God & Logic

I’ve been studying to works of Frege, one of the inventors of modern symbolic logic. He has some very interesting ideas about the nature of logic. The project that consumed the whole of his career was trying to establish logic as foundational to all of thought. He attempted to argue that logic was the absolute bedrock of all thought. There is no way to think except in the framework of logic.
The question/thought can up last week about the relationship of God and logic. It doesn’t seem that, at least in the way Frege frames the argument, there is anyway for God to be outside of logic. I’m sure that most would dispute this claim ipso facto, but let us push this aside for the most and consider what that could mean. What would it mean to think of logic as an essential element of God’s character? Is it even possible to put God into this kind of conception. If logic is the basic foundation upon which truth is even possible, it seems that God must somehow be connected with it. Another question that arises would be wonder how this could be possible if our conception of God is one of strong seemingly contradictory terms. Because if God is one with logic then it would seem that God himself would be logically sound.
For those that are still skeptical, think about the statements of God when describing himself in the Bible, the “I am that I am” — it doesn’t seem to get much more logically basic that a statement as such.