Written by
K. Srinagesh in The Principles of Experimental Research. London: Elsevier.2006. pp. 15-28
The need for definitions in experimental research emanates from the fact that experimental researchers in a given domain of nature are spread out widely over space and time. Ideally, there would be no second-guessing among them on the meaning of a word or combination of words.
I. Defining 'Definition'
How do we define 'definition'? It is somewhat disappointing to learn that there is no one definition, acceptable to most, if not all,logicians. This surprise will soon disappear when we notice that several functions performed as a way of clarifying expressions (or statements), either completely with words or with combinations of words and symbols, have all been considered legitimate acts of defining. Consequently, there are many variations of the meaning of “definition.” Having accepted this situation, we will mention (rather, quote somewhat freely) a few variations, meant to give the breadth of the word “definition,” though not its depth.
(A) A real definition involves two sets of expressions, each with a meaning of its own, and these meanings are equivalent if the definition is true.
(B) A definition is a phrase signifying a thing’s essence.(Furthermore,) A definition contains two terms as components, the genus and the differentia. A genus is what is predicated in the category of essence of a
number of things exhibiting differences in kind, and the differentia is that part of the essence that
distinguishes the species from the other species in the same genus.
(C) A definition is a way of restricting the meaning of a term that has several meanings to prevent ambiguity
and equivocation.
(D) A definition is true . . . if the defining term has the same designation as the term to be defined.
(E) Definition is a rule of substitution.
(F) “Definition” = statement that one term has the same designation as another term.
(G) A definition is the statement of the meaning of a word, etc.
(H) A definition is a brief description of a thing by its properties.
(I) A definition is an explanation of the meaning of a word or expression.
II. Common Terms Used in Definitions
Though the word “definition” itself defies definition, the components that constitute a definition are delimited fairly well as follows:
Term: Word or group of words, such as phrases, clauses, or one or more assertive sentences. To the extent that terms are defined, when need be, communication between or among researchers becomes precise. There may be occasions when the term is a group of related words, a phrase,wherein it is not the literal meaning of individual words that is significant, but that of the bunch of words as a whole, such as “shadow boxing,” “end of the tunnel”; these are often referred to as idioms. In such cases, we need to go to books of idioms, which, though not as common as dictionaries, are available in most well developed languages like English. The language of science is usually sober; there is little room for idioms like those above or for other figurative words or word combinations.
The need to define a term when the term is a whole sentence is less often encountered; when it is, the definition usually takes the form of an explanation, often with illustrative example(s). It is worthy of note that in his great work, the Principia, Isaac Newton starts with definitions, covering the first dozen or so pages,before even mentioning the problems addressed therein.
III. Varieties of Definitions
A. Direct Definitions
Direct definitions are explicit in nature; hence, the definiens can replace the definiendum without any further need for elaboration or explanation. If a definition forms a part of a whole statement, and if after replacing the definiendum with the definiens, the statement can be repeated without any loss or alteration in the original meaning, it is also a case of direct definition.
B. Indirect Definitions
Indirect definitions are such that by replacing the definiendum with definiens, both of these being either isolated or part of a statement, the meaning of the statement remains open to further relevant questions. There are two variations within this.
Firstly, when a word or a combination of words conveys meaning far beyond what a usual-length definiens can clarify, because the definiendum may have several aspects, some of which are implied and cannot be demonstrated, the definition is referred to as an implied definition: “religion,” “democracy,” and “honesty” are some examples. It is often the case that such definitions have emotional overtones.
Secondly, if y is the descendent (the word to be defined) of x, then y may be a son, a grandson, or many more generations removed, and yet be the descendent of x. The definition then for “descendent,” the definiendum, is uncertain and open to further question, in this case, as to how many generations removed or recurring. The definition, whichever way it is offered, needs to be qualified; this is often referred to as a recursive definition.
C. Informal Definitions
In most cases of human discourse, definitions are blended so nicely that we do not notice them as such. In a sense, every word of every language, either spoken or written, may be considered a definition. We live with these without needing to be conscious of their definitional nature. Most experimental scientists, most of the time, enjoy the same privilege. But occasions may arise unnoticed,though rare, when additional effort may be necessary to highlight the aspect of “definition” in their discourse. The degree of highlighting required and the amount of clarity intended, among other circumstances, decide the degree of formality that is desirable in the process of defining. Defining done with a low degree of formality is usually referred to as informal definition.
D. Formal Definitions
However, we require formal definition most often in research, and it needs to be done with a tighter grip on the words. One possible way is, “‘Brainwashing’ has the same designation as ‘Changing the other person’s opinion by subtle repetitions of slogans.’” Even more formal definitions avoid the words altogether between the definiendum (x) and the definiens (y) and connect the two with the “=” sign in the form “x = y”; the “=” does not have the same meaning as in mathematics. Originating from Principia Mathematica by Alfred Whitehead and Bertrand Russell, a formal way of defining has come to be widely accepted. It has the following form:
Beauty . = . that which is pleasing to look at. Df.
The term on the left-hand side is the definiendum and that on the right-hand side is the definiens, ending with “Df.” to denote that this is a definition.
E. Lexical Definitions
Lexical definitions, obviously, are the meanings as listed in the dictionaries. As such, we find the current and established meaning(s) of a word. For instance, in the United States, currently, the word “suck” has acquired a meaning that has sexual connotation, unlike in other English-speaking societies or in the past. It is reasonable that in the near future, we will see this new usage reflected in American dictionaries. Also, dictionaries list more than one meaning for many words. It is then left to the individual to find the appropriate meaning by context.
F. Stipulated Definitions
Stipulated definitions assign special or restrictive meanings to words (or combinations of words) that otherwise have a colloquial usage, which is most often obvious. “Stress,” for instance, is a word commonly used to connote that someone is mentally tired, but engineers take the same word, define it as “load per unit area,” and assign to it a mathematical format:
s = P ÷ A where s stands for stress, P for load, and A for area.
A variation of the stipulated definition will occur when a word (or a combination of words) is improvised to describe a certain thing or phenomenon within a limited and exclusive domain. The use of the word “bubbleballing” within the game of tennis is an example. In such circumstances, the definition is known as an impromptu definition. It is obvious that such definitions should not have currency outside the particular domain, in this case, the game of tennis.
G. Nominal Definitions
A nominal definition is most often a common understanding of what a certain word or group of words should mean for the users. In this sense, the dictionary meanings of words in any language have this characteristic. The entire human discourse depends on words, though we seldom have occasions to notice these as definitions.In mathematics and the sciences, we depend on a large number of symbols. That “3” stands for “three” and “23” stands for “the sum of two tens and three ones” is so much a part of our routine that we do not think of them as definitions. In addition to the economy of space and time, both in writing and reading,
such symbols are instrumental for the clear thinking needed for further development. What distinguishes a nominal definition is that it is neither true nor false and, hence, cannot be a proposition.
H. Real Definitions
In contrast, a real definition can serve as a proposition, which means that it is either true or false, not by itself, but as decided by individual people. If “music” is defined as “a series of sound variations, capable of producing a pleasing sensation,” then there is plenty of room to dispute whether some of modern music is music or something else, to be defined using different words as definiens.
I. Definitions by Denotation
Denotation is a way of further clarifying the meaning of a term by means of examples or instances, which most often follow, but may precede, the formal part of the definition. A good example is Newton’s definition that we quoted earlier, wherein the passage “the force of the same loadstone is greater at less distance” is used to substantiate “the accelerative quantity of a centripetal force” that he is defining.
J. Ostensive Definitions
Ostensive definitions cannot be described exhaustively by words alone but can be demonstrated or pointed to easily to obtain complete satisfaction. If a painter is asked to describe (or define) yellow ochre as a color, the one way most suitable to him is to squeeze on his palette a thread of paint from his tube of yellow ochre and ask the other person to look at it.
IV. 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 definiendum—
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 Principia.
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:
a. Hinduism . = . the religion followed by the Hindus. Df. This is obviously and completely circular.
b. 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.
c. 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:
d. 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. Be phrased in the negative when it can be phrased in the positive
Example:
a. Night . = . part of the day wherein there is no sunlight. Df.
b. 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:
c. Orphan . = . child who has no parents. Df.
This is acceptable, though it is possible to remove “no” by defining the word differently as
d. 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.
