Hempel's paradox redux

From: Ben Goertzel (ben@goertzel.org)
Date: Thu Sep 15 2005 - 20:25:40 MDT

Just one more thing...

I started out this whole silly thread by saying that:

> > If probability theory as standardly deployed states that an observation
> > of a non-black non-raven provides a NON-ZERO amount of evidence toward
> > the hypothesis that all ravens are black, then this shows there is
> > something wrong with probability theory as standardly deployed.
> >
> > Of cousre, an approach that yields small errors may still be valuable
> > for practical AI purposes.
> >
> > However, what frustrates me about the quote you cite, and your attitude,
> > is that you seem to be denying that probability theory as standardly
> > deployed is conceptually and logically erroneous in this case -- albeit
> > the magnitude of its error is generally small.

I admit that in my followup discussions, after making this statement,
I manifestly failed to demonstrate its truth...

Instead, I made some careless and silly errors, both with the standard
formulation of probability theory and with my own PTL formulation. I
apologize for this -- I'm not usually quite *that* error-prone even
when badly overworked, but what can I say, it happens from time to

However, after all that, I *still* hold the same intuition that I had
originally. And this is with the probabilistic arguments regarding the
Hempel paradox quite fresh in my mind and quite fully understood both
conceptually and arithmetically.

I don't doubt the math of probability theory, but I still have a nagging
intuitive suspicion that the way the math is being applied to this situation
is not conceptually right. Furthermore, I still have the same suspicion
that this conceptual wrongness is related to other problematic issues
with standard AI deployments of probability theory such as Bayes nets.

I will be traveling for most of the next two weeks, so don't expect any
brilliant insights or stupid errors from me in this regard in the immediate
future -- but I suspect we haven't heard the last of this issue.

-- Ben G

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