The so-called ontological argument for the existence of God was formulated by the medieval and philosopher, St. Anselm (1033-1109), though it did not acquire its modern name till that was assigned by Kant in the eighteenth century (Cahn, Kitcher, and Sher, p. 557; all subsequent page references are from this work).
Anselm's argument is, briefly, as follows: Imagine the greatest entity that can possibly be conceived of as existing -- setting aside for the moment whether it actually does exist or not. Now, since by definition the greatest entity we can conceive of existing is God, what we are imagining is in fact God. Thus, by stipulation, we are imagining God, whether or not God actually exists.
We now turn to the question of whether or not this greatest imaginable entity--God--does in fact exist. Suppose, hypothetically, that it does not. But if this is the case, then what we are imagining here is not, in fact, the "greatest imaginable entity," since it is possible to imagine a greater one, namely a greatest imaginable entity that does, in fact, exist (p 559).
Thus, in Anselm's view, a non-existent "greatest imaginable entity" is a contradiction in terms, since it is necessarily not so great as an actual "greatest imaginable entity." Among the attributes of the greatest imaginable entity is, necessarily, its existence. Therefore, God, so defined, must exist. This is the essential structure of the ontological argument.
To this argument, Anselm's contemporary, the monk Gaunilo, made the following response: It is possible, Gaunilo, to imagine an island that, though physically undiscoverable, is greater in wealth and beauty than all known lands. Yet this hypothetical island, if it did not exist, would not be more wonderful than any real land. Therefore, the island that meets this conceptual standard, must, by an argument parallel to Anselm's, really exist (p. 561).
We could extend this counter-argument to...