St. Anselm's ontological argument for dummies.

St. Anselm, Archbishop of Cantebury (1033-1109), is the originator of the ontological argument, which he describes in the Proslogium as follows:

[Even a] fool, when he hears of … a being than which nothing greater can be conceived … understands what he hears, and what he understands is in his understanding.… And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.… Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.

The argument in this difficult passage can accurately be summarized in standard form:

It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).
God exists as an idea in the mind.
A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).
But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)
Therefore, God exists.