>From sasha
OK for FTP storage

        This is my answer to somebody's message that I wanted to post
in comp.ai.philosophy some time ago; I think at least some of it can be
of interest for [other] extropians:
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> ... ~ " There are infinitely many theories interpreting a given finite
>         set of experimental data"...
 
     There seems to be just one object that is unique for a given
set of data, and it is the CLASS of all theories that explain it.
 
  Just a few related ideas:
 
   - Additional data can narrow the class, but not 'refute' it.
   
   - A class of theories for a combination of two sets of data is an
     intersection of their two classes.
   
   - "Minimized class" : Class stripped of the member theories that are
     supersets of other member theories (get rid of irrelevant pieces and 
     unnecessary complexity).
   - "Independent phenomena": sets of data whose minimized classes of
     theories don't intersect.
   
   - "Acceptable explanation": any part of the class which has a non-empty
     intersection with My Current Understanding of The Subject 
     (an arbitrary subset of the Class of theories explaining previously
      observed data).
   - "An open mind (class)": one that excludes a situation when the
     only acceptable theory for new data is the "Wrong data" theory.
   
   - "Useless/redundant data": any set of experimental data whose class
     of theories includes the class we already have.
   - "Useless experiment": one that can yield nothing but useless data.
   
   - "A simple theory": one that doesn't stick out too much after
     its projection on the existing class of theories.
   
   - "The Ultimate Wisdom": the projection of the SuperClass of theories
     on the SuperSet of data = intersection of all classes of theories
     for all [potentially] observable data.  Can be a pretty rich class
     of theories, if the [potentially observable] world as a whole allows
     alternative explanations; can be The Only One True Theory (?).
     I suspect that it might be  The Wrong Data Theory.   ;-)
 
   - "Sufficient data": a set of data whose class of theories = 
     The Ultimate Wisdom.   Probably a lot smaller than The Whole World,
     in which case the rest of the world is unnecessary.   Which might
     mean that the whole thing was not designed by a perfect being - or
     was intended for observers with a larger field af accessible data.
 
                           - - -   
     
   All this stuff  can  be formally defined in terms of sets of theories,
 functional operators in semantic space, projections, factorizations,
 or some other form,  and probably even  should  (or maybe it was?).