There are five rules by means of which we can evaluate the success of connotative definitions by genus and differentia:
1. A definition should state the entire connotation of the term, neither less nor more. The entire connotation of the term is given by stating the genus and the differentia of the term. If more than the logical connotation is stated, it becomes over complete definition. If less than the entire connotation is stated, it becomes an incomplete definition.
For example, the definition of human beings as language-speaking rational animals states more than the connotation. If we define human beings as rational, it would be a case of incomplete definition.
Further, the connotation of a term consists of the essential attributes of the class the definition should focus on essential features shared by all and only the member’s the class. The things to which a term applies may share many distinctive properties. But all these properties do not indicate the true nature of the term. The definition of “human beings” as “featherless bipeds” is not a good definition even if it picks out the right individuals. Violation of this rule leads to the fallacy of incomplete or over complete definition.
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2. The denotation of the definiendum and the definiens should be identical. This rule states that the definition of a term should capture the correct denotation of the term. A good definition will apply exactly to the same things as the term being defined, no more and no less. When this rule is violated we have a fallacy of either too broad or too narrow definition.
For instance, the definition of “bird” as “warm-blooded animal” will be too broad, since it would include not only birds but also horses, cattle and dogs as well. On the other hand, the definition of “bird” as “feathered egg-laying animal” will be too narrow, since it would exclude male birds. So a good connotative definition must be satisfied by all and only those things that are included in the denotation of the term they define.
3. A definition should not be circular. A definition is circular if the definiendum turns up in the definiens. A circular definition uses the term being defined as part of its own definition. Since the purpose of a definition is to explain the meaning of a term or to make its meaning clear, this purpose is defeated if the term is included in the definition.
Someone who does not understand the term will not be benefited by such a definition. “A cordless phone is a telephone that has no cord”, “Man is human”, “Circles are circular in shape” are examples of circular definition.
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4. A definition should not be expressed in ambiguous, obscure, or figurative language. While defining a term one should avoid figurative and obscure language. The aim of definition is to explain the meaning of a term to someone who is unfamiliar with its proper application. So the use of ambiguous, obscure, or figurative language will not help such a person learn how to apply the term. Thus, “happiness is a warm puppy” is a good poetic metaphor, but as a definition it will be useless.
5. A definition should not be negative where it can be affirmative. A definition should state what a term means rather than what it does not mean. A good definition should use positive designations whenever it is possible to do so. The difficulty with negative definition is that there are too many things a term does not signify. For example, a table is not a chair, not a sofa, not a bed, not a house and so on and so forth. Similarly defining “triangle” as “a figure which is not a circle” is a negative definition. It is not possible to explain the application of a term by identifying some of the things to which it does not apply in a few instances, however, this may be the only way to go.
A proper definition of the mathematical term “infinite” might well be negative. Terms having negative content, such as ‘blind’ or ‘opaque’, are to be defined negatively. But in ordinary circumstances, it is advisable to offer positive definitions.