1.) Consider these analogues to the stone paradox:
If Mozart were a better musician he could write a song even he couldn’t play.
If Achilles were a faster runner he could set a record in the mile that even he couldn’t break.
If Aristotle was wiser he could write an argument even he couldn’t understand.
2.) Set aside physical limitations since these have no analogue with omnipotence. We can imagine, or at least talk about a musical piece that exceeds the possibilities of a human hand or even a physical system (like playing a Wagner opera in a nanosecond) but these are beside the point when talking about what spirits are capable of.
3.) Say we’re sympathetic to the stone paradox. It seems we have to say that capabilities develop to the point where they become incapable. But it is strange to the point of incoherence to call this a development of a skill or capability.
4.) Even if we look around for physical limitations, the description of a wisdom so great that it can’t understand what its saying is an extremely odd claim. We can make sense of a wisdom that understands its ignorance but not a wisdom that is constituted by its ignorance. Thus the stone paradox, when applied to the power of intelligence has consequences for omniscience, but they strike me as absurd consequences.
5.) Here’s an argument against omnipotence: any power that extends to something extends to its contrary. Vision sees colors and darkness, hearing hears sound and silence, etc. So the power over all that is logically possible is a power over all that is impossible. There is no such thing as a power over the impossible, and so also no such thing as omnipotence.
One response is that the possible and impossible aren’t related as light and darkness but as light and non-light. But “non-light” is undefined and undefinable since a thing need not even exist to be described in this way. To use “non-light” as a domain outside of light is not to specify any domain that pertains to sight, or even a domain that is definable. “Non-light” has a perfect analogue in “non-liftable stone”.
It is only accidentally true that we see non-light (that is, it is only true in a sense that also makes it false). This is how omnipotence relates to non-lifable stones.
6.) In classical theism omnipotence extends not to the logically possible as such but to logically possible composites. Divine power does not extend to making another instance of divine power (which is not contradicted, but in fact preserved in the doctrine of the Trinity.) In light of this the stone paradox translates into the question whether a simple power could ever give rise to a complexity that it had no power over. The claim is the equivalent of asking whether an atomic reductionist could say that atoms could give rise to atomic complexities that they could not explain. Such a state of affairs is incoherent since anything that counted as evidence of a complexity that did not arise from atomic simplicity would count as evidence against atomic reductionism. Taken in this sense the stone paradox needs to give way to the question of divine simplicity as a reductive source of angelic-cosmic-Incarnational complexity.