# Re: predictions

From: Nick Bostrom <bostrom.domain.name.hidden>
Date: Tue, 3 Mar 1998 22:28:27 +0000

Hal Finney <hal.domain.name.hidden> wrote:

> Nick Bostrom, <bostrom.domain.name.hidden>, writes:
> > > > 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.
> > [...]
> > I agree that there are two continuations of the experimenter who
> > observe heads at time 2. But, I think, the total number of
> > continuations of the experimenter at time 2 is three: the two you
> > mention plus the one that exists in the other universe where the coin
> > landed tail. That observer-instance is no less a continuation of my
> > present observer-instance than are the two observer-instances that
> > observe heads. So the correct probability, on definition A, is 2/3.
>
> But wouldn't this 2/3 be "the probability that I observe heads at time 2"
> irrespective of whether you observed heads at time 1?

Yes. We haven't defined conditional probabilities; my
statement above would mean that conditional probabilities default to
the probability of the conditional event. It would be nicer if the
theory could be extended to deal with conditional probabilties also.

In order to do thins, I think we have to be careful to avoid
ambiguity when using the term "I" at different times. Perhaps that
can be done by operationalizing the statements leading to Dai's

A1. At time 1 I will observe heads with probability 1/2.

"If I have my eyes closed, and somebody tells me it's time 1, then I
should expect with probability 1/2 that when I open my eyes I will

A2. If I observe heads at time 1, at time 2 I will observe heads with
probability 1.

Can similarly be interpreted as meaning roughly: "If I have my eyes
closed, and somebody tells me it is time 2, and I remember having
observed heads at time 1, then I should believe with probability 1
that when I open my eyes I will see heads."

A3. At time 2 I will observe heads with probability 2/3.

"If I have my eyes closed, and I'm told it's time 2, then I should
expect with probability 2/3 that when I open my eyes I will see

This would seem to block the contradiction that follows if A1-3 are
taken at face value. Each translation captures the gist
of the corresponding A-statement. And I think it should be possible
to come up with similar translations for other probabilistic
sentences we might want to consider. Is that a way out of this
(interesting!) mess?

_____________________________________________________
Nick Bostrom
Department of Philosophy, Logic and Scientific Method
London School of Economics
n.bostrom.domain.name.hidden
http://www.hedweb.com/nickb
Received on Tue Mar 03 1998 - 14:35:32 PST

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