LOGIC OF CLASSES

     The following discussion of logic assumes 3 classes of objects,
Animals, Dogs, and Spaniels.

     This can be represented visually by a large circle encompassing all
Animals.

     Entirely inside that circle is another smaller circle encompassing
all Dogs.

     Entirely inside the circle of Dogs, is yet another smaller circle
encompassing all Spaniels.

     Thus all Spaniels are Dogs, and All Dogs are Animals.

     This then lays out the rules of logic, for if you say

     All Spaniels are Dogs, and all Dogs are Animals, but some Spaniels
are not Animals, what have you said?

     Logic thus is the ethics of language.

     English has many ways of stating these relationships, the below are
the most used in formal scientific debate.

     The words common and unique come from the technical defintion of a
class:

     "A class is defined by its pertinent quality set, which is the set
of all qualities that are common and unique (as a group) to the objects
in the class."

     Most bad logic comes from misunderstanding and misuse of the unique
column.

     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

     Homer