Abstraction is the process of reducing the information content of a concept, typically in order to retain only information which is relevant for a particular purpose. For example, abstracting a leather soccer ball to a ball retains only the information on general ball attributes and behaviour. Similarly, abstracting happiness to an emotional state reduces the amount of information conveyed about the emotional state. This article is in need of attention. ... A concept is an abstract idea or a mental symbol, typically associated with a corresponding representation in language or symbology, that denotes all of the objects in a given category or class of entities, interactions, phenomena, or relationships between them. ... Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ... Purpose is deliberately thought-through goal-directedness. ... computed tomography of a soccer ball (Video) A ball is a guys testicles. ... An attribute is the following: Generally, an attribute is an abstraction characteristic of an entity In database management, an attribute is a property inherent in an entity or associated with that entity for database purposes. ... Behavior or behaviour refers to the actions or reactions of an object or organism, usually in relation to the environment. ... People show happiness in many ways. ... It has been suggested that Feeling be merged into this article or section. ...

Complexity reduction

Abstraction typically results in complexity reduction leading to a simpler conceptualization of a domain in order to facilitate processing or understanding of many specific scenarios in a generic way. A concept is an abstract, universal psychical entity that serves to designate a category or class of entities, events or relations. ... The domain of discourse, sometimes called the universe of discourse, is an analytic tool used in deductive logic, especially predicate logic. ... A scenario (from the Italian, that which is pinned to the scenery) is a brief description of an event. ... Look up Generic in Wiktionary, the free dictionary. ...

Thought process

In philosophical terminology, abstraction is the thought process wherein ideas are distanced from objects. To meet Wikipedias quality standards, this article may require cleanup. ... Thought or thinking is a mental process which allows beings to model the world, and so to deal with it effectively according to their goals, plans, ends and desires. ... An idea (Greek: ιδέα) is a specific thought which arises in the mind. ... In philosophy, an object is a thing, an entity, or a being. ...

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. A strategy is a long term plan of action designed to achieve a particular goal, as differentiated from tactics or immediate actions with resources at hand. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Intuition has many meanings across many cultures, including: quick and ready insight seemingly independent of previous experiences and empirical knowledge immediate apprehension or cognition knowledge or conviction gained by intuition the power or faculty of attaining to direct knowledge or cognition without evident rational thought and inference. ...

Cat on Mat (picture 1)

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 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. Image File history File links JerryFelix. ... Image File history File links JerryFelix. ... Red is any of a number of similar colors at the lowest frequencies of light discernible by the human eye. ... Red is any of a number of similar colors at the lowest frequencies of light discernible by the human eye. ... Look up Relation in Wiktionary, the free dictionary In mathematics, a relation is a generalization of arithmetic relations, such as = and <, which occur in statements, such as 5 < 6 or 2 + 2 = 4. See relation (mathematics), binary relation (of set theory and logic) and relational algebra. ... This article is about sitting in its general sense. ...

Graph 1 details some explicit relationships between the objects of the diagram. For example the arrow between the agent and CAT:Elsie depicts an example of an is-a relationship, as does the arrow between the location and the MAT. The arrows between the gerund SITTING and the nouns agent and location express the diagram's basic relationship; "agent is SITTING on location"; Elsie is an instance of CAT. In computer science, the term inheritance may be applied to a variety of situations in which certain characteristics are passed on from one context to another. ... In linguistics, a gerund is a kind of verbal noun that exists in some languages. ... A noun, or noun substantive, is a part of speech (a word or phrase) which can co-occur with (in)definite articles and attributive adjectives, and function as the head of a noun phrase. ... Sample flowchart diagram A diagram is a simplified and structured visual representation of concepts, ideas, constructions, relations, statistical data, anatomy etc used in all aspects of human activities to visualize and clarify the topic. ...

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

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 R. Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979): Cat-on-Mat, a conceptual graphs classic example File links The following pages link to this file: Abstraction Conceptual Graphs Talk:Tractatus Logico-Philosophicus (5. ... Cat-on-Mat, a conceptual graphs classic example File links The following pages link to this file: Abstraction Conceptual Graphs Talk:Tractatus Logico-Philosophicus (5. ... John F. Sowas Conceptual Graphs allow the graphical statement of logic propositions, or predicates. ... Douglas Richard Hofstadter (born February 15, 1945) is an American academic. ... GEB cover Gödel, Escher, Bach: an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, published in 1979 by Basic Books. ...

(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 might seek to learn about some thing, at progressively deeper levels of detail, to solve a crime or a puzzle.

Referents

Abstractions sometimes have ambiguous referents; for example, "happiness" (when used as an abstraction) can refer to as many things as there are people and events or states of being which make them happy. Likewise, "architecture" refers not only to the design of safe, functional buildings, but also to elements of creation and innovation which aim at elegant solutions to construction problems, to the use of space, and at its best, to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building. In general, a reference is something that refers or points to something else, or acts as a connection or a link between two things. ... People show happiness in many ways. ... In ontology, a being is anything that can be said to be, either transcendantly or immanently. ... The Parthenon on top of the Acropolis, Athens, Greece Architecture (from Latin, architectura and ultimately from Greek, αρχιτεκτων, a master builder, from αρχι- chief, leader and τεκτων, builder, carpenter) is the art and science of designing buildings and structures. ... Cranes are essential in large construction projects, such as this skyscraper In project architecture and civil engineering, construction is the building or assembly of any infrastructure. ... Emotion, in its most general definition, is an intense neural impulse-produced mental state that arises subjectively rather than through conscious effort and evokes either a positive or negative psychological response to move an organism to action. ...

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. Orders Didelphimorphia Paucituberculata Microbiotheria Dasyuromorphia Peramelemorphia Notoryctemorphia Diprotodontia Marsupials are mammals in which the female typically has a pouch (called the marsupium, from which the name Marsupial derives) in which it rears its young through early infancy. ...

Physicality

A physical object (a possible referrent of a concept or word) is considered concrete (not abstract) if it is a particular individual that occupies a particular place and time.

Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experience, 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. Reality in everyday usage means everything that exists. The term reality, in its widest sense, includes everything that is, whether it is observable, accessible or understandable by science, philosophy, or any other system of analysis. ... Red is any of a number of similar colors at the lowest frequencies of light discernible by the human eye. ...

An approach to resolving such difficulty is to use predicates as a general term for whether things are variously real, abstract, concrete, or of a particular property (e.g. good). Questions about the properties of things are then propositions about predicates, which propositions remain to be evaluated by the investigator. In the graph 1 above, the graphical relationships like the arrows joining boxes and ellipses might denote predicates. Different levels of abstraction might be denoted by a progression of arrows joining boxes or ellipses in multiple rows, where the arrows point from one row to another, in a series of other graphs, say graph 2, etc. In mathematics, a predicate is a relation. ... In modern philosophy, logic and linguistics, a proposition is what is asserted as the result of uttering a declarative sentence. ...

Abstraction used in philosophy

Abstraction in philosophy is the process (or, to some, the alleged process) in concept-formation of recognizing some set of common features in individuals, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals. It has also recently become popular in formal logic under predicate abstraction. Another philosophical tool for discussion of abstraction is Thought space. To meet Wikipedias quality standards, this article may require cleanup. ... In common speech, the word individual most often refers to a person, or, by analogy, to any specific object in a group of things. ... In philosophy generally, empiricism is a theory of knowledge emphasizing the role of experience. ... The problem of universals is a phrase used to refer to a nest of intertwined problems about universals within the philosophy of language, cognitive psychology, epistemology, and ontology. ... In logic, predicate abstraction is the result of creating a predicate from an open sentence. ...

Ontological status

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. In metaphysics (in particular, ontology), the different kinds or ways of being are called categories of being or simply According to the Aristotelian tradition, a being is anything that can be said to be in the various senses of this word. ... This article is about the philosophical term . ... In metaphysics, particulars are, one might say, identified by what they are not: they are not abstract, not multiply instantiated. ... In common speech, the word individual most often refers to a person, or, by analogy, to any specific object in a group of things. ... In philosophy, ontology (from the Greek , genitive : of being (part. ...

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. To meet Wikipedias quality standards, this article may require cleanup. ... A trope is a rhetorical figure of speech that consists of a play on words, i. ... Red is any of a number of similar colors at the lowest frequencies of light discernible by the human eye. ... Binomial name Malus domestica Borkh. ...

In linguistics

Reification, also called hypostatization, might be considered a logical 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: Reification, also called hypostatization, is treating a concept, an abstraction, as if it were a real, concrete thing. ... In philosophy, the term logical fallacy properly refers to a formal fallacy: a flaw in the structure of a deductive argument which renders the argument invalid. ... Linguistics is the scientific study of human language. ... In rhetoric, metonymy (from Greek beyond/changed and , a suffix used to name figures of speech from name (OED)) (IPA //) is the substitution of one word for another with which it is associated. ... A noun, or noun substantive, is a part of speech (a word or phrase) which can co-occur with (in)definite articles and attributive adjectives, and function as the head of a noun phrase. ...

1805: Horatio Nelson (Battle of Trafalgar) - "England expects that every man will do his duty"

Lord Nelson Horatio Nelson, 1st Viscount Nelson (September 29, 1758 &#8211; October 21, 1805) was a British admiral who won fame as a leading naval commander. ... Combatants United Kingdom of Great Britain and Ireland First French Empire, Spain Commanders The Viscount Nelson † Pierre Charles Silvestre de Villeneuve Strength 27 ships of the line France: 18 ships of the line Spain: 15 ships of the line Casualties 449 killed 1,214 wounded Total: 1,673 4,480... The Battle of Trafalgar by J. M. W. Turner (oil on canvas, 1822–1824) shows the last three letters of this famous signal flying from the Victory. ...

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). A constituent is someone who can or does appoint or elect (and often by implication can also remove or recall) another as her agent or representative. ... This article is about the philosophical term . ...

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". PSYCHOLOGY In psychology and the cognitive sciences, perception is the process of acquiring, interpreting, selecting, and organizing sensory information. ... In geometry, two sets have the same shape if one can be transformed to another by a combination of translations, rotations and uniform scalings. ... In general, semantics (from the Greek semantikos, or significant meaning, derived from sema, sign) is the study of meaning, in some sense of that term. ...

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 compression of detail. A hierarchy (in Greek hieros = sacred, arkho = rule) is a system of ranking and organizing things. ... Look up taxonomy in Wiktionary, the free dictionary. ... Look up compressor, compression in Wiktionary, the free dictionary. ...

The neurology of abstraction

Some research into the human brain suggests that the left and right hemispheres differ in their handling of abstraction. One side handles collections of examples (eg: examples of a tree) whereas the other handles the concept itself. ^{[citation needed]} In animals, the brain, or encephalon (Greek for in the head), is the control center of the central nervous system. ...

Abstraction in art

Most typically abstraction is used in the arts as a synonym of abstract art in general. It can, however, refer to any object or image which has been distilled from the real world, or indeed another work. In the truest sense, abstract art is not really abstract. Look up Synonym in Wiktionary, the free dictionary. ... Black square by Kazimir Malevich Abstract art is now generally understood to mean art that does not depict objects in the natural world, but instead uses shapes and colors in a non-representational or subjective way. ...

The artist Robert Stark wrote:

"Ten years after abandoning formal landscape painting to explore the more direct act of freely applying paint to a surface without a representational motive, I have developed a new vocabulary; light and dark, warm and cool, making marks, brush-strokes like heart-rhythms. Every day is a test of each painting's ability to stand on its own. Each painting is subject to being changed, to being reworked or scraped and repainted as long as it remains in the studio. Where I often used to spend weeks on a painting, attempting to 'make a picture,' now my concerns are more about the energy of light, the mass of space, the emotions of shadows."

"I want the painting to meet the viewer somewhere in the middle, where the viewer brings his own experiences to bear in understanding and feeling what he is seeing. I want my paintings to achieve the complexity and density of poetry or of a symphony, to build suggestive layers, implicit felt meaning, not merely to be entertaining bit of color to seduce the eye. I want my paintings to be accessible to children as well as adults, and to be so simply and directly painted that it shows the act of painting for the joy and excitement of it."

See also

Black square by Kazimir Malevich Abstract art is now generally understood to mean art that does not depict objects in the natural world, but instead uses shapes and colors in a non-representational or subjective way. ... In computer science, abstraction is a mechanism and practice to reduce and factor out details so that one can focus on few concepts at a time. ... 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 generalising it so that it has wider applications. ... An abstract structure is a set of laws, properties and relationships that is defined independently of any physical objects. ... An abstract is an abbreviated summary of a research article, 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 papers purpose. ... In 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. ... Charles Sanders Peirce (pronounced purse), (September 10, 1839 – April 19, 1914) was an American polymath, born in Cambridge, Massachusetts. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, Bad Kleinen) was a German mathematician who evolved into a logician and philosopher. ... Hypostatic abstraction, also known as hypostasis or subjectal abstraction, is the process or the product of a formal operation that takes an element of information, such as might be expressed in a proposition of the form X is Y, and conceives its information to consist in the relation between a... An abstract model (or conceptual model) is a theoretical construct that represents physical, biological or social processes, with a set of variables and a set of logical and quantitative relationships between them. ... In philosophy, ontology (from the Greek , genitive : of being (part. ... Prescisive abstraction or prescision, variously spelled as precisive abstraction or prescission, is a formal operation that marks, selects, or singles out one feature of a concrete experience to the disregard of others. ...

External links

Look up abstraction in Wiktionary, the free dictionary.

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

Wikipedia does not have an article with this exact name. ... Wiktionary is a Wikimedia Foundation project intended to be a free wiki dictionary (hence: Wiktionary) (including thesaurus and lexicon) in every language. ...

References

• 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