On 01-18-98 William Elliot wrote to John Boone... 
 
        Hello William and thanks for writing, 
  
 WE> JB> So far some defintions via the logo, Greek meaning word,  
 WE> JB> method with out any mathematical treatment, so far no   
 WE> JB> theoriums, proofs, formulas.  
 
 WE> What's the logo method of definition? 
   
  "Logo" is Greek for word.  IOW, descriptive. 
It was a mild attempt at humor . 
  
        [snip] 
  
 WE> But the trouble with descriptive stuff is that nominal 
 WE> semantics blur or even confuse the understanding.  Note the  
 WE> above example. 
   
  Yep, fuzzy logic is supposed to help us with this fuzziness. 
  
 WE>  JB> Ah, but in the world of fuzzy, a half eaten apple belongs to 
 WE>  JB> the set apple.  Take a apple, take a bite, does it belong to  
 WE>  JB> the set apples?   
 
 WE> Now if I were to take apple to mean a whole apple, it wouldn't belong. 
  
 Ok, now take, an "whole apple" but showing some signs of 
wear, rot.  Does it belong to the set "whole apple?" 
  
 WE>  WE> an apple core.  A half eaten apple is half apple.  A slice 
 WE>  WE> of an apple is 1/8 apple.  Simple enuf.  Now when a apple   
 WE>  WE> is rotten, how included in Apples is it?  How about apple   
 WE>  WE> sauce, cider?  Oh how language can out strip mathematical   
 WE>  WE> formalism.  
 
 WE>  JB> You got it, this is what Fuzzy logis is supposed to help with. 
 
 WE> It doesn't.  These are semantic determinations that have to be worked 
 
  Ok, according to Bart Kosko, it does.  I am not in a position 
to argue the point. 
  For example, in smelting, it might take temperature 
to be raised "a bit" to increase efficiency.  How much 
is "a bit" on the Temperature scale? 
 
 WE> out by 
 WE> people.  Fuzz doesn't help except that it gives a formal  
 WE> way to increase and sharpen concepts and vocabulary.  For  
 WE> example, a rotten apple is a whole apple, but not a  
 WE> wholesome apple.  Consider also green apples.  Now when we  
 
  I see you took my example . 
  
 WE> decide upon a numeric degree of appleness for rotten, 
 WE> green, bitten, apple sauce, etc, we have sharpened our  
 WE> notion of apple beyond conventional senses.  These  
 WE> determinations are difficult as they force greenness,  
 WE> rottenness and wholeness into a single linear measure.  Try  
 WE> vinegar, compare it with hard cider.  Is vinegar more or  
 WE> less apple than hard cider?  I'm alluding to a  multiple  
 WE> dimensionality of appleness. 
  
  Bart Kosko used another example of cups.  He said, take a 
coffee cup, a glass and a car  (actually he used something 
else which I don't remember)?  Does the coffeee cup belong 
the set "cups"?  Does the "glass" belong the set "cup?" 
Kosko, makes the point, fuzzy allows us say a glass belongs 
to the set "cup" a bit while belong to the set "glass" more. 
  
 WE> Closeness is an interesting example.  It can be measured in 
 WE> time and in distance.  Consider 
 WE>   Time   Distance 
 WE> A  0      0 
 WE> B  1      0 
 WE> C  0      1 
 WE> D  1      1 
 WE> Which pairs are closer?  Which are farther? 
 WE> Is AB closer or father than AC? 
 WE> AB and CD have the same separation, namely one time unit. 
 WE> AD is farther than CD by one distance unit. 
 
  Yep. 
 
Take care, 
John 
 
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