Abstraction
Abstraction is the process of generalizing rules and concepts from specific examples, literal signifiers, first principles, or other methods. The result of the process, an abstraction, is a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a group, field, or category.
Abstractions and levels of abstraction play an important role in the theory of general semantics originated by Alfred Korzybski. Anatol Rapoport wrote "Abstracting is a mechanism by which an infinite variety of experiences can be mapped on short noises." An abstraction can be constructed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects that are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, excluding but not eliminating the other phenomenal and cognitive characteristics of that particular ball. In a type–token distinction, a type is more abstract than its tokens.
Origins
in abstractions is considered by anthropologists, archaeologists, and sociologists to be one of the key traits in modern human behaviour, believed to have developed between 50,000 and 100,000 years ago. Its development is likely to have been closely connected with the development of human language, which appears to both involve and facilitate abstract thinking. Max Müller suggests an interrelationship between metaphor and abstraction in the development of thought and language.History
Abstraction involves induction of ideas or the synthesis of particular facts into one general theory about something. Its opposite, specification, is the analysis or breaking-down of a general idea or abstraction into concrete facts. Abstraction can be illustrated by Francis Bacon's Novum Organum, a book of modern scientific philosophy written in the late Jacobean era of England to encourage modern thinkers to collect specific facts before making any generalizations.Bacon used and promoted induction as an abstraction tool; his induction complemented but was distinct from the ancient deductive-thinking approach that had dominated the Western intellectual world since the times of Greek philosophers like Thales, Anaximander, and Aristotle. Thales believed that everything in the universe comes from one main substance, water. He deduced or specified from a general idea, "everything is water," to the specific forms of water such as ice, snow, fog, and rivers.
Early-modern scientists used the approach of abstraction. Newton derived the motion of the planets from Copernicus' simplification, that the Sun is the center of the Solar System; Kepler compressed thousands of measurements into one expression to finally conclude that Mars moves in an elliptical orbit about the Sun; Galileo compressed the results of one hundred specific experiments into the law of falling bodies.
Themes
Compression
An abstraction can be seen as a compression process, 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.Chains of abstractions can be construed, 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".
Instantiation
Non-existent things in any particular place and time are often seen as 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 [|below]. 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 below. 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 or monotreme.
Perhaps confusingly, some philosophies refer to tropes as abstract particulars—e.g., the particular redness of a particular apple is an abstract particular. This is similar to qualia and sumbebekos.
Material process
Still retaining the primary meaning of 'abstrere' or 'to draw away from', the abstraction of money, for example, works by drawing away from the particular value of things allowing completely incommensurate objects to be compared.The state as both concept and material practice exemplifies the two sides of this process of abstraction. Conceptually, 'the current concept of the state is an abstraction from the much more concrete early-modern use as the standing or status of the prince, his visible estates'. At the same time, materially, the 'practice of statehood is now constitutively and materially more abstract than at the time when princes ruled as the embodiment of extended power'.
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.Physicality
A physical [|object] is considered concrete if it is a particular individual that occupies a particular place and time. However, in the secondary sense of the term 'abstraction', this physical object can carry materially abstracting processes. For example, record-keeping aids throughout the Fertile Crescent included calculi which represented counts of items, probably livestock or grains, sealed in containers. According to, these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as something of a bill of lading or an accounts book. In order to avoid breaking open the containers for the count, marks were placed on the outside of the containers. These physical marks, in other words, acted as material abstractions of a materially abstract process of accounting, using conceptual abstractions to communicate its meaning.Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experiences, like the color red. That definition, however, suffers from the difficulty of deciding which things are real. 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. Questions about the properties of things are then propositions about predicates, which propositions remain to be evaluated by the investigator. In the graph 1 below, the graphical relationships like the arrows joining boxes and ellipses might denote predicates.
Referencing and referring
Abstractions sometimes have ambiguous referents. For example, "happiness" can mean experiencing various positive emotions, but can also refer to life satisfaction and subjective well-being. 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 to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building. Architecture also refers to the __abstract__ arrangement, design of computer code to implement complex software systems.Simplification and ordering
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. This is true for all verbal/abstract communication.For example, many different things can be red. Likewise, many things sit on surfaces. 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, 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/present participle 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 is more abstract than the graphic image of a cat sitting on a mat, 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 Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach :
An abstraction can thus encapsulate each of these levels of detail with no loss of generality. But perhaps a detective or philosopher/scientist/engineer might seek to learn about something, at progressively deeper levels of detail, to solve a crime or a puzzle.