Uniqueness of God

There are many arguments for God's existence. But what about his uniqueness?

One argument for his uniqueness is the ontological argument.
Another is the moral argument.

Another is:

Let both G1 and G2 be distinct omnipotent beings.
G1 can do anything that is logically possible.
G2 can do anything that is logically possible.
Let X and "not X" both be logically possible.
G1 is able to bring about X.
G2 is able to bring about not X.

Another might be:
G1 knows everything that G2 knows.
G2 knows everything that G1 knows.
Therefore, G1 and G2 are not distinct minds.


Both would be completely aware of each other's thoughts. Both halves of your brain are only partly aware of each other's thoughts, but you still count yourself as a single person. G1 and G2 are completely aware of each other's thoughts, they certainly count as one person.

"G1 and G2" has infinite power.
Therefore "G1 and G2" is an all-powerful being

Another thing: two necessary things cannot exist without each other. In maths, any statement follows from a false statement. Two necessary being cannot exist without each other any more than two necessary facts can be true without each other. You cannot have 3+3=6 without 30+30=60, or 30+30=60 without 3+3=6. In a sense, they would be the same being.