Attributes of God: Omnipotence

David Cramer in one of his posts had a couple of brief comments about omnipotence with respect to logical contradictions:

The historic, orthodox definition of omnipotence can be stated as follows: "God can do anything that it is logically possible to do." Don’t get too wrapped up in the "logically possible" language. All that means is, if something can be done, God can do it. So, for example, God can’t both exist and not exist at the same time, because that is not "logically possible" to do. But, I don’t think this places any limitations on what he can do.

These comments of his recalled to my mind a question, related to this issue, that someone had asked me earlier this year. I want to share with both the readers and Cramer himself the answer I had replied to her with. Her question was posed to me in the following way (followed by my response):

Perhaps you can answer why God would not be able to create a state of affairs that violates the law of non-contradiction in some way?

Sure, but perhaps in a way that you might not expect.

Let nT stand for some self-contradiction.

It is not the case that God is unable to actualize nT. Rather, it is that nT is incapable of actualization. The former is a statement about God (and incompatible with omnipotence). The latter is a statement about nT (and says nothing about God). This is why Thomas Aquinas notes, "It is more exact to say that the intrinsically impossible is incapable of production, than to say that God cannot produce it."

The distinction that Aquinas underscores here is the fact that its impossibility is not due to some extrinsic feature (that which it has in relation to some thing outside itself); in other words, the idea that no agent can produce it is not what makes nT impossible. Rather, it is due to an intrinsic feature (that which it has in and of itself); in other words, the idea that it is incapable of production in and of itself, regardless of any agent, is what makes nT impossible.

Omnipotence is a concept which conveys the ability of God to perform all tasks subject to power, the accomplishment of which can never be frustrated by an obstacle. But a self-contradiction is an intrinsically impossible non-entity (i.e., it cannot be analytically conceived in itself without contradiction), which means that it is neither a task to be performed nor an obstacle against the accomplishment of one.

I shall borrow from an argument presented roughly ten years ago by Chuck Johnson (an atheist from the newsgroup talk.atheism) to underscore this distinction.

Let U stand for 'the universal set of tasks' and let T stand for 'some proposed task'.

1. Omnipotence is the ability to perform every member of U.
2. If T is logically possible, then T is a member of U.
3. If T is logically impossible, then T is not a member of U.
4. If T is not a member of U, then T is a non-task nT.
5. All nT form a null set Ø.

So it is immediately obvious that to ask if an omnipotent being can perform any members of a null set Ø is very absurd. It would be incorrect to say that he cannot; rather, it is that there is nothing there to perform. Aquinas again: "It is more exact to say that the intrinsically impossible is incapable of production, than to say that God cannot produce it."

Let me elaborate on this.

Intrinsic impossibilities do not limit omnipotence at all. Self-contradictions, by virtue of being two mutually exclusive properties, carry their impossibility within themselves; i.e., it is intrinsically impossible for them to have occupancy in the same universe at the same time—under all conditions and in all worlds and for all agents. "All agents" here includes God himself, Lewis notes in his book The Problem of Pain (HarperCollins, 2001), explaining further that God's 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 them [with] the two other words 'God can'. It remains true that all things are possible with God: the intrinsic impossibilities are not things but non-entities. It is no more possible for God than for the weakest of his creations 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 (p.18).

Herein lies the key concept: omnipotence regards power, but self-contradictions have nothing to do with power. Why? Because omnipotence has no reference to that which is not an object of power, e.g., that which is self-contradictory. Let this be our maxim: If the impossible could become possible or actual simply by applying power to it, then it was never impossible to begin with, but merely difficult. That which is impossible remains impossible regardless of any power applied. Think about what the paradox question implies. To suggest that nothing is impossible given sufficient power (omnipotence) is to deny that real contradictions exist; i.e., given sufficient power, the impossible is actually possible, albeit difficult. But to toss logic out the window is to toss out the baby with the bathwater! The non-believer who makes such an argument accidentally proves too much: if neither logic nor contradictions really exist, well then, the very objection he started out with vanishes.

Omnipotence regards the power of God to accomplish all things which are subject to power, and that power is never frustrated by an obstacle; self-contradictions, as non-entities, can be neither objects of power nor possible obstacles to it. (Refer to my argument at the beginning.)

What does omnipotence actually mean? "God can do all things the accomplishment of which is a manifestation of power," said twelfth-century philosopher and theologian Hugh de St. Victor. "Omnipotence is maximal power," cites the Stanford Encyclopedia of Philosophy. Omnipotence regards the power of God to accomplish all things which are subject to power. In all dictionaries, encyclopedias, and systematic theologies I have encountered, omnipotence is defined as: having unlimited or universal power; all-powerful; the state or quality of being all-powerful; the state of having unlimited power. Omnipotence does not mean—and has never meant—the ability to bring about a self-contradiction.