>>> John Boone on Fuzzy Logic 
 WE> Good, take your time.  Did you print it out to a file? 
 JB> Thanks, no, to my printer, piece of paper. 
Hm.  Can you also archive it in a file?  May be useful for inclusion in 
subsequent discussion.
 
 WE> First there is fuzzy set theory in which a set is an 
 WE> assignment of a degree of belonging to each element.  For  
 WE> simplicity, elements are consider to be distinct from sets.  
 
 WE>  The second notion is fuzzy logic or multi-value logic 
 WE> which assigns multiple truth values to statements. 
 JB> Yes, but I do believe they are related.   For example, 
 JB> when I examine a system of statements, I often use set 
 JB> theory to help me. 
Yes they are.  The non-fuzzy propositional 'and', 'or', 'not', and 'implies' 
are in parallel with the set multiplication, addition, complimentation and 
inclusion.  not(x or y) = notx and noty or -(x + y) = (-x) * (-y) is true for 
both sets and propositions.  Indeed, the duality theorem of set theory is a 
rerun of the duality theorem for the propositional calculus.  However note 
the difference.  Logic will go into (x)P and (Ex)P while sets are concerned 
about x e A.  For all x P, there exists a x such that P, x is a member of A.  
Here we see divergence.
... I think, therefore the universe thinks.
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