View source for Philosophy:Definition

{{short description|Statement that attaches a meaning to a term}}

[[File:Blacks-Law-Dictionary.jpg|thumb|A definition states the meaning of a word using other words. This is sometimes challenging. Common dictionaries contain lexical descriptive definitions, but there are various types of definition – all with different purposes and focuses.]]

A '''definition''' is a statement of the meaning of a term (a word, [[Social:Phrase|phrase]], or other set of [[Symbol|symbol]]s).<ref>Bickenbach, Jerome E., and Jacqueline M. Davies. [https://books.google.com/books?id=mAjMaRr9d5gC&q=definition Good reasons for better arguments: An introduction to the skills and values of critical thinking]. 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: intensional definitions (which try to give the sense of a term), and extensional definitions (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 [[Philosophy:Ostensive definition|ostensive definition]]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. [https://books.google.com/books?id=C5TdV8LgtaQC Semantics and Pragmatics of English: Teaching English as a Foreign Language]. Univ. Autònoma de Barcelona, 2006. p.48 and on</ref>{{efn|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.}}

In [[Mathematics|mathematics]], a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not. Definitions and axioms 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>

==Basic terminology==

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>

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"/>

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," [said while pointing to a large grey animal], "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"/>

==Intensional definitions vs extensional definitions==
{{Main|Philosophy:Intension|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 (mathematics)|set]].<ref name=Lyons/> 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 (semantics)|extension]]''. It is a list naming every [[Philosophy:Object|object]] that is a member of a specific [[Set (mathematics)|set]].<ref name=Lyons/>

Thus, the "[[Religion:Seven deadly sins|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 "[[Social:Prime minister|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|Genus–differentia definition}}
A ''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'').<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 [[Biology:Genus|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.<ref name=":0" />

For example, consider the following genus–differentia definitions:
* ''a [[Triangle|triangle]]'': A plane figure that has three straight bounding sides.
* ''a [[Quadrilateral|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:
* ''a square'': a [[Rectangle|rectangle]] that is a [[Rhombus|rhombus]].
* ''a square'': a [[Rhombus|rhombus]] that is a [[Rectangle|rectangle]].

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 ''[[Philosophy:Ostensive definition|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 [[Biography:Ludwig Wittgenstein|Ludwig Wittgenstein]].<ref>''Philosophical investigations'', Part 1 §27–34</ref>

An ''[[Philosophy:Enumerative definition|enumerative definition]]'' of a concept or a term is an ''extensional definition'' that gives an explicit and exhaustive listing of all the [[Philosophy:Object|objects]] that fall under the concept or term in question. Enumerative definitions are only possible for finite sets (and in fact only practical for relatively small sets).

===''Divisio'' and ''partitio''===
''Divisio'' and ''partitio'' are [[Social:Classics|classical]] terms for definitions. A ''partitio'' is simply an intensional definition. A ''divisio'' is not an extensional definition, but an exhaustive list of [[Subset|subset]]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|Philosophy:Essence}}
In classical thought, a definition was taken to be a statement of the essence of a thing. [[Biography:Aristotle|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>[[Philosophy:Posterior Analytics|Posterior Analytics]], 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'' essence—a distinction originating with Aristotle. In the [[Philosophy:Posterior Analytics|Posterior Analytics]],<ref>[[Philosophy:Posterior Analytics|Posterior Analytics]] 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 "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. [[Philosophy:Analytic philosophy|Analytic philosophy]], in particular, is critical of attempts to elucidate the essence of a thing. [[Biography:Bertrand Russell|Russell]] described essence as "a hopelessly muddle-headed notion".<ref>''A History of Western Philosophy'', p. 210.</ref>

More recently [[Kripke semantics|Kripke's]] formalisation of [[Philosophy:Possible world|possible world]] semantics in [[Modal logic|modal logic]] led to a new approach to [[Philosophy:Essentialism|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 [[Philosophy:Rigid designator|rigid designator]]s.

==Operational vs. theoretical definitions==
A definition may also be classified as an [[Philosophy:Operational definition|operational definition]] or [[Theoretical definition|theoretical definition]].

==Terms with multiple definitions==

===Homonyms===
A homonym 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">[http://dictionary.reference.com/browse/homonym homonym], ''Random House Unabridged Dictionary'' at dictionary.com</ref>  Thus homonyms are simultaneously homographs (words that share the same spelling, regardless of their pronunciation) ''and'' [[Philosophy:Homophone|homophone]]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 [[Philosophy:Polysemy|polysemes]], 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>[https://books.google.com/books?id=AefSOW9MW5UC&pg=PA123 Semantics: a coursebook, p. 123], James R. Hurford and Brendan Heasley, Cambridge University Press, 1983</ref>

===Polysemes===
{{main|Philosophy:Polysemy}}
[[Philosophy:Polysemy|Polysemy]]  is the capacity for a sign (such as a word, [[Social:Phrase|phrase]], or [[Symbol|symbol]]) to have multiple meanings (that is, multiple semes or sememes and thus multiple [[Philosophy:Word sense|senses]]), usually related by contiguity of [[Philosophy:Meaning (linguistics)|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 and mathematics==
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 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,<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 [[Set (mathematics)|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|real number]] has nothing more (or less) real than an [[Imaginary number|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|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.<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 ''[[Philosophy:Precising definition|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.

[[Biography:Charles Stevenson (philosopher)|C.L. Stevenson]] has identified ''[[Philosophy:Persuasive definition|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"&nbsp;– their object is to create or alter rights, duties, or crimes.<ref>Stevenson, C.L., ''Ethics and Language'', Connecticut 1944</ref>

===Recursive definitions===
A [[Recursive definition|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 [[Recursion|recursive]].
# All other things are excluded from the set

For instance, we could define a [[Natural number|natural number]] as follows (after [[Peano axioms|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|self-reference]]. Although this sort of definition involves a form of [[Philosophy:Circular definition|circularity]], it is not [[Vicious circle principle|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, [[Medicine:Medical guideline|guideline]]s and other [[Medicine:Medical consensus|consensus statements]] and [[Medicine:Medical classification|classification]]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|Philosophy:Fallacies of definition}}

===Limitations of definition===
Given that a [[Philosophy:Natural language|natural language]] such as [[Social:English language|English]] contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon [[Primitive notion|primitive notion]]s. If every term of every ''definiens'' must itself be defined, "where at last should we stop?"<ref>Locke, ''Essay'', [https://books.google.com/books?id=0OoNAAAAYAAJ&dq=%22where+at+last+should+we+stop%22+inauthor:locke&pg=PA33 Bk. III, Ch. iv, 5]</ref><ref>This problem parallels the diallelus, but leads to scepticism about meaning rather than knowledge.</ref> A dictionary, for instance, insofar as it is a comprehensive list of [[Philosophy:Lexical definition|lexical definition]]s, must resort to circularity.<ref>Generally [[Social: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 [[Biography:J. L. Austin|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 [[Biography:Geoffrey Warnock|G. J. Warnock]]. Oxford: Oxford UP, 1961. 1979.)</ref><ref>In the game of [[Philosophy:Vish (game)|Vish]], players compete to find circularity in a dictionary.</ref>

Many philosophers have chosen instead to leave some terms undefined. The [[Philosophy:Scholasticism|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 [[Philosophy:Being|being]], unity and similar concepts cannot be defined.<ref name="Joyce, Ch. X"/> [[Biography:John Locke|Locke]] supposes in ''[[Philosophy:An Essay Concerning Human Understanding|An Essay Concerning Human Understanding]]''<ref>Locke, ''Essay'', Bk. III, Ch. iv</ref> that the names of simple concepts do not admit of any definition. More recently [[Biography:Bertrand Russell|Bertrand Russell]] sought to develop a formal language based on [[Philosophy:Logical atomism|logical atoms]]. Other philosophers, notably [[Biography:Ludwig Wittgenstein|Wittgenstein]], rejected the need for any undefined simples. Wittgenstein pointed out in his ''[[Philosophy:Philosophical Investigations|Philosophical Investigations]]'' that what counts as a "simple" in one circumstance might not do so in another.<ref>See especially ''[[Philosophy:Philosophical Investigations|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&nbsp;– unless ''we'' require it to prevent a misunderstanding. One might say: an explanation serves to remove or to avert a misunderstanding&nbsp;– one, that is, that would occur but for the explanation; not every one I can imagine." [[Philosophy:Philosophical Investigations|Philosophical Investigations]], Part 1 §87, italics in original</ref> claiming instead that explanation of a term is only needed to avoid misunderstanding.

Locke and [[Biography:John Stuart Mill|Mill]] also argued that [[Philosophy:Principle of individuation|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.<ref>This theory of meaning is one of the targets of the [[Philosophy:Private language argument|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>Locke, ''Essay'', Bk. III, Ch. iii, 3</ref> Russell offered his [[Philosophy:Theory of descriptions|theory of descriptions]] in part as a way of defining a proper name, the definition being given by a [[Philosophy:Definite description|definite description]] that "picks out" exactly one individual. [[Biography:Saul Kripke|Saul Kripke]] pointed to difficulties with this approach, especially in relation to [[Modal logic|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.<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 and indeed not necessary to state a definition; rather, one simply comes to understand the ''use'' of the term.{{efn|Note that one learns inductively, from [[Philosophy:Ostensive definition|ostensive definition]], in the same way, as in the [[Philosophy:Ramsey–Lewis method|Ramsey–Lewis method]].}}

==See also==
{{div col|colwidth=20em|small=yes}}
*Analytic proposition
*[[Philosophy:Circular definition|Circular definition]]
*[[Definable set]]
*[[Definitionism]]
*Extensional definition
*[[Philosophy:Fallacies of definition|Fallacies of definition]]
*Indeterminacy
*Intensional definition
*[[Philosophy:Lexical definition|Lexical definition]]
*[[Philosophy:Operational definition|Operational definition]]
*[[Philosophy:Ostensive definition|Ostensive definition]]
*[[Philosophy:Ramsey–Lewis method|Ramsey–Lewis method]]
*[[Philosophy:Semantics|Semantics]]
*Synthetic proposition
*[[Theoretical definition]]
{{div col end}}

==Notes==
{{notelist}}

==References==
{{Reflist}}

{{refbegin}}
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*{{cite book |last= |first= |others= |title= |publisher= |location=  }}
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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 |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 }} [https://archive.org/details/anintroductiont00josegoog (full text of 1st ed. (1906))]
*{{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}} [http://www.worldcat.org/oclc/220674509 (worldcat)] [https://archive.org/details/principleslogic00joycgoog (full text of 2nd ed. (1916))]
*{{cite book |last=Locke |first=John |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: [https://books.google.com/books?id=2qV-5lIBYfIC vol 1], [https://books.google.com/books?id=0OoNAAAAYAAJ vol 2])
*{{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|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
  | last = Wittgenstein
  | first = Ludwig
  | title = Philosophical Investigations
  | publisher = Blackwell Publishing
  | year = 1953
  | isbn =  0-631-23127-7| title-link = Philosophical Investigations
 }}
{{refend}}

==External links==
*[http://plato.stanford.edu/entries/definitions/ Definitions], [[Stanford Encyclopedia of Philosophy]] Gupta, Anil (2008)
*[https://www.sfu.ca/philosophy/swartz/definitions.htm Definitions, Dictionaries, and Meanings, Norman Swartz 1997]
*Guy Longworth (ca. 2008) [https://warwick.ac.uk/fac/soc/philosophy/people/longworth/definitions.pdf "Definitions: Uses and Varieties of"]. = in: K. Brown (ed.): ''Elsevier Encyclopedia of Language and Linguistics'', [[Company:Elsevier|Elsevier]].
*[http://www.philosophypages.com/lg/e05.htm Definition and Meaning], a very short introduction by Garth Kemerling (2001).

{{Defining}}
{{logic}}
{{Aristotelian logic}}

[[Category:Definition| ]]
[[Category:Philosophical logic]]
[[Category:Philosophy of language]]
[[Category:Linguistics terminology]]
[[Category:Mathematical terminology]]
[[Category:Concepts in logic]]
[[Category:Meaning (philosophy of language)]]

{{Sourceattribution|Definition}}