Anselm, Descartes, and in recent times Plantinga have employed various versions of the ontological argument. Whatever be the version, the general progress of an ontological argument is from the rational to the real. The two main versions, namely the analytical (that predicates existence to the concept of God) and the modal (that conceives of divine possibility as actuality) attempt to prove that the denial of divine existence is logically self-contradictory; for if the concept of God is possible, then His existence must of necessity be actual, they hold. An important critique was made by Immanuel Kant who argued that defining a triangle as a polygon with three angles doesn't prove the actual existence of a triangle. Of course, protagonists of the ontological argument contend that the definition of God is unlike the definition of triangles. For to define God as "the one than whom a greater cannot be conceived" or as "the being who possesses maximal greatness" necessarily entails (at least, as a logical necessity) the affirmation of the existence of God (to deny Him would involve a contradiction). To say that "the one than whom a greater cannot be conceived" does not exist is to claim that whatever exists is greater than "the one than whom a greater cannot be conceived" which is a contradiction. Similarly, to say that "the being who possesses maximal greatness" doesn't exist is to affirm (since an infinite negation is not possible) that the existence of "the being who possesses maximal greatness" is an impossibility. But, that is an infinite negation as well. Modality is always open in this regard. But, if possibility is allowed, actuality cannot be denied.
Still, the ontological argument can only accomplish a rational purpose; it cannot empirically establish divine reality. The greatest drawback to the argument is that rational arguments cannot be used to establish or deny empirical facts. Epistemologists should learn this lesson from the Paradoxes of Zeno, the Arguments of Gaudapada, and the Antinomies of Kant. Rational analysis does play a role in understanding the empirical world (for instance, reason provides us the categories of quantity, affirmation, and negation that help us understand experience categorically). However, reason bereft of experience is empty and experience bereft of reason is blind.
But, for sure, the negation of divine existence is logically impossible; for no finite being can make an infinite negation (only unless the negation involves an issue of rational fact or possibility). For instance, a finite being can make an infinite negation like "a circular-square doesn't exist"; however, he cannot make an infinite negation of the existence of "the one than whom a greater cannot be conceived", since that definition does not involve a logical contradiction or impossibility (i.e. it is both logical consistent and possible).
Thus, perhaps the greatest significance of the ontological argument lies in its rational establishment of the concept of God as logically non-negatable. However, there will be problems if one attempts to use the argument beyond the realm of conceptual logic.