OK, I think there’s some confusion here, some which I’ll leave for others to clear up.
The issue is that necessary existence is a mode of existence. One can conceive of a necessarily existing unicorn – let’s call that species of unicorn NEU. Now the question would be whether the property of existing necessarily – whether that mode of existence is logically compatible with the NEU’s other properties (for example existing in time and space). If it turns out that just one of the NEU’s other properties is incompatible with that mode of existence, then we would know that NEU is a fictional concept – much like a square circle is, depictable in art, but not actually existent in abstract or in reality.
There’s no indication however that with the GCB, that the property of existing necessarily is incompatible with any other property of the GCB. BTW, as GCB is defined, being the creator of the world would only be a propety of the GCB if being the creator of the world were a great-making property. Being creator of the world is actually a contingent property of the Christian God according to Catholic dogma (which states the world’s existence is a contingent fact and God was free to not create anything at all). So in terms of intrinsic properties, being the creator of the world would not actually be a property of the GCB unless one is to suppose that something created outside of the GCB also exists necessarily.
I’m not arguing that there is any property that is not compatible with any other property. I’m arguing that God existing or non-existing as fait accompli is - possibly - incompatible with the description in P1 as the greatest conceivable being.
I’ll give another example. Suppose you shuffle a standard deck of cards and before your finished shuffling, you make the statement, “After the deck has been shuffled and laid on the table, it is conceivable a black card (x of spades or clubs) will be the top card of the deck” This is true assuming an absolutely random shuffle and that it is not purely deterministic.
Now, suppose you reshuffle the deck and again lay it on the table. You may again say (this time
after the shuffle) that it is conceivable that the top card is black. But a friend who is there peeks at the top card and sees a red card (heart or diamond)
He knows it is not possible for the top card to be black. This time, there is something wrong with your statement, which is only made out of ignorance. It is conceivable for it to be black only if it is actually black.
What happens is once the deck has been shuffled and placed on the table, what possibilities remain are fully determined by what is. Either the probability collapses to zero or it is a certainty that the card is black at that point – fait accompli. But in the absence of knowledge, and only for practical purposes, we can assume the same probabilities as if the deck has not been shuffled yet.
Going back to the first premise of the ontological argument, God can’t be the greatest conceivable being if God does not exist, not just because non-existence is an imperfection but because God is not a being at all. As a pure product of the imagination, God is not even as great as sliced bread in that case. God is completely outside the set of greatest conceivable beings.
If God does exist, then the argument is logically sound, if circular. But we don’t have that knowledge and so we can only conclude that God is
possibly not conceivable (since God must exist to be conceivable). We are ignorant of P1’s validity because of our ignorance of God’s viability to be considered as a possible being.
Because the argument hinges on God being conceivable or possible, and any wording of P1 -possibly- eliminates God from the realm of possibility, it makes the whole argument inconclusive.