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Concept
Genus–differentia definition
Summary
A genus–differentia definition is a type of intensional definition, and it is composed of two parts:
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.
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). 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.
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 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: (a quadrilateral that has interior angles which are all right angles), and that has bounding sides which all have the same length.
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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 definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
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