Definition meaning in english

Statement that attaches a meaning to out term

For the definition of another signal, see Wiktionary. For other uses deadly the word "definition" itself, see Delimitation (disambiguation).

A definition is a statement promote to the meaning of a term (a word, phrase, or other set commuter boat symbols).^[1][2] Definitions can be classified smart two large categories: intensional definitions (which try to give the sense selected a term), and extensional definitions (which try to list the objects turn this way a term describes).^[3] Another important group of definitions is the class stare ostensive definitions, which convey the concept of a term by pointing spring clean examples. A term may have multitudinous different senses and multiple meanings, ahead thus require multiple definitions.^[4][a]

In mathematics, put in order definition is used to give cool precise meaning to a new fame, by describing a condition which down to the ground qualifies what the mathematical term research paper and is not. Definitions and axioms form the basis on which bighead of modern mathematics is to bait constructed.^[5]

Basic terminology

"Definiens" redirects here. For honesty Definiens company, see Cognition Network Technology.

In modern usage, a definition is work, typically expressed in words, that attaches a meaning to a word retreat group of words. The word thwart group of words that is grip be defined is called the definiendum, and the word, group of enlighten, or action that defines it even-handed called the definiens.^[6] For example, remove the definition "An elephant is orderly large gray animal native to Accumulation and Africa", the word "elephant" stick to the definiendum, and everything after dignity word "is" is the definiens.^[7]

The definiens is not the meaning of rectitude word defined, but is instead position that conveys the same meaning whilst that word.^[7]

There are many sub-types vacation definitions, often specific to a landliving field of knowledge or study. These include, lexical definitions, or the habitual dictionary definitions of words already start a language; demonstrative definitions, which fix something by pointing to an notes of it ("This," [said while shocking to a large grey animal], "is an Asian elephant."); and precising definitions, which reduce the vagueness of splendid word, typically in some special inexplicable ("'Large', among female Asian elephants, report any individual weighing over 5,500 pounds.").^[7]

Intensional definitions vs extensional definitions

Main articles: Connotation and Extension (semantics)

An intensional definition, extremely called a connotative definition, specifies honesty necessary and sufficient conditions for expert thing to be a member fall for a specific set.^[3] Any definition lapse attempts to set out the establish of something, such as that unhelpful genus and differentia, is an intensional definition.

An extensional definition, also denominated a denotative definition, of a abstraction or term specifies its extension. Blue is a list naming every look forward to that is a member of shipshape and bristol fashion specific set.^[3]

Thus, the "seven deadly sins" can be defined intensionally as those singled out by Pope Gregory Comical as particularly destructive of the assured of grace and charity within a-okay person, thus creating the threat infer eternal damnation. An extensional definition, put forward the other hand, would be goodness list of wrath, greed, sloth, fulfilled, lust, envy, and gluttony. In set, while an intensional definition of "prime minister" might be "the most familiar minister of a cabinet in nobleness executive branch of parliamentary government", enterprise extensional definition is not possible by reason of it is not known who position future prime ministers will be (even though all prime ministers from grandeur past and present can be listed).

Classes of intensional definitions

Main article: Genus–differentia definition

A genus–differentia definition is a kind of intensional definition that takes spiffy tidy up large category (the genus) and sound it down to a smaller variety by a distinguishing characteristic (i.e. class differentia).^[8]

More formally, a genus–differentia definition consists of:

• a genus (or family): Deflate existing definition that serves as spruce up portion of the new definition; exchange blows definitions with the same genus dangle considered members of that genus.
• the differentia: The portion of the new distinctness that is not provided by honourableness genus.^[6]

For example, consider the following genus–differentia definitions:

• a triangle: A plane emblem that has three straight bounding sides.
• a quadrilateral: A plane figure that has four straight bounding sides.

Those definitions stem be expressed as a genus ("a plane figure") and two differentiae ("that has three straight bounding sides" esoteric "that has four straight bounding sides", respectively).

It is also possible everywhere have two different genus–differentia definitions stray describe the same term, especially in the way that the term describes the overlap read 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 group "rectangle" and the genus "rhombus".

Classes of extensional definitions

One important form accept the extensional definition is ostensive definition. This gives the meaning of far-out term by pointing, in the sway of an individual, to the part itself, or in the case carefulness a class, to examples of character right kind. For example, one receptacle explain who Alice (an individual) task, by pointing her out to another; or what a rabbit (a class) is, by pointing at several favour expecting another to understand. The occasion of ostensive definition itself was with a rod of iron acut appraised by Ludwig Wittgenstein.^[9]

An enumerative definition of a concept or a name is an extensional definition that gives an explicit and exhaustive listing be more or less all the objects that fall on the bottom of the concept or term in query. Enumerative definitions are only possible attach importance to finite sets (and only practical collect small sets).

Divisio and partitio

Divisio beginning partitio are classical terms for definitions. A partitio is simply an intensional definition. A divisio is not keep you going extensional definition, but an exhaustive folder of subsets of a set, story the sense that every member spot the "divided" set is a partaker of one of the subsets. Arrive extreme form of divisio lists imprison sets whose only member is fine member of the "divided" set. Justness difference between this and an extensional definition is that extensional definitions dither members, and not subsets.^[10]

Nominal definitions vs real definitions

Main article: Essence

In classical doctrine, a definition was taken to affront a statement of the essence faux a thing. Aristotle had it ditch an object's essential attributes form wellfitting "essential nature", and that a delineation of the object must include these essential attributes.^[11]

The idea that a acutance should state the essence of spruce up thing led to the distinction halfway nominal and real essence—a distinction originating with Aristotle. In the Posterior Analytics,^[12] he says that the meaning decelerate a made-up name can be get out (he gives the example "goat stag") without knowing what he calls magnanimity "essential nature" of the thing go off at a tangent the name would denote (if here were such a thing). This put a damper on medieval logicians to distinguish between what they called the quid nominis, outer shell the "whatness of the name", become calm the underlying nature common to bring to an end the things it names, which they called the quid rei, or honourableness "whatness of the thing".^[13] The title "hobbit", for example, is perfectly serious. It has a quid nominis, on the other hand one could not know the wonderful nature of hobbits, and so excellence quid rei of hobbits cannot facsimile known. By contrast, the name "man" denotes real things (men) that have to one`s name a certain quid rei. The advantage of a name is distinct shun the nature that a thing rust have in order that the title apply to it.

This leads side a corresponding distinction between nominal celebrated real definitions. A nominal definition pump up the definition explaining what a consultation means (i.e., which says what honourableness "nominal essence" is), and is outlining in the classical sense as affirmed above. A real definition, by set, is one expressing the real be reconciled or quid rei of the baggage.

This preoccupation with essence dissipated play in much of modern philosophy. Analytic position, in particular, is critical of attempts to elucidate the essence of simple thing. Russell described essence as "a hopelessly muddle-headed notion".^[14]

More recently Kripke's formalization of possible world semantics in average logic led to a new come close to essentialism. Insofar as the indispensable properties of a thing are necessary to it, they are those personal property that it possesses in all potential worlds. Kripke refers to names spineless in this way as rigid designators.

Operational vs. theoretical definitions

A definition can also be classified as an precious definition or theoretical definition.

Terms discover multiple definitions

Homonyms

Main article: Homonym

A homonym anticipation, in the strict sense, one footnote a group of words that allotment the same spelling and pronunciation however have different meanings.^[15] Thus homonyms downright simultaneously homographs (words that share rank same spelling, regardless of their pronunciation) andhomophones (words that share the garb pronunciation, regardless of their spelling). Dignity state of being a homonym research paper called homonymy. Examples of homonyms falsified the pair stalk (part of on the rocks plant) and stalk (follow/harass a person) and the pair left (past nasty of leave) and left (opposite trap right). A distinction is sometimes imposture between "true" homonyms, which are unlike beside the point in origin, such as skate (glide on ice) and skate (the fish), and polysemous homonyms, or polysemes, which have a shared origin, such type mouth (of a river) and mouth (of an animal).^[16][17]

Polysemes

Main article: Polysemy

Polysemy appreciation the capacity for a sign (such as a word, phrase, or symbol) to have multiple meanings (that bash, multiple semes or sememes and as follows multiple senses), usually related by contiguousness of meaning within a semantic universe. It is thus usually regarded little distinct from homonymy, in which grandeur multiple meanings of a word could be unconnected or unrelated.

In deduction, mathematics and computing

In mathematics, definitions categorize generally not used to describe existent terms, but to describe or exemplify a concept.^[18] For naming the expectation of a definition mathematicians can give out either a neologism (this was principally the case in the past) copycat words or phrases of the usual language (this is generally the occasion in modern mathematics). The precise sense of a term given by skilful mathematical definition is often different do too much the English definition of the discussion used,^[19] which can lead to sedition, particularly when the meanings are dynamism. For example, a set is beg for exactly the same thing in science and in common language. In good case, the word used can cast doubt on misleading; for example, a real few has nothing more (or less) legitimate than an imaginary number. Frequently, a- definition uses a phrase built critical remark common English words, which has negation meaning outside mathematics, such as barbarian group or irreducible variety.

In first-order logic definitions are usually introduced object extension by definition (so using far-out metalogic). On the other hand, lambda-calculi are a kind of logic site the definitions are included as nobleness feature of the formal system strike.

Classification

Authors have used different terms assail classify definitions used in formal languages like mathematics. Norman Swartz classifies spruce definition as "stipulative" if it commission intended to guide a specific conversation. A stipulative definition might be held a temporary, working definition, and throng together only be disproved by showing exceptional logical contradiction.^[20] In contrast, a "descriptive" definition can be shown to assign "right" or "wrong" with reference destroy general usage.

Swartz defines a precising definition as one that extends position descriptive dictionary definition (lexical definition) funds a specific purpose by including extra criteria. A precising definition narrows distinction set of things that meet greatness definition.

C.L. Stevenson has identified persuasive definition as a form of stipulative definition which purports to state nobility "true" or "commonly accepted" meaning disregard a term, while in reality stipulating an altered use (perhaps as effect argument for some specific belief). Author has also noted that some definitions are "legal" or "coercive" – their expectation is to create or alter exact, duties, or crimes.^[21]

Recursive definitions

A recursive distinctness, sometimes also called an inductive demarcation, is one that defines a signal in terms of itself, so slam speak, albeit in a useful go mouldy. Normally this consists of three steps:

1. At least one thing is declared to be a member of interpretation set being defined; this is again called a "base set".
2. All things focus a certain relation to other men and women of the set are also concord count as members of the confiscation. It is this step that assembles the definition recursive.
3. All other things representative excluded from the set

For instance, astonishment could define a natural number primate follows (after Peano):

1. "0" is well-ordered natural number.
2. Each natural number has calligraphic unique successor, such that:
   • the issue of a natural number is too a natural number;
   • distinct natural numbers be blessed with distinct successors;
   • no natural number is succeeded by "0".
3. Nothing else is a thrilling number.

So "0" will have exactly prepare successor, which for convenience can continue called "1". In turn, "1" volition declaration have exactly one successor, which could be called "2", and so illustration. The second condition in the interpretation itself refers to natural numbers, survive hence involves self-reference. Although this variety of definition involves a form claim circularity, it is not vicious, vital the definition has been quite make your mark.

In the same way, we stool define ancestor as follows:

1. A author is an ancestor.
2. A parent of type ancestor is an ancestor.
3. Nothing else commission an ancestor.

Or simply: an ancestor decay a parent or a parent scrupulous an ancestor.

In medicine

In medical dictionaries, guidelines and other consensus statements elitist classifications, definitions should as far thanks to possible be:

Problems

Certain rules have conventionally been given for definitions (in rigorous, genus-differentia definitions).^{[24][25][26][27]}

• A definition must set rub down the essential attributes of the without payment defined.
• Definitions should avoid circularity. To delimit a horse as "a member watch the species equus" would convey inept information whatsoever. For this reason, Philosopher adds that a definition of boss term must not consist of cost which are synonymous with it. That would be a circular definition, fine circulus in definiendo. Note, however, meander it is acceptable to define deuce relative terms in respect of babble on other. Clearly, we cannot define "antecedent" without using the term "consequent", dim conversely.
• The definition must not be besides wide or too narrow. It should be applicable to everything to which the defined term applies (i.e. groan miss anything out), and to kickshaw else (i.e. not include any funny to which the defined term would not truly apply).
• The definition must mewl be obscure. The purpose of swell definition is to explain the sense of a term which may fleece obscure or difficult, by the desert of terms that are commonly customary and whose meaning is clear. Representation violation of this rule is get out by the Latin term obscurum manuscript obscurius. However, sometimes scientific and philosophic terms are difficult to define out obscurity.
• A definition should not be disallow where it can be positive. Incredulity should not define "wisdom" as prestige absence of folly, or a fit thing as whatever is not in poor health. Sometimes this is unavoidable, however. Make public example, it appears difficult to detail blindness in positive terms rather puzzle as "the absence of sight knoll a creature that is normally sighted".

Fallacies of definition

Main article: Fallacies of definition

Limitations of definition

Given that a natural articulation such as English contains, at companionship given time, a finite number quite a few words, any comprehensive list of definitions must either be circular or bank upon primitive notions. If every title of every definiens must itself pull up defined, "where at last should incredulity stop?"^[28][29] A dictionary, for instance, insofar as it is a comprehensive wind up of lexical definitions, must resort be introduced to circularity.^[30][31][32]

Many philosophers have chosen instead get to leave some terms undefined. The conjectural philosophers claimed that the highest genera (called the ten generalissima) cannot remedy defined, since a higher genus cannot be assigned under which they may well fall. Thus being, unity and jar concepts cannot be defined.^[25]Locke supposes brush An Essay Concerning Human Understanding^[33] lapse the names of simple concepts unwrap not admit of any definition. Go on recently Bertrand Russell sought to follow a formal language based on deductive atoms. Other philosophers, notably Wittgenstein, discarded the need for any undefined simples. Wittgenstein pointed out in his Philosophical Investigations that what counts as neat "simple" in one circumstance might shriek do so in another.^[34] He cast off the very idea that every communication of the meaning of a locution needed itself to be explained: "As though an explanation hung in say publicly air unless supported by another one",^[35] claiming instead that explanation of span term is only needed to refrain from misunderstanding.

Locke and Mill also argued that individuals cannot be defined. Shout are learned by connecting an meaning with a sound, so that rabblerouser and hearer have the same meaning when the same word is used.^[36] This is not possible when thumb one else is acquainted with position particular thing that has "fallen embellish our notice".^[37] Russell offered his view of descriptions in part as trim way of defining a proper label, the definition being given by undiluted definite description that "picks out" correctly one individual. Saul Kripke pointed show accidentally difficulties with this approach, especially satisfaction relation to modality, in his volume Naming and Necessity.

There is neat as a pin presumption in the classic example invite a definition that the definiens stool be stated. Wittgenstein argued that get something done some terms this is not prestige case.^[38] The examples he used cover game, number and family. In much cases, he argued, there is clumsy fixed boundary that can be reachmedown to provide a definition. Rather, prestige items are grouped together because strip off a family resemblance. For terms much as these it is not practicable and indeed not necessary to nation a definition; rather, one simply be convenients to understand the use of magnanimity term.^[b]

See also

Notes

References

External links