Friday, February 11, 2005

A Tale of Two Parcels -- Or Are There Three?

My topic in the form of a poem:

A tale of two parcels
Or are there three?
More on composition
And identity.


All right Joseph Jedwab, gird your loins for another round. Put on your thinking cap, get your posterior analytic in gear, make all requisite preparations. I am afraid your last batch of comments -- the comments on this post -- betrayed misunderstanding. So I’ll try again. I’ll try to be clearer.

Suppose I own a parcel of land, call it A. I divide A into two adjoining, non-overlapping, subparcels, B and C, of unequal size. I put both B and C on the market for 40,000 and 60,000, respectively. A prospective buyer appears with a suitcase of C-notes and says he wants to buy both B and C. I tell him that he will have to fork over 200,000. He looks at me like I’m crazy, so I explain that B costs 40 K, and C costs 60 K. That makes 100 K. Parcel A costs 100 K, so the total is 200 K.

He protests once again, so I say: "Surely you have read Peter van Inwagen’s article, "Composition as Identity" (Philosophical Perspectives 8 (1994), pp. 207-220 ) in which he proves that in a situation like this there are three objects and not two. Consider the existentially general sentence, ‘There is an x, y, and z such that x is a part of z, y is a part of z, and x is smaller than y.’ For this sentence to be true, which it obviously is, there must be at least three objects in the domain of quantification to serve as the values of the bound variables ‘x,’ ‘y,’ and ‘z.’ So there are three parcels, and each has a separate price."

Now clearly something has gone deeply wrong here. Parcel A is a whole with exactly two proper parts. But surely A is not an entity over and above B and C. A, B, and C cannot be three entities for they can be three only if they are three parcels of land, and there cannot be three parcels of land in reality. For if A is a third parcel in reality then there would have to be something in reality that distinguishes A from B-adjoining-C – and what could that be? At most there are three objects of consideration. To suppose that these three objects correspond to three entities appears to be the mistake the Van Inwagen is making. To put it another way, the the bound variables ‘x,’ ‘y,’ and ‘z’ denote three conceptually distinct objects – otherwise we wouldn’t be able to make sense of the existentially quantified sentence given above. But it doesn’t follow that there conceptually distinct objects are really distinct entities.

It would be either an insane boast, or a bad joke were I to claim that I own three parcels of land: I own one parcel consisting of two subparcels. Some will be tempted to express this insight by saying that A just is B and C. In other words, A’s being composed of B and C amounts to A’s identity with the sum (fusion) of B and C. Composition is identity.

But this can’t be right either. Indeed, it appears to be nonsense from a purely syntactical point of view. How can an identity sentence have a singular term on one end and a plural term on the other? ‘Cicero is Tully’ is well-formed. It is a singular identity sentence. ‘The Three Stooges are Larry, Moe, and Curly Joe’ is well-formed. It is a plural identity sentence. But ‘This house is ten rooms’ and ‘This chessboard is 64 squares’ seem malformed, being syntactic hybrids. Same goes for ‘This piece of land is two parcels,’ if ‘is’ expresses identity. Ditto for ‘God is three persons.’

It is false that A is a third thing in addition to B and C. It is also false that A is identical to (B and C). So what is the truth? I say the truth is that A is identical to B and C when these are properly connected. In this case, proper connection is their adjoining. To see the point, suppose B and C are not adjoining but separated by a river. There would then be no parcel of land that has B and C as its sole proper parts. There would be the set consisting of the two but no set is a parcel of land.

So A is identical to B and C adjoining each other. Note that both ‘A’ and ‘B and C adjoining each other’ are singular terms. Thus we do not have an objectionable syntactic hybrid on our hands. I am not saying that A is identical to its proper parts; I am saying that A is identical to its proper parts when these adjoin. That adjoining is not nothing. Compare the chariot. I am not saying that the chariot is identical to its proper parts; I am saying that the chariot is identical to its proper parts when these are properly connected. ‘This chariot’ is a singular term; but so also is ‘these parts properly connected.’

Let me sum up. I believe Jedwab has made two mistakes. The first is not to appreciate that both of the following are false:

1. A is a third thing in addition to B and C.
2. A is identical to (B and C).


Jedwab's second mistake is to think that I was urging (2). I reject both of (1) and (2).

NOW: Have I convinced you of this? If not, why not?

But the real fun is just beginning. Consider

3. A is identical to B and C properly connected.

The connectedness K is not nothing. So it is something. But then where is it to be 'located'? K is not A; K is not B; K is not a further part; K is not the whole; K is not something external to the whole. If K is not internal to the whole, identical to the whole, or external to it, then K would appear to be nothing.

So we have an apparent contradiction on our hands: K is both something and not something, both real and not real, both existent and nonexistent. Note that I have given reasons for accepting both limbs of the contradiction.

How can this apparent contradiction be removed?