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Re: [ontolog-forum] Inconsistent Theories

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Mon, 8 Feb 2010 23:35:49 -0600
Message-id: <FB41616B-868E-4D77-8E58-945111BDE82B@xxxxxxxx>
On Feb 8, 2010, at 10:59 PM, Rich Cooper wrote:
> John and Chris, please let me butt in with a clarifying question; are you
> using "=" in a definitional or in a comparative way?    (01)

Rich, it is being used as it is always used in first-order logic with identity 
to mean identity, the relation that holds between, and only between, any 
arbitrary thing and itself; consult any standard text on the subject.  Your 
questions concern issues in the semantics of procedural programming languages 
that, for the most part, really have nothing at all to do with identity in FOL.    (02)

-chris    (03)

> For example, the function below compares two values, which happen to be
> named A and B respectively in order of introduction.  
> -------------- -------------- -------------- 
> function FEqual(A,B): ('<','=','>');
> begin
>  Result := (A=B);
> end;
> var A, B : Integer := 72;
> begin
>  ShowMessage('A=B returns : '+FEqual(A,B));
> end
> -------------- -------------- -------------- 
> But A and B have VALUE properties which are compared in FEqual above, not
> their NAME properties; 'A' is a name, so is 'B', and 'A' is greater than 'B'
> in alphabetical name order, but definitely NOT EQUAL to 'B' in any ordering
> not involving substitutions of symbols into variables (unification).  
> But of course, by definition (the definitional way mentioned way earlier
> above, in .. 'definitional or comparative'; QED), 'A' is EQUAL to 'A' in
> most universes.  
> So maintaining multiple orderings on sets, which is extremely useful for
> efficiently solving problems while minimizing time penalties, is useful both
> in tracking the elements (ThingS as I call them, atoms for chemists, people
> for politicians, grains as physicists say, chunks as .. ) and in tracking
> the sets themselves as they dynamically reflect the dynamic reorderings
> among the (gasp) terminals in the universe of discourse.  
> HTH,
> -Rich
> Sincerely,
> Rich Cooper
> EnglishLogicKernel.com
> Rich AT EnglishLogicKernel DOT com    (04)

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