LOGIC OF CLASSES

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

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Homer Wilson Smith Clean Air, Clear Water, Art Matrix - Lightlink
(607) 277-0959 A Green Earth, and Peace, Internet, Ithaca NY
homer@lightlink.com Is that too much to ask? http://www.lightlink.com