What exactly is the paradox of the stone? Quite simply it’s an argument against the Omnipotence of God.
A common modern version of the omnipotence paradox is expressed in the question: “Can [an omnipotent being] create a stone so heavy that it cannot lift it?” This question generates a dilemma. The being can either create a stone which it cannot lift, or it cannot create a stone which it cannot lift. If the being can create a stone that it cannot lift, then it seems that it can cease to be omnipotent. If the being cannot create a stone which it cannot lift, then it seems it is already not omnipotent
I have some responses to this.
“Why cannot God do logically impossible things?”. What they really mean is, “Why cannot God make contradictions true?” Well God cannot make contradictions true because contradictions by definition are always and necessarily false.
Furthermore, if we say God can make contradictions true then the logical problem of evil collapses on itself. It collapses on itself because the entire problem is predicated on a supposed contradiction, which is that evil exists and God exists. God can just simply make that supposed contradiction true, and thus we have no logical problem of evil!
So it the paradox is really a series of non-sensical questions. Also, the paradox is attacking a strawman definition of Omnipotence that most theologians have rejected. When we say Omnipotence in everyday life we use the terms less formally. In Philosophy we say that Omnipotence means the ability to do anything……that’s logically possible.
But are we somehow making the definition of omnipotence meaningless if there are certain things God cannot do? I do not see how this follows. We say that God cannot cease to exist because of His nature, but is that in anyway lessen His power? I do not see how, and we could also argue that an omnipotent being always has to exist because if it ceases to exist then really is not all-powerful because if it ceases to exist forever then it cannot bring itself back into existence.
God is himself rational, He must be consistent with his attributes! Therefore we conclude that God can do anything that does not violate his nature. This is not controversial among most atheist philosophers.