I think Ontological Arguments (OAs) are useful for motivating theistic belief. That’s a controversial take, but I’ve seen the argument motivate people on the ground and have found it to be compelling personally.
(a) Parity arguments are the strongest objections and are usually taken as decisive in the philosophical community. These types of objections reconstruct parallel type premises, like “it’s possible for God to not exist,” and then conclude that he doesn’t exist.
(b) Existence is not a predicate is often pressed as a mantra against the argument, but has evaporated in light of the modal versions of the OA. With its best face, this objection clarifies that we’re concerned with hypothetical beings that, if they existed, would be greater than non-existing beings. The greatness of a being existing in reality would be greater than a being existing only in the mind if it existed, so this premise cannot be used to establish the existence of the being in reality. But modal versions are immune to this objection.
(c) Arguments from value-nihilism are also popular, and in my experience are the most often used objection by the internet atheist community. These reject that there are actually greater or lesser objects, so there’s no possible “greatest” being.
So (a) and (c) are viable. To break the parity objection, we need to find a way to support the possibility of God existing over against the possibility of his not existing. Rasmussen has done some great work in this area with his modal continuity thesis: We see some degrees of value instantiated in the world, and this gives us reason to think that more of it could possibly be instantiated, all the way up to maximal instantiation. This maneuver may itself be vulnerable to a parity objection--Rasmussen argues that it isn’t, given that we observe the presence of value, but not its absence. I think this is a promising way forward and should be pursued further.
What about (c)? I think, even if we have to bite the bullet and say that OAs are committed to the objective existence of value, that the argument still has weight. We may be able to defend objective value on independent grounds. It’s also the case that many non-theistic philosophers believe in objective value, and if this concession is all that’s required for the argument to go through, it should have weight for these sort of non-theistic philosophers.
But perhaps the OA doesn’t need to make value judgments. Maybe it’d work on a weaker commitment: Instead of the term “maximally great being,” we can substitute with the phrase “without limits.” Speaking of “limits” does not seem to necessarily imply a value judgement. I think we can see something like this approach in Leibniz’s version of the OA: "I call 'perfection' every simple quality which is positive and absolute, i.e., which expresses whatever it expresses without any limits." While the word “perfection” certainly seems like a value judgment, the way he explains the term is much less clearly a value judgment.
