definite description operator See Appendix of. Special Symbols. definition, specification of the meaning or, alternatively, conceptual content, of an expression. For example, ‘period of fourteen days’ is a definition of ‘fortnight’. Definitions have traditionally been judged by rules like the following: (1) A definition should not be too narrow. ‘Unmarried adult male psychiatrist’ is too narrow a definition for ‘bachelor’, for some bachelors are not psychiatrists. ‘Having vertebrae and a liver’ is too narrow for ‘vertebrate’, for, even though all actual vertebrate things have vertebrae and a liver, it is possible for a vertebrate thing to lack a liver. (2) A definition should not be too broad. ‘Unmarried adult’ is too broad a definition for ‘bachelor’, for not all unmarried adults are bachelors. ‘Featherless biped’ is too broad for ‘human being’, for even though all actual featherless bipeds are human beings, it is possible for a featherless biped to be non-human. (3) The defining expression in a definition should (ideally) exactly match the degree of vagueness of the expression being defined (except in a precising definition). ‘Adult female’ for ‘woman’ does not violate this rule, but ‘female at least eighteen years old’ for ‘woman’ does. (4) A definition should not be circular. If ‘desirable’ defines ‘good’ and ‘good’ defines ‘desirable’, these definitions are circular. Definitions fall into at least the following kinds: analytical definition: definition whose corresponding biconditional is analytic or gives an analysis of the definiendum: e.g., ‘female fox’ for ‘vixen’, where the corresponding biconditional ‘For any x, x is a vixen if and only if x is a female fox’ is analytic; ‘true in all possible worlds’ for ‘necessarily true’, where the corresponding biconditional ‘For any P, P is necessarily true if and only if P is true in all possible worlds’ gives an analysis of the definiendum. contextual definition: definition of an expression as it occurs in a larger expression: e.g., ‘If it is not the case that Q, then P’ contextually defines ‘unless’ as it occurs in ‘P unless Q’; ‘There is at least one entity that is F and is identical with any entity that is F’ contextually defines ‘exactly one’ as it occurs in ‘There is exactly one F’. Recursive definitions (see below) are an important variety of contextual definition. Another important application of contextual definition is
Russell’s theory of descriptions, which defines ‘the’ as it occurs in contexts of the form ‘The so-and-so is such-and-such’. coordinative definition: definition of a theoretical term by non-theoretical terms: e.g., ‘the forty-millionth part of the circumference of the earth’ for ‘meter’. definition by genus and species: When an expression is said to be applicable to some but not all entities of a certain type and inapplicable to all entities not of that type, the type in question is the genus, and the subtype of all and only those entities to which the expression is applicable is the species: e.g., in the definition ‘rational animal’ for ‘human’, the type animal is the genus and the subtype human is the species. Each species is distinguished from any other of the same genus by a property called the differentia. definition in use: specification of how an expression is used or what it is used to express: e.g., ‘uttered to express astonishment’ for ‘my goodness’. Wittgenstein emphasized the importance of definition in use in his use theory of meaning. definition per genus et differentiam: definition by genus and difference; same as definition by genus and species. explicit definition: definition that makes it clear that it is a definition and identifies the expression being defined as such: e.g., ‘Father’ means ‘male parent’; ‘For any x, x is a father by definition if and only if x is a male parent’. implicit definition: definition that is not an explicit definition. lexical definition: definition of the kind commonly thought appropriate for dictionary definitions of natural language terms, namely, a specification of their conventional meaning. nominal definition: definition of a noun (usually a common noun), giving its linguistic meaning. Typically it is in terms of macrosensible characteristics: e.g., ‘yellow malleable metal’ for ‘gold’. Locke spoke of nominal essence and contrasted it with real essence. ostensive definition: definition by an example in which the referent is specified by pointing or showing in some way: e.g., ‘ ‘Red’ is that color,’ where the word ‘that’ is accompanied with a gesture pointing to a patch of colored cloth; ‘ ‘Pain’ means this,’ where ‘this’ is accompanied with an insertion of a pin through the hearer’s skin; ‘ ‘Kangaroo’ applies to all and only animals like that,’ where ‘that’ is accompanied by pointing to a particular kangaroo. persuasive definition: definition designed to affect or appeal to the psychological states of the party to whom the definition is given, so that a claim will appear more plausible to the party than it is: e.g., ‘self-serving manipulator’ for ‘politician’, where the claim in question is that all politicians are immoral. precising definition: definition of a vague expression intended to reduce its vagueness: e.g., ‘snake longer than half a meter and shorter than two meters’ for ‘snake of average length’; ‘having assets ten thousand times the median figure’ for ‘wealthy’. prescriptive definition: stipulative definition that, in a recommendatory way, gives a new meaning to an expression with a previously established meaning: e.g., ‘male whose primary sexual preference is for other males’ for ‘gay’. real definition: specification of the metaphysically necessary and sufficient condition for being the kind of thing a noun (usually a common noun) designates: e.g., ‘element with atomic number 79’ for ‘gold’. Locke spoke of real essence and contrasted it with nominal essence. recursive definition (also called inductive definition and definition by recursion): definition in three clauses in which (1) the expression defined is applied to certain particular items (the base clause); (2) a rule is given for reaching further items to which the expression applies (the recursive, or inductive, clause); and (3) it is stated that the expression applies to nothing else (the closure clause). E.g., ‘John’s parents are John’s ancestors; any parent of John’s ancestor is John’s ancestor; nothing else is John’s ancestor’. By the base clause, John’s mother and father are John’s ancestors. Then by the recursive clause, John’s mother’s parents and John’s father’s parents are John’s ancestors; so are their parents, and so on. Finally, by the last (closure) clause, these people exhaust John’s ancestors. The following defines multiplication in terms of addition: ‘0 $ n % 0. (m ! 1) $ n % (m $ n) ! n. Nothing else is the result of multiplying integers’. The base clause tells us, e.g., that 0 $ 4 % 0. The recursive clause tells us, e.g., that (0 ! 1) $ 4 % (0 $ 4) ! 4. We then know that 1 $ 4 % 0 ! 4 % 4. Likewise, e.g., 2 $ 4 % (1 ! 1) $ 4 % (1 $ 4) ! 4 % 4 ! 4 % 8. stipulative definition: definition regardless of the ordinary or usual conceptual content of the expression defined. It postulates a content, rather than aiming to capture the content already associated with the expression. Any explicit definition that introduces a new expression into the language is a stipulative definition: e.g., ‘For the purpose of our discussion ‘existent’ means ‘perceivable’ ‘; ‘By ‘zoobeedoobah’ we shall mean ‘vain millionaire who is addicted to alcohol’.’ synonymous definition: definition of a word (or other linguistic expression) by another word synonymous with it: e.g., ‘buy’ for ‘purchase’; ‘madness’ for ‘insanity’. See also ANALYSIS , ESSENTIALISM , MEAN – ING , PHILOSOPHY OF LANGUAGE , THEORY OF DESCRIPTION. T.Y.