Abstraction

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Abstraction is a process by which concepts are derived from the usage and classification of literal ("real" or "concrete") concepts, first principles, or other methods. "An abstraction" is the product of this process—a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.[1]

Abstractions may be formed by reducing the information content of a concept or an observable phenomenon, typically to retain only information which is relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball retains only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball.[1]

Origins[edit]

Thinking in abstractions is considered[by whom?] to be one of the key traits in modern human behaviour, which is 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 (whether spoken or written) appears to both involve and facilitate abstract thinking.

Abstraction involves induction of ideas or the synthesis of particular facts into one general theory about something. It is the opposite of specification, which is the analysis or breaking-down of a general idea or abstraction into concrete facts. Abstraction began with Francis Bacon's Novum Organum (1620), a book of modern scientific philosophy written in the late Elizabethan era[citation needed] of England to encourage modern thinkers to collect specific facts before making any generalizations. Bacon used and promoted induction as an abstraction tool, and it countered the ancient deductive-thinking approach that had dominated the intellectual world since the times of Greek philosophers like Thales, Anaximander, and Aristotle.

Thales (c. 624 BC – c. 546 BCE) 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. The modern scientist uses the opposite approach of abstraction, or going from particular facts first collected into one general idea. To determine that the sun is the center of our solar system, Copernicus (1473-1543) and Galileo (1564-1642) had to make thousands of measurements or assemble multiple specific facts to finally conclude that the earth moves in an elliptical orbit about the sun, as do the other planets.

Thought process[edit]

In philosophical terminology, abstraction is the thought process wherein ideas[2] 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. This is true for all verbal/abstract communication.

Cat on Mat (picture 1)

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 five 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/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.[3]

Conceptual graph for A Cat sitting on the Mat (graph 1)

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 Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979):[4]

(1) a publication
(2) a newspaper
(3) The San Francisco Chronicle
(4) the May 18 edition of the The San Francisco Chronicle
(5) my copy of the May 18 edition of the The San Francisco Chronicle
(6) my copy of the May 18 edition of the The San Francisco 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/engineer might seek to learn about something, at progressively deeper levels of detail, to solve a crime or a puzzle.

Referents[edit]

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 to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building.

Instantiation[edit]

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 or monotreme.

Physicality[edit]

A physical object (a possible referent of a concept or word) is considered concrete (not abstract) if it is a particular individual that occupies a particular place and time. For example, record keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers.[5][6]

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 (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[edit]

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. Another philosophical tool for discussion of abstraction is thought space.

Ontological status[edit]

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. This is similar to qualia and sumbebekos.

Compression[edit]

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 exclusion of detail.

Abstraction in linguistics[edit]

Abstraction is frequently applied in linguistics so as to allow phenomena of language to be analyzed at the desired level of detail. A commonly considered abstraction is the phoneme, which abstracts speech sounds in such a way as to neglect details that cannot serve to differentiate meaning. Other analogous kinds of abstractions (sometimes called "emic units") considered by linguists include morphemes, graphemes, and lexemes.

Abstraction also arises in the relation between syntax, semantics, and pragmatics. Pragmatics involves considerations that make reference to the user of the language; semantics considers expressions and what they denote (the designata) abstracted from the language user; and syntax considers only the expressions themselves, abstracted from the designata.

Abstraction in mathematics[edit]

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

The advantages of abstraction in mathematics are:

  • It reveals deep connections between different areas of mathematics
  • Known results in one area can suggest conjectures in a related area
  • Techniques and methods from one area can be applied to prove results in a related area

The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.

Abstraction in computer science[edit]

Computer scientists use abstraction and communicate their solutions with the computer in some particular computer language. Abstraction allows program designers to separate categories and concepts from instances of implementation, so that they do not depend on concrete details of software or hardware, but on an abstract contract.[vague]

Abstraction in psychology[edit]

Carl Jung's definition of abstraction broadened its scope beyond the thinking process to include exactly four mutually exclusive, different complementary psychological functions: sensation, intuition, feeling, and thinking. Together they form a structural totality of the differentiating abstraction process. Abstraction operates in one of these functions when it excludes the simultaneous influence of the other functions and other irrelevancies, such as emotion. Abstraction requires selective use of this structural split of abilities in the psyche. The opposite of abstraction is concretism. Abstraction is one of Jung's 57 definitions in Chapter XI of Psychological Types.

There is an abstract thinking, just as there is abstract feeling, sensation and intuition. Abstract thinking singles out the rational, logical qualities ... Abstract feeling does the same with ... its feeling-values. ... I put abstract feelings on the same level as abstract thoughts. ... Abstract sensation would be aesthetic as opposed to sensuous sensation and abstract intuition would be symbolic as opposed to fantastic intuition. (Jung, [1921] (1971):par. 678).

Neurology of abstraction[edit]

A recent meta-analysis suggests that the verbal system has greater engagement for abstract concepts when the perceptual system is more engaged for processing of concrete concepts. This is because abstract concepts elicit greater brain activity in the inferior frontal gyrus and middle temporal gyrus compared to concrete concepts which elicit greater activity in the posterior cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus.[7]

Other research into the human brain suggests that the left and right hemispheres differ in their handling of abstraction. For example, one meta-analysis reviewing human brain lesions has shown a left hemisphere bias during tool usage.[8]

Abstraction in art[edit]

Typically, abstraction is used in the arts as a synonym for abstract art in general. Strictly speaking, it refers to art unconcerned with the literal depiction of things from the visible world—it can, however, refer to an object or image which has been distilled from the real world, or indeed, another work of art.[9] Artwork that reshapes the natural world for expressive purposes is called abstract; that which derives from, but does not imitate a recognizable subject is called nonobjective abstraction. In the 20th century the trend toward abstraction coincided with advances in science, technology, and changes in urban life, eventually reflecting an interest in psychoanalytic theory.[10] Later still, abstraction was manifest in more purely formal terms, such as color, freedom from objective context, and a reduction of form to basic geometric designs.[11]

In music, the term abstraction can be used to describe improvisatory approaches to interpretation, and may sometimes indicate abandonment of tonality. Atonal music has no key signature, and is characterized by the exploration of internal numeric relationships.[12]

See also[edit]

Notes[edit]

  1. ^ a b Suzanne K. Langer (1953), Feeling and Form: a theory of art developed from Philosophy in a New Key p. 90: "Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through touch and sight."
  2. ^ But an idea can be symbolized. "A symbol is any device whereby we are enabled to make an abstraction." -- p.xi and chapter 20 of Suzanne K. Langer (1953), Feeling and Form: a theory of art developed from Philosophy in a New Key: New York: Charles Scribner's Sons. 431 pages, index.
  3. ^ Sowa, John F. (1984). Conceptual Structures: Information Processing in Mind and Machine. Reading, MA: Addison-Wesley. ISBN 978-0-201-14472-7.
  4. ^ Douglas Hofstadter (1979) Gödel, Escher, Bach
  5. ^ According to Schmandt-Besserat 1981, 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, marks were placed on the outside of the containers, for the count. Eventually (Schmandt-Besserat estimates it took 4000 years) the marks on the outside of the containers were all that were needed to convey the count, and the clay containers evolved into clay tablets with marks for the count.
  6. ^ Robson, Eleanor (2008). Mathematics in Ancient Iraq. ISBN 978-0-691-09182-2. . p. 5: these calculi were in use in Iraq for primitive accounting systems as early as 3200–3000 BCE, with commodity-specific counting representation systems. Balanced accounting was in use by 3000–2350 BCE, and a sexagesimal number system was in use 2350–2000 BCE.
  7. ^ Jing Wang, Julie A. Conder, David N. Blitzer, and Svetlana V. Shinkareva "Neural Representation of Abstract and Concrete Concepts: A Meta-Analysis of Neuroimaging Studies" Human Brain Mapping (2010). http://dx.doi.org/10.1002/hbm.20950
  8. ^ James W. Lewis "Cortical Networks Related to Human Use of Tools" 12 (3): 211–231 The Neuroscientist (June 1, 2006).
  9. ^ Encyclopædia Britannica
  10. ^ Catherine de Zegher and Hendel Teicher (eds.), 3 X Abstraction. NY/New Haven: The Drawing Center/Yale University Press. 2005. ISBN 0-300-10826-5
  11. ^ National Gallery of Art: Abstraction.
  12. ^ Washington State University: Glossary of Abstraction.

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