Definition By Genus and Differentia
A genus–differentia definition is a type of intensional definition, and it is composed by 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 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:
- a genus: A plane figure.
- 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.
Read more about this topic: Definition
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