Editing Genus–differentia definition (section)

== Differentiation and abstraction ==
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&nbsp;abstraction'' and it is said to have been ''abstracted away from'' the existing definition.

For instance, consider the following:
* ''a [[square (geometry)|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 (geometry)|square]]'': (<span style="background:LightSalmon">a quadrilateral that has interior angles which are all right angles</span>), and that has bounding sides which all have the same length.
and with that part, an abstraction may be formed:
* <span style="background:LightSalmon">''a [[rectangle]]'': a quadrilateral that has interior angles which are all right angles.</span>
Then, the definition of ''a&nbsp;square'' may be recast with that abstraction as its genus:
* ''a [[square (geometry)|square]]'': <span style="background:LightSalmon">a rectangle</span> that has bounding sides which all have the same length.

Similarly, the definition of ''a&nbsp;square'' may be rearranged and another portion singled out:
* ''a [[square (geometry)|square]]'': (<span style="background:LightBlue">a quadrilateral that has bounding sides which all have the same length</span>), and that has interior angles which are all right angles.
leading to the following abstraction:
* <span style="background:LightBlue">''a [[rhombus]]'': a quadrilateral that has bounding sides which all have the same length.</span>
Then, the definition of ''a&nbsp;square'' may be recast with that abstraction as its genus:
* ''a [[square (geometry)|square]]'': <span style="background:LightBlue">a rhombus</span> that has interior angles which are all right angles.

In fact, the definition of ''a&nbsp;square'' may be recast in terms of both of the abstractions, where one acts as the genus and the other acts as the differentia:
* ''a square'': <span style="background:LightSalmon">a rectangle</span> that is <span style="background:LightBlue">a rhombus</span>.
* ''a square'': <span style="background:LightBlue">a rhombus</span> that is <span style="background:LightSalmon">a rectangle</span>.
Hence, abstraction is a means of simplifying definitions.