The basic problem here is that Plantinga claims to understand what Anselm was talking about in the first place. SEP describes no less than five different formulations of Anselm's argument which have been suggested by various commentators, criticizes all five interpretations on various grounds, and then suggests that Anselm may in fact have made an elementary logical error (thus putting forward a sixth interpretation). While it is possible that Plantinga's interpretation of Anselm happens to match what Anselm intended, it strikes me as rather unlikely given the diversity of opinion which the text has produced.
If we set that problem aside, the next problem is with this line in (Plantinga's interpretation of) Anselm's argument:
(2) Existence in reality is greater than existence in the understanding alone.
(premise)
Plantinga writes that:
If this is what [Kant] means, he's certainly right. But is it relevant to the ontological
argument? Couldn't Anselm thank Kant for this interesting point and proceed merrily on his
way? Where did he try to define God into being by adding existence to a list of properties
that defined some concept? According to the great German philosopher and pessimist
Arthur Schopenhauer, the ontological argument arises when "someone excogitates a
conception, composed out of all sorts of predicates, among which, however, he takes care
to include the predicate actuality or existence, either openly or wrapped up for decency's
sake in some other predicate, such as perfection, immensity, or something of the kind." If
this were Anselm's procedure -- if he had simply added existence to a concept that has
application contingently if at all -- then indeed his argument would be subject to the Kantian
criticism. But he didn't, and it isn't.
Unfortunately, at this point Plantinga turns away from Kant and proceeds to "take an independent look at" the ontological argument, so we don't get any further elaboration on why (2) does not constitute exactly what Plantinga is describing.
Maybe Plantinga meant something like this: Anselm is not adding existence to God's set of predicates, he is merely arguing that "existence in the understanding alone" is "less great" than "existence in reality" - i.e. that an object which "exists in the understanding alone" is necessarily less great than an object which "exists in reality." Plantinga then goes on to examine what it means for an object to "exist in the understanding alone," eventually concluding that we may speak of such "possible objects" as a shorthand for a set of predicates which may or may not be instantiated in a given possible world. For example, the claim that "Black swans could possibly exist" is reformulated as the claim that "In at least one possible world, there is an object which is a black swan." Thus, his interpretation of Anselm is formulated in terms of modal logic and Kripke semantics (which, IMHO, doesn't really sound a lot like what Anselm actually wrote). This sidesteps Kant's objection to "non-existent objects" and existence-as-a-predicate. However, in the context of the rest of Plantinga's discussion of "greatness" and "excellence," it also makes the assertion that "God's existence in reality is conceivable" a great deal stronger than it might appear, to the point that the atheist can reasonably reject this premise as unfounded or at least not self-evident.
