**From:** Marc Geddes (*marc_geddes@yahoo.co.nz*)

**Date:** Fri May 27 2005 - 22:46:37 MDT

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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
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*>
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*>
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*>So using deductive reasoning:
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*>
*

*>
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*>A
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*>A -> B
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*>-------
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*>B
*

*>
*

*>
*

*>And using probabilistic reasoning:
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*>
*

*>
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*>P(B) = P(A) * P(B | A) + (1 - P(A)) * P(B | ~A)
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*>= 1 * 1 + 0 * P(B | ~A) = 1
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*>
*

*>
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*>Mr. Geddes, I think you may be interested in reading
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*>_Probability
*

*>Theory: The Logic of Science_ by ET Jaynes. It's a
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*>large book, but
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*>reading the first 30 pages or so should be enough to
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*>clear these matters
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*>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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