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Re: [ontolog-forum] Inconsistent Theories

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Mon, 8 Feb 2010 22:56:05 -0800
Message-id: <20100209065608.9E11A138D22@xxxxxxxxxxxxxxxxx>
Chris,    (01)

Actually, it's more complicated than that.  Value is simply one property of
a Thing in a universe.  Identity wrt a Definition property is a complete
different issue.  You are confusing a logical specification of value with a
logical instance of a value.      (02)

For example, in the equation    (03)

F(x) = x^3+27*x^2    (04)

The left hand side is 'equal' to the right hand side, and evaluation of both
sides leads to the same results.      (05)

But if I want to represent the symbolic function F(x), for example, as a
Lisp structure of operators and operands that can be used in evaluation of
F(x), or that can be manipulated algebraically to create new expressions, it
might be better to state it this way (forget the messy Lisp notation):    (06)

        Define( F(x), (x^3+27*x^2) )    (07)

Which states that the identify of the symbol F(x) is defined to be equal to
the evaluable structure (x^3+27*x^2) which can be used to calculate the
value of F(x) bound to any x.      (08)

Those are two different views of '=' - by value and by defined structure
(expression or object, perhaps).  The interpretation can be calculated to
get the value, but the interpretation is distinct from the value it gets at
any given time.      (09)

HTH,
-Rich    (010)

Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com    (011)

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher
Menzel
Sent: Monday, February 08, 2010 9:36 PM
To: [ontolog-forum] 
Subject: Re: [ontolog-forum] Inconsistent Theories    (012)

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?    (013)

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.    (014)

-chris    (015)



> 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    (016)


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