I think a good argument can be made for the existence of God based on the existence of the universe. We know the universe began to exist. Given that whatever begins to exist requires a cause external to itself to bring it into existence, there must be a cause external to the universe to explain why it came into being. Whatever brought time, space, and matter into existence cannot itself be temporal, spatial, and material, and thus the cause of the universe must be eternal, non-spatial, and immaterial. Furthermore, the cause must be personal in nature since there are only two known sources of causation—events and personal agents—and it is impossible to explain the first event in terms of a prior event. Therefore, an agent must be the cause of the universe. A personal, eternal, non-spatial, and immaterial being is what most theists mean by “God.”
While I think this argument demonstrates the existence of the divine, it cannot tell us anything about the number of divine beings responsible for creating the universe. There could be one, or there could be billions. An additional argument is needed if one is going to prove the existence of one and only one God. In the past I argued for monotheism on the basis of divine omnipotence. I reasoned that the property of omnipotence cannot belong to more than one being, for if two or more beings have to share power, then neither being can be said to have “all” power. So God, then, must be one if He is omnipotent.
It came to me recently, however, that this argument fails on the grounds that it falsely construes power as a substance. Power is not a substance that can be divided up and distributed. Power is simply the ability do some particular thing. Indeed, if power is a substance, and God has all power, that would mean humans have no power. Clearly this is false. We have the ability to do a wide range of things. So to say a being is omnipotent is only to say that such a being possesses the ability to do any logically possible thing. It says nothing about the amount of power that other beings possess. It is logically possible, then, for there to be more than one omnipotent being. The argument for monotheism from omnipotence, then, fails. The only logical grounds I am aware of for thinking God to be one is parsimony: no more than one God is needed to explain the origin of the universe. If, according to Ockham’s Razor, we should not multiply entities beyond necessity, and if it is not necessary to postulate the existence of more than one divine being, then there is no good reason to think there exists more than one divine being. If you have any other argument I would be interested in hearing it.