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The celebrated argument for the existence of God first propounded by Anselm in his Proslogion, ch. 2. The argument is notable as being purely a priori, and is usually interpreted as an attempt to prove the existence of God without using any contingent premise. Anselm follows Boethius by defining God as ‘something than which nothing greater can be conceived’ (id quo maius cogitare nequit ). God then exists in the understanding, since we understand this concept. But if He only existed in the understanding, something greater could be conceived, for a being that exists in reality is greater than one that exists only in the understanding. But then we can conceive of something greater than that than which nothing greater can be conceived, which is contradictory. Hence, God cannot exist only in the understanding, but exists in reality. In Anselm's own time the argument was criticized by a monk called Gaunilo, who urged that the same pattern of reasoning would prove the existence of a perfect island (for a perfect island existing only in the imagination is obviously not as good as one that really exists). The argument was not accepted by Aquinas, but was resurrected by Descartes, who made plain the requirement that existence be thought of as part of the definition or essence of a supremely perfect being. This, in turn, opened the way to criticism by Hume and especially Kant, that existence is not a property or predicate on all fours with others, that can be added or subtracted from definitions at will. This criticism has been generally sustained by modern logic (see quantifier, variable ).

The argument has been treated by modern theologians such as Barth, following Hegel, not so much as a proof with which to confront the unconverted, but as an exploration of the deep meaning of religious belief. Collingwood regards the argument as proving not that because our idea of God is that of id quo maius cogitare nequit, therefore God exists, but proving that because this is our idea of God, we stand committed to belief in its existence: its existence is a metaphysical posit, or absolute presupposition of certain forms of thought.

In the 20th century, modal versions of the ontological argument have been propounded by the American philosophers Charles Hartshorne, Normal Malcolm, and Alvin Plantinga. One version is as follows. Let us define something as unsurpassably great if it exists and is perfect in every possible world . Now let us allow that it is at least possible that an unsurpassably great being exists. This means that there is a possible world in which such a being exists. But if it exists in one world, it exists in all (for the fact that such a being exists in one world entails that it exists and is perfect in every world). So it exists necessarily. The correct response to this argument is to disallow the apparently reasonable concession that it is possible that such a being exist. This concession is much more dangerous than it looks, since in the modal logic involved, from possibly necessarily p, we can derive necessarily p .