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 definitio ...

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. An intensional definition gives meaning to a term by sp ...

, and it is composed of two parts: # a

genus Genus (; : genera ) is a taxonomic rank above species and below family (taxonomy), family as used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In bino ...

(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'' (also called ''differentia specifica'') 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 pa ...

: 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 corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

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

quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...

'': 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 a genus (Greek: ''genos'') and a differentia (Greek: ''diaphora'') in constructing a definition goes back at least as far as

Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...

(384–322 BCE). Furthermore, a genus may fulfill certain characteristics (described below) that qualify it to be referred to as ''a species'', a term derived from the Greek word ''eidos'', which means "

form Form is the shape, visual appearance, or configuration of an object. In a wider sense, the form is the way something happens. Form may also refer to: *Form (document), a document (printed or electronic) with spaces in which to write or enter dat ...

" in

Plato Plato ( ; Greek language, Greek: , ; born BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...

's dialogues but should be taken to mean "species" in

's corpus.

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 is a process where general rules and concepts are derived from the use and classifying of specific examples, literal (reality, real or Abstract and concrete, concrete) signifiers, first principles, or other methods. "An abstraction" ...

; 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 geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

'': 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 geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that a ...

'': 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 (: 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 rhom ...

'': 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 a means of 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 '' rectangle'' and the genus '' 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 Ancient Greek, 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 ...

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'' (1996 film), a film including Laura Girling * The Successor (2023 film), a French drama film * ''The Successor'' ( ...

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

tail The tail is the elongated section at the rear end of a bilaterian animal's body; in general, the term refers to a distinct, flexible appendage extending backwards from the midline of the torso. In vertebrate animals that evolution, evolved to los ...

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 A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...

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

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

'' (or ''an

entity An entity is something that Existence, exists as itself. It does not need to be of material existence. In particular, abstractions and legal fictions are usually regarded as entities. In general, there is also no presumption that an entity is Lif ...

'') 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: * '' heJohn Smith'': a human that has the name 'John Smith'. In this case: * The whole definition is ''an individual''; that is, '' heJohn Smith'' is an individual. * The genus of '' heJohn Smith'' (which is "a human") may be called synonymously ''the species'' of '' heJohn Smith''; that is, '' heJohn Smith'' is an individual of the species '' human''. * The differentia of '' heJohn Smith'' (which is "that has the name 'John Smith'") may be called synonymously ''the identity'' of '' heJohn Smith''; that is, '' heJohn Smith'' is identified among other individuals of the same species by the fact that '' heJohn 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 language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds ...

as a '' pars pro toto

synecdoche Synecdoche ( ) is a type of metonymy; it is a figure of speech that uses a term for a part of something to refer to the whole (''pars pro toto''), or vice versa (''totum pro parte''). The term is derived . Common English synecdoches include '' ...

''.

References

{{DEFAULTSORT:Genus-differentia definition Abstraction Definition Dichotomies Conceptual distinctions Philosophy of language Theories in ancient Greek philosophy Ancient Greek logic

Differentiation and abstraction

Multiplicity

Structure

See also

References