There are necessary truths, but might there not have been? The actual world contains necessities, but are there possible worlds in which nothing is necessary? Is necessity necessary?
If necessity were a matter of language or human convention, the answer would be that necessity is not necessary, since language and human convention do not necessarily exist; but what about good old-fashioned Aristotelian de re necessity? Things have essences as matters stand, but could there be things that lack essence—a world in which everything is contingent? The question divides into several sub-questions, according to the type of necessity we are considering: logical and mathematical necessity, analytic necessity, necessity of identity, necessity of kind, necessity or origin, necessity of constitution. If logical laws and mathematical truths hold in all worlds, then presumably the attendant necessities will also hold. In every world it will be necessary that there are no contradictions; there is no world in which 2+2+=4 is not necessary; the number 2 exists in every world and in every world it is necessarily even. In the case of analytic necessity it depends on whether every world contains concepts: if some do not, then there will be no analytic necessities concerning concepts in that world. What about the necessity of identity? Surely this will hold in every world, since all it takes is for the existence of things with self-identity, i.e. things of any conceivable kind. But the really interesting cases are the last three on my list, and here the answers are less obvious.
If a given world contains such things as chemical elements and animal species, it presumably instantiates the relevant necessities: it will be necessary that water is H2O and a cat will necessarily be a cat. There are no worlds in which volumes of water are not necessarily H2O and cats are not necessarily cats. It is not just that all (actual) cats are necessarily cats but that necessarily all (possible) cats are necessarily cats. There are no possible cats that are not cats in their essence. But it doesn’t follow that every possible object is necessarily of the kind that it is—couldn’t there be a type of object that had no essence at all? The idea does not seem manifestly contradictory or absurd. What about a basic point particle? It would occupy a particular position in space but that would be a contingent property of the particle—and couldn’t that be its only property? But this is not so obvious on reflection: Is it not necessarily a point-like entity? Would it not have such properties as mass or charge and wouldn’t they be essential properties of it? In fact, given that every possible existent has a nature, must it not follow that it has an essence? If something constitutes an object’s nature, isn’t it part of that object’s essence, i.e. what it could not lack?
It might be retorted that we need to strip the object down still further—not an elementary material particle but a bare particular—something that simply is but without any determinate nature. But doesn’t even this putative particular also have a nature of sorts—as bare and as a particular? So aren’t these its essence? Even if the notion of a bare particular makes metaphysical sense, it doesn’t avoid necessity, because it is necessarily what it is intrinsically, i.e. a bare particular. Everything must be of some kind, and that kind will form its essence, however thin and simple the kind may be. Nothing has only contingent properties. It is not that some things have essences but others don’t.
Necessity of origin is trickier. Again, we need not assume that all worlds will contain organisms or artifacts, so this kind of necessity of origin will not hold across all worlds, while other kinds may (planets, particles). But might there be worlds in which there are objects that lack any origin and hence don’t exhibit necessity of origin? What about a world of eternal objects or a world in which nothing comes from anything distinct from itself? Consider a world of eternal and immutable material particles–they come from nothing and have no time of origin: how can they be subject to the necessity of origin? To be concrete, do electrons exhibit necessity of origin? Actual electrons had their origin in the big bang, so this might be necessary to their identity as the electron they are (thiselectron could not have originated in anything but the actual big bang); but what about conceivable electrons that originate from nothing at all? Numbers cannot have necessary origin because they have no origin, and electrons might follow suit. But isn’t there room for an extended necessity of origin thesis, namely that these (non-actual) electrons necessarily come from nothing? That is, they are necessarily causeless and timeless—these electrons could not exist in a world in which they were caused and temporally finite. They necessarily don’t have an origin—or they necessarily have an origin that is confined to themselves and the reaches of eternity (the necessity of non-origin). So again, it is hard to avoid these kinds of de re necessity, though we may have to modify and extend such necessities to fit the merely possible entities we are postulating.
Similarly with necessity of constitution: we can postulate a world in which things have no constitution—in which everything is a primitive particular—but we can’t rid that world of an analogous modal thesis, namely that every such particular is necessarily not constituted by something other than itself. Even if the objects don’t break down into parts or stem from something with which they are not numerically identical, we can still formulate the thesis—which appears true—that they are necessarily constituted by themselves or necessarily not constituted at all. We are still trafficking in essence as it relates to constitution; we have not got beyond such questions.
None of this is to say that necessities must necessarily be recognized: the point is metaphysical not epistemological. There can clearly be worlds in which the prevailing necessities are not recognized by any thinking being, since such beings may not exist in those worlds; but that has no relevance to the question of what worlds are metaphysically possible. The world would exhibit the necessities it does irrespective of anyone’s knowledge of necessity. People could entirely repudiate the existence of necessities in every world, but that doesn’t show that there are no necessities. The point I have been urging is that it is hard to escape the existence of necessity: no matter what world you travel to, even some very fanciful ones, necessity will be staring back at you, even if it exists in an unfamiliar form. Reality always contains necessities, no matter what kind of reality it is.
This raises a difficult question: Why is necessity so deeply embedded in reality? What is the reason that necessity is (metaphysically) inescapable? On the face of it the world could have consisted of nothing but contingent truths (this is what many philosophers still believe about the actual world), so why is it that necessity is so deeply embedded in reality? Why did God have to make a world exhibiting necessities? Don’t say, “Because everything has to have a nature”: that is no doubt true, but it just re-raises the question, viz. why must everything have a nature? Everything must have properties, to be sure, but why must these properties form a nature in the strong modal sense, i.e. properties that a thing cannot lack and still be itself? Why can’t things instantiate all their properties contingently? And yet nothing does, either actual or possible. The universe is necessarily a home for necessity—necessity is not just an accidental feature of the universe. Nor can God do much about it: even he could not choose to create a world devoid of necessity—the “null necessity world”. Once he creates anything he necessarily builds necessity into it, even the barest of bare particulars. However, it is not clear what the explanation of this metaphysical fact is, or whether there could be an explanation of it: but fact it appears to be. No one said modal metaphysics would be easy.
And then there is this puzzle: if necessity is as pervasive and inescapable as it appears to be, why has it been so controversial? Why have so many people rejected its very existence, let alone its ubiquity? Why has it been so difficult to get people to take it seriously? If it is present in everything—actual and conceivable—why is it so hard for people to recognize? 
 Of course, necessity cannot be literally seen, but it is difficult to believe that crude empiricism could be the reason for the widespread suspicion of necessity. It must have to do with how different necessity is from other aspects of reality (space, time, matter, causality, etc). Modality presents itself as another dimension of reality—another plane of existence (all those worlds). It is tempting to postulate a dualism of the modal and the non-modal so different are the two. If the essence of matter is extension, as Descartes maintained, then the fact that matter is necessarily extended is not itself a mode of extension—so it cannot be a material property: hence matter-modality dualism. Modal realism is metaphysically disturbing.