Hi, My roommate claims that it is impossible for an omnipotent being to exist. His logic is that if a being can create a rock so big it cannot lift it, then that being is not omnipotent because its lifting power is not infinite. But also, if it cannot create the rock so big it cannot lift, then it's creation power is not infinite. And because of this paradox, an omnipotent being cannot possibly exist. My boss was a philosophy major in school. He claims that this explanation is completely wrong. However, I do not understand his explanation as he said it very quickly and with many names of old philosophers and theorems and such that I cannot remember. So who is right? Regardless of whether or not an omnipotent being does exist or not, can one exist? Thanks.

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This is a version of an old problem, one discussed endlessly by theologians. In its simplest form, it goes like this: Can God make a rock both big and small? Obviously not. So God isn't omnipotent.

If you think that's a cheat, I'm with you. It's not possible for there to be a rock that is both big and small, so it's not limit on God's power that God can't make a rock like that. We have to be more careful in how we understand omnipotence. It's a delicate question how we should understand it, but a first stab might be: A being is omnipotent if, whenever it is possible that p, that being can bring about that p.

The puzzle your roommate presents you is of this same form. If Fred is omnipotent, then it simply isn't possible for a rock to be so big that Fred can't lift it. So it's no limit on Fred's power that he can't create a rock that big. Of course, maybe Fred isn't omnipotent, and maybe it's not even possible for there to be a being that is omnipotent. But the argument your roommate offered does not prove either conclusion.

There are two traditional theistic answers to this question (well, three, if you count: “you’re a heretic, where are my matches”). The first, favored by Descartes, is that God’s powers are truly unlimited, and He is not even limited by the laws of logic. It is not for us finite and imperfect beings to understand or criticize an infinite and perfect being’s ways. The second, favored by Thomas Aquinas, is like Richard Heck’s answer above. To be omnipotent means to be able to do anything; a contradiction is not a thing: therefore not being able to create a stone so heavy one can’t lift it is not a thing that can’t be done. To some readers this puzzle might seem silly, but it actually mirrors some contemporary controversies about the nature of logic. Are logical inferences hardwired into our brains? That is similar to Descartes’ answer. Are logical inferences constitutive of rationality? That is similar to Aquinas’ answer.

I'd like to add one further point to the two made so far. Many contemporary philosophers infer from the so-called Paradox of the Stone that omnipotence is not a matter of being able to do anything, but only a matter of *being able to do anything it is possible to do*. That observation suggests another possible insight. Consider the Problem of Evil. If God exists, then it might seem puzzling that God should permit the extent and kinds of evil that we can find. Now there are many things to say about this, but one pertinent to God's omnipotence is this: Certain moral virtues seem to require some evil, and in such a way that even God can't have one without the other. Even God, it might be remarked, can't make a world in which there is, for instance, forgiveness in the absence of any wrongdoing. (I can't forgive you unless you've wronged me in some way.) This is not to say that all virtues require evil, but just that some seem to, even if you're God. As it happens, contemporary philosophical theologians like Alvin Plantinga have made much of how God's powers might be surprisingly limited, while remaining omnipotent!

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