConspiracy

Um, Jesus Christ, just so we get things clear here, let me just explain logic to you. I'm a philosophy doctoral student; I've taught formal logic about a billion times. My argument is not a circular argument (a petitio principii) and does not beg the question.

The argument is based upon Godel's famous first incompleteness theorem. Basically, the theorem shows that any truth system capable of referring to itself can describe truths that it is incapable of proving.

The statement refers to God, but it is not circular. Rather, the form of this argument is known by various names: indirect proof, validation through denial, reductio ad absurdum. It starts by assuming the negation of a point, showing that it leads to contradiction, and this necessarily entails that the assumption was false. In more formal language, if the assumption of P entails absurdity (in this case it entails ~P and P), then ~P.

The criticism that this is a circular argument is completely false. Please learn logic before using it to criticize others.

Here is the justification of each step from the previous argument.

1. Assume not-G.
--This is a hypothetical assumption for the sake of indirect proof. One cannot prove not-G from the assumption, but we are allowed to see where it leads.
2. If not-G, then God will at some point soundly prove G.
--This is a reiteration of 1. G claims that God will never soundly prove G, so the negation of G is that God will at some point soundly prove G.
3. If God soundly proves G, then G.
--This is from the definition of sound proof. If Xis soundly proven, it must be the case that X. A sound proof is a valid argument with true premises.
4. G and not-G.
--Not-G is established by 1,2 modus ponens. G is established by not-G, 3 modus ponens. Not-G and G together are then established by conjunction.
5. Therefore, G.
This is established by 1-4, indirect proof. The assumption that G is false leads to absurdity (specifically, the assumption that G is false necessarily entails that G is true), so it must be the case that G is not false, i.e. G is true.

This is a valid, sound proof that does not commit any fallacies. The charge of begging the question is not only wrong, but ridiculous. One begs the question when one assumes one's conclusion inside an argument. I assumed the opposite of my conclusion!

If anyone objects, however, to the double negation, I can provide a permutation of this proof that satisfies intuitionist logic.

TheJesusConspiracy

By the way, watch the insults. There's about a 1 in 30000 chance that you qualify as more of an intellectual than I.

sotzo

Well, I am certainly not a philosophy major, minor or otherwise but your definition of God's omnipotence being "God can do anything" is incorrect. If God can do anything then he is unintelligible because he would be full of violations of the law of non-contradiction.

That point aside I don't see how assuming non-G (your premise 1) for the sake of argument has anything to do with the ontological issue of whether or not God can fulfill G. Seems to me premise 1 has to have some justification for it.

I understand what Godel's theorem entails but I'm not sure if applying it to particular claims is what Godel had in mind. Seems to me that his theorem is only an axiom that describes the ultimate circular nature of reasoning.

Of course, I'm drawing from a limited understanding and am willing to learn from you, since unless we're going to talk about Rush albums, my chances of being more intellectual than you is 1 in 6E10!

cheers,
jkb

ShottleBop

Can you prove that statement ("If I can do something that God cannot do, God sucks")?

On what do you base your claim that JesusChrist has about a 1 in 30,000 chance of being more of an intellectual than you? (That's a pretty definite statement!) Doesn't that assume that there is some objective manner in which to define "intellectual" and to measure the level of someone's quality of "intellectuality"?

TheJesusConspiracy

Five points.
1. This argument is meant to demonstrate that if we mean by omnipotence literally capable of doing anything, it entails absurdity. As we are all probably familiar with, there is the argument that if God can literally do anything, then God must be able to make a rock so heavy that He can't lift it. This is absurd, so most theologians resort to the belief that omnipotence means able to do anything that is (logically or materially) possible. This proof shows that it is possible for me to do something God cannot. Confronted with such things, one might reduce omnipotence to mean God can do anything that he is logically capable of doing, but that is a simple truism. Additionally, if one concludes from the statement that 'for all x, if it is logically possible that God can do x then God can do x', that God can actually do something, one commits the existential fallacy, for the statement does not assert the existence of God but merely posits hypothetical attributes. An example of this is that a unicorn can do anything that a unicorn can do. This is consistent with the assertion that unicorns can't do anything and unicorns don't exist.

2. The comment about being intellectual was not directed against Jesus but against echidna. An intellectual is a man of letters who is concerned primarily with ideas. I am an intellectual; moreover it is my profession. If echidna is a random person from the English speaking world, he has about that chance of being more qualified for that epithet based upon vocational distributions. Echidna is an engineer, which might qualify him as a scientist, but is not sufficient to be an intellectual.

3. I didn't intend to state that I have proven that God sucks. The statement beneath it was unfinished--I'd meant to erase it. Lo siento. I was just kidding at the end and had forgotten I'd started to write something else.

4. Premise 1 is assumed for the sake of argument. I made it very clear that assuming premise 1 does not mean that premise 1 is true. This argument illustrates what would happen if premise 1 were true--it shows that premise one entails absurdity. Rather than justifying premise 1, the entire proof is meant to show that premise 1 cannot be justified and instead must be rejected as absurd.

5. Godel's point was not that all reasoning is circular. Godel didn't think that. He first incompleteness theorem was meant to show that number systems cannot be explained naturalistically as they entail truths that are irreducible to phenomena and are beyond the scope of any particular system itself to prove.

hezekiah jones

Formal logic is both barren and sterile.

I want to believe in God anyway.

*cry*

Clutch

Conspiracy,

I think what more than one respondant might mean by "circularity" is just the self-referentiality of G. G has look of a "fixpoint" assumption, of the sort that is well-known to produce paradoxes of self-reference. Not every such assumption is reasonable. On the assumption that God is omniscient, an available conclusion is that there is no G of sort you introduce. (Or, perhaps more felicitously, that G does not express a coherent proposition.)

You might be finding one of a variety of ways of drawing out the problem of unrestricted predication in all those "omni"s in the definition of the Christian god. (A friend of mine wrote a paper on something similar, showing that Anselm's OA leads to Russell's Paradox.) If so, it would be useful to rejigger the rhetoric in order to nail down why it would be [pick one: unmotivated/ad hoc/catastrophic/cowardly...] for a theist to regard your argument as a demonstration of the ill-formedness of G.