+159.  The Logical Definition.+—­The logical definition sets exact limits to the meaning of a term.  An exact definition must include all the members of a class indicated by the term defined, and it must exclude everything that does not belong to that class.  A logical definition is composed of two parts.  It first names the class to which the term to be defined belongs, and then it names the characteristic that distinguishes that term from all other members of the same class.  The class is termed the genus, and the distinguishing characteristics of the different members of the class are termed the differentia.  Notice the following division into genus and differentia.

TERM TO BE      |       CLASS          |    DISTINGUISHING
DEFINED        |     (Genus)        |    CHARACTERISTIC
|                      |    (Differentia)
|                      |
A parallelogram   |  is a quadrilateral  |  whose opposite sides
|                      |  are parallel
|                      |
Exposition        |  is that form of     |  which seeks to explain
|  discourse           |  the meaning of a term.
|                      |

Each definition includes three elements:  the term to be defined, the genus, and the differentia; but these are not necessarily arranged in the order named.

EXERCISE

Select the three elements (the term to be defined, the genus, and the differentia) in each of the following:—­

1.  A polygon of three sides is called a triangle.

2.  A square is an equilateral rectangle.

3.  A rectangle whose sides are equal is a square.

4.  Description is that form of discourse which aims to present a picture.

5.  The characters composing written words are called letters.

6.  The olfactory nerves are the first pair of cranial nerves.

7.  Person is that modification of a noun or pronoun which denotes the speaker, the person spoken to, or the person or things spoken of.

8.  The diptera, or true flies, are readily distinguishable from other insects by their having a single pair of wings instead of two pairs, the hind wings being transformed into small knob-headed pedicles called balancers or halters.

+160.  Difficulty of Framing Exact Definitions.+—­In order to frame a logical definition, exactness of thought is essential.  Even when the thought is exact, it will be found difficult and often impossible to frame a satisfactory definition.  Usually there is little difficulty in selecting the genus, still care should be taken to select one that includes the term to be defined.  We might begin the definition of iron by saying, “Iron is a metal,” since all iron is metal, but it would be incorrect to begin the definition of rodent by saying, “A rodent is a beaver,” because the term beaver does not include all rodents.  We must also take care to choose for the genus some term familiar to the reader, because the object of the definition is to make the meaning clear to him.