Branching worlds

I’ve recently discovered some really interesting papers on how to think about belief in a future with branching time. Folks are interested in branching time as it (putatively) emerges out of “decoherence” in the Everett interpretation of standard Quantum mechanics.

The first paper linked to above is forthcoming in BJPS, by Simon Saunders and David Wallace. In it, they argue for a certain kind of parallel between the semantics for personal fission cases and the semantics most charitably applied to language users in branching time, and argue that this sheds lights on the way that beliefs should behave.

Now, lots of clever people are obviously thinking about this, and I haven’t absorbed all the discussion yet. But since it’s really cool stuff, and since I’ve been thinking about related material recently (charity-based metasemantics, fission cases, semantics in branching time) I thought I’d sit down and figure out how things look from my point of view.

I’m sceptical, in fact, whether personal fission itself (and associated de se uncertainty about who one will be) will really help us out here in the way that Saunders and Wallace think. Set aside for now the question of whether faced with a fission case you should feel uncertain which fission-product you will end up as (for discussion of that question, on the assumption that it’s indeterminate which of the Lewisian continuing persons is me, see the indeterminate survival paper I just posted up). But suppose that we do get some sense in which, when you’re about to fission, you have de se uncertainty about where you’ll be, even granted full knowledge of the de dicto facts.

The Saunders-Wallace idea is to try to generalize this de se ignorance as an explanation of the ignorance we’d have if we were placed in a branching universe, and knew what was to happen on every branch. We’d know all the de dicto truths about multiple futures—and we would literally be about to undergo fission, since I’d be causally related in the right kind of ways to multiple person stages in the different futures. So—they claim—ignorance of who I am maps onto ignorance of what I’m about to see next (whether I’m about to see the stuff in the left branch, or in the right). And that explains how we can get ignorance in a branching world, and so lays the groundwork for explaining how we can get a genuine notion of uncertainty/probability/degree of belief off the ground.

I’m a bit worried about the generality of the purported explanation. The basic thought there is that to get a complete story about beliefs in branching universes, we’re going to need to justify degrees of beliefs in matters that happen, if at all, long after we would go out of existence. And so it just doesn’t seem likely that we’re going to get a complete story about uncertainty from consideration of uncertainty about which branch I myself am located within.

To dramatize, consider an instantaneous, omniscient agent. She knows all the de dicto truths about the world (in every future branch) and also exactly where he is located—so no de se ignorance either. But still, this agent might care about other things, and have a certain degree of belief as to whether, e.g. the sea-battle will happen in the future. The kind of degree of belief she has (and any associated “ignorance”) can’t, I think, be a matter of de se ignorance. And I think, for events that happen if at all in the far future, we’re relevantly like the instantaneous omniscient agent.

What else can we do? Well—very speculatively—I think there’s some prospect for using the sort of charity-based considerations David Wallace has pointed to in the literature for getting a direct, epistemic account of why we should adopt this or that degree of belief in borderline cases. The idea would be that we *mimimize inaccuracy of our beliefs* by holding true sentences to exactly the right degrees.

A first caveat: this hangs on having the *right* kind of semantic theory in the background. A Thomason-style supervaluationist semantics for the branching future just won’t cut it, nor will MacFarlane-style relativistic tweaks. I think one way of generalizing the “multiple utterances” idea of Saunders and Wallace holds out some prospect of doing better—but best of all would be a degree-theoretic semantics.

A second caveat: what I’ve got (if anything) is epistemic reason for adopting certain kinds of graded attitude. It’s not clear to me that we have to think of these graded attitudes as a kind of uncertainty. And it’s not so clear why expected utility, as calculated from these attitudes, should be a guide to action. On the other hand, I don’t see clearly the argument that they *don’t* or *shouldn’t* have this pragmatic significance.

So I’ve written up a little note on some of these issues—the treatment of fission that Saunders-Wallace use, the worries about limitations to the de se defence, and some of the ideas about accuracy-based defences of graded beliefs in a branching world. It’s very drafty (far more so than anything I usually put up as work in progres). To some extent it seems like a big blog post, so I thought I’d link to it from here in that spirit. Comments very welcome!


9 responses to “Branching worlds

  1. Hi Robbie,

    This is a really valuable contribution to a difficult debate – thanks. I’ve talked a fair bit with Simon and David, so I think I have a reasonable idea of what they’d say in response, but of course I’m not trying to put words into their mouths and they will disagree with some of the following. I’ll definitely point them at this entry in any case.

    I’m still absorbing quite a lot of what you say in your draft. But an instinctive first response is that you’re wrong in ascribing position 2) to Saunders and Wallace. In particular, they’re keen to avoid having one semantics for first-person thoughts and another for everything else. The Lewis-style account of identity through branching they provide is supposed to apply to everything – branching persons, branching hedgehogs, branching tables, branching worlds. Once we realise that this multiplication of whole worlds – utterers, objects of ostension, and everything else – is part of the SW picture, it starts to look a lot more like your proposal 3). But their view does definitely retain multiple utterances, rather than the notion of a single utterance assessed at multiple contexts. I need to think more about the relation between the two proposals.

    One place where I think you’ve misread SW is the paragraph beginning ‘The advantage only lasts so long as first-person thinking is our focus’. You ask the rhetorical question whether I speak truly or falsely in saying of a fission subject prior to fission ‘he will be rich’ and imply it can’t be answered. But Saunders and Wallace think they do have a straightforward answer; I am speaking either truly or falsely, though I can’t know which. There are two salient types of world, one containing utterers truly uttering of L that he will be rich, one containing utterers falsely uttering of R that he will be rich. Since I can’t know which type of world the actual world belongs to, and hence I can’t know which type of utterer I belong to, I can’t know whether I’m speaking truly or falsely. This is intended to ground my uncertainty about whether he will be rich.

    Another place where I think you misread SW is here: ‘We now know that tokening “there will be a sea battle in the year 3000” will give rise to some true utterances and some false utterances (even holding fixed which person is speaking).’ I don’t think SW would agree with the parenthetical clause. For them, once we hold fixed which person (which cradle-to-grave person, inhabiting a specific big-bang-to-heat-death world) is speaking, there is only one utterance and it is either true or false. Then as we do not know which person we are, we do not know which utterance we are making, so we do not know whether our utterance is true or false.

    Your accuracy semantics for future-directed assertions are new to me and sound very interesting. I don’t think I’ve absorbed all the implications yet, so take this with a pinch of salt but: it looks like a perfectly workable semantics and I suspect you’d be able to iron out the difficulties. However, the availability of the accuracy semantics wouldn’t preclude the availability of a SW-style Lewisian semantics which also gets things broadly right (assuming, of course, that SW can respond to your objections in the first part of the paper). Then deciding between the two semantics might come down to some quite subtle theoretical virtues. But the claim that SW are interested in is that at least one candidate semantics is available which makes broadly charitable sense of everyday discourse. If more than one candidate semantics is available – great. Their real opponent is someone who says ‘Everettian QM can’t be right, because it makes it impossible to give a coherent account of future-directed uncertainty, and without such an account we can’t make sense of probability.’ There are a lot of people who think along those lines.


  2. Hi Alastair,

    Thanks for this! I wouldn’t be surprised if the view they’re actually going for is more sophisticated than my reconstruction.

    I had assumed that they’d go with Lewis through the identity-through-branching thing (with the hedgehogs n all!) So I was thinking that what was left to understand is how this fits with the semantics.

    However, I am now thinking maybe something else has to going on, at least as you interpret them. For consider that chunk of the branching universe which consists of two histories diverging in 2999. In one history, there’s a sea battle, in the other, there’s not. Now, the common stem of these two histories will contain a person-shaped space time region that begins in 1978 and ends sometime before 2999—the region we’d think that cradle-to-grave me occupies.

    At some point, there’s an event where the sounds “there will be a sea battle in the year 3000” eminate from around there. And—as I understand your reading of S/W—there’ll have to be (at least) two utterances associated with those sounds, one which latches onto the sea-battle history (and is true) and the other which latches on to the non-sea-battle alternative.

    Groovy so far. But you say “once we fix which person (which cradle-to-grave person..) is speaking, then there’s only one utterance”. But we need two utterances in the case here, so there have to be two persons here. But these two persons coincide exactly in their spatio-temporal (cradle-to-grave) location.

    Lewisian ontology–supplemented with branching—just won’t get you this, as far as I can see. He allows for overlapping distinct persons, but not for entirely overlapping distinct persons. If a thing shares all its parts its identical. It sounds to me more like the picture that McGonigal and Hawthorne advocate in their forthcoming Phil Studies piece, where we do get multiple persons entirely colocated, uttering sentences with slightly different meanings (they use that to argue for ignorance of truth value of vague utterances—sounds like an interesting parallel to be explored here).

    [NB: I’ve elided one bit of the quote from you, where you say “which cradle-to-grave person, inhabiting a specific big-bang-to-heat-death world”. Maybe the idea is that people (and other objects?) are essentially attached to complete world-histories, so that two persons can be distinct solely in virtue of some metaphysical relation to a complete world-history. That’s an interesting idea. I’d *really* like to see how it would work out, e.g. is the leg that belongs to the sea-battle history a part of the person that belongs to the non-sea-battle history? and so on…

    Hmmm. Maybe the idea would be that the space-times overlap, but the objects, while being colocated in the common space-time during some periods, only stand in mereological relations to other objects that “belong” to the same world as them. In that case, only the space-time would fission in anything like Lewis’s sense—for people and hedgehogs, it’d be a matter of being colocated up to a certain point, and then branching off.

    If something like this is going in, I do see how some other stuff that was puzzling me would fall into place—e.g. maybe when I point to someone and say “he will be rich”, then I’ll point to that person who stands in the special relation to the same world that I (the utter) does. In the case where fission is due to branching worlds, that seems to resolve a worry. I can’t see any analogue of it for standard fission cases though.]

    I do, I guess, understand the form of the de se ignorance proposal if the one-person-one-utterance principle is maintained. But—because I thought that in the year 3000 cases we couldn’t maintain that principle—I was pessimistic about its prospects. So that’s why I presented what I thought of as the best we could do with the one-person-one-utterance (proposal 2) and something that gives up on that, but just goes on multiplying utterances even of a single individual (proposal 3). And of course, the accuracy-based rationale for assigning the degrees of belief we do may apply to proposal (3), as much as to the degree-theoretic one that I thought made things a bit cleaner… But I was inclined to give up on the de se ignorance thing by that point.

    The two misreadings you diagnose seem to me to turn exactly on whether there’s some metaphysics going on in S/W that allows them to maintain one-person-one-utterance. If the metaphysics is more Lewis-like—if, in particular, we’re not going to get exactly colocated distinct objects, but rather genuinely fissioning hedgehogs and people—then I’m inclined to think that the dilemma still stands.

    Does that seem right to you?

    (BTW, there is a usage on which “utterance” is identified with type-context pairs, and distinguished from the concrete event of producing sounds or inscribing marks—I’m using the terminlogy this way in describing my (3) as a multiple-utterance proposal.).

  3. You’re right in your parenthetical suggestion that on the SW proposal objects are somehow attached to world-histories. SW give a deflationary account of this ‘attachment’ – more below. Your suggestion that the space-time fissions, while objects in the branching spacetime merely cease to be collocated, may well be how SW are thinking. Although this implies that it’s literally true that (if we count by identity) there are many people located in the same place as you, this gets explained away by saying that we usually count by world-indexed identity (the Everettian analogue of tensed identity) in such cases.
    I agree that it’s very useful to consider the case of someone uncertain about ‘there will be a sea battle in 2999, though I will be dead by then’. I’m fairly sure that SW are indeed keen to say that we still have multiple utterances here, some of which are true and some of which are false. You’re right that this is a major deviation from the Lewisian semantics of ‘Survival and Identity’. The Lewisian view doesn’t allow for completely co-located objects. But that’s not surprising; the problem which motivates the Lewisian account in the case of partly-overlapping persons doesn’t generalize to completely overlapping persons.
    The (morbid) analogy of the post-death sea-battle in the Parfittian splitting case is an agent who knows that he will be killed, and his body fed into a splitting machine. Two corpses are produced. If we applied the Lewisian strategy in this case, we would end up saying that there are two people present all along, and that the right-hand corpse belongs to one and the left-hand corpse to the other. This would give each agent indexical uncertainty about which body is his. But I can’t see anyone wanting to adopt this view – while some might see a metaphysically important tie between a person at different stages of their life, or between a person and their immortal soul, nobody is concerned to procure a metaphysical tie between a person and their corpse. The supposed gain, of being able to ground uncertainty about which body is the agent’s, just doesn’t seem to be worth the cost of multiplying agents and utterances up to the moment of death.
    When branching is ubiquitous as in Everettian QM, the price of multiplying utterances even in the case of completely collocated agents becomes acceptable because the gains (being able to make sense of quantum probabilities) are indispensable. The SW strategy ties everything to all of its branch-mates, in the same way as each of the two agents sharing a body prior to death is linked to one particular corpse. But SW reject the demand for explanation of what this tie consists in. They’re not after, as they put it, deep metaphysical truths about identity:
    “We do not, in particular, accept that there is a correct semantics, whether or not consistent with ours, as determined by metaphysical principles. For we do not believe there are any metaphysical truths when it comes to the meanings of everyday words like ‘person’ and ‘I’, over and above those that are fixed by observable linguistic useage.”
    I confess I’m not sure whether this rejection of the demand for explanation will do. I wouldn’t be surprised if you found it unacceptable. Here’s a (very speculative) sketch of the way SW are thinking. They may want to disown this but:
    Our discourse about ordinary objects is systematically misleading, in that it works as if there is a metaphysical tie between the portion of the quantum state which realizes some particular ordinary object (eg me) and one particular big-bang to heat-death branch. But all there is is the branching structure – there are no metaphysical ties between stages and branches over and above it. Why does the structure of our discourse appear to presuppose that such ties exist? Because our discourse presupposes that there is only one real world of ordinary objects, and so it follows straightforwardly that each ordinary object is linked to that single real world. It’s not surprising that a form of language which evolved under the presupposition of a single real world of ordinary objects should encode this presupposition.
    Now EQM comes along and undermines the presupposition of a single real world of ordinary objects. But branches are made of ordinary objects in just the same way as we incorrectly took the entirety of reality to be made of ordinary objects. As a result, when trying to make charitable sense of our ordinary discourse in the lights of EQM, we have to adopt a ‘one-branch-one-utterance’ policy. Any other policy would undermine the presuppositions of our thought about ordinary objects too much to be a charitable interpretation of it. Never mind that the policy involves ordered pairs [branch,stage] which do not themselves appear anywhere in our fundamental physical theory. They’re there as artefacts of the model, which can’t be removed without breaking the model.
    Wild speculation over. I’d be glad to hear your thoughts.
    A few other things:
    The Hawthorne/McGonigal view is indeed very similar to the SW picture. I’ve heard Andrew talk about it, and I thought his motivations for the view were too weak to justify the commitments in a single-world set-up, but that the balance of arguments might well change in a branching set-up.
    I’m still a bit unsure about how your contextualist proposal is going to work. In particular, I don’t like the string-of-coordinates conception of context. If we adopt the centred-world conception, modifying it to be a centred-branch not a centred world, isn’t the resulting view just equivalent to the SW view? In particular, isn’t there some burden on you to explain what grounds which context is the correct one to use in a particular assessment? It seems like this is as much a problem as SW’s burden to explain what grounds which of the various collocated agents I am (if you accept this is a problem.)
    Something else you might like to look at in connection with your ‘contextualist’ proposal is the ‘ambiguity’ semantics discussed in an earlier paper on this subject by Wallace:

  4. Ok, I see a couple of options now.

    Option 1. You might have some kind of identification of epistemic agents as history-material object pairs. That gives you objects which are intimiately connected to goings-on we’d think of as persons, but which also are tied to the branches. If I really am one of those things, then maybe we can get your version of SW off the ground as a purely semantic proposal, without the need for a metaphysics that allows for collocated material objects.

    Option 2. On the other hand, there’s the view whereby people/epistemic agents are material objects, but allows that material objects be entirely collocated, and stand in the special “belonging” relation to space-time.

    (Note that the issue here isn’t the multiplication of utterances—I’ll spot them that. It’s the multiplication of persons I’m worried about. We need enough distinct thinkers to ground the de se ignorance story.)

    Those seem very different proposals—only the first one, it seems to me, could be argued to be “deflationary”.

    Fair enough about the contexts—in most circs, I’d go for centred somethings as well. As to whether it’s equivalent to the SW view—I say not, because it doesn’t preserve the one-person-one-utterance principle. In the cases we’ve been talking about, there can be just one person, me, making noises which secure the existence of two utterances—one true and one false. And because of the lack of multiple people to whom the utterances “belong”, the de se ignorance story is unavailable.

    Could you say a bit more about the challenge for the non-SW multiply-utterances view—not quite catching it…?

  5. That clarifies things.

    Option 1 is unattractive because it draws a distinction between epistemic agents and other material objects. The story SW and I want to give has epistemic agents being just particularly interesting material objects – interpreting QM should not require giving agents a special metaphysical status. (That’s part of what’s wrong with the ‘Copenhagen interpretation’). Instead, SW identify all material objects, including agents, with stage/world pairs. So this does amount to your option 2. I suppose it’s not a deflationary proposal, except insofar as SW are deflationary about material ontology in general (they both espouse some form of ‘ontic structural realism’.)

    So what’s worrying about option 2? Is it the intuitive cost of the multiplication of objects/persons? We have to be careful here about which intuitions we’re trying to recover. We don’t need to bring in branch-indexed counting to recover the straight-forward truth of (eg), ‘Exactly one person is sitting in this chair’, or ‘Exactly two rivers flow through Oxford’, because on the SW proposal proposal this chair and Oxford only exist in the actual branch. What sentences of ordinary language do you think come out false on option 2?

    Perhaps the problem is ontological parsimony. The way I see the situation is like the debate between branching and divergence in modal realism. If you’re inclined towards modal realism, or towards Everettian QM, you’ll already be comfortable with a massive multiplication of individual entities (while of course remaining parsimonious about types of entities). No modal realist has tried (as far as I know) to defend branching over divergence on the grounds that branching involves the existence of fewer individual entities. So what’s wrong with multiplication of agents as well as utterances?

    If we go with the multiple-utterance proposal, we still have a choice about what to say about spacetime. Either we treat spacetime the same way as other objects (in which case spacetime doesn’t literally fission, and there is exactly one object in each spatio-temporal location even counting by identity) or we treat it as a common background to all the branches (in which case it literally fissions, and we need to count by world-indexed identity if we want to say that there is exactly one object in a particular spatio-temporal region.) This choice is exactly the choice of whether spacetimes diverge or branch.

    If we go the former way, what remains of the notion that reality is branching? One way of setting up the picture would be as follows:
    1) At the fundamental metaphysical level, there is just the universal state.
    2) Decoherence picks out an approximate basis to decompose the universal state, approximately defining an emergent branching structure.
    3) Pick out big-bang-to-heat-death histories from this emergent branching structure and call them branches.
    4) Pick out parts of branches and call them branch segments. Branch segments are common to multiple branches.
    5) Ordered pairs [branch segment,branch] are identified with spacetime regions. A special case of this is when the branch segment is the whole branch; the spacetime region [branch x, branch x] just is the spacetime of branch x.
    6) Via supersubstantivalism, subregions of a spacetime are identified with objects and agents.
    So spacetime and ordinary objects do not branch, but the underlying emergent branching structure does. Comments?

    I was still a bit confused about your multiple-utterance-single-agent proposal, but you’ve cleared that up now; thanks. As you’re not trying to ground de se ignorance, there isn’t any analogue for you of the (alleged) challenge to SW to explain what grounds which of their multiple agents I am.

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  8. I’ve found the Saunders and Wallace paper and the subsequent discussion here and on other blogs to be really interesting.

    The cases involving the ‘post-mortem future-contingents’ such as Robbie Williams’ case of the omniscient instantaneous agent and the subsequent sea battle/no sea battle branching are nice examples in which presumably S&W will want to say that there is uncertainty, but there don’t seem to be enough agents to ground the de se ignorance story. It seems to me that there will also be cases in which we wouldn’t want to say that there is uncertainty, yet the S&W proposal entails that there will be uncertainty.
    Consider a case like Parfit’s everlasting bodies case (“Personal Identity”, 217-219) or Lewis’s example of Methuselah (‘Survival and Identity”, 65-66).
    Suppose that in 2008 a person is born whose body lives for 1,000 years. Over that time, new memories take the place of old memories, and psychological characteristics gradually change. Let us suppose that any two person-stages are part of the same person (are I-related) if and only if they are no more than 100 years apart. Consider the person-stage existing in 2990. Assuming that time is continuous and there is a person-stage for each moment in time, the 2990 person-stage is shared by continuum many persons. One is the person who lives from 2895 to 2995. Call this person ‘C2895’. Another is the person living from 2905 to 3005. Call this person ‘C2905’.
    Suppose the 2990 person-stage produces an utterance “I will survive to see the year 3000”. According to the S&W proposal, there are continuum many sentences uttered. One sentence has the propositional content that C2895 will survive to see the year 3000. Another has the propositional content that C2905 will survive to see the year 3000. There are continuum many other propositions that are uttered, one for each continuant that has the 2990-person-stage as a part. Some of these sentences are true and some of these sentences are false. For example, the sentence is true in the mouth of C2905, but false in the mouth of C2895. According to the S&W proposal, no one can know the truth-value of what he says. In 2990, C2905 cannot know that the utterance he produces is true because C2905 lacks the de se knowledge the he, himself, is C2905. For similar reasons, C2895 cannot know in 2990 that the utterance he produces is false.
    If we adopt the S&W proposal, we should say that each of the continuum many persons is uncertain in 2990 about whether he will survive to see the year 3000. But that seems to be the wrong result. After all, the 2990 person-stage is I-related to the 3000 person-stage. The 3000 person-stage has most of the same memories, most of the same psychological traits, etc. as the 2990 person-stage. There are continuum many persons that have both the 2990 person-stage and the 3000 person-stage as parts. Lewis would presumably say that the persons in 2990 (assuming they know all the relevant de dicto facts) can be certain about weak survival (the 2990 person-stage can confidently self-ascribe the property of being such that some continuants of which it is a part will survive to see the year 3000). The S&W proposal, however, seems to entail that each person in 2990 should be uncertain of whether he will survive to see the year 3000.

  9. Hi Stephen,

    Nice comment! Sorry it’s taken months for me to get to it.

    I hadn’t thought of the de se issue for Methusaleh before. It does seem really interesting—problematic for S&W, I agree, but also it’s not quite clear what to say about it anyway.

    As you suggest, the “weak plural” strategy in Lewis looks like it has nice results—e.g. if I’m now in Methusaleh situation, commonsensically, desires that I survive to 2010 are met if my current stage has strong psych connections of the right kind with a 2010 stage.

    Here’s one thing S&W might say. Grant that *uncertainty* about the survival occurs in this case. That doesn’t mean we should be anything like 0.5 credence about whether we survive. It can’t be for S&W of course—they better say be able to say of a biased coin, that you’re uncertain of which way it comes down (because uncertain of which branch you’re in), but still proportion your credences to the bias. Indeed, we could have abitrarily high credence in the proposition we are uncertain about.

    In the Methusulah case, it’s not a matter of fixing credences to the weight of branches. Maybe the right kind credence to have is one that tracks the proportion of person-continuants that I’m currently a stage of, that survive to 2010. In a Methusuleh situation, on this view I should be 0.99 sure of surviving (given I know the de dicto facts). Stretch out the time-span longer and longer and I become less and less confident of surviving, as less and less of the continuants I’m a stage of survive.

    On the Lewis weak survival proposal, what happens is that so long as I know that *one* of the continuants I’m a stage of will be present, I should be perfectly confident of survival. At the extreme, this gives *very* different results. In a Methuselah scenario, the measures-over-continuants option will mean that I have 0.01 confidence that I’ll survive to the year 2108, but, but the Lewis proposal gives me degree 1 confidence in this.

    It’s not obvious to me what the phenomenology of Methuselah’s de se beliefs and desires should be. But the view I’m suggesting in opposition to Lewis seems a reasonable option. (I’d pair it with the backdrop that it’s indeterminate which of the continuants “I” refers to, on a view on which indeterminacy comes in degrees, very much as Lewis proposes in a slightly different connection in the “survival and identity” paper).

    Very cool case to think about!

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