180 ARGUMENTS: MONOTHEISTIC CONCEPTIONSExposition of the Ontological Argument
From 3 on, the argument is correct. You might object to 4, but what 4 says
is this: Possibly, God has maximal excellence entails God has maximal
excellence. What you need to keep in mind is that God has maximal
excellence entails God exists in all possible worlds ( = Necessarily, God
exists). Thus God has maximal excellence ascribes the modality necessarily
true to the proposition God has maximal greatness. Thus, given that
necessary truths are necessarily necessarily true and necessary falsehoods
are necessarily necessarily false, it follows that God has maximal
excellence is either necessarily true, or else is a contradiction.
Further discussion of Ontological Argument
There is a problem with the argument, and it starts earlier. It lies exactly in
premise 1 (in contrast to version 1, where the problem arises with premise
2). Suppose what is true is The proposition that God exists is logically
contingent. Then the following things are true: (i) God exists is not a
contradiction; (ii) God does not exist is not a contradiction; and (iii)
Necessarily, God exists is a contradiction, and (iv) Necessarily, God does
not exist is a contradiction. If (iii) is true, then premise 1 of the Ontological
Argument is false. Thus if it is true that The proposition that God exists is
logically contingent is true, premise 1 of the argument is false. Nothing in
the argument shows that The proposition that God exists is logically
contingent is not true. So the argument fails.
A proof that something has logically necessary existence
Consider this brief argument:
1 Necessarily, if it is possible that something has logically necessary
existence, then something has logically necessary existence.
2 It is possible that something has logically necessary existence. So:
3 Something has logically necessary existence.
In other terms:
1* Necessarily, (Possibly, something has logically necessary existence)
entails (Something has logically necessary existence.)