Genus–differentia definition explained

A genus–differentia definition is a type of intensional definition, and it is composed of two parts:

  1. a 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.
  2. the differentia: The portion of the definition that is not provided by the genus.

For example, consider these two definitions:

Those definitions can be expressed as one genus and two differentiae:

  1. one genus:
    • the genus for both a triangle and a quadrilateral: "A plane figure"
  2. 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).[1] 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" 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 abstraction and it is said to have been abstracted away from the existing definition.

For instance, consider the following:

A part of that definition may be singled out (using parentheses here):

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: 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 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 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: 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 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 rectangle that is a rhombus. 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 rectangle and a rhombus.or completely equivalently: 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:

could be recast as:

Structure

A genus of a definition provides a means by which to specify an is-a relationship:

The non-genus portion of the differentia of a definition provides a means by which to specify a has-a relationship:

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 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 is a most differentiated (or a most derived) definition.

When a definition, S, is the tail 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 of each of its successors, and each direct successor of S is often called an individual (or an entity) 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 of that individual. For instance, consider the following definition:

In this case:

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 synecdoche.

See also

Notes and References

  1. Book: Parry . William Thomas . Hacker . Edward A. . Aristotelian Logic . G - Reference, Information and Interdisciplinary Subjects Series . Albany . State University of New York Press . 1991 . 86 . 9780791406892 . 8 Feb 2019 . Aristotle recognized only one method of real definition, namely, the method of genus and differentia, applied to defining real things, not words..

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