Thursday, January 24, 2008

Parts

Let us suppose that there is a proper part P of me such that every part of me beyond P could perish, while P would remain. Some think the soul is such a part. Others think the brain is. Yet others might think that the head, or the head plus soul, or my upper half are such. Suppose now that at t0, this part P is a proper part of me, but later, at t1, everything making me up outside of P perishes, and no new stuff accretes, so that P is my only part, at least not counting the subparts of P. Maybe I am a brain in a vat or a disembodied soul at t1.

What is my relationship to P at t1? It cannot be identity. For if I were identical to P at t1, then by transitivity, I would also be identical to P at t0, and thus at t0 I would be a proper part of myself, which is absurd. Yet at t1, there is a sense in which there is nothing to me but P.

It seems that if identity is not the relation, then the relation is constitution, or some other such relation that falls short of identity. Thus, I am constituted by P at t1. This is pretty standard. But it bothers me. Here's why. At t1, P is still a part of me--it didn't cease to be a part of me just because all the other parts of me have gone away (e.g., if I have a brain, then a brain is a part of me, even if nothing beyond it is). Is P a proper or improper part? If a proper part, then there ought to be other stuff beyond P making me up. But ex hypothesi, at t1, P is all that's left of me. So P is an improper part. But the only improper parts of something are the thing as a whole and, on some views, nothing (or an empty or trivial part). Plainly P is not nothing. So then P is the whole of me, which we've already seen isn't true. Either way, we have a problem.

To rephrase, suppose:

  1. Everything excepting some proper part of me could perish with nothing new accreting to me, and with that part not coming to be beyond me.
  2. If a part x of y survives and y survives, and x does not come to be beyond y, then x will still be a part of y.
  3. Identity is transitive.
  4. If x is a proper part of y, then there is stuff beyond x in y.
Then a contradiction follows. (I may have forgotten some assumption here from the informal argument. But the basic idea is here.)

A slightly different argument is to note that at t0, both P and I are parts of me in the same sense--one a proper and the other an improper part. (One might question this: maybe proper and improper parts are "parts" by analogy or equivocation.) This shouldn't change at t1: both P and I should still be parts of me in the same sense. But it doesn't seem categorially right to suppose that x and y can both be parts of z in the same sense when x constitutes y (the atoms of my heart and my heart are parts of me in different senses).

I am inclined to say that these arguments push one to reject (1)--the idea that I have a proper part such that everything beyond that part could perish while I survived with that one part. However, I also think that if any object has proper parts, surely there will be some object with a proper part that is such that the object could survive being "reduced to" that part. Indeed, very plausibly, if any object has proper parts, likewise my mind is a proper part of me, and I could surivve being "reduced to" just the mind (regardless whether the mind is a brain or a soul).

And so we have another argument for the denial of the thesis that some objects have proper parts.

10 comments:

Mike Almeida said...

t seems that if identity is not the relation, then the relation is constitution, or some other such relation that falls short of identity. Thus, I am constituted by P at t1. This is pretty standard

Alex,

Do you want to say this? If you are constituted by P at t, then certainly you were constituted by P earlier. How could you not be? No part of the stuff that now consistutes you, viz. P was missing at t-n. So if P consistutes you now, it constituted you then. But in that case, P is not a proper part of you. You have to make some decision on which of the many sets of simples that MIGHT constitute you at any time is the set that does constitute you. You seem to have decided on P (though that seems to me radically arbitrary--why not P + x?). But if P is it, and you are not vaguely constituted, then P constitutes you at t-n as well as at t.

Alexander R Pruss said...

Are you assuming that being constituted by P is an essential property?

Mike Almeida said...

I don't think I need such an assumption. I say that if you are constituted by P at t, then you are constituted by P at t-n, if no part of P has changed from t-n to t. In that case, it is false at t-n that P is a proper part of you. How could it be? There is no time between t-n and t when you when you did not have P as a part. It must have constituted you all along or not at all. Maybe you think it does not constitute you at all, but your soul does?

Alexander R Pruss said...

Mike:

Your objection seems to me to contradict the main point of bringing in the relation of material constitution. Let M be the matter of Tibbles minus tail. Then before Tibbles has lost his tail, M doesn't constitute Tibbles (M only partly constitutes Tibbles). After Tibbles loses his tail, M constitutes (all of) Tibbles.

On the other hand, one might wonder how it is that something can, with no internal change, at one time constitute an F and at another not constitute an F. I think this worry is another objection to the constitution story, and hence another argument against parts. But it may not be a very serious objection.

Alexander R Pruss said...

Mike:

A bit more. Your objection seems to show that in general "P's constituting an F" cannot be an intrinsic property of P, since without any internal change in P, P can cease to constitute an F, simply because another part sprouts outside of P.

But I am not sure how strong an objection this is. For it may be that another part cannot sprout outside of P without that part being in some way in interaction with P, and thus changing P. Certainly, in the case of organisms this seems to be true.

(In the case of artifacts it's not. But I think a constitution theorist who believes in artifacts just has to be bite the bullet. Otherwise, she is committed to the Hermes existing in the stone, since the stone that will later constitute the Hermes is not changed by the rest of the stone being chipped away.)

Mike Almeida said...

Your objection seems to me to contradict the main point of bringing in the relation of material constitution. Let M be the matter of Tibbles minus tail. Then before Tibbles has lost his tail, M doesn't constitute Tibbles (M only partly constitutes Tibbles). After Tibbles loses his tail, M constitutes (all of) Tibbles.

This is tendentious, no? Suppose I ask you which of all the candidates for Tibbles actually constitutes him at t (before he loses his tail). It does not matter whether you are a universalist or not (it does not matter whether you believe there are countless cats in the room or not before Tibbles loses his tail). Now suppose you say that what constitutes Tibbles at t+1 is Tibbles-Tail. If that indeed is what constitutes Tibbles at t+1, and Tibbles-Tail is present (as by hypothesis he is) at t, then I should think you'd believe that Tibbles-Tail constitutes Tibbles at t as well. I can't see a reason why you wouldn't. After all, it is true at t that had Tibbles lost his tail no proper part of him would be missing.

Alexander R Pruss said...

"After all, it is true at t that had Tibbles lost his tail no proper part of him would be missing."

I think "no proper part of him would be missing" is ambiguous. If "proper part of him" means "proper part that he has", then necessarily never does someone exist with a proper part of him missing. But this is just a tautology. On the other hand, if "proper part of him" means "something he once had as a proper part" or "something he ought to have as a proper part", then in that sense a proper part of Tibbles is missing--his tail.

Justin said...

Alexander,

Interesting puzzle.

I think there are better things to say, though, than that there are no composite objects.

We could be perdurantists about persistence. Then, assuming that you are a persisting thing, you will have proper parts distinct from your t1 temporal part. So, your t1 temporal part will be a proper part of you.

Suppose, though, that we want to be endurantists. I think the best thing to say, then, is that you stand in the constituted by relation to P at t1. We'll have to say one of three things about parthood. First, we can say that weak supplementation fails. Though P is a proper part of you, there is nothing that is a part of you and is mereologically distinct from P. Second, we can claim that P does not stand in the parthood relation to you. Still, P's parts do stand in that relation to you. Finally, we can claim that the standard definition of part is inadequate. Instead, x is a part of y just in case x is a proper part of y, x is identical to y, or x constitutes y.

Mike Almeida said...

if "proper part of him" means "something he once had as a proper part" or "something he ought to have as a proper part", then in that sense a proper part of Tibbles is missing--his tail.

I thought you were suggesting that what remains at t+1, Tibble-Tail, is what constitutes Tibbles. If so then it is true at t, that were he to lose his tail, he would not lose a proper part. How could that not be true, given what you say about Tibbles-Tail? Go to the closest world in which Tibbles is tailess and he is missing no proper parts. Introducing time indexed parts just changes the subject. We were not talking about parts-at-t of Tibbles but parts of Tibbles.

Alexander R Pruss said...

In that world he's not missing a part he has--that is impossible--but he's missing a part he could have.