From: Nick Bostrom <bostrom@ndirect.co.uk>

Date: Mon Apr 27 1998 - 18:07:18 PDT

Date: Mon Apr 27 1998 - 18:07:18 PDT

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

*
This archive was generated by hypermail 2.1.8
: Tue Mar 07 2006 - 14:45:30 PST
*