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Generalization



 
 
Generalization is a foundational element of logic
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
 and human reasoning
Reasoning

Reasoning is the Cognition process of looking for reasons for beliefs, conclusions, actions or feelings. Although reasoning was once thought to be a uniquely human capability, other animals also engage in Animal_cognition#Reasoning_and_problem_solving....
. Generalization posits the existence of a domain or set
Set theory

Set theory is the branch of mathematics that studies Set , 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 inference. The process of verification
Falsifiability

Falsifiability is the logical possibility that an assertion can be shown false by an observation or a physical experiment. That something is "falsifiable" does not mean it is false; rather, that if it is false, then this can be shown by observation or 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.

For any two related concepts, A and B; A is considered a generalization of concept B if and only if:

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....
 is a generalization of bird
Bird

Birds are wing, Bipedalismal, endothermic , vertebrate animals that lay egg . There are around 10,000 living species, making them the most numerous tetrapod vertebrates....
 because every bird is an animal, and there are animals which are not birds (dog
Dog

The dog is a domesticated subspecies of the Gray Wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties....
s, for instance).






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Generalization is a foundational element of logic
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
 and human reasoning
Reasoning

Reasoning is the Cognition process of looking for reasons for beliefs, conclusions, actions or feelings. Although reasoning was once thought to be a uniquely human capability, other animals also engage in Animal_cognition#Reasoning_and_problem_solving....
. Generalization posits the existence of a domain or set
Set theory

Set theory is the branch of mathematics that studies Set , 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 inference. The process of verification
Falsifiability

Falsifiability is the logical possibility that an assertion can be shown false by an observation or a physical experiment. That something is "falsifiable" does not mean it is false; rather, that if it is false, then this can be shown by observation or 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.

For any two related concepts, 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....
 is a generalization of bird
Bird

Birds are wing, Bipedalismal, endothermic , vertebrate animals that lay egg . There are around 10,000 living species, making them the most numerous tetrapod vertebrates....
 because every bird is an animal, and there are animals which are not birds (dog
Dog

The dog is a domesticated subspecies of the Gray Wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties....
s, for instance). (See also: specialization
Specialization

Specialisation, also spelt specialization, is an important way to generate propositional knowledge, by applying general knowledge, such as the theory of gravity, to specific instances, such as "when I release this apple, it will fall to the floor"....
).

On a side note, a common joke goes like this:

"All generalizations are false!"

This is known as a self-contradictory statement.

Hypernym and hyponym


This kind of generalization versus specialization (or particularization) is reflected in either of the contrasting words of the word pair hypernym
Hypernym

In linguistics, a hyponym is a word or phrase whose semantics range is included within that of another word. For example, scarlet, vermilion, carmine, and crimson are all hyponyms of red , which is, in turn, a hyponym of colour....
 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 lily and daisy are included in flower, and bird and fish in animal. A hypernym is superordinate to a hyponym, and a hyponym is subordinate to hypernym.

Cartographic generalization of geo-spatial data

Generalization has a long history in cartography
Cartography

File:Mediterranean chart fourteenth century2.jpgCartography is the study and practice of making Geography Map. Combining science, aesthetics, and technique, cartography builds on the premise that we can model reality in ways that communicate spatial information effectively....
 as an art of creating maps for different scale and purpose. Cartographic generalization
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....
 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 is a term widely used to describe the combination of spatial software and analytical methods with terrestrial or geographic datasets....
 information within their representation of the world.

Generalization is meant to be context-specific. This is to say that 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.

See also

  • Abstraction
    Abstraction

    Abstraction is the process or result of generalization by reducing the information content of a concept or an observable phenomenon, typically in order to retain only information which is relevant for a particular purpose....
  • Ceteris paribus
    Ceteris paribus

    is a Latin phrase, literally translated as "with other things the same." It is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal relation or logical connections between two states of affairs, is qualified by ceteris paribus in order to acknowledge, and to rule out, the possibil...
  • Generic
    Generic

    Generic is something that is general, comon, or inclusive rather than specific, unique, or selective.* Generic mood, a grammatical mood used to make generalized statements like Snow is white...
  • Generic antecedent
    Generic antecedent

    Generic antecedents are representatives of classes, indicated by a reference in ordinary language , where gender is typically unknown or irrelevant....
  • inheritance (object-oriented programming),
  • Faulty generalization
    Faulty generalization

    A faulty generalization, also known as an inductive fallacy, is any of several errors of Inductive reasoning:...
  • Hasty generalization
    Hasty generalization

    Hasty generalization is a logical fallacy of faulty generalization by reaching an inductive reasoning generalization based on insufficient evidence....
  • Homotopy lifting property
    Homotopy lifting property

    In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property is a technical condition on a continuous function from a topological space E to another one, B....
  • Mutatis mutandis
    Mutatis mutandis

    Mutatis mutandis, Latin literal meaning "with those things having been changed which need to be changed" or simpler "the necessary changes having been made"....
  • -onym
    -onym

    The Affix ?onym, in English language, means "word, name," and words ending in ?onym refer to a specified kind of name or word, most of which are classical compounds....
  • Class diagram
    Class diagram

    In software engineering, a class diagram in the Unified Modeling Language , is a type of static structure diagram that describes the structure of a system by showing the system's class es, their attributes, and the Object-oriented programming between the classes....
  • Ramer-Douglas-Peucker algorithm
    Ramer-Douglas-Peucker algorithm

    The Douglas-Peucker algorithm is an algorithm for smoothing curves. The initial form of the algorithm was independently suggested in 1972 by Urs Ramer and 1973 by David Douglas and Thomas Peucker....
  • Specialization
    Specialization

    Specialisation, also spelt specialization, is an important way to generate propositional knowledge, by applying general knowledge, such as the theory of gravity, to specific instances, such as "when I release this apple, it will fall to the floor"....
    , the opposite process