Re: predictions

From: Wei Dai <weidai.domain.name.hidden>
Date: Sun, 5 Apr 1998 18:09:17 -0700

On Sun, Apr 05, 1998 at 11:06:13PM +0000, Nick Bostrom wrote:
> 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.)

This operationalization allows you to make explanations, but not
predictions.
At time 1, it doesn't help me to know that "If I'm at time 2 and I
remember observing coin landing heads at time 1, then the probability of
observing x is p." I mean it is not helpful in the sense of helping me
make decisions at time 1, because the probability is conditional on my
state of knowledge at time 2. According to decision theory, I can only use
probabilities that are conditional on my current state of knowledge.

It is helpful to me at time 2, but only in the sense that it explains why
I am observing x, namely that I remember observing heads at time 1 and
therefore now have a probability p of observing x.
Received on Sun Apr 05 1998 - 18:11:51 PDT