Abstraction

Abstraction is method and result of a cognitive action that results in a new entity with a reduced number of properties to describe a real existing object. An abstraction itself if assigned to a symbol can become a real existing object and by that token can be further abstracted to an even higher level of abstraction.

The graph shows how an abstraction is constructed from two entities E1 and E2 that share properties A0-A3. The abstraction holds only these properties ignoring properties B1 and B2 of entity 1 and C1 and C2 of entity 2. An optional symbol is added to the abstraction.

[Error: Macro 'mathequation' doesn't exist] [Error: Macro 'mathequation' doesn't exist]

Conclusion

An abstraction never reflects all properties of all entities that belong to this abstraction. Therefore deductions, that is conclusions drawn from the abstraction, may fail. Usually those conclusions need some empirical confirmation. By the way that is why this website includes an abstraction proviso.

An abstraction allows a special method of definition, definition by genus and differentia. We will use this method of definition throughout our wiki.

It is a complex cognitive process to evolve abstractions that lead to the most possible correct deductions.

Example

The picture shows some apples. Apple is an abstract term. As in this picture apples come in various sizes and shapes. They have some common properties though. They grow on the same apple trees, for instance.
[Error: Wrong macro arguments: "AppleAbstraction" for macro 'img' (maybe wrong macro tag syntax?)]
Apples may be further subdivided depending on their home apple tree, the apple sort.
[Error: Wrong macro arguments: "AppleSorts" for macro 'img' (maybe wrong macro tag syntax?)]
Of course, everybody is free to construct new subgroups as illustrated in this picture. The usefulness of those abstractions may be questioned and they will probably soon forgotten.
[Error: Wrong macro arguments: "AppleSubclassified" for macro 'img' (maybe wrong macro tag syntax?)]

Misuse

An abstract expression may rather obscure and hide information. For instance, the sentence "I gave my cat Mimi a piece of my sausage." is more informative than this translation into abstract terms "I provided my canine pet some meal." George Orwell criticized in his essay about the English language the 'bad habit' of politicians to disguise their intentions in abstract terms. Often abstractions are misused in connection with sweeping generalizations, a known fallacy, or to construct euphemisms, such as reform.

In its attempt to define terms as fauceirs and thereby by explicitly stating which sub-fauceirs belong to it and which not fauceir theory reduces the possibilities of misunderstanding and hopefully even prevents manipulations.

For instance, the progress in some humanities such as psychology and sociology is so slow because of incompatible terminology among those who call themselves the leading scientists in the field. Often discussions with such experts are suffocated by a teacher-like instructions how all that has to be understood.

Such behavior so common in humanities is nearly impossible in physics. If you don't accept the abstraction of a mass point or try to redefine it all calculations go wrong. The same is true with humanities, but nobody cares.