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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
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*> > > > 2/3 chance that I observe heads at time 2. This might sound
*

*> > > > paradoxical, but the strangeness, I suspect, comes from the fact that
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*> > > > the normal conditions for thinking about personal identity are not
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*> > > > satisfied when there exist several copies of one mind.
*

*> > [...]
*

*> > I agree that there are two continuations of the experimenter who
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*> > observe heads at time 2. But, I think, the total number of
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*> > continuations of the experimenter at time 2 is three: the two you
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*> > mention plus the one that exists in the other universe where the coin
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*> > landed tail. That observer-instance is no less a continuation of my
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*> > present observer-instance than are the two observer-instances that
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*> > observe heads. So the correct probability, on definition A, is 2/3.
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*>
*

*> 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

paradox roughly as follows:

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

see heads."

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

heads."

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

Date: Tue, 3 Mar 1998 22:28:27 +0000

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

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

paradox roughly as follows:

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

see heads."

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

heads."

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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