EQM, spacetime points, and mereology

In my last post I talked about individuation of material objects by their branches. The proposal was, roughly, that material objects and events should be thought of as sets; in particular, pairs of a branch and some aggregate of temporal parts of that branch. The major worry I have with this approach, pointed out by Andrew in the comments, is that this will affect mereology. To make ordinary talk about parthood come out true, we’d have to adopt a mereology for sets whereby set {a,b} has as its parts not {a} or {b} but {a,c} where c is a part of b.

This deviance from normal mereology is bad enough. But we’d also need to stipulate that {d,b} would not be a part of {a,b} if a is larger than b. Otherwise pairs of non-maximal aggregates of temporal parts with other non-maximal aggregates of temporal parts would come out as material objects, even though they’re not individuated by any branch. This is a bad result.

There’s a very simple modification to the view which in a stroke avoids all the mereological problems, and also goes some way towards reducing the intuitive weirdness of the view. Instead of identifying all material objects and events with pairs, just identify spacetime points with pairs {a,b}, where a is a pointlike part of a branch, and b is a branch. Then identify regions with sets of points exactly as is usually done by a substantivalist. Then identify events with spacetime regions, and material objects with events,  exactly as is usually done by a supersubstantivalist.

The resulting view avoids the problems with mereology which dogged the earlier proposal. The mereology of material objects works just as it usually does. Objects are still individuated by their branches, but in virtue of all of their pointlike parts being individuated by branches. Is there still a problem with the mereology of the spacetime points themselves? Not really – if we take it that sets are simple, then spacetime points have no parts (as is usually supposed). If we take it (with Lewis) that sets have their subsets as parts, then each spacetime point has as a part an entire branch – perhaps counterintuitive, but not in serious tension with ordinary usage.

The supposed counterintuitive consequences of the view are ameliorated, too. The identification of objects and events with spacetime regions is familiar from supersubstantivalism – no new counterintuitive consequences there. And the identification of spacetime points with sets is also familiar from Quine’s proposal in ‘Propositional Objects’ to identify points with quadruples of real numbers. Indeed, the current proposal seems less radical than Quine’s, since the elements of the set are more naturally thought of as concrete than real numbers are.  Spacetime points are anyway a case where the abstract/concrete distinction is at its most problematic.

EQM, spacetime points, and mereology

Macroscopic individuation in Everettian quantum mechanics

This entry concerns the Saunders/Wallace proposal for solving the incoherence problem in Everettian quantum mechanics as it appears in BJPS 2008. My thoughts draw heavily on this post of Robbie’s, and on subsequent discussions I’ve had with him; John Hawthorne has independently mentioned the motivating worry to me in conversation. I’ll assume that the non-probabilistic presuppositions of the SW proposal are granted; for example, that decoherence provides an adequate solution to the ‘preferred basis problem’. I also will ignore Tappenden-style worries involving locality requirements on the qualities which determine the reference of our terms.

The SW proposal identifies persisting material objects, including agents, with non-branching aggregates of temporal parts, and identifies worlds with maximal non-branching aggregates of temporal parts. A result of this is that each persisting material object has temporal parts in common with objects in different branches, and each world has temporal parts in common with each other world. This sharing of temporal parts is just what makes the proposal a proposal about branching.

I have no objection to the claim that the SW proposal can account for uncertainty about propositions such as ‘I will see spin-up’, when an agent is about to perform a quantum measurement which could give the result spin-up or spin-down. Nor will I quibble with its extension to uncertainty about propositions such as ‘the apparatus will read spin-up’, which goes via the idea that your branchmates (in this case the apparatus) are the most natural referents for your terms.

The problem is that the proposal doesn’t, and cannot, generalize to give us an account of an agent’s uncertainty about events occurring futurewards of that agent’s death. Consider, for example, the claim ‘at least one sea-battle will occur after my death’ (call this claim SB). I’m neglecting complications due to special relativity – but we could easily use instead the claim that a sea-battle occurs in some event in the forwards light-cone of my death.

Now I take it that after my death, various chance events will occur which affect the probability of sea-battles occurring. Perhaps a year after my death crucial peace talks will occur between some feuding island nations. Hence, I take it that we ought to be able to recover uncertainty about SB at some time t (at which I am still alive), and to assign SB non-trivial objective chance at t.

However, uncertainty about SB cannot be accounted for on the Saunders-Wallace view. For I, as a complete continuant, will appear both in branches containing sea-battles futurewards of my death, and in branches containing no sea-battles futurewards of my death. Both sea-battle branches and non-sea-battle branches contain the same aggregate of temporal parts which make up the continuant that Saunders and Wallace would identify with me. I am on both branches, so how can I be uncertain about which branch is mine? Something has to give.

It would be an act of desperation to give one semantics for uncertainty about future events before my death, and another semantics for uncertainty about events futurewards of my death. After all, if there is an unproblematic semantics available for uncertainty about events futurewards of my death, why not simply apply it to all cases of uncertainty about the future and avoid any dualism? And the difference between these types of uncertainty doesn’t seem to be linguistically marked. It would be in the minimalist spirit of the SW picture to try for a single account to cover all cases.

The problem seems to lie with SW’s claim that it is invisible, on the level of the semantics, whether histories diverge or branch. In the branching case, the complete sum of temporal parts which I’m identified with is common to both sea-battle branches and non-sea-battle branches. But then it is true, with certainty, that I am on a sea-battle branch, so we cannot capture uncertainty about SB this way. In contrast, if histories diverge, then there are two, qualitatively indiscernible, complete sums of temporal parts, only one of which is me. Then uncertainty about future contingents can be recovered straightforwardly, as it is by Lewisian modal realism.

The upshot is that although the semantics SW give does remove the distinction between  branching and divergence in cases of uncertainty about events prior to an agent’s demise, the distinction is still there when it comes to uncertainty about events following an agent’s demise. And to get the right semantics for the latter sorts of claims, we need to go with macroscopic divergence. Since the multiverse patently can’t be partly branching and partly diverging, to make the self-locating uncertainty view work we need to commit to macrosopic diverging. Is this really so bad? Of course, Everettian QM is distinctively a branching theory, but perhaps we can cash this out in terms other than as involving the sharing of temporal parts by macroscopic objects and events.

Endorsing divergence requires a different account of how macroscopic objects are individuated. In their BJPS paper, SW seem to individuate macroscopic objects by their temporal parts; any two objects which have all their temporal parts in common are the same. But in more recent, unpublished, work, Saunders instead appeals to the view that macroscopic objects and events are to be individuated by their branches. I’m not sure whether he realises that this is incompatible with the sharing of temporal parts by objects in different branches. But in any case, individuating macroscopic objects via their branches does seem necessary for the self-locating uncertainty view to make sense.

So what metaphysical picture could underly the claim that objects and events are individuated by their branch? One proposal I’d like to explore is to distinguish between the underlying and the emergent ontology, such that the former, but not the latter, is taken to be branching in the sense of sharing of temporal parts. The next move is then to identify material objects and events not with aggregates of temporal parts, but with pairs (aggregate of temporal parts, branch). Maximal material objects (or events), namely possible worlds, could be identified with pairs (branch, branch).

At first glance, this proposal is likely to strike the reader as pretty counter-intuitive. Here are some natural complaints (thanks to Andrew for raising them here), and some quick rejoinders:

1) We don’t feel like we are pairs!

How would you know what it feels like to be a pair of this sort? Without knowing that, how could you know that we don’t feel like we are pairs!  Compare the situation with materialism; if materialism is right, human beings are just identical with their bodies, and bodies are lumps of meat. The complaint ‘I don’t feel like a lump of meat’ isn’t likely to cut much ice in the materialism debate, instead what is wanted is an argument that it couldn’t feel like anything to be a lump of meat. Likewise here; we need to distinguish the worry that it seems implausible that we are a pair from the worry that we can imagine what it would like to be a pair, and that we know our experience is not of this sort.

2) Pairs are abstract; we are concrete!

Various other complaints can be subsumed under this one; for example, that pairs don’t seem to be causally active, while material objects are. On this proposal, concrete objects are a subclass of abstract objects: the pair (aggregate of my temporal parts, my branch) is identified with a concrete object (me). So this view probably involves some revisionism about the abstract-concrete distinction. But is this really too big a deal? As Lewis famously complained, our grasp of the abstract-concrete distinction is nothing like as clear as it ought to be. Incidentally, I think there’s independent reason to want to bring the domains of the abstract and concrete closer together; in particular, the huge and difficult problem of explaining the ‘unreasonable effectiveness of mathematics’ in the natural sciences.

3) There are various ways of defining ordered pairs. Are you the Kuratowski worm/branch pair or the Quine-Rosser worm/branch pair?

The pairs in question don’t need to be ordered. One element of any pair will always be a proper part of the other, except for the case in which the pair is (branch, branch) and is being identified with a world. So we don’t need to appeal to ordered pairs at all; the set with the two elements will do. (In any case, we reasonably might take a problem of this sort as motivating a form of structuralism, analogous to the mathematical structuralism motivated by the non-unique definability of the natural numbers in terms of set theory).

These responses are all very quick indeed, but I think they give the flavour of the way the proposal would go. Are there other ways to set the metaphysics up so that objects and events are individuated by their branches? Probably. Suggestions more than welcome!

Macroscopic individuation in Everettian quantum mechanics

Is fragility intrinsic?

Jonathan Ichikawa suggests a disarmingly simple argument that fragility is not intrinsic; consider a fragile material object like a glass slipper. A exact intrinsic duplicate of the slipper in a world with different laws of nature might not be fragile; perhaps glass slippers are used as hammers in those worlds.

I think the first stage in responding to this is to invoke the weak nomic necessitarianism which is a part of dispositional essentialism. Any world in which there exist stable glass slippers is a world in which something extremely close to the usual laws of electromagnetism hold. But any world in which these laws (or something extremely close to them) hold is also a world in which glass slippers are fragile. This response is an instance of the argument form deployed by Bird in Bird, A. 2001. Necessarily, salt dissolves in water. Analysis 61: 267–74 – in later work, he calls it the ‘down-and-up structure of laws’.

This, however, merely shifts the question to whether an intrinsic duplicate of a glass slipper is possible which does not obey the laws of electromagnetism. It would not be made of glass (Ichikawa concedes this point in the comments, at least for the sake of argument), but nor could it involve instantiations of mass and charge – these, by weak nomic necessitarianism, obey the laws they do by necessity.

But perhaps there are possible intrinsic duplicates of glass slippers which are made of glassch, and involve instantiations of schmass and scharge. The argument could then run as follows: these glassch schlippers are not fragile, but they are intrinsic duplicates of glass slippers, so fragility is not preserved over intrinsic duplication, and fragility is not intrinsic.

The obvious place to resist this second argument is the premise that glassch schlippers could be intrinsic duplicates of glass slippers. Ichikawa seems to motivate this by the claim that both glass slippers and glassch schlippers could have atomic structure XYZ. But this still seems wrong. Glassch schlippers are made of schatoms, not atoms, so they don’t have any atomic structure at all, let alone the same atomic structure as glass slippers.

At this point, the only way I can see to resurrect the argument that fragility is not intrinsic would be to make a strongly structuralist move , and say:

1) that the identities (quiddities) of the properties involved in an object are irrelevant to that object’s structure.
2) that the structure (and only the structure) of an object is preserved under intrinsic duplication.

Now most metaphysicians would demur from at least one of these claims, and hence they can recover the view that fragility is intrinsic. But I’m tempted by both claims, since I reject quiddities altogether. Must I then say that fragility is extrinsic?

Not if I make the stronger necessitarian move of denying that schmass, scharge and therefore schlippers are possibilities. This requires a necessitarianism stronger than WNN (see my previous post for discussion of grades of nomic necessitarianism). SNN certainly permits this response. Does FNN permit it? Only if schmass and scharge do not number among the genuinely possible fundamental natural properties. If FNN is true, this is not a question we can answer on a priori grounds. So if, as I suspect, FNN is true, then whether fragility is intrinsic is a question whose answer we can only know a posteriori.

Is fragility intrinsic?