Anselm's First and Second Arguments

Anselm wrote from the perspective of 'fides quaerens intellectum' (faith seeking understanding), which is the concept of beginning with faith in God's existence and arguing in order to further understand him, as opposed to prove his existence. 
The Ontological Argument for the existence of God follows such a structure. It is an a priori argument, coming from the Greek "ontos" for "being", and thus is examining the nature of God's existence. 

The first argument is posed as a response, or rather, development, of the biblical verse "The Fool says to himself 'There is no God.'" [Psalms 14:1 and 53:1] Anselm then defines God as "that than which nothing greater can be conceived" (ttwngcbc). The fool clearly has a concept of "God", as he refers to him. Anselm holds the belief that reality is greater than concept, and so in order for God to fulfill his definition, he must exist. 

However, this argument presents several problems, which Anselm's contemporary Gaunilo, highlights. In his essay "On Behalf of the Fool", Gaunilo points out that in order to have an idea of a concept, so to speak, you must have experienced it in some way. This creates a weakness in Anselm's argument as it challenges the assumption that one's concept of a thing is innate. Gaunilo uses the example of an island to illustrate the flaws in Anselm's argument. He uses the same argument, but replaces God ("ttwngcbc") with "island". This shows that just because you conceive of something, does not necessitate it's existence. Gaunilo argues that if the argument can be used to prove the existence of a non-existent argument (as it would suggest), then it is flawed. 

Anselm's retort to this is that it is an unfair comparison - the island is contingent, as is any other example he could use. God is the only appropriate subject of the argument as he is 'necessary', and therefore not contingent upon anything for his existence. 

He improves upon his argument in his second version - presented in the Proslogion - by arguing that in order for God to be "ttwngcbc", he must be thought of as something that cannot, not, exist. He also argues that if 'God' exists in the mind only, then that being is not actually God. 

This argument differs from his first through the more specific definition, or rather, distinction, of what God is. It closes the loophole in the argument that Gaunilo exploited in his "island" argument.