Varieties of Definitions

1. Direct and B. Indirect 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. In contrast, 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, ify 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.

2. Informal and D. Formal 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. Suppose I were writing for a tennis magazine on the advantages and disadvantages of “bubbleballing.” I might write something like this: “Some players are likely to return the balls to the oppo­nent intentionally and repeatedly, hitting the ball high above the net, making the ball drop to their opponent almost vertically near the baseline. For our purpose we may call this ‘bubble-balling.’ Here are some advantages of bubbleballing.” I would proceed to write on, using bubbleballing instead of the rather long definiendum mentioned above. This is an example of infor­mal definition.

Informal definitions can be stated in several different ways, using different sets of words; a few variations follow:

  1. Bubbleballing is the act of returning balls, the path of which to the opponent resembles a bubble.
  2. The word “bubbleballing” is applied to the way a tennis player returns the ball to his opponent with a big upswing, followed by a big downswing.
  3. A player who does “bubbleballing” is understood to be returning the ball to his opponent in tennis, deliberately hit high into the sky.

So long as the sense in the expression is conveyed, some resid­ual vagueness or ambiguity is not frowned upon. 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 definien- dum (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.

3. Lexical and F. Stipulated 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.

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:

σ = P + A

where σ 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.

4. Nominal and H. Real 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. No Briton can charge an American with being “untrue” if the latter writes “center” where it ought to be, according to the Briton, “centre.” The same is true for symbols; for instance, the current symbol for gold (in chemistry) is “Au.” If there is a move in some future time among chemists, who agree to do so, it may be changed to “Go,” or any other letter or group of letters, with­out rendering any statement made thus far “false.”

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.

5. 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.

6. 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.

7. Definitions by Genus and Difference

Attributed to Aristotle, such a method of definition depends on showing a particular entity as belonging to a set and nonetheless being different from all other elements of the set. The famous example is “Man is a rational animal”; in all respects, man is another animal, with the difference that he alone is endowed with rationality.

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

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