The Ontological Argument
(a semantic argument)

"The existence of God follows from the very concept of God."

TRADITIONAL FORMULATION OF ARGUMENT

(a) "God is that than which nothing greater can be conceived." In other words, it's part of the concept of "God" that nothing is greater than God; God is the greatest possible being, God is perfect.

(b) Now if X and Y are alike in all respects except that X actually exists while Y is merely imaginary, then X is in some sense better than Y. Therefore actual existence is part of greatness/perfection. Therefore God, being perfect, actually exists.

Objection: Perfection incoherent

It's not clear that the concepts of "greatest possible" and "perfection" are even objectively cogent, let alone that they entail existence. (What, for example, do the following have in common: a perfect gentleman, a perfect lady, a perfect ass, a perfect monster, a perfect crime, a perfect number?) To raise the issue of perfection, when there is a better version of the Ontological Argument available, is to court unnecessary trouble. Reply

References

Defenders: St Anselm; Descartes (Meditations); Charles Hartshorne, Anselm's Discovery (Open Court, 1965); Alvin Plantinga, God, Freedom, Evil, (Harper & Row, 1974) and The Nature of Necessity (Oxford,  1979).

Critics: Gaunilo; Aquinas; Kant; Graham Oppy, Ontological Arguments and Belief in God (Cambridge, 1996); <Oppy against Gödel>; <Oppy against Plantinga>.

Anthology: Alvin Plantinga (editor), The Ontological Argument (Doubleday, 1965).