From: Hal Finney <hal@rain.org>

Date: Mon Apr 27 1998 - 09:24:31 PDT

Date: Mon Apr 27 1998 - 09:24:31 PDT

Nick Bostrom, <bostrom@ndirect.co.uk>, writes:

*> When I say "The probability of H is 40%." I could mean to:
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*>
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*> 1. Say something about my personal subjective probability.
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*>
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*> 2. Say something about the common subjective probability relative to
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*> the present knowledge basis of humankind
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*>
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*> 3. Say something about the objective probability of the event.
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*> Depending on which sense of probability we have in mind, we might
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*> give very different numerical estimates. Consider the question: "What
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*> is the probability that nanotechnology will cause the extinction of
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*> earth-descendent intelligent life?"
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*>
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*> In sense 1, I might answer: "25%".
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*>
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*> In sense 2, I might say: "I don't know, but I would guess somewhere
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*> between 2% and 70%."
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*>
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*> In sense 3, I might say: "I don't know but I think it more probable
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*> that it is somewhere between 99.9% and 100% than that it is between
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*> 50% and 60%.
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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,

rather than the probability that you would assign to it. I personally

might believe an event to have 25% probability while the common person

would give it a 50% probability. However I suspect that is not what

you mean.

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?

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? That seems to

be a reasonable way to understand the notion of uncertainty.

And isn't case 2 really just identifying the kind of information you

take into consideration in generating the probabilities you describe in

cases 1 and 3? Of course you will attempt to take into consideration

all the information available to you in making a probability judgement.

That will be a subset of the present knowledge of humankind, of course,

but 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.

If you were just being philosophical and identifying different aspects

or ways we might think of probability, I'd let it go. But the fact

that you get different answers for the different approaches suggests

that there is some objective difference. In that case it would be

important to understand what sense of probability is being used in order

to interpret a statement of uncertainty.

Hal

Received on Mon Apr 27 16:38:13 1998

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