Anselm's ontological argument for the existence of God is, in one sense, quite simple; God is that-than-which-no-greater-can-be-thought, and he must, therefore, exist, for otherwise he would not be that-than-which-no-greater-can-be-thought. Careful analysis of Anselm's Proslogion and his Reply to Gaunilo, however, will show that Anselm proposes not one, but six ontological arguments which, while relying on common premises about the nature of thought and the identity of God, differ in their contents, sometimes markedly. These six arguments may be conveniently divided into four classes: the arguments from God's perfection, the argument from His necessity, the argument from His eternity, and the arguments from His simplicity. As analysis of these arguments will show, Anselm proposes in the Proslogion and the Reply not merely a simple argument, but a whole method of reasoning about God fertile in its implications for His nature and existence.
The basic premises about God and the nature of thought which Anselm's arguments hold in common are four: that that-than-which-no-greater-can-be-thought is God, that God can be thought, that God is thought, and that God exists in the mind. The first premise, that the maximal being, or that-than-which-no-greater-can-be-thought, is identical to the Christian God, Anselm derives from Christian revelation.  He derives his second and third premises, that God can be thought and that God is thought, from this same source although he provides a three-fold philosophical defense of their plausibility.
First, Anselm argues that the partial incomprehensibility of God gives no legitimate grounds to the Fool to deny that he can think about God at all. Such an objection, Anselm argues, would be like saying that one cannot see daylight, because he cannot stare directly at the sun.  Second, Anselm argues that his conception of God is not entirely negative. For since the supremely good resembles things less good insofar as they are both good, one who knows things less good already knows something of the supreme good. In addition, he may augment his knowledge of the maximal being by thinking of better and better things until he reaches the limits of what he can think. That which transcends even these limits he knows is the maximal being.  Third, Anselm proves that even if the concept that-than-which-no-greater-can-be-conceived were entirely negative, that would not prevent one from thinking about it. This contention he vindicates by distinguishing between the thing, that-than-which-no-greater-can-be-thought, and the concept which signifies it. Just as one can understand the concepts of the ineffable and the inconceivable, Anselm argues, without understanding the things they signify, so can one understand the concept, that-than-which-no-greater-can-be-thought, without understanding God Himself. Since his argument depends on the notion that human beings can think of the concept of the maximal being, and not that they can think of the being Himself, Anselm concludes that the concept of the maximal being would be adequate for his purposes even if it were purely negative. 
To complete the groundwork for his six ontological arguments, Anselm contends that the idea of God exists "in the mind". By this he means that the idea is thought and can, therefore, be considered a kind of mental object. This Anselm explains in the somewhat obscure passage,
- "For, just as what is thought is thought by means of a thought, and what is thought by a thought is thus, as thought, in thought, so also, what is understood is understood by the mind, and what is understood by the mind is thus, as understood, in the mind." 
One might conclude from this passage that Anselm posits a fifth premise for his six ontological arguments. An earlier passage, however, makes it clear that Anselm regards it as sufficient, for the purposes of his arguments, that God merely be thought. "I insist, however, that simply if it can be thought it is necessary that it exists." 
On these four premises, therefore, that the maximal being is the God of Christian revelation, that God can be thought, that God is thought, and that God is "in the mind", Anselm proceeds to construct his six arguments for the existence of God. These, likewise, may be divided into four classes: the arguments from God's perfection, the argument from His necessity, the argument from His eternity, and the arguments from His simplicity. The arguments from God's perfection are two. The first relies on, in addition to the four premises stated above, two premises: (a) if the maximal being exists in the mind, it can exist in reality as well, and (b) that being referred to in the second case is greater than the first. It follows from these premises that God cannot exist merely in the mind. But we know from Anselm's fourth general premise that God does exist in the mind. God, therefore, also exists in reality.  The second argument from the perfection of God is slightly simpler than the first. It relies on a single premise: it is greater to exist than not to exist. Since God is that-than-which-no-greater-can-be-thought, he must, therefore, exist. 
Anselm supplements these arguments with an argument from God's necessity, perhaps the most complex of the six arguments he proposes. He relies, in this proof, on the general premises stated above and on two additional assertions about the necessity of God. First, Anselm, asserts, that the maximal being, if he does exist, cannot not exist either actually or in the mind. To this he adds a second premise, viz., that whatever can be thought to exist and does not exist could, if it were to exist, possibly not exist either in actuality or the mind. It follows from these premises and Anselm's second introductory premise, that God can be thought, that God does, indeed, exist. For, otherwise, if the maximal being did exist, his existence would not be necessary, which is absurd. 
Anselm's fourth argument, the argument from eternity, relies, similarly, on two premises. The maximal being, Anselm argues, can only be thought of as without a beginning. Yet whatever can be thought of as existing, but does not actually exist, can be thought of as with a beginning. Since, according to Anselm's third introductory premise, God is actually thought, he must, therefore, exist, because, if he did not he could be thought of as having a beginning, which is self-contradictory.  Anselm's fifth and sixth arguments, the arguments from simplicity have precisely the same structure as the fourth. Just as one cannot think of God as having a beginning, so one cannot think of him as not being whole or as having parts. But whatever can be thought to exist, yet does not exist, can be thought of as other than a whole and as with parts. The very fact that God is thought, therefore, proves he exists, for he is thought in a way (i.e., as a whole and without parts) that is inconsistent with non-existence. 
The logic of St. Anselm's arguments is impeccable. While one may quibble with his premises, he combines them in such a way that he who admits their validity cannot but assent to Anselm's conclusions. Indeed, it seems that one could generate from the outline of Anselm's last three arguments as many arguments for the existence of God as there are known divine attributes, e.g. omnipotence, which are not shared with created things. Anselm has, therefore, overcome much of the gap between faith and understanding; for the more one knows through faith about God's nature, the more, with the help of Anselm's techniques, can one defend that knowledge.
1. Charlesworth, M.J., St. Anselm's Proslogion with 'A Reply on Behalf of the Fool' by Gaunilo and 'The Author's Reply to Gaunilo' (London: Oxford University Press, 1965), p. 169.
2. ibid., p. 173
3. ibid., p. 187
4. ibid., p. 187-89
5. ibid., p. 173-75
6. ibid., p. 169
7. ibid., p. 117
8. ibid., pp. 119
9. ibid., p. 171
10. ibid., p. 171
11. ibid., p. 171-73