Ontological argument

In the philosophy of religion, an ontological argument is a deductive philosophical argument, made from an ontological basis, that is advanced in support of the existence of God. Such arguments tend to refer to the state of being or existing. More specifically, ontological arguments are commonly conceived a priori in regard to the organization of the universe, whereby, if such organizational structure is true, God must exist.
The first ontological argument in Western Christian tradition was proposed by Saint Anselm of Canterbury in his 1078 work, Proslogion, in which he defines God as "a being than which no greater can be conceived," and argues that such a being must exist in the mind, even in that of the person who denies the existence of God. From this, he suggests that if the greatest possible being exists in the mind, it must also exist in reality, because if it existed only in the mind, then an even greater being must be possible one who exists both in mind and in reality. Therefore, this greatest possible being must exist in reality. Similarly, in the East, Avicenna's Proof of the Truthful argued, albeit for very different reasons, that there must be a "necessary existent".
Seventeenth-century French philosopher René Descartes employed a similar argument to Anselm's. Descartes published several variations of his argument, each of which center on the idea that God's existence is immediately inferable from a "clear and distinct" idea of a supremely perfect being. In the early 18th century, Gottfried Leibniz augmented Descartes's ideas in an attempt to prove that a "supremely perfect" being is a coherent concept. A more recent ontological argument was formulated by Kurt Gödel in private notes, using modal logic. Although he never published or publicly presented it, a version was later transcribed and circulated by Dana Scott. Norman Malcolm also revived the ontological argument in 1960 when he located a second, stronger ontological argument in Anselm's work; Alvin Plantinga challenged this argument and proposed an alternative, based on modal logic. Attempts have also been made to validate Anselm's proof using an automated theorem prover. Other arguments have been categorised as ontological, including those made by Islamic philosophers Mulla Sadra and Allama Tabatabai.
Just as the ontological argument has been popular, a number of criticisms and objections have also been mounted. Its first critic was Gaunilo of Marmoutiers, a contemporary of Anselm's. Gaunilo, suggesting that the ontological argument could be used to prove the existence of anything, uses the analogy of a perfect island. Such would be the first of many parodies, all of which attempted to show the absurd consequences of the ontological argument. Later, Thomas Aquinas rejected the argument on the basis that humans cannot know God's nature. David Hume also offered an empirical objection, criticising its lack of evidential reasoning and rejecting the idea that anything can exist necessarily. Immanuel Kant's critique was based on what he saw as the false premise that existence is a predicate, arguing that "existing" adds nothing to the essence of a being. Thus, a "supremely perfect" being can be conceived not to exist. Finally, philosophers such as C. D. Broad dismissed the coherence of a maximally great being, proposing that some attributes of greatness are incompatible with others, rendering "maximally great being" incoherent.
Contemporary defenders of the ontological argument include Alvin Plantinga, Yujin Nagasawa, and Robert Maydole.

Classification

The traditional definition of an ontological argument was given by Immanuel Kant. He contrasted the ontological argument with the cosmological and physio-theoretical arguments. According to the Kantian view, ontological arguments are those founded through a priori reasoning.
Graham Oppy, who elsewhere expressed that he "see no urgent reason" to depart from the traditional definition, defined ontological arguments as those which begin with "nothing but analytic, a priori and necessary premises" and conclude that God exists. Oppy admits, however, that not all of the "traditional characteristics" of an ontological argument are found in all ontological arguments and, in his 2007 work Ontological Arguments and Belief in God, suggested that a better definition of an ontological argument would employ only considerations "entirely internal to the theistic worldview."
Oppy subclassified ontological arguments, based on the qualities of their premises, using the following qualities:

definitional: arguments that invoke definitions.
conceptual : arguments that invoke "the possession of certain kinds of ideas or concepts."
modal: arguments that consider possibilities.
meinongian: arguments that assert "a distinction between different categories of existence."
experiential: arguments that employ the idea of God existing solely to those who have had experience of him.
mereological: arguments that "draw on…the theory of the whole-part relation."
higher-order: arguments that observe "that any collection of properties, that does not include all properties and is closed under entailment, is possibly jointly instantiated."
Hegelian: the arguments of Hegel.

William Lane Craig criticised Oppy's study as too vague for useful classification. Craig argues that an argument can be classified as ontological if it attempts to deduce the existence of God, along with other necessary truths, from his definition. He suggests that proponents of ontological arguments would claim that, if one fully understood the concept of God, one must accept his existence.
William L. Rowe defines ontological arguments as those which start from the definition of God and, using only a priori principles, conclude with God's existence.

Development

Although a version of the ontological argument appears explicitly in the writings of the ancient Greek philosopher Xenophanes and variations appear in writings by Parmenides, Plato, and the Neoplatonists, the mainstream view is that the ontological argument was first clearly stated and developed by Anselm of Canterbury. Some scholars argue that Islamic philosopher Avicenna developed a special kind of ontological argument before Anselm, while others have doubted this position.
Daniel Dombrowski marked three major stages in the development of the argument:

Anselm's initial explicit formulation,
the 18th-century criticisms of Kant and Hume, and
the identification of a second ontological argument in Anselm's Proslogion by 20th-century philosophers.
Anselm

Theologian and philosopher Anselm of Canterbury proposed an ontological argument in the 2nd and 3rd chapters of his Proslogion. Anselm's argument was not presented in order to prove God's existence; rather, Proslogion was a work of meditation in which he documented how the idea of God became self-evident to him.
In Chapter 2 of the Proslogion, Anselm defines God as a "being than which no greater can be conceived." While Anselm has often been credited as the first to understand God as the greatest possible being, this perception was actually widely described among ancient Greek philosophers and early Christian writers. He suggests that even "the fool" can understand this concept, and this understanding itself means that the being must exist in the mind. The concept must exist either only in our mind, or in both our mind and in reality. If such a being exists only in our mind, then a greater being—that which exists in the mind and in reality—can be conceived. Therefore, if we can conceive of a being than which nothing greater can be conceived, it must exist in reality. Thus, a being than which nothing greater could be conceived, which Anselm defined as God, must exist in reality.
Anselm's argument in Chapter 2 can be summarized as follows:

It is a conceptual truth that God is a being than which none greater can be imagined.
God exists as an idea in the mind.
A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God.
But we cannot imagine something that is greater than God
Therefore, God exists.

In Chapter 3, Anselm presents a further argument in the same vein:

By definition, God is a being than which none greater can be imagined.
A being that necessarily exists in reality is greater than a being that does not necessarily exist.
Thus, by definition, if God exists as an idea in the mind but does not necessarily exist in reality, then we can imagine something that is greater than God.
But we cannot imagine something that is greater than God.
Thus, if God exists in the mind as an idea, then God necessarily exists in reality.
God exists in the mind as an idea.
Therefore, God necessarily exists in reality.

This contains the notion of a being that cannot be conceived not to exist. He argued that if something can be conceived not to exist, then something greater can be conceived. Consequently, a thing than which nothing greater can be conceived cannot be conceived not to exist and so it must exist. This can be read as a restatement of the argument in Chapter 2 – Norman Malcolm, however, considers it to be a different, stronger argument.

René Descartes

proposed a number of ontological arguments that differ from Anselm's formulation. Generally speaking, they are less formal arguments than they are natural intuition.
In Meditation, Book V, Descartes wrote:
Descartes argues that God's existence can be deduced from his nature, just as geometric ideas can be deduced from the nature of shapes he used the deduction of the sizes of angles in a triangle as an example. He suggested that the concept of God is that of a supremely perfect being, holding all perfections. He seems to have assumed that existence is a predicate of a perfection. Thus, if the notion of God did not include existence, it would not be supremely perfect, as it would be lacking a perfection. Consequently, the notion of a supremely perfect God who does not exist, Descartes argues, is unintelligible. Therefore, according to his nature, God must exist.