>>> John Boone on Fuzzy Sets 
 WE> Substance is explicit definitions, theorems, proofs, formulas. 
 JB> So far some defintions via the logo, Greek meaning word, 
 JB> method with out any mathematical treatment, so far no  
 JB> theoriums, proofs, formulas. 
What's the logo method of definition?
 WE> Note that every fuzzy set contains all of the elements x e 
 WE> U to varying degrees.  The fuzzy set U contains all the  
 JB> Yep, it would appear that way, if we have the definition 
 JB> correct. 
But semantically this can mean an element contained in a set with degree 0 
doesn't belong.
 
 WE> This sounds like descriptive stuff. 
 JB> Yes, but I think attempts to explain the point. 
But the trouble with descriptive stuff is that nominal semantics blur or even 
confuse the understanding.  Note the above example.
 JB> Ah, but in the world of fuzzy, a half eaten apple belongs to 
 JB> the set apple.  Take a apple, take a bite, does it belong to 
 JB> the set apples?  
Now if I were to take apple to mean a whole apple, it wouldn't belong.
 
 WE> an apple core.  A half eaten apple is half apple.  A slice 
 WE> of an apple is 1/8 apple.  Simple enuf.  Now when a apple  
 WE> is rotten, how included in Apples is it?  How about apple  
 WE> sauce, cider?  Oh how language can out strip mathematical  
 WE> formalism. 
 JB> You got it, this is what Fuzzy logis is supposed to help with. 
It doesn't.  These are semantic determinations that have to be worked out by 
people.  Fuzz doesn't help except that it gives a formal way to increase and 
sharpen concepts and vocabulary.  For example, a rotten apple is a whole 
apple, but not a wholesome apple.  Consider also green apples.  Now when we 
decide upon a numeric degree of appleness for rotten, green, bitten, apple 
sauce, etc, we have sharpened our notion of apple beyond conventional senses. 
 These determinations are difficult as they force greenness, rottenness and 
wholeness into a single linear measure.  Try vinegar, compare it with hard 
cider.  Is vinegar more or less apple than hard cider?  I'm alluding to a  
multiple dimensionality of appleness.
Closeness is an interesting example.  It can be measured in time and in 
distance.  Consider
  Time   Distance
A  0      0
B  1      0
C  0      1
D  1      1
Which pairs are closer?  Which are farther?
Is AB closer or father than AC?
AB and CD have the same separation, namely one time unit.
AD is farther than CD by one distance unit.
... Is Occam's razor sharp enuf to split hairs?
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