A common argument against the coherence of omnipotence is the famous ‘Can God create a stone so big even He can’t lift it?’. The aim of this type of argument is to demonstrate how omnipotence is an incoherent notion, and if it can be shown that this property of God is internally contradictory, then God cannot possibly be omnipotent. It seems to me like many arguments brought forth and settled long ago tend to somehow come back and trickle down to the masses and are resurrected among popularizers and polemicists (hear that Existential Blues?).
So, in the interest of hopefully putting a stop to this silly line of argumentation and hopefully encouraging people to dig a little deeper into these topics, I’m going to attempt to show why this argument fails.
The traditional argument goes something like this:
1) Either X can create a stone that X cannot lift, or X cannot create a stone that X cannot lift
2)If X can create a Stone that X cannot lift, then necessarily, there is at least one task that X cannot perform (namely, lift the stone in question)
3)If X cannot create a stone that X cannot lift, then necessarily, there is at least one act that X cannot perform (namely, create the stone in question).
4)Hence, there is at least one task that X cannot perform.
5)If X is an omnipotent being, then X can perform any task.
6)Therefore, X is not omnipotent.
Now, a little background to the concept of omnipotence is necessary. Starting with Aquinas, an attempt to explain what the notion of omnipotence really meant was put forth. To Aquinas, and many philosophers/theologians since him, the concept of omnipotence has traditionally been defined as the ability to do all things logically possible. What logical possibility entails is simply anything that is not internally incoherent. In its logical form, an internally incoherent/contradictory statement would state something along the lines of ‘P and simultaneously not P’; or something being the case and not being the case at the same time.
Aquinas writes: “It remains therefore, that God is called omnipotent because he can do all things that are possible absolutely; which is the second way of saying a thing is possible. For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another: possible, if the predicate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as for instance, that a man is an ass”
The doctrine of omnipotence according to Aquinas simply asserts that God can do anything. “Anything” in this sense should be here construed to refer only to objects, actions, or states of affairs whose descriptions are not self-contradictory. The reason why an inability to do a logically incoherent task is because as many have noted, a logical incoherency is not a possible state of affairs at all. There is no possible world in which square circles could exist, and since these things can never become actual, “it is more appropriate to say these things cannot be done, than that God cannot do them.”
It should be noted that this is precisely the position C.S. Lewis took:
“His Omnipotence means power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to him, but not nonsense. This is no limit to his power. If you choose to say ‘God can give a creature free will and at the same time withhold free will from it,’ you have not succeeded in saying anything about God: meaningless combinations of words do not suddenly acquire meaning simply because we prefix to them the two other words ‘God can.’… 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.”
The reason this dilemma fails is because it consists of asking whether God can do a self-contradictory thing. And replying that He can’t does no damage at all to the doctrine of omnipotence.
On the notion that God is omnipotent, the phrase “a stone too heavy for God to lift” becomes a self-contradictory statement, as it it would be saying “A stone which cannot be lifted by Him whose power is sufficient for lifting anything.” But the ‘thing’ described by a self-contradictory phrase has nothing to do with the doctrine of omnipotence. Not being an object of power at all, its failure to exist cannot be the result of some lack of power in God. It is the very omnipotence of God that makes it impossible for such a stone to exist.
Yet, what if someone holds that the phrase ‘a stone which cannot be lifted by Him whose power is sufficient for lifting anything’ is not incoherent. What then? What if somehow someone is convinced that this paradox forces the theologian to give up omnipotence? What exactly would this paradox take away from an omnipotent being? Very little. All this paradox would show is that there is at least 1 limit to an omnipotent being’s power: The ability to create a certain type of stone. A stone that is too heavy for Him to lift. Beyond that, there is absolutely no restriction to His power. The only restriction this would place on this being is that God must not be able to create a stone too heavy for Him to lift. God still retains his infinite power of lifting, contains His infinite power in regards to everything else, except for creating a certain type of stone. That’s not much of a handicap is it?
But, let us suppose that Descartes was right, that God’s power is not even limited by the rules of logic. Let us suppose that God can indeed perform tasks are logically contradictory. That maybe our failure to be able to imagine how God could create a square circle has absolutely no bearing on His ability to do so. Perhaps God simply created our minds as to not be able to comprehend the notion of a square circle, while He himself can create them. What then? This paradox would fail again. Suppose that God can even do what is logically impossible and that He actually does create a stone too heavy for him to lift it. The atheist would be mistaken in thinking that this supports his view. He would claim that when God has created a stone which He cannot lift, then He is then faced with a task beyond His ability and is therefore seen to be limited in power. But this claim is false.
Why should God not be able to perform the task in question? The task of lifting a stone which He cannot lift is indeed a logical contradiction, but remember, in this view, God isn’t bound by the laws of logic, so then, if God is supposed to be capable of performing one task whose description is self-contradictory-that of creating the problematic first stone in the first place- why should He not be supposed capable of performing another-that of lifting the stone? Is there any greater trick in performing two logically impossible tasks than there is in performing one?
If an omnipotent being can do what is logically impossible, then He can not only create situations which He cannot handle, but also, since He is not bound by the limits of consistency, he can handle situations which He cannot handle.
To conclude, this doesn’t show that God is omnipotent. All this shows is that these paradoxes do nothing to undermine the concept of omnipotence. Omnipotence is a perfectly coherent attribute that can be attributed to a being which the atheist has failed to show the incoherence of.