Generalize

{{Short description|Form of abstraction}} {{Other uses}} {{Use dmy dates|date=December 2020}} {{Wiktionary|generalization}}

A '''generalization''' is a form of [[abstraction]] whereby common properties of specific instances are formulated as general concepts or claims.{{Cite web|url=https://www.dictionary.com/browse/generalization|title=Definition of generalization {{!}} Dictionary.com|website=www.dictionary.com|language=en|access-date=30 November 2019}} Generalizations posit the existence of a domain or [[set theory|set]] of elements, as well as one or more common characteristics shared by those elements (thus creating a [[conceptual model]]). As such, they are the essential basis of all valid [[deductive]] inferences (particularly in [[logic]], mathematics and science), where the process of [[falsifiability|verification]] is necessary to determine whether a generalization holds true for any given situation.

Generalization can also be used to refer to the process of identifying the parts of a whole, as belonging to the whole. The parts, which might be unrelated when left on their own, may be brought together as a group, hence belonging to the whole by establishing a common relation between them.

However, the parts cannot be generalized into a whole—until a common relation is established among ''all'' parts. This does not mean that the parts are unrelated, only that no common relation has been established yet for the generalization.

The concept of generalization has broad application in many connected disciplines, and might sometimes have a more specific meaning in a specialized context (e.g. generalization in psychology, [[Generalization (learning)|generalization in learning]]).

In general, given two related concepts ''A'' and ''B,'' ''A'' is a "generalization" of ''B'' (equiv., ''B'' is a [[special case]] of ''A'') if and only if both of the following hold:

• Every instance of concept ''B'' is also an instance of concept ''A.''
• There are instances of concept ''A'' which are not instances of concept ''B''.

For example, the concept ''animal'' is a generalization of the concept ''bird'', since every bird is an animal, but not all animals are birds (dogs, for instance). For more, see [[Specialisation (biology)]].

==Hypernym and hyponym== {{See also|Semantic change}} The connection of ''generalization'' to ''specialization'' (or ''[[particularization]]'') is reflected in the contrasting words [[hypernym]] and [[hyponym]]. A hypernym as a [[generic antecedents|generic]] stands for a class or group of equally ranked items, such as the term ''tree'' which stands for equally ranked items such as ''peach'' and ''oak'', and the term ''ship'' which stands for equally ranked items such as ''cruiser'' and ''steamer''. In contrast, a hyponym is one of the items included in the generic, such as ''peach'' and ''oak'' which are included in ''tree'', and ''cruiser'' and ''steamer'' which are included in ''ship''. A hypernym is superordinate to a hyponym, and a hyponym is subordinate to a hypernym.{{Cite web|url=https://www.thoughtco.com/hypernym-words-term-1690943|title=Definition and Examples of Hypernyms in English|last=Nordquist|first=Richard|website=ThoughtCo|language=en|access-date=30 November 2019}}

==Examples==

===Biological generalization=== [[File:Generalization process using trees.svg|thumb|right|alt=Diagram|When the mind makes a generalization, it extracts the essence of a concept based on its analysis of similarities from many discrete objects. The resulting simplification enables higher-level thinking.]] An animal is a generalization of a [[mammal]], a bird, a fish, an [[amphibian]] and a reptile.

===Cartographic generalization of geo-spatial data=== {{Main|Cartographic generalization}} Generalization has a long history in [[cartography]] 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 cartographic scale maps, which cannot convey every detail of the real world. As a result, cartographers must decide and then adjust the content within their maps, to create a suitable and useful map that conveys the [[geospatial]] information within their representation of the world.{{Cite web|url=https://www.axismaps.com/guide/general/scale-and-generalization/|title=Scale and Generalization|date=14 October 2019|website=Axis Maps|access-date=30 November 2019}}

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—so as to preserve the distinguishing characteristics of what makes the map useful and important.

===Mathematical generalizations=== In [[mathematics]], one commonly says that a concept or a result {{mvar|B}} is a ''generalization'' of {{mvar|A}} if {{mvar|A}} is defined or proved before {{mvar|B}} (historically or conceptually) and {{mvar|A}} is a special case of {{mvar|B}}.

• The [[complex numbers]] are a generalization of the [[real numbers]], which are a generalization of the [[rational numbers]], which are a generalization of the [[integers]], which are a generalization of the [[natural numbers]].
• A [[polygon]] is a generalization of a 3-sided [[triangle]], a 4-sided [[quadrilateral]], and so on to [[Variable (mathematics)|''n'']] sides.
• A [[hypercube]] is a generalization of a 2-dimensional square, a 3-dimensional [[cube]], and so on to ''n'' [[dimension]]s.
• A [[quadric]], such as a [[hypersphere]], [[ellipsoid]], [[paraboloid]], or [[hyperboloid]], is a generalization of a [[conic section]] to higher dimensions.
• A [[Taylor series]] is a generalization of a [[MacLaurin series]].
• The [[binomial formula]] is a generalization of the formula for (1+x)^n.
• A [[ring (mathematics)|ring]] is a generalization of a [[field (mathematics)|field]].

==See also== {{wikiquote}}

• [[Anti-unification]]
• [[Categorical imperative]] (ethical generalization)
• ''[[Ceteris paribus]]''
• {{section link|Class diagram|Generalization/Inheritance}}
• [[External validity]] (scientific studies)
• [[Faulty generalization]]
• [[Generic (disambiguation)]]
• [[Critical thinking]]
• [[Generic antecedent]]
• [[Hasty generalization]]
• [[Inheritance (object-oriented programming)]]
• ''[[Mutatis mutandis]]''
• [[-onym]]
• [[Ramer–Douglas–Peucker algorithm]]
• [[Semantic compression]]
• [[Inventor's paradox]]

== References == [[Category:Generalizations]] [[Category:Critical thinking skills]] [[Category:Inductive_reasoning]]