Genus–differentia definition
A genus–differentia definition is a type of intensional definition which defines a species (that is, a type — not necessarily a biological category) as a subtype of a genus satisfying certain conditions (the differentia). Thus, the definiendum in such definitions is always a species (and not an individual), while the definiens consists of two parts:
- a genus (or family): An pre-defined term that includes the species defined as a subtype.
- the differentia: The condition that distinguishes the species from other instances of the same genus.
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 one genus and two differentiae:
- one genus: A plane figure.
- two differentiae:
- the differentia for a triangle: that has 3 straight bounding sides.
- the differentia for a quadrilateral: that has 4 straight bounding sides.
Note that the genus-species relation is relative. One may define "dog" as a species of the genus "animal", while "puppy" is a species of the genus "dog". Thus, whether "dog" is a species or a genus depends on context.[1]
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.
Examples
This can be clarified with a well-known example. Suppose we wanted to define the phrase human being. Following the ancient Greeks (Socrates and his successors) and modern biologists, we say that human being is a species and that each individual person is a member of the species human being. So we ask what the genus, or general category, of the species is; the Greeks (but not the biologists) would say that the genus is animal. What is the differentia of the species, that is, the distinguishing characteristic of human being that other animals do not have? The Greeks said it is rationality; thus, Aristotle said, A human being is a rational animal.[2]
However, the use of the genus–differentia definition is by no means restricted to science. Rather, it is a fairly natural definitional strategy. Here are some examples from everyday life:
| Species |
Genus of definition |
Differentia of definition |
| Phylum |
A taxonomic rank... |
...that is below a kingdom and above a class. |
| Paperweight |
An object... |
...that is small, heavy, and used to prevent papers from scattering. |
| Homesickness |
A feeling... |
...of unhappiness one may experience when away from home. |
| Subtitles |
A transcript... |
...of the script of a show or movie printed along the bottom of the viewing screen. |
| Mosque |
A building... |
...often with high towers and domes, where Muslims worship. |
Criteria for genus-differentia definitions
There are some more or less standard criteria for judging the appropriateness of a genus-differentia definition [3][4]. These criteria include the following:
- A definition should state the essential attributes of the species.
- For instance[1], a circle is uniquely described as "a planar closed figure enclosing greater area than any other planar closed figure of equal perimeter." However, this definition, while having the appropriate extension, fails to capture the "essence" of circle as a type of planar closed figure. The difference stated here is not the conventional connotation of the term circle.
- A definition must not be circular.
- The definiens should not appear in the definiendum, as in the definition, "A compulsive gambler is a person who gambles compulsively." [5]
- A definition must not be too broad.
- The difference must be chosen so that every member of the genus with that difference is a member of the species being defined. Thus, the definition, "A bird is an animal with wings," is too broad, since bats (for example) are also animals with wings, and bats are not birds.[4]
- A definition must not be too narrow.
- The difference must be chosen so the every member of the species has that property. Thus, the definition, "A bird is a feathered animal that can fly," is too narrow, since ostriches are birds, but they cannot fly.[4]
- A definition must not be expressed in ambiguous, obscure or figurative language.
- This catch-all criterion aims at making the definition as precise and easily understood as one can. Thus, technical jargon should be avoided in non-technical contexts and the terms chosen should not be easily misinterpreted. For instance, one may define "faith" as "true belief", but it is unclear whether this definition means "a belief which is truly held" or "a belief which is true," since English allows either interpretation.[4].
- One should also avoid figurative or metaphorical definitions, since such definitions tend to obscure rather than elucidate meaning. Thus, the definition of "bread" as "the staff of life" is a poor definition per this criterion.[1]
- A definition should not be negative where it can be affirmative.
- As Copi writes, "The reason for this rule is that a definition is supposed to explain what a term means, not what it does not mean."[1] Thus, one prefers to define "drunkard" as "a person who drinks excessively" rather than "a person who is not temperate in drink."[1]
References
- ^ a b c d e Copi, Irving, "Introduction to Logic", second ed., The Macmillan Company, 1961.
- ^ Aristotle's Metaphysics. Stanford Encyclopedia of Philosophy
- ^ Copi, Irving and Cohen, Carl, "Introduction to Logic", thirteenth ed., Pearson Prentice Hall, 2009.
- ^ a b c d Layman, C. Stephen, "The Power of Logic", third edition, McGraw-Hill, 2005.
- ^ Copi and Cohen cite this example, from Livingston, Jay, "Compulsive Gamblers", Harper & Row, 1974.