Wei Dai wrote [interesting stuff]:
> This is an attempt to save baysianism in the face of the coin-toss copying
> paradox. There are two parts to this solution:
>
> 1. Statements which use the word "I", "me", or "my" do not count as well
> defined hypotheses. They are not assigned probabilities.
> 2. There is only one real universe. (The One Universe Hypothesis or 1UH)
>
> The justification for 1 is that the word "I" is being used to refer to
> different objects in different statements, so what appears to be
> P(AB|C) <> P(A|BC)P(B|C)
> is actually
> P(AB|C) <> P(A|DC)P(D|C)
> which is not interesting. Instead of "I", we need to be more specific. For
> example, "I will perceive X at time t" should be replaced with "Everyone
> at time t who remembers being in mind state M will perceive X" or "At
> least one person at time t who remembers being in mind state M will
> perceive X".
The problem with this, as I hinted at in my two previous posts, is
that in most relevant contexts we can replace "I" or "me" with a
definite description that singles out the same individual. This
definite description can be phrased in terms that are clearly
meaningful and unambigous. For example, you say:
> This solution takes care of the Doomsday Argument as well. (See Nick's
> paper for a description of the DA.) Consider two possible universes.
> Universe A ends after the 100th birth. Universe B ends after the 200th
> birth. Suppose someone in one of these universes has not yet learned his
> birth rank, and denote his mind state as M. His P(universe A is real) =
> P(universe B is real) = 1/2. Now suppose someone tells him that his birth
> rank is 40. Since "My birth rank is 40" is not a well defined hypothesis,
> he restates that as E = "At least one person with mind state M has birth
> rank 40." Since P(E | universe A is real) = P(E | universe B is real) = 1,
> this knowledge does not change his beliefs about which universe is real.
So far so good. But what if we replace "M" with "The guy whose name
is Nick Bostrom." Now, without knowing anybody's rank, I can ask the
question: "What is the probability that the guy whose name is Nick
Bostrom has a rank less than or equal to 100?" And we can ask: "What
is the probability that there the real universe is B, given that the
guy whose name is Nick Bostrom turns out to have a rank of 74?" There
seem to be well-posed questions, and they seem to suffice to produce
the Doomsday argument. For suppose I suffer from amnesia and can't
remember anything about my birth rank. Based on other considerations,
I assign a fifty-fifty probability that the universe is A/B. I can
then, in this situation, ask: "What's the probability that the guy
who's called Nick Bostrom should have a rank less than or equal to
100, given that the universe is B?" Since I don't have any other
relevant information, by the principle of indifference I should
answer: "1/2". The same question for universe B get the answer: "1".
When I then discover that the guy called Nick Bostrom has birth rank
#74, I have to make a probability shift. The Doomsday conclusion
follows from this.
_____________________________________________________
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 Apr 14 1998 - 16:09:19 PDT