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From: Nick Bostrom <nick.bostrom.domain.name.hidden>

Date: Tue, 26 Sep 2000 18:15:07 -0500

Jacques Mallah wrote some time back:

[referring to my "Adam's hunting system" thought experiment - see

chapter 8 of my doctoral thesis:

http://www.anthropic-principle.com/phd/]

*>>>If he believes the MWI however, then he knows there is a branch
*

*>>>where a
*

*>>>deer turns up and one where it doesn't. He knows that for a usual
*

*>>>day the
*

*>>>effective probability of a deer turning up is about 1%.
*

*>>>Since he has no reason to believe the laws of nature are specially
*

*>>>configured to correlate the amplitude of the wavefunction's branches
*

*>>>with
*

*>>>his actions (especially since such correlation would be hard to
*

*>>>reconcile
*

*>>>with QM), he will still believe the effective probability of a deer
*

*>>>turning
*

*>>>up is just 1%.
*

*>>You may be confusing subjective and objective probability.
*

*> Nope. Why would you think I might do so?
*

Adam might have reason to think that the objective chance of Deer is 1%,

and nonetheless have reason assign a 90% (say) credence to Deer. Compare

the situation to the case of a coin which has just been tossed in what

you think is a fair manner; so you think there was a 50% chance of

Heads. But suppose you have cought a brief glimps of the coin after it

landed, and it looked like Tails, although you aren't absolutely sure.

So your subjective credence may be 95%.

David Lewis discusses the relation between objective chance and

subjective credence. The upshot is that one should only set one's

subjective credence equal to the objective chance if (1) one knows about

the objective chance, and (2) one does not have impermissible evidence -

such as having seen how the coin landed, but there are more subtle forms

of inadmissible evidence as well.

*> In both cases I have so far discussed, his Bayesian probaility
*

*>distribution for the objective probability is sharply peaked about a
*

*>(stochastic xor effective) probability of 1%.
*

*> A common way this might occur is if he has observed, over the
*

course of

*>10 years (3652 days) that about 37 times a deer has turned up. If he
*

*>assumes that there is a fixed probability p, and initially has a
*

*>uniform
*

*>Bayesian distribution for p on (0,1), then his final distribution will
*

*>be
*

*>sharply peaked about 1%.
*

*> The point, here, is that in such a case he *can't* suddenly assume
*

*>"today is different, so while on a usual day p=.01, I'll just have a
*

*>uniform
*

*>Bayesian prior for p_today.", and then apply the "Adam paradox". So,
*

*>in
*

*>both the non-MWI and the MWI case, p~=.01 is his prior probability
*

*>before he
*

*>considers his own situation regarding reproduction, but the effect of
*

*>the
*

*>latter is different. So far I think you agree with that.
*

Yes, I think that's right so far. But prior probability is not the same

as objective probability. If there is a wounded deer in the

neighborhood, then the objective chance may be quite high (say, 78%).

But Adam doesn't know whether there is such a deer in the neighboorhood,

so his subjective credence that the objective chance is that high, is

low (say 0.1%). So he shouldn't think that a deer will turn up; that has

a low prior probability. But when he forms the appropriate reproductive

intentions, then (assuming SSA with a universal reference class), he

obtain reason to think that the objective chance is actually quite high.

This also results in his subjective credence in Deer increases.

(Note that I'm talking about an objective chance here which varies from

day to day, depending on what the deer in the region are up to. The more

deer nearby, the greater the objective physical chance that some will

pass by Adam's cave within a certain time interval.)

*>>If there are all these other fat branches in the world, then yes, I
*

*>>agree
*

*>>with that. However, Adam and Eve were there from the beginning,
*

*>>before
*

*>>there deer paths had begun to spread out much as a probability cloud
*

*>>over
*

*>>the terrain. Or at least we can suppose they were - that's the nice
*

*>>thing
*

*>>about thought experiments!
*

*> But it would be foolish of Adam to believe that. Take his name, >for
*

*>example. (Other examples are easily found.) There are millions of
*

*>other
*

*>names he could have had. The laws of physics (or initial conditions)
*

*>would
*

*>have to be set up in a very contrived way in order for the effective
*

*>probability of just the one name for the first man, Adam, to be of
*

*>order
*

*>one. Of course, in the biblical story things are very contrived
*

*>because
*

*>some guy (god) contrived it, and because this original guy was himself
*

*>unique to start with. It's not a coincidence that such a situation is
*

*>implausible, and even if it was true, only a fool would believe it.
*

Let's suppose then that Adam was a fool in that respect. It's irrelevant

to the point of the gedanken. (Besides, I don't think Adam needs to have

been that foolish, if we assume that he has had the right sorts of

revelations etc., and no exposure to other religions; in such cases, a

reasonable man might easily be led to believe in the christian God.)

*>>And I do find the premise that he can be certain that no
*

*>>type of MWI can be true hard to swallow.
*

*>>
*

*>>He wouldn't have to be certain about that.
*

*> Well, he would certainly have to assign a ludicrously high
*

*>probability
*

*>(e.g. 50%) to the idea that the MWI might be false.
*

1. That is not ludicrous even today.

2. Adam might not know contemporary physics.

3. Adam would not have to assign a 50% probability to MWI being false;

as long as there's some finite chance, one would get a shift in his

posterior probabilty after forming the intention, and that is the point

of the gedanken.

*>>You still haven't presented any way to determine the
*

*>>proper "reference class". I suggest you use the logical approach:
*

*>>include
*

*>>all observers.
*

*>>I don't see what's so particularly "logical" about that. In either
*

*>>case, we
*

*>>have to deal with borderline cases and such, and make some seemingly
*

*>>rather
*

*>>arbitrary postulations.
*

*> Much less so if all observers are included. And it's certainly
*

*>simpler
*

*>than any alternative.
*

We don't know that yet, since we haven't figured out what the

alternatives are.

*> As I see it, it is a priori possible that I could have been any
*

*>observer. Thus all observers must be included, by definition.
*

I find the "I could have been you" talk quite suspicious and murky. It's

not clear to me that this is the way to cast light on the situtation.

Nick Bostrom

Department of Philosophy

Yale University

Personal Homepage: http://www.nickbostrom.com

Email: nick.domain.name.hidden

Received on Tue Sep 26 2000 - 15:17:26 PDT

Date: Tue, 26 Sep 2000 18:15:07 -0500

Jacques Mallah wrote some time back:

[referring to my "Adam's hunting system" thought experiment - see

chapter 8 of my doctoral thesis:

http://www.anthropic-principle.com/phd/]

Adam might have reason to think that the objective chance of Deer is 1%,

and nonetheless have reason assign a 90% (say) credence to Deer. Compare

the situation to the case of a coin which has just been tossed in what

you think is a fair manner; so you think there was a 50% chance of

Heads. But suppose you have cought a brief glimps of the coin after it

landed, and it looked like Tails, although you aren't absolutely sure.

So your subjective credence may be 95%.

David Lewis discusses the relation between objective chance and

subjective credence. The upshot is that one should only set one's

subjective credence equal to the objective chance if (1) one knows about

the objective chance, and (2) one does not have impermissible evidence -

such as having seen how the coin landed, but there are more subtle forms

of inadmissible evidence as well.

course of

Yes, I think that's right so far. But prior probability is not the same

as objective probability. If there is a wounded deer in the

neighborhood, then the objective chance may be quite high (say, 78%).

But Adam doesn't know whether there is such a deer in the neighboorhood,

so his subjective credence that the objective chance is that high, is

low (say 0.1%). So he shouldn't think that a deer will turn up; that has

a low prior probability. But when he forms the appropriate reproductive

intentions, then (assuming SSA with a universal reference class), he

obtain reason to think that the objective chance is actually quite high.

This also results in his subjective credence in Deer increases.

(Note that I'm talking about an objective chance here which varies from

day to day, depending on what the deer in the region are up to. The more

deer nearby, the greater the objective physical chance that some will

pass by Adam's cave within a certain time interval.)

Let's suppose then that Adam was a fool in that respect. It's irrelevant

to the point of the gedanken. (Besides, I don't think Adam needs to have

been that foolish, if we assume that he has had the right sorts of

revelations etc., and no exposure to other religions; in such cases, a

reasonable man might easily be led to believe in the christian God.)

1. That is not ludicrous even today.

2. Adam might not know contemporary physics.

3. Adam would not have to assign a 50% probability to MWI being false;

as long as there's some finite chance, one would get a shift in his

posterior probabilty after forming the intention, and that is the point

of the gedanken.

We don't know that yet, since we haven't figured out what the

alternatives are.

I find the "I could have been you" talk quite suspicious and murky. It's

not clear to me that this is the way to cast light on the situtation.

Nick Bostrom

Department of Philosophy

Yale University

Personal Homepage: http://www.nickbostrom.com

Email: nick.domain.name.hidden

Received on Tue Sep 26 2000 - 15:17:26 PDT

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