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The ontological argument
Unlike the cosmological causal and teleological fine-tuning arguments which are either partially or wholly a posteriori, the ontological argument is wholly a priori.
St Anselm first developed the ontological argument in the eleventh century in his Proslogium Chapter II. It has been translated from Latin, as follows:
Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived. For, when he hears of this, he understands it. And whatever is understood exists in the understanding. And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For, suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.
Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. However obviously this is impossible. Hence, there is no doubt that there exists a being than which nothing greater can be conceived, and it exists both in the understanding and in reality.[1]
Therefore, St Anselm develops his argument from the concept of God to the reality of God and this is broken down in the following stages:
Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived.
In other words, God is that than which nothing greater [or more perfect] can be conceived.
For, when he hears of this, he understands it
In other words, something than which nothing greater or more perfect can be conceived is understood, even by the fool.
Here, St Anselm makes an implicit assumption that the something than which nothing greater or more perfect can be conceived is that which is not contingent on anything. Were it to be contingent on anything, there would something else that would not be and therefore there would be something that would be greater or more perfect than it.
So, in other words, something than which nothing greater or more perfect can be conceived is understood to mean something which is not contingent on anything.
And whatever is understood exists in the understanding.
In other words, the concept of whatever is understood exists in the understanding.
Therefore, the concept of God exists in the understanding.