Immanuel Kant stated that there were types of arguments to prove the existence of God;.
The Cosmological Argument, which is based on the general fact of the existence of the world, .
The Teleological Argument, which is based on particular features of design in the world.
And The Ontological Argument, which is based on reason alone.
The Ontological Argument is based on the very being of God. It is not based on any observations of the world, nor any form of experience or external knowledge. It attempts to prove the existence of God from the meaning of the word God. E.g. If you understand what God is, you understand that he must exist.
The Ontological Argument is also an "A priori" argument, meaning that it uses logic to prove that an initial definition is true.
The Ontological Argument (ontos meaning "being") is not one single argument. It is best referred to as a group of related arguments, argued by different philosophers such as, Anselm, Descartes, Malcolm and Plantinga.
As with any Argument or theory, there are criticisms as well, proposed by philosophers such as, Hume, Kant, Gaunilo and Russell.
The most well known form of the Ontological Argument was thought of by St Anselm of Canterbury. He claimed that you cannot think of God as NOT existing and that existence is essential to his very idea of God. His main argument is set out in two parts; "What is God?" and, "Is His existence necessary?".
He described God as,.
"That than which nothing greater can be conceived.".
In other words, God is the greatest and most perfect being. Anselm does not mean however that God is something that is greater than everything else on a long list of things, but means that God is perfect and absolute. According to Anselm, even an atheist MUST have a definition of God, even if only to dismiss God's existence. From this he concluded that God exists even in the mind of someone who denies His existence.
He then takes the argument a step further - God exists in the mind, but does he exist in any other sense? Anselm states that the answer must be yes.