Miguel wrote:

It's more about how to defend and explain S5 for a popular audience, because while S5 is seen as self-evident by a lot of people more acquainted with logic, its use can appear strange to common folk. Which is why, I think, the ontological argument never became a "popular" argument, unlike the cosmological and design arguments. If you say to a normal person that something actually is the case just because it possibly is the case, it can seem like crazy talk to them.

Well, the first thing to point out is that, yes, it seems crazy to say that something actually is the case because it possibly is the case, but that is only a manifestation of a more general and entirely benign point: there are ways of describing every instance of every inference schema in such a way that the logic behind it is obscured. You can, for instance, describe any instance of modus ponens as an inference that something is the case from the fact that something else is the case, as "p and q; therefore r". True: every instance of modus ponens has that form. False: it is by virtue of having that form that any instance of modus ponens is an instance of modus ponens and therefore valid. Similarly, it is true that every instantiation of axiom S5 has the form "possibly p; therefore p", but it is false that in virtue of having that form any instance of axiom S5 is an instance of axiom S5. That the inference, put that way, looks ridiculous simply has nothing to do with its validity. The relevant logical structure has to be articulated for the validity of any inference to be manifest. p, in other words, must have the form "necessarily q".

I commend van Inwagen's explanation of what is being claimed by axiom S5. Part of the reason why the inference strikes non-philosophers as strange is because it can only be stated by regimenting our modal vocabulary in a way that is basically never done in ordinary language. "Possibly" and "necessary" are words with many--of course related--meanings. To the extent that "possibly necessary" might occur in ordinary language, the inference to "necessary" won't hold. For instance, if I say it's possibly necessary for you to brush your teeth after every meal, I would usually mean that the situation might be that you need to brush your teeth after every meal, for the sake of the health of your teeth or gums. But here we have epistemic and practical modalities mixed, and of course it does not follow that you need to brush your teeth after every meal. If we try hard to mean "possibly" and "necessary" to be of the same kind of modality, then we often end up with nonsense. ("It is permissible that it ought to be the case that p" is not a sentence to which I can attach any sense.)

It is hard to think of a case where "possibly necessary" has the right sense. So when you ask a non-philosopher to consider axiom S5, you are asking the non-philosopher to fix his attention on a special metaphysical conception of modality. S5 won't hold for every conception for modality, so if axiom S5 is self-evident, it could only be self-evident to those who are capable of holding this conception before their minds.

So, again, I commend van Inwagen, though I find it hard to regard S5 as self-evident, because I do not see an immediate connection between understanding S5 and assenting to it. It appears to be most obvious when one is taking possible worlds semantics most literally: there just is some set of possible worlds, and what is true at all of them surely does not have anything to do with which one is actual; the possibility operator just moves us to another world, so what is necessary at some world is necessary at each. But again, I don't think putting the matter this way goes very far toward recommending S5.

On the subject of S5 I have recently published a blog entry offering an objection to it which I don't think exists elsewhere.

https://ontologicalinvestigations.blogspot.com/2018/06/origin-essentialism-and-disappearing.html