Wei Dai <weidai.domain.name.hidden>:
> It's very difficult to follow your reasoning here. Let me try to simplify
> things as much as possible. (You're right that the paradox can be reduced
> to just one coin toss.) Suppose there are just two universes. In universe
> A the experimenter flips a coin at time 1 and observes heads, and at time
> 2 he is duplicated. In universe B the experimenter flips a coin at time 1
> and observes tails, and at time 2 he is not duplicated. Both universes
> start at time 0 and end at time 3 and contain no other observers.
And we assume that the people in these two universes know all this,
right? (Otherwise their rational subjective probabilities could be
anything, depending on what disinformation we give them.)
> Now let's use this collection of universes to test our two definitions of
> sensory probability P(X|Y). With definition A, the experimenter believes
> at time 0:
>
> A1. At time 1 I will observe heads with probability 1/2.
>
> A2. If I observe heads at time 1, at time 2 I will observe heads with
> probability 1.
This is what want to dispute. If I observe heads at time 1 there is a
2/3 chance that I observe heads at time 2. This might sound
paradoxical, but the strangeness, I suspect, comes from the fact that
the normal conditions for thinking about personal identity are not
satisfied when there exist several copies of one mind.
> A3. At time 2 I will observe heads with probability 2/3.
>
> These probabilities are not consistent with each other. But with
> definition B we have:
>
> B1. At time 1 I will observe heads with probability 1/2.
>
> B2. If I observe heads at time 1, at time 2 I will observe heads with
> probability 2.
That is what I would be tempted to say is inconsistent. Normally when
one says "probability" one means an assignment satisfying
Kolmogorov's probability axioms, one of which says that p<=1. Of
course you can try to redefine the notion of probability, but so far
I think definition A is much better.
> B3. At time 2 I will observe heads with probability 2/3.
>
> These probabilities are consistent.
_____________________________________________________
Nick Bostrom
Department of Philosophy, Logic and Scientific Method
London School of Economics
n.bostrom.domain.name.hidden
http://www.hedweb.com/nickb
-----End of forwarded message-----
Received on Sun Mar 01 1998 - 17:46:48 PST