St. Anselm and the Ontological Argument of God

1. God exists in our understanding. This means that the concept of God resides as an idea in our minds.
2. God is a possible being, and might exist in reality. He is possible because the concept of God does not bear internal contradictions.
3. If something exists exclusively in our understanding and might have existed in reality then it might have been greater. This simply means that something that exists in reality is perfect (or great). Something that is only a concept in our minds could be greater by actually existing.
4. Suppose (theoretically) that God only exists in our understanding and not in reality.
5. If this were true, then it would be possible for God to be greater then he is (follows from premise #3).
6. This would mean that God is a being in which a greater is possible.
7. This is absurd because God, a being in which none greater is possible, is a being in which a greater is possible. Herein lies the contradiction.
8. Thus it follows that it is false for God to only exist in our understanding.
9. Hence God exists in reality as well as our understanding.

"That which nothing greater can be thought"

Descartes, in his Fifth Meditation, wrote that the conception of a perfect being who lacks existence is like imagining a triangle whose interior angles don't sum to 180 degrees (he was big on the notion of innate ideas and the doctrine of clear and distinct perception). So, because we have the idea of a supremely perfect being, we have to conclude that a supremely perfect being exists; to Descarte, God's existence was just as obvious, logical, and self-evident as the most basic mathematical truths.