What is the basis for claiming the unity of "God"?
I'm curious about the concept of one used here considering that God is probably something big. Why does this necessarily mean that God is one?
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The earliest instance known is from the Rig Veda (verse 1.164.46) several thousand years B.C. It says "Ekam Sat Vipra Bahudha Vadanti" - "Truth [meaning Supreme Being or God] is One, men call It by various names". There are several other references in the Rig Veda to both monotheism and monism.
Based on the causal arguments for the existence of God, all we know must have a cause. You can't create something out of nothing and infinite causal chains don't make sense. That means that there must be a first cause which is called God.
We come to the conclusion God is a necessary being instead of a contingent being. That is, God is a being that must exist and is itself not subject to causes since God was the originator of causal chains to begin with. God being a necessary being means being free from causes and not contingent on anything. God can only be one, since the existence of two of them would mean that the distinction between both would be contingent on the other making them not necessary anymore.
If I remember correctly, this argument was first formulated as such by Avicenna (Muslim), although Christianity borrowed the concept through Aquinas. Hinduism also believes that there is a God that unifies the others, if you will.
See the following thread: Why can there only be one necessary being, as opposed to two or thirty seven? .
Great question. I don't want to wade evolution of religious ideas that lead to monotheism, which is quite an interesting subject, and worth looking into.
Very compactly, the ontological argument states that God is "a being than which no greater can be conceived" (St. Anselm) and started a debate that's been quite vigorous for about 1000 years now.
I find another useful way to look at it is in the context of Conway's Game of Life, where the game is an analogue for a universe. The discrete cells in the automata only have limited information based on spacial position, with hard limits on communication speed (analogous perhaps to c). The only entity that comprehends the entire system is the system itself, which may be taken as a commentary on Laplace's Demon.
Rationality is bounded, and always subjective, except in the case of the model, which is itself a rational system.
1 - One God
It is logically possible for there to be many gods or only one (limited) God). But once you develop concepts of God in which God possesses attributes such as omniscience and omnipotence, then you run into logical difficulties if you posit more than one God. Two Gods could not both be omnipotent, for example : if both could do anything then each would limit the power of the other, and neither would be omnipotent.
This isn't the only argument for monotheism; and it does not prove that there is an omnipotent God. But if there is an omnipotent God, then there can only be one such God.
2 - Unity of God
This is a separate matter, and I've a sense it may be of concern to you. If there could be only one God, it would not follow that there was no diversity within the Godhead. The Christian doctrine of the Trinity is certainly a doctrine of One God but also of a God in which three elements are perfectly unified : 'Three Persons in One Substance' or (better) three elements in one nature. The doctrine is one of One God but also of God as a Tri-Unity.
Negotiating the logic and coherence of the doctrine of the Trinity is another issue. I simply introduce the concept to show that One God and the Unityof God are different if related issues.