(Statue of Averroes who first discussed the paradox in the 12th century)
The Omnipotence Paradox is usually stated this way:
“Can an Omnipotent Being create a stone so heavy that it cannot lift it?” (1)
1) It’s akin to asking, “can 2 + 2 not equal 4?” Of course God, being All-Powerful, could have made it not 4, but He chose it to be that way. Does it make Him less powerful for choosing one way rather than another? No. He might have been “able” to do something other than what He did, but He did do what was done. No matter which way it was done, we would be asking why it was done that particular way.
2) When Christians talk about God being "All Powerful," they really mean "Eternal in Power." So the question really is, "what does Eternal mean?" Though there are many aspects to it, the aspect most pertinent to the paradox is the aspect of continuity. In light of that definition, there is no problem.
3) The question also begs the question of what the “stone” (or whatever object) really is. If the question were similar to the 2 + 2, then it’s just a play on semantics. Though I believe that the stone argument is, in essence, a question of whether God (the Greatest Possible Being) could create a being “greater” than Himself. But a being greater than the Greatest is illogical (because a precondition of being Greatest presupposes that there is none greater).
4) It's a misrepresentation of privation. The paradox is about what is not, rather than what is. The argument tries to make the point that God is “less” of a being because He does not do things one way rather than another. Though the problem with this reasoning is that God is the “Greatest Possible Being.” Anything He does is the standard of perfection. Anything which is contrary to the way it is, is itself, a lack of perfection.
For example: For the rock analogy, it’s a vie against logic. Is God less powerful because He does not defy logic? No. Logic is the standard of perfection. Anything which is contrary to that standard is less powerful; which means the question is asked under false pretense. It’s like saying, “Can God be less powerful to be more powerful?” The question itself is illogical.
When I lay these questions before God I get no answer. But a rather special sort of “No answer”. It is not the locked door. It is more like a silent, certainly not uncompassionate, gaze. As though He shook His head not in refusal but waiving the question. Like, “Peace, child; you don’t understand.”
Can a mortal answer questions which God finds unanswerable? Quite easily, I should think. All nonsense questions are unanswerable. How many hours are there in a mile? Is yellow square or round? Probably half the questions we ask–half our great theological and metaphysical problems–are like that.
And now that I come to think of it, there’s no practical problem before me at all. I know the two great commandments, and I’d better get on with them. (2)
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(1) “Omnipotence Paradox.” Wikipedia. Wikimedia Foundation, 09 June 2012. Web. 08 Sept. 2012. .
(2) Lewis, C. S. A Grief Observed. New York: Phoenix, 1961. 65. Print.
Note: A variation of this is the omniscience paradox–namely, “Can God create something He cannot know?”