Wolfgang Schwarz

Hey wo,

According to you, T(v>w) = 1/|{u: vRu}| if vRw; and 0 otherwise. Is this meant to hold in general? Suppose we add a twist to your flies example. Suppose you know that God slightly prefers a world with an even number of flies to one with an odd number of flies. Then it seems, for example, that T(w3>w2) should be slightly greater than T(w3>w1). How would you deal with such a case?

Thanks WH!

you're right, 1/|{u: vRu}| doesn't hold in general. Should probably make that clear. If we know that God prefers even-numbered worlds, this will show up in the transition table (for propositions). As I say later in the paper, I think the transition probabilities for individual worlds are constant and not affected by whatever you learn, even from God. So unfortunately the stuff in the afterlife section doesn't perfectly fit what I say later.

Hey Wo,

Really interesting stuff!

I'm sympathetic to the conservatism methodology. I'm wondering about the "successor" notion. I'm not quite sure how to interpret it: is this one gloss? Radical cartesian says divide your transition prob equally between all possible psych duplicates. HH cartesian says divide transition prob equally between all possible psych duplicates that occupy the same world. Conservatism says divide transition prob equally between all psych duplicates that are stages in the same life (where personal identity is assumed to be a matter of psych continuity/connectedness).

That way of describing it makes it sound a lot more continuous with Cartesianism than on your presentation, so I was wondering whether you intended other constraints to be in place. The advantage of this formulation is that it gives a clear idea why in the SB case we divide transition probability equally between monday-tails and tuesday-tails stages.

If we don't fill things out in this way, I'm wondering why it's obvious that the conservative should say the things you say about the SB case. A naive thought would be that monday-tails SB should be the successor of the Sunday SB; and that tuesday-tails SB should be the successor of monday-tails SB. The shift on Monday would then be 50/50 between monday-tails and tuesday-heads. On Tuesday the transition probability puts everything onto tuesday-tails. Obviously SB couldn't introspect to find out whether she should be assigning 50/50 to monday-tails/monday-heads or rather 1 to tuesday-tails---how she should shift her probabilities is not transparent to her. But why is that a bad thing? Maybe that's what we should expect from these models in such puzzling cases.

Just something in defense of this idea. Suppose that SB is told that on a tails-flip it will be ensured that she'll be kidnapped when 80 and given the pill which'll make her wake up in a state subjectively indistinguishable from her state on waking tomorrow. I'm not inclined, off the cuff, to think the transition probabilities should take into account these far-away future selves into account, any more than they should take into account subjectively indistinguishable states of people other than me or in different worlds (the suggestion I might be a far-in-the-future psychological duplicate feels a bit like a sceptical scenario---perhaps my feeling is that it's not a close enough possibility that I now am at the centre of that case).

The idea would be that if SB woke on Monday and divided her credence evenly between monday-tails and monday-heads, she'd be doing as she should. In the ancient-SB-duplicate case that seems to me the right thing to say. And I'm not sure why we shouldn't say the same thing in the standard case.

Arguably, in the standard case SB, waking on Monday, she can't know she's waking on Monday (since there's a close possibility where she's waking on Tuesday), whereas in the new case maybe SB can know she's waking on Monday (since her subjectively indistinguishable waking is not a close possibility). The lack of knowledge in the standard SB case may make it irresponsible of SB to just implement the Monday transitions and ignore the Tuesday ones (it's a familiar externalist thought that what one should do and what it's responsible for you to do can come apart). Of course, what the responsible thing to do with credences in such a scenario is a hard question---so unlike your recipe, this doesn't give a complete description of the case.

Anyway, that's just a sketch of what seemed to be a fairly natural elaboration of the conservativism idea. Just to summarize: if conservatism was really a life-restricted version of Cartesianism, then to me it seems to get the wrong results in the ancient-beauty twist on the case. But if conservatism isn't elaborated in this way, I'm not sure why we should describe the original SB case in the way you do, rather than the more "externalist" way sketched above.

Sorry if I've missed stuff!

Thanks Robbie!

You're right, conservatism shouldn't be understood as a life-restricted version of Cartesianism. I want to treat psychological duplicates in our distant future (or past) as ordinary sceptical alternatives. That's why successors are meant to be immediate successors, not descendants.

Does this mean Beauty should be certain that it's Monday on Monday morning? I do think this option should be taken seriously, but it seems a bit counter-intuitive. And worse, it makes it harder to explain the credence spreading in Arntzenius's prisoner case. I thought I could circumvent these problems by emphasizing the role of psychological continuity: both tails-Tuesday-Beauty and tails-Monday-Beauty are immediate psychological successors of tails-Sunday-Beauty.

To motivate this, imagine A knows that he will fission into B and C tonight. When B wakes up in the morning, he should not be certain that he is B. Next, imagine A will fission tonight, and one of his descendants, C, will immediately time travel one day into the future. Then upon waking up, B should not be certain what day it is. Finally, imagine A will fission into B and C tonight, C will time travel one day ahead, and B will disappear the following night. Isn't this pretty much SB's situation?

The idea is that fission and time travel cases independently support using a successor relation that gives the traditional halfer result in SB (and explains the spreading in the omniscient prisoner case). Does that make sense?

I agree that the conservative model raises interesting issues about knowledge and epistemic responsibility -- if not in SB, then definitely in other cases (such as Shangri La). There will be cases where you should strongly believe p even though you can't point to any evidence in support of it. And then the degree of belief can appear unjustified or irresponsible, and the lack of evidence can be seen as undermining your claim to knowledge. I'm not entirely sure what to say about these things.

Hi wo,

Thanks---that makes good sense.

In the fission cases I see why you get the results you sketch. And I don't have too much of a problem with it in the prisoner case either (I'd like to think about what happens in that case if you said rather that it was vague which state was the successor, rather than there were multiple successors). But I guess I couldn't see why tuesday-tails SB was an immediate psychological successor to sunday SB.

Alter the case slightly so that what happens on monday has a great psychological effect on SB (though she has no idea it would happen). She sees something that makes her acquire a new understanding and compassion for the world's poor. When she wakes on tuesday with her memories of monday wiped, she retains these new dispositions.

Or suppose on monday she loses some of her memories of older times.

I'm supposing the puzzle can get going just as before---either she can't introspectively detect these new/absent psych states in the tuesday morning environment, or she does detect them but can't treat them as evidence that it is tuesday.

Elaborating the case in these ways, it seems very far from clear cases of immediate psychological successor----much more like a case where tuesday SB is a "descendent" in your terms. Somehow it feels a bit ad hoc to insist tuesday SB is a successor in order to make shifting give the results we'd like.

Do you think that's a fair concern? I guess with a technical term like this, I'm reminded of the methodology in Lewis's treatment of counterfactuals. "Similarity" plays a big theoretical role, but if you rely on pretheoretic judgements of all-in similarity of worlds, you get the wrong results. So we look at what we want the outcomes to be in various cases, and use those as evidence to construct a principled story about what exact sense of similarity is involved, which then explains and predicts the cases. At the moment I sort of feel that "psychological successor" is playing a role a bit like "similarity"---just relying on snap judgements is going to lead me astray---but I don't yet have a sense of how to explicate it.

Right, that's a very fair concern.

I guess my treatment of SB will depend on what exactly happens to her on tails-Monday night. If the researchers merely ensure that upon awakening, she has no episodic or introspective memory experiences of Monday events, then she arguably ought to believe on Monday that it's Monday and on Tuesday that it's Tuesday. On Tuesday morning, she ought to conclude from her lack of Monday memories that the coin has landed tails, not that it may well be Monday morning, given that before receiving this evidence, she was already certain that Monday morning has past, and the new evidence doesn't undermine her reasons to think so.

On the other hand, if the researchers not only undo Beauty's episodic memories, but also any belief changes that occurred to her on Monday, and in particular if they make Beauty's Tuesday morning state a perfect copy of her Monday morning state, then her situation looks a lot like fission with time travel. I was thinking of the case more along these lines.

We could of course make tails-Tuesday Beauty count as an 'immediate successor' even in the first type of case by suitably redefining 'successor'. But then we'd probably get the wrong results in ancient Beauty type cases.

In general, you're right that 'successor' is a placeholder that needs to be filled in. One way would be to use our judgments about good and bad belief changes to reverse-engineer a suitable successor notion. But at least my judgments are not very clear in many relevant cases. It would be better to have principled reasons for preferring one notion over others, in the way one can perhaps argue against the radically Cartesian notion (on which everything is a successor of everything) on grounds of information loss.

My fallback position is that transition probabilities are like prior credences in so far as it's hard to pick out a unique rational distribution: some distributions are clearly crazy, but there's little ground to choose between some others.