Abstract and concrete are classifications that denote whether the object that a term describes has physical referents. Abstract objects have no physical referents, whereas concrete objects do. They are most commonly used in philosophy and semantics. Abstract objects are sometimes called abstracta (sing. abstractum) and concrete objects are sometimes called concreta (sing. concretum). An abstract object is an object that does not exist at any particular time or place, but rather exists as a type of thing—i.e., an idea, or abstraction.^{[1]} The term abstract object is said to have been coined by Willard Van Orman Quine.^{[2]} The study of abstract objects is called abstract object theory.
The type–token distinction identifies physical objects that are tokens of a particular type of thing.^{[3]} The "type" of which it is a part is in itself an abstract object. The abstract-concrete distinction is often introduced and initially understood in terms of paradigmatic examples of objects of each kind:
Abstract | Concrete |
Tennis | A tennis match |
Redness | Red light reflected off of an apple and hitting one's eyes |
Five | Five cars |
Justice | A just action |
Humanity (the property of being human) | Human population (the set of all humans) |
Abstract objects have often garnered the interest of philosophers because they raise problems for popular theories. In ontology, abstract objects are considered problematic for physicalism and some forms of naturalism. Historically, the most important ontological dispute about abstract objects has been the problem of universals. In epistemology, abstract objects are considered problematic for empiricism. If abstracta lack causal powers or spatial location, how do we know about them? It is hard to say how they can affect our sensory experiences, and yet we seem to agree on a wide range of claims about them.
Some, such as Edward Zalta and arguably, Plato in his Theory of Forms, have held that abstract objects constitute the defining subject matter of metaphysics or philosophical inquiry more broadly. To the extent that philosophy is independent of empirical research, and to the extent that empirical questions do not inform questions about abstracta, philosophy would seem especially suited to answering these latter questions.
In modern philosophy, the distinction between abstract and concrete was explored by Immanuel Kant^{[4]} and G. W. F. Hegel.^{[5]}
Gottlob Frege said that abstract objects, such as numbers, were members of a third realm,^{[6]}^{[7]} different from the external world or from internal consciousness.^{[8]}
Another popular proposal for drawing the abstract-concrete distinction contends that an object is abstract if it lacks any causal powers. A causal power has the ability to affect something causally. Thus, the empty set is abstract because it cannot act on other objects. One problem for this view is that it is not clear exactly what it is to have a causal power. For a more detailed exploration of the abstract-concrete distinction, follow the link below to the Stanford Encyclopedia article.^{[9]}
Recently, there has been some philosophical interest in the development of a third category of objects known as the quasi-abstract. Quasi-abstract objects have drawn particular attention in the area of social ontology and documentality. Some argue that the over-adherence to the platonist duality of the concrete and the abstract has led to a large category of social objects having been overlooked or rejected as nonexisting because they exhibit characteristics that the traditional duality between concrete and abstract regards as incompatible.^{[10]} Specially, the ability to have temporal location, but not spatial location, and have causal agency (if only by acting through representatives).^{[11]} These characteristics are exhibited by a number of social objects, including states of the international legal system.^{[12]}
Jean Piaget uses the terms "concrete" and "formal" to describe two different types of learning. Concrete thinking involves facts and descriptions about everyday, tangible objects, while abstract (formal operational) thinking involves a mental process.
Concrete idea | Abstract idea |
---|---|
Dense things sink. | It will sink if its density is greater than the density of the fluid. |
You breathe in oxygen and breathe out carbon dioxide. | Gas exchange takes place between the air in the alveoli and the blood. |
Plants get water through their roots. | Water diffuses through the cell membrane of the root hair cells. |
Abstract particulars are metaphysical entities which are both abstract objects and particulars.
AbstractionAbstraction in its main sense is a conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods.
"An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts, and connects any related concepts as a group, field, or category.Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only the aspects which are relevant for a particular subjectively valued purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, excluding, but not eliminating, the other phenomenal and cognitive characteristics of that particular ball. In a type–token distinction, a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').
Abstraction in its secondary use is a material process, discussed in the themes below.
Category of relationsIn mathematics, the category Rel has the class of sets as objects and binary relations as morphisms.
A morphism (or arrow) R : A → B in this category is a relation between the sets A and B, so R ⊆ A × B.
The composition of two relations R: A → B and S: B → C is given by:
(a, c) ∈ S o R if (and only if) for some b ∈ B, (a, b) ∈ R and (b, c) ∈ S.
Category of topological spacesIn mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps or some other variant; for example, objects are often assumed to be compactly generated. This is a category because the composition of two continuous maps is again continuous, and the identity function is continuous. The study of Top and of properties of topological spaces using the techniques of category theory is known as categorical topology.
N.B. Some authors use the name Top for the category with topological manifolds as objects and continuous maps as morphisms.
Category theoryCategory theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms). A category has two basic properties: the ability to compose the arrows associatively, and the existence of an identity arrow for each object. The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups. Informally, category theory is a general theory of functions.
Several terms used in category theory, including the term "morphism", are used differently from their uses in the rest of mathematics. In category theory, morphisms obey conditions specific to category theory itself.
Samuel Eilenberg and Saunders Mac Lane introduced the concepts of categories, functors, and natural transformations in 1942–45 in their study of algebraic topology, with the goal of understanding the processes that preserve mathematical structure.
Category theory has practical applications in programming language theory, for example the usage of monads in functional programming. It may also be used as an axiomatic foundation for mathematics, as an alternative to set theory and other proposed foundations.
Class (computer programming)In object-oriented programming, a class is an extensible program-code-template for creating objects, providing initial values for state (member variables) and implementations of behavior (member functions or methods). In many languages, the class name is used as the name for the class (the template itself), the name for the default constructor of the class (a subroutine that creates objects), and as the type of objects generated by instantiating the class; these distinct concepts are easily conflated.When an object is created by a constructor of the class, the resulting object is called an instance of the class, and the member variables specific to the object are called instance variables, to contrast with the class variables shared across the class.
In some languages, classes are only a compile-time feature (new classes cannot be declared at runtime), while in other languages classes are first-class citizens, and are generally themselves objects (typically of type Class or similar). In these languages, a class that creates classes is called a metaclass.
Commutative diagramIn mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. Commutative diagrams play the role in category theory that equations play in algebra (see Barr–Wells, Section 1.7).
Complete categoryIn mathematics, a complete category is a category in which all small limits exist. That is, a category C is complete if every diagram F : J → C (where J is small) has a limit in C. Dually, a cocomplete category is one in which all small colimits exist. A bicomplete category is a category which is both complete and cocomplete.
The existence of all limits (even when J is a proper class) is too strong to be practically relevant. Any category with this property is necessarily a thin category: for any two objects there can be at most one morphism from one object to the other.
A weaker form of completeness is that of finite completeness. A category is finitely complete if all finite limits exists (i.e. limits of diagrams indexed by a finite category J). Dually, a category is finitely cocomplete if all finite colimits exist.
Evald IlyenkovEvald Vassilievich Ilyenkov (Russian: Э́вальд Васи́льевич Илье́нков; 18 February 1924 – 21 March 1979) was a Marxist author and Soviet philosopher.
Grammatical FrameworkGrammatical Framework (GF) is a programming language for writing grammars of natural languages. GF is capable of parsing and generating texts in several languages simultaneously while working from a language-independent representation of meaning. Grammars written in GF can be compiled into different formats including JavaScript and Java and can be reused as software components. A companion to GF is the GF Resource Grammar Library, a reusable library for dealing with the morphology and syntax of a growing number of natural languages.
Both GF itself and the GF Resource Grammar Library are open-source. Typologically, GF is a functional programming language. Mathematically, it is a type-theoretic formal system (a logical framework to be precise) based on Martin-Löf's intuitionistic type theory, with additional judgments tailored specifically to the domain of linguistics.
Hiroshi SugitoHiroshi Sugito (杉戸 洋, Sugito Hiroshi, born 1970) is a contemporary Japanese painter who has been recognized as a part of the Tokyo-Pop movement. He specializes in Nihonga painting (literally "Japanese painting"). However, instead of the traditional scenic imagery of Nihonga, his paintings focus on abstract and recognizable elements. Oftentimes his artwork consists of dreams, altered realities and childlike fantasies. They consist of both abstract and concrete elements and are also influenced by both Eastern and Western paintings.
Nicolete GrayNicolete Gray (sometimes Nicolette Gray) (20 July 1911–8 June 1997) was an English art scholar and exponent and scholar of calligraphy. She was the youngest daughter of the poet, dramatist and art scholar Laurence Binyon and his wife, writer, editor and translator Cicely Margaret Pryor Powell. In 1933, she married Basil Gray (1904–1989), with whom she had five children, two sons and three daughters.She attended St Paul's School where she won a scholarship to Lady Margaret Hall at Oxford to read History in 1929.In 1936 she curated the touring exhibition Abstract and Concrete, the first showing of abstract art, and of the work of Mondrian, in England.Her books include Nineteenth century ornamented types and title pages (Faber & Faber 1938; 2nd edition, as Nineteenth century ornamented typefaces, 1976) and A History of Lettering (Phaidon, 1976).
She died in London on 8 June 1997.
Preordered classIn mathematics, a preordered class is a class equipped with a preorder.
Pulation squareIn category theory, a branch of mathematics, a pulation square (also called a Doolittle diagram) is a diagram that is simultaneously a pullback square and a pushout square. It is a self-dual concept.
Skeleton (category theory)In mathematics, a skeleton of a category is a subcategory which, roughly speaking, does not contain any extraneous isomorphisms. In a certain sense, the skeleton of a category is the "smallest" equivalent category which captures all "categorical properties". In fact, two categories are equivalent if and only if they have isomorphic skeletons. A category is called skeletal if isomorphic objects are necessarily identical.
Stone functorIn mathematics, the Stone functor is a functor S: Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms. It assigns to each topological space X the Boolean algebra S(X) of its clopen subsets, and to each morphism fop: X → Y in Topop (i.e., a continuous map f: Y → X) the homomorphism S(f): S(X) → S(Y) given by S(f)(Z) = f−1[Z].
Three FormsThree Forms (BH 72) is an abstract sculpture by Barbara Hepworth, completed in 1935.
The sculpture was one of the first works completed by Hepworth after the birth of her triplets with Ben Nicholson in October 1934. It marks a point of departure in her style: her earlier abstract works are based on the human form, but Three Forms is more purely abstract, reduced to simple geometric shapes with little colour. Her subsequent work continued in a more formal, abstract and non-representational vein. Hepworth wrote in 1952 that she became "absorbed in the relationships in space, in size and texture and weight, as well as the tensions between forms".
The work consists of three rounded elements positioned on a flat rectangular base, all in polished Seravezza marble (largely white, but small brown marks, grey flecks, and pale grey graining are visible on close inspection). Each element has a precise shape and size, and they are arranged in a similarly precise triangular relationship. The original base has been replaced, but the spatial arrangement of each element remains the same, with a spherical element placed at a distance from two larger and elongated oval forms, the smaller of which lies flat and the larger of which rests on its long edge, both aligned with the longer edge of the rectangular base. The 12 centimetres (4.7 in) diameter of the sphere reflects one of the dimensions of both larger elements, each of which also shares a dimension of 18 centimetres (7.1 in) (1.5 times as large). The medium spheroid measures 8.5 × 18 × 12 centimetres (3.3 × 7.1 × 4.7 in) and the larger one is 18 × 25.5 × 12 centimetres (7.1 × 10.0 × 4.7 in). Each object was shaped by hand and so is slightly imperfect. The choice of three forms - two alike and one different - may be connected with the birth of Hepworth's triplets - two girls and one boy.
The abstract sculpture in a pure white recalls the contemporary architecture of Le Corbusier, and may also have been inspired by Hepworth's visits to the studios of Brancusi and Arp on a visit to France with Nicholson in 1932. Hepworth later accepted criticism from physicist John Desmond Bernal that the elements are all positively curved, and suggested that the work could have been improved by the sphere being replaced by a cylinder.
The whole work measures 21 × 53.2 × 34.3 centimetres (8.3 × 20.9 × 13.5 in) and weighs 23 kilograms (51 lb). It was exhibited at the "7&5" exhibition in 1935 and the "Abstract and Concrete Art" exhibition in 1936. It was bought from Hepworth by Mr and Mrs J.R. Marcus Brumwell in late 1935, who donated it to the Tate Gallery in 1964. It is now displayed at Tate Britain.
Visualization (graphics)Visualization or visualisation (see spelling differences) is any technique for creating images, diagrams, or animations to communicate a message. Visualization through visual imagery has been an effective way to communicate both abstract and concrete ideas since the dawn of humanity. Examples from history include cave paintings, Egyptian hieroglyphs, Greek geometry, and Leonardo da Vinci's revolutionary methods of technical drawing for engineering and scientific purposes.
Visualization today has ever-expanding applications in science, education, engineering (e.g., product visualization), interactive multimedia, medicine, etc. Typical of a visualization application is the field of computer graphics. The invention of computer graphics may be the most important development in visualization since the invention of central perspective in the Renaissance period. The development of animation also helped advance visualization.
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