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!