Here’s St. Anselm’s original argument:
Thus even the fool is convinced that something than which nothing greater can be conceived is in the understanding, since when he hears this, he understands it; and whatever is understood is in the understanding.
And certainly that than which a greater cannot be conceived cannot be in the understanding alone.
For if it is even in the understanding alone, it can be conceived to exist in reality also, which is greater. Thus if that than which a greater cannot be conceived is in the understanding alone, then that than which a greater cannot be conceived is itself that than which a greater can be conceived.
But surely this cannot be. Thus without doubt something than which a greater cannot be conceived exists, both in the understanding and in reality.
Let X be a proper name, much like Chernikov is my own proper name, of a thing described by essence Ex = “than which nothing greater can be thought.” Let’s spell it out. Ex = “X is infinite & X is happy & X can create the world & X ought to be worshipped & …” Ex is a conjunction of propositions describing X and is itself a proposition.
Ex is the meaning of X. Now if we propose that X exists in reality or has a reference, then we assert something new. X becomes greater by virtue of now designating two things, one in the understanding and the other in reality. But Ex is unaltered and is no greater than before. Kant then noticed rightly that “existence is not a predicate.”
If, on the other hand, we say that Ex includes into itself the postulation of X’s real existence, Ex‘ = Ex & “X exists in reality,” then it’s true that Ex‘ is now greater than Ex. But to no avail. For the idea of X or the form in the understanding is not infinite or happy or anything else; it’s a mere abstraction. Therefore, it is to be understood as Ex‘ = “if X existed in reality, then it would be infinite, …, and would exist.” But that, “if X existed, then it would exist,” obviously tells us nothing new. This time, Ex increases in greatness, but X does not, since it, even if described by Ex‘, need not exist really.
It follows that we can’t just up and define things into real existence. But is that what the ontological argument is trying to do? Perhaps all it needs to do in order to succeed is stop at constructing Ex‘. Then again, perhaps Ex‘ only seems to exceed Ex but not really.