Arguments for the Existence of God: The Argument of Ontology
The ontological argument was devised by Anselm of Canterbury (1033-1109), who wanted to produce a single, simple demonstration which would show that God is and what God is. As straightforward as it may be, but it is far from simple. It is, perhaps, the most controversial proof for the existence of God.
The ontological argument attempts to prove God’s existence through abstract reasoning alone. The argument is entirely a priori, i.e. it involves no empirical evidence at all. Rather, the argument begins with an explication of the concept of God, and seeks to demonstrate that God exists on the basis of that concept alone.
It is greater for a thing to exist in the mind and in reality than in the mind alone.
"God" means "that than which a greater cannot be thought."
Suppose that God exists in the mind but not in reality.
Then a greater than God could be thought (namely, a being that has all the qualities our thought of God has plus real existence).
But this is impossible, for God is "that than which a greater cannot be thought."
Therefore God exists in the mind and in reality.
Maximal excellence: To have omnipotence, omniscience and moral perfection in some world.
Maximal greatness: To have maximal excellence in every possible world.
There is a possible world (W) in which there is a being (X) with maximal greatness.
But X is maximally great only if X has maximal excellence in every possible world.
Therefore X is maximally great only if X has omnipotence, omniscience and moral perfection in every possible world.
In W, the proposition "There is no omnipotent, omniscient, morally perfect being" would be impossible—that is, necessarily false.
But what is impossible does not vary from world to world.
Therefore, the proposition, "There is no omnipotent, omniscient, morally perfect being" is necessarily false in this actual world, too.
Therefore, there actually exists in this world, and must exist in every possible world, an omnipotent, omniscient, morally perfect being.
There have been few critiques of this argument because it is rather ingenious. It combines varying degrees of philosophical arguments. For more on this you may read Alvin Platinga's books.