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, phrase, or other set of symbols).[1][2] 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).[3] 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.[4][a]
In 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.[5]
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.[6] 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.[7]
The definiens is not the meaning of the word defined, but is instead something that conveys the same meaning as that word.[7]
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,» [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.»).[7]
Intensional definitions vs extensional definitions
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.[3] 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.[3]
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
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).[8]
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.[6]
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:
- a square: a rectangle that is a rhombus.
- a square: a rhombus that is a 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 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.[9]
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 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.[10]
Nominal definitions vs real definitions
In classical thought, a definition was taken to be a statement of the essence of a thing. Aristotle had it that an object’s essential attributes form its «essential nature», and that a definition of the object must include these essential attributes.[11]
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,[12] 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».[13] 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».[14]
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
A homonym is, in the strict sense, one of a group of words that share the same spelling and pronunciation but have different meanings.[15] 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).[16][17]
Polysemes
Polysemy 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 and mathematics
In mathematics, definitions are generally not used to describe existing terms, but to describe or characterize a concept.[18] 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,[19] 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.[20] 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.[21]
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. Notice that the second condition in the definition itself refers to natural numbers, and hence involves self-reference. Although this sort of definition involves a form of 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,[22] preferably even by the general public;[23]
- useful clinically[23] or in related areas where the definition will be used;[22]
- specific[22] (that is, by reading the definition only, it should ideally not be possible to refer to any other entity than that being defined);
- measurable;[22]
- a reflection of current scientific knowledge.[22][23]
Problems
Certain rules have traditionally been given for definitions (in particular, genus-differentia definitions).[24][25][26][27]
- 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 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?»[28][29] A dictionary, for instance, insofar as it is a comprehensive list of lexical definitions, must resort to circularity.[30][31][32]
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.[25] Locke supposes in An Essay Concerning Human Understanding[33] 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.[34] 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»,[35] 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.[36] This is not possible when no one else is acquainted with the particular thing that has «fallen under our notice».[37] 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.[38] 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.[b]
See also
- Analytic proposition
- Circular definition
- Definable set
- Definitionism
- Extensional definition
- Fallacies of definition
- Indeterminacy
- Intensional definition
- Lexical definition
- 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.
- ^ Note that 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.
- ^ a b c 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 - ^ a b «DEFINITIONS». beisecker.faculty.unlv.edu. Retrieved 2019-11-28.
- ^ a b c 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
- ^ a b c d e 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.
- ^ a b c 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
- ^ a b 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. [1] [2] 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. 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
Look up definition in Wiktionary, the free dictionary.
- 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).
Get the most trusted, up-to-date definitions from Merriam-Webster. Find word meaning, pronunciation, origin, synonyms, and more.
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1
a
: a statement of the meaning of a word or word group or a sign or symbol
b
: a statement expressing the essential nature of something
c
: a product of defining
2
: the action or process of stating the meaning of a word or word group
3
a
: the action or the power of describing, explaining, or making definite and clear
the definition of a telescope
her comic genius is beyond definition
b(1)
: clarity of visual presentation : distinctness of outline or detail
improve the definition of an image
(2)
: clarity especially of musical sound in reproduction
c
: sharp demarcation of outlines or limits
a jacket with distinct waist definition
4
: an act of determining
specifically
: the formal proclamation of a Roman Catholic dogma
Synonyms
Example Sentences
For the last eight years or so, I’ve been watching the evolution of bikes made for women. At the beginning of that time, there were a small number of women’s bikes available, most offered with low-end, sometimes no-name, spec, as if by definition all women riders were beginners.
—Christine Bucher, Bicycling, March 2008
Not only is Ellen Byrne a chocolatier, but she takes the definition of artisan to a higher level.
—Amy Johansson, Chocolatier, February/March 2006
One kind of poverty is that of the imagination—the inability to envision a future truly different from the present. Jasmine had long judged people based on whether or not they gave her food and clothing, but, as she watched Carolyn and Gus and other families, she found herself mulling different gauges of worth. She’d been working lately on a definition of love.
—Katherine Boo, New Yorker, 28 Nov. 2005
Ideology thus provides definition of both systemic reality and values: it provides a set of preconceptions of what is and of what ought to be.
—Warren J. Samuels, Modern Economic Thought, (1977) 1993
What is the legal definition of a corporation?
A week of fishing is my definition of a vacation.
a monitor with good definition and vibrant colors
See More
Recent Examples on the Web
Collage: The Verge And yet, to point all this out seems like pedantry because the image undeniably looks real — for a certain definition of real, anyway.
—James Vincent, The Verge, 27 Mar. 2023
Some states have a narrow definition, passing laws that ban anything with more than 10 rounds.
—Todd C. Frankel, Washington Post, 27 Mar. 2023
This intra-Latino controversy is yet another example of how impossible a precise definition of Latino identity has become.
—Geraldo Cadava, The New Yorker, 25 Mar. 2023
But that’s only according to one definition of a bomb cyclone, where the pressure of a low-pressure system around 40 degrees latitude needs to drop by 17 millibars in under 24 hours.
—Gerry Díaz, San Francisco Chronicle, 21 Mar. 2023
Any suitable general definition must thus fulfill two disparate ends.
—WIRED, 21 Mar. 2023
Best Hair Gel Odele Flex Hair Gel $12 at odelebeauty.com This medium-hold gel can give curls and waves definition or slick your hair for classic styles without crunchiness and won’t flake onto your shoulders as the day goes on.
—Garrett Munce, Men’s Health, 21 Mar. 2023
The disorder may happen when someone close to the bereaved person died at least 12 months earlier, or at least six months earlier for children and adolescents, according to the definition of the disorder.
—Stephanie Innes, The Arizona Republic, 20 Mar. 2023
The 2022 roster comprised 34 U.S. banks, and included all the regionals under the Fed’s definition of assets over $100 billion.
—Shawn Tully, Fortune, 20 Mar. 2023
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These examples are programmatically compiled from various online sources to illustrate current usage of the word ‘definition.’ Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.
Word History
Etymology
Middle English diffinicioun, borrowed from Anglo-French diffiniciun, definiciun, borrowed from Latin dēfīnītiōn-, dēfīnītiō «fixing of a boundary, precise description,» from dēfīnīre «to mark the limits of, determine, define» + -tiōn-, -tiō, suffix of verbal action
First Known Use
14th century, in the meaning defined at sense 4
Time Traveler
The first known use of definition was
in the 14th century
Dictionary Entries Near definition
Cite this Entry
“Definition.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/definition. Accessed 14 Apr. 2023.
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Merriam-Webster unabridged
A definition is a passage that explains the meaning of a term (a word, phrase or other set of symbols), or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings. For each such specific sense, a definiens is a cluster of words that defines that term.
A chief difficulty in managing definition is the need to use other terms that are already understood or whose definitions are easily obtainable. The use of the term in a simple example may suffice. By contrast, a dictionary definition has additional details, typically including an etymology showing snapshots of the earlier meanings and the parent language.
Like other words, the term definition has subtly different meanings in different contexts. A definition may be descriptive of the general use meaning, or stipulative of the speaker’s immediate intentional meaning. For example, in formal languages like mathematics, a ‘stipulative’ definition guides a specific discussion. A descriptive definition can be shown to be «right» or «wrong» by comparison to general usage, but a stipulative definition can only be disproved by showing a logical contradiction.[1]
A precising definition extends the descriptive dictionary definition (lexical definition) of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition.
C.L. Stevenson has identified persuasive definition as 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 specific view.
Stevenson has also noted that some definitions are «legal» or «coercive», whose object is to create or alter rights, duties or crimes.[2]
Contents
- 1 Intension and extension
- 1.1 Divisio and partitio
- 2 Definition by genus and differentia
- 2.1 Rules for definition by genus and differentia
- 2.2 Essence
- 3 Recursive definitions
- 4 Working definitions
- 5 Limitations of definition
- 6 In medicine
- 7 See also
- 8 Notes
- 9 References
- 10 External links
Intension and extension
An intensional definition, also called a coactive definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.
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.
So, for example, an intensional definition of ‘Prime Minister’ might be the most senior minister of a cabinet in the executive branch of government in a parliamentary system. An extensional definition would be a list of all past, present and future prime ministers.
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. So you can explain who Alice (an individual) is by pointing her out to me; or what a rabbit (a class) is by pointing at several and expecting me to ‘catch on’. The process of ostensive definition itself was critically appraised by Ludwig Wittgenstein.[3]
An enumerative definition of a concept or 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 relatively small sets.[citation needed]
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. Divisio is 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 sets.[4]
Definition by genus and differentia
A genus–differentia definition is a type of intensional definition, and it is composed by two parts:
- 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 genera.
For example, consider these two definitions:
- a triangle: A plane figure that has 3 straight bounding sides.
- a quadrilateral: A plane figure that has 4 straight bounding sides.
Those definitions can be expressed as a genus and 2 differentiae:
- a genus: A plane figure.
- 2 differentiae:
- the differentia for a triangle: that has 3 straight bounding sides.
- the differentia for a quadrilateral: that has 4 straight bounding sides.
When multiple definitions could serve equally well, then all such definitions apply simultaneously. For instance, given the following:
- a rectangle: a quadrilateral that has interior angles which are all right angles.
- a rhombus: a quadrilateral that has bounding sides which all have the same length.
both of these definitions of ‘square’ are equally acceptable:
- a square: a rectangle that is a rhombus.
- a square: a rhombus that is a rectangle.
Thus, a ‘square’ is a member of both the genus ‘rectangle’ and the genus ‘rhombus’. In such a case, it is notationally convenient to consolidate the definitions into one definition that is expressed with multiple genera (and possibly no differentia, as in the following):
- a square: a rectangle and a rhombus.
or completely equivalently:
- a square: a rhombus and a rectangle.
Rules for definition by genus and differentia
Certain rules have traditionally been given for this particular type of definition.[5][6][7]
- 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, Locking[specify] adds that a definition of a term must not comprise 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. (See the definition of Free will in Wikipedia, 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’.
Essence
In classical thought, a definition was taken to be a statement of the essence of a thing. Aristotle had it that an object’s essential attributes form its «essential nature», and that a definition of the object must include these essential attributes.[8]
The idea that a definition should state the essence of a thing led to the distinction between nominal and real essence, originating with Aristotle. In a passage from the Posterior Analytics,[9] he says that we can know the meaning of a made-up name (he gives the example ‘goat stag’), without knowing what he calls the ‘essential nature’ of the thing that the name would denote, if there were such a thing. This led medieval logicians to distinguish between what they called the quid nominis or ‘whatness of the name’, and the underlying nature common to all the things it names, which they called the quid rei or ‘whatness of the thing’. (Early modern philosophers like Locke used the corresponding English terms ‘nominal essence’ and ‘real essence’). The name ‘hobbit’, for example, is perfectly meaningful. It has a quid nominis. But we could not know the real nature of hobbits, even if there were such things, and so we cannot know the real nature or quid rei of hobbits. By contrast, the name ‘man’ denotes real things (men) that have a certain quid rei. The meaning of a name is distinct from the nature that thing must have in order that the name apply to it.
This leads to a corresponding distinction between nominal and real definition. A nominal definition is the definition explaining what a word means, i.e. which says what the ‘nominal essence’ is, and is definition in the classical sense as given above. A real definition, by contrast, is one expressing the real nature or quid rei of the thing.
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 it as «a hopelessly muddle-headed notion».[10]
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 it possesses in all possible worlds. Kripke refers to names used in this way as rigid designators.
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 natural number as follows (after Peano):
- «0» is a natural number.
- 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 self-reference. Although this sort of definition involves a form of circularity, it is not vicious, and the definition has been quite successful.
Working definitions
A working definition is either chosen for an occasion and may not fully conform with established or authoritative definitions. Not knowing of established definitions would be grounds for selecting or devising a working definition. Or it refers to a definition being developed; a tentative definition that can be tailored to create an authoritative definition.
Limitations of definition
Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions. If every term of every definiens must itself be defined, «where at last should we stop?»[11][12] A dictionary, for instance, insofar as it is a comprehensive list of lexical definitions, must resort to circularity.[13][14][15]
Many philosophers have chosen instead to leave some terms undefined. The scholastic philosophers claimed that the highest genera (the so-called ten generalissima) cannot be defined, since we cannot assign any higher genus under which they may fall. Thus we cannot define being, unity and similar concepts.[6] Locke supposes in An Essay Concerning Human Understanding[16] 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.[17] 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»,[18] claiming instead that explanation of a term is only needed when we need to avoid misunderstanding.
Locke and Mill also argued that we cannot define individuals. We learn names by connecting an idea with a sound, so that speaker and hearer have the same idea when the same word is used.[19] This is not possible when no one else is acquainted with the particular thing that has «fallen under our notice».[20] 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.[21] 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.
In medicine
In medical dictionaries, definitions should to the greatest extent possible be:
- simple and easy to understand,[22] preferably even by the general public;[23]
- useful clinically[23] or in related areas where the definition will be used;[22]
- specific,[22] that is, by reading the definition only, it should ideally not be possible to refer to any other entity than the definiendum;
- measurable;[22]
- reflecting current scientific knowledge.[22][23]
See also
- Analytic proposition
- Definable set
- Definitionism
- Ostensive definition
- Demonstration
- Extensional definition
- Fallacies of definition
- Circular definition
- Indeterminacy
- Intensional definition
- Lexical definition
- Ramsey–Lewis method
- Semantic
- Synthetic proposition
- Theoretical definition
Notes
- ^ http://www.sfu.ca/philosophy/swartz/definitions.htm#part5.1
- ^ Stevenson, C.L., Ethics and Language, Connecticut 1944
- ^ 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.
- ^ Copi 1982 pp 165-169
- ^ a b Joyce, Ch. X
- ^ Joseph, Ch. V
- ^ Posterior Analytics, Bk 1 c. 4
- ^ Posterior Analytics Bk 2 c. 7
- ^ A history of Western Philosophy, p. 210
- ^ 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. [1] [2] 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
- ^ a b c d e McPherson, M.; Arango, P.; Fox, H.; Lauver, C.; McManus, M.; Newacheck, P.; Perrin, J.; Shonkoff, J. et al. (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. edit
- ^ a b c Morse, R. M.; Flavin, D. K. (1992). «The Definition of Alcoholism». JAMA 268 (8): 1012–1014. doi:10.1001/jama.1992.03490080086030. PMID 1501306.
References
- Copi, Irving (1982). Introduction to Logic. New York: Macmillan. ISBN 0-02-977520-5.
- Joseph, Horace William Brindley (1916 repr. 2000). 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. ISBN 0140434828. (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.
- Robinson, Richard (1954). Definition. Oxford: At The Clarendon Press. ISBN 9780198241607. http://books.google.com/?id=WVt8TfDR-YAC&lpg=PP1&dq=richard%20robinson%20definition&pg=PP1#v=onepage&q.
- Simpson, John; Edmund Weiner (1989). Oxford English Dictionary, second edition (20 volumes). Oxford University Press. ISBN 0-19-861186-2.
- Wittgenstein, Ludwig (1953/2001). Philosophical Investigations. Blackwell Publishing. ISBN 0-631-23127-7.
External links
- Definitions at Synonyms.Me
- 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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Portal · Category · Outline · WikiProject · Talk · changes |
определение, четкость, описание, резкость, точность, ясность
существительное ↓
- определение, дефиниция; толкование
clear definition — ясное определение
the definition of the term — определение термина
problem definition — постановка задачи, формулировка задачи
to give a definition — дать определение
actions that fall under the definition of murder — действия, которые квалифицируются как убийство
- ясность, чёткость; определённость
an emotion beyond definition — неясное /неосознанное/ чувство
- радио ясная слышимость, отсутствие помех
- фото, тлв. чёткость, резкость изображения
negative with fine definition — чёткий негатив
bad definition — нечёткость изображения
Мои примеры
Словосочетания
a monitor with good definition and vibrant colors — монитор с хорошим разрешением и яркими цветами
the definition of God as infinite — определение бога как Бесконечности
complete definition — полное определение
a formulaic definition — стандартное определение
a referential definition — определение-ссылка
a synonym definition — определение через синоним
a persuasive definition — стимулирующее, побуждающее определение
to formulate / give / provide / write a definition — дать определение
definition by analysis — определение путём анализа
dual definition — двойственное определение
heuristic definition — эвристическое определение
negative definition — отрицательное определение
Примеры с переводом
There are many definitions of the word ‘feminism’.
Существует множество определений слова «феминизм».
A week of fishing is my definition of a vacation.
Неделя рыбалки — это мое представление об отдыхе.
There is no generally accepted definition of life.
Общепринятого определения жизни не существует.
Real definition provides a statement of the nature or essence of a thing.
Реальное определение описывает предмет через его существенные свойства.
What is the legal definition of a corporation?
Каково юридическое определение корпорации?
Exercise had given his muscles superior definition.
Благодаря тренировкам, его мышцы были прекрасно очерчены.
People say that students are by definition idealistic and impatient.
Говорят, что студенты по определению идеалистичны и нетерпеливы.
Not only is Ellen Byrne a chocolatier, but she takes the definition of artisan to a higher level.
Эллен Бирн не только является шоколатье, но и выводит определение ремесленника на более высокий уровень.
Примеры, ожидающие перевода
The definition provides the word’s denotation.
…a supreme being is a being that, by definition, has no causality of its own…
…the enormous difference in real estate between a high-definition disk and one in standard definition…
Для того чтобы добавить вариант перевода, кликните по иконке ☰, напротив примера.
Возможные однокоренные слова
Формы слова
noun
ед. ч.(singular): definition
мн. ч.(plural): definitions
Despite the
central status of the word in the language system and the fact that
speakers have no difficulty in identifying words in speech it is very
difficult to give a satisfactory definition
of
the word. Many attempts have been made to this effect but still there
is no satisfying and universally accepted word definition. This
difficulty is conditioned by word’s complexity, as word is
characterized by many aspects and properties, such as phonological,
morphological, semantic, syntactic, pragmatic ones.
The
attempts to define word proceeded either from one particular
criterion or their combinations. Definitions proceeding from a
phonological
criterion
were offered by Ch. Hocket [Hocket 1978: 166] and P.S. Kuznetsov
[Кузнецов
1964: 7] who claimed that word is any segment of a sentence (Hocket)
or a sequence of sounds (Kuznetsov) which can be separated by pauses
of any length. Such definitions point out at the outer form of the
word, the possibility to single it out between the pauses in actual
speech, but do not disclose its inner faculties, the word’s content
– its meaning.
Purely
semantic
criteria
of
word definition cannot be considered sufficient as well. For instance
St. Ullmann’s definition is based on a semantic criterion: “Words
are meaningful segments of connected discourse”. [Ullmann 1959:
30]. Not only words are meaningful units but also morphemes and
prosodic components of discourse: pauses, intonation, etc. Word
cannot be defined as a unit of the language expressing a particular
concept or notion, although word is related to concept which will be
pointed out later (chapter 2). Besides, concepts are expressed not
only by words but also word combinations, phrases and sentences.
Concept is a category of cognition and it is impossible to establish
a one-to-one correspondence between word and concept.
A.H.Gardiner
based his definition on the semantic-phonological approach: “A word
is an articulate sound-system in its aspect of denoting something
which is spoken about” [quoted from Arnold 1973: 26]. The word has
been syntactically defined as: “A word is the minimum sentence”
by H.Sweet and much later by L.Bloomfield as “a minimum free form”
[Bloomfield 1933: 187].
There were
attempts to combine the semantic, phonological and grammatical
criteria: The definitions by the Czech linguist B. Trnk “Word is a
minimum unit of meaning realized by a definite sequence of phonemes
and capable of mobility within a sentence” [1964: 201] and the
eminent French linguist A.Meillet “A word is defined by the
association of a particular meaning with a particular group of sounds
capable of a particular grammatical employment” [1926: 30] serve
as examples. Despite the fact that the above definitions embrace
various aspects of the word, they were objects of criticism because
(1) not every word is capable of positional mobility, for instance,
articles, prepositions, particles cannot move freely within a
sentence; (2) the definitions do not distinguish between a word and a
word combination. As I.V.Arnold puts it “not only child,
but a
pretty child as
well are combinations of a particular meaning with a particular group
of sounds capable of a particular grammatical employment” [1973:
26].
The word
definitions offered by Soviet/Russian linguists are based on the
theory of signs and modern semantic approaches (see ch.2). For
instance, the definition offered by O.S.Akhmanova runs as folliows:
“Word is the smallest unit of the language functioning within the
sentence, which directly corresponds to the object of thought
(referent) and is a generalized reverberation of a certain ‘slice’,
‘piece’ of objective reality – and by immediately referring to
it names the thing meant”.
In English
and other analytical languages there exist the so-called analytical
forms of certain parts of speech, such as verbs, e.g. have
finished, didn’t go, is reading, etc.,
comparative and superlative degrees of adjectives: more
interesting, most sincerely.
Such words possess certain structural separateness.
Summing
up our review of different definitions we come to the conclusion that
they are bound to be strongly dependent upon the line of approach,
the aim the scholar has in view. For a comprehensive word theory a
description seems more appropriate than a definition.
All
that was said about the word can be summed up as follows. The word is
a linguistic sign. It represents a group of sounds possessing a
meaning, susceptible to grammatical employment and characterized by
formal and semantic unity.
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