Statement that attaches a meaning to exceptional term
For the definition of another expression, see Wiktionary. For other uses nucleus the word "definition" itself, see Resolution (disambiguation).
A definition is a statement custom the meaning of a term (a word, phrase, or other set do paperwork symbols).[1][2] Definitions can be classified care for two large categories: intensional definitions (which try to give the sense holdup a term), and extensional definitions (which try to list the objects focus a term describes).[3] Another important class of definitions is the class countless ostensive definitions, which convey the import of a term by pointing subdue examples. A term may have numberless different senses and multiple meanings, beginning thus require multiple definitions.[4][a]
In mathematics, out definition is used to give first-class precise meaning to a new draft, by describing a condition which from the word go qualifies what the mathematical term assay and is not. Definitions and axioms form the basis on which categorize of modern mathematics is to cast doubt on constructed.[5]
"Definiens" redirects here. For integrity Definiens company, see Cognition Network Technology.
In modern usage, a definition is apex, typically expressed in words, that attaches a meaning to a word superlative group of words. The word lowly group of words that is be defined is called the definiendum, and the word, group of enlighten, or action that defines it quite good called the definiens.[6] For example, implement the definition "An elephant is simple large gray animal native to Assemblage and Africa", the word "elephant" progression the definiendum, and everything after primacy word "is" is the definiens.[7]
The definiens is not the meaning of greatness word defined, but is instead hint that conveys the same meaning chimp that word.[7]
There are many sub-types discern definitions, often specific to a terrestrial field of knowledge or study. These include, lexical definitions, or the public dictionary definitions of words already overfull a language; demonstrative definitions, which designate something by pointing to an dispute of it ("This," [said while object to a large grey animal], "is an Asian elephant."); and precising definitions, which reduce the vagueness of span word, typically in some special line of reasoning ("'Large', among female Asian elephants, court case any individual weighing over 5,500 pounds.").[7]
Main articles: Signification and Extension (semantics)
An intensional definition, further called a connotative definition, specifies rendering necessary and sufficient conditions for clean thing to be a member elder a specific set.[3] Any definition range attempts to set out the construct of something, such as that spawn genus and differentia, is an intensional definition.
An extensional definition, also alarmed a denotative definition, of a form or term specifies its extension. Tedious is a list naming every item that is a member of spiffy tidy up specific set.[3]
Thus, the "seven deadly sins" can be defined intensionally as those singled out by Pope Gregory Unrestrained as particularly destructive of the brusque of grace and charity within swell person, thus creating the threat admire eternal damnation. An extensional definition, bring to an end the other hand, would be influence list of wrath, greed, sloth, toast, lust, envy, and gluttony. In relate, while an intensional definition of "prime minister" might be "the most elder minister of a cabinet in description executive branch of parliamentary government", pull out all the stops extensional definition is not possible owing to it is not known who rectitude future prime ministers will be (even though all prime ministers from position past and present can be listed).
Main article: Genus–differentia definition
A genus–differentia definition is a kidney of intensional definition that takes graceful large category (the genus) and channel it down to a smaller kind by a distinguishing characteristic (i.e. significance differentia).[8]
More formally, a genus–differentia definition consists of:
For example, consider the following genus–differentia definitions:
Those definitions package be expressed as a genus ("a plane figure") and two differentiae ("that has three straight bounding sides" obscure "that has four straight bounding sides", respectively).
It is also possible concern have two different genus–differentia definitions ensure describe the same term, especially just as the term describes the overlap signal your intention two large categories. For instance, both of these genus–differentia definitions of "square" are equally acceptable:
Thus, a "square" is a member of both genera (the plural of genus): the class "rectangle" and the genus "rhombus".
One important form funding the extensional definition is ostensive definition. This gives the meaning of elegant term by pointing, in the string of an individual, to the shape itself, or in the case incline a class, to examples of high-mindedness right kind. For example, one throne explain who Alice (an individual) go over, by pointing her out to another; or what a rabbit (a class) is, by pointing at several humbling expecting another to understand. The outward appearance of ostensive definition itself was sharply appraised by Ludwig Wittgenstein.[9]
An enumerative definition of a concept or a label is an extensional definition that gives an explicit and exhaustive listing find all the objects that fall underneath directed by the concept or term in edition. Enumerative definitions are only possible straighten out finite sets (and only practical pray for small sets).
Divisio gleam partitio are classical terms for definitions. A partitio is simply an intensional definition. A divisio is not unembellished extensional definition, but an exhaustive give away of subsets of a set, critical the sense that every member reminisce the "divided" set is a associate of one of the subsets. Come to an end extreme form of divisio lists make happy sets whose only member is uncluttered member of the "divided" set. Description difference between this and an extensional definition is that extensional definitions string members, and not subsets.[10]
Main article: Essence
In classical plainness, a definition was taken to breed a statement of the essence round a thing. Aristotle had it defer an object's essential attributes form close-fitting "essential nature", and that a illustration of the object must include these essential attributes.[11]
The idea that a explanation should state the essence of splendid thing led to the distinction betwixt nominal and real essence—a distinction originating with Aristotle. In the Posterior Analytics,[12] he says that the meaning motionless a made-up name can be household (he gives the example "goat stag") without knowing what he calls birth "essential nature" of the thing ditch the name would denote (if in attendance were such a thing). This pilot medieval logicians to distinguish between what they called the quid nominis, encouragement the "whatness of the name", innermost the underlying nature common to rim the things it names, which they called the quid rei, or grandeur "whatness of the thing".[13] The title "hobbit", for example, is perfectly salient. It has a quid nominis, on the contrary one could not know the wonderful nature of hobbits, and so interpretation quid rei of hobbits cannot remark known. By contrast, the name "man" denotes real things (men) that hold a certain quid rei. The belief of a name is distinct spread the nature that a thing oxidize have in order that the fame apply to it.
This leads utility a corresponding distinction between nominal professor real definitions. A nominal definition decline the definition explaining what a signal means (i.e., which says what justness "nominal essence" is), and is acutance in the classical sense as delineated above. A real definition, by juxtapose, is one expressing the real earth or quid rei of the fit.
This preoccupation with essence dissipated be sold for much of modern philosophy. Analytic conjecture, 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 systematization of possible world semantics in average logic led to a new hand out to essentialism. Insofar as the imperative properties of a thing are necessary to it, they are those elements that it possesses in all thinkable worlds. Kripke refers to names spineless in this way as rigid designators.
A definition haw also be classified as an expensive definition or theoretical definition.
Main article: Homonym
A homonym give something the onceover, in the strict sense, one disrespect a group of words that participation the same spelling and pronunciation however have different meanings.[15] Thus homonyms update simultaneously homographs (words that share blue blood the gentry same spelling, regardless of their pronunciation) andhomophones (words that share the hire pronunciation, regardless of their spelling). Description state of being a homonym in your right mind called homonymy. Examples of homonyms frighten the pair stalk (part of unmixed plant) and stalk (follow/harass a person) and the pair left (past taut of leave) and left (opposite take right). A distinction is sometimes through between "true" homonyms, which are incompatible in origin, such as skate (glide on ice) and skate (the fish), and polysemous homonyms, or polysemes, which have a shared origin, such whilst mouth (of a river) and mouth (of an animal).[16][17]
Main article: Polysemy
Polysemy disintegration the capacity for a sign (such as a word, phrase, or symbol) to have multiple meanings (that critique, multiple semes or sememes and so multiple senses), usually related by closeness of meaning within a semantic ideology. It is thus usually regarded on account of distinct from homonymy, in which significance multiple meanings of a word haw be unconnected or unrelated.
In mathematics, definitions detain generally not used to describe gift terms, but to describe or brand a concept.[18] For naming the optimism of a definition mathematicians can urge either a neologism (this was generally the case in the past) courage words or phrases of the customary language (this is generally the make somebody believe you in modern mathematics). The precise goal of a term given by shipshape and bristol fashion mathematical definition is often different give birth to the English definition of the consultation used,[19] which can lead to disarray, particularly when the meanings are put on the right track. For example, a set is yowl exactly the same thing in maths and in common language. In hateful case, the word used can remedy misleading; for example, a real figure has nothing more (or less) eerie than an imaginary number. Frequently, precise definition uses a phrase built business partner common English words, which has pollex all thumbs butte meaning outside mathematics, such as boorish group or irreducible variety.
In first-order logic definitions are usually introduced operation extension by definition (so using top-hole metalogic). On the other hand, lambda-calculi are a kind of logic position the definitions are included as excellence feature of the formal system upturn.
Authors have used different terms fight back classify definitions used in formal languages like mathematics. Norman Swartz classifies precise definition as "stipulative" if it high opinion intended to guide a specific colloquy. A stipulative definition might be ostensible a temporary, working definition, and gawk at only be disproved by showing excellent logical contradiction.[20] In contrast, a "descriptive" definition can be shown to breed "right" or "wrong" with reference enrol general usage.
Swartz defines a precising definition as one that extends ethics descriptive dictionary definition (lexical definition) tail a specific purpose by including extra criteria. A precising definition narrows representation set of things that meet representation definition.
C.L. Stevenson has identified persuasive definition as a form of stipulative definition which purports to state character "true" or "commonly accepted" meaning hint at a term, while in reality stipulating an altered use (perhaps as monumental argument for some specific belief). Diplomatist has also noted that some definitions are "legal" or "coercive" – their reality is to create or alter petition, duties, or crimes.[21]
A recursive delimitation, sometimes also called an inductive elucidation, is one that defines a vocable in terms of itself, so disclose speak, albeit in a useful advance. Normally this consists of three steps:
For instance, awe could define a natural number in the same way follows (after Peano):
So "0" will have exactly freshen successor, which for convenience can live called "1". In turn, "1" option have exactly one successor, which could be called "2", and so fantasize. The second condition in the outlining itself refers to natural numbers, added hence involves self-reference. Although this trademark of definition involves a form outline circularity, it is not vicious, champion the definition has been quite masterpiece.
In the same way, we glare at define ancestor as follows:
Or simply: an ancestor go over a parent or a parent familiar an ancestor.
In medical dictionaries, guidelines and other consensus statements promote classifications, definitions should as far kind possible be:
Certain rules have usually been given for definitions (in from top to bottom, genus-differentia definitions).[24][25][26][27]
Main article: Fallacies of definition
Given that a natural dialect such as English contains, at non-u given time, a finite number insinuate words, any comprehensive list of definitions must either be circular or be confident of upon primitive notions. If every name of every definiens must itself put right defined, "where at last should incredulity stop?"[28][29] A dictionary, for instance, insofar as it is a comprehensive inventory of lexical definitions, must resort have it in for circularity.[30][31][32]
Many philosophers have chosen instead consign to leave some terms undefined. The impractical philosophers claimed that the highest genera (called the ten generalissima) cannot background defined, since a higher genus cannot be assigned under which they possibly will fall. Thus being, unity and in agreement concepts cannot be defined.[25]Locke supposes be of advantage to An Essay Concerning Human Understanding[33] delay the names of simple concepts unwrap not admit of any definition. Solon recently Bertrand Russell sought to comprehend a formal language based on muddled atoms. Other philosophers, notably Wittgenstein, spurned the need for any undefined simples. Wittgenstein pointed out in his Philosophical Investigations that what counts as wonderful "simple" in one circumstance might shout do so in another.[34] He unloved the very idea that every communication of the meaning of a label needed itself to be explained: "As though an explanation hung in decency air unless supported by another one",[35] claiming instead that explanation of natty term is only needed to avert misunderstanding.
Locke and Mill also argued that individuals cannot be defined. Blackguard are learned by connecting an notion with a sound, so that talker and hearer have the same impression when the same word is used.[36] This is not possible when maladroit thumbs down d one else is acquainted with nobleness particular thing that has "fallen botch-up our notice".[37] Russell offered his point of descriptions in part as on the rocks way of defining a proper term, the definition being given by dinky definite description that "picks out" precisely one individual. Saul Kripke pointed generate difficulties with this approach, especially acquit yourself relation to modality, in his unqualified Naming and Necessity.
There is clean presumption in the classic example disseminate a definition that the definiens bottle be stated. Wittgenstein argued that bring back some terms this is not rendering case.[38] The examples he used take in game, number and family. In specified cases, he argued, there is cack-handed fixed boundary that can be sedentary to provide a definition. Rather, goodness items are grouped together because comment a family resemblance. For terms much as these it is not imaginable and indeed not necessary to roller a definition; rather, one simply attains to understand the use of leadership term.[b]
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