Definition
- For other uses, see Definition (disambiguation).
A definition is a form of words which states the meaning of a term. This may either be the meaning which it bears in general use (a descriptive definition), or that which the speaker intends to impose upon it for the purpose of his or her discourse (a stipulative definition). The term to be defined is known as the definiendum (Latin: that which is to be defined). The form of words which defines it is known as the definiens (Latin: that which is doing the defining).
Traditionally, such a definition consists of the genus (the family) of thing to which the defined thing belongs, and the differentia (the distinguishing feature which marks it off from other members of the same family). Thus 'triangle' is defined as 'a plane figure (genus) bounded by three straight sides (differentia).[1]
Limitations of definition
Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or leave some terms undefined. If every term of every definiens could itself be defined, where at last should we stop?[2] A dictionary, for instance, in so far as it is a comprehensive list of lexical definitions, must resort to circularity. An alternative approach is to leave some terms undefined. Locke supposes in An Essay Concerning Human Understanding [3] that the names of simple concepts do not admit of any definition. The scholastic philosophers in contrast claimed that the highest genera (the so-called ten generalissimi) cannot be defined, since we cannot assign any higher genus under which they may fall. Thus we cannot define Being, Unity and similar concepts [4]. More recently Bertrand Russell sort to develop a formal language based on logical atoms. Other philosophers, notably Wittgenstein, rejected the need for any undefined simples. Wittgenstein pointed out in his Philosophical Investigations that what counts as a "simple" in one circumstance might not do so in another.[5] He rejected the very idea that every explanation of the meaning of a term needed itself to be explained: "As though an explanation hung in the air unless supported by another one. Whereas an explanation may indeed rest on another one that has been given, but none stands in need of another - unless we require it to prevent a misunderstanding. One might say: an explanation serves to remove or to avert a misunderstanding - one, that is, that would occur but for the explanation; not every one I can imagine."[6]
Locke and Mill also argued that we cannot define individuals. We learn names by connecting an idea with a sound, so that speaker and hearer have the same idea when the same word is used.[7] This is not possible when no one else is acquainted with the particular thing that has fallen under our notice [8]. Russell offered his theory of descriptions in part as a way of defining a proper name, the definition being given by a definite description that "picks out" exactly one individual. Saul Kripke pointed to difficulties with this approach, especially in relation to modality, in his book Naming and Necessity.
Rules for definition
1. Definitions should avoid circularity. To define a horse as 'a member of the species equus' would convey no information whatsoever. For this reason, Locke adds that a definition of a term must not consist of terms which are synonymous with it. This error is known as circulus in definiendo. Note, however, that it is acceptable to define two relative terms in respect of each other. Clearly, we cannot define 'antecedent' without using the term 'consequent', nor conversely.
2. The definition must not be too wide or too narrow. It must be applicable to everything to which the defined term applies (i.e. not miss anything out), and to no other objects (i.e. not include any things to which the defined term would not truly apply).
3. The definition must not be obscure. The purpose of a definition is too explain the meaning of a term which may be obscure or difficult, by the use of terms that are commonly understood and whose meaning is clear. The violation of this rule is known by the Latin term obscurum per obscurius. However, sometimes scientific and philosophical terms are difficult to define without obscurity. (See the definition of Free will in Wikipedia, for instance).
4. A definition should not be negative where it can be positive. We should not define 'wisdom' as the absence of folly, or a healthy thing as whatever is not sick. Sometimes this is unavoidable, however. We cannot define a point except as 'something with no parts', or blindness as 'the absence of sight in a creature that is normally sighted'. [9]
5. Definitions should avoid being what C.L. Stevenson calls 'persuasive'. A persuasive definition is a form of stipulative definition which purports to describe the 'true' or 'commonly accepted' meaning of a term, while in reality stipulating an altered use, perhaps as an argument for some view, for example that some system of government is democratic. Stevenson also notes that some definitions are 'legal' or 'coercive', whose object is to create or alter rights, duties or crimes. [10]
See also Fallacies of definition.
Real and Nominal definitions
The distinction between nominal and real essence originates with Aristotle. In the passage from the Posterior Analytics [Bk 2 c. 7]], he says that we can know the meaning of a made-up name (he gives the example 'goat stag'), without knowing what he calls the 'essential nature' of the thing that the name would denote, if there were such a thing. This led medieval logicians to distinguish between the so-called quid nominis or 'whatness of the name', and the underlying nature common to all the things it names, which they called the quid rei or 'whatness of the thing'. (Early modern philosophers like Locke used the corresponding English terms 'nominal essence' and 'real essence'). The name 'hobbit', for example, is perfectly meaningful. It has a quid nominis. But we could not know the real nature of hobbits, even if there were such things , and so we cannot know the real nature or quid rei of hobbits. By contrast, the name 'man' denotes real things (men) that have a certain quid rei. The meaning of a name is distinct from the nature that thing must have in order that the name apply to it.
This leads to a corresponding distinction between nominal and real definition. A nominal definition is the definition explaining what a word means, i.e. which says what the 'nominal essence' is, and is definition in the classical sense as given above. A real definition, by contrast, is one expressing the real nature or quid rei of the thing.
Other kinds of definition
A number of different kinds and techniques of definition can be distinguished, including:
An extensional definition of a concept or term specifies its extension, that is, every object that falls under the definition of the concept or term in question.
An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question. Enumerative definitions are only possible for finite sets and only practical for relatively small sets.
An operational definition of a quantity is a specific process whereby it is measured.
A genetic definition describes the process or method by which a thing is formed.[11]
A recursive definition or inductive definition is one that defines a word in terms of itself, so to speak, albeit in a useful way. Normally this consists of two (or three) steps: (I) Several specific objects (a "base set") are stated to fall under the term X being described. (II) All and only the things bearing a certain relation to members of X are also stated to be members of X. For instance, we could define natural number as follows: (I) 1 is a natural number. (II) The successor of a natural number is also a natural number, and nothing else is. ("Nothing else is", the closure step, is sometimes considered a separate step.) For this to work well, the definition in any given case must be well-founded, avoiding a circle or an infinite regress. (See the following.)
See also
- Analytic proposition
- Fallacies of definition
- Ramsey-Lewis method
- Synthetic proposition
- Indeterminacy
Notes
- ↑ See Genus-differentia definition
- ↑ This parallels the diallelus, but leading to scepticism about meaning rather than knowledge
- ↑ Essay, Bk III, c. 4
- ↑ Joyce, G.H. Principles of Logic, Chapter x
- ↑ See especially Philosophical Investigations Part 1 §48
- ↑ Philosophical Investigations, Part 1 §87, italics in original
- ↑ This theory of meaning is one of the targets of the private language argument
- ↑ Essay III. iii. 3
- ↑ Joyce, ibidem
- ↑ Stevenson, C.L., Ethics and Language, Connecticut 1944
- ↑ "But if you define the circle as a pattern resulting from having a segment of a line revolve around one of its ends, this is a genetic definition because it tells you bow to make a circle." Claude Lévi-Strauss. "Discussion of Lévi-Strauss's paper 'Social Structure'" ([1952] 1962) in An appraisal of anthropology today. Edited by Sol Tax. University of Chicago Press 1953
ReferencesISBN links support NWE through referral fees
- Oxford English Dictionary, second edition, edited by John Simpson and Edmund Weiner, Clarendon Press, 1989, twenty volumes, hardcover, ISBN 0-19-861186-2
External links
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