On 01-18-98 William Elliot wrote to John Boone... 
 
        Hello William and thanks for writing, 
  
 WE> No problem.  Does the Offline 1.5+ have a save to file  
 WE> facility.  It is -very- useful.  I'm taking notes on atomic  
 
  I am sure it does, but unable to find out how.  I do use 
DOS "edit" which can allow me to save something to another 
file, but it destroys my response packet for some reason. 
  Perhaps, it is something I am doing wrong.  I haven't 
taken the time to "figure it out." 
  
 WE> structure which go thru much review and revision as the 
 WE> discussion continues. 
    
 WE>  WE> Let P be the statement (x is weird).  Then (x)(x is weird)  
 WE>  WE> is 'all is weird' and (Ex)(x is weird) is 'something is   
 WE>  JB> (x) P seems to be the universal qualifier.    
 
 WE> (x)P is a universal -quantifier-, (Ex)P is an existential 
 WE> -quantifier-. 
   
  Thanks! 
  
 WE>  JB> All things x and not x are weird? 
 
 WE> Makes no sense. 
   
  Wouldn't be the first nor the last time I made or 
make no sense . 
  
 WE>  WE> weird', or formally 'for all x, x is weird' and 'there 
 
 WE>  JB> Or perhaps, "if x, then weird"?? 
 
 WE> No.  x is a thing, it is not a statement. 
   
 WE>  WE> exists an x such that x is weird'.  Note that (x)P is  
 WE>  WE> equivalent to not (Ex)(not P) and (Ex)P is equivalent to   
 WE>  WE> not (x)(not P).  
 
 WE>  JB> I wait for this until I get an understanding on the other. 
 
 WE> Indeed.  The grammatical sense of quantifiers is quaint 
 WE> compared to English.  x is a pronoun of sorts.  x is an  
 WE> element, a thing, for example a number.  P is a statement.   
 WE> P has also is also used -ambigously- as a property.  A  
 WE> statement could be 'this ball is blue'.  A related property  
 WE> of blueness could be expressed 'it is blue'.  Let B be this  
 WE> property of blueness.  Then B(this ball) is 'this ball is  
 WE> blue' and B(it) is 'it is blue' which is about the same as  
 WE> saying B(x), 'x is blue'.   
   
  Thanks! 
  
 WE> The property B of blueness and the set B' of blue things are related 
 WE> by  
 WE> (x)(B(x) = x e B').  For all x, x is blue if and only if x  
 
  In "(x) (B(x)", why the third "(?"  Typo? 
  
 WE> belongs to the set of blue things.  For everything, it is 
 WE> blue if and only if it belongs to the set of blue things.   
 WE> Everything is blue if and only if it belongs to the set of  
 WE> blue things.  This last statement contains just a bit of  
 WE> grammatical ambiguity noticeable mostly by pedantic  
 WE> logicians.  That is why symbolic logic instead of verbal  
 WE> logic.  The grammar of symbolic logic is vastly simpler.   
 WE> Hence clearer and more precise. 
   
 WE>  JB> I just started "Logic and Philosophy" by Kahane just  
 WE>  JB> started chapter 4 and haven't got to this yet, but it  
 WE>  JB> does seem similar to something I have seen. ,  
 
 WE> Indeed.  Is this a text book that you're plowing thru? 
 
  Yes, it is a text book I am reading.  
  
 WE> Propositional Calculus, Quantifier Calculus, Set Theory. 
 WE> Duality Theorems, Incompleteness.  What beyond truth tables? 
 
  It doesn't contain Godels', but it does contain "introductory" 
stuff such as set theory, quantifier calculus, etc.  
 
Take care, 
John 
 
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