On 01-18-98 William Elliot wrote to John Boone... 
 
        Hello William, 
  
 WE>  JB> Yep, but would require me to type and save with some sort  
 WE>  JB> of editor.  
 
 WE> Shouldn't.  BlueWave offline reader has a save to file feature.  My 
 
  I don't have BlueWave, I have Offline 1.5?.  
IAE, I have already printed it out and I don't save my 
response packets. 
  
 WE> WE> Yes they are.  The non-fuzzy propositional 'and', 'or', 'not', 
 WE> WE> and  
 WE> WE> 'implies' are in parallel with the set multiplication, addition,  
 WE> WE> complimentation and inclusion.  not(x or y) = notx and noty   
 WE> WE> or -(x + y) = (-x) * (-y) is true for both sets and   
 WE> WE> propositions.  Indeed, the duality theorem of set theory is   
 WE> WE> a rerun of the duality theorem for the propositional   
 WE> WE> calculus.  However note the difference.  Logic will go into  
 WE> WE> (x)P and (Ex)P while sets are concerned about x e A.  For   
  
 WE> JB> Not sure what you mean by (x)P and (Ex)P??????  
 
 WE>  WE> all x P, there exists a x such that P, x is a member of A. 
 WE>  WE> Here we see divergence.  
 
 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  
 
   (x) P seems to be the universal qualifier.   All things x 
and not x are weird?     
  
 WE> weird', or formally 'for all x, x is weird' and 'there
 
  Or perhaps, "if x, then weird"?? 
  
 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). 
 
  I wait for this until I get an understanding on the other. 
  
 WE> Perhaps I should write P(x) for 'x has the property P', 'P 
 WE> is true for x', etc.  Then (x)P(x) is 'for all x, P is true  
 WE> of x'. 
   
  Sorry, I think it my lack of familarity of such. 
I just started "Logic and Philosophy" by Kahane just 
started chapter 4 and haven't got to this yet, but it 
does seem similar to something I have seen. , 
  
 WE> JB> Are these set statements or propositional statements? 
 WE> JB> At points such as "x is a member of A" reminds me of  
 WE> JB> set theory, while "For all x P", leaves me wondering what  
 WE> JB> P is (the set of Propositional statements)?   
 
 WE> They are quantifiers in the sense that 'for all', and 'there exists' 
 WE> quantify  
 WE> how many.  Another quantifier in use is (E!x)P 'there  
 WE> exists exactly one x such that P'.  These are logical 
 WE> statements.  They are not part of propositional calculus,  
 WE> they are included in an extension called quantifier  
 WE> calculus.  P or actually P(x) is a property of x such as  
 WE> 'blue' or 'x is blue'.  When you take a thing, a, and apply  
 WE> a property P to a, just as with a function, you get P(a)  
 WE> which is a statement (about a).  This statement is true or  
 WE> false according to whether a has the property P or not. 
 
Take care, 
John 
 
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