- Mereology is a theory about parts and wholes, and, more generally, about composition. If it is formulated in terms of plural variables and plural quantifiers (in addition to ordinary variables and quantifiers), it consists of the logical consequences of the following two axioms:
→ Parthood is transitive.
→ For any xs, those xs have one and only one fusion.
The range of the variables of Mereology is usually taken to be unrestricted, but in this paper I shall consider only material objects (whatever those are) and their parts – if material objects can have parts that are not themselves material objects. (Some people would not be comfortable with the idea that, say, quarks and electrons are "material objects"; but most people would want to say that material objects have quarks and electrons as parts. And then, of course, there are – or, rather, in my view, there aren't – "tropes" and "immanent universals1" and various other things that some people think are parts of material objects and yet are not themselves material objects.)
- David Lewis has recently advanced2 the thesis that Mereology is "ontologically innocent." One can well imagine this thesis being received with incredulous stares. There might be speeches behind some of these stares. Here are two speeches that I can imagine.
- I believe only in metaphysical simples, things without proper parts. This makes for a neat, manageable ontology of the material world, although (I concede) I have to do a lot of hard philosophical work to explain what's "good" about typical utterances of 'There are three apples in the bowl' and "bad" about typical utterances of 'There are three pixies in the bowl'. (For, by my lights, the world is, in the strict and philosophical sense, as empty of apples – which would be composite objects if they existed – as it is of pixies.) If I were to accept Mereology, I'd have to believe in all sorts of things I don't believe in now. I'd have to believe that all sorts of properties that I now believe have empty extensions had non-empty extensions. I'd face all sorts of philosophical problems that I don't face now – problems about the identities of composite objects across time or across worlds, for example. Tell me that if I accept Mereology I'll end up with a more satisfactory metaphysic, and I'll listen. Tell me that the new problems I'll face have solutions or are more tractable than the problems I currently face, and I'll listen. But don't tell me that Mereology is innocent. If you tell me that, you're no better than the salesman who tells me that a new Acme furnace is free because the money it saves me will eventually equal its cost. "Innocent" is like "free," and "free" does not mean the same as "well worth it."
- I believe that the statue and the lump of gold3 that constitutes it are numerically distinct. I believe this because I believe that the statue4 and the lump have different properties. Even if God created the statue5 (and, of course, the lump) ex nihil, and the statue6 remained in existence and unchanged for a year, after which God annihilated the statue7 (and the lump), the lump had the property could survive radical deformation and the statue8 did not have that property. And the statue9 had the property is necessarily conterminous with a statue10, and the lump did not have this property. But there are certain gold atoms such that the statue11 was one fusion of those gold atoms and the lump was another. My thesis (I concede) faces philosophical problems. Ask me how each of the two properties I've mentioned manages to get associated with one of the fusions of the gold atoms and not with the other, and I'll agree that I need to address that very serious question. But don't tell me that any theory that – like Mereology, with its unique fusions – is incompatible with my ontology of the material world is innocent.
- Lewis has an argument for the innocence of mereology. Sometimes he puts the argument like this: Composition is a kind of identity. Therefore, in accepting fusions, you are accepting only something that is identical with what you have already accepted, and nothing could be more ontologically innocent than that. And Mereology asks you to accept nothing more than fusions of what you already accept. Lewis eventually qualifies the thesis that composition is a kind of identity, and his qualifications seem to me to be significant enough that I should want to call the argument based on the qualified premise a statement of a new and different argument. For the present, I shall consider only the unqualified argument.
Philosophical Perspectives, Vol. 8, Logic and Language (1994), pp. 207-220
Footnote 2: in "Lewis (David) - Parts of Classes", pp. 81-7.
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