Mereological universalism
I used to agree with Lewis that classical mereology, including mereological universalism, is "perfectly understood, unproblematic, and certain". But then I fell into a dogmatic slumber in which it seemed to me that the debate over mereology is somehow non-substantive: that there is no fact of the matter. I was recently awakened from this slumber by a footnote in Ralf Busse's forthcoming article "The Adequacy of Resemblance Nominalism" (you should read the whole thing: it's terrific). So now I once again think that Lewis was right. Let me describe the slumber and the awakening.
I'll need the following premise, which I won't defend:
The world is not a book.
By this I mean that the world does not have linguistic structure in any meaningful sense. The structure of the world is rather like the structure of a picture.
To illustrate, here is a picture.
The picture has structure insofar as it's not just a blob. Some ways of carving it up are objectively better than others. But the picture's structure does not mirror the structure of the sentences we might use when describing the picture.
Moreover, and more importantly, the picture does not specify a "domain of individuals". One may talk about the picture in a language that quantifies only over the two squares and the circle. Or one could use a language that quantifies over arbitrary fusions of these things. Or one could use a language that doesn't quantify over any individuals at all. None of these ways of talking are wrong. Interpreting a first-order sentence at a picture requires a method that tells us what the quantifiers range over. The picture itself doesn't settle the matter.
Now the world is probably kind of like a picture, except larger and with more dimensions. Like a picture, it doesn't fix a "domain of individuals". Interpreting a first-order sentence at a world, where worlds are things like the actual world rather than set-theoretic models, requires a method that tells us what the quantifiers range over.
From this perspective, it is natural to think that the universalist and nihilist about mereology simply prefer different languages: languages with different interpretations. Each is right in their preferred language, and the world doesn't favour one over the other.
That's the slumber. But as Ralf points out, we can imagine a parallel dispute over conjunction.
Universalists about conjunction hold that from P and Q one can always infer the conjunction P and Q. If you know that it is raining and see that the cat is on the mat, you can infer that it is raining and the cat is on the mat.
Nihilists about conjunction hold that P and Q is only true if P = Q. From the fact that it is raining you can infer that it is raining and it is raining. But you can't combine this information with your knowledge that the cat is on the mat to infer that it is raining and the cat is on the mat. In fact, according to nihilists, it is not true that it is raining and the cat is on the mat.
"Moderates" about conjunction hold that P and Q is sometimes true if P and Q are true (even for distinct P and Q), and sometimes not: it depends on whether "conjunction occurs". Perhaps conjunction occurs whenever P and Q share a common topic.
Here, I think it is obvious that the universalists are right and the others wrong. The others seem to clearly misunderstand what 'and' means. If you think that the inference from P,Q to P and Q is valid only if P=Q, or if you think it is valid only on the assumption that a special event of "conjunction occurs", then you don't understand the meaning of 'and'.
Of course, everyone is free to speak a language without a word for conjunction. It's plausible that one can give an adequate and complete description of fundamental reality in such a language. And of course one can use a language in which 'and' doesn't mean conjunction but, say, disjunction. But arguably that's not what's going on in the above dispute. The imagined nihilist about conjunction doesn't simply think that 'and' expresses propositional identity rather than conjunction. She rather claims to defend the substantive metaphysical hypothesis that conjunction never occurs between distinct propositions. Similarly, the moderate claims that conjunction sometimes occurs and sometimes doesn't. There is no charitable interpretation of their language on which this makes sense.
In the imagined debate over conjunction, the moderates and nihilists presuppose that the world has linguistic structure in an extreme sense. Perhaps they think the world contains irreducible facts (ontological mirror images of sentences), and that any sentence (in English or Ontologese) is true iff there is a corresponding fact. This allows for the possibility that there is a P fact and a Q fact but no P and Q fact, and hence that the conjunction is false even though the conjuncts are true.
But the world is not a book. It does not have linguistic structure, and couldn't possibly have one. So the moderates and nihilists are wrong and confused. They wrongly and confusedly think that for P and Q to be true something more is required in the world than the truth of P and the truth of Q: that a mysterious "conjunction event" or "conjunction fact" must "occur".
Some universalists may share this false and confused idea. They might hold that the mysterious conjunction event always occurs. But one can also be a universalist by correctly and unconfusedly seeing that the truth of P and Q requires nothing more from the world than what's required by the truth of P and the truth of Q: any world that satisfies both of the individual requirements automatically satisfies the requirement imposed by the conjunction.
The same is true for mereology. Of course one can mean all sorts of things by 'part' and 'fusion'. But sensible universalists use these expressions in a metaphysically non-committal way. Fusion of individuals is much like conjunction of propositions. If there's an individual A and an individual B, nothing else is required of the world for there to be the fusion A+B. No mysterious "composition" must "occur".
There's nothing wrong with speaking a language that only quantifies over simples. But this language can't have the 'fusion' operator, if that is supposed to have anything like the meaning it has for the universalist. It's fine to use 'fusion' with an entirely different meaning, so that 'C is a fusion of A and B' means, say, that C is a unicorn, or that C is an organism. But that's not what nihilists or moderates about mereology mean. Rather, they assume that the world directly specifies a domain of individuals, and that a special composition event would have to occur for there to be a fusion of two individuals. And that's not a harmless matter of linguistic choice. It's wrong and confused.