Re: poly: What probabilities?

Hal Finney wrote:

> Nick Bostrom, <bostrom@ndirect.co.uk>, writes:
> > When I say "The probability of H is 40%." I could mean to:
> >
> > 1. Say something about my personal subjective probability.
> >
> > 2. Say something about the common subjective probability relative to
> > the present knowledge basis of humankind
> >
> > 3. Say something about the objective probability of the event.
>
> > Depending on which sense of probability we have in mind, we might
> > give very different numerical estimates. Consider the question: "What
> > is the probability that nanotechnology will cause the extinction of
> > earth-descendent intelligent life?"
> >
> > In sense 1, I might answer: "25%".
> >
> > In sense 2, I might say: "I don't know, but I would guess somewhere
> > between 2% and 70%."
> >
> > In sense 3, I might say: "I don't know but I think it more probable
> > that it is somewhere between 99.9% and 100% than that it is between
> > 50% and 60%.
>
> I don't understand why you give different answers for these
> interpretations. It seems to me that they are different ways of stating
> the same basic concept.
>
> The one possible exception is case 2, where it sounds like you might be
> referring to the probability that other people would assign to the event,

Roughly, yes.

> Looking at your examples, in case 1 you have given a specific value,
> in case 2 you give a range, and in case 3 you hint at a probability
> distribution over probabilities. Is that meant to be a general
> distinguishing characteristic of your three interpretations? Would you
> expect that interpretation 1 would always lead to a specific value,
> interpretation 2 to a range, and interpretation 3 to a distribution over
> probabilty ranges?

As was pointed out, one could make sense
of a probability range or distribution in sense 1; it would be my
present guess of what I would come to believe if I thought about it
for a while. Probabilities in both sense 2 and 3 are scalars, but
since I don't know their value, I could express my opinion on them by
saying that I think they are in a certian range (or I could be
more specific and give a distribution).

> Couldn't your personal subjective probability be *defined* based on
> the case 3 interpretation, where you imagine a set of possible worlds
> which are consistent with your present knowledge, and you guess at
> what percentage of them lead to the specified outcome?

I'm not sure I undestand this, but I think the following will help
you see what I have in mind:

What is the probability that this die will show a five? Suppose you
have no other relevant information. Then the subjective (sense 1)
probability for you is 1/6. But as it happens, the dice is loaded, so
it always shows a five. Hence the probability of a of a five (in
sense 3) is 100%.

>surely you didn't literally mean that case 2 probabilites are based
> on all of the information available, since no person can hold that much
> information in his mind.

I see no reason why that would be a problem. We could call that
probability in sense 4. However, I didn't in fact mean to make sense
2 probabilities relative to all knowledge possessed by humans. I
rather meant something like: the odds that a rational, ideally
well-educated person ought to give.

> If you were just being philosophical and identifying different aspects
> or ways we might think of probability, I'd let it go.

I'm never being just philosophical. I leave that business to my
honored colleges :-)

> But the fact
> that you get different answers for the different approaches suggests
> that there is some objective difference.

Yes, that's what I'm claiming.

_____________________________________________________
Nick Bostrom
Department of Philosophy, Logic and Scientific Method
London School of Economics
n.bostrom@lse.ac.uk
http://www.hedweb.com/nickb
Received on Tue Apr 28 00:13:32 1998