Definition - Definition By Genus and Differentia

Definition By Genus and Differentia

A genus–differentia definition is a type of intensional definition, and it is composed by 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 new definition that is not provided by the genera.

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 a genus and 2 differentiae:

1. a genus: A plane figure.
2. 2 differentiae:
   • the differentia for a triangle: that has 3 straight bounding sides.
   • the differentia for a quadrilateral: that has 4 straight bounding sides.

When multiple definitions could serve equally well, then all such definitions apply simultaneously. For instance, given the following:

• a rectangle: a quadrilateral that has interior angles which are all right angles.
• a rhombus: a quadrilateral that has bounding sides which all have the same length.

both of these definitions of 'square' are equally acceptable:

• a square: a rectangle that is a rhombus.
• a square: a rhombus that is a rectangle.

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.