From: Marc Geddes (marc_geddes@yahoo.co.nz)
Date: Fri May 27 2005 - 22:46:37 MDT
Peter de Blanc wrote:
>Here's an example, then. Let's suppose we know that
>A, and we know that
>A->B. This can also be written as:
>
>
>P(A) = 1 and P(B | A) = 1
>
>
>So using deductive reasoning:
>
>
>A
>A -> B
>-------
>B
>
>
>And using probabilistic reasoning:
>
>
>P(B) = P(A) * P(B | A) + (1 - P(A)) * P(B | ~A)
>= 1 * 1 + 0 * P(B | ~A) = 1
>
>
>Mr. Geddes, I think you may be interested in reading
>_Probability
>Theory: The Logic of Science_ by ET Jaynes. It's a
>large book, but
>reading the first 30 pages or so should be enough to
>clear these matters
>up for you.
This looks good on paper. It does superficially
appear to be the case that deduction is just a special
case of Bayesian reasoning.
Some problems though. For one thing, there's more to
intelligence than just calculation of probabilities -
there is also the goal system. The thing about
deduction is that there is more going on than just
calculation of probabilities. There is a switch to
descriptions of reality at higher levels of
organization where classifications are being made that
go beyond mere associations. This implicitly
introduces an 'extra' ingredient over and above mere
calculation of probabilities. In Pinker's book 'How
The Mind Works' there is a good explanation of why
conceptual (deductive) reasoning cannot in practice be
reduced to mere associations (which is what Bayesian
Induction really is).
I wouldn't be so quick to embrace the religion of
Bayes if I were you. Reading more widely in
philosophy reveals that there are dissenting opinions
as to whether the Bayesian framework really is the
ultimate epistemology that it is touted to be. For
instance I recommend the excellent book 'Theory and
Reality' by leading philosopher of science
Godfrey-Smith. He devotes a whole chapter to the
philosophy of Bayesianism, beginning with this:
'Although Bayesian is most popular approach to solving
these problems today, I am not in the Bayesian camp.
Some parts of Bayesianism are undeniably powerful, but
I would cautiously put my money on some different
ideas. These will be introduced at the end of the
chapter...'
Go read the book if you want to see what ideas he's
referring to:
http://www.amazon.com/exec/obidos/ASIN/0226300633/
--- THE BRAIN is wider than the sky, For, put them side by side, The one the other will include With ease, and you beside. -Emily Dickinson 'The brain is wider than the sky' http://www.bartleby.com/113/1126.html --- Please visit my web-site: Mathematics, Mind and Matter http://www.riemannai.org/ --- Find local movie times and trailers on Yahoo! Movies. http://au.movies.yahoo.com
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