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From: meron@cars3.uchicago.edu
Subject: Re: Zero, a bad concept for logic, math and science?
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References: <ecox.68.003376EB@paltech.com> <671.6603T67T1351@portal.ca> <ecox.72.00082C83@paltech.com>
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Date: Tue, 30 Jan 1996 22:16:00 GMT
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Xref: glinda.oz.cs.cmu.edu sci.physics:168117 comp.ai:36566 comp.ai.philosophy:37257 sci.philosophy.meta:23964 sci.math:134429

In article <ecox.72.00082C83@paltech.com>, ecox@paltech.com (Earl Cox) writes:
>In article <671.6603T67T1351@portal.ca> lance@portal.ca (Lance Neustaeter) writes:
>>From: lance@portal.ca (Lance Neustaeter)
>>Subject: Re: Zero, a bad concept for logic, math and science?
>>Date: 30 Jan 1996 10:55:02 GMT
>
>
>>On 28-Jan-96 11:22:50, Earl Cox ecox@paltech.com wrote:
>
>>> Well, I don't agree with Tom on this point, BUT, the excluded middle is
>>> faulty  as a representation of most real-world phenomena. Most of us in
>>> fuzzy logic  have recognized this for many years. What's the opposite of
>>> TALL, FAST, HIGH,  and other continuous processes? 
>
>>not-tall, not-fast, not-high.
>
>>And, taken together (eg: high OR not-high) you have a jointly exhaustive
>>and mutually exclusive representation.  Surely you're not suggesting a third
>>alternative to high and not-high?  Or are you? (high, that is).
>
>===================================================================
>Since TALL does not have precise boundaries, the intersection of TALL and 
>not(TALL) is not an empty set but a set containing those individuals that have 
>some degree of Tallness and not-Tallness. This is one of the basic 
>epistemological rules of fuzzy logic. See any basic book on fuzzy systems 
>(such as my "Fuzzy Systems Handbook", _Counterintuitives and the Law of 
>Noncontradicition", page 125.
>
So, if you use fuzzy terms you have fuzzy boundaries, therefore fuzzy 
logic.  That's not great news.  Certainly not a basis for saying that 
"the excluded middle is faulty".  Its like complaigning that 
screwdrivers are faulty since they don't chop firewood very well.  
Tools are designed for specific purposes and situations and that's 
where they are applicable.  If you try to use one beyond its range of 
applicability and it doesn't work it is you who is at fault, not the 
tool.

Mati Meron			| "When you argue with a fool,
meron@cars3.uchicago.edu	|  chances are he is doing just the same"
