Wolfgang Schwarz :: Spacetime and Recombination

Spacetime and Recombination

Posted on Monday, 10 Jan 2005.

According to the Principle of Recombination,

for any things at any worlds there is a world containing a duplicate of each of these things and nothing else (that is, nothing that is not a part of the fusion of the duplicates).

Applied to the mereological fusion of David Hume and David Lewis, this says that there is a world containing nothing but a duplicate of the fusion of Hume and Lewis. This duplicate presumably has a part that is a duplicate of Hume and another that is a duplicate of Lewis. How are these parts spatiotemporally related?

a) they are adjacent or overlapping: some part of the Hume duplicate touches or is identical with some part of the Lewis duplicate;

b) they are separated by some spatiotemporal distance, perhaps by the distance between the actual Hume and the actual Lewis;

c) they are neither adjacent nor overlapping nor separated by any spatiotemporal distance.

(a) is odd, because the spatiotemporal arrangement of a thing's parts appears to be an intrinsic property of the thing. A perfect intrinsic duplicate of a molecule should not be some different molecule with rearranged atoms. (Thus Lewis says that spatiotemporal relations are intrinsic to their pairs, or to the fusions of their pairs.)

Moreover, if ordinary objects like David Hume are composed of particles with empty space in between, (a) would presumably imply that at the duplicate world, all that space were missing. Then the 'duplicate' of Hume would be much smaller and have rather different shape than the actual Hume.

(b) looks more natural, but it seems to contradict the Principle of Recombination. For (b) assumes that besides the duplicate of Hume and the duplicate of Lewis, the other world also contains a region of spacetime linking the two. This is why Phillip Bricker (in "Island universes and the analysis of modality") takes (c) to be the correct account.

But (c) is strange, too. It obviously contradicts the unification of worlds by spatiotemporal relations (which is Bricker's point), but it also fails to respect the idea that composite objects have the spatiotemporal arrangement of their parts intrinsically. If we give up this idea, we might as well go for (a).

One could perhaps defend (b) with the help of some kind of spacetime relationalism, on which the spacetime that exists in (b) is nothing over and above the Hume duplicate and the Lewis duplicate. I know too little about relationalism to see if this could work. But it would be interesting if relationalism followed from the Recombination Principle. Though what would strictly follow is only the possibility of relationalism: relationalism holds at the recombined world, it need not hold at our world.

Another way to defend (b) could be to excempt spacetime regions from the Recombination Principle (contrary to what Lewis says on p.2 of "Void and Object"). After all, it isn't obvious that Hume, say, is a fusion of spacetime regions or points, as opposed to occupants of such regions or points. And if the region he occupies is no part of him, then the Recombination Principle would require that a Hume duplicate exist without occupying any spacetime at all, which seems impossible.

In defense of (a), one could say that ordinary objects like molecules are fusions of both bits of matter and various bits of mostly empty spacetime in between the bits of matter. Creating a duplicate of a molecule therefore requires duplicating also some regions of spacetime. So there are two things we could mean by "the fusion of Lewis and Hume": the ordinary fusion, containing also the region of spacetime linking the two, or the strict fusion containing really just Lewis and Hume. Contrary to Lewis, spatiotemporal relations are then not intrinsic to strict fusions. So the adjacent duplicates count as an intrinsic duplicate of the strict fusion of Lewis and Hume.

Comments

# Irem K. Steen on 11 January 2005, 22:01

"Applied to the mereological fusion of David Hume and David Lewis, this says that there is a world containing nothing but a duplicate of the fusion of Hume and Lewis."

Let's call the fusion of 4d Lewis and 4d Hume, Humis. Humis is 4d. A large chunk of it is spatiotemporally separated from another large chunk of it. What does it take for an x to be a duplicate of Humis? It is necessary that x's parts do not differ from Humis' parts with respect to the perfectly natural external relations between the parts of Humis. Suppose that spatiotemporal relations are perfectly natural. (He says they are natural, I don't see that he says that they are perfectly natural.)
Then any duplicate of Humis will also have the same spatiotemporal distance between its Lewis-like part and its Hume-like part.
This entails that in a world where there is only a duplicate of Humis and nothing else, there must be something in addition to the Lewis-like thing and the Hume-like thing: the region of spacetime linking the two. But this doesn't conflict the recombination principle.

It's as if the principle says:
- if you want a world with Humis and nothing else in it, you've got it. (And points to the world where there is a duplicate of Lewis, a duplicate of Hume, and a duplicate of the spacetime region which separates them in the actual world.)
And you say:
-But, that has a spatiotemporal region in addition to the Humis-duplicate!
- No, The spatiotemporal region is not something in addition to the Humis-duplicate, it is a part of the duplicate. But if you don't want that spatiotemporal region, then you don't want a world with a duplicate of Humis and nothing else. What you want is a world with a duplicate of Lewis and a duplicate of Hume and nothing else. Okay, there's one.

- But, but...They're adjacent! Lewis wasn't adjacent to Hume (or a Hume-like thing). This Lewis-like thing is adjacent to the Hume-like thing. So this Lewis-like thing isn't a duplicate of Lewis.

- Duplication doesn't have to preserve external relations of a thing to other things (no matter how natural the relations are). It preserves the perfectly natural external relations between the parts of the thing. For instance the heart and the brain of this Lewis-like thing are spatiotemporally related just in the same way as the heart and the brain of Lewis. This is a duplicate of Lewis. And that is a duplicate of Hume. Since you ordered that there be nothing else (as was promised) , I had to pull out a world in which the two are adjacent.
-----------
Okay, I fudged a couple of things. I didn't say anything about the spacetime region which is included in the Humis-duplicate. Is it empty spacetime? What's empty spacetime? I cannot remember what Lewis says about that, of if he says anything.
Secondly, it turns out that we cannot have a fusion of Lewis and Hume ONLY, they come with the spatiotemporal region between them (not the occupants of that region, but the region "itself" somehow.)

# Rich on 12 January 2005, 13:57

I'm kind of with Irem on this... As i understand the principle of recombination, it ends up being something like

(R): For any worldbound individuals x1...xn, there is a world containing any number of duplicates of them (if there is a spacetime big enough to hold them all), and such that for any spatiotemporal relation, said duplicates are so related.

# wo on 12 January 2005, 21:43

I'm not sure I understand the suggestion. As I understand it, "fusion" is a quasi-logical notion, whose definition rules out that the fusion of x and y may contain anything that does not overlap either x or y. So by definition, the fusion of Lewis and Hume does not contain any region of spacetime linking Lewis and Hume (since that region has parts which clearly don't overlap either Lewis or Hume).

So what you, Irem, call "Humis" is not really the quasi-logical fusion of Lewis and Hume (what I called "strict fusion" in the posting), it seems to be something else (perhaps what I called an "ordinary fusion" in the posting), something that escapes the problem. But what about the real fusion of Lewis and Hume? I can't believe that it simply does not exist.

# rich on 12 January 2005, 22:15

am i following this point right? given unrestricted summing, the fusion of Hume and Lewis is an individual. Given recombination, there is a world containing a duplicate of that individual. But that duplicate has parts that are not spatiotemporally related. Which contradicts Lewis's take on what worlds are.

Lets look at a parallel worry. Given unrestricted summing, there is a fusion on me and some non-actual individual, which is itself an individual. Given recombination, there is a world containing a duplicate of that individual. But since that duplicate has parts that are not spatiotemporally related, we contradict Lewis's take on what worlds are.

The latter problem is solved by restricting the recombination to worldbound individuals. Since the fusion of me and the non-actual individual is not world bound, the recombination principle isnt in play.

No simple restriction looks to work in the former case.

But look at my (R) principle. What we get is worlds containing Lewis duplicates and Hume duplicates related in any way we wish.

# wo on 12 January 2005, 22:34

Thanks. Yes, we get all kinds of Lewis duplicates and Hume duplicates. But I'm not worried about those. I'm worried about Hume+Lewis duplicates, where '+' is strict fusion. Are all possible Hume+Lewis duplicates fusions of spatiotemporally related Hume duplicates and Lewis duplicates? If yes, don't all their worlds then contain regions of spacetime in addition to the duplicate of Hume+Lewis?

If you mean (R) to be the general Recombination Principle, the first question is whether regions of spacetime count as 'individuals'. If not, that takes spacetime relationalism for granted (which indeed solves the problem). If yes, (R) seems to say that in some world, two things may be 2 km apart even though there is no region of spacetime spanning 2 km. Which sounds impossible.

# Rich on 13 January 2005, 14:14

i do intend (R) as the general recombination principle. I also think that Lewis's ontology has two basic types of entities, sets and individuals. I dont think regions of spacetime are sets, so i guess they are indiviudals! But im unsure if (R) entails the scenario you suggest. I need to think about it more. Still, its a nice puzzle. I've still got a feeling that any world containing a Hume+Lewis duplicate will have some spacetime region linking them. So they are all sums of spatiotemporally related duplicates of Hume and Lewis.

# Daniel Nolan on 15 January 2005, 14:13

I think (a) and(b) don't have the problem you suggest unless it's necessary that spatiotemporal relations hold in virtue of substantial spacetime. Otherwise a duplicate of Humis can exist on its own, with spatio-temporal relations that aren't ancestrals of adjacency between its Hume bits and its Lewis bits. (And a duplicate of Hume can exist on his own without having all of his parts adjacent.)

Myself, I'm inclined to think of a lot more of the spatiotemporal relationships between an objects' own parts as being extrinsic than e.g. Lewis seems to. I think shape is typically extrinsic. But if you want to keep Lewis's intuitions about the intrinsicness of shape, I think it's probably best to allow that ordinary things have duplicates in worlds where there is no spacetime, but only spatiotemporal relations. (Unless ordinary objects are pieces of spacetime, but even then, they have duplicates where there are gaps of spacetime between them and duplicates of other ordinary objects, though they remain spatiotemporally related.)

# wo on 17 January 2005, 09:16

Many thanks, Daniel. It also seems to me at the moment that accepting the possibility of relationalism as a consequence of Recombination is the best answer.

Do you think shape is typically extrinsic because it typically (?) depends on the curvature of spacetime? I sometimes believe that "intrinisc" is a gradual concept (shape is *more* intrinsic than ownership), but for the Recombination Principle an absolute notion is required. If hardly any non-trivial property is absolutely intrinisic, the Principle becomes strangely week.

# Daniel Nolan on 17 January 2005, 16:36

I have some alternative reasons to think shape is extrinsic, depending on how we occupy space and time.

If some sort of "container" view is correct, then it strikes me that our relations to spacetime are extrinsic to us. (It's normally thought that something can move without undergoing intrinsic change.) I expect something's shape is largely a matter of how it is related to space, and so is about as extrinsic as position is (though there might be plenty of nomic connections between how a thing is intrinsically and what shape it has).

On the other hand, shape of regions of spacetime themselves is an extrinsic matter, it seems to me. (And my reason for this will carry over as a second reason why objects "contained" in spacetime have shape extrinsically.) I think shape is partly a matter of what distances there are between parts of an object, and this can be changed by modifying the space outside where the object is - create a worm-hole area linking the space next to my left ear to the space next to my right ear, and all of a sudden my head is shaped so that my ears are almost touching. (Or consider a straight bar, and make the points at each of it's ends adjacent. Arguably it's changed shape.) If those examples don't convince, there are plenty of more thoroughgoing changes to spacetime one can make that change a lot of the spatiotemporal relationships the object or region's parts have to each other in ways that make it tempting to characterise the object as having a different shape. (Make all of the points equidistant from some other point, and it's hard to deny the object is now a ball, albeit one in a very strange geometry!)

This isn't part of a general scepticism about intrinsic properties, or even a scepticism that many spatiotemporal relations are intrinsic to their relata - it's just that shape isn't intrinsic.

# wo on 19 January 2005, 21:24

Thanks, that sounds fairly convincing to me.

Wolfgang Schwarz

Spacetime and Recombination

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