But if this is true, Anselm says, then God exists. We have proved God’s existence. Why? Because if “that than which no greater can be thought” exists in the mind, then it must also exist in reality. The reason is that to exist in reality is, according to Anselm, “greater” than to exist merely in the mind. What is possible and actual is obviously greater than what is merely possible. Anselm gives the example of a portrait painter whose portrait, actually painted, is the realization of an intuition or idea in his head; thus the actual painting is “greater” than the mere intuition or idea of it. In the same way, in order for “that than which no greater can be thought” to satisfy its own definition, it must exist. Otherwise it would be “that than which a greater can be thought.” Anselm claims to have shown not only that God exists, but that He exists necessarily. If He existed only in fact and not by necessity, He would be a great being indeed, but He would not be “that than which no greater can be thought.”

I offer Anselm’s proof not because it is immediately convincing— we feel sure that Anselm has drawn a theological rabbit out of a rhetorical top hat—but because it is notoriously hard to refute. Descartes and Leibniz considered the argument to be a valid one, and produced their own versions of it. Yet in his book God Is Not Great Christopher Hitchens seeks to expose Anselm’s shortcomings. He offers the example of a child in a novel who is asked why she believes in dragons. The child replies, “If there is a word dragon, then once there must have been dragons.” Clearly it is childish reasoning to infer the object from the mere idea of it. Hitchens triumphantly proclaims Anselm’s argument “overthrown.”