Anselm proposed a famous, fascinating, controversial theistic proof. Some scholars contend that he presented two different versions of the ontological argument or two different ontological arguments. Other thinkers like Scotus, Descartes, Leibniz, Gödel, and Plantinga proposed their own versions.
I don't have an opinion about whether or not Anselm's argument, as it stands, is successful. That's because I don't know what he means, and interpretation is prior to evaluation. I can't assess it before I understand it.
I doubt even he knows what it means. His argument is intuitive and compressed. He had a flash of insight which he labors to sharpen. He may be onto something, but he's fumbling to articulate his insight.
Here's one thing I will say about his argument. It raises the question: is our imagination greater or lesser than reality? Does reality exceed imagination or imagination exceed reality?
For Anselm, God is the greatest conceivable being, and that's a good definition. For Anselm, the idea of a greatest conceivable being must have a counterpart in reality.
Human intelligence is quite limited. A paradox of human intelligence is that we're just smart enough to be aware of our intellectual limitations. Even the very smartest human beings hit a wall, and the distance between their understanding and wall of reality is very short. The distance between a human with Down Syndrome and the smartest man who ever lived is incomparably shorter than the distance between the smartest man who ever lived and reality.
It's quite counterintuitive to suppose our imagination is greater than reality. To the contrary, not only is reality the equal of anything we can imagine, but infinitely beyond what we can imagine.
Therein lines the truth of the ontological argument. Is reality greater or lesser than what we can conceive? Surely reality is much bigger than the human mind.
I'd add a caveat. Not everything conceivable is possible because an isolated idea needn't be consistent with every necessity and truth. We imagine little pieces of things that might not be possible or realistic if developed to their logical conclusion.
But so long as the idea of God, as the greatest conceivable being, is coherent, then the basel insight of the ontological argument must be true, however successful or unsuccessful the precise formulations.
It might be objected that we're talking about a human idea of God. Yes, Anselm has a limited grasp of what it means to be the greatest conceivable being. But in that respect, the reality is inconceivably greater than our idea of a greatest conceivable being.
So it comes down to the question of whether human imagination surpasses reality or reality surpasses human imagination. I think the only reasonable position to take is that human imagination is just a sample of an illimitable, superhuman reality that exceeds the reach of the human mind in all directions.
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