Musings about omnipotence and perfection.

[Ryft]

I also believe that God cannot do the logically impossible things.

I disagree with Rayaan here, and for an important reason. Taking my cue from his statement, I should like to point out that under Christianity it is not the case that God is unable to actualize a self-contradicting state of affairs. Rather, it is that a self-contradicting state of affairs is incapable of actualization—as DvF astutely observed. The former is a statement about God (and incompatible with omnipotence). The latter is a statement about self-contradicting states of affairs (and says nothing about omnipotence). 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."

Omnipotence describes the ability of God to perform every member of the universal set of tasks. But a self-contradiction is an intrinsically impossible non-entity—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."

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 (p. 18, emphasis mine)

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.

Herein lies the key concept: omnipotence regards power, but self-contradictions have nothing to do with power. If the impossible could become possible or actual simply by applying sufficient 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 suggest that the law of non-contradiction is false—that is, given sufficient power the impossible is capable of actualization, which thus means it is possible (albeit difficult). But to toss logic out the window just to prop up an irrational definition of omnipotence is to toss out the baby with the bathwater. Thus the person who proposes such a thing accidentally proves too much: if logic and its law of non-contradiction is false, well then, the very objection he started out with vanishes!

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.