Wei Dai wrote:
> > 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."
> It's a way out, but doesn't it also render the AUH useless? If it can
> only generate predictions of the form "If I had my eyes closed and I'm
> told it's time x, ..." what good would it be?
Well, that's only another way of saying that the prior probability
of observing heads, relative to knowing that it is time 2 and
remembering that the coin landed heads at time 1, is 1. Is there
anything important that the above operationalization does not allow
you to say? The AUH is still active, I think, in two ways: (1) It's
a metaphysical statement about the ontology of the universe; (2)
it generates prior probabilities for all events, and hence tells us
what we should believe in any situation we might find ourselves in.
(Of course, (2) will only obtain if we can satisfactory solve the
problem of deriving specific probabilities from the AUH, which
includes all the problems with infinities, which Turing machines and
which mappings to choose, etc.)
_____________________________________________________
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 Sun Apr 05 1998 - 15:12:10 PDT