There is a common over-used argument ; If some Supreme benevolent Being exists that created everything and can effect anyone's life , the argument is, if this being is 'all-powerful' can the Being make a giant rock that is impossible to lift? Note; this sounds a lot like the argument involving an immovable object and an unstoppable force. What happens if an immovable object is met by an unstoppable force 'trying' to move the object? The answer here being by 'definition' if the immovable object is existing in 'this universe' the an unstoppable force can not also be existing in 'this universe'. And vis. versa. If a Supreme being is existing 'now' then an immovable object can not exist 'now'. So the question becomes if a Supreme Being can not cause a logically impossible situation to be existing in 'real' life does that mean this Being is limited?
Most people posing this question want not only an answer, but an explanation of why that is the answer. That explanation must always include a precise definition of "all-powerful." Many who are pushing for such an answer want not only an explanation, but something worthy of being called a "proof."
Proof is actually a mathematical term, with a very precise definition. There are many classes of formal systems which can admit proofs, but First Order Logic (FOL) and Second Order Logic (SOL) are by far the most common. The individual posing the question will need to declare what sort of proof they accept. Since FOL and SOL are the most common systems people use, it is most likely they will name one of the two.
FOL is the most commonly referenced formal system with regard for proofs (for reasons we will see in a moment). However, defining "all powerful" within the confines of the language FOL supports is tricky. FOL requires everything it will talk about (officially called the "domain of discourse") to be defined as a set. "All powerful" could be defined as "For-all things that can be done, Supreme-Being can do it," however defining a set of "things that can be done" which includes creation and lifting of this particular rock is not possible. You need to go one step further, using categories rather than sets before you can use such a phrase, but FOL simply doesn't do that. (if you want to go further into why this is true, look into the work of Bertrand Russel into paradoxes and set theory)
SOL also works on a domain of discourse defined by sets. However, its semantics allow some clever structures which define categories using sets, construct the category which includes creation and lifting of the rock, and then you can go about your proof. At first glance, this looks like a winner!
As part of building his incompleteness theorems Gödel demonstrated a major limitation of SOL. It turns out that it is impossible to make any proof about a SOL system unless it happens to be reducible to FOL (i.e. you claimed you were using SOL, but you never actually used any of its fancy abilities). We've argued that the set of things that can be done cannot be described in FOL, so Gödel proves that any result regarding creation and lifting of our rock cannot possibly be proven.
The final answer is to allow admission of other formal systems besides FOL and SOL which can handle this particular case. However, in practice, the reason we use FOL and SOL is because it is remarkably hard to come up with a formal system which others can agree with. You can come up with any formal system you want, but unless both parties agree on what a "proof" should behave like, there really can't be any headway.
So, in all, the anti-ontological argument itself is phrased using a language which is tremendously unfriendly to proofs. Anyone seeking a proof will find themselves bound by the language of the problem.
So the question becomes if a Supreme Being can not cause a logically impossible situation to be existing in 'real' life does that mean this Being is limited?
This becomes dangerous, for at least two reasons:
- There exist many types of logic—which one do we use?
There are more things in heaven and earth, Horatio,(context in Hamlet)
Than are dreamt of in your philosophy.
Take, for example, wave–particle duality. How can a photon be both a wave and a particle? Well, we can say that photons propagate as waves but interact as particles. A contradiction is thereby eliminated by clever distinction. Is there any end to such cleverness? For example, what of an object that looks like a square from one perspective but a circle from another? Suppose we make use of stereo vision so that one eye sees 'square' and the other, 'circle'?
Therefore, I think there is sound wisdom in the following:
A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines.
— Ralph Waldo Emerson, Self-Reliance
Before I go on with this short history, let me make a general observation -- the test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function. One should, for example, be able to see that things are hopeless and yet be determined to make them otherwise. This philosophy fitted on to my early adult life, when I saw the improbable, the implausible, often the "impossible," come true.
— F. Scott Fitzgerald, The Crack-Up
David Politzer, winner of the 2004 Nobel Prize in Physics, told me in 2004 that a crucial stage in intellectual maturity is the ability to hold two contradictory ideas in one's mind without immediately rejecting one of them. Note that he discovered asymptotic freedom, which is predicated upon the then-counterintuitive effect of a binding force which grows stronger with distance. One may have been tempted to call this contradictory to all then-known knowledge.
I end with the fact that general relativity and quantum field theory, two of our best models of reality, contradict each other, seemingly inherently. One is continuous, the other is discrete. Nobody is close to empirically unifying them, although there are many pie-in-the-sky theories. However, to reject one or the other or both on the basis of the contradiction (which becomes measurably relevant near black holes) would be insane. We must remember that the picture of the thing is not the thing. Ceci n'est pas une pipe. Contradictions in model does not mean contradiction in thing/person modeled.
You can note that universal gravitation says that there is no rock that cannot be moved by even the smallest particle. So the answer is that since the size of a rock has nothing to do with the might of the mover, the question is badly framed. The perspective from which it is framed is too Aristotelian, and not realistic enough.
This kind of argument falls into the same kind of hole. Since any respectable Supreme Being creates the rules, if you imagine something He cannot do, the problem is with your imagination, not his ability, and that flaw actually serves some purpose.
The universe is the totality of existence which means it is not infinite as infinity cannot be totaled. So it is possible that one could be omnipotent only in that universe. I understand some smart physicist are talking about the multi-verse now, super string theory and M-Theory.
Revised to include explanation below for those not understanding the distinction between "all" and "infinite":
Infinity cannot be totaled. Omni means "all"; "All" does not mean infinite, it means all in the set. So, one could exist in a universe that is all knowing yet not be infinitely knowledgeable.