The Paradox of the Stone
Some of the various arguments for atheism claim that the concept of God is incoherent, that there are logical problems with the existence of such a being. Perhaps the best known of these is the paradox of the stone: Can God create a stone so heavy that he cannot lift it?
Either God can create such a stone or he can't.
If he can't, the argument goes, then there is something that he cannot do, namely create the stone, and therefore he is not omnipotent.
If he can, it continues, then there is also something that he cannot do, namely lift the stone, and therefore he is not omnipotent.
Either way, then, God is not omnipotent. A being that is not omnipotent, though, is not God. God, therefore, does not exist.
Problems With the Paradox of the Stone
Although this simple argument may appear compelling at first glance, there are some fundamental problems with it. Before identifying these problems, however, it is necessary to make clear what is meant by "omnipotence".
Christian philosophers have understood omnipotence in different ways. Ren Descartes though of omnipotence as the ability to do absolutely anything. According to Descartes, God can do the logically impossible; he can make square circles, and he can make 2 + 2 = 5.
Thomas Aquinas had a narrower conception of omnipotence. According to Aquinas, God is able to do anything possible; he can part the red sea, and he can restore the dead to life, but he cannot violate the laws of logic and mathematics in the way that Descartes thought that he could.
If Descartes' conception of omnipotence is correct, then any attempt to disprove God's existence using logic is hopeless. If God can do the logically impossible, then he can both create a stone so heavy that he cannot lift it, and lift it, and so can do all things. Yes, there's a contradiction in this, but so what? God can, on this understanding of omnipotence, make contradictions true.
Descartes' understanding of omnipotence therefore doesn't seem to be vulnerable to the paradox of the stone. Descartes can answer the question "Yes" without compromising divine omnipotence.
Aquinas' understanding of omnipotence, which is more popular than that of Descartes, also survives the paradox of the stone. For if God exists then he is a being that can lift all stones. A stone that is so heavy that God cannot lift it is therefore an impossible object. According to Aquinas' understanding of omnipotence, remember, God is able to do anything possible, but not anything impossible, and creating a stone that God cannot lift is something impossible.
Aquinas can therefore answer the question "No" without compromising divine omnipotence.
The paradox of the stone, then, can be resolved; it fails to show that there is an incoherence in the theistic conception of God, and so fails to demonstrate that God does not exist.
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