>>> John Boone on Fuzzy Logic 
 JB> I don't have BlueWave, I have Offline 1.5?.  
 JB> IAE, I have already printed it out and I don't save my 
 JB> response packets. 
No problem.  Does the Offline 1.5+ have a save to file facility.  It is 
-very- useful.  I'm taking notes on atomic structure which go thru much 
review and revision as the discussion continues.
 
 WE> Let P be the statement (x is weird).  Then (x)(x is weird) 
 WE> is 'all is weird' and (Ex)(x is weird) is 'something is  
 JB> (x) P seems to be the universal qualifier.   
(x)P is a universal -quantifier-, (Ex)P is an existential -quantifier-.
 JB> All things x and not x are weird?
Makes no sense.
 WE> weird', or formally 'for all x, x is weird' and 'there
 JB> Or perhaps, "if x, then weird"?? 
No.  x is a thing, it is not a statement.
 WE> exists an x such that x is weird'.  Note that (x)P is 
 WE> equivalent to not (Ex)(not P) and (Ex)P is equivalent to  
 WE> not (x)(not P). 
 JB> I wait for this until I get an understanding on the other. 
Indeed.  The grammatical sense of quantifiers is quaint compared to English.  
x is a pronoun of sorts.  x is an element, a thing, for example a number.  P 
is a statement.  P has also is also used -ambigously- as a property.  A 
statement could be 'this ball is blue'.  A related property of blueness could 
be expressed 'it is blue'.  Let B be this property of blueness.  Then B(this 
ball) is 'this ball is blue' and B(it) is 'it is blue' which is about the 
same as saying B(x), 'x is blue'.  
The property B of blueness and the set B' of blue things are related by 
(x)(B(x) = x e B').  For all x, x is blue if and only if x belongs to the set 
of blue things.  For everything, it is blue if and only if it belongs to the 
set of blue things.  Everything is blue if and only if it belongs to the set 
of blue things.  This last statement contains just a bit of grammatical 
ambiguity noticeable mostly by pedantic logicians.  That is why symbolic 
logic instead of verbal logic.  The grammar of symbolic logic is vastly 
simpler.  Hence clearer and more precise.
 JB> I just started "Logic and Philosophy" by Kahane just 
 JB> started chapter 4 and haven't got to this yet, but it 
 JB> does seem similar to something I have seen. , 
Indeed.  Is this a text book that you're plowing thru?
Propositional Calculus, Quantifier Calculus, Set Theory.
Duality Theorems, Incompleteness.  What beyond truth tables?
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