From Vincent Cheung, Systematic Theology (PDF, p. 58-59):

The OMNIPOTENCE of God refers to his unlimited power and ability to create what he wills and to control his creation.

It is often asked whether this means that God can create something that amounts to a contradiction; however, the question suffers from what we may call the CATEGORICAL FALLACY. This means that a term or concept has been misapplied to an issue in question such that one does not even belong in the same category with the other, and thus the statement or question becomes unintelligible and meaningless.

For example, the question "How big is your cat?" makes sense, since size is a category that can be meaningfully applied to animals. The same is true for "How fast is your car?" and "How smart is your son?" However, it makes no sense to ask, "Is the color green fast or slow?" or "Is that rock smart or stupid?" Speed does not apply to color and intelligence does not apply to a rock. Green cannot be fast or slow; a rock cannot be smart or stupid.

There is a similar problem with the question asking whether divine omnipotence implies the ability to perform a contradiction, such as, "Can God create a rock so big or heavy that he cannot lift?" However, God is incorporeal, and thus physical forces do not act upon him at all. When God "lifts" an object, there is no physical force to restrain him. What force is going to make the rock "heavy" to God? Whether the object is big or heavy to us is completely irrelevant. If God creates a rock, he will always be able to do anything he wants with it.

Now, a square circle is a self-contradictory concept. The category of ability does not apply to creating a contradiction, since a contradiction is not something to be created – a contradiction is nothing. Therefore, it is meaningless to ask whether God can create a square circle, since it is nothing to be done at all.

The omnipotence of God is defined as his ability to create what he wills and to exercise complete control over his creation. God does not act contrary to his own will or nature, and he does not perform contradictions, since contradictions are nothing to be performed.

 

Additional Comments:

When responding to the question (often intended as a challenge to the coherence of biblical theism) of whether God can create or perform contradictions, many Christians are too quick to insist that divine omnipotence does not mean that God can do everything. For example, God "cannot" lie or die. Then, they would apply this to contradictions, saying that God cannot create or perform them.

However, this accepts the confusion inherent in the question, and on that basis supplies a compromising response that is often theologically irrelevant to the Christian God, and that makes an unnecessary concession about God's ability.

The answer is often irrelevant because, when it comes to creating a rock too heavy for God to lift, the category of weight does not apply to an incorporeal God in the first place, so to accept "heavy" as applicable to "God" means that one is no longer answering for the Christian God.

Then, the answer makes an unnecessary concession because a contradiction is nothing to be created or performed, such that the issue of ability is inapplicable, and so to say that God "cannot" create or perform a contradiction is to unnecessarily say that God "cannot" do something, when it is really nothing.

Even the common illustrations that are meant to clarify divine omnipotence demand our reconsideration.

First, does the Scripture really say that God "cannot lie" (Titus 1:2, KJV), or is it in fact God "does not lie" (NIV) or God "never lies" (ESV)? Go check the Greek.

Second, even if we have access only to the KJV, so that the verse reads "cannot lie," why must we assume that "cannot" is here used in the same sense as it is in the question under discussion? Depending on the intention and the context, "cannot" sometimes means "does not." Hebrews 6:18 says that it is "impossible for God to lie," but then we still need to know why or in what sense it is impossible. Is it because God is inherently unable to speak falsehood as if it is truth? Or is it because whatever God says becomes the truth (Romans 4:17)? Power and the Word are one in God. Why can he not lie? Is it because of inability, or something else? Does the category of ability apply at all in this case?

Likewise, when we say that God "cannot die," are we saying that he lacks the ability to die, or should we rather say that death does not apply to the Eternal in the first place? Nothing eternal "can" die, but the "can" here has nothing to do with ability — the category does not apply at all. The eternal does not die, and when we say that God "cannot" die, we are referring to the utter impossibility of it, the inconceivability of it, the inapplicability of it, and not his ability or inability.

We should be deathly afraid to say that God cannot do something, that is, in the sense of inability. If we were to attribute inability to God — assuming that there is ever a legitimate and relevant application of inability to God — we must be certain that we use the term in the right sense, that we are not making an unnecessary concession by adopting anti-biblical assumptions, that the biblical verses being used to support our explanation indeed teach what we assert, and that it is not merely an equivocation on our part. We must avoid all silliness and carelessness, such as in the response, "God cannot perform contradictions because he is rational, and he cannot or will not act against his rational nature" — as if an irrational God would be "able" to perform contradictions!

 

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