Abstraction is a conceptual process by which higher A hierarchy (Greek: hierarchia , from hierarches, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above," "below," or "at the same level as" one another and with only one "neighbor" above and below each of, more abstract concepts are derived from the usage and classification of literal, "real," or "concrete" concepts.

An "abstraction" (noun) is a concept that acts as 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, in its most restricted technical sense, is an ordered sequence of symbols. As a concept, however, information has many meanings. Moreover, the concept of information is closely related to notions of constraint, communication, control, form, instruction, knowledge, meaning, mental stimulus, pattern, perception, and representation content of a concept A concept is a cognitive unit of meaning—an abstract idea or a mental symbol sometimes defined as a "unit of knowledge," built from other units which act as a concept's characteristics. A concept is typically associated with a corresponding representation in a language or symbology[citation needed] such as a single meaning of a term or an observable phenomenon A phenomenon , plural phenomena, is any observable occurrence. In popular usage, a phenomenon often refers to an extraordinary event. In scientific usage, a phenomenon is any event that is observable, however commonplace it might be, even if it requires the use of instrumentation to observe it. For example, in physics, a phenomenon may be a, 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 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. Balls made from hard-wearing materials are used in retains only the information on general ball attributes and behavior, eliminating the characteristics of that particular ball.

Origins

The first symbols A symbol is something such as an object, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention. For example, a red octagon may be a symbol for "STOP". On maps, crossed sabres may indicate a battlefield. Numerals are symbols for numbers . All language consists of symbols of abstract thinking in humans can be traced to fossils dating between 50,000 and 100,000 years ago in Africa.^[1][2]

Thought process

In philosophical terminology Philosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing fundamental questions by its critical, generally systematic approach and its reliance on rational argument. The word "philosophy" comes from the, abstraction is the thought process Thoughts are forms conceived in the mind, rather than the forms perceived through the five senses. Thought and thinking are the processes by which these concepts are perceived and manipulated. Thinking allows beings to model the world and to represent it according to their objectives, plans, ends and desires. Similar concepts and processes include wherein ideas 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. Many philosophers consider ideas to be a fundamental^[3] are distanced from objects Object is a technical term used in epistemology, a branch of philosophy concerning itself with the study of knowing. Aristotle had said, "All men by nature desire to know." René Descartes expanded this knowing into the grounds of certainty with cogito ergo sum, typically translated as "I think therefore I am." The thinker.

Abstraction uses a 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. How a battle is fought is a matter of tactics: the terms and of simplification, wherein formerly concrete details are left ambiguous, vague, or undefined; thus effective communication Communication is a process of transferring information from one entity to another. Communication processes are sign-mediated interactions between at least two agents which share a repertoire of signs and semiotic rules. Communication is commonly defined as "the imparting or interchange of thoughts, opinions, or information by speech, writing, about things in the abstract requires an intuitive Intuition is the apparent 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. For this reason, it 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 The word red comes from the Old English rēad. Further back, the word can be traced to the Proto-Germanic rauthaz and the Proto-Indo European root reudh-. In Sanskrit, the word rudhira means red or blood. In the English language, the word red is associated with the color of blood, certain flowers , and ripe fruits (e.g. apples, cherries). Fire is. Likewise, many things sit on surfaces (as in picture 1, to the right). The property of redness The word red comes from the Old English rēad. Further back, the word can be traced to the Proto-Germanic rauthaz and the Proto-Indo European root reudh-. In Sanskrit, the word rudhira means red or blood. In the English language, the word red is associated with the color of blood, certain flowers , and ripe fruits (e.g. apples, cherries). Fire is and the relation 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. It is also closely coincident with the so-called Truths of Reason of Leibniz, which are defined as those statements whose sitting-on Sitting is a rest position supported by the buttocks or thighs where the torso is more or less upright. There are several ways for humans to sit are therefore abstractions of those objects. Specifically, the conceptual diagram graph 1 identifies only three boxes, two ellipses, and four arrows (and their nine 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 In knowledge representation and object-oriented programming and design, 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 In English, the gerund is identical in form to the present participle and can behave as a verb within a clause (so that it may be modified by an adverb or have an object), but the clause as a whole (sometimes consisting of only one word, the gerund itself) acts as a noun within the larger sentence. For example: Eating this cake is easy SITTING and the nouns A noun can co-occur with an article or an attributive adjective. Verbs and adjectives can't. In the following, an asterisk in front of an example means that this example is ungrammatical agent and location express the 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. The word graph is sometimes used as a synonym for 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 Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, literary translation, artistic creation, and discovery in mathematics and physics. He is best known for his book Gödel, Escher, Bach: an Eternal Golden Braid, first published in 1979, for which he was awarded the 1980 Pulitzer Prize for's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach Gödel, Escher, Bach: An Eternal Golden Braid is a Pulitzer Prize-winning book by Douglas Hofstadter, described by the author as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll" (1979):

(1) a publication

(2) a newspaper

(3) The San Francisco Chronicle

(4) the May 18 edition of the Chronicle

(5) my copy of the May 18 edition of the Chronicle

(6) my copy of the May 18 edition of the Chronicle as it was when I first picked it up (as contrasted with my copy as it was a few days later: in my fireplace, burning)

An abstraction can thus encapsulate each of these levels of detail with no loss of generality. But perhaps a detective or philosopher/scientist/engineer might seek to learn about some thing, at progressively deeper levels of detail, to solve a crime or a puzzle.

Referents

Abstractions sometimes have ambiguous referents A reference, or a references point, is the intensional use of one thing, a point of reference or reference state, to indicate something else [citation needed]. When reference is intended, what the reference points to is called the referent; for example, "happiness Happiness is a state of mind or feeling characterized by contentment, love, satisfaction, pleasure, or 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 , is an English word used for conceptualizing subjective aspects 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 refers to a discrete life form that has properties of mind ( which make them happy. Likewise, "architecture A wider definition may comprise all design activity, from the macro-level to the micro-level (construction details and furniture). Architecture is both the process and product of planning, designing and constructing form, space and ambience that reflect functional, technical, social, and aesthetic considerations. It requires the creative" refers not only to the design of safe, functional buildings, but also to elements of creation and innovation Innovation is a change in the thought process for doing something, or the useful application of new inventions or discoveries. It may refer to an incremental emergent or radical and revolutionary changes in thinking, products, processes, or organizations. Following Schumpeter , contributors to the scholarly literature on innovation typically which aim at elegant solutions to 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 multitasking. Normally the job is managed by the project manager and supervised by the construction manager, design engineer, problems, to the use of space, and to the attempt to evoke an emotional response Emotion is a complex psychological and physiological phenomenon involving an individual's state of mind and how it interacts between that individual and their environment. In humans, emotion fundamentally involves "physiological arousal, expressive behaviors, and conscious experience". Emotion is associated with mood, temperament, 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 Marsupials are an infraclass of mammals, characterized by a distinctive pouch , in which females carry their young through early infancy. In modern times, they are well-known for being the dominant group of mammals in Australia, though there are also a number of species found in the Americas, as well as on the island of New Guinea or monotreme Monotremes are mammals that lay eggs (Prototheria) instead of giving birth to live young like marsupials (Metatheria) and placental mammals (Eutheria).

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 is the state of things as they actually exist, rather than as they may appear or may be thought to be. In its widest definition, reality includes everything that is and has being, whether or not it is observable or comprehensible or exist only as sensory experiences, like the color red The word red comes from the Old English rēad. Further back, the word can be traced to the Proto-Germanic rauthaz and the Proto-Indo European root reudh-. In Sanskrit, the word rudhira means red or blood. In the English language, the word red is associated with the color of blood, certain flowers , and ripe fruits (e.g. apples, cherries). Fire is. 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 In traditional grammar, a predicate is one of the two main parts of a sentence . For the simple sentence "John [is yellow]," John acts as the subject, and is yellow acts as the predicate, a subsequent description of the subject headed with a verb 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 In logic and philosophy, the term proposition refers to both (a) the "content" or "meaning" of a meaningful declarative sentence or (b) the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence. The meaning of a proposition includes that it has the quality or property of being either true or false, about predicates, which propositions remain to be evaluated by the investigator. In the graph 1 above, the graphical relationships like the arrows joining boxes and ellipses might denote predicates. Different levels of abstraction might be denoted by a progression of arrows joining boxes or ellipses in multiple rows, where the arrows point from one row to another, in a series of other graphs, say graph 2, etc.

Abstraction used in philosophy

Abstraction in philosophy Philosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing fundamental questions by its critical, generally systematic approach and its reliance on rational argument. The word "philosophy" comes from the is the process (or, to some, the alleged process) in concept A concept is a cognitive unit of meaning—an abstract idea or a mental symbol sometimes defined as a "unit of knowledge," built from other units which act as a concept's characteristics. A concept is typically associated with a corresponding representation in a language or symbology[citation needed] such as a single meaning of a term-formation of recognizing some set of common features in individuals As commonly used, an individual is a person or any specific object in a collection. In the 15th century and earlier, and also today within the fields of statistics and metaphysics, individual means "indivisible", typically describing any numerically singular thing, but sometimes meaning "a person." . From the seventeenth, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism In philosophy, empiricism is a theory of knowledge that asserts that knowledge arises from evidence gathered via sense experience. Empiricism is one of several competing views that predominate in the study of human knowledge, known as epistemology. Empiricism emphasizes the role of experience and evidence, especially sensory perception, in the and the 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 particulars or that individuals or particulars can be. It has also recently become popular in formal logic under 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 (λx.Q(x)), where λ is an abstraction operator. The resultant predicate (λx.Q(x)) is a monadic predicate capable of taking a term t as argument as in (λx.Q(x))(t), which. Another philosophical tool for discussion of abstraction is thought space.

Ontological status

The way that physical objects, like rocks and trees, have 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. A distinction between such categories, in making the categories or applying them, is called an ontological distinction differs from the way that properties of abstract concepts or relations have being, for example the way the concrete An 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 (sing. abstractum) and concrete objects are sometimes called concreta (sing, 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 . Redness, by contrast, is not a particular, because it is abstract and multiply-instantiated (my bicycle, this apple, and that woman's hair, individuals As commonly used, an individual is a person or any specific object in a collection. In the 15th century and earlier, and also today within the fields of statistics and metaphysics, individual means "indivisible", typically describing any numerically singular thing, but sometimes meaning "a person." . From the seventeenth pictured in picture 1 exist differs from the way the concepts illustrated in graph 1 exist. That difference accounts for the ontological Ontology (from the Greek ὄν, genitive ὄντος: of being and -λογία, -logia: science, study, theory) is the philosophical study of the nature of being, existence or reality in general, 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, 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 is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing fundamental questions by its critical, generally systematic approach and its reliance on rational argument. The word "philosophy" comes from the refer to tropes 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 (trepein), "to turn, to direct, to alter, to change"; this (instances of properties) as abstract particulars. E.g., the particular redness of a particular apple is an abstract particular. Akin to qualia and sumbebekos.

In linguistics

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 nouns 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 Trafalgar) - "England expects that every man will do his duty"

Compression

An abstraction can be seen as a process of mapping multiple different pieces of constituent data to a single piece of abstract data based on similarities in the constituent data, for example many different physical cats map to the abstraction "CAT". This conceptual scheme emphasizes the inherent equality of both constituent and abstract data, thus avoiding problems arising from the distinction between "abstract" and "concrete". In this sense the process of abstraction entails the identification of similarities between objects and the process of associating these objects with an abstraction (which is itself an object).

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

Chains of abstractions can therefore be constructed moving from neural impulses arising from sensory perception to basic abstractions such as color or shape to experiential abstractions such as a specific cat to semantic abstractions such as the "idea" of a CAT to classes of objects such as "mammals" and even categories such as "object" as opposed to "action".

For example, graph 1 above expresses the abstraction "agent sits on location".

This conceptual scheme entails no specific hierarchical taxonomy (such as the one mentioned involving cats and mammals), only a progressive exclusion of detail.

The neurology of abstraction

A recent meta-analysis suggests that the verbal system has greater engagement for abstract concepts when the perceptual system is more engaged for processing of concrete concepts. This is because abstract concepts 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.^[4]

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.^[5]

Abstraction in art

Typically, abstraction is used in the arts as a synonym for abstract art in general. Strictly speaking, it refers to art unconcerned with the literal depiction of things from the visible world^[6]—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.^[7] 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.^[8]

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 the exploration of internal numeric relationships.^[9]

Abstraction in psychology

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

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

Abstraction in computer science

Computer scientists use abstraction to understand and solve problems and communicate their solutions with the computer in some particular computer language.

Abstraction in mathematics

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

The advantages of abstraction in mathematics are:

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

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

See also

Notes

1. ^ Abstract Engravings Show Modern Behavior Emerged Earlier Than Previously Thought
2. ^ Ancient Engravings Push Back Origin of Abstract Thought
3. ^ But an idea can be symbolized. "A symbol is any device whereby we are enabled to make an abstraction." -- p.xi and chapter 20 of Suzanne K. Langer (1953), Feeling and Form: a theory of art developed from Philosophy in a New Key: New York: Charles Scribner's Sons. 431 pages, index.
4. ^ Jing Wang, Julie A. Conder, David N. Blitzer, and Svetlana V. Shinkareva "Neural Representation of Abstract and Concrete Concepts: A Meta-Analysis of Neuroimaging Studies" Human Brain Mapping (2010). http://dx.doi.org/10.1002/hbm.20950
5. ^ James W. Lewis "Cortical Networks Related to Human Use of Tools" 12 (3): 211-231 The Neuroscientist (June 1, 2006).
6. ^ Encyclopaedia Britannica
7. ^ Catherine de Zegher and Hendel Teicher (eds.), 3 X Abstraction. NY/New Haven: The Drawing Center/Yale University Press. 2005. ISBN 0-300-10826-5
8. ^ National Gallery of Art: Abstraction.
9. ^ Washington State University: Glossary of Abstraction.

Bibliography

• Eugene Raskin, Architecturally Speaking, 2nd edition, a Delta book, Dell (1966), trade paperback, 129 pages
• The American Heritage Dictionary of the English Language, 3rd edition, Houghton Mifflin (1992), hardcover, 2140 pages, ISBN 0-395-44895-6
• Jung, C.G. [1921] (1971). Psychological Types, Collected Works, Volume 6, Princeton, NJ: Princeton University Press. ISBN 0-691-01813-8.

External links

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

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