Why the ontological argument doesn't work

(This is extracted from an article I wrote in uk.religion.christian on 2002-09-28. The question comes up about once a year, and I thought it was worth saving. I've edited it a bit.)

The ontological argument doesn't work because it's got a sodding great big hole where a logical inference ought to be. No, sorry, my mistake: it's got lots of sodding big holes where logical inferences ought to be. It goes like this:

  1. Consider the greatest possible thing X.
  2. Any possible thing that exists is greater than an otherwise identical possible thing that doesn't exist.
  3. If X doesn't exist then it isn't greatest, by #2.
  4. Therefore X does exist.

#1 is broken because there needn't be a "greatest possible thing". Inviting me to consider it doesn't make it exist, no matter how aetiolated the sense of "exist" that's being used. You can ask me to consider the smallest counterexample to Fermat's last theorem, and I can do so and maybe even prove a few things about "it", but as it happens there isn't one. Not in any possible world.

#1 and #2 are both broken because the meaning of "greatest" isn't specified.

#2 is broken because it doesn't make any sense to talk about how "great" something is that doesn't exist. You can talk about how great it would be if it did exist, but in that case it's far from clear that existing things have to be greater than nonexisting ones. But asking for a comparison of the greatness of an actual object and of a merely hypothetical one is like asking for a comparison of the greatness of pi and of pie.

#2 is broken because it's far from clear that there "are" ever two "things" that are the same except that one actually exists and the other doesn't.

#3 is fine.

#4 is rubbish. If X doesn't exist then it isn't greatest, and so it turns out that there wasn't a greatest thing after all. Too bad. It's no good to go whining "But I told you to consider it, so you can't just say it doesn't exist", because I can, so there.

The argument has more logical holes than it has steps.

Note: I've heard that Anselm didn't really intend the ontological argument to be some sort of absolute proof of the existence of God (or even of a Most Perfect Thing); that it's not so much a proof as an expression of how things look once you get acquainted with the reality of God, or something like that. That's possible. I'm concerned with the ontological argument as it's generally "used" now.