Abstraction

An **Abstraction** keeps only the most important information about something in order to make it easier to reuse.

Abstraction is about the ways by which higher, less _real_ concepts are derived from the usage and classification of literal ("real" or "concrete") information.

Abstractions may be formed by reducing the information content of a concept or a phenomenon as viewed, often to keep only the information which is needed for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball will keep only the information about balls in general  leaving out anything special about that particular sort of ball. The opposite of the adjective _"abstract"_ is commonly the word _"concrete"_.

## Origins

The first symbols of abstract thinking in humans can be traced to fossil objects dating between 50,000 and 100,000 years ago in Africa.

## Thought process

In philosophical terminology, _abstraction_ is the thought process where ideas are distanced from objects.

Abstraction uses a strategy of simplification. Concrete details are left ambiguous, vague, or undefined.  Communication about things in the abstract requires an intuitive or common experience between the communicator and the communication recipient.

Many different things can be the color red. Likewise, many things sit on surfaces (as in _picture 1_, to the right). The property of _redness_ and the relation _sitting-on_ are  abstractions of those objects. Specifically, the conceptual diagram _graph 1_ identifies only three boxes, two ellipses, and four arrows (and their six labels), whereas the _picture 1_ shows much more pictorial detail, with the scores of implied relationships 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 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/engineer 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 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_ or _monotreme_.

### Physicality

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.

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

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

The way in which 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  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_. Akin to qualia and sumbebekos.

### In linguistics

If an abstract concept, such as "society" or "technology" is treated as if it were a concrete object, that is a fallacy (an error). In linguistics, it may happen that abstract concepts are used as if they were nouns that signify concrete objects:
- 1805: Horatio Nelson (Battle of Trafalgar) – "<u/l>England</u/l> expects that every man will do his duty"

This is called _metonymy_. It can blur the distinction between abstract and concrete things.

### 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 exclusion of detail.

## The neurology of abstraction

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 cause greater brain activity in the inferior frontal gyrus and middle temporal gyrus, compared to concrete concepts when concrete concepts cause greater activity in the posterior cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus.

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

## Abstraction in art

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. 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. Later still, abstraction was manifest in more purely formal terms, such as color, freed from objective context, and a reduction of form to basic geometric designs.

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.

## Abstraction in psychology

Carl Jung's definition of abstraction broadened its scope beyond the thinking process to include exactly four mutually exclusive, opposing 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 opposing 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).

## Abstraction in computer science

Computer scientists use abstraction to understand and solve problems, such as organizing data to be stored in a database.

## Abstraction in mathematics

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.

## Related pages

- Abstract algebra
- Abstract art
- Formal language
- Ontology
- Platonic realism

## Other websites

- Internet Encyclopedia of Philosophy: Gottlob Frege
- Stanford Encyclopedia of Philosophy: Abstract Objects
- Discussion at The Well concerning Abstraction hierarchy