RE: Hempel's paradox redux

From: Ben Goertzel (
Date: Thu Sep 15 2005 - 17:35:05 MDT

> 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.

Well, Eli, I don't think you have a strong grasp on my psyche or my
knowledge of mathematics ;-)

I was the 7-year-old kid who could do all sorts of advanced algebra but
still vexed his teachers by sometimes making dumb careless mistakes in
addition problems!

But anyway, your set of misconceptions about my personal strengths and
weaknesses is not a very generally interesting topic, so I don't think I
will pursue it on this list...

Let me just say this: I have pursuing a pretty interesting train of thought
about the nature of evidence, and I'm pretty confident it will lead to
something interesting and valuable in the end. However, this interesting
train of thought seems to have led me to some incorrect ways of analyzing
situations (which contradict my own PTL probability-math formalism, in
fact), as an interim effect.... Ah well. Anyway if this germinal,
at this point still flaky way of thinking about evidence turns up anything
demonstrably valuable, I'll let you know...

> 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.

The big challenge in that little corner of research seems to have been
the assumptions weak enough that the mathematical formalization of the
problem can fairly be considered as matching the intuitive statement of
the problem. According to my own judgment (and I realize this is
a subjective thing) the earlier papers I read didn't meet this criterion
very well, but Fitelson's paper basically does, which is interesting to me.

I only surveyed the literature haphazardly though...


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