I wish to broach an extremely speculative theological question: Is God supervenient on the universe. More precisely, are the properties of God uniquely determined by the properties of the universe? Does any universe qualitatively identical to our universe in all its non-divine attributes contain a god that is qualitatively identical to our God (assuming we have one)? Is divinity supervenient on non-divinity? This is a question of modal dependence: does the nature of the universe necessitate the nature of God? Could the attributes of God vary while the universe stays the same in all non-divine respects?
It is clear that the universe is not supervenient on God. All the attributes traditionally ascribed to God (I am thinking primarily of the Judeo-Christian God) could hold and yet the universe differ from the way it is. The nature of God does not determine the nature of matter, say: nothing in world religions or arcane theology can determine that the matter of the universe should contain the elementary physical particles that we have discovered. Quarks don’t follow from angels and gravity doesn’t follow from God’s omniscience, omnipotence, and moral perfection. The same God (or type of god) could preside over a universe containing a very different physics or biology or psychology. This follows from the fact that God was free to create any number of different universes compatibly with having the nature that he has. We cannot read the nature of the universe off the nature of God. Maybe if pantheism was true and God were identical to the universe we could, but if he stands apart from the universe we can’t.
But the other way about is not so straightforward: could the god of a universe just like ours be totally different in his nature from our God? Could this other god fail to be omniscient, omnipotent, and morally perfect? Could he be ignorant about certain matters, powerless in certain areas, and morally compromised? Could he be mad, bad, and lazy? Could a god be five foot two, three hundred pounds, and an inveterate gambler? Maybe there are divine beings satisfying these descriptions in universes very different from ours, but could universes just like ours harbor such gods? Or is it that there is just one kind of god that all universes like ours must share?
What is important here is the psychology of God’s creatures, especially us: could there be universes with a different type of god that were identical to ours in all psychological respects? This includes spiritual aspirations, values, rituals, religious convictions, and so on. So we need to consider universes that are just like ours in these respects—with the same religions as ours. Specifically, could a god have created a universe like ours and yet have a different nature from our God? Well, he would presumably have to be a deceiver to make this happen: he knowingly creates a universe in which he is characterized by its denizens in a certain way and yet he is nothing like that way. Wouldn’t he rather create a universe in which he is believed to be pretty much the way he is? Why create false religious beliefs in people? It is true that we don’t know everything about God, so our beliefs don’t fix his nature completely, but it would be strange for God to allow us to form radically false theories of his nature, never correcting these theories. We would therefore expect that God is somewhat supervenient on the facts of the universe he has created—on pain of allowing world religions to be completely erroneous. How could we follow God’s commands and wishes if we had no idea what they were? How could we do what is right according to God and yet be totally wrong about what he deems to be right? If God created the world and has certain intentions for us, he cannot allow that his nature departs radically from what we believe: he must be more or less as we believe him to be. Thus God’s nature must supervene on our religious beliefs, at least in part.
There is one way in which divine supervenience is guaranteed: God is just a figment of the human imagination. Sherlock Holmes is supervenient on the psychology of Sir Arthur Conan Doyle because he is a fictional character; if God is a fictional character created by the human mind, then he too will have no nature beyond that which is stipulated by the human mind. Thus atheism implies divine supervenience. But if God is real and ontologically independent of human beings, then his nature will not necessarily follow from human psychology. It may then seem that there should be no bar to divine variation combined with sameness of universe; and yet theology suggests that the relationship cannot be that loose. Humans need true beliefs about God to fulfill God’s purposes, but then God cannot create a universe that belies his nature. He must create a universe that reflects his nature, provides clues to it, does not mislead people about it. And that requires something like supervenience, at least with respect to the more personal qualities of God. God must create a universe such that his nature is at least partially reflected in that universe, so any universe just like ours will contain a god at least very similar to ours. Given God’s purposes for humans, he must create a universe from which his nature more or less follows. And in fact many theologies expressly maintain that God is reflected in his creation—in its beauty, in the existence of conscience, and in its ultimate goodness. If a universe resembles our universe in these respects, then it must contain a god that is similar to our God (assuming it contains any god with the standard sorts of intentions for us)—hence supervenience. Fix the non-divine facts, particularly human psychology, and you fix the divine facts.
An ambitious theology might try to prove that the entire nature of God is necessarily fixed by the nature of his creation, down to the last detail. Nothing in God can vary while keeping his universe fixed; his properties are wholly dependent on the properties of the universe—not causally, of course, but in the sense of supervenience. His nature can be completely read off the universe. It is hard to see how such a proof would go, though it would be nice to see it. What we can say is that standard theology implies that supervenience holds, at least partially. 
 The notion of partial supervenience is not commonly employed, but it has a clear meaning: most or some of what is true of one domain is determined by what is true of some other domain. Thus, for example, the mental might be said to be partially determined by the physical: most or some of what is true of the mental is fixed by what is true of the physical.