>>> John Boone on Fuzzy Logic 
 WE> Hm.  Can you also archive it in a file?  May be useful for 
 WE> inclusion in subsequent discussion. 
 JB> Yep, but would require me to type and save with some sort 
 JB> of editor. 
Shouldn't.  BlueWave offline reader has a save to file feature.  My 
communication software has a screen capture feature.  If you're using windows 
you ought to be able to cut and paste a whole message.  Additionally, BBS 
read messages software may allow a download of messages but this may be 
little different than having offline message reading software.
 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' 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  
 JB> 
 JB> 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. 
Let P be the statement (x is weird).  Then (x)(x is weird) is 'all is weird' 
and (Ex)(x is weird) is 'something is weird', or formally 'for all x, x is 
weird' and 'there exists an x such that x is weird'.  Note that (x)P is 
equivalent to not (Ex)(not P) and (Ex)P is equivalent to not (x)(not P).
Perhaps I should write P(x) for 'x has the property P', 'P is true for x', 
etc.  Then (x)P(x) is 'for all x, P is true of x'.
 JB> Are these set statements or propositional statements? 
 JB> At points such as "x is a member of A" reminds me of 
 JB> set theory, while "For all x P", leaves me wondering what 
 JB> P is (the set of Propositional statements)?  
They are quantifiers in the sense that 'for all', and 'there exists' quantify 
how many.  Another quantifier in use is (E!x)P 'there exists exactly one x 
such that P'.  These are logical statements.  They are not part of 
propositional calculus, they are included in an extension called quantifier 
calculus.  P or actually P(x) is a property of x such as 'blue' or 'x is 
blue'.  When you take a thing, a, and apply a property P to a, just as with a 
function, you get P(a) which is a statement (about a).  This statement is 
true or false according to whether a has the property P or not.
... I think, therefore the universe thinks.
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