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{{Wiktionary|definition}} |
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A '''definition''' is a statement of the [[Meaning (linguistic)|meaning]] of a term, word or phrase. The term to be defined is known as the '''definiendum''' (Latin: ''that which is to be defined''). The words which define it are known as the '''definiens''' (Latin: ''that which is doing the defining'').<ref>[[OED]] and [http://dictionary.reference.com/browse/definition www.dictionary.com].</ref> |
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==Stipulative definitions== |
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{{main|Stipulative definition}} |
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A definition may either give the meaning that a term 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). Stipulative definitions differ from descriptive definitions in that they prescribe a new meaning either to a term already in use or to a new term. A descriptive definition can be shown to be right or wrong by comparison to usage, while a stipulative definition cannot. A stipulative definition, however, may be more or less useful. |
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A [[persuasive definition|''persuasive definition'']], named by C.L. Stevenson, 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.<ref>Stevenson, C.L., ''Ethics and Language'', Connecticut 1944</ref> |
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==Intension and extension== |
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{{main|Intension|Extension (metaphysics)}} |
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An [[intensional definition]], also called a ''connotative'' definition, specifies the [[necessary and sufficient conditions]] for a thing being a member of a specific [[set]]. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition. |
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An ''[[extensional definition]]'', also called a ''denotative'' definition, of a concept or term specifies its ''[[extension (semantics)|extension]]''. It is, a list naming every [[object (philosophy)|object]] that is a member of a specific [[set]]. |
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So, for example, an intensional definition of '[[Prime Minister]]' might be ''the most senior minister of a cabinet in the executive branch of government in a parliamentary system''; whereas an extensional definition would be simply a [[Prime minister#Lists of prime ministers|list of all past and present Prime Ministers]]. |
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One important form of extensional definition is ''[[ostensive definition]]''. This gives the meaning of a term by pointing, in the case of an individual, to the thing itself, or in the case of a class, to examples of the right kind. So you can explain who ''Alice'' (an individual) is by pointing her out to me; or what a ''rabbit'' (a class) is by pointing at several and expecting me to 'catch on'. The process of ostensive definition itself was critically appraised by [[Ludwig Wittgenstein]].<ref>''Philosophical investigations'', Part 1 §27-34</ref> |
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An ''enumerative definition'' of a concept or term is an ''[[extensional definition]]'' that gives an explicit and exhaustive listing of all the [[object (philosophy)|object]]s that fall under the concept or term in question. Enumerative definitions are only possible for finite sets and only practical for relatively small sets. |
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==Definition by genus and differentia== |
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[[Image:Biological classification L Pengo.svg|thumb|right|[[Scientific classification]] of living things uses definition by genus and differentia.]] |
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{{main|Genus-differentia definition}} |
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Traditionally, 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).<ref>See [[Genus-differentia definition]]</ref> |
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=== Rules for definition by genus and differentia=== |
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{{main|Fallacies of definition}} |
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Certain rules have traditionally been given for this particular type of definition.<ref>Copi 1982 pp 165-169</ref><ref>Joyce, ''ibidem''</ref> |
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#A definition must set out the essential attributes of the thing defined. |
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#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. |
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#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). |
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#The definition must not be obscure. The purpose of a definition is to 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). |
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#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', nor blindness except as 'the absence of sight in a creature that is normally sighted'. |
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=== Essence === |
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{{main|Essence}} |
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In classical thought, a definition was taken to be a statement of the essence of a thing. [[Aristotle]] had it that an object's essential attributes form its "essential nature", and that a definition of the object must include these essential attributes.<ref>[[Posterior Analytics]], Bk 1 c. 4</ref> |
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The idea that a definition should state the essence of a thing led to the distinction between ''nominal'' and ''real'' essence, originating with Aristotle. In a passage from the [[Posterior Analytics]],<ref>[[Posterior Analytics]] Bk 2 c. 7</ref> 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. |
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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. |
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This preoccupation with essence dissipated in much of modern philosophy. [[Analytic philosophy]] in particular is critical of attempts to elucidate the essence of a thing. [[Bertrand Russell|Russell]] described it as "a hopelessly muddle-headed notion".<ref>''A history of Western Philosophy'', p. 210</ref> |
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More recently [[Kripke semantics|Kripke's]] formalisation of [[possible world]] semantics in [[Modal logic]] led to a new approach to [[essentialism]]. Insofar as the essential properties of a thing are ''necessary'' to it, they are those things it possesses in all possible worlds. Kripke refers to names used in this way as [[Rigid designator]]s. |
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==Genetic definition== |
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A ''genetic definition'' describes the process or method by which a thing is formed. <blockquote>''"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 how to make a circle."''<ref>[[Claude Lévi-Strauss]]. [http://varenne.tc.columbia.edu/bib/info/tax00sol53appranth.html "Discussion of Lévi-Strauss's paper 'Social Structure'" (<nowiki>[1952]</nowiki> 1962) in An appraisal of anthropology today. Edited by Sol Tax. University of Chicago Press 1953] |
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</ref></blockquote> |
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==Recursive definitions== |
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A [[recursive definition]], sometimes also called an ''inductive'' definition, is one that defines a word in terms of itself, so to speak, albeit in a useful way. Normally this consists of three steps: |
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#At least one thing is stated to be a member of the set being defined; this is sometimes called a "base set". |
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#All things bearing a certain relation to other members of the set are also to count as members of the set. It is this step that makes the definition [[Recursion|recursive]]. |
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#All other things are excluded from the set |
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For instance, we could define [[natural number]] as follows (after [[Peano axioms|Peano]]): |
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#"0" is a natural number. |
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#Each natural number has a distinct successor, such that: |
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#*the successor of a natural number is also a natural number, and |
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#*no natural number is succeeded by "0". |
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#Nothing else is a natural number. |
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So "0" will have exactly one successor, which for convenience we can call "1". In turn, "1" will have exactly one successor, which we would call "2", and so on. Notice that the second condition in the definition itself refers to natural numbers, and hence involves [[self-reference]]. Although this sort of definition involves a form of [[Circular definition|circularity]], it is not vicious, and the definition is quite successful. |
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== Limitations of definition == |
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Given that a [[natural language]] such as [[English language|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'' must itself be defined, where should we stop?<ref> This parallels the [[regress argument|diallelus]], but leading to scepticism about meaning rather than knowledge</ref> A dictionary, for instance, insofar as it is a comprehensive list of [[lexical definition]]s, must resort to [[Symbol grounding|circularity]].<ref>Generally [[Lexicography|lexicographers]] seek to avoid circularity wherever possible, but the definitions of words such as "the" and "a" use those words and are therefore circular. [http://www.m-w.com/dictionary/the] [http://www.m-w.com/dictionary/a] Lexicographer [[Sidney I. Landau]]'s essay "''Sexual Intercourse in American College Dictionaries''" provides other examples of circularity in dictionary definitions. (McKean, p. 73-77) </ref><ref>An exercise suggested by [[J. L. Austin]] involved taking up a dictionary and finding a selection of terms relating to the key concept, then looking up each of the words in the explanation of their meaning. Then, iterating this process until the list of words begins to repeat, closing in a “family circle” of words relating to the key concept.<br>(''[http://www.ditext.com/austin/plea.html A plea for excuses]'' in Philosophical Papers. Ed. [[J. O. Urmson]] and [[Geoffrey Warnock|G. J. Warnock]]. Oxford: Oxford UP, 1961. 1979.)</ref><ref>In the game of [[Circ (game)|Circ]], players compete to find circularity in a dictionary.</ref> |
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Many philosophers have chosen instead to leave some terms undefined. The [[Scholasticism|scholastic philosophers]] claimed that the highest genera (the so-called ten ''generalissima'') cannot be defined, since we cannot assign any higher genus under which they may fall. Thus we cannot define [[being]], unity and similar concepts.<ref>Joyce, G.H. ''Principles of Logic'', Chapter x</ref> [[John Locke|Locke]] supposes in ''[[An Essay Concerning Human Understanding]]''<ref>''Essay'', Bk III, c. 4</ref> that the names of simple concepts do not admit of any definition. More recently [[Bertrand Russell]] sought to develop a formal language based on [[Logical atomism|logical atoms]]. Other philosophers, notably [[Ludwig Wittgenstein|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.<ref> See especially ''[[Philosophical Investigations]]'' Part 1 §48</ref> 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",<ref>He continues: "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." [[Philosophical Investigations]], Part 1 §87, italics in original</ref> claiming instead that explanation of a term is only needed when we need to avoid misunderstanding. |
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Locke and [[John Stuart Mill|Mill]] also argued that we cannot define [[Individuation|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.<ref>This theory of meaning is one of the targets of the [[private language argument]]</ref> This is not possible when no one else is acquainted with the particular thing that has "fallen under our notice".<ref>Essay III. iii. 3</ref> 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 [[modal logic|modality]], in his book ''Naming and Necessity''. |
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There is a presumption in the classic example of a definition that the ''definiens'' can be stated. Wittgenstein argued that for some terms this is not the case.<ref>''Philosophical Investigations</ref> The examples he used include ''game'', ''number'' and ''family''. In such cases, he argued, there is no fixed boundary that can be used to provide a definition. Rather, the items are grouped together because of a [[family resemblance]]. For terms such as these it is not possible to state a definition; rather, one simply comes to understand the ''use'' of the term. |
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==See also== |
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{{wiktionarypar|definition}} |
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*[[Analytic proposition]] |
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*[[Demonstration]] |
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*[[Fallacies of definition]] |
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*[[Ramsey-Lewis method]] |
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*[[Synthetic proposition]] |
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*[[Indeterminacy (Philosophy)|Indeterminacy]] |
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==Notes== |
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<references/> |
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==References== |
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These templates can be copied for additional references. ([[Template:Cite book]], [[Template:Cite journal]]) |
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*{{cite book |last= |first= |authorlink= |coauthors= |others= |title= |year= |publisher= |location= |id= }} |
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*{{cite book |last=Copi|first=Irving|authorlink= |coauthors= |others= |title=Introduction to Logic |year=1982 |publisher=Macmillan |location=New York |id=ISBN 0-02-977520-5}} |
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*{{cite book |last=Joseph |first=Horace William Brindley |authorlink= |coauthors= |title=An Introduction to Logic, 2nd edition |year=1916 repr. 2000 |publisher=Clarendon Press repr. Paper Tiger |location= |id=ISBN 1-889439-17-7 }} [http://books.google.com/books?id=vDgAAAAAMAAJ (full text of 1st ed.)] |
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*{{cite book |last=Joyce |first=George Hayward |authorlink= |coauthors= |title=Principles of logic, 3d ed., new impression |year=1926 |publisher=Longmans, Green and co |location=London, New York |id= }} [http://books.google.com/books?id=L3wYAAAAIAAJ (contents of 1949 ed.)] [http://www.amazon.com/dp/B00086LT0G] [http://catalog.loc.gov/] |
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*{{cite book |last=McKean |first=Erin |authorlink= |coauthors= |others= |title=Verbatim: From the bawdy to the sublime, the best writing on language for word lovers, grammar mavens, and armchair linguists |year=2001 |publisher=Harvest Books |location= |id=ISBN 0-15-601209-X }} |
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*{{cite book |last=Simpson |first=John |authorlink= |coauthors=Edmund Weiner |others= |title=[[Oxford English Dictionary]], second edition (20 volumes) |year=1989 |publisher=Oxford University Press |location= |id=ISBN 0-19-861186-2 }} |
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*{{cite book |
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| last = Wittgenstein |
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| first = Ludwig |
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| authorlink = Ludwig Wittgenstein |
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| coauthors = |
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| title = Philosophical Investigations |
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| publisher = Blackwell Publishing |
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| date = 1953/2001 |
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| location = |
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| url = |
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| id = ISBN 0-631-23127-7}} |
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==External links== |
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*[http://samvak.tripod.com/define.html The structure and internal logic of definitions] |
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*[http://www.dictionary.com Dictionary.com] |
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*[http://www.sfu.ca/philosophy/swartz/definitions.htm Definitions, Dictionaries, and Meanings, Norman Swartz 1997] |
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[[Category:Philosophical concepts]] |
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[[Category:Definition]] |
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[[Category:Philosophy of language]] |
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[[Category:Semantics]] |
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[[Category:Mathematical terminology]] |
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Revision as of 17:49, 3 October 2007
run!!!!!