Clearing Archive Roboposter
roboposter at lightlink.com
Thu Mar 26 00:06:02 EDT 2015
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
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
Unique means every object that has doggishness is a member of the
class of dogs. Thus all dogs have doggishness and ONLY dogs have
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
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
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
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
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
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
OK, the hard part is over.
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
((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.
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
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.'
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.))
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Therefore, Learning with Certainty implies Learning, but
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