**From:** Eliezer S. Yudkowsky (*sentience@pobox.com*)

**Date:** Thu Sep 15 2005 - 16:48:59 MDT

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Ben Goertzel wrote:

*> FYI,
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*>
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*> Just to put the raven paradox to rest, I did a little poking around and
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*> found a paper
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*>
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*> http://fitelson.org/ravens.pdf
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*>
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*> which does a quite nice job of addressing all the issues that intuitively
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*> bothered me with the traditionally-cited Bayesian analyses of the Raven
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*> paradox.
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*>
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*> He shows why the traditional Bayesian arguments depend on unacceptable
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*> assumptions, but then gives a pretty rigorous mathematical analysis based on
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*> fairly minimal assumptions -- it's a nice paper. [In other words, he
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*> criticizes probability theory "as traditionally deployed" in this context,
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*> but does it well ;-) ] *This* kind of probabilistic argumentation is always
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*> convincing to me...
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Actually, it looks like Fitelson is saying pretty much the same thing I

said in my first reply: Say explicitly your background assumptions

about sampling and prior probabilities, because the results will

strongly depend on them. Fitelson also analyzes the dependency on

background assumptions in essentially the same way - albeit at greater

depth and lesser breadth.

The main part of Fitelson's paper focuses narrowly on one challenge:

weakening the assumptions necessary to show that a non-black non-raven

is *much weaker* evidence favoring "All ravens are black" than is a

black raven, assuming both evidences are favorable. I read the paper

quickly, but it looks to me like I discussed a wider range of conditions

and dependencies in my own, fast, nonrigorous presentation. That is,

the main part of Fitelson's paper is a rigorous, narrow analysis of one

of many issues I briefly mentioned.

Where Fitelson and I discuss similar relations between background

assumptions and results, Fitelson's conclusions seem to agree with mine.

Thus I don't see any place where I departed from the practice of good

Bayesians in my first reply to your question - I elaborated on the

traditional Bayesian analysis along the same lines Fitelson does. And

you did criticize my own reply to you, not only probability theory "as

traditionally deployed". Ben, I don't think you have a strong grasp on

Bayesian probability theory "as traditionally deployed" - at the very

least you need more practice applying it to example problems before you

develop a decent feel for it.

I also don't think it's fair to characterize Fitelson's paper as a

criticism arguing that "traditional" Bayesian analysis relies on hidden,

unacceptable assumptions. There are many published works on Hempel's

paradox by authors trying to work within the Bayesian tradition. Those

that I have seen tend to do a decent job of stating their assumptions,

albeit not with the rigor shown by the best Bayesians such as Jaynes.

Fitelson is not criticizing those analyses, he is strengthening a

certain result by weakening its assumptions. The part where Fitelson

tries to characterize the standard assumption as overly strong, is not

so much criticism of traditionally deployed Bayesian probability theory,

as Fitelson trying to show that his new result is interesting.

-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence

**Next message:**Richard Loosemore: "Re: Hempel's paradox redux"**Previous message:**Eliezer S. Yudkowsky: "Re: Hempel's paradox redux"**In reply to:**Ben Goertzel: "RE: Hempel's paradox redux"**Next in thread:**Ben Goertzel: "RE: Hempel's paradox redux"**Reply:**Ben Goertzel: "RE: Hempel's paradox redux"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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