A denotative definition explains the meaning of a term by identifying the things to which the term applies. A denotative definition of the phrase ‘the past prime ministers of India’ will consist of a complete list of persons who have been prime ministers of India in the past. We thus give a denotative definition simply by listing all the things or individuals who are members of the class.
A denotative definition can be either verbal or non-verbal (ostensive). A verbal extensional definition is one that linguistically identifies all objects to which the term can be correctly applied by naming them. For example, to give a verbal extensional definition of ‘planets in the solar system’ one can give the names all the planets that go around the Sun.
A verbal denotational definition of ‘past presidents of India’ will consist of the names all the past presidents of India.
There are, however, several limitations to verbal denotational definitions:
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(a) It is not always possible to name all the objects denoted by a word or expression. General terms refer to infinite number of things. Terms like ‘numbers’ and ‘instants of time’ refer to infinite series.
Even terms such as ‘chairs’ and tables’ denote not only chairs and tables now existing all over the world but also those which existed in the past and those which would exist in the future. Even when an expression refers to a finite set of things (such as ‘the colleges of Orissa in the year 2010’) it is either cumbersome or inconvenient to name all of the things to which the expression refers in order to elucidate the meaning of the expression.
(b) Further, most terms do not have names for each and every individual they include within their denotation. For example, all the individual tables that constitute the denotation of the term ‘table’ do not have names.
To provide a verbal denotative definition of ‘table’ would require providing a list containing the names of all the individual tables. This is an impracticable and impossible task.
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(c) In view of these difficulties, one might suggest that although denotative definition by complete enumeration is not possible, one may try instead to provide a denotative definition by offering a few examples. In practice, we generally follow this procedure to elucidate the meaning a term.
This is a very useful method in practice. Citing of examples often assist us to understand the meaning of a term. But the important question is: Can we provide the definition of a term by this method?
(d) There are some terms for which denotative definition is entirely impossible. The term ‘unicorn’ has an accepted meaning in our language. ‘Unicorns are fictitious’ and ‘There are no unicorns in the world’ are meaningful statements. Thus we do use it to make meaningful statements. Since there are no unicorns in the world, the term lacks any denotation. So although the word ‘unicorn’ is meaningful we cannot indicate its meaning by this method.