Over at Cosmic Variance, Sean Carroll takes on the ontological argument (i.e., God is perfect, anything perfect must exist since existence is a essential criterion of perfection, therefore God exists), and dissects it with formal symbolic logic. As you might expect, he finds it wanting. Carroll sees the argument as logical but unconvincing because its premises are dubious.
Most of us have a vague feeling that one can’t demonstrate that something exists by logic alone, but Carroll hits on one of the critical flaws in this particular “demonstration”.
The basic problem is that our vague notion of “perfection” isn’t really coherent. Anselm assumes that perfection is possible, and that to exist necessarily is more perfect than to exist contingently. While superficially reasonable, these assumptions don’t really hold up to scrutiny. What exactly is this “perfection” whose existence and necessity we are debating? For example, is perfection blue? You might think not, since perfection doesn’t have any particular color. But aren’t colors good, and therefore the property of being colorless is an imperfection? Likewise, and somewhat more seriously, for questions about whether perfection is timeless, or unchanging, or symmetrical, and so on. Any good-sounding quality that we might be tempted to attribute to “perfection” requires the denial of some other good-sounding quality. At some point a Zen monk will come along and suggest that not existing is a higher perfection than existing.
We have an informal notion of one thing being “better” than another, and so we unthinkingly extrapolate to believe in something that is “the best,” or “perfect.” That’s about as logical as using the fact that there exist larger and larger real numbers to conclude that there must be some largest possible number. In fact the case of perfection is much worse, since there is not single ordering on the set of all possible qualities that might culminate in “perfection.” (Is perfection sweet, or savory?) The very first step in the ontological argument rests on a naive construal of ordinary language, and the chain is no stronger than its weakest link.
Another problem with the argument is that God may not be perfect. Some people may find perfection an essential property of a deity, but lots of liberal religious people don’t necessarily buy it. And of course earlier and now-discarded deities, like the Greek gods, weren’t perfect by modern standards.
I’m still amazed that anyone finds this a convincing argument for God’s existence. For other problems, see the excellent discussion in the Stanford Encyclopedia of Philosophy.