In order to understand the place this argument has in the history of philosophy, it is important to understand the essence of the argument as Anselm first conceived it.
A key to understand the ontological argument is understanding the idea of "perfections."
There are various kinds of so-called perfections. Size, intelligence, beauty, power, benevolence, and so forth -- all these qualities are called perfections. And there are various degrees of these perfections. What is more intelligent is more perfect as regards intelligence; what is more beautiful is more perfect as regards beauty; and so forth.
Here's a short, and very general description of the ontological argument.
Of course, Anselm does not present the argument in this form, he presents it as a prayer directed to God. Obviously Anselm thought this argument was valid and persuasive, and it still has many defenders, but there have also been a number of people who claim that the ontological argument, at least as Anselm articulated it, does not stand up to strict logical scrutiny.
One of the earliest recorded objections to Anselm's argument is was raised by one of Anselm's contemporaries, Gaunilo. Gaunilo invited his readers to think of the greatest, or most perfect, conceivable island. No such island exists, right? But in that case we aren't thinking of the greatest conceivable island, because the greatest conceivable island would exist, as well as having all those other desirable properties. Since we can conceive of this greatest or most perfect conceivable island, then it must exist.
Of course, this argument seems silly, but Gaunilo claims that it is no worse than Anselm's. In the same way, you could, if you wanted to, "prove" the existence of the most perfect hamburger, the most perfect dumpster, or the most perfect toilet. Defenders of Anselm's argument responded that the idea of an island does not include the notion of perfection, the perfection is merely tacked on, while the concept of God cannot be separated from the notion of perfection. This explains their claim that there is an explanation for the failure of Gaunilo's argument – namely the fact that the island's perfection is contingent -- which doesn't effect the Ontological Argument.
Another traditional criticism of the argument is that existence is not a perfection, because existence is not a property. If existence were a property of items, including God, then it might be a perfection. But since it's not a property, it cannot be a perfection; only properties of things can be perfections of things. But it is hard to understand how existence could not be a property, and many philosophers have rejected this objection because it entails all kinds of other unwanted consequences.
A third criticism of Anselm's argument rests on the claim that, even if existence is a property, it is still not a perfection. Either something exists or it doesn't; there aren't any degrees of existence. Something can't be more partially existent. It is claimed that this is sufficient reason to believe that existence can't be a perfection because perfections exist along a continuous scale. Defenders of the ontological argument have replied to this objection that, even granted that there aren't degrees of existence, surely existence is more perfect than nonexistence; and in any case, something that exists is greater than something that doesn't.
Obviously Anselm thought this argument was valid and persuasive, and it still has many defenders, but there have also been a number of people who claim that the ontological argument, at least as Anselm articulated it, does not stand up to strict logical scrutiny.
Some of those who've argued that the ontological argument fails are content to leave it at that, either because they don't believe that God exists, or because they believe the existence of God is demonstrated on other grounds. Others, like [Alvin Plantinga]?, Kurt Gödel, Gottfried Leibniz and Aquinas have reformulated the argument in order to create stronger versions of the argument.
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