Gaunilo of Marmoutier, a monk and contemporary of Anselm’s, thought that Anselm’s argument illegitimately moves from the existence of an idea to the existence of a thing that corresponds to the idea. It appears that Anselm simply defines things into existence-and this cannot be done. Gaunilo thought that one could use Anselm’s argument to show the existence of all kinds of non-existent things. Gaunilo writes:
"Now if some one should tell me that there is … an island [than which none greater can be conceived], I should easily understand his words, in which there is no difficulty. But suppose that he went on to say, as if by a logical inference: “You can no longer doubt that this island which is more excellent than all lands exists somewhere, since you have no doubt that it is in your understanding. And since it is more excellent not to be in the understanding alone, but to exist both in the understanding and in reality, for this reason it must exist. For if it does not exist, any land which really exists will be more excellent than it; and so the island understood by you to be more excellent will not be more excellent.”"
Gaunilo’s argument is this:
A perfect island is an island than which none greater can be imagined (that is, the greatest possible island that can be imagined).
A perfect island exists as an idea in the mind. (That is, I can think or conceive of a perfect island.)
A perfect island that exists as an idea in the mind and in reality is greater than a perfect island that exists only as an idea in the mind.
Thus, if a perfect island exists only as an idea in the mind, then we can imagine an island that is greater than a perfect island (that is, a greatest possible island that does exist).
But we cannot imagine an island that is greater than a perfect island.
Therefore, a perfect island exists.
Notice, however, that premise 1 of Gaunilo’s argument is incoherent. The problem here is that the qualities that make an island great are not the sort of qualities that admit of conceptually maximal qualities. No matter how great any island is in some respect, it is always possible to imagine an island greater than that island in that very respect. So, "island" has no intrinsic maximum. Because of this "greatest possible island" is incoherent.
But this is not true of the concept of God as Anselm conceives it. Properties like knowledge, power, and moral goodness, which comprise the concept of a maximally great being, do have intrinsic maximums. For example, perfect knowledge requires knowing all and only true propositions; it is conceptually impossible to know more than this. Likewise, perfect power means being able to do everything that it is possible to do; it is conceptually impossible for a being to be able to do more than this.
The general point here, then, is this: Anselm’s argument works, if at all, only for concepts that are entirely defined in terms of properties that admit of some sort of intrinsic maximum. The philosopher C.D. Broad explains this:
"[The notion of a greatest possible being imaginable assumes that] each positive property is to be present in the highest possible degree. Now this will be meaningless verbiage unless there is some intrinsic maximum or upper limit to the possible intensity of every positive property which is capable of degrees. With some magnitudes this condition is fulfilled. It is, e.g., logically impossible that any proper fraction should exceed the ratio 1/1; and again, on a certain definition of “angle,” it is logically impossible for any angle to exceed four right angles. But it seems quite clear that there are other properties, such as length or temperature or pain, to which there is no intrinsic maximum or upper limit of degree.
If any of the properties that are conceptually essential to the notion of God do not admit of an intrinsic maximum, then Anselm’s argument strategy will not work because, like Gaunilo’s concept of a perfect island, the relevant concept of God is incoherent. But insofar as the relevant great-making properties are limited to omnipotence, omniscience, and moral perfection (which do admit of intrinsic maximums), Anselm’s notion of a greatest possible being seems to avoid the worry expressed by Broad and Gaunilo."