From: James Rogers (jamesr@best.com)
Date: Wed Nov 20 1996 - 14:23:35 MST
At 08:40 PM 11/19/96 -0500, you wrote:
>I've been lurking on the sidelines for awhile, but I thought I would jump in
>with a thought about "fuzzy logic." I have only skimmed Kosko's books, but I
>*did* hear him speak once on the topic.
>
>My main problem with the whole concept is that it seems to require one to
>abandon the *extremely* useful notion of "reductio ad absurdum." That is, I
>can't prove A simply by proving ~ [~A] (i.e., assuming ~A and showing that
>leads to a contradiction. Seems too much to give up.
>
I don't think that fuzzy logic has much place with respect to mathematical
theory and proofs. It is really a computational tool for generating
concrete values in a probability-driven environment. Yes, there are areas
of mathematics (Bayes anyone?) that specifically deal with these types of
situations and constructs, but they are not a replacement for fundamental
logic constructs. I don't think anyone is doing "fuzzy" proofs of any
mathematical theory. The usefulness of fuzzy logic is that it gives
computational methods using non-deterministic logic and values (boolean
sense) in a way that allows you to extrapolate a deterministic boolean
outcome. Or, if you prefer, a probability based solution.
Of course, I am not exactly an expert on this, so feel free to tear this
apart ;-)
-James Rogers
jamesr@best.com
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