Before I begin my breif discussion, I feel that it is necessary to go over something known to philosophers as "Possible worlds semantics" because if you dont understand this concept, then I feel this argument will go WAY over your head, as it did mine the first time I heard a defense of the argument. a Possible world is a possible description of reality, a description which is not inherently self-contradictory or illogical (violating rules of logic or mathematics). Now if something exists contingently, or if something is true contingently, then it is true in one or more possible worlds, but it is not true in every possible world. For instance, this message you are reading exists contingently. Surely there is some possible world in which I did not in fact type this message.
But, when something exists necessarily, or some truth is necessarily true, that means that there is absolutely no possible description of reality in which that thing does not exist, or in which that truth is not true. For instance, the law of non-contradiction is a necessary truth. There is absolutely no possible description of reality in which something can embody a property and not embody that property. also mathematics is true in all possible worlds. there is no possible description of reality in which 2+2=5. Furthermore, abstract objects, like numbers, sets, etc exist in all possible worlds if they do indeed exist and are not merely man-made concepts (I think I will someday make a thread defending the existence of abstract objects and properties)
Now that we've gotten possible worlds semantics out of the way, let us move on to the Ontological proof for God's existence.
First, God is a maximally excellent, or maximally great being. Entailed in maximal excellence are omnipotence, omniscience, omnibenevolence, and necessary (but they of course are not limited to that)
Now that we have articulated this crucial premise, we can give the ontological proof.
P1: It is possible that a maximally great being exist. This is of course true because a maximally great being is concievable and is not inherently self-contradictory.
P2: If a maximally great being can possibly exist, then a maximally great being exists in some possible world.
Simple: There is some possible description of reality in which a maximally great being exists.
P3: If a maximally great being exists in some possible world, then it exists in every possible world
Simple again: Entailed in maximal greatness is necessity. a necessary entity cannot possibly exist in only one or a few possible worlds and not in others, that is inherently self-contradictory. But since a maximally great being is NOT inherently self-contradictory, it therefore follows that a maximally great being must exist in every possible world
P4: If a maximally great being exists every possible world, then a maximally great being exists in the actual world
P5: If a maximally great being exists in the actual world, then it exists
C: Therefore, a maximally great being exists
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