The Ontological Argument
An ontological argument attempts to establish God's existence through reasoning about a concept of God, necessity or possibility. There are several versions, with different premises. Their conclusions are disputed; understanding a definition and showing that something satisfying it exists are distinct tasks.
Anselm
In Proslogion, chapters 2 and 3, Anselm reasons from the idea of a being beyond which nothing greater can be conceived. He argues that such a being cannot exist only in thought, since existence in reality would be greater. His next step concerns a being that cannot be thought not to exist. This is a paraphrase of the argument, not a claim that the inference is accepted by all philosophers. Anselm, Proslogion, chapters 2-3.
Descartes and Leibniz
In the Fifth Meditation, Descartes compares necessary existence in the idea of God with geometrical properties belonging to a triangle. The comparison belongs to his argument about a supremely perfect being. It should not be turned into the unrestricted rule that anything defined as existing thereby exists. Descartes, Meditations on First Philosophy, Fifth Meditation, Jonathan Bennett's adapted text.
Leibniz stresses a further condition: the proposed necessary being must be possible. Monadology section 45 connects possibility and necessary existence. His argument from sufficient reason, and his account of the best possible world, need to be distinguished from this inference. See Gottfried Leibniz Ontological Proof.
Objections and modal versions
Kant's objection challenges treating existence as a property that enriches a concept. Later modal arguments use distinctions between possibility and necessity. In Plantinga's terminology, maximal excellence concerns omnipotence, omniscience and moral perfection; maximal greatness concerns having that excellence in every possible world. Merely existing in every world is not the full definition.
The crucial possibility premise is substantive. It cannot be established simply by stating the desired conclusion in the form "it is possible". The Stanford Encyclopedia surveys these arguments and their objections. "Ontological Arguments", Stanford Encyclopedia of Philosophy.
Relevance to language
The topic illustrates why definition, description and evidence must be distinguished. An analogy may illuminate an argument without proving it. Likewise, naming an experience or giving it a spatial description does not settle every claim about its cause or nature.
Video
Theology lecturer J. R. Gilhooly introduces an ontological argument in this university explainer. The presentation takes a Christian apologetic perspective; compare its treatment of possibility and necessity with the objections discussed above. University programme page.
What Is the Ontological Argument? (4:53). Published by Cedarville University.