Is God a logical contradiction?

[Belacqua]

The material human brain is the most complex thing we know of in the universe, correct? So even if something is "immaterial" the fact that it's intelligent (intelligible as you say) would likely make it complex I should think. William Lane Craig defines God as immaterial, all knowing, very powerful etc etc.

I've already addressed this. When theologians say that God is intelligent, it is not in the same way that a person is intelligent. If you skipped my description of this before you can look again, at my first post here. 

Intelligent and intelligible describe very different things. We'd better make sure we don't mix those up. 

William Lane Craig is, to put it mildly, not my favorite theologian. I'm not aware of much that he says, nor am I impressed with what I've heard. 

If God is "nothing" how could he do something? 

He takes no actions. This would require change, and he doesn't change. 

He causes things to be and to change because of what he is, but this doesn't require his own change. This is a long involved argument, and I guess we could do it later if you want. But it's not quite the same as the intelligence question.

Again, this is classical theology, not what you might hear from rank and file Christians. 

I take nothing to mean "lack of everything", including God. What is lack of everything specifically? Don't know. 

Right. But "not made of anything" means that there are no materials in him. No constituent parts, no elements. 

If God is made of no material how could he think thoughts? He doesn't have any neurons. 

See above. Thoughts come and go, but God is unchanging. He doesn't think, if by "think" you refer to what people do.

EDIT: The Oxford Dictionary of Philosophy has immaterialism defined as "The denial of materialism".

That's true. Materialism in that sense is an opinion about the world -- what it's made of, etc. Does that dictionary say anything about how this is related to your question?