I attempted this question in 25 minutes. It is not one that has come up in any recent exam, but students are required to have knowledge of Gaunilo’s challenges. So it would be useful to look it over.
Gaunilo of Marmoutier disagreed with Anselm that the existence of God could be logically proved based on an understanding of his essence or his definition. Anselm’s claim that only a fool says ‘there is no God’ (because this is like saying ‘the thing that has to exist doesn’t exist’) is disputed by Gaunilo because he doesn’t believe it is possible to have an understanding of who God is in himself anyway.
This kind of belief that it is impossible to know the nature of God is often labelled a kind of agnosticism. This is not the usual use of the term for people who are undecided about God’s existence, but instead it means a more general lack of knowledge about who God is in himself. For instance Aquinas is also convinced that it is impossible to know the nature of God, because as creatures, our knowledge, or rationality is only capable of knowing things concretely. God, being an incorporeal being, and one who surpasses all created things in perfection, thus goes beyond the limits of what we can know with our reason.
Gaunilo claims that Anselm’s dependence in his argument on a definition of God as ‘that than which nothing greater can be conceived’ is flawed, as we simply cannot hold such a definition. Furthermore, to have this notion of God’s nature in one’s mind, as Anselm claims, would also be impossible for our reason.
Gaunilo’s second and more famous challenge to Anselm is that we cannot go from the definition of something to it’s existence. He uses a reductio ad absurdum argument, which aims to show the absurdity of holding the viewpoint of Anselm, by using the example of an island. He says: We can conceive of a perfect island. A perfect island must be more perfect in reality than in the mind. Therefore a perfect island exists. The perfect island stands for Anselm’s perfect being. Gaunilo aims to show with this example that Anselm’s argument is fallacious, as you can use his argument to prove the existence of things such as perfect islands.
Clearly, it is hard to see how a perfect island would have to exist just because of this argument, and Gaunilo believed he had proved that Anselm’s similar argument was flawed. However, in Reply to Gaunilo, Anselm refers him to the Proslogion 3, in which Anselm had pre-empted such a challenge with a second version of the ontological argument.