What an interesting question. I have thought quite a bit about the nature of God over the years. It is obvious that no serious thinker thinks that God is a bearded man in the literal sky, although that is how atheists and some fundamentalists often characterise the concept of God.
Its gets even deeper than that for me when the issue of Gods mind and thoughts are brought up. How does God think and what does he think about? Are questions predicated on God somehow being like physical human beings! There are legitimate questions before those questions however, because thinking is something one does by virtue of not knowing all things. Thinking is a kind of navigation though a world of possibilities that themselves are only possibilities because of being constrained by limitations. One has to think when one doesn’t know the answer. In terms of being human and having a physical brain, even when we know the answer the brain still has to do activity to get the memory of the correct answer out of storage as it were. Although in this no trying to work out the answer type of brain activity has to be done.
If God is the one through all things ultimately come, which is a good philosophical definition for God, then by definition he knows all the answers, so doesn’t have to think in order the get the answers. If God is all powerful and infinite then in some sense he is not going to be subject to time or limitation, so any fact he knows or thinks will not have a greater priority in his so called brain than any other, but if one did as with thinking, then that would not be being all powerful and infinite because he would be subject to change. Change is not compatible with infinity because however much it changes it is always the same. Nothing can be added or taken away or change. So the concept of God thinking is problematic if he is all powerful and infinite.
However God could be all powerful and the one through whom all things come in the sense of not being all powerful to the infinite degree, but all powerful in the sense of being the most powerful it is possible to be, or more so than anyone else. An analogy might be the boss and creator of a company. He is all powerful over the company he created, and by definition the top of the tree in terms of authority. However he still can’t levitate the office. Perhaps a better analogy would be an example like the film `the matrix`. Some being of non-defined origin creates a simulation, and populates it with beings capable of thought and freedom in a universe/world that obeys mathematical laws. That being is functionally God by virtue of being as powerful as it is possible to be, and creating all things from the point of view of those in the simulation. The only constraint would be the mathematical laws the simulation is based. However it would still mean he could do things that the beings created via the simulation that are in the simulation cannot do. If this is the case with our God then he might be able to think in a way humans can relate to.
In both versions of God the question of God actually thinking about the possibility of another greater being than himself would not be relevant. With the infinite God that could not be the case because two infinities is impossible. If there are two, then they limit each other by virtue of not being part of one another. If they are part of one another, then they are one infinity again and thus one God.
In the case of the all-powerful, but never the less limited by mathematics God, who created the simulated world, he would not wonder about a greater being than himself because any such being would only exist in his world, not the simulated world. In terms of the simulated world it would be an irrelevance.
Of course another view is that somehow the infinite and finite are united in a way impossible to understand because of the inherent contraction it creates in minds that think. If this is somehow the case, atheists are doing what they are supposed to be doing and theists are doing what they are supposed to be doing, and all things will be fine as all are part of one another. What people think may be a complete irrelevance ultimately, but relevant in a shorter term view, a finite term.
