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.

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Famous quotes containing the words definition and/or genus:

    “The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
    —Jean Baudrillard (b. 1929)

    “Methinks it would be some advantage to philosophy if men were named merely in the gross, as they are known. It would be necessary only to know the genus and perhaps the race or variety, to know the individual. We are not prepared to believe that every private soldier in a Roman army had a name of his own,—because we have not supposed that he had a character of his own.”
    —Henry David Thoreau (1817–1862)