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Lewis Carroll
Symbolic Logic
Part I: Elementary
Book I: Things and their Attributes
Chapter II: Classification
Building Class
You consider yourself different from your brother, mother, sister, or father. Perhaps your family thinks you are so unique that they say that you are "in a class of your own." But your cousins will see you all together as one family. And yet your neighbor will view your family, your cousins, and your grandparents as all one clan. Someone in another neighborhood will see yours as a separate community. But someone in another city or town will see all your surrounding neighborhoods as part of the same metropolitan region. Those from a different country will consider every city in your nation as members of the same sovereign state. But, we may consider all humans in every region to be a species of mammals. But mammals and other back-boned animals are vertebrates. And so on until we consider all life forms as one class, distinct from inanimate matter. But then both life forms and material objects are things, and we all are members of the whole universe.
Each order or level of grouping is a class. When we establish these groups, we 'classify' the objects. We very easily could have grouped your relatives with sponges, as both in a class of soft things. We use our minds to determine which attribute or attributes will serve to group the things we want to classify. Thus,
'Classification,' or the formation of Classes, is a Mental Process, in which we imagine that we have put together, in a group, certain Things. (2b)
Three Ways to Classify
Carroll distinguishes three ways that we classify.
1) Universalization: We may consider all things in the universe as being in one class.
2) Classification: We may select one attribute, like 'soft,' and place all things with that attribute in the same group. Those without that attribute are excluded. "This Attribute (or Set of Attributes) is said to be 'peculiar' to the Class so formed.'
As we noted, this is entirely a mental process. So using our imaginations, we might also wonder if unicorns are mammals. We do not actually need to go out and find unicorns and place them side-by-side with horses, monkeys, and mice. Hence, because classification is a mental process, we may consider even non-existing things that would have the given attribute, were they actually real. If we grouped all the monsters from Ancient Greek mythology, we would have an imaginary class. But if we grouped all the things sitting in front of us on the desk, we would have a real class. For, the imaginary things do not exist, but the real ones do.
Carroll exemplifies imaginary things as ones that are logically impossible:
we may thus form the Imaginary Class "Things weighing more than apound and also weighing less than a pound." (2d)
3) Subclassification: We might begin with ancient Greek monsters. Then within this class we form a smaller group of all those monsters made-up of many animals, such as the chimera and sphynx.
Individuals
Before when building classes up from family members to the whole universe, we said that your family might say you are so unique that you are in a class all your own. This means that you are truly an individual. No one else shares all your defining attributes. So when there is only one member in a class, we call that class an individual. And hence any single Thing that we designate with a name that distinguishes it from all other Things is as well a one-member class.
One Single Thing:
A Whole Quite Different From Its Parts
We would not consider a soldier to be a square. But when we marshal a regiment of soldiers into a square formation, we then would consider the soldiers together as making-up a square. So a class containing multiple members may all together possess some attribute that is not possessed by any member regarded alone. We call such a class one single Thing.
Images from the text [click on image for an enlargement]:
From:
Carroll, Lewis. Symbolic Logic. London: MacMillan and Co., 1869.
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