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(∀x)(Ox⊃(Cxr�(∀y)(~y=x⊃~Lyr)))

Assuming the Abrahamic God exists, he created the rules of logic. Think of Existance as a computer program. We're all users, so we have no choice but to adhere to and obey the constants and processes created by the programmer. Said programmer, however, can change the variables and scripts as he sees fit.

Solution:

1. ∀x(O(x) -> (C(x,r) & ∀y(x≠y -> ~L(y,r))))

Literally, for all x, if x is omnipotent, then x can create r and for all y such that x is not y, y cannot lift r.

The general meaning of omnipotence is "all-powerful", but it is still open to interpretation. Usually, our concept of an omnipotent being is not the following:

O(x) : x is omnipotent
P(x,y) : x is more powerful than y

2. ∀x(O(x) -> ∀yP(x,y))
(an omnipotent being is more powerful than everything)

Rather, what we mean by omnipotence is:

3. ∀x(O(x) -> ∀y(x≠y -> P(x,y)))
(an omnipotent being is more powerful than everything except itself)

Hence, the unliftable rock argument uses an incorrect definition of omnipotence that allows an omnipotent being to be more powerful than itself. We intuitively reject definition (2) of omnipotence at the outset because it is incoherent. Coming up with (1) is more difficult because the relations are not as obvious.

As I said in the beginning, you may think this solution is ad hoc...

In the end, we do not have a logically sound proof against the existence of God or an omnipotent God, and I remain agnostic.

Contest! Win 1000 gold!

If you are the first person to show that my argument is wrong, I will give you 1000 gold! There are 3 ways you can try to defeat my argument.

1. Argue that my proof is invalid.

If you can show that my conclusions do not follow from the premises, then you win. Make sure you understand the meaning of logical validity.

2. Argue that my proof is unsound.

You can show that my argument that ~∃xO(x) is unsound by showing that it is invalid, or by showing that one or more of my premises are false. For example, if you think one of the assumptions are incorrect, you must provide the correct assumption in logical form. In addition, you must provide a justification in English (or combined with formal logic, if you like) of your logical statement, using proper spelling and grammar.

You cannot claim that (9) is a false assumption, because I said, "If we assume that God has to be omnipotent". You don't have to make that assumption. The first argument that ~∃xO(x) is what we are concerned with.

3. Provide a logical argument why God can defy logic.

You can use formal logic and/or an argument in English, but it has to be rational and logical.

General Rules:

You are allowed to use only propositional logic and predicate logic. All the symbols in propositional and predicate logic are available to you.

HTML character entities for logical symbols are available here.

Hints/Notes:

This is not a rhetorical challenge. I actually have a solution that uses one of the three methods.

There is the possibility that you will consider my solution ad hoc, but this is my thread, so you play by my rules. However, I believe my solution is rational and logical. Of course, if you still think my solution is stupid or unfair, you are welcome to flame me.

If you can explain it without the third year calculus i might stand up and take notice...but it seems to me as though it's a little contrived. I have no reason to believe what you're talking about.

Is this the paradox of can God create a rock so heavy that He cannot lift it? Because I don't have the discipline to look and translate the argument.

You are wrong and I'll tell you why right now. you're using the wrong calculations. You need to calculate the energy levels within the known and unknown universe to determin if there really is a supreme being. Without that formula, you can not tell. so are you wrong? who knows, are you right? no. You're measuring something completely wrong to the question at hand.

I just dont like the analogy in the first place. We seem to be placing such strict logical rules of posing and solving the argument, but the problem itself seems so...open. When we are using this argument we are assuming that we can sufficiently express the argument in terms of language - that a "rock" has "weight," and that God has hands. Even if it is an analogy intended to extrapolate to a general argument, I still don't see how we can avoid being restricted by words and human ideas. I suppose though I am starting to sound like a mystic...