HOME

TheInfoList



OR:

A definition is a statement of the meaning of a term (a
word A word is a basic element of language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, ...
,
phrase In syntax and grammar, a phrase is a group of words or singular word acting as a grammatical unit. For instance, the English language, English expression "the very happy squirrel" is a noun phrase which contains the adjective phrase "very happy". ...
, or other set of
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different ...
s). 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).Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on. Another important category of definitions is the class of
ostensive definition An ostensive definition conveys the meaning of a term by pointing out examples. This type of definition 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 la ...
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. In
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 An axiom, postulate, or assumption is a statement (logic), statement that is taken to be truth, true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that whi ...
form the basis on which all of modern mathematics is to be constructed.


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''. 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, among many others, 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," aid 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."'').


Intensional definitions vs extensional definitions

An '' intensional definition'', also called a ''connotative'' definition, specifies the
necessary and sufficient conditions In logic and mathematics, necessity and sufficiency are terms used to describe a material conditional, conditional or implicational relationship between two Statement (logic), statements. For example, in the Conditional sentence, conditional stat ...
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 Object may refer to: General meanings * Object (philosophy) An object is a philosophy, philosophical term often used in contrast to the term ''Subject (philosophy), subject''. A subject is an observer and an object is a thing observed. For mo ...
that is a member of a specific set. Thus, the "
seven deadly sins The seven deadly sins, also known as the capital vices or cardinal sins, is a grouping and classification of vices within Christian teachings. Although they are not directly mentioned in the Bible, there are parallels with the seven things ...
" can be defined ''intensionally'' as those singled out by
Pope Gregory I Pope Gregory I ( la, Gregorius I; – 12 March 604), commonly known as Saint Gregory the Great, was the bishop of Rome from 3 September 590 to his death. He is known for instigating the first recorded large-scale mission from Rome, the Gregoria ...
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 A prime minister, premier or chief of cabinet is the head of the Cabinet (government), cabinet and the leader of the Minister (government), ministers in the Executive (government), executive branch of government, often in a parliamentary syst ...
" 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

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). More formally, a genus–differentia definition consists of: # a
genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In the hierarchy of biological classification, genus com ...
(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 triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...
'': A plane figure that has three straight bounding sides. * ''a
quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...
'': 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 In Euclidean geometry, Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a par ...
that is a
rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...
. * ''a square'': a
rhombus In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...
that is a
rectangle In Euclidean geometry, Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a par ...
. 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 An ostensive definition conveys the meaning of a term by pointing out examples. This type of definition 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 la ...
''. 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 Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrians, Austrian-British people, British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy o ...
. 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 in fact only practical for relatively 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
subset In mathematics, Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are ...
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''.


Nominal definitions vs real definitions

In classical thought, a definition was taken to be a statement of the essence of a thing.
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...
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 The ''Posterior Analytics'' ( grc-gre, Ἀναλυτικὰ Ὕστερα; la, Analytica Posteriora) is a text from Aristotle's ''Organon'' that deals with Demonstration (teaching), demonstration, definition, and scientific knowledge. The demon ...
, 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 Analytic philosophy is a Academic discipline, branch and Philosophical tradition, tradition of philosophy using philosophical analysis, analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 2 ...
, 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 A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional logic, intensional and mod ...
semantics in
modal logic Modal logic is a collection of formal systems developed to represent statements about Modality (natural language), necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and Formal semantics (natural ...
led to a new approach to
essentialism Essentialism is the view that objects have a set of attributes that are necessary to their Identity (philosophy), identity. In early Western thought, Platonic idealism, Plato's idealism held that all things have such an "essence"—an Theory of F ...
. 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 designator In modal logic and the philosophy of language, a term is said to be a rigid designator or absolute substantial term when it designates (picks out, denotes, refers to) the same thing in ''all possible worlds'' in which that thing exists. A designato ...
s.


Operational vs. theoretical definitions

A definition may also be classified as an
operational definition An operational definition specifies concrete, replicable procedures designed to represent a construct. In the words of American psychologist S.S. Stevens (1935), "An operation is the performance which we execute in order to make known a concept." F ...
or
theoretical definition A theoretical definition defines a term in an academic discipline, functioning as a proposal to see a phenomenon in a certain way. A theoretical definition is a proposed way of thinking about potentially related events. Theoretical definitions cont ...
.


Terms with multiple definitions


Homonyms

A
homonym In linguistics, homonyms are words which are homographs (words that share the same spelling, regardless of pronunciation), or homophones (equivocal words, that share the same pronunciation, regardless of spelling), or both. Using this definition, ...
is, in the strict sense, one of a group of words that share the same spelling and pronunciation but have different meanings.homonym
''Random House Unabridged Dictionary'' at dictionary.com
Thus homonyms are simultaneously
homograph A homograph (from the el, ὁμός, ''homós'', "same" and γράφω, ''gráphō'', "write") is a word that shares the same written form as another word but has a different meaning. However, some dictionaries insist that the words must also ...
s (words that share the same spelling, regardless of their pronunciation) ''and''
homophone A homophone () is a word that is Pronunciation, pronounced the same (to varying extent) as another word but differs in meaning. A ''homophone'' may also differ in spelling. The two words may be Spelling, spelled the same, for example ''rose'' ( ...
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 polysemes, which have a shared origin, such as ''mouth'' (of a river) and ''mouth'' (of an animal).


Polysemes

Polysemy Polysemy ( or ; ) is the capacity for a Sign (semiotics), sign (e.g. a symbol, a morpheme, a word, or a phrase) to have multiple related meanings. For example, a word can have several word senses. Polysemy is distinct from ''monosemy'', where a ...
is the capacity for a
sign A sign is an Physical object, object, quality (philosophy), quality, event, or Non-physical entity, entity whose presence or occurrence indicates the probable presence or occurrence of something else. A natural sign bears a causal relation to ...
(such as a
word A word is a basic element of language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, ...
,
phrase In syntax and grammar, a phrase is a group of words or singular word acting as a grammatical unit. For instance, the English language, English expression "the very happy squirrel" is a noun phrase which contains the adjective phrase "very happy". ...
, or
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different ...
) to have multiple meanings (that is, multiple semes or
sememe __NOTOC__ A sememe () is a semantic language unit of meaning, analogous to a morpheme. The concept is relevant in Structural linguistics, structural semiotics. A seme is a proposed unit of transmitted or intended meaning; it is atomic or indivisib ...
s and thus multiple
senses A sense is a biological system A biological system is a complex biological network, network which connects several biologically relevant entities. Biological organization spans several scales and are determined based different structures dep ...
), usually related by contiguity of meaning within a
semantic field In linguistics, a semantic field is a lexical set of words grouped semantics, semantically (by Semantics, meaning) that refers to a specific subject.Howard Jackson, Etienne Zé Amvela, ''Words, Meaning, and Vocabulary'', Continuum, 2000, p14. The ...
. It is thus usually regarded as distinct from
homonymy In linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and ...
, 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. For naming the object of a definition mathematicians can use either a
neologism A neologism from Ancient Greek, Greek νέο- ''néo''(="new") and λόγος /''lógos'' meaning "speech, utterance"is a relatively recent or isolated term, word, or phrase that may be in the process of entering common use, but that has not ...
(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 than 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 In mathematics, a real number is a number that can be used to measurement, measure a ''continuous'' one-dimensional quantity such as a distance, time, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small var ...
has nothing more (or less) real than an
imaginary number An imaginary number is a real number multiplied by the imaginary unit , is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property . The square (algebra), square of an imagina ...
. Frequently, a definition uses a phrase built with common English words, which has no meaning outside mathematics, such as
primitive group In mathematics, a permutation group ''G'' Group action, acting on a non-empty finite set ''X'' is called primitive if ''G'' acts transitive action, transitively on ''X'' and the only Partition_of_a_set, partitions the ''G''-action preserves are th ...
or
irreducible variety In algebraic geometry Algebraic geometry is a branch of mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quanti ...
. 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 In mathematics and computer science, a recursive definition, or inductive definition, is used to define the Element (mathematics), elements in a Set (mathematics), set in terms of other elements in the set (Peter Aczel, Aczel 1977:740ff). Some exa ...
, 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 In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...
as follows (after
Peano Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much Mathematical notati ...
): # "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. Notice that the second condition in the definition itself refers to natural numbers, and hence involves
self-reference Self-reference occurs in natural or formal language In logic, mathematics, computer science, and linguistics, a formal language consists of string (computer science), words whose symbol (formal), letters are taken from an alphabet (formal ...
. 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 An ancestor, also known as a forefather, fore-elder or a forebear, is a parent or (Recursion, recursively) the parent of an antecedent (i.e., a grandparent, great-grandparent, great-great-grandparent and so forth). ''Ancestor'' is "any person ...
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
classification Classification is a process related to categorization, the process in which ideas and objects are recognized, differentiated and understood. Classification is the grouping of related facts into classes. It may also refer to: Business, organizat ...
s, 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).Joyce, Ch. X #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


Limitations of definition

Given that a
natural language In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has linguistic evolution, evolved naturally in humans through use and repetition without conscious planning or premeditati ...
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 In metaphysics, ontology is the philosophy, philosophical study of being, as well as related concepts such as existence, Becoming (philosophy), becoming, and reality. Ontology addresses questions like how entities are grouped into Category ...
, unity and similar concepts cannot be defined. Locke supposes in ''
An Essay Concerning Human Understanding ''An Essay Concerning Human Understanding'' is a work by John Locke concerning the foundation of human knowledge and understanding. It first appeared in 1689 (although dated 1690) with the printed title ''An Essay Concerning Humane Understand ...
'' that the names of simple concepts do not admit of any definition. More recently
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
sought to develop a formal language based on logical atoms. Other philosophers, notably
Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrians, Austrian-British people, British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy o ...
, rejected the need for any undefined simples. Wittgenstein pointed out in his ''
Philosophical Investigations ''Philosophical Investigations'' (german: Philosophische Untersuchungen) is a work by the philosopher Ludwig Wittgenstein, published posthumously in 1953. ''Philosophical Investigations'' is divided into two parts, consisting of what Wittgens ...
'' 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 An individual is that which exists as a distinct entity. Individuality (or self-hood) is the state or quality of being an individual; particularly (in the case of humans) of being a person unique from other people and possessing one's own Maslow ...
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 Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic philosophy, analytic tradition. He was a Distinguished Professor of Philosophy at the Graduate Center of the City University o ...
pointed to difficulties with this approach, especially in relation to
modality Modality may refer to: Humanities * Modality (theology), the organization and structure of the church, as distinct from sodality or parachurch organizations * Modality (music), in music, the subject concerning certain diatonic scales * Modalities ...
, 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.''Philosophical Investigations'' 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 Family resemblance (german: Familienähnlichkeit, link=no) is a philosophical idea made popular by Ludwig Wittgenstein, with the best known exposition given in his posthumously published book ''Philosophical Investigations'' (1953). It argues tha ...
. 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 A circular definition is a description that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of character ...
* Definable set *
Definitionism Definitionism (also called the classical theory of concepts) is the school of thought in which it is believed that a proper explanation of a theory consists of all the concepts used by that theory being well-defined. This approach has been criticize ...
* Extensional definition * Fallacies of definition * Indeterminacy * Intensional definition * Lexical definition *
Operational definition An operational definition specifies concrete, replicable procedures designed to represent a construct. In the words of American psychologist S.S. Stevens (1935), "An operation is the performance which we execute in order to make known a concept." F ...
*
Ostensive definition An ostensive definition conveys the meaning of a term by pointing out examples. This type of definition 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 la ...
* Ramsey–Lewis method *
Semantics Semantics (from grc, wikt:σημαντικός, σημαντικός ''sēmantikós'', "significant") is the study of reference, Meaning (philosophy), meaning, or truth. The term can be used to refer to subfields of several distinct discipline ...
* Synthetic proposition *
Theoretical definition A theoretical definition defines a term in an academic discipline, functioning as a proposal to see a phenomenon in a certain way. A theoretical definition is a proposed way of thinking about potentially related events. Theoretical definitions cont ...


Notes


References

*
(full text of 1st ed. (1906))

(worldcat)(full text of 2nd ed. (1916))
* (full text
vol 1vol 2
* * * * *


External links


Definitions
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with scholarly peer review, peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by S ...
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 Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as '' The Lancet'', '' Cell'', the ScienceDirect collection of electronic journals, '' Trends'', ...
.
Definition and Meaning
a very short introduction by Garth Kemerling (2001). {{Authority control Philosophical logic Philosophy of language Semantics Linguistics terminology Mathematical terminology Concepts in logic Lexicography Meaning (philosophy of language)