Saint (Anselm's of Canterbury's Ontological argument) goes as follows:
Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.
(1) A maximally great being (one than which nothing
(2) It is greater to exist in reality than to exist merely in the understanding.
(3) Therefore, if the maximally great being existed only in the understanding, it would be less than maximally great.
The earliest objection to this argument was proposed by Anselm's contemporary and fellow monk Gaunilo in his On Behalf of the Fool (Psalm
14: 'The fool has said in his heart "There is no God"'). According to
Gaunilo, the argument must be defective, because we can use an argument
of the very same form to demonstrate the existence of such absurdities
as an island (or chocolate sundae, or hamster, for that matter) than
which none greater can be conceived. (Says Gaunilo: 'I know not which I
ought to regard as the greater fool: myself, supposing that I should
allow this proof; or him, if he should suppose that he had established
with any certainty the existence of this island.') But Anselm has a
reply: the notion of a maximally great island, like that of a largest
integer; does not make sense, cannot be exemplified. The reason is that
the properties that make for greatness in an island - size, number of
palm trees, quality of coconuts - do not have intrinsic maxima; for any
island, no matter how large and no matter how many palm trees, it is
possible that there he one even larger and with more palm trees. But the
properties that make for greatness in a being -knowledge, power and
goodness, for example - do have intrinsic maxima: omniscience,
omnipotence and being perfectly good.
Excerpted from, "Arguments for the Existence of God" found in The Routledge Encyclopedia of Philosophy, Edward Craig ed. Routledge:London, 1998.