[I sent this only to Matthew the first time around and forgot to send it to
the list. So he might have replied to this before it was posted]
Matthew wrote:
>I wrote
> > Knowledge of atypical birth rank is not a simple branch-causing
> > property. Information relevant to birth rank is distributed all
> > over Eve's possible histories, and in different ways in different
> > histories. It is not possible to take birth rank as a fact
> > independent of any of the other properties which make Eve who
> > she is.
>
>Nick Bostrom <nick.domain.name.hidden> replied
>
> > Take each Eve-observer-branch-moment, i.e. each point in time on
> > each branch containing Eve, and define its birth rank as its
> > position in the class of all such observer-branch-moments. As to
> > what Eve should think, she then average[s] over all
> > observer-branch-moments which she, for all she knows, might
> > currently be.
>
>This looks like a natural suggestion but it is not possible in my
>version of the many-minds interpretation.
>[snip]
>Thus we cannot define ``birth rank as [ ] position in the class of all
>[ ] observer-branch-moments''. The best we can do is to look at an
>observer's own personal current evidence as to his birth rank. This
>can be quite ambiguous and, in general, will be a matter for
>interpretation rather than mathematical definition.
Are you saying that it is not possible in your model to define the class of
all points in time on all branches of the universal wave function which are
at a temporal distance of, say, 10 years from the start of the world
(assuming there was a point when the world (i.e. the whole tree of
branching possibilities) started? (This is not a rhetorical question but a
clarificationary one. And I'm not asking whether we could identify those
points, but whether the class of such points is defined.)
> > Only if there was a class of observers all of whom are like Eve
> > except that they have different birth ranks would there be an
> > objective probability which Eve could use as a genuine measure of
> > the improbability of her birth rank. But such classes are
> > undefinable, even in my theory in which the set of all observers is
> > well-defined and countable, because hints about her birth rank
> > have been built into everything Eve has ever known about herself.
>
>Bostrom replied
>
> > That wouldn't make it undefinable, just small. But for reasons
> > spelled out in my dissertation, I think observer-moments should
> > be grouped in the same reference class even when they are
> > subjectively distinguishable, and I'm aware of no reason to limit
> > this only to observer-moments that are subjectively distinct
> > only regarding their knowledge of their birth ranks but not in
> > other ways.
>
>When I said ``undefinable'', I was speaking as a mathematician. I
>meant that I believe that there is no conceivable algorithm which
>could take elements of the set of observers as I define it
>(well-defined and countable although that is) and attach
>unambiguous birth ranks to each one of them.
Do you mean effectively computable algorithm?
I don't see why it would make a difference if the reference could not be
exactly computed in a finite time.
> It is even less
>plausible that there is an algorithm which will tell us whether a
>possible observer is ``like Eve'' or not. And even at the handwaving
>level, I claim that ``like Eve'' can only be interpreted either
>in a wide sense as ``like a woman'' or in a much more narrow sense
>as ``like a woman who has considerable and lifelong evidence of
>social isolation''. This implies that, although it may be
>reasonable for Eve to find her birth rank or social isolation
>improbable, she should not expect to be able to define a precise
>quantification of that improbability.
Well, I agree that with the reference class defined as "all observer-moment
that are like Eve's present one", then no precise quantification is
possible. But this is just another way of saying that we don't yet know
exactly how to define the reference class. Given a choice of reference
class, it seems that exact probabilities exist. In absence of a unique
definition of the reference class, we can still get exact probabilities in
some cases, namely if we assume that the world happens to be kind to us in
the sense that there are no observer-moments of the sort where different
plausible reference class definition would give different verdicts. Such
cases can be stipulated in thought experiments, and might be approximated
in the real world.
>Moreover, we understand probability best when it is applied to
>situations in which we can distinguish sequences of simple repeated
>events with different possible outcomes which have occurred, or at
>least could occur, under the observation of a single individual. My
>comments are also intended to stress how little Eve's social
>isolation is like that paradigm.
Yes, sure, the probabilities are different from the straightforward ones
involved in tossing a coin many times etc. That's why we are having this
discussion.
>Bostrom wrote
>
> > You know what you are; no matter how improbable, you just have
> > to take that for granted. The question is what else is true about
> > the world.
>
>As I see it, *the question* is rather ``Given what I have learned
>from my life up to now, how should I predict my future?''
I'm not sure whether we are really disagreeing on this point, although I
would insist that one sort of question we may meaningfully ask is not just
what my own future will be but also what the world is like (and was like in
the past) in general.
Dr. Nick Bostrom
Department of Philosophy
Yale University
Homepage:
http://www.nickbostrom.com
Received on Thu Oct 19 2000 - 17:24:13 PDT