From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Mon Sep 12 2005 - 14:42:46 MDT
Ben Goertzel wrote:
>
> To get from
>
> NOT(black) ==> NOT(raven)
>
> to
>
> raven ==> black
>
> requires a logical transformation that does not preserve "amount of
> evidence", at least not according to PTL's theory of evidence. And when you
> look at the algebra of evidence transformation that comes along with this
> transformation, you find that in fact the amount of evidence about
> raven==>black ensuing from NOT(black) ==> NOT(raven) comes out to zero...
Actually, let me pose an even simpler question. Will PTL be willing to
bet on different odds for "All ravens are black" and "All non-black
objects are not ravens"? And do you acknowledge that, extensionally,
there is no state of the world where one of these statements is true and
the other is false? If so, then dutch book can be made against
Novamente; that is, Novamente will accept a set of bets for which it is
deductively provable that the result is a loss, regardless of the actual
state of the world.
If evidence has a special meaning in PTL, then let's talk just about
Novamente's betting odds - that translates everything into a language we
can all understand.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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