Thursday, July 24, 2008

Branching time (x-post from TnT)

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 progress). 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!

Update: Oh, and worldle abstract:


Alastair Wilson said...

Also cross-posted from TnT:

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.


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