pqs.txt

Clearing Archive Roboposter roboposter at lightlink.com
Thu Dec 13 00:06:02 EST 2018


     VALENTINE'S DAY LECTURE ADDENDUM

     ((This is intensely dense and long, you might want to read it in
4 or 5 chunks, with a lot of rest in between.))
 
     COMMON AND UNIQUE

     Pertinent quality sets are both common and unique to all the
objects in the classes that they define.

     In short common means every object in the class has the pertinent
quality set as a subset of that object's full quality set, and unique
means only objects in the class have that particular pertinent quality
set.

     More accurately unique means that every object that has the pertinent
quality set is in the class.

     Consider the class of dogs.  The word dog is a CLASS LABEL and
refers to a group of objects that are in the class, namely dogs.  :)
 
     Commonness is easy to understand, all dogs have the quality set
of 'doggishness'.

     Unique means every object that has doggishness is a member of the
class of dogs.  Thus all dogs have doggishness and ONLY dogs have
doggishness.

     Let's do it again, this material is a bit dense and difficult,
but oh so important.
 
     Consider a class named dog with a pertinent quality set of
doggishness.  The quality set of doggishness delineates every quality
that is both necessary and sufficient to be a dog.
 
     Common means the pertinent quality set is common to every object
in the class, and also common to all classes that are SUBsets of the
class.
 
     In other words, ALL members of the class and its subsets have the
pertinent quality set in question.
 
     Doggishness is therefore common to dogs, but it is also common to
all spaniels and beagles and other subsets of dogs.  Thus all beagles
have doggishness, although it is not true that only beagles have
doggishness.
 
     Unique means every object which has the pertinent quality set is
a member of the class and all classes that are SUPERsets of the class.
In other words ONLY members of the class and its supersets have the
pertinent quality set in question.

     Doggishness is therefore unique to dogs, but it is also unique to
mammals and animals which are supersets of dog.  Thus only animals
have doggishness, although it is not true that all animals have
doggishness.

     The above is hard slogging, so I will reword it yet again as
simply as I can.

     Doggishness is common to all objects in the class of dogs and its
subsets.

     Doggishness is unique to the class of dogs and its supersets.

     Doggishness is thus the defining pertinent quality set of the
class of dogs because doggishness is both common and unique to the
class of dogs.

     AND and OR

     Notice the larger and more inclusive a class is (animals), the
*FEWER* qualities it has in its pertinent quality set, which is why it
has more objects in it.

     The smaller and less inclusive a class is (dogs), the more
qualities it has in its pertinent quality set, which is why is has
fewer objects in it.

     The class of metal objects is bigger than the class of metal and
red objects.

     The above assumes that qualities in pertinent quality sets are
ANDed together, if they are ORed together the reverse obtains.

     The class of metal OR red objects is larger than the class of
metal objects.

     OK, the hard part is over.
 
     LABELS

     Qualities, objects and classes have labels.

     Joey, my dog, is brown.

     'Brown' is a quality lable and brown is a quality that belongs to
the quality set of the object named Joey.

     'Joey' is an object label, and belongs to the class of dogs.

     'Dog' is a class label, and is defined by the pertinent quality set
of doggishness that is both common and unique to dogs.

     Notice that the object quality set of Joey has many more qualities
than the pertinent quality set of doggishness.

     Brown may be a quality of Joey as an object, but brown is neither
a quality common nor unique to dogs.
 
     Notice also that 'dog' is a class lable, and 'my dog' is an
object lable.

     ((The following material was not part of the original lecture but
was added later to clarify and expand on the data above.

     You may skip it, if its too much.

     OBJECT QUALITY SETS AND PERTINENT QUALITY SETS

     The qualities that belong to an object make up the object's
Object Quality Set (OQS) and describe the nature of that object.

     For example
 
     Object A is metal and square and red.

     Object B is wood and square and green.

     Object C is glass and round and white.

     Notice that qualities in an object quality set are ANDed, they can
can ever be ORed.

     An object can never be red OR green, as it is now.

     The qualities that define a Class of objects are called the
Pertinent Qualities of that Class, such qualities can be ANDed, ORed
or NOTed.

     For example,

     The class of all square objects.

     The class of all square and red objects.

     The class of all square OR round objects.

     The class of all objects which are round and NOT red.

     The english language has many ways to express the ideas of
commonness and uniqueness.  Below are listed just a few of them.

     Again we use the class of dogs which have the pertinent quality set
of doggishness.  We also use animals as a superset of dogs and spaniels as
as a subset of dogs.

     When we say Dog in the below we mean 'being a dog' or 'having
the qualities of doggishness.'

     COMMON                       UNIQUE
 
     Dog is common to Spaniels    Spaniel is unique to Dogs
     All Spaniels are Dogs        Only Dogs are Spaniels
     Dog is necessary to Spaniel  Spaniel is sufficient to Dog
     Spaniel implies Dog          Not Dog implies not Spaniel
     If Spaniel then Dog          Only if Dog, then Spaniel
     Dog if Spaniel               Spaniel only if Dog
 
     Dog is common to Dogs        Dog is unique to Dogs
     All Dogs are Dogs            Only Dogs are Dogs
     Dog is necessary to Dog      Dog is sufficient to Dog
     Dog implies Dog              Not Dog implies not Dog
     If Dog then Dog              Only if Dog, then Dog
     Dog if Dog                   Dog only if Dog
 
     Animal is common to Dogs     Dog is unique to Animals
     All Dogs are Animals         Only Animals are Dogs
     Animal is necessary to Dog   Dog is sufficient to Animal
     Dog implies Animal           Not Animal implies not Dog
     If Dog then Animal           Only if Animal, then Dog
     Animal if Dog                Dog only if Animal

     Notice for example, that

     "Only if Animal, then Dog"  which is right,

     is NOT the same thing as

     "If animal, then Dog" which is wrong.

     You now have a PhD in the English language and logic.


     End of added data.))

     Homer

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