Abstraction

This article is about the concept of abstraction in general. For specific types of abstraction and other uses of the term, seeAbstraction (disambiguation).For other uses, seeAbstract (disambiguation).

Abstractionis a process wherein generalrulesandconceptsare derived from the usage and classification of specific examples, literal (realorconcrete) signifiers,first principles,or other methods.

"An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as agroup,field,orcategory.

Conceptual abstractions may be formed by filtering theinformationcontent of aconceptor an observablephenomenon,selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of aballselects only the information on general ball attributes and behavior, excluding but not eliminating the other phenomenal and cognitive characteristics of that particular ball.In atype–token distinction,a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').

Abstraction in its secondary use is amaterial process,discussed in thethemes below.

Origins

Main article:Behavioral modernity

Thinking in abstractions is considered byanthropologists,archaeologists,andsociologiststo be one of the key traits inmodern human behaviour,which is believedto have developed between 50,000 and 100,000 years ago. Its development is likely to have been closely connected with the development of humanlanguage,which (whether spoken or written) appears to both involve and facilitate abstract thinking.

History

Abstractioninvolvesinductionof ideas or the synthesis of particular facts into one general theory about something. It is the opposite ofspecification,which is the analysis or breaking-down of a general idea or abstraction into concrete facts. Abstraction can be illustrated byFrancis Bacon'sNovum Organum(1620), a book of modern scientific philosophy written in the lateJacobean eraof England to encourage modern thinkers to collect specific facts before making any generalizations.

Bacon used and promotedinductionas an abstraction tool; it complemented but was distinct from the ancientdeductive-thinking approach that had dominated the intellectual world since the times of Greek philosophers likeThales,Anaximander,andAristotle.Thales (c. 624–546 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.

Modern scientists used the approach of abstraction (going from particular facts collected into one general idea).Newton(1642–1727) derived the motion of the planets fromCopernicus' (1473–1543) simplification, that the Sun is the center of theSolar System;Kepler(1571–1630) compressed thousands of measurements into one expression to finally conclude that Mars moves in an elliptical orbit about the Sun;Galileo(1564–1642) repeated one hundred specific experiments into the law of falling bodies.

Themes

Compression

An abstraction can be seen as acompressionprocess,mapping multiple different pieces ofconstituentdata 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 isitself an object).

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

Chains of abstractions can beconstrued,moving from neural impulses arising from sensoryperceptionto basic abstractions such as color orshape,to experiential abstractions such as a specific cat, tosemanticabstractions 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 belowexpresses the abstraction "agent sits on location". This conceptual scheme entails no specifichierarchicaltaxonomy(such as the one mentioned involving cats and mammals), only a progressiveexclusion of detail.

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 bemultiply instantiated,in the sense ofpicture 1,picture 2,etc., shownbelow.It is not sufficient, however, to defineabstractideas as those that can be instantiated and to defineabstractionas 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" areabstractions,they are notabstractin the sense of the objects ingraph 1below.We might look at other graphs, in a progression fromcattomammaltoanimal,and see thatanimalis more abstract thanmammal;but on the other handmammalis a harder idea to express, certainly in relation tomarsupialormonotreme.

Perhaps confusingly, somephilosophiesrefer totropes(instances of properties) asabstract particulars—e.g., the particularrednessof a particularappleis anabstract particular.This is similar toqualiaandsumbebekos.

Material process

Further information:Power projectionandDisplay behavior

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 (see the section on 'Physicality' below).Karl Marx's writing on thecommodityabstraction recognizes a parallel process.

Thestate (polity)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, havebeingdiffers from the way that properties of abstract concepts or relations have being, for example the way theconcrete,particular,individualspictured inpicture 1exist differs from the way the concepts illustrated ingraph 1exist. That difference accounts for theontologicalusefulness 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

Further information:History of accounting § Ancient history

A physical object (a possible referent of a concept or word) is consideredconcrete(not abstract) if it is aparticular individualthat 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 theFertile Crescentincluded calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers. According toSchmandt-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 abill of ladingor 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 (numbers) to communicate its meaning.

Abstract things are sometimes defined as those things that do not exist inrealityor exist only as sensory experiences, like the colorred.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 likeGod,the number three,andgoodnessare real, abstract, or both.

An approach to resolving such difficulty is to usepredicatesas 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 thenpropositionsabout predicates, which propositions remain to be evaluated by the investigator. In thegraph 1below,the graphical relationships like the arrows joining boxes and ellipses might denote predicates.

Referencing and referring

Abstractions sometimes have ambiguousreferents.For example, "happiness"can mean experiencing various positive emotions, but can also refer tolife satisfactionandsubjective well-being.Likewise, "architecture"refers not only to the design of safe, functional buildings, but also to elements of creation andinnovationwhich aim at elegant solutions toconstructionproblems, to the use of space, and to the attempt to evoke anemotional responsein the builders, owners, viewers and users of the building.

Simplification and ordering

Abstraction uses astrategyof simplification, wherein formerly concrete details are left ambiguous, vague, or undefined; thus effectivecommunicationabout things in the abstract requires anintuitiveor common experience between the communicator and the communication recipient. This is true for all verbal/abstract communication.

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

Cat on Mat(picture 1)

For example, many different things can bered.Likewise, many things sit on surfaces (as inpicture 1,to the right). The property ofrednessand therelationsitting-onare therefore abstractions of those objects. Specifically, the conceptual diagramgraph 1identifies only three boxes, two ellipses, and four arrows (and their five labels), whereas thepicture 1shows 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 1details some explicit relationships between the objects of the diagram. For example, the arrow between theagentandCAT:Elsiedepicts an example of anis-arelationship, as does the arrow between thelocationand theMAT.The arrows between thegerund/present participleSITTINGand thenounsagentandlocationexpress thediagram's basic relationship;"agent is SITTING on location";Elsieis an instance ofCAT.

Although the descriptionsitting-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 inDouglas Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete inGödel, Escher, Bach(1979):

(1) a publication

(2) a newspaper

(3)The San Francisco Chronicle

(4) the May 18 edition ofThe San Francisco Chronicle

(5) my copy of the May 18 edition ofThe San Francisco Chronicle

(6) my copy of the May 18 edition ofThe San Francisco Chronicleas 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 noloss 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.

Thought processes

Inphilosophical terminology,abstractionis thethought processwhereinideasare distanced fromobjects.But an idea can besymbolized.

As used in different disciplines

In art

Main article:Abstraction (art)

Typically,abstractionis used in the arts as asynonymforabstract artin 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, freedom from objective context, and a reduction of form to basic geometric designs.

In computer science

Main article:Abstraction (software engineering)

Computer scientistsuse abstraction to make models that can be used and re-used without having to re-write all the program code for each new application on every different type of computer. Theycommunicatetheir solutions with the computer by writingsource codein some particularcomputer languagewhich can be translated intomachine codefor different types of computers to execute. Abstraction allows program designers to separate a framework (categorical concepts related to computing problems) from specific instances which implement details. This means that the program code can be written so that code does not have to depend on the specific details of supporting applications,operating systemsoftware, or hardware, but on a categorical concept of the solution. A solution to the problem can then be integrated into the system framework with minimal additional work. This allows programmers to take advantage of another programmer's work, while requiring only an abstract understanding of the implementation of another's work, apart from the problem that it solves.

In general semantics

Abstractions and levels of abstraction play an important role in the theory ofgeneral semanticsoriginated byAlfred Korzybski.Anatol Rapoportwrote "Abstracting is a mechanism by which an infinite variety of experiences can be mapped on short noises (words)."

In history

Francis Fukuyamadefineshistoryas "a deliberate attempt of abstraction in which we separate out important from unimportant events".

In linguistics

Main article:Abstraction (linguistics)

Researchers inlinguisticsfrequently apply abstraction so as to allow an analysis of the phenomena of language at the desired level of detail. A commonly used abstraction, thephoneme,abstractsspeech soundsin 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 includemorphemes,graphemes,andlexemes.

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

In mathematics

Main article:Abstraction (mathematics)

Abstraction inmathematicsis the process of extracting the underlying structures, patterns or properties of a mathematical concept or object, 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 suggestconjecturesin another related area.
• Techniques and methods from one area can be applied toproveresults in other related area.
• Patterns from one mathematical object can be generalized to other similar objects in the same class.

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

In music

In music, the termabstractioncan be used to describe improvisatory approaches to interpretation, and may sometimes indicate abandonment oftonality.Atonalmusic has no key signature, and is characterized by the exploration of internal numeric relationships.

In neurology

Further information:Intelligence,Mental rotation,andMental operations

A recent meta-analysis suggests that the verbal system has a greater engagement with abstract concepts when the perceptual system is more engaged in processing 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.Other research into thehuman brainsuggests 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.

In philosophy

See also:Abstract object theory

Abstraction inphilosophyis the process (or, to some, the alleged process) inconceptformation of recognizing some set of common features inindividuals,and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surroundingempiricismand theproblem of universals.It has also recently become popular in formal logic underpredicate abstraction.Another philosophical tool for the discussion of abstraction is thought space.

John Lockedefined abstraction inAn Essay Concerning Human Understanding:

'So words are used to stand as outward marks of our internal ideas, which are taken from particular things; but if every particular idea that we take in had its own special name, there would be no end to names. To prevent this, the mind makes particular ideas received from particular things become general; which it does by considering them as they are in the mind—mental appearances—separate from all other existences, and from the circumstances of real existence, such as time, place, and so on. This procedure is called abstraction. In it, an idea taken from a particular thing becomes a general representative of all of the same kind, and its name becomes a general name that is applicable to any existing thing that fits that abstract idea.' (2.11.9)

In psychology

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 isconcretism.Abstractionis one of Jung's 57 definitions in Chapter XI ofPsychological Types.

There is an abstractthinking,just as there is abstractfeeling,sensationandintuition.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 sensuoussensationand abstract intuition would be symbolic as opposed to fantasticintuition.(Jung, [1921] (1971): par. 678).

In social theory

Social theoristsdeal with abstraction both as an ideational and as a material process.Alfred Sohn-Rethel(1899–1990) asked: "Can there be abstraction other than by thought?"He used the example of commodity abstraction to show that abstraction occurs in practice as people create systems of abstract exchange that extend beyond the immediate physicality of the object and yet have real and immediate consequences. This work was extended through the 'Constitutive Abstraction' approach of writers associated with the JournalArena.Two books that have taken this theme of the abstraction of social relations as an organizing process in human history areNation Formation: Towards a Theory of Abstract Community(1996) and an associated volume published in 2006,Globalism, Nationalism, Tribalism: Bringing Theory Back In. These books argue that anationis an abstract community bringing together strangers who will never meet as such; thus constituting materially real and substantial, but abstracted and mediated relations. The books suggest that contemporary processes ofglobalizationandmediatizationhave contributed to materially abstracting relations between people, with major consequences for how humans live theirlives.

One can readily argue that abstraction is an elementary methodological tool in several disciplines of social science. These disciplines have definite and different concepts of "man" that highlight those aspects of man and his behaviour by idealization that are relevant for the givenhuman science.For example,homo sociologicusis the man as sociology abstracts and idealizes it, depicting man as a social being. Moreover, we could talk abouthomo cyber sapiens(the man who can extend his biologically determined intelligence thanks to new technologies), orhomo creativus(who is simply creative).

Abstraction (combined with Weberianidealization) plays a crucial role ineconomics- hence abstractions such as"the market" and the generalized concept of "business". Breaking away from directly experienced reality was a common trend in 19th-century sciences (especiallyphysics), and this was the effort which fundamentally determined the way economics tried (and still tries) to approach the economic aspects of social life. It is abstraction we meet in the case of both Newton's physics and the neoclassical theory, since the goal was to grasp the unchangeable and timeless essence of phenomena. For example,Newtoncreated the concept of the material point by following the abstraction method so that he abstracted from the dimension and shape of any perceptible object, preserving only inertial and translational motion. Material point is the ultimate and common feature of all bodies.Neoclassical economistscreated the indefinitely abstract notion ofhomo economicusby following the same procedure. Economists abstract from all individual and personal qualities in order to get to those characteristics that embody the essence of economic activity. Eventually, it is the substance of the economic man that they try to grasp. Any characteristic beyond it only disturbs the functioning of this essential core.

See also

• Abstract art
• Abstract and concrete
• Abstract interpretation
• Abstract labour and concrete labour
• Abstract structure
• Abstraction (sociology)
• Charles Sanders Peirce
• Concept
• Conceptual model
• Emergence
• Engaged theory
• Gottlob Frege
• High- and low-level
• Hypostatic abstraction
• Inventor's paradox
• Leaky abstraction
• Lyrical abstraction
• Nucleophilic abstraction
• Object of the mind
• Platonic realism
• Reification (knowledge representation)
• Symbol
• Politechnika Wrocławska
• Theory

References

Sources

• The American Heritage Dictionary of the English Language, 3rd edition.Houghton Mifflin (1992). 1992.ISBN0-395-44895-6.
• Sohn-Rethel, Alfred (1977)Intellectual and manual labour: A critique of epistemology,Humanities Press.
• Schmandt-Besserat, Denise(1981). "Decipherment of the Earliest Tablets".Science.211(4479): 283–285.Bibcode:1981Sci...211..283S.doi:10.1126/science.211.4479.283.PMID17748027..

Further reading

• James, Paul(1996).Nation Formation: Towards a Theory of Abstract Community.London: Sage Publications.
• James, Paul (2006).Globalism, Nationalism, Tribalism: Bringing Theory Back In - Volume 2 of Towards a Theory of Abstract Community.London: Sage Publications.
• Jung, C.G. (1971).Psychological Types.Collected Works. Vol. 6 (1921 ed.). Princeton, NJ: Princeton University Press.ISBN0-691-01813-8..

External links

• Abstractionat theIndiana Philosophy Ontology Project
• AbstractionatPhilPapers
• Internet Encyclopedia of Philosophy: Gottlob Frege
• Discussion at The Well concerning Abstraction hierarchy