Anselm: Existence, when added to something, makes it greater than if it only exists in the mind.
Kant: But existence can’t be added to anything. Specify one thing that is improved when you “add existence to it”, in fact, specify one thing that is there at all before you supposedly “add existence to it”. No, clearly this notion of adding existence is incoherent and impossible.*
John of St. Thomas: Well, sure, if you want to assume right out of the gate that there is no positive, real distinction in creatures between essence and existence, then you can also assume there’s nothing one can add existence to. Your philosophical ancestors, however, had lots of arguments about the paradoxical claim of “adding existence to something” as opposed to claiming in their opening move of the discussion that existence isn’t a real predicate.
Me: The existence we’re talking about is either an act opposed to a potency or a real being opposed to a mental one. If the first, there is a very clear and well defined sense of what it means to add existence to something. This is not to say Kant is wrong, but only that he’s got a good deal more argumentation to do. If the second (and this is what Anselm seemed to mean) then there is a sort of addition that gives rise to existence, since being in itself transcends its division into the mental and the real.
*This is also why those who give cosmological arguments fail, since in order to make sense of an ens realissimum they assume some lofty sort of existence could specify a distinct sort of being, and make it different from things to which a “lower” existence was “added”.