The problem of the stone is whether God can create a stone that he cannot lift. If he can, there is something that he cannot do, namely, lift the stone he has created; and if he can, there is also something he cannot do, namely, make the stone. Since he must either be able to make it or not make it, it follows that there is something he cannot do, and hence that he is not omnipotent. The argument is a straightforward dilemma and may be schematized as follows:

          (1) Either God can create a stone he cannot lift or he cannot.

          (2) If he can, there is something that he cannot do, i.e. lift the stone.

          (3) If he cannot, there is something he cannot do, i.e. create the stone.

          (4) If there is something God cannot do, it follows that he is not omnipotent.

           Thus (5) God is not omnipotent.

Premise (1) is a logical truth and (4) seems to be a condition of omnipotence (i.e. there is nothing an omnipotent being cannot do) while (2) and (3) are true by existential generalization.

To bring out the role of the contradiction in the task asked of God, we can construe the problem in another way:

        (1) God is omnipotent.

        Thus (2) He can (i) create anything and (ii) lift anything.

        Thus (3) He can create a stone that he cannot lift (from (2i)).

        Thus (4) The being who can lift anything cannot lift something.

The conclusion is a contradiction, but it rests on God’s omnipotence and what we take to follow from it. Clearly one of the premises must be false. The Thomistic solution is that (3) is false, but that this is not a limitation on his omnipotence. God can create anything that does not contradict his other powers (and properties), so his power only operates within the limits set by the laws of logic. This might seem to limit him, but, according to Aquinas, it does not, since it is not a deficiency not to be able to do what is impossible. The deficiency is only verbal or nominal, not real.

This is a coherent and plausible position. Consider this example. Suppose that Susan gets a perfect score on all her geometry examinations, including the state Regents exam. But her mother reminds her that even though she has 100s on all her tests, there is still something that she cannot do, namely, square the circle, so she should not be complacent and work even harder. The mother is obviously being too hard on poor Susan, although we understand that her motives are good. Not being able to square the circle does not show that she has some deficiency in geometry that she should work to overcome. No one can do better than to prove all the theorems, so nothing more can reasonably be asked of her.

Despite this, there is another approach to the problem, which I will call ‘voluntarism’. Aquinas’ view is ‘rationalist’, since it takes omnipotence to operate within the realm of logical possibility, while the ‘voluntarist’ holds that God’s will ranges over every possibility and the laws of possibility themselves. Suggestions of this are found in Scotus and Ockham, although they stopped short of drawing what seem to be its natural implications.

How is this relevant to the problem of the stone? The voluntarist would respond that God’s power enables him to go between the horns of the dilemma. Although it is logically true from our perspective within the laws of logic that either God can or cannot create a stone he cannot lift, there is still a sense in which it is possible for him to create a stone he cannot lift without compromising his omnipotence. He can not only create the stone, but rescind the laws of logic, or, to put it differently, it is within his absolute power to create the stone, even though it is not within his ordained power. That is, there is a sense in which the being who can lift anything can create something he cannot lift, namely, from the perspective of his absolute sovereignty over the possibilities as well as the created world. There is also a sense in which he cannot do this. Since he has chosen to work within the laws he has ordained, creating a stone he cannot lift contradicts his ordained power. From this perspective, the Thomist solution is correct, but, according to the voluntarist, this does not get to the root of God’s omnipotence.

One consequence of this is that we are unable to understand God’s will and omnipotence. Since our reason operates within the laws of logic, it is beyond our competence to understand how there can be something that a being who can lift anything cannot lift. We see, as the early Russell liked to put it, that this is impossible, but this is because we are subject to God’s action in the first logical instant. The world of being (i.e. of subsistent entities) is the arena of our operation, but it is not real in the sense of being independent of God’s decision. As a result, his creation of it and the laws of possibility are not subject to human criticism and evaluation. All we can know about what is beyond, i.e. some other range of possibilities, is that it is different from the laws governing us. What they are or the sense of reason that they would define if God had done something else is forever beyond our comprehension.

As I suggested, the disagreement between the rationalist and voluntarist is a dispute over the understanding of omnipotence. Aquinas holds that omnipotence is the absence of all deficiency. As the perfect being, God lacks nothing, and since being able to do what is contradictory is not a deficiency, his inability to create a stone he cannot lift does not imply any defect in him. We might say that he is an infinitely competent being. The voluntarist view is that omnipotence goes beyond competence and implies absolute sovereignty; he is the absolutely sovereign being in the sense that he is the creator of the framework that defines the theater of his creation as well as the creation of the world from the possibilities. Furthermore, both creative acts derive from the exercise of God’s will, not from his nature. Since the Thomist holds that God is existence, he would agree with the voluntarist that the laws of possibility are not independent of him. Since he is existence itself, nothing can be independent of him. The difference is that Aquinas (as I understand him) does not hold that these laws result from an act of will on his part. They are part of his nature and form the basis of his actions. The voluntarist view takes his will to be supreme and holds that God defines himself as a creator by his choices.

The rationalist might argue that, even if we admit the supremacy of will, God is still a rational being by nature and so, even if he creates the framework of rationality, he is still guided in his decision by some standard within himself. But this misses the voluntarist’s central point. According to him, the standard itself depends on God’s will. He creates it, but we cannot say that he is limited in any way in doing so, since a will that is restricted in its choices is not a supreme will, but a circumscribed one. Any restriction on it must stem from the will itself, that is, from God’s decision to operate within the standard he has established.

It might be wondered how we could decide which conception is correct. I suspect that Aquinas holds that his conception can be seen to be correct by reason. Given that we can prove that there is an omnipotent being by arguments such as the third way, it would seem to follow by reason itself that God is governed by reason rather than by an arbitrary will. But this of little value when the question at issue is the very status of reason. God may appear to be rational by something like our standards of contradiction, but this is consistent with God’s ordained will and does not tell us whether his absolute will is guided by an external standard. On the other hand, the voluntarist conception could perhaps be defended on the ground that the infinite being would not be supreme if he were guided in any way by a standard not of his own creation. This intuition seems to be the basis of the dissatisfaction most people feel toward the Thomist proposal about the stone, but it also does not take us very far. The rationalist would argue that the sense in which not being able to create the stone (or lift it) is something he cannot do is purely verbal. We say that it implies that there is something he cannot do, but this just a misleading figure of speech. Ultimately, I suppose, any belief we have about the matter rests on faith, that is, on some more fundamental conviction about the sort of creature God is, if he exists and is infinitely perfect, as the tradition claims.

There are also several consequences of the voluntarist position that many people find disturbing. I shall briefly discuss three of them: 1. the effect of the conception on what is known as the free-will defense to the problem of evil, 2. implications for God’s goodness and justice, and 3. its implications for the conception of him as a necessary being.

1. The free-will defense holds that moral evil results from God’s decision to make humans persons with free will. Although he knows what each of us will do, he is not the cause of our actions. We have free will just as he does and so are uncaused causers of our actions. We are members of the natural order and so our bodies are subject to second causes and the laws of nature, but our decisions spring from our capacity to initiate processes that result in actions independent of these causes. This capacity derives from his decision to create us as persons.

I am not concerned here with the defense of this position as an explanation of suffering in the world, but with just one issue. It is often argued against the proposal that God could create persons with free will while interfering and suspending it in extreme cases such as czarist pogroms, Hitler’s Holocaust and the slaughter of millions in Cambodia. The reply is that there can be no restrictions on free will. Given that God chose to create persons, he was committed to creating creatures with free will and the attendant consequences. To restrict free will to any extent destroys it; it is an all or nothing affair and not a matter of degree. This defense loses its plausibility, if the voluntarist is right. According to him, it is impossible for God to create persons with restricted wills only in the ordained sense. Given that he chose possibilities as we know them, this was impossible, but it is not impossible for him to have done so in the absolute sense. He could have created alternative possibilities that would have allowed for personhood and free will without the horrible consequences we suffer. Surely he knew at the first logical moment that Hitler and other moral monsters would use their free wills as they have and, if he were all loving, as it is claimed, would have done something else.

These consequences extend to our conception of this as the best of all possible worlds. Leibniz held, for instance, that the created world has the greatest total good for the fewest imperfections of all the logically possible worlds, and so is the best. But voluntarism calls any such conception into question. If the possibilities were given to God as the framework for his choices, we could argue from his goodness to the conclusion that this is the best possible world. But this is not the case for voluntarism. God creates the possibilities, then chooses the best (based on a standard he has created), but the result is the best only relative to his creation of the possibilities themselves. Once again, the goodness of God’s action loses its meaning in the face of omnipotence.

3. Finally, voluntarism calls into question the very concept of God as a necessarily existent being. If God’s existence is held to be necessary, the question arises in what sense this is so. If it means that the proposition that God exists is necessary, is this modality in the absolute or the ordained sense? If it is taken to be in the ordained sense, then his existence is contradictory only because he created laws of necessity such that this is the case and presumably could choose to go out of existence, since these laws depend on his will. According to Aquinas and others, this would mean that the universe and everything in it would also go out of existence, since his creation is contingent on him. But even this would not follow. He could change the logical laws that make this the case so that we and the other second causes could continue without him. The result would be that we could go on existing after he decides to go out of existence.

The other option is that his existence is necessary in the absolute sense, but this is totally incomprehensible. Presumably there were no laws of possibility and necessity before God created them in the first stage of creation, so it is unclear in what sense he was necessary prior to that. The only sense of necessity that has any meaning for us is the ordained sense. To claim that he necessarily exists in some prior sense has no meaning at all.

One might try to meet this difficulty by appealing to the principle Np —> NNp, but this is of little help. Aside from being obscure in itself, the idea that the necessity of p implies that p’s necessity is also necessary is inconsistent with the voluntarist’s claim that the system of necessary truths results from a free act of creation on God’s part. Creation of the eternal truths implies that they had no status before the first logical moment of creation, much less that they were necessary in some prior sense. Before this, that is, in the absence of an act of will on God’s part, there were no truths at all except that God exists. We might interpret necessity to accommodate this state in which only he exists and say that when he exists, he necessarily exists, and take this to be necessary existence in the absolute sense. But what can this mean? Without any background of other necessities and possibilities, it seems to mean only that he exists and this by itself does not imply that he could not go out of existence by one last act of supreme will.

There are other puzzles as well. If the voluntarist is right, there also seems to be a sense in which God could go out of existence while seeing that we continue to exist, then come back into existence at a later time. Or, even more absurdly, he could exist and not exist at the same time, so that both the theist and atheist are right.

I admit that none of this is conclusive, but the reason is that the notion of necessity outside the framework of logic and mathematics that we know is as hopelessly unintelligible as the notion of a God who is an independent creator of them. We may take solace in the fact that this appears to confirm Aquinas’ conception of God and necessity, but this of course assumes the network of necessity within which we operate — and this is little solace when the issue is the status of this network.

FOOTNOTES