A short and sweet one today! A fairly common question, with a fairly simple answer.
While omnipotence is now commonly seen as the ability to do absolutely anything (even apparently meaningless combinations of words), it has not always been understood that way. Traditionally, it would come with several clauses, one being that omnipotence does not include the ability to perform an act which, if performed, would lead to a logical contradiction. Since a stone too heavy for an omnipotent being to lift would, it seems, be contradictory, creating such a stone would not fall under omnipotence. This is consistent with, for example, Aquinas’ understanding: “Therefore, everything that does not imply a contradiction in terms, is numbered amongst those possible things, in respect of which God is called omnipotent: whereas whatever implies contradiction does not come within the scope of divine omnipotence, because it cannot have the aspect of possibility.”
Such a conception of divine omnipotence has been wisely recognised in the modern academic sphere: philosopher Richard Swinburne writes, “God is omnipotent in the sense (roughly) that he can do whatever it is logically possible that he do. The qualification in the last clause is important. There are some apparent states of affairs, the description of which involves a logical contradiction-for example, me existing and not existing at the same time. God cannot bring about such apparent states, not because he is weak, but because the description ‘me existing and not existing at the same time’ does not really describe a state of affairs at all, in the sense of something that it is coherent to suppose could occur.” Similarly, popular writer C.S. Lewis wrote, “It remains true that all things are possible with God: the intrinsic impossibilities are not things but nonentities. It is no more possible for God than for the weakest of His creatures to carry out both of two mutually exclusive alternatives; not because His power meets an obstacle, but because nonsense remains nonsense even when we talk it about God.”
So we can see that, although we have only considered limited examples here, there is an understanding throughout the Christian philosophical tradition of seeing omnipotence as limited in certain respects, viz. that omnipotence does not include logical contradictions. So, since the state of affairs in question is logically inconsistent, we can affirm that God cannot create such a stone, but also that his not being able to create such a stone is in no way inconsistent with his omnipotence.
1. Aquinas, Thomas. Summa Theologica. I, Q XXV, art. 3.
2. Swinburne, Richard. The Existence of God. 94.
3. Lewis, C.S. The Problem of Pain. 18.