Of course it's valid! A world-renowned philosopher like Plantinga wouldn't publish a proof that's not valid. That's like saying Dijkstra's code compiles :)
The main problem with ontological arguments (and why, even as a Christian, I don't like them) is because they seem to embed the conclusion in their first premise. E.g.: the possibility of a maximally great being seems to definitionally imply its necessity. Why? Because such a being B must have some properties P = { ? ? ? ... }. We may not be sure what's inside P, but we know, with absolute certainty, that existence is in there.
Kant would disagree. He thinks that existence is not a property. This is a rare case when I think he's right.
> E.g.: the possibility of a maximally great being seems to definitionally imply its necessity.
One of my favourite tongue-in-cheeek replies I read to these ontological arguments: Ah, but surely there is no greater being than one who could create the universe despite not existing!
> The main problem with ontological arguments (and why, even as a Christian, I don't like them) is because they seem to embed the conclusion in their first premise
But that is also true of the informal rhetorical arguments that are more common in (christian) apologetics.
The gift of formal proofs is that they make explicit and unavoidable this embedding of conclusion in premise, which is fundamental to all (epistemologically rational) apologetics
The main problem with ontological arguments (and why, even as a Christian, I don't like them) is because they seem to embed the conclusion in their first premise. E.g.: the possibility of a maximally great being seems to definitionally imply its necessity. Why? Because such a being B must have some properties P = { ? ? ? ... }. We may not be sure what's inside P, but we know, with absolute certainty, that existence is in there.
Kant would disagree. He thinks that existence is not a property. This is a rare case when I think he's right.