Anselm's ontological argument

Here is my favorite version of the “existence is not a property” objection to Anselm’s first ontological argument.

It makes no sense to talk of the greatness of a nonexistent being except hypothetically as the greatness it would have if it existed. When we compare the greatness of things, we compare what the things would be like if they existed. Thus, when we say that Thor is greater than Hermes, we mean something like this: if Thor existed, he would be greater than Hermes would be if Hermes existed. And to exist is to exist in reality.

But now take the crucial claim in Anselm’s argument that it is greater for x to exist in mind and in reality than just in mind. This claim is simply false when we understand it in the hypothetical way. For we need to compare the greatness of the x that exists in mind and reality to the greatness that the x that exists only in mind would have if it existed in reality. But that’s the same greatness!

Anselm’s second argument makes no such slip, for it is based on a comparison between contingent and necessary existence, and that comparison survives the criticism.