Strong necessities and reductive theories of modality
I would like to believe that all necessary truths fall into the following two kinds.
1. Analytic truths. By processing the semantic content of such a sentence we can find out that its truth conditions are universally satisfied, no matter how the world turns out and no matter what other world we talk about.
2. Truths whose evaluation at other worlds depends on contingent features of the actual situation. What we can know by linguistic processing is that if these features are so as to make such a sentence true, then it remains true even when we talk about other worlds, that is, when the sentence is embedded in "at world such-and-such" or "necessarily". For example, if we know that there are sheep, we can figure out that "actually, there are sheep" is necessary, because it is a rule of our language that (roughly) "actually p" is true at a world w iff p is true at the actual world. Knowledge about ordinary, contingent features of the current situation together with linguistic competence always suffices to learn that these a posteriori necessary sentences are true.
As I said, I would like to believe that there are no other kinds of necessities. The rival picture is that of modal space as a kind of contingent extension of actuality, inhabited by other universes, or ways things could be (or whatever) that could, for all we know without looking, be any way at all; just as we need telescopes to investigate what galaxies there are, we need verneoscopes (also known as 'modal intuition') to find out what possible worlds there are, whether some of them contain talking donkeys or zombies. This picture, I believe, misunderstands the nature of modality. But I don't want to argue for this here.
Are there necessities that do not belong to the above two kinds? De re necessities, like "Kripke is essentially human", might come to mind. But I think they fall into the second category: if we know about Kripke's non-modal, actual properties, it follows from the rules of our language whether "Kripke is essentially human" is true or not (in a given context).
Modal truths also seem unproblematic. If knowledge of actuality together with linguistic competence suffices to know that "Kripke is essentially human" is true, then it also suffices to know that "necessarily, Kripke is essentially human" is true, because it is a rule of language that for unrestricted modality, iterated modal operators collapse.
But what happens when we reduce modal truths to non-modal truths about spatiotemporally isolated universes or maximal properties (or whatever)? Well, linguistic competence suffices to figure out that whenever something contains more than 12 donkeys, then it also contains more than 11 donkeys. So if we interpret "necessarily, if there are more than 12 donkeys, then there are more than 11 donkeys" as a quantification about spatiotemporally isolated universes containing donkeys, linguistic competence suffices to figure out that the sentence is true.
The problem comes with statements like "possibly, there is a talking donkey", which we might interpret as "there is a spatiotemporally isolated universe containing a talking donkey". This is arguably not a necessity of the second kind: it doesn't contain any rigidifiers. But nor does it seem to be an analytic truth. Denying it is not a sign of linguistic incompetence. And anyway, how could our linguistic conventions guarantee that talking donkeys and spatiotemporally isolated universes (or maximal, uninstantiated properties, or whatever) exist?
Or consider "there are two spatiotemporally unrelated objects". This is not a contradiction. So if there are no strong, brute necessities that prevent it, there could be two spatiotemporally unrelated objects. Alas, on Lewis' conception, there could not: no universe contains two spatiotemporally unrelated objects.