Re: another paradox and a solution

From: Nick Bostrom <bostrom.domain.name.hidden>
Date: Sat, 28 Feb 1998 11:45:08 +0000

Wei Dai wrote:

> The problem is that nothing a person does can affect the outside view,
> which is static.

Only on the AUH, right?

> > There might be many instances of the experimenter after the
> > experiment. Whose satisfaction are you talking about? If you are
> > talking about average satisfaction among the actual instances of the
> > experimenter that will exist after the experiement, and all you care
> > about is this average (you don't care at all about how many instances
> > are enjoying this satisfaction) then you might indeed get the
> > implication that you should play Russian roulette in your thought
> > example, but what's so paradoxical about that? It wouldn't mean that
> > I would have any reason to play Russian roulette in that situation,
> > for I don't think I have the goals that your argument presupposes. I
> > care about how many branches I will continue to exist on/how many
> > copies there will be of me.
>
> These things are part of the outside view. They will remain the
> same no matter what you do, so how does it make sense to have a goal of
> changing them?

Isn't it the case that on the AUH, *everything* remains the same no
matter what I do?

In one sense, yes; in another sense, no. I think it's the same as
with any other physical theory.

The sense in which I *can* make a difference,on the AUH, is I think
the following: If I choose to do action X, then that indicates that X
is a rather probable thing to happen (it has a big measure, even
though in some universes I will not do X in a similar situation). It
might not matter whether we say that I "cause" X to have a big
measure by wanting it, or we say that the ground why I want X is
that the event of me bringing X about by wanting it has a relatively
big measure.

> > That's how you define the probability, yes, but how do you define the
> > proposition "I will perceive X."?
>
> I don't know how to define it directly, but its meaning is implicit in the
> definition of the probability.

It looks to me now as if your definition of this probability agrees
with the (second) one I suggested (and which you say that Tegmark
also uses), except that I assumed a finite number of discrete
universes, whereas you stated the definition in terms of measures.

> > But your argument, it seems, presupposes that I can't care about how
> > many instances there will exist of me. That seems wrong.
>
> Part of my argument is that it doesn't make sense to have goals that refer
> to the outside view because the outside view is fixed. But I also showed
> (with the first paradox) that Tegmark's definition of probability is not
> self-consistent. I think that is the more serious problem, since if we
> have a consistent definition of probability that isn't compatible with our
> current version of decision theory, we can always modify decision theory
> or change our ideas of what is rational.

on it later.

> > Well I think that's problematic. How do we interpret these
> > "measures"? I.e. what does it mean to say that a certain instance of
> > experience has a certain measure m?
>
> One possible interpretation is that every string has an infinite number of
> instances, but some have relatively more instances than others. This is
> somewhat analagous to intervals of real numbers between 0 and 1. There are
> an infinite number of real numbers in every such interval, but some
> intervals have relatively more real numbers than others.

Some intervals may have a greater measure, but surely they have
equally many real numbers in them. That follows from the fact that R
is a dense order-type.

_____________________________________________________
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 Sat Feb 28 1998 - 03:49:35 PST

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