Wednesday, September 5, 2007

Wormy Lumps

Two of Lewis' Five Objections:

Trans-World Glue
(found on pages 49-50 in Weatherson's “Stages, Worms, Slices and Lumps”, and 218 of Lewis' Possible Worlds)

“The general worry here is determining which stages are part of a particular worm and/or lump. That is, the worry is about how the worm or lump is held together. There are two ways in which this seems more problematic for lumps than for worm. First, the various parts of a worm are held together by a causal dependence of some parts on others. But since worlds are causally isolated, this cannot be the way that worms are held together. Secondly, to the extent that we need a similarity relation on top of the causal relation for worms, it is the similarity of one part to the nearby parts. Because there is no one-dimensional ordering of modal space matching the ordering of temporal space, the relevant similarities will have to be “a matter of direct similarity between stages.” (Lewis 1986a: 218).” (49)

Run-down of the above argument in two pieces:

A.)

(1)If the worm / lump theory is true, then the various parts of a worm are held together by a causal dependence of some parts on others.

(2)If the various parts of a worm are held together by a causal dependence of some parts on others, then worlds must not be causally isolated.

(3)So, if the worm / lump theory is true, then worlds must not be causally isolated.

(4)Worlds are causally isolated.

(5)Therefore, the worm / lump theory is not true.

(1) p → q premise (1)
(2) q → ~r premise (2)
(3) p → ~r sub-conclusion (1)-(2) HS
(4) ~~r → ~p (3) CONTRA
(5) r → ~p (4) DN
(6) r premise (4)
(7) ~p conclusion (5)-(6) MP

(N.B. Yes, I know there are two extra steps in the inference argument when reconstructed. I put in contraposition and double negation in there as extra steps to make everything explicit.)

B.)

(1)If the worm / lump theory is true, then the various parts of a worm are held together by both a causal dependence of some parts on others and a direct similarity relation between the stages or worms.

(2)If the various parts of a worm are held together by both a causal dependence of some parts on others and a direct similarity relation between the stages or worms, then there is a one-dimensional ordering of modal space matching the ordering of temporal space.

(3)So, if the worm / lump theory is true, then there is a one-dimensional ordering of modal space matching the ordering of temporal space.

(4)There is no one-dimensional ordering of modal space matching the ordering of temporal space.

(5)So, the worm / lump theory is not true.

(1) p → (q & r) premise (1)
(2) (q & r) → s premise (2)
(3) p → s (1)-(2) HS
(4) ~s premise (4)
(5) ~p (3)-(4) MT

Now here is the Lewis version of the argument from Possible Worlds:

“(1) The temporal parts of an ordinary thing that perdures through time are united as much by relations of causal dependence as by qualitative similarity. In fact, both work together: the reason the thing changes only gradually, for the most part, is that the way it is at any time depends causally on the way it was at the time just before, and this dependence is by and large conservative. However, there can be no trans-world causation to unite counterparts. Their unification into trans-world individual can only be by similarity.
(2) To the extent that unification by similarity does enter into perdurance through time, what matters is not so much the long-range similarity between separated stages, but rather the linkage of separated stages by many steps of short-range similarity between close stages in a one-dimensional ordering. Change is mostly gradual, but not much limited overall. There is no such one-dimensional ordering given in the modal case. So any path is as good as any other; and what's more, in logical space anything that can happen does. So linkage by a chain of short steps is too easy: it will take us more or less from anywhere to anywhere. Therefore it must be disregarded; the unification of trans-world individuals must be a matter of direct similarity between stages.”( L 218)

Here's my difficulty. After the first couple of readings of Weatherson it seemed that his rendition of Lewis' argument was reasonably faithful to Lewis. But, now after reading it over again a few times, I'm not so sure it is. The reason being is that the argument presented causes problems for any wormy theory, which is Lewis' theory as well. Which means Lewis has a hard time denying any of the premises above, as they are writen. Bad. Lewis forwards these as arguments that cause greater difficulties for lumps, then for worm theories such as his own. Something needs to be added that will capture the difference between Weatherson's lumps and Lewis' worm. Hopefully, I'm not completely wrong here, but the something should be that Lewis can chose between the counterpart or mereological components of his view. Whereas Weatherson doesn't accept counterparts (it's just the lump, even if the lump includes what Lewis would refer to as a counterpart of x), so he cannot divide as finely as Lewis can in his response. Which as far as I can tell is what is needed for Lewis to show that there are greater difficulties for the lump view as opposed to the worm view.

Anyhow tell me what ya' think. And yeah, tell me what needs to be clarified and further explicated.

7 comments:

Adam said...

Hi.
Just so I'm clear on the issue, is the following basically right?

Lewis is considering the possiblity of modelling trans-world individuals in the manner of stage/worm termporal persistence or perdurance. The arguments he gives are meant to show that, while perdurance is an ok picture in the termporal case, it won't work in the modal case.
Is that right?

If it is, then I'm not sure if I understand your worry, when you write that "the argument presented causes problems for any wormy theory, which is Lewis' theory as well. Which means Lewis has a hard time denying any of the premises above, as they are writen. Bad."

Could you clarify?

Chelsey Booth said...

Hey Chris... just as a side question... Is there any other papers that spell out lump theory a little more thoroughly then this one? As per usual, I'm pretty sure I get how they are suposed to, well, work. But I know better than to assume, because what I think, is often incorrect (as I am usually told by others).

Chelsey Booth said...

Let me try... Lewis, according to his theory has two different ways of explaining how an individual can have different properties at either different worlds and/or different times:

x is F at t iff x has a part at t which is F
or
x is F at w iff x has a part at w which is F

Lewis' out for part A.) is to say that his theory does show (some sort) of causality between stages of the worm: x is F at t iff x has a part at (all sequentially placed t times) which is F . This may not be the greatest account of causality, but it is some sort. Unfortunately, I don't see which premise from the above reconstruction that Lewis can deny. The consequent of (2) perhaps? But, if he does you still end up with the same conclusion. Gggrrrrr!!!

Whereas Weatherson's response:

“It is hard to see what the objection here is meant to be. Assume we think there is a (salient) counterpart relation such that x is F in w iff x's counterpart in w is F. Then the lump is just the fusion of all worms y such that y is a counterpart of x in some world. The counterpart relation will have to be determined by direct similarity, rather than similarity between adjacent parts or causal connections, but the lump can be determined to just the extent that the counterpart relation can be determined. There is some indeterminacy in the counterpart relation, but that just corresponds to some harmless indeterminacy regarding which lump is being referred to. The counterpart relation varies with our interests, but the lump to which we refer also varies with our interests.” (W 49)

First, (and this isn't really an objection) but, why is he explaining his objection in terms of counterparts when lumps don't include, or rely, on counterparts? I know it is for ease of explanation, but if it ain't part of your view, don't use it.

Second, I think Lewis' point is that on the lump view you can only refer to either the lump (i.e. the whole thing, or the fusion of all worms) or a worm component of the lump (i.e. not fused). If you can only refer to the whole thing, there is no causal explanation to be had as to it's interior parts. If you can only refer to an interior worm of the lump then there is no causal story to be had about how the different worms are connected.

As for Weatherson's point that, “[t]here is some indeterminacy in the counterpart relation, but that just corresponds to some harmless indeterminacy regarding which lump is being referred to.” That is the point, indeterminacy is bad. And his view has is, whereas Lewis' doesn't.

Third, is Weatherson's response a weird kind of haecceistic response? He seems to be saying that all that is needed to explain similarities between the lumps is that they all share the essential property of Fness?

Is this a little more crystal, Adam?

Chelsey Booth said...
This comment has been removed by the author.
Chelsey Booth said...

Sorry the third part should have said: "...is needed to explain similarities between the worms of the lump is that they all share the essential property of Fness?"

Adam said...

If you were to rewrite each occurence of 'worm/lump theory' in your standardized arguments with 'transworld worm/lump theory' or 'modal worm/lump theory', then would the arguments pose any problem for Lewis?
If they still do, how is that?

Chris Tillman said...

Replace 'worm/lump' with 'lump' throughout. Worms are fusions of temporal parts; Lumps are fusions of modal parts. Lewis thinks ordinary objects are worms and not lumps. The arguments in question are supposed to support that. Weatherson's view is that there's no great reason to think ordinary objects are worms and not lumps. A main problem that Lewis points out for the "ordinary objects are lumps" view is that principles that govern whether something is part of a lump are ill-behaved. Weatherson thinks they're not too ill-behaved. Weatherson thinks that there is tolerable (harmless) indeterminacy in which things count as parts of a lump; he is not saying that it is a virtue of his view that there is no indeterminacy on it.

Lewis does not need to deny any premise in Weatherson's reconstruction of his arguments because those are arguments that Lewis endorses and Weatherson rejects. So I think I was missing your point about that.

It's interesting to think about the impact of QML vs counterpart theory for these issues, but put that aside. Weatherson is basically assuming Lewis's metaphysics is correct and arguing that, given that, there's no great reason from Lewis for not taking ordinary objects to be lumps. Note that Lewis and Weatherson agree that there are lumps and there are worms. So the dispute is not ontological. The dispute is about which are the ordinary objects.