Generalization
Encyclopedia
A generalization of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic
and human reasoning. Generalizations posit the existence of a domain or set
of elements, as well as one or more common characteristics shared by those elements. As such, it is the essential basis of all valid deductive inferences. The process of verification
is necessary to determine whether a generalization holds true for any given situation.
The concept of generalization has broad application in many related disciplines, sometimes having a specialized context-specific meaning.
Of any two related concepts, such as A and B, A is considered a "generalization" of concept B if and only if:
For instance, animal
is a generalization of bird
because every bird is an animal, and there are animals which are not birds (dog
s, for
instance). (See also: specialization).
and hyponym. A hypernym as a generic stands for a class or group of equally-ranked items such as tree does for peach and oak; or ship for cruiser and steamer. Whereas a hyponym is one of the items included in the generic, such as peach and oak are included in tree, and cruiser and steamer in ship, "brother" and "sister" in "family". A hypernym is superordinate to a hyponym, and a hyponym is subordinate to a hypernym.
is a generalization of a mammal
, a bird
, etc.
as an art of creating maps for different scale and purpose. Cartographic generalization
is the process of selecting and representing information of a map in a way that adapts to the scale of the display medium of the map. In this way, every map has, to some extent, been generalized to match the criteria of display. This includes small-scale maps, which cannot convey every detail of the real world. Cartographers must decide and then adjust the content within their maps to create a suitable and useful map that conveys geospatial
information within their representation of the world.
Generalization is meant to be context-specific. That is to say, correctly generalized maps are those that emphasize the most important map elements while still representing the world in the most faithful and recognizable way. The level of detail and importance in what is remaining on the map must outweigh the insignificance of items that were generalized, as to preserve the distinguishing characteristics of what makes the map useful and important.
is a generalization of a 3-sided triangle
, a 4-sided quadrilateral
, and so on to n
sides. A hypercube
is a generalization of a 2-dimensional square, a 3-dimensional cube
, and so on to n dimensions.
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
and human reasoning. Generalizations posit the existence of a domain or set
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
of elements, as well as one or more common characteristics shared by those elements. As such, it is the essential basis of all valid deductive inferences. The process of verification
Falsifiability
Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment...
is necessary to determine whether a generalization holds true for any given situation.
The concept of generalization has broad application in many related disciplines, sometimes having a specialized context-specific meaning.
Of any two related concepts, such as A and B, A is considered a "generalization" of concept B if and only if:
- every instance of concept B is also an instance of concept A; and
- there are instances of concept A which are not instances of concept B.
For instance, animal
Animal
Animals are a major group of multicellular, eukaryotic organisms of the kingdom Animalia or Metazoa. Their body plan eventually becomes fixed as they develop, although some undergo a process of metamorphosis later on in their life. Most animals are motile, meaning they can move spontaneously and...
is a generalization of bird
Bird
Birds are feathered, winged, bipedal, endothermic , egg-laying, vertebrate animals. Around 10,000 living species and 188 families makes them the most speciose class of tetrapod vertebrates. They inhabit ecosystems across the globe, from the Arctic to the Antarctic. Extant birds range in size from...
because every bird is an animal, and there are animals which are not birds (dog
Dog
The domestic dog is a domesticated form of the gray wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties. The dog may have been the first animal to be domesticated, and has been the most widely kept working, hunting, and companion animal in...
s, for
instance). (See also: specialization).
Hypernym and hyponym
This kind of generalization versus specialization (or particularization) is reflected in the mirror of the contrasting words of the three word pair hypernymHypernym
In linguistics, a hyponym is a word or phrase whose semantic field is included within that of another word, its hypernym . In simpler terms, a hyponym shares a type-of relationship with its hypernym...
and hyponym. A hypernym as a generic stands for a class or group of equally-ranked items such as tree does for peach and oak; or ship for cruiser and steamer. Whereas a hyponym is one of the items included in the generic, such as peach and oak are included in tree, and cruiser and steamer in ship, "brother" and "sister" in "family". A hypernym is superordinate to a hyponym, and a hyponym is subordinate to a hypernym.
Biological generalization
An animalAnimal
Animals are a major group of multicellular, eukaryotic organisms of the kingdom Animalia or Metazoa. Their body plan eventually becomes fixed as they develop, although some undergo a process of metamorphosis later on in their life. Most animals are motile, meaning they can move spontaneously and...
is a generalization of a mammal
Mammal
Mammals are members of a class of air-breathing vertebrate animals characterised by the possession of endothermy, hair, three middle ear bones, and mammary glands functional in mothers with young...
, a bird
Bird
Birds are feathered, winged, bipedal, endothermic , egg-laying, vertebrate animals. Around 10,000 living species and 188 families makes them the most speciose class of tetrapod vertebrates. They inhabit ecosystems across the globe, from the Arctic to the Antarctic. Extant birds range in size from...
, etc.
Cartographic generalization of geo-spatial data
Generalization has a long history in cartographyCartography
Cartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...
as an art of creating maps for different scale and purpose. Cartographic generalization
Cartographic generalization
Cartographic generalization is the method whereby information is selected and represented on a map in a way that adapts to the scale of the display medium of the map, not necessarily preserving all intricate geographical or other cartographic details...
is the process of selecting and representing information of a map in a way that adapts to the scale of the display medium of the map. In this way, every map has, to some extent, been generalized to match the criteria of display. This includes small-scale maps, which cannot convey every detail of the real world. Cartographers must decide and then adjust the content within their maps to create a suitable and useful map that conveys geospatial
Geospatial
Geospatial analysis is an approach to applying statistical analysis and other informational techniques to geographically based data. Such analysis employs spatial software and analytical methods with terrestrial or geographic datasets, including geographic information systems and...
information within their representation of the world.
Generalization is meant to be context-specific. That is to say, correctly generalized maps are those that emphasize the most important map elements while still representing the world in the most faithful and recognizable way. The level of detail and importance in what is remaining on the map must outweigh the insignificance of items that were generalized, as to preserve the distinguishing characteristics of what makes the map useful and important.
Geometric generalizations
A polygonPolygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
is a generalization of a 3-sided triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
, a 4-sided quadrilateral
Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four sides and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on...
, and so on to n
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
sides. A hypercube
Hypercube
In geometry, a hypercube is an n-dimensional analogue of a square and a cube . It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.An...
is a generalization of a 2-dimensional square, a 3-dimensional cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...
, and so on to n dimensions.
See also
- AbstractionAbstractionAbstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....
- Ceteris paribusCeteris paribusor is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...
- Generic (disambiguation)
- Generic antecedentGeneric antecedentGeneric antecedents are representatives of classes, referred to in ordinary language by another word , in a situation in which gender is typically unknown or irrelevant. These mostly arise in generalizations and are particularly common in abstract, theoretical or strategic discourse...
- inheritance (object-oriented programming)Inheritance (object-oriented programming)In object-oriented programming , inheritance is a way to reuse code of existing objects, establish a subtype from an existing object, or both, depending upon programming language support...
, - Faulty generalizationFaulty generalizationA fallacy of defective induction reaches a conclusion from weak premises. Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions yet only weakly buttress the conclusions. A faulty generalization is thus produced...
- Hasty generalizationHasty generalizationHasty generalization is a logical fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence essentially making a hasty conclusion without considering all of the variables...
- Mutatis mutandisMutatis mutandisMutatis mutandis is a Latin phrase meaning "by changing those things which need to be changed" or more simply "the necessary changes having been made"....
- -onym-onymThe suffix onym, in English and other languages, means "word, name," and words ending in onym refer to a specified kind of name or word, most of which are classical compounds. For example, an acronym is a word formed from the initial letter or letters of each of the successive parts or major parts...
- Class diagram
- Ramer–Douglas–Peucker algorithm
- Specialization (logic), the opposite process
- Generalization (logic)Generalization (logic)In mathematical logic, generalization is an inference rule of predicate calculus. It states that if \vdash P has been derived, then \vdash \forall x \, P can be derived....
- Ethical GeneralizationCategorical imperativeThe Categorical Imperative is the central philosophical concept in the moral philosophy of Immanuel Kant, as well as modern deontological ethics...