A traditional objection to the possibility of God’s omnipotence (and therefore the existence of the Judaeo-Christian God) comes in the form of a question: can God create a rock so big that he can’t lift it? Or, another: can God create a square circle? The fact that it is difficult (or impossible) to answer these questions is supposed to demonstrate that an omnipotent being could not exist. How serious are these objections? Let’s take a look at the latter question first.
Wittgenstein, the 20th century Austrian philosopher, took the view (for a time, at least) that many of the problems of philosophy were actually problems with language. While it seems obvious that not all problems of philosophy reduce to a matter of unclear language, at least some problems can genuinely be seen as merely illusions due to language. The idea of a square circle is supposed to pose an unsolvable problem for an omnipotent being, demonstrating that such a being could not exist. Upon closer inspection, asking an omnipotent being to create a square circle is very much like asking them nothing at all. What is a square circle? It is not a thing. These two words joined together in the English language simply do not mean anything. We should not be bothered, then, by the fact that an omnipotent being cannot create a non-thing we pretend exists by stringing together two words. I can imagine someone demanding that God create a square circle, or else they won’t believe that he is omnipotent. One may as well stand before God and demand that he “couch shave while plant big in beer toe.” If he can’t, so much for God. I think the problem is that "square" and "circle" are such simple words that it is easy to pretend such a small phrase is intelligible when in fact it is no more intelligible than the above beer toe example. The phrase is literally nonsense and as such cannot tell us anything about God.
What about the first question? Can God create a rock so big that he can’t lift it? This objection seems to be the stronger of the two. Assuming the existence of such a being, obviously the answer must be either God can create a rock so big that he can’t lift it, or that God can’t create a rock so big that he can’t lift it. So perhaps the question should be which answer should be true for God to be as omnipotent as is logically possible. Let’s see. Would it be more impressive if God could create a rock that he then could not lift, or if God created the heaviest rock possible but could still lift it?
First, the very form of this question is problematic, as we are assuming that God has a physical body subject to physical laws (e.g. gravity). The heaviest rock possible? There is no logical limit to how massive an object may be; infinite mass is a possibility. This makes the question difficult to answer sensibly. I suggest a reformulation; this question, at its base, is asking: can an omnipotent being impose limits of power on itself? Imagine it this way: an omnipotent being creates maximally strong unbreakable (and let's say metaphysical too) handcuffs for itself and then cannot escape. Or, the being creates maximally strong unbreakable handcuffs for itself and then breaks them. It is clear that if an omnipotent being could impose limits of power on itself that it would only be taking away from its own omnipotence (e.g. if it could not break the handcuffs). Logically then, an omnipotent being cannot take away its own power without violating its own omnipotence. On the other hand, why couldn’t such a being willingly impose limits on itself? If it then decreases its own power, so what? How does any of this suggest that such a being could not exist? At best it suggests that we should approach the term “omnipotence” with care. Perhaps an omnipotent being’s omnipotence is tentative, contingent on its will. Or perhaps no matter what God does he could always later undo it.
Either way, it is not clear to me that these objections go very far in arguing against the existence of God (or superbeings in general).