Date: Wed, 9 Apr 1997 23:25:28 -0700
From: jmgs (jmgs)
Subject: Re: Fuzzy logic example

Hi Richard,

   Thanks for your example application of fuzzy logic (a non-Aristotelian
'logic').  I've added it to the related thread in the g-s. web archive
I'm maintaining.

   I'll add that, as I understand it, we can make a clear distinction
between "fuzzy logic" and "probabilistic logic" (statistical reasoning):
when reasoning with probabilities, we're concerned with the "likelihood"
that an event will happen 100% or that a statement is 100% true ... and 
when reasoning with fuzzy sets, we're more concerned about a statement
being partially true (and partially false) or an event happening only
to some degree.  For better or for worse, a probability-distribution
curve can provide a reasonable measure of fuzzy-set membership ... which,
I believe, has led a number of theorists to claim there 'is no' difference
between fuzzy and statistical theory!

   This brings up a related consideration: some g-s'ists (including  
Korzybski himself, I believe!) seem to have assumed that Aristotelian
'logic' has a place in a non-Aristotelian system.  K wrote of 'logical
existence' and 'logical fate' (premises1 "lead to" theories1 and not
to theories2 ... one needs to adopt premises2 which "lead to" theories2).
Stuart Mayper wrote a paper (in one of the GSB's) about using non-A means
to derive higher-order abstractions in the form of hypotheses, and then
use A-logic to derive predictions to be tested.  Many g-s'ists, along
with K, hold the practice of 'mathematics' as an example of one of the
"best" ways to use our 'neural-systems', yet most of traditional 
'mathematics' relies on A-logic.  It seems to me the key aspect of A-logic
used in these examples relies on the validity of "inference" (e.g., 
if A always leads to B, and we have A, then "certainly" we have B).
I briefly searched in various 'Logic' texts for some "proofs" of the
validity of inference, but could find none (admittedly, I didn't perform
an exhaustive search).  The closest I got was a statement by Bertrand
Russell to the effect that he couldn't prove it; it just seemed quite
reasonable to him, and he posited that perhaps this neural-hardwiring
of the practice of "inferring" evolved in us over the past few million
years, and was apparently successful enough to allow our ancestors to
reproduce.  Well ...!  Every "inferring" that a human being performs,
he/she performs it neurally ... and perhaps the "automatic" action is
not necessarily the _only_ neural action that can be performed.  If we
can "delay our reactions" to some degree, then that opens the door to
some other possible actions, such as "non-Aristotelian inferring".
I believe the fuzzy-theorists have been working on this very problem,
though most perhaps don't realize the 'implications' (:-) this has for
the very workings of their own brain-minds (some, however, do seem to
realize this).  So, they've developed fuzzy-inference, fuzzy-arithmetic,
fuzzy-mathematics, etc. ... rooting out the A-logic from fields previously
dominated by its use.  This, of course, leads to the possibility of
rooting out its use in general-semantics as well.  We no longer need
to assume we have to use A-logic in part of our system ... and I suggest
we consider the possibility of going "fully" non-Aristotelian (and I hope
you don't consider that "fully" to 'be' an implicitly "Aristotelian"
qualifier ... it takes place on the next higher level of abstraction,
as in Einstein's theory that "all" motion is relative and Korzybski's
theory that "all" knowledge about the imperceptible process/event level
of 'reality' is to be regarded as tentative).

--
John McPherson (jmgs@lumina.ucsd.edu)
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