November 20, 2008

What Is Composition?

I am currently doing research for a term paper in which I will argue that composition requires a 'principle of unity'. That is (to a first approximation), that given some objects, the xs, there cannot be any y which has all and only the xs as parts unless there is some feature of the world which bestows some degree of unity or oneness on y. I hope to argue that this is a conceptual truth - that is, that it flows from what we mean by composition. I haven't finished reading up on the subject yet, so there may already be some arguments in the literature against my claims, but what I want to do here is to try out some ideas about what composition is supposed to be, in the hope of getting some feedback. I am not going to try to argue for my claim about principles of unity (yet).

Composition is the relation which holds between a composite object and its parts. Peter van Inwagen gives this formal definition of composition: "the xs compose y [=df.] the xs are all parts of y and no two of the xs overlap and every part of y overlaps at least one of the xs." (Material Beings, p 29) Van Inwagen goes on to present his famous 'Special Composition Question' as follows:

When is it true that:
∃y the xs compose y?

More formally, can we find a sentence which contains no mereological terms and in which no variable but 'the xs' is free and which is necessarily extensionally equivalent to '&exits;y the xs compose y'? ... Less formally, in what circumstances do things add up to or compose something? When does unity arise out of plurality? (pp. 30-31)


What would it mean for the xs to compose some y? It would mean that there was some one object in the world such that it has all and only the xs as its parts (at some one level of decomposition). Trenton Merricks describes the question of whether the water molecules which fill a swimming pool compose a whole as follows:
Consider the water in the swimming pool. Some - such as those who endorse unrestricted composition or those who believe in a kind of entity called 'a mass' - say that 'the water in the swimming pool' refers to a big material object. That object, they maintain, is shaped like a plaster cast of the swimming pool; it is about as tall as the pool is deep; it, like all material objects, has a mass and a centre of gravity ... Why believe there is a big wet chunky thing that fits snugly into the pool? (Objects and Persons, pp. 30-31)

To say that the water molecules compose a whole is to say that there is some one thing, 'the water in the pool' that has all of them as parts. It is to say that there exists such a thing as 'the water in the pool.'

We might next ask, what does it mean to assert that such a thing exists? How does this differ from the claim that the molecules exist?

If we have a linguistic bent, we might, like Aristotle, say that a thing exists, in the relevant sense, if it is an ultimate subject of predication (see Categories 5). Or, equivalently, we might adopt Quine's 'semantical formula:' "to be is to be the value of a variable" ("On What There Is," reprinted in Mellor and Oliver, eds., Properties, p. 85). That is, we might say that the things that exist are those to which someone would have to attribute certain properties in order to fully and correctly describe the world.

If we say this, then we can better understand what is meant by the assertion that the xs compose some y. We mean that there are many things, the xs, which are the parts of some thing, y, and the xs and y all instantiate properties which would have to be included in a full description of the world.

Consider my desk. It is, let us suppose, composed of physical simples. That is, there are some physical simples (things which have no parts; in this case, presumably quarks, leptons, and bosons) which are the parts of my desk. I say, 'each of the simples composing my desk has wave-like properties' and 'my desk is black'. If these references are ineliminable from the correct description of the world, then the simples and the desk all exist, and the simples are parts of the desk, so if there are 1,000,000 simples composing my desk (I have no idea how many there actually would be), then there would be (at least) 1,000,001 things in the region fully occupied by my desk. We don't normally count this way. We normally count at one level of decomposition at a time - counting, for instance, one desk, or four desk parts (two legs, one set of drawers, and a surface), or lots of molecules, or lots of atoms, or lots of fundamental particles. Nevertheless, the truth of the matter is, by hypothesis, that there are 1,000,001 things.

There is, however, a challenge to this. The challenge considers a possibility I ignored earlier. We said that if the xs compose some y, then there is some thing y, such that it has all and only the xs as parts (at some level of decomposition). But it will only follow that (if there are 1,000,000 xs) there are at least 1,000,001 things if y has not already been counted. This might, at first, seem silly. After all, it's not as if y is one of the xs. y is, in this case, my desk, and the xs are all simples. Surely my desk is not a simple! After all, in addition to being made of particles, I can take it apart with a screwdriver (it came from Ikea). Surely, then, it has parts. But (ex hypothesi) none of the xs has parts. Furthermore, each of the xs is a proper part of y and, by definition, no object is a proper part of itself. So y is not identical to any one of the xs.

This much is obvious, and is not at all what the objector intended. The objector intended to make the claim that composition is identity. She claims that the xs are, collectively, identical to y.

This is not such obvious nonsense as the claim that y is among the xs. We might attempt to repel the objection by a simple appeal to Leibniz's Law, which states that, if x=y, then anything that can be correctly predicated of x can be correctly predicated of y (in transparently referential contexts, or some such). We might attempt to repel it this way: there are 1,000,000 xs, and only one y, and the same thing cannot be both 1,000,000 and one. But, the objector continues, isn't this just the way composition works? This thing is 1,000,000 particles, but it is one desk.

Let us consider what identity is supposed to be. Identity is, quite simply, that relation which holds all and only between every object and itself. This is where Leibniz's Law comes from: if x=y, then there are not two objects, x and y. Rather, there is some one object which is called both x and y, and that object, if it is to exist or even be possible, had better not have contradictory properties! So, if my desk is identical to its parts, then there is some one object which is sometimes called 'my desk', and sometimes called 'the parts of my desk'. But 'the parts of my desk' refers to 1,000,000 objects. If there is no one object called 'the parts of my desk' then surely there is no one object sometimes called 'my desk' and sometimes called 'the parts of my desk'!

Or is there some one object called ' the parts of my desk'? Perhaps grammar misleads us: the one expression encourages us to consider the object as one, and the other encourages us to consider the object as many. What is a composite object if not an object which is at once both one and many?

This is nonsense again. No object can be both one and many. A composite object, if such things exist, is one object which has a number of other objects as parts. We cannot say of my desk 'it is 1,000,000 particles,' but only, 'it has 1,000,000 particles as parts.'

Composition, then, is the relation that holds between a composite object and its parts. In order to enter into this relation, the object and its parts must be distinct. No object composes itself.

Posted by Kenny at November 20, 2008 3:03 PM
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Comments

Your contact page is busted.

This made me think of your writings page.
w.weblogcartoons.com/cartoons/sifting-through-ideas.gif

Not because the blog is trash (far from it)... just the 3 stacks for writings.

Posted by: Jen at November 23, 2008 11:40 AM

Hmm... You seem to be right. I have a contact link, but no contact page. I'll have to fix that. Sorry.

Posted by: Kenny at November 23, 2008 2:37 PM

I think you're very close to correct, but why characterize composition as a relation rather than as a state of affairs? Relations between wholes and their parts are suspicious, since such relations involve a redundancy: a part must show up on both sides of the relation, as incorporated into the whole on the whole-side, and "by itself" on the part-side. For this reason, the purported relata are not wholly distinct, but overlap precisely in the part.

Posted by: Aaron Preston at December 9, 2008 8:04 AM

Aaron - If I recall correctly, Armstrong (who wrote the book, A World of States of Affairs, so I kind of consider him the 'state of affairs' guy) defines a 'state of affairs' as simply a particular instantiation of a property or relation, so that won't help here. Did you have some other definition in mind?

I don't know why a relation between a whole and its parts should be suspicious or redundant. The identity relation, for instance, involves the same object on both sides, but is not redundant in any important sense. Furthermore, my claim is that the whole is in fact distinct from its parts, in what sense, then, are the parts 'on both sides'? You say that they "are not wholly distinct, but overlap precisely in the part." I suppose this is true by the definitions of 'wholly', 'overlap', and 'part', but I don't see why it's important here.

It seems to me that what you are concerned with is what Ted Sider, in his recent paper 'Parthood', calls the 'peculiar intimacy' of the part-whole relation, and which he explains in part by two inheritance theses: the inheritance of intrinsicality and the inheritance of location. Perhaps I will write another post discussing this issue.

Posted by: Kenny at December 9, 2008 10:24 AM

Hi Kenny,

By a "state of affairs" I have in mind something closer to a Wittgensteinian "fact" or a Reinachian "sachverhalt". On Reinach, see this informative paper by Barry Smith:

http://ontology.buffalo.edu/smith/articles/cogsvh/cogsvh.html

I know that in logic we *treat* identity as a relation, but it can't really *be* a relation, can it? Relations stand between things, but in identity you don't have multiple things, just one thing. I'm wary of letting the demands of formal systems carry too much weight in metaphysics...

Posted by: Aaron Preston at December 9, 2008 7:03 PM

Aaron - I suppose this all depends on the theory of properties, relations, and abstracta generally. If one has an ontology of (sparse) relations (or properties), then it presumably doesn't include 'purely logical' relations (properties).

However, I do not here intend to use 'relation' in an ontological way. I'm providing an analysis of the term composition (and its cognates), and I simply mean to say that, as a matter of semantic analysis, we mean to pick out a particular relation, in the formal logic/set theory sense of relation: a set of ordered sequences of entities. So when I say "Composition is the relation which holds between a composite object and its parts" I just mean (more formally):

Composition =df. {(x1, x2, x3 ... xn, y) : y is a composite whole & x1, x2, x3 ... xn are the parts of y}

(Note that an ordered sequence can have duplicate entries.)

We write this in philosophical psuedo-English as 'y1, y2, y3 ... yn compose x'. We then ask, when do such entities exist?

None of this has to depend on any particular ontology of relations.

I am, however, interested in this sort of thing independently. I may take a look at the Barry Smith article you link some if I get a chance before the beginning of next quarter.

Posted by: Kenny at December 9, 2008 10:17 PM

Kenny,

If you haven't already, you might read what Mark Johnston has to say about constitution. Take a look at:

"Constitution is not Identity" (on JSTOR)
"Constitution" (in the Oxford Handbook of Contemporary Philosophy, edited by Michael Smith and Frank Jackson)
"Hylomorphism" (in the recent issue of the Journal of Philosophy on parts and wholes)

Posted by: Eden at December 31, 2008 12:57 PM

Eden - Nice to hear from you! I have previously made some blog remarks on Johnston's 'Constitution is not Identity'. I am puzzled by his 'minimalist ontology' and what he thinks he is accomplishing by his theorizing. I haven't seen the other two papers you mention. Perhaps I will check them out.

Posted by: Kenny at January 1, 2009 11:33 AM

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