Genus–differentia Definition - Differentiation and Abstraction

Differentiation and Abstraction

This 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:

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 (in italics):

square

a quadrilateral that has interior angles which are all right angles, and that has bounding sides which all have the same length.

and with that part, an abstraction may be formed:

rectangle

a quadrilateral that has interior angles which are all right angles.

Then, the definition of a square may be recast with that abstraction as its genus:

square

a rectangle that has bounding sides which all have the same length.

Similarly, the definition of a square may be rearranged and another portion singled out:

square

a quadrilateral that has bounding sides which all have the same length, and that has interior angles which are all right angles.

leading to the following abstraction:

rhombus

a quadrilateral that has bounding sides which all have the same length.

Then, the definition of a square may be recast with that abstraction as its genus:

square

a rhombus that has interior angles which are all right angles.

In fact, the definition of a square may be recast in terms of both of the abstractions, where one acts as the genus and the other acts as the differentia:

square

a rectangle that is a rhombus and a rhombus that is a rectangle.