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{{short description|Statement that attaches a meaning to a term}} | |||
{{otheruses}} | |||
{{Wiktionary|definition}} | {{about||the definition of another word|wikt:Main Page{{!}}Wiktionary|other uses of the word "definition" itself}} | ||
{{pp|small=yes}} | |||
] | |||
A '''definition''' is a statement of the ] of a 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>] and .</ref> | |||
A '''definition''' is a statement of the meaning of a term (a ], ], or other set of ]s).<ref>Bickenbach, Jerome E., and Jacqueline M. Davies. . Broadview Press, 1996. p. 49</ref><ref>{{Cite web|url=https://www.dictionary.com/browse/definition|title=Definition of definition {{!}} Dictionary.com|website=www.dictionary.com|language=en|access-date=2019-11-28}}</ref> Definitions can be classified into two large categories: ]s (which try to give the sense of a term), and ]s (which try to list the objects that a term describes).<ref name=Lyons>Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on.</ref> Another important category of definitions is the class of ]s, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.<ref>Dooly, Melinda. . Univ. Autònoma de Barcelona, 2006. p.48 and on</ref>{{efn|Terms with the same pronunciation and spelling but unrelated meanings are called ], while terms with the same spelling and pronunciation and related meanings are called ].}} | |||
==Stipulative definitions== | |||
{{main|Stipulative definition}} | |||
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. | |||
A ], 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> | |||
In ], a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what the mathematical term is and is not. Definitions and ] form the basis on which all of modern mathematics is to be constructed.<ref>Richard J. Rossi (2011) Theorems, Corollaries, Lemmas, and Methods of Proof. John Wiley & Sons p.4</ref> | |||
==Intension and extension== | |||
==Basic terminology== | |||
{{main|Intension|Extension (metaphysics)}} | |||
{{redirect|Definiens|the Definiens company|Cognition Network Technology}} | |||
An ], also called a ''connotative'' definition, specifies the ] for a thing being a member of a specific ]. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition. | |||
In modern usage, a definition is something, typically expressed in words, that attaches a meaning to a word or group of words. The word or group of words that is to be defined is called the ''definiendum'', and the word, group of words, or action that defines it is called the ''definiens''.<ref name=":0">{{Cite web|url=http://beisecker.faculty.unlv.edu//Courses/Phi-102/Definitions.html|title=DEFINITIONS|website=beisecker.faculty.unlv.edu|access-date=2019-11-28}}</ref> For example, in the definition ''"An elephant is a large gray animal native to Asia and Africa"'', the word "elephant" is the ''definiendum'', and everything after the word "is" is the ''definiens''.<ref name="hurley9">{{cite book |last1=Hurley |first1=Patrick J. |title=A Concise Introduction to Logic |chapter=Language: Meaning and Definition |edition=9 |publisher=Wadsworth |year=2006 |pages=86–91 }}</ref> | |||
An '']'', also called a ''denotative'' definition, of a concept or term specifies its '']''. It is, a list naming every ] that is a member of a specific ]. | |||
The ''definiens'' is not ''the meaning'' of the word defined, but is instead something that ''conveys the same meaning'' as that word.<ref name="hurley9"/> | |||
So, for example, an intensional definition of ']' 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 ]. | |||
There are many sub-types of definitions, often specific to a given field of knowledge or study. These include, ''lexical definitions'', or the common dictionary definitions of words already in a language; ''demonstrative definitions'', which define something by pointing to an example of it (''"This," , "is an Asian elephant."''); and ''precising definitions'', which reduce the vagueness of a word, typically in some special sense (''"'Large', among female Asian elephants, is any individual weighing over 5,500 pounds."'').<ref name="hurley9"/> | |||
One important form of extensional definition is '']''. 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 ].<ref>''Philosophical investigations'', Part 1 §27-34</ref> | |||
==Intensional definitions vs extensional definitions== | |||
An ''enumerative definition'' of a concept or term is an '']'' that gives an explicit and exhaustive listing of all the ]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. | |||
{{Main|Intension|Extension (semantics)}} | |||
An '']'', also called a ''connotative'' definition, specifies the ] for a thing to be a member of a specific ].<ref name=Lyons/> Any definition that attempts to set out the essence of something, such as that by ], is an intensional definition. | |||
==Definition by genus and differentia== | |||
] of living things uses definition by genus and differentia.]] | |||
{{main|Genus-differentia definition}} | |||
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 ]</ref> | |||
An '']'', also called a ''denotative'' definition, of a concept or term specifies its '']''. It is a list naming every ] that is a member of a specific ].<ref name=Lyons/> | |||
=== Rules for definition by genus and differentia=== | |||
{{main|Fallacies of definition}} | |||
Certain rules have traditionally been given for this particular type of definition.<ref>Copi 1982 pp 165-169</ref><ref>Joyce, ''ibidem''</ref> | |||
#A definition must set out the essential attributes of the thing defined. | |||
#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. | |||
#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). | |||
#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 ] in Misplaced Pages, for instance). | |||
#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'. | |||
Thus, the "]" can be defined ''intensionally'' as those singled out by ] as particularly destructive of the life of grace and charity within a person, thus creating the threat of eternal damnation. An ''extensional'' definition, on the other hand, would be the list of wrath, greed, sloth, pride, lust, envy, and gluttony. In contrast, while an intensional definition of "]" might be "the most senior minister of a cabinet in the executive branch of parliamentary government", an extensional definition is not possible since it is not known who the future prime ministers will be (even though all prime ministers from the past and present can be listed). | |||
=== Essence === | |||
{{main|Essence}} | |||
===Classes of intensional definitions=== | |||
{{Main|Genus–differentia definition}} | |||
A ''genus–differentia definition'' is a type of ] that takes a large category (the ''genus'') and narrows it down to a smaller category by a distinguishing characteristic (i.e. the ''differentia'').<ref>Bussler, Christoph, and Dieter Fensel, eds. Artificial Intelligence: Methodology, Systems and Applications: 11th International Conference, AIMSA 2004: Proceedings. Springer-Verlag, 2004. p.6</ref> | |||
More formally, a genus–differentia definition consists of: | |||
* ''a ]'' (or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus. | |||
* ''the differentia'': The portion of the new definition that is not provided by the genus.<ref name=":0" /> | |||
For example, consider the following genus–differentia definitions: | |||
* ''a ]'': A plane figure that has three straight bounding sides. | |||
* ''a ]'': A plane figure that has four straight bounding sides. | |||
Those definitions can be expressed as a genus ("a plane figure") and two ''differentiae'' ("that has three straight bounding sides" and "that has four straight bounding sides", respectively). | |||
It is also possible to have two different genus–differentia definitions that describe the same term, especially when the term describes the overlap of two large categories. For instance, both of these genus–differentia definitions of "square" are equally acceptable: | |||
* ''a square'': a ] that is a ]. | |||
* ''a square'': a ] that is a ]. | |||
Thus, a "square" is a member of both genera (the plural of ''genus''): the genus "rectangle" and the genus "rhombus". | |||
===Classes of extensional definitions=== | |||
One important form of the extensional definition is '']''. 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. For example, one can explain who ''Alice'' (an individual) is, by pointing her out to another; or what a ''rabbit'' (a class) is, by pointing at several and expecting another to understand. The process of ostensive definition itself was critically appraised by ].<ref>''Philosophical investigations'', Part 1 §27–34</ref> | |||
An '']'' of a concept or a term is an '']'' that gives an explicit and exhaustive listing of all the ] that fall under the concept or term in question. Enumerative definitions are only possible for finite sets (and only practical for small sets). | |||
===''Divisio'' and ''partitio''=== | |||
''Divisio'' and ''partitio'' are ] terms for definitions. A ''partitio'' is simply an intensional definition. A ''divisio'' is not an extensional definition, but an exhaustive list of ]s of a set, in the sense that every member of the "divided" set is a member of one of the subsets. An extreme form of ''divisio'' lists all sets whose only member is a member of the "divided" set. The difference between this and an extensional definition is that extensional definitions list ''members'', and not ''subsets''.<ref>Katerina Ierodiakonou, "The Stoic Division of Philosophy", in ''Phronesis: A Journal for Ancient Philosophy'', Volume 38, Number 1, 1993, pp. 57–74.</ref> | |||
===Nominal definitions vs real definitions=== | |||
{{Main|Essence}} | |||
In classical thought, a definition was taken to be a statement of the essence of a thing. ] 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>], Bk 1 c. 4</ref> | In classical thought, a definition was taken to be a statement of the essence of a thing. ] 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>], Bk 1 c. 4</ref> | ||
The idea that a definition should state the essence of a thing led to the distinction between ''nominal'' and ''real'' |
The idea that a definition should state the essence of a thing led to the distinction between ''nominal'' and ''real'' essence—a distinction originating with Aristotle. In the ],<ref>] Bk 2 c. 7</ref> he says that the meaning of a made-up name can be known (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 what they called the ''quid nominis'', or the "whatness of the name", and the underlying nature common to all the things it names, which they called the ''quid rei'', or the "whatness of the thing".<ref>. Early modern philosophers like Locke used the corresponding English terms "nominal essence" and "real essence".</ref> The name "]", for example, is perfectly meaningful. It has a ''quid nominis'', but one could not know the real nature of hobbits, and so the ''quid rei'' of hobbits cannot be known. 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 a thing must have in order that the name apply to it. | ||
This leads to a corresponding distinction between ''nominal'' and ''real'' |
This leads to a corresponding distinction between ''nominal'' and ''real'' definitions. 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. | ||
This preoccupation with essence dissipated in much of modern philosophy. ] in particular is critical of attempts to elucidate the essence of a thing. ] described |
This preoccupation with essence dissipated in much of modern philosophy. ], in particular, is critical of attempts to elucidate the essence of a thing. ] described essence as "a hopelessly muddle-headed notion".<ref>''A History of Western Philosophy'', p. 210.</ref> | ||
More recently ] formalisation of ] semantics in ] led to a new approach to ]. 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 ]s. | More recently ] formalisation of ] semantics in ] led to a new approach to ]. Insofar as the essential properties of a thing are ''necessary'' to it, they are those things that it possesses in all possible worlds. Kripke refers to names used in this way as ]s. | ||
==Operational vs. theoretical definitions== | |||
==Genetic definition== | |||
A definition may also be classified as an ] or ]. | |||
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>]. </nowiki> 1962) in An appraisal of anthropology today. Edited by Sol Tax. University of Chicago Press 1953] | |||
</ref></blockquote> | |||
== |
==Terms with multiple definitions== | ||
A ], 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: | |||
#At least one thing is stated to be a member of the set being defined; this is sometimes called a "base set". | |||
#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 ]. | |||
#All other things are excluded from the set | |||
===Homonyms=== | |||
For instance, we could define ] as follows (after ]): | |||
{{main|Homonym}} | |||
#"0" is a natural number. | |||
A ] is, in the strict sense, one of a group of words that share the same spelling and pronunciation but have different meanings.<ref name="RHUD">, ''Random House Unabridged Dictionary'' at dictionary.com</ref> Thus homonyms are simultaneously ]s (words that share the same spelling, regardless of their pronunciation) ''and'' ]s (words that share the same pronunciation, regardless of their spelling). The state of being a homonym is called ''homonymy''. Examples of homonyms are the pair ''stalk'' (part of a plant) and ''stalk'' (follow/harass a person) and the pair ''left'' (past tense of leave) and ''left'' (opposite of right). A distinction is sometimes made between "true" homonyms, which are unrelated in origin, such as ''skate'' (glide on ice) and ''skate'' (the fish), and polysemous homonyms, or ], which have a shared origin, such as ''mouth'' (of a river) and ''mouth'' (of an animal).<ref>{{cite web |url=http://pandora.cii.wwu.edu/vajda/ling201/test3materials/semanticsHANDOUT.htm |title=Linguistics 201: Study Sheet for Semantics |publisher=Pandora.cii.wwu.edu |access-date=2013-04-23 |archive-url=https://web.archive.org/web/20130617090717/http://pandora.cii.wwu.edu/vajda/ling201/test3materials/semanticsHANDOUT.htm |archive-date=2013-06-17 |url-status=dead }}</ref><ref>, James R. Hurford and Brendan Heasley, Cambridge University Press, 1983</ref> | |||
#Each natural number has a distinct successor, such that: | |||
#*the successor of a natural number is also a natural number, and | |||
#*no natural number is succeeded by "0". | |||
#Nothing else is a natural number. | |||
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 ]. Although this sort of definition involves a form of ], it is not vicious, and the definition is quite successful. | |||
===Polysemes=== | |||
== Limitations of definition == | |||
{{main|Polysemy}} | |||
] is the capacity for a ] (such as a ], ], or ]) to have multiple meanings (that is, multiple ] or ]s and thus multiple ]), usually related by contiguity of ] within a ]. It is thus usually regarded as distinct from ], in which the multiple meanings of a word may be unconnected or unrelated. | |||
==In logic, mathematics and computing== | |||
Given that a ] such as ] 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 ], but leading to scepticism about meaning rather than knowledge</ref> A dictionary, for instance, insofar as it is a comprehensive list of ]s, must resort to ].<ref>Generally ] seek to avoid circularity wherever possible, but the definitions of words such as "the" and "a" use those words and are therefore circular. Lexicographer ]'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 ] 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>('''' in Philosophical Papers. Ed. ] and ]. Oxford: Oxford UP, 1961. 1979.)</ref><ref>In the game of ], players compete to find circularity in a dictionary.</ref> | |||
In mathematics, definitions are generally not used to describe existing terms, but to describe or characterize a concept.<ref>David Hunter (2010) Essentials of Discrete Mathematics. Jones & Bartlett Publishers, Section 14.1</ref> For naming the object of a definition mathematicians can use either a ] (this was mainly the case in the past) or words or phrases of the common language (this is generally the case in modern mathematics). The precise meaning of a term given by a mathematical definition is often different from the English definition of the word used,<ref>Kevin Houston (2009) How to Think Like a Mathematician: A Companion to Undergraduate Mathematics. Cambridge University Press, p. 104</ref> which can lead to confusion, particularly when the meanings are close. For example, a ] is not exactly the same thing in mathematics and in common language. In some case, the word used can be misleading; for example, a ] has nothing more (or less) real than an ]. Frequently, a definition uses a phrase built with common English words, which has no meaning outside mathematics, such as ] or ]. | |||
In first-order logic definitions are usually introduced using ] (so using a metalogic). On the other hand, ] are a kind of logic where the definitions are included as the feature of the formal system itself. | |||
Many philosophers have chosen instead to leave some terms undefined. The ] 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 ], unity and similar concepts.<ref>Joyce, G.H. ''Principles of Logic'', Chapter x</ref> ] supposes in '']''<ref>''Essay'', Bk III, c. 4</ref> that the names of simple concepts do not admit of any definition. More recently ] sought to develop a formal language based on ]. Other philosophers, notably ], rejected the need for any undefined simples. Wittgenstein pointed out in his '']'' that what counts as a "simple" in one circumstance might not do so in another.<ref> See especially '']'' 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." ], Part 1 §87, italics in original</ref> claiming instead that explanation of a term is only needed when we need to avoid misunderstanding. | |||
===Classification=== | |||
Locke and ] also argued that we cannot define ]. 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 ]</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 ] in part as a way of defining a proper name, the definition being given by a ] that "picks out" exactly one individual. ] pointed to difficulties with this approach, especially in relation to ], in his book ''Naming and Necessity''. | |||
Authors have used different terms to classify definitions used in formal languages like mathematics. ] classifies a definition as "stipulative" if it is intended to guide a specific discussion. A stipulative definition might be considered a temporary, working definition, and can only be disproved by showing a logical contradiction.<ref>{{cite web|url=https://www.sfu.ca/philosophy/swartz/definitions.htm#part5.1|title=Norman Swartz - Biography|work=sfu.ca}}</ref> In contrast, a "descriptive" definition can be shown to be "right" or "wrong" with reference to general usage. | |||
Swartz defines a '']'' as one that extends the descriptive dictionary definition (lexical definition) for a specific purpose by including additional criteria. A precising definition narrows the set of things that meet the definition. | |||
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 ]. For terms such as these it is not possible to state a definition; rather, one simply comes to understand the ''use'' of the term. | |||
] has identified '']'' as a form of stipulative definition which purports to state the "true" or "commonly accepted" meaning of a term, while in reality stipulating an altered use (perhaps as an argument for some specific belief). Stevenson has also noted that some definitions are "legal" or "coercive" – their object is to create or alter rights, duties, or crimes.<ref>Stevenson, C.L., ''Ethics and Language'', Connecticut 1944</ref> | |||
==See also== | |||
===Recursive definitions=== | |||
{{wiktionarypar|definition}} | |||
A ], 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: | |||
# At least one thing is stated to be a member of the set being defined; this is sometimes called a "base set". | |||
# 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 ]. | |||
# All other things are excluded from the set | |||
For instance, we could define a ] as follows (after ]): | |||
# "0" is a natural number. | |||
# Each natural number has a unique successor, such that: | |||
#* the successor of a natural number is also a natural number; | |||
#* distinct natural numbers have distinct successors; | |||
#* no natural number is succeeded by "0". | |||
# Nothing else is a natural number. | |||
So "0" will have exactly one successor, which for convenience can be called "1". In turn, "1" will have exactly one successor, which could be called "2", and so on. The second condition in the definition itself refers to natural numbers, and hence involves ]. Although this sort of definition involves a form of ], it is not ], and the definition has been quite successful. | |||
In the same way, we can define ] as follows: | |||
#A parent is an ancestor. | |||
#A parent of an ancestor is an ancestor. | |||
#Nothing else is an ancestor. | |||
Or simply: an ancestor is a parent or a parent of an ancestor. | |||
==In medicine== | |||
In ], ]s and other ] and ]s, definitions should as far as possible be: | |||
*simple and easy to understand,<ref name=McPherson1998>{{Cite journal | |||
| doi = 10.1542/peds.102.1.137 | |||
| last1 = McPherson | first1 = M. | |||
| last2 = Arango | first2 = P. | |||
| last3 = Fox | first3 = H. | |||
| last4 = Lauver | first4 = C. | |||
| last5 = McManus | first5 = M. | |||
| last6 = Newacheck | first6 = P. W. | |||
| last7 = Perrin | first7 = J. M. | |||
| last8 = Shonkoff | first8 = J. P. | |||
| last9 = Strickland | first9 = B. | |||
| title = A new definition of children with special health care needs | |||
| journal = Pediatrics | |||
| volume = 102 | |||
| issue = 1 Pt 1 | |||
| pages = 137–140 | |||
| year = 1998 | |||
| pmid = 9714637 | |||
| s2cid = 30160426 }}</ref> preferably even by the general public;<ref name=Morse1992>{{cite journal | last1 = Morse | first1 = R. M. | last2 = Flavin | first2 = D. K. | year = 1992 | title = The Definition of Alcoholism | journal = JAMA | volume = 268 | pmid = 1501306 | issue = 8 | pages = 1012–1014 | doi = 10.1001/jama.1992.03490080086030 }}</ref> | |||
*useful clinically<ref name=Morse1992/> or in related areas where the definition will be used;<ref name=McPherson1998/> | |||
*specific<ref name=McPherson1998/> (that is, by reading the definition only, it should ideally not be possible to refer to any other entity than that being defined); | |||
*measurable;<ref name=McPherson1998/> | |||
*a reflection of current scientific knowledge.<ref name=McPherson1998/><ref name=Morse1992/> | |||
==Problems== | |||
Certain rules have traditionally been given for definitions (in particular, genus-differentia definitions).<ref>Copi 1982 pp 165–169</ref><ref name="Joyce, Ch. X">Joyce, Ch. X</ref><ref>Joseph, Ch. V</ref><ref>Macagno & Walton 2014, Ch. III</ref> | |||
*A definition must set out the essential attributes of the thing defined. | |||
*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 would be a circular definition, a ''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. | |||
*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 nothing else (i.e. not include any things to which the defined term would not truly apply). | |||
*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. | |||
*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. For example, it appears difficult to define blindness in positive terms rather than as "the absence of sight in a creature that is normally sighted". | |||
===Fallacies of definition=== | |||
{{Main|Fallacies of definition}} | |||
===Limitations of definition=== | |||
Given that a ] such as ] contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon ]s. If every term of every ''definiens'' must itself be defined, "where at last should we stop?"<ref>Locke, ''Essay'', </ref><ref>This problem parallels the ], but leads to scepticism about meaning rather than knowledge.</ref> A dictionary, for instance, insofar as it is a comprehensive list of ]s, must resort to ].<ref>Generally ] seek to avoid circularity wherever possible, but the definitions of words such as "the" and "a" use those words and are therefore circular. Lexicographer ]'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 ] 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>('''' in Philosophical Papers. Ed. ] and ]. Oxford: Oxford UP, 1961. 1979.)</ref><ref>In the game of ], players compete to find circularity in a dictionary.</ref> | |||
Many philosophers have chosen instead to leave some terms undefined. The ] claimed that the highest genera (called the ten ''generalissima'') cannot be defined, since a higher genus cannot be assigned under which they may fall. Thus ], unity and similar concepts cannot be defined.<ref name="Joyce, Ch. X"/> ] supposes in '']''<ref>Locke, ''Essay'', Bk. III, Ch. iv</ref> that the names of simple concepts do not admit of any definition. More recently ] sought to develop a formal language based on ]. Other philosophers, notably ], rejected the need for any undefined simples. Wittgenstein pointed out in his '']'' that what counts as a "simple" in one circumstance might not do so in another.<ref>See especially '']'' 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." ], Part 1 §87, italics in original</ref> claiming instead that explanation of a term is only needed to avoid misunderstanding. | |||
Locke and ] also argued that ] cannot be defined. Names are learned 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 ]</ref> This is not possible when no one else is acquainted with the particular thing that has "fallen under our notice".<ref>Locke, ''Essay'', Bk. III, Ch. iii, 3</ref> Russell offered his ] in part as a way of defining a proper name, the definition being given by a ] that "picks out" exactly one individual. ] pointed to difficulties with this approach, especially in relation to ], in his book ''Naming and Necessity''. | |||
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 ]. For terms such as these it is not possible and indeed not necessary to state a definition; rather, one simply comes to understand the ''use'' of the term.{{efn|One learns inductively, from ], in the same way, as in the ].}} | |||
==See also== | |||
{{Portal|Linguistics|Philosophy|Mathematics}} | |||
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*{{cite book |last=Copi|first=Irving|title=Introduction to Logic |year=1982 |publisher=Macmillan |location=New York |isbn=0-02-977520-5}} | ||
*{{cite book |last=Joseph |first=Horace William Brindley |
*{{cite book |last=Joseph |first=Horace William Brindley |title=An Introduction to Logic, 2nd edition |year=1916 |publisher=Clarendon Press repr. Paper Tiger |isbn=1-889439-17-7 |url-access=registration |url=https://archive.org/details/introductiontolo00jose_301 }} | ||
*{{cite book |last=Joyce |first=George Hayward |
*{{cite book |last=Joyce |first=George Hayward |title=Principles of logic, 3d ed., new impression |year=1926 |publisher=Longmans, Green and co |location=London, New York}} | ||
*{{cite book |last=Locke |first=John |author-link=John Locke |title=An Essay Concerning Human Understanding |year=1690 |isbn=0-14-043482-8 |title-link=An Essay Concerning Human Understanding |publisher=National Geographic Books }} (full text: , ) | |||
*{{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 }} | |||
*{{cite book |last=McKean |first=Erin |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 |isbn=0-15-601209-X |url-access=registration |url=https://archive.org/details/verbatim00erin }} | |||
*{{cite book |last=Simpson |first=John |authorlink= |coauthors=Edmund Weiner |others= |title=], second edition (20 volumes) |year=1989 |publisher=Oxford University Press |location= |id=ISBN 0-19-861186-2 }} | |||
*{{cite book|last1=Macagno|first1=Fabrizio|last2=Walton|first2=Douglas|title=Emotive Language in Argumentation|date=2014|publisher=Cambridge University Press|location=New York}} | |||
*{{cite book |last=Robinson |first=Richard |title=Definition|year=1954 |publisher=At The Clarendon Press |location= Oxford|isbn= 978-0-19-824160-7|url= https://books.google.com/books?id=WVt8TfDR-YAC&q=richard%20robinson%20definition&pg=PP1}} | |||
*{{cite book |last=Simpson |first=John |author2=Edmund Weiner |title=Oxford English Dictionary, second edition (20 volumes) |year=1989 |publisher=Oxford University Press |isbn=0-19-861186-2}} | |||
*{{cite book | *{{cite book | ||
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| title = Philosophical Investigations | | title = Philosophical Investigations | ||
| publisher = Blackwell Publishing | | publisher = Blackwell Publishing | ||
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*, ] Gupta, Anil (2008) | |||
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*Guy Longworth (ca. 2008) in: K. Brown (ed.): ''Elsevier Encyclopedia of Language and Linguistics'', ]. | |||
*, a very short introduction by Garth Kemerling (2001). | |||
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Latest revision as of 17:59, 14 October 2024
Statement that attaches a meaning to a term For the definition of another word, see Wiktionary. For other uses of the word "definition" itself, see Definition (disambiguation).
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what the mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed.
Basic terminology
"Definiens" redirects here. For the Definiens company, see Cognition Network Technology.In modern usage, a definition is something, typically expressed in words, that attaches a meaning to a word or group of words. The word or group of words that is to be defined is called the definiendum, and the word, group of words, or action that defines it is called the definiens. For example, in the definition "An elephant is a large gray animal native to Asia and Africa", the word "elephant" is the definiendum, and everything after the word "is" is the definiens.
The definiens is not the meaning of the word defined, but is instead something that conveys the same meaning as that word.
There are many sub-types of definitions, often specific to a given field of knowledge or study. These include, lexical definitions, or the common dictionary definitions of words already in a language; demonstrative definitions, which define something by pointing to an example of it ("This," , "is an Asian elephant."); and precising definitions, which reduce the vagueness of a word, typically in some special sense ("'Large', among female Asian elephants, is any individual weighing over 5,500 pounds.").
Intensional definitions vs extensional definitions
Main articles: Intension and Extension (semantics)An intensional definition, also called a connotative definition, specifies the necessary and sufficient conditions for a thing to be 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.
An extensional definition, also called a denotative definition, of a concept or term specifies its extension. It is a list naming every object that is a member of a specific set.
Thus, the "seven deadly sins" can be defined intensionally as those singled out by Pope Gregory I as particularly destructive of the life of grace and charity within a person, thus creating the threat of eternal damnation. An extensional definition, on the other hand, would be the list of wrath, greed, sloth, pride, lust, envy, and gluttony. In contrast, while an intensional definition of "prime minister" might be "the most senior minister of a cabinet in the executive branch of parliamentary government", an extensional definition is not possible since it is not known who the future prime ministers will be (even though all prime ministers from the past and present can be listed).
Classes of intensional definitions
Main article: Genus–differentia definitionA genus–differentia definition is a type of intensional definition that takes a large category (the genus) and narrows it down to a smaller category by a distinguishing characteristic (i.e. the differentia).
More formally, a genus–differentia definition consists of:
- a genus (or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus.
- the differentia: The portion of the new definition that is not provided by the genus.
For example, consider the following genus–differentia definitions:
- a triangle: A plane figure that has three straight bounding sides.
- a quadrilateral: A plane figure that has four straight bounding sides.
Those definitions can be expressed as a genus ("a plane figure") and two differentiae ("that has three straight bounding sides" and "that has four straight bounding sides", respectively).
It is also possible to have two different genus–differentia definitions that describe the same term, especially when the term describes the overlap of two large categories. For instance, both of these genus–differentia definitions of "square" are equally acceptable:
Thus, a "square" is a member of both genera (the plural of genus): the genus "rectangle" and the genus "rhombus".
Classes of extensional definitions
One important form of the 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. For example, one can explain who Alice (an individual) is, by pointing her out to another; or what a rabbit (a class) is, by pointing at several and expecting another to understand. The process of ostensive definition itself was critically appraised by Ludwig Wittgenstein.
An enumerative definition of a concept or a term is an 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 small sets).
Divisio and partitio
Divisio and partitio are classical terms for definitions. A partitio is simply an intensional definition. A divisio is not an extensional definition, but an exhaustive list of subsets of a set, in the sense that every member of the "divided" set is a member of one of the subsets. An extreme form of divisio lists all sets whose only member is a member of the "divided" set. The difference between this and an extensional definition is that extensional definitions list members, and not subsets.
Nominal definitions vs real definitions
Main article: EssenceIn 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.
The idea that a definition should state the essence of a thing led to the distinction between nominal and real essence—a distinction originating with Aristotle. In the Posterior Analytics, he says that the meaning of a made-up name can be known (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 what they called the quid nominis, or the "whatness of the name", and the underlying nature common to all the things it names, which they called the quid rei, or the "whatness of the thing". The name "hobbit", for example, is perfectly meaningful. It has a quid nominis, but one could not know the real nature of hobbits, and so the quid rei of hobbits cannot be known. 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 a thing must have in order that the name apply to it.
This leads to a corresponding distinction between nominal and real definitions. 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.
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. Russell described essence as "a hopelessly muddle-headed notion".
More recently 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 that it possesses in all possible worlds. Kripke refers to names used in this way as rigid designators.
Operational vs. theoretical definitions
A definition may also be classified as an operational definition or theoretical definition.
Terms with multiple definitions
Homonyms
Main article: HomonymA homonym is, in the strict sense, one of a group of words that share the same spelling and pronunciation but have different meanings. Thus homonyms are simultaneously homographs (words that share the same spelling, regardless of their pronunciation) and homophones (words that share the same pronunciation, regardless of their spelling). The state of being a homonym is called homonymy. Examples of homonyms are the pair stalk (part of a plant) and stalk (follow/harass a person) and the pair left (past tense of leave) and left (opposite of right). A distinction is sometimes made between "true" homonyms, which are unrelated in origin, such as skate (glide on ice) and skate (the fish), and polysemous homonyms, or polysemes, which have a shared origin, such as mouth (of a river) and mouth (of an animal).
Polysemes
Main article: PolysemyPolysemy is the capacity for a sign (such as a word, phrase, or symbol) to have multiple meanings (that is, multiple semes or sememes and thus multiple senses), usually related by contiguity of meaning within a semantic field. It is thus usually regarded as distinct from homonymy, in which the multiple meanings of a word may be unconnected or unrelated.
In logic, mathematics and computing
In mathematics, definitions are generally not used to describe existing terms, but to describe or characterize a concept. For naming the object of a definition mathematicians can use either a neologism (this was mainly the case in the past) or words or phrases of the common language (this is generally the case in modern mathematics). The precise meaning of a term given by a mathematical definition is often different from the English definition of the word used, which can lead to confusion, particularly when the meanings are close. For example, a set is not exactly the same thing in mathematics and in common language. In some case, the word used can be misleading; for example, a real number has nothing more (or less) real than an imaginary number. Frequently, a definition uses a phrase built with common English words, which has no meaning outside mathematics, such as primitive group or irreducible variety.
In first-order logic definitions are usually introduced using extension by definition (so using a metalogic). On the other hand, lambda-calculi are a kind of logic where the definitions are included as the feature of the formal system itself.
Classification
Authors have used different terms to classify definitions used in formal languages like mathematics. Norman Swartz classifies a definition as "stipulative" if it is intended to guide a specific discussion. A stipulative definition might be considered a temporary, working definition, and can only be disproved by showing a logical contradiction. In contrast, a "descriptive" definition can be shown to be "right" or "wrong" with reference to general usage.
Swartz defines a precising definition as one that extends the descriptive dictionary definition (lexical definition) for a specific purpose by including additional criteria. A precising definition narrows the set of things that meet the definition.
C.L. Stevenson has identified persuasive definition as a form of stipulative definition which purports to state the "true" or "commonly accepted" meaning of a term, while in reality stipulating an altered use (perhaps as an argument for some specific belief). Stevenson has also noted that some definitions are "legal" or "coercive" – their object is to create or alter rights, duties, or crimes.
Recursive definitions
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:
- At least one thing is stated to be a member of the set being defined; this is sometimes called a "base set".
- 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 recursive.
- All other things are excluded from the set
For instance, we could define a natural number as follows (after Peano):
- "0" is a natural number.
- Each natural number has a unique successor, such that:
- the successor of a natural number is also a natural number;
- distinct natural numbers have distinct successors;
- no natural number is succeeded by "0".
- Nothing else is a natural number.
So "0" will have exactly one successor, which for convenience can be called "1". In turn, "1" will have exactly one successor, which could be called "2", and so on. 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 circularity, it is not vicious, and the definition has been quite successful.
In the same way, we can define ancestor as follows:
- A parent is an ancestor.
- A parent of an ancestor is an ancestor.
- Nothing else is an ancestor.
Or simply: an ancestor is a parent or a parent of an ancestor.
In medicine
In medical dictionaries, guidelines and other consensus statements and classifications, definitions should as far as possible be:
- simple and easy to understand, preferably even by the general public;
- useful clinically or in related areas where the definition will be used;
- specific (that is, by reading the definition only, it should ideally not be possible to refer to any other entity than that being defined);
- measurable;
- a reflection of current scientific knowledge.
Problems
Certain rules have traditionally been given for definitions (in particular, genus-differentia definitions).
- A definition must set out the essential attributes of the thing defined.
- 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 would be a circular definition, a 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.
- 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 nothing else (i.e. not include any things to which the defined term would not truly apply).
- 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.
- 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. For example, it appears difficult to define blindness in positive terms rather than as "the absence of sight in a creature that is normally sighted".
Fallacies of definition
Main article: Fallacies of definitionLimitations 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 rely upon primitive notions. If every term of every definiens must itself be defined, "where at last should we stop?" A dictionary, for instance, insofar as it is a comprehensive list of lexical definitions, must resort to circularity.
Many philosophers have chosen instead to leave some terms undefined. The scholastic philosophers claimed that the highest genera (called the ten generalissima) cannot be defined, since a higher genus cannot be assigned under which they may fall. Thus being, unity and similar concepts cannot be defined. Locke supposes in An Essay Concerning Human Understanding 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 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. 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", claiming instead that explanation of a term is only needed to avoid misunderstanding.
Locke and Mill also argued that individuals cannot be defined. Names are learned by connecting an idea with a sound, so that speaker and hearer have the same idea when the same word is used. This is not possible when no one else is acquainted with the particular thing that has "fallen under our notice". 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.
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. 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 and indeed not necessary to state a definition; rather, one simply comes to understand the use of the term.
See also
- Analytic proposition
- Circular definition
- Definable set
- Definitionism
- Denotation
- Extensional definition
- Fallacies of definition
- Indeterminacy
- Intensional definition
- Lexical definition
- Logic programming
- Operational definition
- Ostensive definition
- Ramsey–Lewis method
- Semantics
- Synthetic proposition
- Theoretical definition
Notes
- Terms with the same pronunciation and spelling but unrelated meanings are called homonyms, while terms with the same spelling and pronunciation and related meanings are called polysemes.
- One learns inductively, from ostensive definition, in the same way, as in the Ramsey–Lewis method.
References
- Bickenbach, Jerome E., and Jacqueline M. Davies. Good reasons for better arguments: An introduction to the skills and values of critical thinking. Broadview Press, 1996. p. 49
- "Definition of definition | Dictionary.com". www.dictionary.com. Retrieved 2019-11-28.
- ^ Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on.
- Dooly, Melinda. Semantics and Pragmatics of English: Teaching English as a Foreign Language. Univ. Autònoma de Barcelona, 2006. p.48 and on
- Richard J. Rossi (2011) Theorems, Corollaries, Lemmas, and Methods of Proof. John Wiley & Sons p.4
- ^ "DEFINITIONS". beisecker.faculty.unlv.edu. Retrieved 2019-11-28.
- ^ Hurley, Patrick J. (2006). "Language: Meaning and Definition". A Concise Introduction to Logic (9 ed.). Wadsworth. pp. 86–91.
- Bussler, Christoph, and Dieter Fensel, eds. Artificial Intelligence: Methodology, Systems and Applications: 11th International Conference, AIMSA 2004: Proceedings. Springer-Verlag, 2004. p.6
- Philosophical investigations, Part 1 §27–34
- Katerina Ierodiakonou, "The Stoic Division of Philosophy", in Phronesis: A Journal for Ancient Philosophy, Volume 38, Number 1, 1993, pp. 57–74.
- Posterior Analytics, Bk 1 c. 4
- Posterior Analytics Bk 2 c. 7
- . Early modern philosophers like Locke used the corresponding English terms "nominal essence" and "real essence".
- A History of Western Philosophy, p. 210.
- homonym, Random House Unabridged Dictionary at dictionary.com
- "Linguistics 201: Study Sheet for Semantics". Pandora.cii.wwu.edu. Archived from the original on 2013-06-17. Retrieved 2013-04-23.
- Semantics: a coursebook, p. 123, James R. Hurford and Brendan Heasley, Cambridge University Press, 1983
- David Hunter (2010) Essentials of Discrete Mathematics. Jones & Bartlett Publishers, Section 14.1
- Kevin Houston (2009) How to Think Like a Mathematician: A Companion to Undergraduate Mathematics. Cambridge University Press, p. 104
- "Norman Swartz - Biography". sfu.ca.
- Stevenson, C.L., Ethics and Language, Connecticut 1944
- ^ McPherson, M.; Arango, P.; Fox, H.; Lauver, C.; McManus, M.; Newacheck, P. W.; Perrin, J. M.; Shonkoff, J. P.; Strickland, B. (1998). "A new definition of children with special health care needs". Pediatrics. 102 (1 Pt 1): 137–140. doi:10.1542/peds.102.1.137. PMID 9714637. S2CID 30160426.
- ^ Morse, R. M.; Flavin, D. K. (1992). "The Definition of Alcoholism". JAMA. 268 (8): 1012–1014. doi:10.1001/jama.1992.03490080086030. PMID 1501306.
- Copi 1982 pp 165–169
- ^ Joyce, Ch. X
- Joseph, Ch. V
- Macagno & Walton 2014, Ch. III
- Locke, Essay, Bk. III, Ch. iv, 5
- This problem parallels the diallelus, but leads to scepticism about meaning rather than knowledge.
- Generally lexicographers seek to avoid circularity wherever possible, but the definitions of words such as "the" and "a" use those words and are therefore circular. Lexicographer Sidney I. Landau's essay "Sexual Intercourse in American College Dictionaries" provides other examples of circularity in dictionary definitions. (McKean, p. 73–77)
- 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.
(A plea for excuses in Philosophical Papers. Ed. J. O. Urmson and G. J. Warnock. Oxford: Oxford UP, 1961. 1979.) - In the game of Vish, players compete to find circularity in a dictionary.
- Locke, Essay, Bk. III, Ch. iv
- See especially Philosophical Investigations Part 1 §48
- 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
- This theory of meaning is one of the targets of the private language argument
- Locke, Essay, Bk. III, Ch. iii, 3
- Philosophical Investigations
- Copi, Irving (1982). Introduction to Logic. New York: Macmillan. ISBN 0-02-977520-5.
- Joseph, Horace William Brindley (1916). An Introduction to Logic, 2nd edition. Clarendon Press repr. Paper Tiger. ISBN 1-889439-17-7. (full text of 1st ed. (1906))
- Joyce, George Hayward (1926). Principles of logic, 3d ed., new impression. London, New York: Longmans, Green and co. (worldcat) (full text of 2nd ed. (1916))
- Locke, John (1690). An Essay Concerning Human Understanding. National Geographic Books. ISBN 0-14-043482-8. (full text: vol 1, vol 2)
- McKean, Erin (2001). Verbatim: From the bawdy to the sublime, the best writing on language for word lovers, grammar mavens, and armchair linguists. Harvest Books. ISBN 0-15-601209-X.
- Macagno, Fabrizio; Walton, Douglas (2014). Emotive Language in Argumentation. New York: Cambridge University Press.
- Robinson, Richard (1954). Definition. Oxford: At The Clarendon Press. ISBN 978-0-19-824160-7.
- Simpson, John; Edmund Weiner (1989). Oxford English Dictionary, second edition (20 volumes). Oxford University Press. ISBN 0-19-861186-2.
- Wittgenstein, Ludwig (1953). Philosophical Investigations. Blackwell Publishing. ISBN 0-631-23127-7.
External links
- Definitions, Stanford Encyclopedia of Philosophy Gupta, Anil (2008)
- Definitions, Dictionaries, and Meanings, Norman Swartz 1997
- Guy Longworth (ca. 2008) "Definitions: Uses and Varieties of" in: K. Brown (ed.): Elsevier Encyclopedia of Language and Linguistics, Elsevier.
- Definition and Meaning, a very short introduction by Garth Kemerling (2001).
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