Ontological arguments: There is a host of arguments under this title; all of them are based principally on conceptual, a priori grounds which do not involve a posteriori empirical investigation. If a version of the argument works, then it can be deployed using only the concept of God and some modal principles of inference, that is, principles concerning possibility and necessity. The argument need not resist all empirical support, however, as I shall indicate.

The focus of the argument is the thesis that, if there is a God, then God's existence is necessary. God's existence is not contingent—God is not the sort of being that just happens to exist. That this is a plausible picture of what is meant by God may be shown by appealing to the way God is conceived in Jewish, Christian, and Islamic traditions. This would involve some a posteriori, empirical research into the way God is thought of in these traditions. Alternatively, a defender of the ontological argument might hope to convince others that the concept of God is the concept of a being that exists necessarily by beginning with the idea of a maximally excellent being. If there were a maximally excellent being what would it be like? It has been argued that among its array of great-making qualities (omniscience and omnipotence) would be necessary existence. Once fully articulated, it can be argued that a maximally excellent being, which existed necessarily, could be called “God.”

The ontological argument goes back to St. Anselm (1033/34–1109), but I shall explore a current version relying heavily on the principle that if something is possibly necessarily the case, then it is necessarily the case (or, to put it redundantly, it is necessarily necessary). The principle can be illustrated in the case of propositions. Six is the smallest perfect number (that number which is equal to the sum of its divisors including one but not including itself) does not seem to be the sort of thing that might just happen to be true. Rather, either it is necessarily true or necessarily false. If the latter, it is not possible, if the former, it is possible. If one knows that it is possible that six is the smallest perfect number then one has good reason to believe that. Do we have reason to think it is possible God exists necessarily? In support of this, one can also appeal to a posteriori matters, noting the extant religious traditions that uphold such a notion. The fact that the concept of God as a necessarily existing reality seems to be coherently conceived widely across time and cultures is some evidence that the concept is coherent (it is possible there is a God), for God's existence has plausibility, thus can also contribute to believing it is possible God exists. There is an old philosophical precept that from the fact that something exists, it follows that it is possible (ab esse ed posse valet consequential). A related principle is that evidence that something exists is evidence that it is possible that such a thing exists. There does not appear to be anything amiss in their thinking of God as necessarily existing; if the belief that God exists is incoherent this is not obvious. Indeed, a number of atheists think God might exist, but conclude God does not. If we are successful in establishing the possibility that God necessarily exists, the conclusion follows that it is necessarily the case that God exists.

There have been hundreds of objections and replies to this argument. Perhaps the most ambitious objection is that the argument can be used with one minor alteration to argue that God cannot exist. Assume all the argument above but also that it is possible God does not exist. Atheists can point out that many theists who believe there is a God at least allow for the bare possibility that they could be wrong and there is no God. If it is possible that there is no God, then it would necessarily follow that there is no God. Replies to this objection emphasize the difficulty of conceiving of the non-existence of God. The battle over whether God is necessary or impossible is often fought over the coherence of the various divine attributes is discussed in section 3. If you think these attributes are compossible, involve no contradictions, and violate no known metaphysical truths, then you may well have good grounds for concluding that God is possible and therefore necessary. However, if you see a contradiction, say, in describing a being who is at once omniscient and omnipotent, you may well have good grounds for concluding that God's existence is impossible.

Another objection is that it makes no sense to think of a being existing necessarily; propositions may be necessarily true or false, but objects cannot be necessary or contingent. Some philosophers reply that it makes no less sense to think of an individual (God) existing necessarily than it does to think of propositions being necessarily true.

A further objection is that the ontological argument cannot get off the ground because of the question-begging nature of its premise that if there is a God, then God exists necessarily. Does admitting this premise concede that there is some individual thing such that if it exists, it exists necessarily? Replies have claimed that the argument only requires one to consider an ostensible state of affairs, without having to concede initially whether the state of affairs is possible or impossible. To consider what is involved in positing the existence of God is no more hazardous than considering what is involved in positing the existence of unicorns. One can entertain the existence of unicorns and their necessary features (that necessarily if there were unicorns, there would exist single-horned beasts) without believing that there are unicorns.

Finally, consider the objection that, if successful in providing reasons to believe that God exists, the ontological argument could be used to establish the existence of a whole array of other items, like perfect islands. Replies to this sort of objection have typically questioned whether it makes sense to think of an island (a physical thing) as existing necessarily or as having maximal excellence on a par with God. Does the imagined island have excellences like omniscience, omnipotence (a power which would include the power to make indefinitely many islands), and so on?

Classical, alternative versions of the ontological argument are propounded by Anselm, Spinoza, and Descartes, with current versions by Alvin Plantinga, Charles Hartshorne, Norman Malcolm, and C. Dore; classical critics include Gaunilo and Kant, and current critics are many, including William Rowe, J. Barnes, G. Oppy, and J. L. Mackie. The latest book-length treatment of the ontological argument is a vigorous defense: Rethinking the Ontological Argument by Daniel Dombrowski (2006).