I came across this post and this post recently, addressing the question of whether God can do the illogical. From the first post:

Can God do the illogical?
On John DePoe’s Yahoo! Group “JerusalemAndAthens,” this question was asked of a Dooyeweerdian. The reason it was asked was because Dooyeweerd held that God is the creator of all of the laws for His creation – including the laws of logic. As the creator of all the laws for His creation, he is not bound by those laws.

I believe that the very question here is based on a faulty presupposition — that God is either “over” or “under” logic. In fact, God is the standard by which logic is defined. It’s very like the question, “Can God lie?” Well, God can say something we would believe to be a lie, but the moment He says it, it will become Truth. For example, God can say, “The grass is purple,” and the instant He says it, the grass will be purple. (“And God said, ‘Light be,’ and there was light.”)

Likewise, God can do something we currently view as illogical, but as soon as He does it, logic will realign and it will be logical. God is not (merely) the creator of logic, nor is He subject to logic, God is logic. Logic is defined by what God is, just as truth is defined by what God is.

In the follow-up post, the author says:

I’m not attempting to argue from authority, but trying to point out a basic theme found in all these men’s thoughts about the nature and attributes of God. That theme I will call the accommodation view. Under this view, God’s essence — his essential nature — is unknowable and “free from qualities altogether.” It is to be “left alone” and he doesn’t “wish us to deal with him [in his essence].” Rather, God accommodates to us by revealing to us that which we can understand. We know God because he relates to us and “communicates himself to us.”

This accommodation view, combined with the principle of pancreationism, leads us to say that God’s attributes are created attributes that he freely takes on so as to accommodate himself to us. God’s uncreated essence is unknowable to us, but His created attributes are the same as the attributes that we can have (although His are not affected by sin). Clouser points out that this view fits in very well with the covenantal nature of God. God has entered into covenants with his people in which he promises to do things. But if God’s attributes are uncreated, then it doesn’t make sense that God would promise to do something since one of God’s attributes is faithfulness. He couldn’t help but be faithful and would have no need to make promises.

I simply cannot agree with this notion that God’s “essence” is unknowable, or that His attributes are somewhat separate from what He is, because it doesn’t line up with Scripture.

Romans 1:20 tells us that His invisible attributes are clearly seen, having been understood through creation, including His “Godhead,” or “divine nature” (depending on your translation). What is this “divine nature,” if not His “essence,” His “essential nature”?

As far as attributes are concerned, an attribute is not something one “takes on.” It is a partial description of the one being described. The Bible does not tell us that God only “loves,” or that God “has love.” It tells us that God is love. (1 John 4:8) God does not simply tell the truth, or “have truth,” He is the Truth. (John 14:6)

The difference between God’s attribute of “truth” and our attribute of “truth” (or any other similar attribute) is that, with God, it is part of His essence. Because everything that exists, exists by and in and through Him (Colossians 1:16b-17), His very being defines those attributes. What is truth? God. What is love? God. What is logic? God. We, on the other hand, do not inherently possess those attributes; we are simply a picture of them (Romans 1:20, again), and hold them once the Spirit resides within us.