Editing Genus–differentia definition

{{Short description|Type of intensional definition}}
{{More citations needed|date=December 2021}}

A '''genus–differentia [[definition]]''' is a type of [[Extensional and intensional definitions#Intensional definition|intensional definition]], and it is composed of two parts:

# '''a [[Genus (philosophy)|genus]]''' (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]]''': The portion of the definition that is not provided by the genus.
For example, consider these two definitions:
* ''a [[triangle]]'': A plane figure that has 3 straight bounding sides.
* ''a [[quadrilateral]]'': 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]] (384–322 BCE).<ref>
{{cite book
 | last1 = Parry
 | first1 = William Thomas
 | last2 = Hacker
 | first2 = Edward A.
 | title = Aristotelian Logic
 | series = G - Reference, Information and Interdisciplinary Subjects Series
 | url = https://books.google.com/books?id=rJceFowdGEAC
 | location = Albany
 | publisher = State University of New York Press
 | publication-date = 1991
 | page = 86
 | isbn = 9780791406892
 | access-date = 8 Feb 2019
 | quote = Aristotle recognized only one method of real definition, namely, the method of ''genus'' and ''differentia'', applied to defining real things, not words.
}}
</ref> 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 "[[Platonic form|form]]" in [[Plato]]'s dialogues but should be taken to mean "species" in [[Aristotle]]'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]]'''; the new definition is called ''an&nbsp;abstraction'' and it is said to have been ''abstracted away from'' the existing definition.

For instance, consider the following:
* ''a [[square (geometry)|square]]'': 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 [[square (geometry)|square]]'': (<span style="background:LightSalmon">a quadrilateral that has interior angles which are all right angles</span>), and that has bounding sides which all have the same length.
and with that part, an abstraction may be formed:
* <span style="background:LightSalmon">''a [[rectangle]]'': a quadrilateral that has interior angles which are all right angles.</span>
Then, the definition of ''a&nbsp;square'' may be recast with that abstraction as its genus:
* ''a [[square (geometry)|square]]'': <span style="background:LightSalmon">a rectangle</span> that has bounding sides which all have the same length.

Similarly, the definition of ''a&nbsp;square'' may be rearranged and another portion singled out:
* ''a [[square (geometry)|square]]'': (<span style="background:LightBlue">a quadrilateral that has bounding sides which all have the same length</span>), and that has interior angles which are all right angles.
leading to the following abstraction:
* <span style="background:LightBlue">''a [[rhombus]]'': a quadrilateral that has bounding sides which all have the same length.</span>
Then, the definition of ''a&nbsp;square'' may be recast with that abstraction as its genus:
* ''a [[square (geometry)|square]]'': <span style="background:LightBlue">a rhombus</span> that has interior angles which are all right angles.

In fact, the definition of ''a&nbsp;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'': <span style="background:LightSalmon">a rectangle</span> that is <span style="background:LightBlue">a rhombus</span>.
* ''a square'': <span style="background:LightBlue">a rhombus</span> that is <span style="background:LightSalmon">a rectangle</span>.
Hence, abstraction is a means of simplifying definitions.

== Multiplicity ==
When multiple definitions could serve equally well, then all such definitions apply simultaneously. Thus, ''a&nbsp;square'' is a member of both the genus ''<span style="white-space: nowrap">[a] rectangle</span>'' and the genus ''<span style="white-space: nowrap">[a] rhombus</span>''. 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'': <span style="background:LightSalmon">a rectangle</span> and <span style="background:LightBlue">a rhombus</span>.
or completely equivalently:
* ''a square'': <span style="background:LightBlue">a rhombus</span> and <span style="background:LightSalmon">a rectangle</span>.

More generally, a collection of <math>n>1</math> equivalent definitions (each of which is expressed with one unique genus) can be recast as one definition that is expressed with <math>n</math> genera.{{citation needed|date=December 2021}} Thus, the following:
* ''a Definition'': a Genus<sub>1</sub> that is a Genus<sub>2</sub> and that is a Genus<sub>3</sub> and that is a... and that is a Genus<sub>n-1</sub> and that is a Genus<sub>n</sub>, which has some non-genus Differentia.
* ''a Definition'': a Genus<sub>2</sub> that is a Genus<sub>1</sub> and that is a Genus<sub>3</sub> and that is a... and that is a Genus<sub>n-1</sub> and that is a Genus<sub>n</sub>, which has some non-genus Differentia.
* ''a Definition'': a Genus<sub>3</sub> that is a Genus<sub>1</sub> and that is a Genus<sub>2</sub> and that is a... and that is a Genus<sub>n-1</sub> and that is a Genus<sub>n</sub>, which has some non-genus Differentia.
* ...
* ''a Definition'': a Genus<sub>n-1</sub> that is a Genus<sub>1</sub> and that is a Genus<sub>2</sub> and that is a Genus<sub>3</sub> and that is a... and that is a Genus<sub>n</sub>, which has some non-genus Differentia.
* ''a Definition'': a Genus<sub>n</sub> that is a Genus<sub>1</sub> and that is a Genus<sub>2</sub> and that is a Genus<sub>3</sub> and that is a... and that is a Genus<sub>n-1</sub>, which has some non-genus Differentia.
could be recast as:
* ''a Definition'': a Genus<sub>1</sub> and a Genus<sub>2</sub> and a Genus<sub>3</sub> and a... and a Genus<sub>n-1</sub> and a Genus<sub>n</sub>, which has some non-genus Differentia.

== Structure ==

A genus of a definition provides a means by which to specify an ''[[is-a|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|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]] or—more generally—a [[directed acyclic graph]]; a node that has no [[Directed graph|predecessor]] is ''a&nbsp;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 [[Directed graph|successor]] is ''a&nbsp;most differentiated'' (or ''a&nbsp;most derived'') definition.

When a definition, ''S'', is the [[Directed graph|tail]] of each of its successors (that is, ''S'' has at least one successor and each [[Directed graph|direct successor]] of ''S'' is a most differentiated definition), then ''S'' is often called <span style="white-space: nowrap">''the '''[[species]]'''''</span> of each of its successors, and each direct successor of ''S'' is often called <span style="white-space: nowrap">''an '''[[individual]]'''''</span> (or <span style="white-space: nowrap">''an '''[[wikt:entity|entity]]'''''</span>) of the species ''S''; that is, the genus of an individual is synonymously called ''the&nbsp;species'' of that individual. Furthermore, the differentia of an individual is synonymously called <span style="white-space: nowrap">''the [[Identity (philosophy)|identity]]''</span> of that individual. For instance, consider the following definition:
* ''[the] John Smith'': a human that has the name 'John&nbsp;Smith'.
In this case:
* The whole definition is ''an&nbsp;individual''; that is, ''[the] John Smith'' is an individual.
* The genus of ''[the] John Smith'' (which is "a&nbsp;human") may be called synonymously ''the&nbsp;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&nbsp;Smith'") may be called synonymously ''the&nbsp;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]] as a ''[[pars pro toto|pars&nbsp;pro&nbsp;toto]] [[synecdoche]]''.

==See also==
* [[Hyponymy and hypernymy]]

==References==
{{Reflist}}

{{Defining}}
{{Ancient Greek philosophical concepts}}
{{Aristotelianism |ideas}}

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