From Conservapedia

According to the Stanford Encyclopedia of Philosophy, "Ontological arguments are arguments, for the conclusion that God exists, from premises which are supposed to derive from some source other than observation of the world — e.g., from reason alone."[1] Anselm of Canterbury's ontological argument uses the definition of God to prove His existence. Anselm's ontological argument remained influential for centuries, and was later used by Descartes. Mathematician Kurt Gödel proposed a variation of it based on modern logic.

Anselm's proof is as follows:

God is that for which no greater being is conceivable.

That which exists is greater than that which does not exist.

That which does not exist fails to satisfy the definition of God.

Therefore God exists.

In a sense this proof of the existence of God is similar to the mathematical proofs based on deriving a contradiction of something is not true. Accepting the definition of God, as most would, while then denying that God exists leads to a contradiction as existence is a necessary element of perfection in this context.

Recent Ontological Arguments

The Stanford Encyclopedia of Philosophy states the following regarding recent developments in ontological arguments for the existence of God:

“ In more recent times, Kurt Gödel, Charles Hartshorne, Norman Malcolm and Alvin Plantinga have all presented much-discussed ontological arguments which bear interesting connections to the earlier arguments of St. Anselm, Descartes and Leibniz. Of these, the most interesting are those of Gödel and Plantinga; in these cases, however, it is unclear whether we should really say that these authors claim that the arguments are proofs of the existence of God.[2] ”

Criticism

Gaunilo, a contemporary of Anselm, played devil's advocate by using reductio ad absurdum and envisaged a "lost, yet most perfect island." Gaunilo argued that just because we can imagine this island does not mean it actually exists. Anselm responded by arguing that such an island is not intrinsically necessary to existence because the concept of no greater conceivable being existing would only apply to God, not to something tangible such as an island.

Kant weighed in against Descartes' version, challenging the premise that existence is a predicate of perfection. Kant said he could imagine a hundred thalers (coins) in such great detail that whether or not they actually existed was arbitrary, as there was no difference other than this between the imagined and the existent thalers.

Davies insisted that Anselm's argument begs the question- it assumes what it sets out to prove. In other words, if a God existed, he would be supremely perfect, and would therefore exist. In explicit form, the first might be construed to mean 'The concept of God is the most supremely perfect concept'. It has been suggested that the ontological argument is therefore flawed in that it uses equivocation to progress from a concept of God to property of God to an existent God, and flawed in that the entire argument collapses irreparably once this is exposed.

Repaired Ontological Argument

A fixed version of the argument might go as follows:

1. It's possible that a Maximally Great Being exists - this being, then, exists in some possible world

2. A Maximally Great Being, if it exists in some possible world, must exist in all possible world, to satisfy its definition

3. If a Maximally Great Being exists in all possible worlds, it must exist in the real world

4. Therefore, a Maximally Great Being actually exists.

In this presentation of the argument, steps 2 through 4 are mostly agreed upon. The conclusion rests on step 1. That is, if the idea of a Maximally Great Being - God - is logically coherent, then this being does exist. It was Anselm's response, then, to Gaunilo, that created the circular reasoning. His response was wrong. The maximally great island does not exist because it does not fit step 1. This maximally great island exists in no possible world, because the qualities that make an island great are subjective, not objective. While one person may want sand all over the ideal island, Anakin Skywalker may think that any island containing any sand is a bad one. There are objective qualities, however, when it comes to a being: moral perfection, omnipresence, optipotence, etc.

Notes

Further reading

Essay: Why Is There Something Rather Than Nothing?

Essay: One person's view of the Ontological Argument