"By whatever and by however many predicates we may think a thing - even if we completely determine it - we do not make the least addition to the thing when we further declare that this thing is." [Kant, from Critique of Pure Reason.] This sentence provides a clue. We might note that to every existing object there corresponds its whole concept: the concept whose content includes all (and only) the properties the object in question has. ... Suppose ... that the Taj Majal is pink and let C1 and C2 be, respectively, the whole concept of the Taj Mahal and the whole concept of the Taj Mahal diminished with respect to pinkness [i.e., roughly speaking, C2 is what remains of C1 when pinkness is deleted from its content]. Evidently there are possible circumstances in which C2 but not C1 would be exemplified by some actually existing object: perhaps these circumstances would obtain if the Taj Mahal were green, for example. ... Now perhaps Kant means to point out that existence differs from pinkness in the following respect. If C3 is the whole concept of the Taj Mahal diminished with respect to existence, there are no possible circumstances in which C3 but not C1 has application; it is a necessary truth that if C3 is exemplified, so is C1. Since the converse is also true, C1 and C3 are, we might say, equivalent concepts; in annexing existence to C3, we don’t really get a different concept. And if we add that a predicate (or property) P is a real predicate (or property) only if it is not the case that any whole concept diminished with respect to P is equivalent to the corresponding whole concept, we may conclude that existence, unlike pinkness, is not a real predicate; it "is not a concept of something which could be added to the concept of a thing."
Giving a clear explanation of the claim that existence is not a real predicate, this interpretation also shows an interesting respect in which existence differs from other predicates or properties. Unfortunately, it seems to have no particular bearing on Anselm's argument. For Anselm can certainly agree, so far as his argument is concerned, that existence is not a real predicate in the explained sense. Anselm maintains that the concept the being than which none greater can be conceived is necessarily exemplified; that this is so is in no way inconsistent with the suggestion that the whole concept of a thing diminished with respect to existence is equivalent to the undiminished whole concept of that thing. Anselm argues that the proposition God exists is necessarily true; but neither this claim nor his argument for it entails or presupposes that existence is a predicate in the sense just explained.
What does Kant's argument show then? How could anyone be led to suppose that Kant's claim did dispose of the ontological argument? This last question is not altogether easy to answer. What Kant’s argument does show, however, is that one cannot "define things into existence"; it shows that one cannot, by adding existence to a concept that has application contingently if at all, get a concept that is necessarily exemplified. For let C' be any whole concept and C be that concept diminished with respect to existence. ... Kant's argument shows that the proposition There is an object to which C applies is logically equivalent to There is an object to which C’ applies. ... From a concept which has application contingently - for example, crow, we cannot, by annexing existence to it, get a concept that necessarily applies; for if it is a contingent truth that there are crows, it is also a contingent truth that there are existent crows.
But of course Anselm need not have thought otherwise. Schopenhauer describes the ontological argument as follows: "On some occasion or other 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 started with some concept that has instances contingently if at all and then annexed existence to it - then indeed his argument would be subject to Kant's criticism. But he didn't, and it isn't. And Kant's objection shows neither that there are no necessary existential propositions nor that the proposition God exists is not necessary - any more than it shows that There is a prime [number] between fifty and fifty-five is a contingent proposition.