What Definitions Should and Should Not Do

Even among logicians, there is no unanimity as to what ought to be called “definitions.” Having said this, we mention below briefly, without the constraints of quotation, some of the desir­able and some of the undesirable traits of definitions, as expressed by logicians.

A definition should

1. Make communication possible when it is impossi­ble without it, or make communication clear when it would be fuzzy without it
2. Have two terms: (a) the term to be defined (the meaning of which, in the context, is doubtful), and (b) the term that does the defining (the mean­ing of which is expected to be understood)

Example: Painter . = . one who paints pictures. Df.

3. Distinguish between things and words

Example: In “Anger is harmful,” we are talking about the thing (emotion) “anger.” In contrast, in “‘Anger’ has five letters,” we are talking about the word “anger” (not about the emotion “anger”).

The means of making this distinction is to use the quotation marks judiciously.

4. Distinguish between the noun and verb forms of some words, which can be used in both forms.

Example: “I am writing this passage,” versus “This writing is done well.”

5. Give the essence of that which is to be defined. The definiens must be equivalent to the definien- dum—it must be applicable to everything of which the definiendum can be predicated, and applicable to nothing else.
6. Be so selected that, whether explicit or implicit, the attributes known to belong to the thing defined must be formally derivable from the definition.

A definition should not

1. Use examples as the sole means of defining, though examples may supplement a given defini­tion. We have seen this done, as it should be, in the definition quoted from Newton’s
2. Use description as the sole means of defining. Here again, the definition quoted from Newton’s Principia, done as it should be, may be considered as containing a supplementary description.
3. Use exaggeration (as a form of definition)

Example: “Definition” by Bernard Shaw:

Teacher: He who can, does. He who cannot, teaches.

4. Be circular; it must not, directly or indirectly, con­tain the subject to be defined (some times referred to as tautology)

Examples:

• Hinduism . = . the religion followed by the Hindus. Df.

This is obviously and completely circular.

• Hinduism . = . the religious and social doc­trines and rites of the Hindus. Df.

This is from a respectable dictionary; the circu­larity is obvious, though not direct.

• Hinduism . = . the religious and social system of the Hindus, a development of ancient Brah­manism. Df.

This is from another respectable dictionary. The addition of the phrase “a development of ancient Brahmanism” is an improvement, but not in the direction of reducing the circularity.

Instead, use the form:

• Hinduism . = . religious and social rites and doctrines that are a development of ancient Brah­manism. Df.

The circularity is completely avoided, though the new word introduced, “Brahmanism,” needs to be defined, in turn.

5. Be phrased in the negative when it can be phrased in the positive

Example:

1. Night . = . part of the day wherein there is no sunlight. Df.
2. Night . = . the time from sunset to sunrise. Df.

Though (a) may be literally correct, (b) fulfills the logical requirement better.

However, there are legitimate exceptions.

Example:

• Orphan . = . child who has no parents. Df.

This is acceptable, though it is possible to remove “no” by defining the word differently as

• Orphan . = . one who is bereaved of parents. Df.

6. Contain obscure term(s)

This pertains to the purpose of definition, namely, to clarify, not to complicate, confuse, or lead astray. The earlier example, in which “Brah­manism” was used to define “Hinduism,” is an instance.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.