Abstraction

Abstraction is the process of reducing the information content of a concept, typically in order to retain only information which is relevant for a particular purpose. For example, abstracting a leather soccer ball to a ball retains only the information on general ball attributes and behaviour. Similarly, abstracting an emotional state to happiness reduces the amount of information conveyed about the emotional state.

Complexity reduction

Abstraction typically results in complexity reduction leading to a simpler conceptualization of a domain in order to facilitate processing or understanding of many specific scenarios in a generic way.

Thought process

In philosophical terminology, abstraction is the thought process wherein ideas are distanced from objects.

Abstraction uses a strategy of simplification, wherein formerly concrete details are left ambiguous, vague, or undefined; thus effective communication about things in the abstract requires an intuitive or common experience between the communicator and the communication recipient.

For example, many different things can be red. Likewise, many things sit on surfaces (as in picture 1, to the right). The property of redness and the relation sitting-on are therefore abstractions of those objects. Specifically, the conceptual diagram graph 1 identifies only three boxes, two ellipses, and four arrows (and their nine labels), whereas the picture 1 shows much more pictorial detail, with the scores of implied relationships as implicit in the picture rather than with the nine explicit details in the graph.

Graph 1 details some explicit relationships between the objects of the diagram. For example the arrow between the agent and CAT:Elsie depicts an example of an is-a relationship, as does the arrow between the location and the MAT. The arrows between the gerund SITTING and the nouns agent and location express the diagram's basic relationship; "agent is SITTING on location"; Elsie is an instance of CAT.

Although the description sitting-on (graph 1) is more abstract than the graphic image of a cat sitting on a mat (picture 1), the delineation of abstract things from concrete things is somewhat ambiguous; this ambiguity or vagueness is characteristic of abstraction. Thus something as simple as a newspaper might be specified to six levels, as in Douglas R. Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979):

(1) a publication
(2) a newspaper
(3) The San Francisco Chronicle
(4) the May 18 edition of the Chronicle
(5) my copy of the May 18 edition of the Chronicle
(6) my copy of the May 18 edition of the Chronicle as it was when I first picked it up (as contrasted with my copy as it was a few days later: in my fireplace, burning)

An abstraction can thus encapsulate each of these levels of detail with no loss of generality. But perhaps a detective or philosopher/scientist might seek to learn about some thing, at progressively deeper levels of detail, to solve a crime or a puzzle.

Referents

Abstractions sometimes have ambiguous referents; for example, "happiness" (when used as an abstraction) can refer to as many things as there are people and events or states of being which make them happy. Likewise, "architecture" refers not only to the design of safe, functional buildings, but also to elements of creation and innovation which aim at elegant solutions to construction problems, to the use of space, and at its best, to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building.

Instantiation

Things that do not exist at any particular place and time are often considered abstract. By contrast, instances, or members, of such an abstract thing might exist in many different places and times. Those abstract things are then said to be multiply instantiated, in the sense of picture 1, picture 2, etc., shown above.

It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts 'cat' and 'telephone' abstract ideas since despite their varying appearances, a particular cat or a particular telephone is an instance of the concept "cat" or the concept "telephone". Although the concepts "cat" and "telephone" are abstractions, they are not abstract in the sense of the objects in graph 1 above.

We might look at other graphs, in a progression from cat to mammal to animal, and see that animal is more abstract than mammal; but on the other hand mammal is a harder idea to express, certainly in relation to marsupial.

Physicality

A physical object (the referrent of a concept or word) is considered concrete (not abstract) if it is a particular individual that occupies a particular place and time.

Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experience, like the color red. That definition, however, suffers from the difficulty of deciding which things are real (i.e. which things exist in reality). For example, it is difficult to agree to whether concepts like God, the number three, and goodness are real, abstract, or both.

An approach to resolving such difficulty is to use predicates as a general term for whether things are variously real, abstract, concrete, or of a particular property (e.g. good). Questions about the properties of things are then propositions about predicates, which propositions remain to be evaluated by the investigator. In the graph 1 above, the graphical relationships like the arrows joining boxes and ellipses might denote predicates. Different levels of abstraction might be denoted by a progression of arrows joining boxes or ellipses in multiple rows, where the arrows point from one row to another, in a series of other graphs, say graph 2, etc.

Abstraction used in philosophy

Abstraction in philosophy is the process (or, to some, the alleged process) in concept-formation of recognizing some set of common features in individuals, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals. It has also recently become popular in formal logic under predicate abstraction.

Ontological status

The way that physical objects, like rocks and trees, have being differs from the way that properties of abstract concepts or relations have being, for example the way the concrete, particular, individuals pictured in picture 1 exist differs from the way the concepts illustrated in graph 1 exist. That difference accounts for the ontological usefulness of the word "abstract". The word applies to properties and relations to mark the fact that, if they exist, they do not exist in space or time, but that instances of them can exist, potentially in many different places and times.

Perhaps confusingly, some philosophies refer to tropes (instances of properties) as abstract particulars. E.g., the particular redness of a particular apple is an abstract particular.

In linguistics

Reification, also called hypostatization, might be considered a logical fallacy whenever an abstract concept, such as "society" or "technology" is treated as if it were a concrete object. In linguistics this is called metonymy, in which abstract concepts are referred to using the same sorts of nouns that signify concrete objects. Metonymy is an aspect of the English language and of other languages. It can blur the distinction between abstract and concrete things:

1805: Horatio Nelson (Battle of Trafalgar) - "England expects that every man will do his duty"

Compression

An abstraction can be seen as a process of mapping multiple different pieces of constituent data to a single piece of abstract data based on similarities in the constituent data, for example many different physical cats map to the abstraction "CAT". This conceptual scheme emphasizes the inherent equality of both constituent and abstract data, thus avoiding problems arising from the distinction between "abstract" and "concrete". In this sense the process of abstraction entails the identification of similarities between objects and the process of associating these objects with an abstraction (which is itself an object).

For example, picture 1 above illustrates the concrete relationship "Cat sits on Mat".

Chains of abstractions can therefore be constructed moving from neural impulses arising from sensory perception to basic abstractions such as color or shape to experiential abstractions such as a specific cat to semantic abstractions such as the "idea" of a CAT to classes of objects such as "mammals" and even categories such as "object" as opposed to "action".

For example, graph 1 above expresses the abstraction "agent sits on location".

This conceptual scheme entails no specific hierarchical taxonomy (such as the one mentioned involving cats and mammals), only a progressive compression of detail.

The neurology of abstraction

Some research into the human brain suggests that the left and right hemispheres differ in their handling of abstraction. One side handles collections of examples (eg: examples of a tree) whereas the other handles the concept itself.

Abstraction in art

Most typically abstraction is used in the arts as a synonym of abstract art in general. It can, however, refer to any object or image which has been distilled from the real world, or indeed another work.

Artist Robert Stark wrote:

"Ten years after abandoning formal landscape painting to explore the more direct act of freely applying paint to a surface without a representational motive, I have developed a new vocabulary; light and dark, warm and cool, making marks, brush-strokes like heart-rhythms. Every day is a test of each painting's ability to stand on its own. Each painting is subject to being changed, to being reworked or scraped and repainted as long as it remains in the studio. Where I often used to spend weeks on a painting, attempting to 'make a picture,' now my concerns are more about the energy of light, the mass of space, the emotions of shadows."

"I want the painting to meet the viewer somewhere in the middle, where the viewer brings his own experiences to bear in understanding and feeling what he is seeing. I want my paintings to achieve the complexity and density of poetry or of a symphony, to build suggestive layers, implicit felt meaning, not merely to be entertaining bit of color to seduce the eye. I want my paintings to be accessible to children as well as adults, and to be so simply and directly painted that it shows the act of painting for the joy and excitement of it."

External links

References

Eugene Raskin, Architecturally Speaking, 2nd edition, a Delta book, Dell (1966), trade paperback, 129 pages
The American Heritage Dictionary of the English Language, 3rd edition, Houghton Mifflin (1992), hardcover, 2140 pages, ISBN 0395448956

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