The arguments of St. Anselm and of Gaunilo, two eleventh-century thinkers, are both ontological in character. Ontological arguments about the existence of God, based in premises ostensibly derived from a source that is different from observation, or put another way, from reason. By working through a sequence of logical steps, such arguments necessarily arrive at the conclusion that God exists.
St. Anselm of Canterbury, England, wrote in the Proslogion how he derived the existence of God by beginning with the concept of the greatest possible being. His reasoning was that if such a being fails to exist, then a greater being can be conceived. The flaw of the argument is that the premise is absurd: nothing can be greater than a being than which no greater can be conceived. Such a being does exist, which is God.
Gaunilo, a monk contemporary with Anselm, wrote a “Reply on Behalf of the Fool” in which raised several objections to Anselm's argument. He stated that this reasoning could not offer a reason for the Psalmist's fool to believe that that than which a greater cannot be thought actually exists. Famously, Gaunilo raised a countering argument intended which is parallel to Anselm's, and followed through with the idea that it generates an obviously absurd conclusion. Rather than consider “that than which a greater cannot be thought,” Gaunilo suggested substituting “island,” as in “that island than which a greater cannot be thought.” By substituting a concrete, observable entity, Gaunilo was able to prove logically that Anselm’s argument is fallacious.