. A definition gives a definiens or defining expression for a definiendum or what is to be defined. ‘Definition’ itself can stand for the sentence doing the defining, for the process of doing it, or for the definiens. Various rules for definitions have traditionally been given, but these are now widely regarded as unduly restrictive, or as mere practical guides.
In a real or essentialist definition the definiendum is an essence or concept. A real definition is therefore an analysis of a concept (but see Mill). In a nominal definition the definiendum is a term or word. ‘Real’ here means applying to the thing to concept, as against the word. ‘Nominal’ means ‘applying to the word, as against the thing or concept’. The phrase ‘real definition’ is little used now. However, even a nominalist (i.e. here, one who accepts only nominal definitions) may reserve a word for a certain concept and then use a definition of the word to analyse the concept.
A definition may aim to clarify the meaning of an already existing term (lexical or dictionary definitions, e.g., ‘“Puppy” in English means “young dog”’.) Or it may introduce an abbreviation or stipulate how a term is going to be used (stipulative definitions, e.g. ‘By “puppy” I shall mean any dog shorter than twelve inches’.) Stipulative definitions are prescriptive in that they prescribe how a word is to be used, as are lexical definitions in so far as they do not merely report usage but prescribe standards of ‘good’ usage. Normally it is not the case that just any explanation of a term counts as a definition. A definition must have a certain adequacy, completeness, and universality. A definition should normally state NECESSARY AND SUFFICIENT CONDITIONS for applying the definiendum. ‘A puppy is a dog’ is true, but not a definition for not all dogs are puppies.
Contextual definitions or definitions in use define a term indirectly by giving an equivalent for a whole context in which it occurs. One might define ‘average’ by explaining how it is used in sentences like ‘The average man has two and a half children’. Two rather technical notions may be briefly mentioned. In a recursive definition the term defined occurs in the definiens, but in a way that avoids circularity. The term ‘ancestor of’ might be recursively defined as ‘parent of, or ancestor of a parent of’. Cf. RECURSIVE. An inductive definition or definition by induction defines what it is for a term x in a series to have a certain property; it does this by defining what it is for the first term in the series to have the property, and then defining what it is for any term to have it, given that its predecessor has it. Taking the above example we define x as being an ancestor of y by saying that a parent of y is an ancestor of y, and any parent of an ancestor of y is an ancestor of y. Recursive and inductive definitions thus come to the same thing.
In an ostensive definition (not properly a definition at all) an instance of what the term applies to is physically pointed to (‘Red is that colour there’, or just ‘Red!’, said while pointing to a tomato). For impredicative definitions see theory of TYPES. In persuasive defi-nitions an emotionally charged term is given a revised factual significance, to which the emotional charge than attaches. If one dislikes those who live on rent, one might redefine ‘fascist’ to include them. For extensional and intensional definitions, see UNIVERSALS.
What kinds of words can be defined will largely depend on the kind of definition, and on how rigorously we interpret ‘definition’. A common problem is whether a given term can be defined without going outside a specified set of terms, e.g. can ‘life’ be defined in chemical terms?
J.S.Mill, A System of Logic, Longmans, Green and Co., 1843, book 1 chapter 8. (See § 5 for real definitions.)
K.R.Popper, The Open Society and its Enemies, RKP, 1945. (Vol. 2 includes famous attack on use of definitions outside technical contexts.)
R.Robinson, Definition, Clarendon, 1950. (Full-scale study, taking very liberal view of what counts as definition.)
