Tuesday, October 6, 2009

Parthood

I've run this argument before. But let's do it again, maybe more clearly. If some things can have non-mereological parts, the following scenario is possible: an entity has m parts to begin with, and then it loses k and is left with n=mk parts. It would be really weird if this couldn't happen in the case where n=1, but could happen in the case where n=2, say. So, plausibly, this can happen in the case where n=1. Suppose Fred, thus, loses all but one of his parts. The remaining part is not identical with Fred—if it were identical with Fred, then prior to the loss of the other parts, Fred would have been identical with a proper part of himself. So at the end, Fred has one part. But the following two claims seem plausible, too:

  1. x is a proper part of y if x is a part of y and x is not identical with y
  2. if x is a proper part of y, then y has at least one other proper part than x.
And the case contradicts the conjunction of (1) and (2).

I take it that the advocate of non-mereological parts will have to deny (2). This introduces a new class of quasi-simples. A quasi-simple is an entity that has at most one proper part. Like a simple, it is not possible to subdivide a quasi-simple any further. But unlike a simple, a quasi-simple is allowed to have a proper part. This is weird indeed.

It is a puzzling question when two or more simples compose a whole. But once one allows quasi-simples, we get the further puzzling question when a simple composes a quasi-simple.

15 comments:

larryniven said...

I dunno, I don't think it's a valid inference from "this part is now the entirety of Fred (or whatever)" to "this part was always the entirety of Fred (or whatever)." I guess maybe you could pull that off in the case of people, but it doesn't work with inanimate objects, right?

Alexander R Pruss said...

I am not clear where I make this inference.

PFS said...

Is this the other post that you're referring to?

http://alexanderpruss.blogspot.com/2008/01/parts.html

PFS said...

Sorry, the link was cut off. Try

alexanderpruss.blogspot.com/2008/01/parts.html

(Alex, you may want to link it in the original post?)

larryniven said...

Uh: "Suppose Fred, thus, loses all but one of his parts. The remaining part is not identical with Fred—if it were identical with Fred, then prior to the loss of the other parts, Fred would have been identical with a proper part of himself."

So Fred, after losing all but one part, is identical to just that part, from which you say that Fred "prior to the loss of the other parts" would also have been identical to just part A. Unless I'm misreading that?

Alexander R Pruss said...

Well, after losing all but one of the parts, he has only one part left. But it does not follow that he is identical with that part. If he were identical with that part, absurdity would follow. (Let's say at t0 he consists of A, B and C. Then A and B are destroyed, and only C is left at t1. Now, C-at-t1 = Fred-at-t1. C-at-t1 = C-at-t0. Therefore, by symmetry and transitivity of identity, C-at-t0 = Fred-at-t1. But Fred-at-t1 = Fred-at-t0. So, C-at-t0 = Fred-at-t0. And that's absurd.)

larryniven said...

Right, that's just what I'm arguing against. I understand the formal line of reasoning, but it doesn't make sense to me to carry equality across times like that - I mean, I'm the same person now as I was ten years ago, but that doesn't mean that Liebniz's laws all apply to my current and teenage self.

So, for another example, if I have a mug with a handle and the handle falls off...how am I supposed to interpret that? It's still the same mug, and it's now identical to just one of its pieces, but surely the handle was part of that mug beforehand. I guess you could say that it really is a different mug, but (a) I don't believe that and (b) then you have a mysterious special case when it comes to living things (possibly only people?). (Although actually that may not be so mysterious for someone who believes in souls.)

Alexander R Pruss said...

The standard move is to distinguish constitution from identity. The mug is not identical with what was a part of itself. Rather, that part constitutes the mug. What is weird is that in this case there are no parts besides that one.

larryniven said...

Oh, good - there is already a word for that. I may have to go do some research (care to point me somewhere?), but it sort of seems like that causes an even bigger problem.

If I'm following this, the mug is never identical to either its body or its body-plus-handle, but it is at various points in time constituted of just its body and its body-plus-handle. And likewise Fred can be constituted of any number of combinations of limbs and organs and so on without ever being any of those combinations. Right?

But then in both of these cases, what does identity add to the situation? How does it even enter in? I can see maybe how Fred could be one identical thing the whole time if that thing is nonphysical, because then Fred's identity and his constitution are distinct. But the mug? I'm stumped on that one.

Anyway, I'm not sure this resolves the problem. Your original argument went (roughly):

1. F(t1) = F(t2) ("Fred at t1 is equal to Fred at t2")
2. F(t1) = A+B+C (etc.)
3. F(t2) = C
4. C != A+B+C
.: F(t1) = C
.: X

But then why can't I say:

1. F(t1) = F(t2)
2. c(F[t1], A+B+C) ("Fred at t1 is constituted of A+B+C")
3. c(F[t2], C)
4. C != A+B+C
.: c(F[t1], C)
.: X

Unless "being constituted of x" isn't a predicate...? I have to say, I'm a bit at sea on this one.

larryniven said...

Well, okay, and it's also worth pointing out before we continue that this would be just as contradictory if Fred were just B+C at t2, so long as A+B+C != B+C. So I'm also not sure what the one-part condition brings to the situation.

Alexander R Pruss said...

We need to talk of the time at which F is constituted by A+B+C. Thus, at one time F is constituted by A+B+C and at another by C.

I think the problem may occur in any case in which an object F has a proper part P such that F can lose all the parts outside of P, being left with P, and its subparts, as the only part. (We don't need P to be a simple part, as in my formulation in the post.) For then P either is or is not a part of F. It would be weird if it ceased to be a part of F simply because the other parts disappeared. So, it seems, it is a part of F. But it's not identical with F. So, by a plausible criterion of proper parthood it's a proper part--it's a part of F that isn't F. But it's an odd proper part, however, because there is nothing outside it that's in F.

Andrew said...

Very interesting... E.J. Lowe has an argument in his new book 'Personal Agency', which I think he calls the "simplicity argument" (it is about 1/2 way thru the book)which is similar to this one you are making...He argues that persons are 'simple.' Although I cannot recall the exact arguement, so to avoid botching it I will leave it at that.

Alexander R Pruss said...

Thanks! I hadn't seen that argument. On a quick skim, I think the simplicity argument is quite different. For one, it only works for persons. For another, it assumes, I think incorrectly, that "part of" is used univocally between mereological and non-mereological cases.

larryniven said...

"We need to talk of the time at which F is constituted by A+B+C. Thus, at one time F is constituted by A+B+C and at another by C."

Oh, of course. The way to do that is:

1. F=A+B+C | t1
2. F=C | t2
3. c(F, A+B+C) | t1
4. c(f, C) | t2

(You may be familiar with this same sort of thing in modal logic with respect to possible worlds.)

And then identity laws would all operate within a fixed timeframe:

\-/t,x,y (x=y | t) <-> (y=x | t)
\-/t,x,y,z {(x=y | t) & (x=z | t)} -> (y=z |t)

And so on. And then all of this stuff goes away. The question then becomes how to formalize the concept of identity over time, but I think that pretty clearly deserved its own special rules all along. It can't be the same "=" as in the identity of indiscernibles, because the things are in fact discernible (again, you could easily tell the difference between me now and my teenage self; the same is presumably true of my this-world self and most or all of my other-possible-world selves). I dunno necessarily how to do this or which concomitant rules should apply, but you yourself admit that the other system is untenable:

"I think the problem may occur in any case in which an object F has a proper part P such that F can lose all the parts outside of P"

In other words, there's a problem every time anything changes physically? (Because, after all, this is just as bad when you add parts as when you take them away.) Things change physically literally all the time, so I can't imagine that a system that's incapable of describing this is a very useful system.

Alexander R Pruss said...

1. The problem of identity over time and change in properties is the problem of temporary intrinsics. There are different ways of handling it. One is presentism. Another, which is what I'd like to do, is some variant on time-indexing of predicates. Once we time-index our predicates Leibniz's law holds without any problems.

2. Actually, I don't think that the kind of change where everything outside a part disappears happens very often. Consider everyday cases. You lose a bit of skin. But before you lost the bit of skin, the complement of the bit of skin wasn't a part. Not every collection of parts is a part. This goes against mereology, but we are talking of non-mereological parthood here.