Pre-fission possibilities
Suppose tonight you will fission into two persons. One of your successors will wake up Mars and one on Venus. There are then two possibilities for how things might be for you tomorrow: you might wake up on Mars, and you might wake up on Venus. These are distinct centered possibilities that do not correspond to distinct uncentered possibilties. There is just one possibility for the world, but two possibilities for you. Indeed, the two possibilities are two actualities: you will wake up on Mars, and you will wake up on Venus. It is tempting to go further and say that there are also two possibilities for you now. I want to discuss three quite different reasons for making this move.
The first comes from intuitions about attitudes: when you think about your situation, couldn't you wonder where you will wake up? Couldn't you hope that it will be on Mars? Couldn't you imagine having the future on Venus? If the content of your wondering, hoping and imagining are centered possibilities, then these possibilities must have a unique, determinate future: since your hope to wake up on Mars differs in content from your fear to wake up on Venus, there must be one centered possibility verifying "I will wake up on Mars" and another verifying "I will wake up on Venus".
Dilip Ninan offers this motivation in his recent paper "Persistence and the First-Person Perspective", and he cites several authors who apparently put forward similar intuitions. I have to admit that I don't share these intuitions. In fact, they seem clearly false to me. If you wonder where you will wake up, you have misunderstood your situation. Perhaps you think you are a non-physical soul that won't fission at all. But that's not your actual situation.
If there were two pre-fission possibilities, it should make sense to ask which of them obtains. But the only sensible anwer is 'both'. And then you can't reasonably wonder which of them obtains. Moreover, if the two possibilities are genuine alternatives, it should be possible (in principle) to learn which of them obtains. But if you understand your situation, you know that anyone who comes along and tells you that you'll wake up on Mars and not on Venus is a liar. Even if it is God.
So the first reason doesn't work.
The second reason for postulating distinct possibilities comes from certain views about the metaphysics of people and the nature of centered worlds. On the popular "worm" view, there are two people in the fission scenario, one who wakes up on Mars (call her M) and one who wakes up on Venus (V). Both M and V exist today, although they somehow coincide. If centered worlds are something like world-time-individual triples, then we naturally have two possibilities at times t before the fission: <w,t,M> and <w,t,V>.
Something like this reasoning can be found in recent papers by David Wallace and Simon Saunders. I find both steps unconvincing. I don't believe in the worm view of persons, and I don't think centered worlds can be modeled as triples of a world, a time and an individual.
But the issue is subtle. Let's say that a centered world is a maximally specific way things might be, or a maximally specific property. Such a property must include historical information: "x is presently F and G and H" is less specific than "x is presently F and G and H and will be J and used to be K". So a maximally specific property can't be silent on whether and where x will wake up tomorrow. However, among the maximally specific futures a thing can have is to wake up both on Mars and on Venus. For instance, consider your present time-slice S. A maximal specification of S's properties would include having successors on both Mars and Venus. Or consider the fusion F of V and M. A maximal specification of F's properties would include having future parts on both Mars and Venus.
Lewis once suggested that although fissioning involves two persons M and V, any pre-fission thinking and wondering is done by a stage S that is common to M and V. This seems to imply that if you believe that you are temporally extended, then what you believe is false: the belief content is a class of extended objects, but the believer is unextended; so the content is false. Better say that what does the thinking and wondering is the fusion F; then your belief that you exist tomorrow on Mars is true, and so is your belief that you exist tomorrow on Venus.
Apart from S and F, of course the two worms M and V also exist, as do their maximally specific properties. But I don't think you can reasonably believe or hope to have one of these properties rather than the other. Compare the gerrymandered fusion of your present stage S together with some past stages of the Eiffel tower and some future stages of Barack Obama. You can't reasonably wonder whether you are this object rather than some other, equally gerrymandered fusion (unless, of course, you misunderstand your situation e.g. by thinking that only one of those fusions exists).
So the second reason also doesn't work.
Not only that, in both cases the relevant considerations seem to support exactly the opposite conclusion: that your distinct future possibilities do not correspond to distinct present possibilities.
This is unfortunate, because distinct pre-fission possibilities would be very convenient for the epistemology of branching subjects. They would help a lot to simplify my centered form of conditionalisation, and they might be useful in the confirmation theory of quantum mechanics (this is what Wallace and Saunders use them for). That's the third reason.
Hi Wo,
I am very sympathetic to the claim that centered worlds cannot be modeled as (w, i, t). But I am a little puzzled by the objection you have against the first reason you mention. I think your intuition about which one you are is right. However, why isn't `both' a legitimate answer to `which one obtains?'?
Compare: suppose there is an older man and an older woman in a room with me and my friend. My friend asks me `which one is your parent?' and I answer `both'. That sounds okay to me. So the reason that `both' is not a legimitate answer cannot simply be that `which' forces the choice or either one or the other. Can you say more why you don't think `both' is a legitimate answer in the fission case?
Furthermore, if `both' is a legitimate answer, then that's good reason for us to think that there are indeed two distinct possibilities.