RE: Hempel's paradox redux

From: Ben Goertzel (
Date: Thu Sep 15 2005 - 21:25:05 MDT

Wow!!! Yes, that is exactly it, Jef!! That is an extremely keen
observation of your part, demonstrating a lot of insight to my world-view
(flawed as it may or may not be ;-)

My current suspicion is that if one formulates Hempel's Paradox in terms of
"experience based semantics" rather than "objectivity based semantics" then
one find there is no paradox, and one finds that observations of nonblack
nonravens don't count as evidence of black ravens.

However, I don't have time today to try and make this idea rigorous, so I
had decided to keep the idea to myself for the moment. But you sucked it
out of me ;-)

The idea would then be that

-- from an objective perspective, the standard probabilistic formulation of
the Hempel situation is the best one and the "paradox" (i.e. the
counterintuitive conclusion) holds

-- from a subjective perspective, a different formulation of the Hempel
situation is the best one and the "paradox" (the counterintuitive
conclusion) does not hold

However, I didn't yet finish checking over my drafty subjectivist
formulation of the Hempel situation, and so I'm not going to post anything
substantive on it now, for fear of posting more silly mistakes. I'll wait
till my current bout of overwork finishes up and then check the idea
carefully and see if it works...

-- Ben
  -----Original Message-----
  From: []On Behalf Of Jef
  Sent: Thursday, September 15, 2005 11:03 PM
  Subject: Re: Hempel's paradox redux

  Ben -

  I've been watching the last few days' discussion and wondering how closely
this relates to your position that subjective experience is primary relative
to the "objective".

  I suspect both of these positions of yours may have some basis in common.

  - Jef

  On 9/15/05, Ben Goertzel <> wrote:

    Just one more thing...

    I started out this whole silly thread by saying that:

> > If probability theory as standardly deployed states that an
> > of a non-black non-raven provides a NON-ZERO amount of evidence
> > 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
> > for practical AI purposes.
> >
> > However, what frustrates me about the quote you cite, and your
> > is that you seem to be denying that probability theory as standardly
> > deployed is conceptually and logically erroneous in this case --
> > 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
    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
    future -- but I suspect we haven't heard the last of this issue.

    -- Ben G

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