Abstraction in its main sense is a conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") 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 a group, field, or category.
Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only the aspects which are relevant for a particular subjectively valued 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 (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').
Abstraction in its secondary use is a material process,discussed in the themes below.
Thinking in abstractions is considered by anthropologists, archaeologists, and sociologists 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 can be illustrated with Francis Bacon's Novum Organum (1620), a book of modern scientific philosophy written in the late Jacobean eraof 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. 624–546 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 can also use the opposite approach of abstraction, or going from particular facts collected into one general idea, such as the motion of the planets (Newton (1642–1727)). When determining that the sun is the center of our solar system (Copernicus (1473–1543)), scientists had to utilize thousands of measurements to finally conclude that Mars moves in an elliptical orbit about the sun (Kepler (1571–1630)), or to assemble multiple specific facts into the law of falling bodies (Galileo (1564–1642)).
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 (which is itself an object).
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".
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 (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.
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 the commodity abstraction recognizes a parallel process.
The state (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'.
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.
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. 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 (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers. 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 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 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 below, the graphical relationships like the arrows joining boxes and ellipses might denote predicates.
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.
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 (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.
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 San Francisco Chronicle
- (5) my copy of the May 18 edition of The San Francisco Chronicle
- (6) my copy of the May 18 edition of 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.
In philosophical terminology, abstraction is the thought process wherein ideasare distanced from objects.
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, freedom from objective context, and a reduction of form to basic geometric designs.
Computer scientists use 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. They communicate their solutions with the computer by writing source code in some particular computer language which can be translated into machine code for 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 doesn't have to depend on the specific details of supporting applications, operating system software, 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.
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 (words)."
Francis Fukuyama defines history as "a deliberate attempt of abstraction in which we separate out important from unimportant events".
Researchers in linguistics frequently apply abstraction so as to allow analysis of the phenomena of language at the desired level of detail. A commonly used abstraction, the phoneme , 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 is 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:
The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and might require a degree of mathematical maturity and experience before they can be assimilated.
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.
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.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.
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.
John Locke defined abstraction in An 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
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,  (1971): par. 678).
In social theory, abstraction is used as both an ideational and material process. Alfred Sohn-Rethel, 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 Journal Arena. Two books that have taken this theme of the abstraction of social relations as an organizing process in human history are Nation Formation: Towards a Theory of Abstract Community.(1996) and the second volume of Towards a Theory of Abstract Community, published in 2006: Globalism, Nationalism, Tribalism: Bringing Theory Back In – Volume 2 of Towards a Theory of Abstract Community. These books argue that the nation is 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 of globalization and mediatization have contributed to materially abstracting relations between people, with major consequences for how we live our lives.
It can be easily argued that abstraction is an elementary methodological tool in several disciplines of social science. These disciplines have definite and different man concepts that highlight those aspects of man and his behaviour by idealization that are relevant for the given human science. For example, homo sociologicus is the man as sociology abstracts and idealizes it, depicting man as a social being. Moreover, we could talk about homo cyber sapiens (the man who can extend his biologically determined intelligence thanks to new technologies), or homo creativus (who is simply creative).
Abstraction (combined with Weberian idealization) plays a crucial role in economics. Breaking away from directly experienced reality was a common trend in 19th century sciences (especially physics), and this was the effort which was 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, Newton created 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 economists created the indefinitely abstract notion of homo economicus by 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.
Abstracting is a mechanism by which an infinite variety of experiences can be mapped on short noises (words).
[...] 'history' is not a given, not merely a catalog of everything that has happened in the past, but a deliberate attempt of abstraction in which we separate out important from unimportant events.
Concepts are defined as abstract ideas or general notions that occur in the mind, in speech, or in thought. They are understood to be the fundamental building blocks of thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science.
Nominalism is a philosophical view which comes at least in two varieties. In one of them it is the rejection of abstract objects, in the other it is the rejection of universals.
Ontology is the philosophical study of being. More broadly, it studies concepts that directly relate to being, in particular becoming, existence, reality, as well as the basic categories of being and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology often deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, and subdivided according to similarities and differences.
Process philosophy — also ontology of becoming, processism, or philosophy of organism — identifies metaphysical reality with change. In opposition to the classical model of change as illusory or accidental, process philosophy regards change as the cornerstone of reality—the cornerstone of being thought of as becoming.
Platonic realism is the philosophical position that universals or abstract objects exist objectively and outside of human minds. It is named after the Greek philosopher Plato who applied realism to such universals, which he considered ideal forms. This stance is ambiguously also called Platonic idealism but should not be confused with idealism as presented by philosophers such as George Berkeley: as Platonic abstractions are not spatial, temporal, or mental, they are not compatible with the later idealism's emphasis on mental existence. Plato's Forms include numbers and geometrical figures, making them a theory of mathematical realism; they also include the Form of the Good, making them in addition a theory of ethical realism.
In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs both share the quality of "chairness", as well as greenness or the quality of being green; in other words, they share a "universal". There are three major kinds of qualities or characteristics: types or kinds, properties, and relations. These are all different types of universals.
In any of several studies that treat the use of signs—for example, in linguistics, logic, mathematics, semantics, and semiotics—the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question.
A 'conceptual schema' is a high-level description of a business's informational needs. It typically includes only the main concepts and the main relationships among them. Typically this is a first-cut model, with insufficient detail to build an actual database. This level describes the structure of the whole database for a group of users. The conceptual model is also known as the data model that can be used to describe the conceptual schema when a database system is implemented. It hides the internal details of physical storage and targets on describing entities, datatype, relationships and constraints.
In cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another. An example of this is the understanding of quantity in terms of directionality or the understanding of time in terms of money.
Categorization is an activity that consists of putting things into categories based on their similarities or common criteria. It allows humans to organize things, objects, and ideas that exist around them and simplify their understanding of the world. Categorization is something that humans and other organisms do: "doing the right thing with the right kind of thing." The activity of categorizing things can be nonverbal or verbal. For humans, both concrete objects and abstract ideas are recognized, differentiated, and understood through categorization. Objects are usually categorized for some adaptive or pragmatic purposes.
A data model is an abstract model that organizes elements of data and standardizes how they relate to one another and to the properties of real-world entities. For instance, a data model may specify that the data element representing a car be composed of a number of other elements which, in turn, represent the color and size of the car and define its owner.
An abstract structure is a formal object that is defined by a set of laws, properties and relationships in a way that is logically if not always historically independent of the structure of contingent experiences, for example, those involving physical objects. Abstract structures are studied not only in logic and mathematics but in the fields that apply them, as computer science, and in the studies that reflect on them, such as philosophy. Indeed, modern mathematics has been defined in a very general sense as the study of abstract structures.
Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties 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. Two of the most highly abstract areas of modern mathematics are category theory and model theory.
Abstract and concrete are classifications that denote whether the object that a term describes has physical referents. Abstract objects have no physical referents, whereas concrete objects do. They are most commonly used in philosophy and semantics. Abstract objects are sometimes called abstracta and concrete objects are sometimes called concreta. An abstract object is an object that does not exist at any particular time or place, but rather exists as a type of thing—i.e., an idea, or abstraction. The term abstract object is said to have been coined by Willard Van Orman Quine. The study of abstract objects is called abstract object theory.
Process and Reality is a book by Alfred North Whitehead, in which the author propounds a philosophy of organism, also called process philosophy. The book, published in 1929, is a revision of the Gifford Lectures he gave in 1927–28.
We diverge from Descartes by holding that what he has described as primary attributes of physical bodies, are really the forms of internal relationships between actual occasions. Such a change of thought is the shift from materialism to Organic Realism, as a basic idea of physical science.
Abstractionism is the theory that the mind obtains some or all of its concepts by abstracting them from concepts it already has, or from experience. One may, for example, abstract 'green' from a set of experiences which involve green along with other properties. Also, for example, one may abstract a generic concept like 'vegetable' from the already possessed concepts of its instances. This view was criticized by George Berkeley and Peter Geach.
Diagrammatic reasoning is reasoning by means of visual representations. The study of diagrammatic reasoning is about the understanding of concepts and ideas, visualized with the use of diagrams and imagery instead of by linguistic or algebraic means.
Reification is a fallacy of ambiguity, when an abstraction is treated as if it were a concrete real event or physical entity. In other words, it is the error of treating something that is not concrete, such as an idea, as a concrete thing. A common case of reification is the confusion of a model with reality: "the map is not the territory".
A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics.
Contemporary ontologies share many structural similarities, regardless of the language in which they are expressed. Most ontologies describe individuals (instances), classes (concepts), attributes, and relations.
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