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SUO: Re: Examples! Examples! Examples!




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EEE.  Note 30

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Example 1.  John Sowa's "Top Level Categories" (cont.)

At this point, the little program whose last line of code
I laid down in 1989, when Turbo Pascal could address only
about 640 Kb of heap space, and a good chunk of that gets
nibbled up by the ambient operating system, starts to run
out of elbow room, but there is just enough space left to
answer one or two more pressing questions.

I started out accepting Proposition !a! as an axiom for the
intended subset of TLC = <|a_1, ... a_25|>, and now I have
found a Proposition !c! that appears to indicate the very
same set of models.  I cannot tell for sure at this point
because the particular function of Theme One that creates
the "outline summary" of models does not produce a fully
equivalent canonical form, but only one that suffices in
a common set of circumstances.  Ideally, one would like
to write out the proposition of the form (!a! , !c!),
that expresses the difference or inequality between
!a! and !c!, or the proposition ((!a! , !c!)), that
expresses their equality, and then find the models
of one of these propositions as a negative or
a positive way, respectively, of testing
the validity of the equality.

I was not able to do that with the amount of memory space that
I currently have, but I was able to test the two propositions
!a! (!c!) and !c! (!a!) independently, and thereby verified
the logical equivalence of !a! and !c!.

The Model output for !a! (!c!) is too long
to show here, but the output for !c! (!a!)
looks like this:

 Independent
  Relative -
  (Relative )
   Mediating -
   (Mediating )
    Prehension -
    (Prehension )
     Proposition -
     (Proposition )
      Nexus -
      (Nexus )
       Intention -
       (Intention )
        Juncture -
        (Juncture )
         Participation -
         (Participation )
          Description -
          (Description )
           History -
           (History )
            Structure -
            (Structure )
             Situation -
             (Situation )
              Reason -
              (Reason )
               Purpose -
               (Purpose )
                Physical
                 Abstract -
                 (Abstract )
                  Form -
                  (Form )
                   Schema -
                   (Schema )
                    Script -
                    (Script )
                     Continuant
                      Occurrent -
                      (Occurrent )
                       Process -
                       (Process )
                        Actuality
                         Object -
                         (Object ) -
                        (Actuality ) -
                     (Continuant )
                      Object -
                      (Object )
                       Occurrent
                        Actuality
                         Process -
                         (Process ) -
                        (Actuality ) -
                       (Occurrent ) -
                (Physical )
                 Actuality -
                 (Actuality )
                  Object -
                  (Object )
                   Process -
                   (Process )
                    Abstract
                     Continuant
                      Occurrent -
                      (Occurrent )
                       Script -
                       (Script )
                        Form
                         Schema -
                         (Schema ) -
                        (Form ) -
                     (Continuant )
                      Schema -
                      (Schema )
                       Occurrent
                        Form
                         Script -
                         (Script ) -
                        (Form ) -
                       (Occurrent ) -
                    (Abstract ) -
 (Independent )
  Actuality -
  (Actuality )
   Form -
   (Form )
    Object -
    (Object )
     Process -
     (Process )
      Schema -
      (Schema )
       Script -
       (Script )
        Relative
         Mediating -
         (Mediating )
          Nexus -
          (Nexus )
           Intention -
           (Intention )
            Structure -
            (Structure )
             Situation -
             (Situation )
              Reason -
              (Reason )
               Purpose -
               (Purpose )
                Physical
                 Abstract -
                 (Abstract )
                  Proposition -
                  (Proposition )
                   Description -
                   (Description )
                    History -
                    (History )
                     Continuant
                      Occurrent -
                      (Occurrent )
                       Participation -
                       (Participation )
                        Prehension
                         Juncture -
                         (Juncture ) -
                        (Prehension ) -
                     (Continuant )
                      Juncture -
                      (Juncture )
                       Occurrent
                        Prehension
                         Participation -
                         (Participation ) -
                        (Prehension ) -
                       (Occurrent ) -
                (Physical )
                 Prehension -
                 (Prehension )
                  Juncture -
                  (Juncture )
                   Participation -
                   (Participation )
                    Abstract
                     Continuant
                      Occurrent -
                      (Occurrent )
                       History -
                       (History )
                        Proposition
                         Description -
                         (Description ) -
                        (Proposition ) -
                     (Continuant )
                      Description -
                      (Description )
                       Occurrent
                        Proposition
                         History -
                         (History ) -
                        (Proposition ) -
                       (Occurrent ) -
                    (Abstract ) -
        (Relative )
         Prehension -
         (Prehension )
          Proposition -
          (Proposition )
           Juncture -
           (Juncture )
            Participation -
            (Participation )
             Description -
             (Description )
              History -
              (History )
               Mediating
                Physical
                 Abstract -
                 (Abstract )
                  Intention -
                  (Intention )
                   Reason -
                   (Reason )
                    Purpose -
                    (Purpose )
                     Continuant
                      Occurrent -
                      (Occurrent )
                       Situation -
                       (Situation )
                        Nexus
                         Structure -
                         (Structure ) -
                        (Nexus ) -
                     (Continuant )
                      Structure -
                      (Structure )
                       Occurrent
                        Nexus
                         Situation -
                         (Situation ) -
                        (Nexus ) -
                       (Occurrent ) -
                (Physical )
                 Nexus -
                 (Nexus )
                  Structure -
                  (Structure )
                   Situation -
                   (Situation )
                    Abstract
                     Continuant
                      Occurrent -
                      (Occurrent )
                       Purpose -
                       (Purpose )
                        Intention
                         Reason -
                         (Reason ) -
                        (Intention ) -
                     (Continuant )
                      Reason -
                      (Reason )
                       Occurrent
                        Intention
                         Purpose -
                         (Purpose ) -
                        (Intention ) -
                       (Occurrent ) -
                    (Abstract ) -
               (Mediating ) -

Any models would have been marked with stars (*),
and the absence of any models says that nothing
in TLC satisfies !c! without satisfying !a!.

Jon Awbrey

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