“the greatest conceivable being must have existence”
Bzzzzzzzzzzzzzzzzzzzzzzzzzzzz.
Ok my greatest conceivable being is a giant red hamster that has 5 heads and an IQ of 10000000000000000000000000000000000 it also fires god killing peanuts from its eyes.
Does my rabbit now exist?
You have no logic reason to suggest the greatest conceivable being must have existence.
This is a false and purely humorist argument, a red hamster (or the big spaghetti and other platitudes of the kind) isn’t an infinite being.
I like very much the Anselmian argument, but its problem to me is that it pressuposes an Platonistic worldview, and not everyone accepts it.
Like I read the argument:
God is the greatest conceivable being
Therefore, God is the infinitely transcendent, yes, no problem with it, this is mostly the definition of God we have in Exodus. And there is no binding on “greatness” being subjetive, relatively to this question it isn’t, God is greatest in every conceivable positive way: the more just, the more intelligent, the more beautiful, not that I think htat, it is his definition.
the greatest conceivable being must have existence
This is the central argument, which has been shallowly treated here. Anselm himself goes further and says.
You can imagine the greatest possible of beings, therefore it exists as concept in your mind.
But if it exists in your mind only, and not in the world, then it is not the most perfect of beings. You can always think of a greater being, which, besides having all these qualities, exists in reality, therefore it exists.
Therefore God must exist
As I said before, the greatest problem with this formulation (i’m not so acquainted with Leibniz or new, modal, formulations) is that it concedes that a conceptual existence is a true existence, that’s why I’m a little uneasy with the original Anselmian formulation.
As for a very common objection of this argument, mentioned above, that it is not possible to conceive an infinite being, I strongly disagree as I can’t see any contradiction in any of God’s concepts and, even more, an infinite source of being is actually pressuposed by much of metaphysical tought.
But as I said, the Platonic twist to the original argument makes me uneasy to procclaim it proved. But the idea that the concept of God is its proof of existence strikes me as something quite plausible.