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From: hubey@pegasus.montclair.edu (H. M. Hubey)
Subject: Re: Fuzzy theory or probability theory?
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Date: Sat, 3 Dec 1994 18:27:33 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.fuzzy:3540 sci.stat.math:3479

sthomas@decan.gate.net (S. F. Thomas) writes:

>H. M. Hubey (hubey@pegasus.montclair.edu) wrote:

>: So then if not(tall) is short, and not(short) is tall, then
>: "tall and not(tall)" is equivalent to "not(short) and not(tall)".
>: But this is not a contradiction is normal everyday conversation

>I disagree.  In the English language as I understand it, there is a
>big difference between "short" and "not tall".  "Tall and not tall"
>remains a contradiction in my mind, while "not(short) and not(tall)"
>is perfectly understandable to me as an English speaker approximating


The good thing about fuzzy reasoning is that it always seems to work :-).
But joking aside, from the view of classical bivalent logic, either words
like tall/short, hot/cold, near/far are related or not. If we don't take
tall=not(short) or short=not(tall), then I don't see how standard logic
will work without producing contradictions. We don't have any choice
[from the standard logic view] except to accept them. If we then attempt
to fuzzify, we can produce ranges. Tall, very tall, extremely tall, 
not too tall, not short, neither tall nor short, tallish, not short, 
medium,,,,,, etc.

I was comparing fuzzy logic to bivalent logic, as you can see. If we
start out with already a whole range of values, then if this is not
from the point of view of standard logic, then why do we need to save
either the LEM or L of Contradiction at all?


In any case, you can already see something like this in Chomsky's 
phonemics, in which two distinctive features High and Low are used
and it's possible to assign High&Low or Not(high)&Not(Low).


--
						-- Mark---
....we must realize that the infinite in the sense of an infinite totality, 
where we still find it used in deductive methods, is an illusion. Hilbert,1925
