Now, sure, this has a lot of problems. First of all, I can conceive of many things greater than a God who forbids the eating of bacon but commands the death of rape victims, one has arbitrary rules about eating from a tree of knowledge and arbitrary preference for the people of one part of the world to receive his message, one who can't think of a better way to solve problems than through the human sacrifice of his own son and can't find a way to convince people that this even happened when know much more clearly that Amenhotep IV, the closest thing we have on record to an inventor of monotheism, existed over 1,300 years before the possible existence of what would have been the most important thing ever to have lived...
...sorry. Anyway, second, it is possible that existence is not a predicate for greatness. I can imagine the world's greatest dragon, but that doesn't mean that dragon actually exists. Maybe a real dragon is greater than a false one, but it's also arguable that a nonexistent dragon is even better than an existing one, since it then won't burn you and eat you and steal all your gold. Likewise, it's arguable that a nonexistent deity is even better than an existing one. After all, wouldn't an imaginary deity who still managed to create everything that exists in reality be much more impressive than one that was real?
And finally, this all falls apart because it is based upon subjective terminology like "greatness." Our brains are limited- I can't really conceive infinity, and I can't even really conceive of a person that can. For God to be than than which nothing greater can be conceived, it would have to be not only greater than that which I can conceive personally (since there are people capable of greater thoughts than I am), but also greater than that which any human mind can conceive. Which means that God, if that's what we want to call it, is something that we can't ever talk about or even think about, since chances are that whatever we are thinking of could not possibly the greatest thing that can ever be conceived.
So there's that. Turned your logic back on you, dead 11th-Century monk! But this is only one of the Ontological arguments, and by far not the most complex. I'd like to show you another:

Now that's what an argument for God should look like! This is the Ontological Proof of God, made by the mathematician Kurt Godel, a friend of Einstein's and a believer in...well, something. "My belief is theistic, not pantheistic, following Leibniz rather than Spinoza." Which basically means that he believed in a logical, personal god rather than Einstein's impersonal God, which was basically a term for the entire universe seen as a whole.
Kurt was most famous for his incompeteness theorems, which basically (and I'm talking super-basic here) stated that we can't ever know everything about anything, and that you can't ever use logic to prove you're right because logic can't prove logic is logical. These are fascinating ideas, totally worth reading about sometime- but not now! Now you are going to read about Godel's much less famous (mainly because he refused to publish it since it might have thrust him into theological debates) Ontological Proof!
What this basically says is that, given an infinite number
of parallel universes, the chances of an infinitely perfect, omnipotent, omnipresent,
omnibenevolent, omniscient being existing in at least one of them is exactly
1:1. Now, if that being is truly infinite, it must therefore exist in all
universes. If not, it is not that infinitely powerful being, and given infinite
universes that very infinite being must exist. Ergo, God, being that than which
nothing greater can be conceived, exists.
So where does this fall apart? Well, one, an infinite number of universes is a total conjecture. That's, um, still not any more of a scientific fact than luminiferous aether or phrenology. Second, wouldn’t the possibility of a universe where an omniscient omnipresent omnipotent being DOESN’T exist also be at least 1:1? Which, I think, would mean that an omnipresent, omnipotent being by definition also CAN’T exist.
So where does this fall apart? Well, one, an infinite number of universes is a total conjecture. That's, um, still not any more of a scientific fact than luminiferous aether or phrenology. Second, wouldn’t the possibility of a universe where an omniscient omnipresent omnipotent being DOESN’T exist also be at least 1:1? Which, I think, would mean that an omnipresent, omnipotent being by definition also CAN’T exist.
Third, the possibility of an omnimalevolent omnipresent
being is just as equally 1:1, as is an omnimelancholy being or an omniinebriated
being or anything else. If these beings overlap into one, that God would be
just as malevolent as benevolent, true, but also just as infinitely imperfect
as infinitely perfect. There could be a universe where there is an omnipresent
being who is, say, infinitely impotent that would likewise have to overlap, or
one who is omnipotent but infinitely ignorant. Therefore, if these beings overlap,
they would, to the best of my knowledge, infinitely cancel themselves out to a
state of infinite zero, which means that if an infinite number of gods exist
and they all overlap infinitely into one being, this one being would nullify
itself into an infinitely aexistential being, both infinitely one thing and
infinitely its opposite, infinitely existing and infinitely not existing, something
which has a net potential for existing as infinity but a net effect of existence of zero.
So finally, let’s say they do not overlap- and the chances, in an
infinite number of universes, of an infinite number of non-overlapping infinite
beings is, I guess, at least as close to 1:1 as there being only one or any
other number of other beings. So there are multiple infinite beings, meaning
that the chances of one deity are equal to the chances of their being any
number of other deities, onwards to infinity. So, in effect, the chances of
there being one single god rather than any number of other gods are one divided
by infinity, which is effectively zero but even more effectively an imaginary
number. Ergo, um, yeah.
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