On 01-16-98 William Elliot wrote to John Boone... 
 
        Hello William and thanks for writing, 
  
 WE>  WE> Good, take your time.  Did you print it out to a file?  
 WE>  JB> Thanks, no, to my printer, piece of paper.  
 
 WE> Hm.  Can you also archive it in a file?  May be useful for 
 WE> inclusion in subsequent discussion. 
    
  Yep, but would require me to type and save with some sort 
of editor. 
  
 WE>  WE> First there is fuzzy set theory in which a set is an 
 WE>  WE> assignment of a degree of belonging to each element.  For   
 WE>  WE> simplicity, elements are consider to be distinct from sets.   
 WE>  WE>  The second notion is fuzzy logic or multi-value logic  
 WE>  WE> which assigns multiple truth values to statements.  
 
 WE>  JB> Yes, but I do believe they are related.   For example, 
 WE>  JB> when I examine a system of statements, I often use set  
 WE>  JB> theory to help me.  
 
 WE> Yes they are.  The non-fuzzy propositional 'and', 'or', 'not', and 
 WE> 'implies'  
 WE> are in parallel with the set multiplication, addition,  
 WE> complimentation and inclusion.  not(x or y) = notx and noty  
 WE> or -(x + y) = (-x) * (-y) is true for both sets and  
 WE> propositions.  Indeed, the duality theorem of set theory is  
 WE> a rerun of the duality theorem for the propositional  
 WE> calculus.  However note the difference.  Logic will go into 
 WE> (x)P and (Ex)P while sets are concerned about x e A.  For  
 
  Not sure what you mean by (x)P and (Ex)P?????? 
  
 WE> all x P, there exists a x such that P, x is a member of A. 
 WE> Here we see divergence. 
 
  Are these set statements or propositional statements? 
At points such as "x is a member of A" reminds me of 
set theory, while "For all x P", leaves me wondering what 
P is (the set of Propositional statements)?  
 
Take care, 
John 
 
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