Microphysical mereological nihilists believe that only simples exist---things like leptons and quarks, perhaps. You can be a mereological nihilist without being a microphysical mereological nihilist (e.g. you can believe that ordinary objects are simples, or that the whole world is one great lumpy simple. Elsewhere I use this observation to respond to some objections to microphysical mereological nihilism). But it's not so much fun.
If you're a microphysical mereological nihilist, you're likely to start getting worried that you're committed to an almost universal error-theory of ordinary discourse. (Even if you're not worried by that, your friends and readers are likely to be). So the MMN-ists tend to find ways of sweetening the pill. Van Inwagen paraphrases ordinary statements like "the cat is on the mat" into plural talk (the things arranged cat-wise are located above the things arranged mat-wise"). Dorr wants us to go fictionalist: "According to the fiction of composition, the cat is on the mat"). There'll be some dispute at this point about the status of these substitutes. I don't want to get into that here though.
I want to push for a different strategy. The way to do semantics is to do possible world semantics. And to do possible world semantics, you don't merely talk about things and sets of things drawn from the actual world: you assign possible-worlds intensions as semantic values. For example, the possible-worlds semantic value of "is a cordate" is going to be something like a function from possible worlds to the things which have hearts in those worlds. And (I assume, contra e.g. Williamson) that there could be something that doesn't exist in the actual world, but nevertheless has a heart. I'm assuming that this function is a set, and sets that have merely possible objects in their transitive closure are at least as dubious, ontologically speaking, as merely possible objects themselves.
Philosophers prepared to do pw-semantics, therefore, owe some account of this talk about stuff that doesn't actually exist, but might have done. And so they give some theories. The one that I like best is Ted Sider's "ersatz pluriverse" idea. You can think of this as a kind of fictionalism about possiblia-talk. You construct a big sentence that accurately describes all the possibilities. Statements about possibilia will be ok so long as they follow from the pluriverse sentence. (I know this is pretty sketchy: best to look at Sider's version for the details).
Let's call the possibilia talk vindicated by the construction Sider describes, the "initial" possibila talk. Sider mentions various things you might want to add into the pluriverse sentence. If you want to talk about sets containing possible objects drawn from different worlds (e.g. to do possible world semantics) then you'll want to put some set-existence principles into your pluriverse sentence. If you want to talk about transworld fusions, you need to put some mereological principles into the pluriverse sentence. If you add a principle of universal composition into the pluriverse sentence, your pluriverse sentence will allow you to go along with David Lewis's talk of arbitrary fusions of possibilia.
Now Sider himself believes that, in reality, universal composition holds. The microphysical mereological nihilist does not believe this. The pluriverse sentence we are considering says that in the actual world, there are lots of composite objects. Sider thinks this is a respect in which it describes reality aright; the MMN-ist will think that this is a respect in which it misdescribes reality.
I think the MMN-ist should use the pluriverse sentence we've just described to introduce possibilia talk. They will have to bear in mind that in some respects, it misdescribes reality: but after all, *everyone* has to agree with that. Sider thinks it misdescribes reality in saying that merely possible objects, and transworld fusions and sets thereof, exist---the MMN-ist simply thinks that it's inaccuracy extends to the actual world. Both sides, of course, can specify exactly which bits they think accurately describe reality, and which are artefactual.
The MMN-ist, along with everyone else, already has the burden of vindicating possibilia-talk (and sets of possibilia, etc) in order to get the ontology required for pw-semantics. But when the MMN-ist follows the pluriverse route (and includes composition priniciples within the pluriverse sentence), they get a welcome side-benefit. Not only do they gain the required "virtual" other-worldly objects; they also get "virtual" actual-worldy objects.
The upshot is that when it comes to doing possible-world semantics, the MMN-ist can happily assign to "cordate" an intension that (at the actual world) contains macroscopic objects, just as Sider and other assign to "cordate" an intension that (at other worlds) contain merely possible objects. And sentences such as "there exist cordates" will be true in exactly the same sense as it is for Sider: the intension maps the actual world to a non-empty set of entities.
So we've no need for special paraphrases, or special-purpose fictionalizing constructions, in pursuit of some novel sense in which "there are cordates" is true for the MMN-ist. The flipside is that we can't read off metaphysical commitments from such true existential sentences. Hey ho.
(cross-posted on Metaphysical Values)