One of the most subtle arguments to prove God's existence is the ontological, first articulated by Saint Anselm of Canterbury during the eleventh century. The arguments goes more or less like this:
God is “that than which nothing greater can be thought”; in other words, he is a being so great, so full of metaphysical oomph, that one cannot so much as conceive of a being who would be greater than God. The Psalmist, however, tells us that “The fool has said in his heart, ‘There is no God’ ” (Psalm 14:1; 53:1). Is it possible to convince the fool that he is wrong? It is. All we need is the characterization of God as “that than which nothing greater can be thought.” The fool does at least understand that definition. But whatever is understood exists in the understanding, just as the plan of a painting he has yet to execute already exists in the understanding of the painter. So that than which nothing greater can be thought exists in the understanding. But if it exists in the understanding, it must also exist in reality. For it is greater to exist in reality than to exist merely in the understanding. Therefore, if that than which nothing greater can be thought existed only in the understanding, it would be possible to think of something greater than it (namely, that same being existing in reality as well). It follows, then, that if that than which nothing greater can be thought existed only in the understanding, it would not be that than which nothing greater can be thought; and that, obviously, is a contradiction. So that than which nothing greater can be thought must exist in reality, not merely in the understanding.
To me, the ontological argument does not prove the existence of God, but rather, the existence in the human brain of the need of a God's idea; the need of constrain the infinite in space and time in a finite framework in space and time. In other words, why we produce concepts that we cannot constrain, why we have the skills to think on unthinkable problems?
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