A genus-differentia definition is one in which a word or concept that indicates a species—a specific type of item, not necessarily a biological category—is described first by a broader category, the genus, then distinguished from other items in that category by a differentia. The differentiae of a species are those properties which other species of the same genus do not have. In short, the genus is the broad category, the species is a type within that category, and the differentiae are the distinguishing characteristics of the species. This is a type of intensional definition.
In other words, a new definition can be composed by two parts:
For example, consider these two definitions:
- a triangle: A plane figure bounded by 3 straight sides.
- a quadrilateral: A plane figure bounded by 4 straight sides.
Those definitions can be expressed as a genus and 2 differentiae:
- the differentia for a triangle: bounded by 3 straight sides.
- the differentia for a quadrilateral: bounded by 4 straight sides.
Continuing the process of differentiation:
- a rectangle: a quadrilateral with 4 right angles.
- a rhombus: a quadrilateral with all 4 sides having the same length.
Importantly, differentiae can include genera. For instance, consider the following:
- a square: a rectangle where all 4 sides are the same length.
This definition could be recast as follows:
- a square: a rectangle that is a rhombus.
- a square: a rhombus that is a rectangle.
- a square: a quadrilateral that is both a rectangle and a rhombus.
- a square: both a rectangle and a rhombus.
In other words, a genus of a definition provides a means by which to specify an is-a relationship, and the non-genus portions 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 predecessors is a most general definition; each node along a directed path is more differentiated (or more derived) than its predecessors, and a node with no successors is a most differentiated (or a most derived) definition. When a definition, S, is the tail of all of its successors (that is, S has at least one successor and all of the direct successors of S are most differentiated definitions), then S is often called a species and each of its direct successors is often called an individual or an entity; the differentia of an individual is called an identity. For instance:
- [the] Mfwitten: a Wikipedia user with the account name 'Mfwitten'.
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 synechdoche.
Under the "genus" and "species" description, this sort of definition is used to categorize different plants, animals and other things into biological categories. See also genus and species and Linnaean taxonomy.
This can be clarified with a hackneyed example. Suppose we wanted to define the phrase human being. Following the ancient Greeks (Socrates and his successors) and modern biologists, we say that human being is a species and that each individual person is a member of the species human being. So we ask what the genus, or general category, of the species is; the Greeks (but not the biologists) would say that the genus is animal. What is the differentia of the species, that is, the distinguishing characteristic of human being that other animals do not have? The Greeks said it is rationality; thus, Aristotle said, A human being is a rational animal.
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