Anselm's ontological argument.
Basic bio: Anselm called the "second Augustine." Anselm was born in NW Italy, spent much of his life in the Norman French monastery of Bec. From 1089-death was Archbishop of Canterbury. (1093 according to Hyman and Walsh). Hyman and Walsh cite his response to the news of his own death as characteristic of the man:
"If it is his will I shall gladly obey, but if He should prefer me to stay with you just long enough to solve the question of the origin of the soul which I have been turning over in my mind, I would gratefully accept the chance, for I doubt whether anybody else will solve it when I'm gone." [Hyman and Walsh, p. 148, citing M. Charlesworth, St. Anselm's P Proslogion, Oxford, 1965, p. 21.] He is praised by Hyman and Walsh for not following the pedagogical trend of beating students. Following Augustine, Anselm believed that reason sans faith was worthless. But with faith, reason extremely powerful. Those with faith can demonstrate not only existence of G, but also the incarnation, and Trinity.

Quotes from p. 147 Hyman and Walsh: "Ontological truth--truth of things--fulfillment of the relevant standard or ideal". Conception of truth as rightness perceptible to the mind alone with G as the ultimate truth."
Define ontological as of or pertaining to being or nature.
Chapter 1, Note Bene: The Augustinian conclusion of this chapter.
Chapter 2: The proof by reduction that G exists. Discuss Reductio proofs.
Chapter 3: The proof by reductio that G necessarily exists.
Chapter 4: How the fool can deny this in his heart. One way to think a thesis T is to think the words, the other way is to understand it and affirm it (i.e., given the apparent Augustinian meaning of "understanding" to know it).
conclusion: EVen If Anselm did not want to believe in G's existence, Anselm would understand it.
Gaunilo's reply on behalf of the fool
1. Summarizes Anselm's argument
2. Reduction in reply: clearly if to think it and affirm it is the same thing, then to think it as object in mind is same as understanding that it exists. But it isn't. Pragmatic criticism: if it were, the argument would not be necessary in the first place.
3. This kind of argument only appropriate to mental things; G is not a mental thing.
4. I don't really have the clear concept of G, only a verbal formula. If I don't understand it, the argument won't work. (Didn't Anselm acknowledge this?)
5. Gaunilo grants that the concept exists in his mind . Gaunilo does not see how Anselm bridges the gap between mental and extra-mental existence.
6. The island rejection--reduction to foolishness.
7. Argument that Anselm needs more argument for the concept of necessary existence of G.
8. Ends with praise

Anselm's Reply
I. We can so thus conceive G--Anselm appeals to Gaunilo's faith and conscience. Anselm reasserts the argument about necessary existence of G. Furthermore, G's non-existence cannot be thought of in the same way as other entities since . . . he reasserts the reductio regarding G.
II. Reasserts reductio.
III. regarding the island. G is sui generis; if not, then the island ok! G, for example, has necessary existence. DISCUSS MATERIAL OJECTS AND CONTINGENT BEINGS.
IV. "Even if none of those things that exist can be understood not to exist, all however can be thought as non-existing, save that which exists to the supreme degree."
V. Anselm points out that the greatest not equivalent for the purpose of the argument to "that than which none greater can be conceived."
VI. I'm not clear on this one; what do you think?
VII. IF you wish, we can leave G's name out of it, relying on Anselm's definition to make the argument work, making the divine connexion later.
VIII. Proof texts and experience show we can so have this concept of "that than which none greater can be conceived."
IX. Even if G were beyond thought and understanding , this formula is not--just as we can speak of the ineffable and the inconceivable.
X. Reassertion of his own correctness and gracious praise for his critic.