On Fri, 09 Feb 2007 11:19:52 -0500, Ben Goertzel <[EMAIL PROTECTED]> wrote:
Note that coherency does not constrain one to be especially accurate in
one'sjudgemental probabilities. A coherent entity needn't be very smart
about thetrue state of nature. The coherency constraint merely defines
the outer limitsof what one may rationally consider possible.
This is incorrect, I believe. Coherency requires one to be reasonably
consistent in one's assignment of probabilities to various interdependent
outcomes, otherwise a dutch book can be made against one.
That would depend on the meaning of "reasonably consistent" but in any
case I believe this is at the root of our differences of opinion about De
Finetti coherence.
You may mean something else by coherence, but as I understand De Finetti
it does not entail anything like in-depth knowledge or omniscience about
the world of complex interdependences. To be coherent one need only avoid
self-contradiction.
Here is a quote from a source I've found very helpful in understanding De
Finetti coherence:
"Naturally, coherence does not determine a single degree of rational
belief but leaves open a wide variety of choices... The idea here is that
we have to make sure our various degrees of belief fit together so to
avoid the 'contradiction' of a Dutch book being made against us. The term
'coherence' is now generally preferred..." [1]
Thus, to be coherent, we need to ensure that our beliefs "fit together"
(logically). This is separate from considerations about whether those
beliefs are actually true.
This coherency constraint is entirely subjective, a sort of first order
rational constraint which comes before other logical constraints which
might be related to what is actually true 'out there' in the world of
complex interdependencies, which I certainly do not deny exists.
Guaranteed losses to dutch books in De Finetti-style arguments are not
evidence of a lack of knowledge about the complex interdependencies in the
world --- they are evidence of self-contradiction, evidence of incoherent
thinking on the part of the better no matter his degree of knowledge about
the world.
To avoid a dutch book, an entity need only check first before acting to
make sure its relevant assumptions are logically compatible. And in the
case where it has no relevant assumptions then no book can be made against
it.
[Concerning the interesting conjunction fallacy post by Eliezer, I should
read it again but under the assumptions given, (concerning Kolmogorov
complexity and so forth), it seemed to me that the example as stated was
not actually an example of fallacious reasoning.]
1. D. Gillies (2000)_Philosophical Theories of Probability_, pg 59
-gts
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