"Rationality" is not a (meta-)logical property. You're right that the proof shows that, logically speaking, if one buys the premises, God must exist. But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God.
> But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God.
I think that is a very weak conclusion, there are an infinite number of proofs for god that are valid so long as you accept their particular premises. It is the specific plausibility of the premises and definitions implied in St. Anselm’s Ontological Argument that make it of interest.
What this shows colloquially is that if you are arguing against god, you must either reject this definition of god or one of the other premises. If you don't your argument is self-contradictory.
That's kind of my point. It's not some knock-down argument, but it's a very nuanced result that achieved a few very neat things:
1) Formalized Anselm's "greatest of which can be conceived of" notion.
2) The concept of "accidental" (contingent) and "non-accidental" (necessary) properties had existed since antiquity, but modal logic essentially formalized the idea.
3) Showed that Anselm's argument was indeed valid. Again, this project took around 1000 years.
Plantinga did a lot of work in trying to make the premises more palatable, but of course, the argument for the existence of God still rages on. (As I'm sure it will far after we're gone.)
