JB> I'll give you -his-, Bart Kosko's, words. 
 JB> At first I worked with symbols on abstract math theorums." 
So far this is gab, where's the math?
 JB> In Fuzzy logic set theroy, a "thing" may belong to a set 
 JB> (A) -AND- (not A) at the same time giving truth values 
 JB> between and inclusive of zero and one.  
Gab, gab, gab.  What's the definitions?  What I understand is that in fuzzy 
set theory an element x belongs to a set A with degree d, 0 <= d <= 1, x 
member A (d).  For example, A = {rocks in river}, r a rock. r member A (1) if 
r is completely submerged.  r member A (1/2) if r is half submerged, r member 
A (1/3) if r is 1/3 submerged, r member A (0) if r is completely out of the 
river.
So a half submerged rock is in A with degree 1/2 and in not A with degree 
1/2, while a fully submerged rock is in A with degree 1 and in not A with 
degree 0.  In general x member notA (d) when x member A (1-d), the definition 
of not A.
Now probability is different.  An infinite multi valued propositional 
calculus that is successful is probability theory.  If two independent 
events, P and Q have probability p and q, then probability P and Q is pq, not 
P is 1 - p, and P or Q is, of course, from PorQ equivalent not(notP and notQ) 
is 1 - (1-p)(1-q) = p + q - pq.  This method however is not applicable for a 
finite valued propositional calculus.  
Of interest is P implies Q, not(P and notQ) witch has probability 1 - p(1-q) 
= 1 - p + pq.  So if p = 1 then probability of P implies Q is q and if p = 0 
it's 1.  Which is to be expected.  Now if p = 1/2, it's 1/2 + q/2.  Brain 
teaser, is it not?
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