A genus–differentia

definition A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definiti ...

is a type of

intensional definition In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition give ...

, and it is composed of two parts: # a

genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nom ...

(or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus. # the

differentia In scholastic logic, differentia is one of the predicables. It is that part of a definition which is predicable in a given genus only of the definiendum; or the corresponding " metaphysical part" of the object. Origin Plato implicitly emplo ...

: The portion of the definition that is not provided by the genus. For example, consider these two definitions: * ''a

triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...

'': A plane figure that has 3 straight bounding sides. * ''a

quadrilateral In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...

'': A plane figure that has 4 straight bounding sides. Those definitions can be expressed as one genus and two ''differentiae'': # ''one genus'': #* ''the genus for both a triangle and a quadrilateral'': "A plane figure" # ''two differentiae'': #* ''the differentia for a triangle'': "that has 3 straight bounding sides." #* ''the differentia for a quadrilateral'': "that has 4 straight bounding sides." The use of genus and differentia in constructing definitions goes back at least as far as

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...

(384–322 BCE).

Differentiation and Abstraction

The process of producing new definitions by ''extending'' existing definitions is commonly known as differentiation (and also as derivation). The reverse process, by which just part of an existing definition is used itself as a new definition, is called

abstraction Abstraction in its main sense is a conceptual process wherein 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 abst ...

; the new definition is called ''an abstraction'' and it is said to have been ''abstracted away from'' the existing definition. For instance, consider the following: * ''a

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...

'': a quadrilateral that has interior angles which are all right angles, and that has bounding sides which all have the same length. A part of that definition may be singled out (using parentheses here): * ''a

'': (a quadrilateral that has interior angles which are all right angles), and that has bounding sides which all have the same length. and with that part, an abstraction may be formed: * ''a

rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram contain ...

'': a quadrilateral that has interior angles which are all right angles. Then, the definition of ''a square'' may be recast with that abstraction as its genus: * ''a

'': a rectangle that has bounding sides which all have the same length. Similarly, the definition of ''a square'' may be rearranged and another portion singled out: * ''a

'': (a quadrilateral that has bounding sides which all have the same length), and that has interior angles which are all right angles. leading to the following abstraction: * ''a

rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...

'': a quadrilateral that has bounding sides which all have the same length. Then, the definition of ''a square'' may be recast with that abstraction as its genus: * ''a

'': a rhombus that has interior angles which are all right angles. In fact, the definition of ''a square'' may be recast in terms of both of the abstractions, where one acts as the genus and the other acts as the differentia: * ''a square'': a rectangle that is a rhombus. * ''a square'': a rhombus that is a rectangle. Hence, abstraction is crucial in simplifying definitions.

Multiplicity

When multiple definitions could serve equally well, then all such definitions apply simultaneously. Thus, ''a square'' is a member of both the genus ''[a] rectangle'' and the genus ''[a] rhombus''. In such a case, it is notationally convenient to consolidate the definitions into one definition that is expressed with multiple genera (and possibly no differentia, as in the following): * ''a square'': a rectangle and a rhombus. or completely equivalently: * ''a square'': a rhombus and a rectangle. More generally, a collection of

n>1

equivalent definitions (each of which is expressed with one unique genus) can be recast as one definition that is expressed with

n

genera. Thus, the following: * ''a Definition'': a Genus₁ that is a Genus₂ and that is a Genus₃ and that is a… and that is a Genus_n-1 and that is a Genus_n, which has some non-genus Differentia. * ''a Definition'': a Genus₂ that is a Genus₁ and that is a Genus₃ and that is a… and that is a Genus_n-1 and that is a Genus_n, which has some non-genus Differentia. * ''a Definition'': a Genus₃ that is a Genus₁ and that is a Genus₂ and that is a… and that is a Genus_n-1 and that is a Genus_n, which has some non-genus Differentia. * … * ''a Definition'': a Genus_n-1 that is a Genus₁ and that is a Genus₂ and that is a Genus₃ and that is a… and that is a Genus_n, which has some non-genus Differentia. * ''a Definition'': a Genus_n that is a Genus₁ and that is a Genus₂ and that is a Genus₃ and that is a… and that is a Genus_n-1, which has some non-genus Differentia. could be recast as: * ''a Definition'': a Genus₁ and a Genus₂ and a Genus₃ and a… and a Genus_n-1 and a Genus_n, which has some non-genus Differentia.

Structure

A genus of a definition provides a means by which to specify an '' is-a relationship'': * A square is a rectangle, which is a quadrilateral, which is a plane figure, which is a… * A square is a rhombus, which is a quadrilateral, which is a plane figure, which is a… * A square is a quadrilateral, which is a plane figure, which is a… * A square is a plane figure, which is a… * A square is a… The non-genus portion of the differentia of a definition provides a means by which to specify a '' has-a relationship'': * A square has an interior angle that is a right angle. * A square has a straight bounding side. * A square has a… When a system of definitions is constructed with genera and differentiae, the definitions can be thought of as nodes forming a

hierarchy A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important ...

or—more generally—a

directed acyclic graph In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called ''arcs''), with each edge directed from one ...

; a node that has no predecessor is ''a most general definition''; each node along a directed path is ''more differentiated'' (or ''more derived'') than any one of its predecessors, and a node with no

successor Successor may refer to: * An entity that comes after another (see Succession (disambiguation)) Film and TV * ''The Successor'' (film), a 1996 film including Laura Girling * ''The Successor'' (TV program), a 2007 Israeli television program Musi ...

is ''a most differentiated'' (or ''a most derived'') definition. When a definition, ''S'', is the

tail The tail is the section at the rear end of certain kinds of animals’ bodies; in general, the term refers to a distinct, flexible appendage to the torso. It is the part of the body that corresponds roughly to the sacrum and coccyx in mammal ...

of each of its successors (that is, ''S'' has at least one successor and each direct successor of ''S'' is a most differentiated definition), then ''S'' is often called ''the

species In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriat ...

'' of each of its successors, and each direct successor of ''S'' is often called ''an

individual An individual is that which exists as a distinct entity. Individuality (or self-hood) is the state or quality of being an individual; particularly (in the case of humans) of being a person unique from other people and possessing one's own need ...

'' (or ''an

entity An entity is something that exists as itself, as a subject or as an object, actually or potentially, concretely or abstractly, physically or not. It need not be of material existence. In particular, abstractions and legal fictions are usually ...

'') of the species ''S''; that is, the genus of an individual is synonymously called ''the species'' of that individual. Furthermore, the differentia of an individual is synonymously called ''the

identity Identity may refer to: * Identity document * Identity (philosophy) * Identity (social science) * Identity (mathematics) Arts and entertainment Film and television * ''Identity'' (1987 film), an Iranian film * ''Identity'' (2003 film), an ...

'' of that individual. For instance, consider the following definition: * ''[the] John Smith'': a human that has the name 'John Smith'. In this case: * The whole definition is ''an individual''; that is, ''[the] John Smith'' is an individual. * The genus of ''[the] John Smith'' (which is "a human") may be called synonymously ''the species'' of ''[the] John Smith''; that is, ''[the] John Smith'' is an individual of the species ''[a] human''. * The differentia of ''[the] John Smith'' (which is "that has the name 'John Smith'") may be called synonymously ''the identity'' of ''[the] John Smith''; that is, ''[the] John Smith'' is identified among other individuals of the same species by the fact that ''[the] John Smith'' is the one "that has the name 'John Smith'". As in that example, the identity itself (or some part of it) is often used to refer to the entire individual, a phenomenon that is known in

linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Ling ...

as a '' pars pro toto

synecdoche Synecdoche ( ) is a type of metonymy: it is a figure of speech in which a term for a part of something is used to refer to the whole ('' pars pro toto''), or vice versa ('' totum pro parte''). The term comes from Greek . Examples in common E ...

''.

References

{{DEFAULTSORT:Genus-differentia definition Abstraction Definition Dichotomies Difference Philosophy of language Theories in ancient Greek philosophy