The ontological argument is widely thought to have been first clearly articulated by St. Anselm of Canterbury, who defined God as the greatest conceivable being. Anselm’s reasoning was that, if a being existed only in the mind but not in reality, then a greater being was conceivable (a being which exists both in the mind and in reality). The famed seventeenth-century French philosopher René Descartes utilized the ontological argument. The ontological argument was revived by Norman Malcolm in 1960. Variants of the ontological argument have been supported and defended by contemporary philosophers such as Alvin Plantinga (who bases his argument on modal logic) and William Lane Craig.
The ontological argument was first criticized by Gaunilo of Marmoutiers, a contemporary of Anselm of Canterbury. He argued that the ontological argument could be used to demonstrate the existence of anything, utilizing an analogy of a perfect island. The argument was also criticized by the famed Catholic philosopher Thomas Aquinas and also by David Hume and Immanuel Kant.
Ontological Argument: Possible Worlds
To properly understand the ontological argument, it is necessary to specify what philosophers mean when they talk about “possible worlds.” A “possible world” refers to a counterfactual—a state of affairs that could have been true. For something to exist in a “possible world” simply means that its existence is logically possible.
The ontological argument for the existence of God refers to the claim that the very logical possibility of God’s existence entails His actuality. The ontological argument begins with the claim that God, by definition, is infinitely great. Thus, no entity can surpass God’s greatness. God, in other words, is the greatest conceivable being (if one could conceive of a greater being, then that would be God). Being infinitely great entails existence in every possible world since a being that existed in merely some possible worlds would be superseded in greatness by a being that existed in every possible world. Moreover, a maximally great being is one that possesses the property of necessary existence. Thus, if a being of maximal greatness exists in some possible world, then it exists in every possible world. If an infinitely great being exists in every possible world then that being must exist in the actual world. Since God is an infinitely great being, therefore, God must exist.
Ontological Argument: The Premises
The conclusion of the ontological argument, as formulated by Alvin Plantinga and others, depends on a form of modal axiom S5 (which contends that if the truth of a proposition is possible, then it is possible in all worlds). This axiom also contends that, if it is possible that a proposition is necessarily true (that is to say, it is necessarily true in some possible world), then it is necessarily true in all possible worlds.
This logic of the ontological argument is formally summarised by philosopher Alvin Plantinga as follows:
Ontological Argument: Is It Sound?
While the ontological argument has been the subject of fierce criticism by many contemporary philosophers, many of the criticisms of it result from a failure to properly understand the argument.
The ontological argument is clearly logically valid—that is to say, the conclusion necessarily follows provided that Premises 1 to 5 are true. The crucial Premise, therefore, is Premise 3, namely, that it is possible that a maximally great being exists. To refute this Premise, one would need to show that the very concept of an infinitely great being is somehow logically incoherent—like a “married bachelor.” Since no argument to that effect has been forthcoming, however, it follows necessarily and inescapably that “Therefore, a maximally great being exists.”