Abstraction
Encyclopedia
Abstraction is a process by which higher
concepts are derived from the usage and classification of literal ("real" or "concrete") concepts, first principles, or other methods.
An "abstraction" (noun) is a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.
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.
s of abstract thinking in humans can be traced to fossils dating between 50,000 and 100,000 years ago in Africa. However, language
itself, whether spoken or written, involves abstract thinking.
, abstraction is the thought process wherein idea
s are distanced from object
s.
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 red
ness 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
SITTING and the noun
s 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):
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.
" (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.
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
.
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 predicate
s 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 proposition
s 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.
is the process (or, to some, the alleged process) in concept
-formation of recognizing some set of common features in individual
s, 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.
In the Urantia Book glossary Dr. William S. Sadler
commented that "Philosophers commit their gravest error when they are misled into the fallacy of abstraction, the practice of focusing the attention upon one aspect of reality and then of pronouncing such an isolated aspect to be the whole truth." (42.6) 2:7.5
differs from the way that properties of abstract concepts or relations have being, for example the way the concrete, particular
, individual
s 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 red
ness of a particular apple
is an abstract particular. Akin to qualia
and sumbebekos.
, semantics
, and pragmatics
has also been cashed out in terms of what could be called an "abstraction hierarchy." For instance, Rudolf Carnap
in his Introduction to Semantics (1942, Harvard University Press) writes:
A related statement was made a few years earlier by Carnap's fellow American philosopher Charles W. Morris
, PhD student of the sociologist and pragmatist philosopher George Herbert Mead
, and heavily influenced by the pragmatist and founder of (analytical) semiotics
, Charles Sanders Peirce:
The relation between abstraction and Morris' influential trichotomy is a matter of ongoing discussion.
Reification
, also called hypostatization, might be considered a formal fallacy
whenever an abstract concept, such as "society" or "technology" is treated as if it were a concrete object. In linguistics
this is called metonymy
, in which abstract concepts are referred to using the same sorts of noun
s that signify concrete objects. Metonymy is an aspect of the English language and of other languages. It can blur the distinction between abstract and concrete things:
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".
This conceptual scheme entails no specific hierarchical taxonomy
(such as the one mentioned involving cats and mammals), only a progressive exclusion of detail.
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.
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.
'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
.
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 software or hardware.
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:
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.
Hierarchy
A hierarchy is an arrangement of items in which the items are represented as being "above," "below," or "at the same level as" one another...
concepts are derived from the usage and classification of literal ("real" or "concrete") concepts, first principles, or other methods.
An "abstraction" (noun) is a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.
Abstractions may be formed by reducing the information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
content of a concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
or an observable phenomenon
Phenomenon
A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...
, 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
Ball
A ball is a round, usually spherical but sometimes ovoid, object with various uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used for simpler activities, such as catch, marbles and juggling...
retains only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball.
Origins
The first symbolSymbol
A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for...
s of abstract thinking in humans can be traced to fossils dating between 50,000 and 100,000 years ago in Africa. However, language
Language
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
itself, whether spoken or written, involves abstract thinking.
Thought process
In philosophical terminologyPhilosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
, abstraction is the thought process wherein idea
Idea
In the most narrow sense, an idea is just whatever is before the mind when one thinks. Very often, ideas are construed as representational images; i.e. images of some object. In other contexts, ideas are taken to be concepts, although abstract concepts do not necessarily appear as images...
s are distanced from object
Object (philosophy)
An object in philosophy is a technical term often used in contrast to the term subject. Consciousness is a state of cognition that includes the subject, which can never be doubted as only it can be the one who doubts, and some object or objects that may or may not have real existence without...
s.
Abstraction uses a strategy
Strategy
Strategy, a word of military origin, refers to a plan of action designed to achieve a particular goal. In military usage strategy is distinct from tactics, which are concerned with the conduct of an engagement, while strategy is concerned with how different engagements are linked...
of simplification, wherein formerly concrete details are left ambiguous, vague, or undefined; thus effective communication
Communication
Communication is the activity of conveying meaningful information. Communication requires a sender, a message, and an intended recipient, although the receiver need not be present or aware of the sender's intent to communicate at the time of communication; thus communication can occur across vast...
about things in the abstract requires an intuitive
Intuition (knowledge)
Intuition is the ability to acquire knowledge without inference or the use of reason. "The word 'intuition' comes from the Latin word 'intueri', which is often roughly translated as meaning 'to look inside'’ or 'to contemplate'." Intuition provides us with beliefs that we cannot necessarily justify...
or common experience between the communicator and the communication recipient. This is true for all verbal/abstract communication.
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...
. Likewise, many things sit on surfaces (as in picture 1, to the right). The property of red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...
ness and the relation
Relation of Ideas
A Relation of Ideas, in the Humean sense, is the type of knowledge that can be characterized as arising out of pure conceptual thought and logical operations . In a Kantian philosophy, it is equivalent to the analytic a priori...
sitting-on
Sitting
Sitting is a rest position supported by the buttocks or thighs where the torso is more or less upright.- Sitting on the floor :The most common way of sitting on the floor involves bending the knees...
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
Is-a
In knowledge representation, object-oriented programming and design, is-a or is_a or is a is a relationship where one class D is a subclass of another class B ....
relationship, as does the arrow between the location and the MAT. The arrows between the gerund
Gerund
In linguistics* As applied to English, it refers to the usage of a verb as a noun ....
SITTING and the noun
Noun
In linguistics, a noun is a member of a large, open lexical category whose members can occur as the main word in the subject of a clause, the object of a verb, or the object of a preposition .Lexical categories are defined in terms of how their members combine with other kinds of...
s agent and location express the diagram
Diagram
A diagram is a two-dimensional geometric symbolic representation of information according to some visualization technique. Sometimes, the technique uses a three-dimensional visualization which is then projected onto the two-dimensional surface...
'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
Douglas Hofstadter
Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach
Gödel, Escher, Bach
Gödel, Escher, Bach: An Eternal Golden Braid is a book by Douglas Hofstadter, described by his publishing company as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll"....
(1979):
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 some thing, at progressively deeper levels of detail, to solve a crime or a puzzle.
Referents
Abstractions sometimes have ambiguous referents; for example, "happinessHappiness
Happiness is a mental state of well-being characterized by positive emotions ranging from contentment to intense joy. A variety of biological, psychological, religious, and philosophical approaches have striven to define happiness and identify its sources....
" (when used as an abstraction) can refer to as many things as there are people and events or states of being
Being
Being , is an English word used for conceptualizing subjective and objective aspects of reality, including those fundamental to the self —related to and somewhat interchangeable with terms like "existence" and "living".In its objective usage —as in "a being," or "[a] human being" —it...
which make them happy. Likewise, "architecture
Architecture
Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...
" refers not only to the design of safe, functional buildings, but also to elements of creation and innovation
Innovation
Innovation is the creation of better or more effective products, processes, technologies, or ideas that are accepted by markets, governments, and society...
which aim at elegant solutions to construction
Construction
In the fields of architecture and civil engineering, construction is a process that consists of the building or assembling of infrastructure. Far from being a single activity, large scale construction is a feat of human multitasking...
problems, to the use of space, and to the attempt to evoke an emotional response
Emotion
Emotion is a complex psychophysiological experience of an individual's state of mind as interacting with biochemical and environmental influences. In humans, emotion fundamentally involves "physiological arousal, expressive behaviors, and conscious experience." Emotion is associated with mood,...
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
Marsupial
Marsupials are an infraclass of mammals, characterized by giving birth to relatively undeveloped young. Close to 70% of the 334 extant species occur in Australia, New Guinea, and nearby islands, with the remaining 100 found in the Americas, primarily in South America, but with thirteen in Central...
or monotreme
Monotreme
Monotremes are mammals that lay eggs instead of giving birth to live young like marsupials and placental mammals...
.
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
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
or exist only as sensory experiences, like the color red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...
. 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 predicate
Predicate (grammar)
There are two competing notions of the predicate in theories of grammar. Traditional grammar tends to view a predicate as one of two main parts of a sentence, the other being the subject, which the predicate modifies. The other understanding of predicates is inspired from work in predicate calculus...
s 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 proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
s 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 philosophyPhilosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
is the process (or, to some, the alleged process) in concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
-formation of recognizing some set of common features in individual
Individual
An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...
s, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism
Empiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...
and the problem of universals
Problem of universals
The problem of universals is an ancient problem in metaphysics about whether universals exist. Universals are general or abstract qualities, characteristics, properties, kinds or relations, such as being male/female, solid/liquid/gas or a certain colour, that can be predicated of individuals or...
. It has also recently become popular in formal logic under predicate abstraction
Predicate abstraction
In logic, predicate abstraction is the result of creating a predicate from an open sentence. If Q is any formula with x free then the predicate formed from that sentence is , where λ is an abstraction operator...
. Another philosophical tool for discussion of abstraction is thought space.
In the Urantia Book glossary Dr. William S. Sadler
William S. Sadler
William Samuel Sadler was a well-known American psychiatrist and professor at McCormick Theological Seminary. For over sixty years he practiced medicine in Chicago, thirty-three years being associated in practice with his wife, Lena Kellogg....
commented that "Philosophers commit their gravest error when they are misled into the fallacy of abstraction, the practice of focusing the attention upon one aspect of reality and then of pronouncing such an isolated aspect to be the whole truth." (42.6) 2:7.5
Ontological status
The way that physical objects, like rocks and trees, have beingCategory of being
In metaphysics , the different kinds or ways of being are called categories of being or simply categories. To investigate the categories of being is to determine the most fundamental and the broadest classes of entities...
differs from the way that properties of abstract concepts or relations have being, for example the way the concrete, particular
Particular
In philosophy, particulars are concrete entities existing in space and time as opposed to abstractions. There are, however, theories of abstract particulars or tropes. For example, Socrates is a particular...
, individual
Individual
An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...
s 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
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
refer to tropes
Trope (philosophy)
The term "trope" is both a term which denotes figurative and metaphorical language and one which has been used in various technical senses. The term trope derives from the Greek τρόπος , "a turn, a change", related to the root of the verb τρέπειν , "to turn, to direct, to alter, to change"; this...
(instances of properties) as abstract particulars. E.g., the particular red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...
ness of a particular apple
Apple
The apple is the pomaceous fruit of the apple tree, species Malus domestica in the rose family . It is one of the most widely cultivated tree fruits, and the most widely known of the many members of genus Malus that are used by humans. Apple grow on small, deciduous trees that blossom in the spring...
is an abstract particular. Akin to qualia
Qualia
Qualia , singular "quale" , from a Latin word meaning for "what sort" or "what kind," is a term used in philosophy to refer to subjective conscious experiences as 'raw feels'. Examples of qualia are the pain of a headache, the taste of wine, the experience of taking a recreational drug, or the...
and sumbebekos.
In linguistics
The relation among syntaxSyntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
, semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
, and pragmatics
Pragmatics
Pragmatics is a subfield of linguistics which studies the ways in which context contributes to meaning. Pragmatics encompasses speech act theory, conversational implicature, talk in interaction and other approaches to language behavior in philosophy, sociology, and linguistics. It studies how the...
has also been cashed out in terms of what could be called an "abstraction hierarchy." For instance, Rudolf Carnap
Rudolf Carnap
Rudolf Carnap was an influential German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism....
in his Introduction to Semantics (1942, Harvard University Press) writes:
If… explicit reference is made to the speaker, or, to put it in more general terms, to the user of a language, then we assign it to the field of pragmatics. (Whether in this case reference to designata is made or not makes no difference for this classification.) If we abstract from the user of the language and analyze only the expressions and their designata, we are in the field of semantics. And if, finally, we abstract from the designata also and analyze only the relations between the expressions, we are in (logical) syntax. The whole science of language, consisting of the three parts mentioned, is called semiotic. (p. 9)
A related statement was made a few years earlier by Carnap's fellow American philosopher Charles W. Morris
Charles W. Morris
Charles W. Morris was an American semiotician and philosopher.-Background:A son of Charles William and Laura Morris, Charles William Morris was born on May 23, 1901...
, PhD student of the sociologist and pragmatist philosopher George Herbert Mead
George Herbert Mead
George Herbert Mead was an American philosopher, sociologist and psychologist, primarily affiliated with the University of Chicago, where he was one of several distinguished pragmatists. He is regarded as one of the founders of social psychology and the American sociological tradition in general.-...
, and heavily influenced by the pragmatist and founder of (analytical) semiotics
Semiotics
Semiotics, also called semiotic studies or semiology, is the study of signs and sign processes , indication, designation, likeness, analogy, metaphor, symbolism, signification, and communication...
, Charles Sanders Peirce:
"Syntactics, as the study of the syntactical relations of signs to one another in abstraction from the relations of signs to objects [i.e., semantics] or to interpreters [i.e., pragmatics], is the best developed of all the branches of semiotic." (p. 13)
The relation between abstraction and Morris' influential trichotomy is a matter of ongoing discussion.
Reification
Reification (fallacy)
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 as a "real thing" something which is not a real thing, but merely an idea...
, also called hypostatization, might be considered a formal fallacy
Formal fallacy
In philosophy, a formal fallacy is a pattern of reasoning that is always wrong. This is due to a flaw in the logical structure of the argument which renders the argument invalid...
whenever an abstract concept, such as "society" or "technology" is treated as if it were a concrete object. In linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
this is called metonymy
Metonymy
Metonymy is a figure of speech used in rhetoric in which a thing or concept is not called by its own name, but by the name of something intimately associated with that thing or concept...
, in which abstract concepts are referred to using the same sorts of noun
Noun
In linguistics, a noun is a member of a large, open lexical category whose members can occur as the main word in the subject of a clause, the object of a verb, or the object of a preposition .Lexical categories are defined in terms of how their members combine with other kinds of...
s that signify concrete objects. Metonymy is an aspect of the English language and of other languages. It can blur the distinction between abstract and concrete things:
- 1805: Horatio Nelson (Battle of TrafalgarBattle of TrafalgarThe Battle of Trafalgar was a sea battle fought between the British Royal Navy and the combined fleets of the French Navy and Spanish Navy, during the War of the Third Coalition of the Napoleonic Wars ....
) - "England expects that every man will do his dutyEngland expects that every man will do his duty"England expects that every man will do his duty" was a signal sent by Admiral Horatio Nelson, 1st Viscount Nelson from his flagship HMS Victory as the Battle of Trafalgar was about to commence on 21 October 1805. Trafalgar was the decisive naval engagement of the Napoleonic Wars...
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
Perception
Perception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...
to basic abstractions such as color or shape
Shape
The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...
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
Taxonomy
Taxonomy is the science of identifying and naming species, and arranging them into a classification. The field of taxonomy, sometimes referred to as "biological taxonomy", revolves around the description and use of taxonomic units, known as taxa...
(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 elicit greater brain activity in the inferior frontal gyrus and middle temporal gyrus compared to concrete concepts when concrete concepts elicit greater activity in the posterior cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus.Other research into the human brain
Human brain
The human brain has the same general structure as the brains of other mammals, but is over three times larger than the brain of a typical mammal with an equivalent body size. Estimates for the number of neurons in the human brain range from 80 to 120 billion...
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 art
Typically, abstraction is used in the arts as a synonymSynonym
Synonyms are different words with almost identical or similar meanings. Words that are synonyms are said to be synonymous, and the state of being a synonym is called synonymy. The word comes from Ancient Greek syn and onoma . The words car and automobile are synonyms...
for abstract art
Abstract art
Abstract art uses a visual language of form, color and line to create a composition which may exist with a degree of independence from visual references in the world. Western art had been, from the Renaissance up to the middle of the 19th century, underpinned by the logic of perspective and an...
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
Tonality
Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...
. Atonal music has no key signature, and is characterized by the exploration of internal numeric relationships.
Abstraction in psychology
Carl JungCarl Jung
Carl Gustav Jung was a Swiss psychiatrist and the founder of Analytical Psychology. Jung is considered the first modern psychiatrist to view the human psyche as "by nature religious" and make it the focus of exploration. Jung is one of the best known researchers in the field of dream analysis and...
'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
Psychological Types
Psychological Types is the title of the sixth volume in the Princeton / Bollingen edition of the Collected Works of Carl Jung. The original German language edition, "Psychologische Typen", was first published by Rascher Verlag, Zurich in 1921....
.
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 and communicateCommunication
Communication is the activity of conveying meaningful information. Communication requires a sender, a message, and an intended recipient, although the receiver need not be present or aware of the sender's intent to communicate at the time of communication; thus communication can occur across vast...
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 software or hardware.
Abstraction in mathematics
Abstraction in mathematicsMathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
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
Mathematical maturity
Mathematical maturity is an informal term used by mathematicians to refer to a mixture of mathematical experience and insight that cannot be directly taught...
and experience before they can be assimilated.
See also
- Abstract structureAbstract structureAn abstract structure in mathematics 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 (summary)Abstract (summary)An abstract is a brief summary of a research article, thesis, review, conference proceeding or any in-depth analysis of a particular subject or discipline, and is often used to help the reader quickly ascertain the paper's purpose. When used, an abstract always appears at the beginning of a...
- Abstract interpretationAbstract interpretationIn computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which gains information about its semantics In...
- Abstract objectAbstract objectAn abstract object is an object which does not exist at any particular time or place, but rather exists as a type of thing . In philosophy, an important distinction is whether an object is considered abstract or concrete. Abstract objects are sometimes called abstracta An abstract object is an...
- EmergenceEmergenceIn philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....
- Gottlob FregeGottlob FregeFriedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
- Hypostatic abstractionHypostatic abstractionHypostatic abstraction in mathematical logic, also known as hypostasis or subjectal abstraction, is a formal operation that transforms an assertion to a relation; for example "Honey is sweet" is transformed into "Honey has sweetness"...
- Leaky abstractionLeaky abstractionA leaky abstraction is any implemented abstraction, intended to reduce complexity, where the underlying details are not completely hidden. The term is most frequently used to call attention to a flaw in a software or hardware abstraction.-History:...
- Model (abstract)
- Object of the mindObject of the mindAn object of the mind is an object which exists in the imagination, but which, in the real world, can only be represented or modeled. Some such objects are mathematical abstractions, literary concepts, or fictional scenarios....
- Charles Sanders Peirce
- Platonic realismPlatonic realismPlatonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato , a student of Socrates. As universals were considered by Plato to be ideal forms, this stance is confusingly also called...
- Symbolism (disambiguation)Symbolism (disambiguation)Symbolism is the applied use of symbols. It is a representation that carries a particular meaning. It is a device in literature where an object represents an idea.A symbol is an object, action, or idea that represents something other than itself....