Omnipotence and the Stone Paradox

(D1) A being S is omnipotent =df S can perform any action A

The Stone Paradox

Either God can create a stone which God cannot lift, or God cannot create a stone which God cannot lift.

If God can create a stone which God cannot lift, then He is not omnipotent (since He cannot lift the stone in question.

If God cannot create a stone which God cannot lift, then He is not omnipotent (since He cannot create the stone in question).
Therefore,

God is not omnipotent. (1), (2), (3)

Let's consider what Aquinas says about omnipotence:

All confess that God is omnipotent; but it seems difficult to explain in what his omnipotence precisely consists. For there may be doubt as to the precise meaning of the word 'all' when we say that God can do all things. If, however, we consider the matter aright, since power is said in reference to possible things, this phrase, God can do all things, is rightly understood to mean that God can do all things that are possible; and for this reason he is said to be omnipotent. Summa theologica I, 25, a.3

(D2) S is omnipotent =df S can do any action A which is logically possible.

Mavrodes suggests applying Aquinas' insight to the Stone Paradox. If we accept (D2), we can say that premiss (3) is false, on the grounds that creating a stone that God cannot lift is an impossible action. If it's an impossible action, then God doesn't, according to (D2), have to be able to do it in order to be omnipotent. Hence, when (3) says that if God can't do it then He is not omnipotent, (3) is mistaken. So the argument, on this view, is unsound.

Objections to Mavrodes' solution:

Consider:

creating a stone which God cannot lift

creating a stone which its maker cannot lift

building a house which its builder cannot lift

(3') If God cannot create a stone which its maker cannot lift, then He is not omnipotent, or

(3'') If God cannot build a house which its builder cannot lift, then He is not omnipotent.

authoring a book whose sole author is Bertrand Russell

(D3) S is omnipotent =df S can do any action A such that it's logically possible that S do A

Several classical theists endorse the project of recognizing limitations on ability that are compatible with being omnipotent.

Augustine said that God "cannot do some things for the very reason that he is omnipotent" City of God, V, 10.

Anselm held that "God cannot be corrupted, or tell lies, or make the true into the false (such as to undo what has been done)" Proslogion, VII.

The tenth-century Jewish philosopher, Saadia ben Joseph spoke of "those absurdities that cannot be ascribed to divine omnipotence, such as the bringing back of yesterday and causing the number five to be more than ten" The Book of Beliefs and Opinions, Treatise VII (variant), ch. 1.

In the twelfth century Moses Maimonides wrote,

That which is impossible has a permanent and constant property, which is not the result of some agent, and cannot in any way change, and consequently we do not ascribe to God the power of doing what is impossible. No thinking man denies the truth of this maxim; none ignore [sic] it, but such as have no idea of Logic. ...[i]t is impossible that God should produce a being like Himself, or annihilate, corporify, or change himself. The power of God is not assumed to extend to any of these impossibilities.