Omnipotence

[Versión en castellano]

I'm sure you've all heard this before:

Can God create a rock so heavy that even He cannot lift? If He can't, then He isn't omnipotent, because his powers of creation are limited. But if He can, then He isn't omnipotent either, because his power to move any object is limited. Therefore, omnipotence cannot exist

This is of course a paraphrasing, I don't know who came up with it originally and I didn't check any sources, but I assume you get the idea.

Now, someone such as myself who believes in a non-omnipotent God would be glad to use this argument as support, right? Well, not really. You see, there are many ways to solve the paradox of omnipotence, in a more or less satisfactory way. These are the ones I know. There are probably others, much better than these, but I don't know them. The first two are what I call the "He's omnipotent anyway" approaches. They are the least satisfactory.

1) The "Shut up" Approach.
This has many variations, such as "Who are we, limited humans, to question God?" or "You just need to have faith". It basically consists of ignoring the issue and asking the questioner not to think about it. It's not really a solution for the paradox, but it is absurdly common, so I consider it deserves being mentioned.

2) The Illogical Approach
This one consists of saying "Yes, God can create it, but He can also lift it." How, you may be wondering? "Because the laws of logic don't apply to God." The problem with this approach is that it touches on a really big issue: Is logic universal, and what proves logic is necessarily true? I won't go there right now. This approach is highly debatable, and accepting it creates a whole bunch of problems that we are better off without. It's not really the way to go, in my opinion.

The following 2 approaches are based on what I like to call "functional omnipotence". That is to say, an extent and amount of power that is not true omnipotence but behaves in the same way in most relevant cases.

3) God The Writer
Simply, imagine God as the author of a book. He determines everything that happens in the story, and he can do whatever he wants with it, right?. Isn't He, at least from the point of view of the characters in the story, omnipotent? And yet, He really isn't. In His own universe, His powers are limited. This solves the paradox by putting God and his omnipotence in different realms. He can create rocks as big as He likes, but asking Him to lift them is nonsensical because the rock doesn't really exist for Him. Essentially, God is omnipotent in our world, but not in His.

4) Absolute vs. Relative
The basis of this is to say that God can do anything, as long as He can describe it in absolute terms. For example, he can create a rock as big as he likes, as long as he specifies how large it is. He can create a rock that weighs 20g or 400kg or 10^10000000 tons, if he wants to, but he cannot create a rock that's only described as "heavier than I can lift". Simlarly, he can create a lifting force as big as he likes, that can be similar to the attraction of a small magnet or the gravity of a black hole, but he can't define it as "greater than the weight of the heaviest rock I can create"

I'm sure there are flaws with these approaches, but I'm also sure there are better ones around, that rely on similar principles or something completely different. I'll keep looking.

Edit: I'd include the most obvious one, "God can do anything, as long as that doesn't contradict the laws of logic", if not for the fact I can't shake the feeling there's something fallacious about it. I'd put this one along with the last two, as it is in fact limited omnipotence.