What jobs would a being have to perform to qualify as God?
I count four sorts of job, ontological, epistemological, axiological, and soteriological, the first two more 'Athenian,' the second two more 'Hierosolymic.' The fruitful tension between Athens and Jersualem is a background presupposition. (The tension is fruitful in that it helps explain the vitality of the West; its lack in the Islamic world being part of the explanation of the latter's inanition.) This macro-tension between philosophy and Biblical revelation is mirrored microcosmically in human beings in the tension, fruitful or not, between reason and faith, autonomy and authority. (Man is a microcosm as Nicholas Cusanus maintained.)
1. Ontological Jobs. Why does anything exist at all? To be precise: why does anything contingent exist at all? A God worth his salt must play a role, indeed the main role, in any explanation. In brief: the reason why contingent beings exist is because God, a necessary being, (i) created them out of nothing and (ii) maintains them in existence. God is thus the unsourced source of all finite and contingent existents. Maybe nothing does this job. It might be that the existence of contingent beings is a factum brutum. But nothing could count as God that did not do this explanatory job. Or at least so I claim.
But I hear an objection. "Why couldn't there be a god who was a contingent being among contingent beings or even a contingent god among a plurality of contingent gods?" I needn't deny that there are such minor deities, not that I believe in any. I needn't even deny that they could play an explanatory role or a soteriological role. (I discuss soteriology in #4 below.) My argument would be that they cannot play an ultimate explanatory role or an ultimate soteriological role. Suppose a trio of contingent gods, working together, created the universe. I would press the question: where did they come from? If each of these gods is possibly such as not to exist, then it is legitimate to ask why each does exist. And if each is contingent and in need of explanation, then the same goes for the trio. (Keep your shirts on, muchachos, that is not the fallacy of composition.)
If you say that they always existed as a matter of brute fact, then no ultimate explanation has been given. Suppose time is infinite in both directions and x exists at every time. It doesn't follow that x necessarily exists. To think otherwise would be to confuse the temporal with the modal. An ultimate explanation must terminate in a being whose existence is self-explanatory, where a self-explanatory being is one that exists as a matter of metaphysical necessity and thus has no need of explanation in terms of anything distinct from it.
"Perhaps an ultimate explanation in your sense is not to be had." Well then, the ontological job -- the job of explaining why anything contingent exists at all -- won't get done, and there is no God. Here I may be approaching a stand-off with my interlocutor. I say: nothing counts as God unless it does all four types of job, including the ontological job. My opponent, however, balks at my criterion. He does not see why the God-role can be played only by an absolutely unique being who exists a se and thus by metaphysical necessity.
If you believe in a contingent god or a plurality of contingent gods, and stop there, then I can conceive of something greater, a God who exists of metaphysical necessity and who not only is one without a second, but one without the possibility of a second. But this just brings us back to the Anselmian conception of God as 'that than which no greater can be conceived,' God as the greatest conceivable being, or the maximally perfect being, or the ens reallisimum/perfectissimum, etc. This conception of deity is very Greek and very unanthropomorphic residing as it does in the conceptual vicinity of the Platonic Good and the Plotinian One. But that is what I like about it and my interlocutor doesn't. It's inhuman, 'faceless,' impersonal, he complains. I prefer to say that God is transpersonal and transhuman -- not below but beyond the personal and the human.
As I have said before, religion is about transcendence and transformation, not about a duplicate world behind the scenes, a hinterworld if you will. Whatever God is, he can't be a Big Guy in the Sky. And whatever survival of bodily death might be, it is not the perpetuation of these petty selves of ours. An immortality worth wanting is one in which we are transformed and transfigured. The proper desire for immortality is not an egotistical desire but a desire to be purged of one's egotism. This is an extremely important point typically missed by atheists and mortalists.
2. Epistemological Jobs. What accounts for the intelligibility of the world and what is its source? A God worth his salt (salary) must play a role, indeed the main role, in any explanation of why the world can be understood by us. The explanation, in outline, is that the world is intelligible because it it is the creation of an intelligent being. As an embodiment and expression of the divine intelligence of the intellectus archetypus it is intelligible to an intellectus ectypus. Maybe the world has no need of a ground or source of its intelligibility. Some will say, incoherently, that we are the source of all intelligibility and project it outward onto what is in itself devoid of intelligibility. But if the world is intelligible, and if this intelligibility is not a projection by us, and if the world has a ground of its intelligibility, then God must play a role, the main role, in the explanation of this intelligibility. Nothing could be called God that did not play this role.
Now if God is the ultimate source of intelligibility and the ultimate ground of ontic truth and, as such, the ultimate condition of the possibility of propositional truth as adequatio intellectus ad rem, then he cannot be just one more intelligible among intelligibles any more than he can be just one more being among beings. A God worthy of the name must be Being itself (self-existent Existence) and Intelligibility itself (self-intelligent Intelligibility), and ontological truth. And so God could not be a contingent being, or a material being, or a collection of contingent material beings. He couldn't be what Mormons apparently believe God to be.
3. Axiological Jobs. By a similar pattern of reasoning, I would argue that nothing could count as God that did not function as the unsourced source of all goodness and the ultimate repository of all value. God is not just another thing that has value, but the paradigm case of value. God is not a good being, but Goodness itself in its prime instance.
4. Soteriological Jobs. Every religion, to count as a religion, must include a doctrine of salvation, a soteriology. Religions exist to cater to the felt need for salvation. It is not essential to a religion that it be theistic, as witness the austere forms of Buddhism, but it is essential to every religion as I define the term that it have a soteriology. A religion must show a way out of our unsatisfactory predicament, and one is not religious unless one perceives our life in this world as indeed a predicament, one that is profoundly unsatisfactory, but also one from which escape is possible. Sarvam dukkham! as the First Noble Truth has it. I would go a step further and add that out unsatisfactory predicament is one that we cannot escape from by our own power. Self-power alone won't cut it; other-power is also needed. 'Works' are not sufficient, though I suspect they are necessary.
When it comes to salvation we can ask four questions: of what? from what? to what? by what? Here is one possible answer. Salvation is of the soul, not the body, or at least not the gross body; from our unsatisfactory present predicament of sin, ignorance, and meaninglessness; to a state of moral perfection, intellectual insight, peace, happiness, and meaning; by an agent possessing the power to bring about the transformation of the individual soul. God is the agent of salvation. To be worth his salt he must possess the power to save us. Since the only salvation worth wanting involves a complete overhaul and cleansing of our present wretched selves, this God will have to have impressive powers. He cannot be a supplier of material or quasi-material goodies in some hinterworld in which we carry on in much the same way as we do here, though with the negatives removed. The crudest imaginable paradise is the carnal paradise of the Muslims with its 72 black-eyed virgins who never tire out the lucky effer; but if I am not badly mistaken, Mormon conceptions are also crudely materialistic and superstitiously anthropomorphic to boot.
What I'm driving towards is the thesis that a God who can play the ultimate soteriological role cannot be some minor deity among minor deities who just happens to exist. He must be a morally perfect being with the power to confer moral perfection. This moral and soteriological perfection would seem to require as their ground ontological and epistemological perfection. Not that I have quite shown this . . . .