A definition is a passage that explains the meaning The field of semantics is often understood as a branch of linguistics, but non-idealized meaning as a type of semantics is more accurately a branch of psychology and ethics. Meaning in so far is it is objectified by not considering particular situations and the real intentions of speakers and writers examines the ways in which words, phrases, and of a term (a word A word is the smallest free form in a language, in contrast to a morpheme, which is the smallest unit of meaning. A word may consist of only one morpheme (e.g. wolf), but a single morpheme may not be able to exist as a free form (e.g. the English plural morpheme -s), phrase In grammar, a phrase is a group of words functioning as a single unit in the syntax of a sentence or other set of symbols A symbol is something such as an object, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention. For example, a red octagon may be a symbol for "STOP". On maps, crossed sabres may indicate a battlefield. Numerals are symbols for numbers . All language consists of symbols), or a type of thing. The term to be defined is the definiendum (plural definienda). A term may have many different senses or meanings. For each such specific sense, a definiens (plural definientia) is a cluster of words that defines it.

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 The lexical definition of a term, also known as the dictionary definition, is the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a has additional details, typically including an etymology Etymology is the study of the history of words, their origins, and how their form and meaning have changed over time 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 [3].

A precising definition A precising definition is a definition that extends the lexical definition of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the 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 Charles Leslie Stevenson was an American analytic philosopher best known for his work in ethics and aesthetics has identified persuasive definition A persuasive definition is a form of definition which purports to describe the 'true' or 'commonly accepted' meaning of a term, while in reality stipulating an uncommon or altered use, usually to support an argument for some view, or to create or alter rights, duties or crimes. The terms thus defined will often involve emotionally charged but 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.[1]

Contents

Intension and extension

Main articles: Intension In linguistics, logic, philosophy, and other fields, an intension is any property or quality connoted by a word, phrase or other symbol. In the case of a word, it is often implied by the word's definition. The term may also refer to all such intensions collectively, although the term comprehension is technically more correct for this and Extension (semantics) In any of several studies that treat the use of signs, for example in linguistics, logic, mathematics, semantics, and semiotics, the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are

An intensional definition In logic and mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined, also called a coactive definition, specifies the necessary and sufficient conditions In logic, the words necessity and sufficiency refer to the implicational relationships between statements. The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true for a thing being a member of a specific set A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Although it was invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In. Any definition that attempts to set out the essence of something, such as that by genus and differentia A genus-differentia definition is one in which a word or concept that indicates a species -- a specific type of item, not necessarily a biological category -- is described first by a broader category, the genus, then distinguished from other items in that category by a differentia. The differentiae of a species are the species' properties that, is an intensional definition.

An extensional definition An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question, also called a denotative definition, of a concept or term specifies its extension In any of several studies that treat the use of signs, for example in linguistics, logic, mathematics, semantics, and semiotics, the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are. It is a list naming every object Object is a technical term used in epistemology, a branch of philosophy concerning itself with the study of knowing. Aristotle had said, "All men by nature desire to know." René Descartes expanded this knowing into the grounds of certainty with cogito ergo sum, typically translated as "I think therefore I am." The thinker that is a member of a specific set A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Although it was invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In.

So, for example, an intensional definition of 'Prime Minister A prime minister is the most senior minister of cabinet in the executive branch of government in a parliamentary system. In many systems, the prime minister selects and can dismiss other members of the cabinet, and allocates posts to members within the Government. In most systems, the prime minister is the presiding member and chairman of the' 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 A prime minister is the most senior minister of cabinet in the executive branch of government in a parliamentary system. In many systems, the prime minister selects and can dismiss other members of the cabinet, and allocates posts to members within the Government. In most systems, the prime minister is the presiding member and chairman of the and future prime ministers A prime minister is the most senior minister of cabinet in the executive branch of government in a parliamentary system. In many systems, the prime minister selects and can dismiss other members of the cabinet, and allocates posts to members within the Government. In most systems, the prime minister is the presiding member and chairman of the.

One important form of the extensional definition is ostensive definition An ostensive definition conveys the meaning of a term by pointing out examples. This type of definition is often used where the term is difficult to define verbally, either because the words will not be understood or because of the nature of the term (such as colors or sensations). It is usually accompanied with a gesture pointing out the object. 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 Ludwig Josef Johann Wittgenstein was an Austrian-British philosopher who worked primarily in the areas of logic, philosophy of mathematics, philosophy of mind, and philosophy of language.[2]

An enumerative definition An enumerative definition of a concept or term is a special type of 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 of a concept or term is an extensional definition An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question that gives an explicit and exhaustive listing of all the objects Object is a technical term used in epistemology, a branch of philosophy concerning itself with the study of knowing. Aristotle had said, "All men by nature desire to know." René Descartes expanded this knowing into the grounds of certainty with cogito ergo sum, typically translated as "I think therefore I am." The thinker 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 Classics is the branch of the Humanities comprising the languages, literature, philosophy, history, art, archaeology and other culture of the ancient Mediterranean world (Bronze Age ca. BC 3000 – Late Antiquity ca. AD 300–600); especially Ancient Greece and Ancient Rome during Classical Antiquity (ca. BC 600 – AD 600). Initially, study of terms for definitions. A partitio is simply an intensional definition. A divisio is not an extensional definition. Divisio is an exhaustive list of subsets In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment. Correspondingly, set B is a superset of A since all elements of A are also elements of B 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.[3]

Definition by genus and differentia

Life Domain Kingdom Phylum Class Order Family Genus Species
The hierarchy of biological classification Biological classification, or scientific classification in biology, is a method by which biologists group and categorize organisms by biological type, such as genus or species. Biological classification is a form of scientific taxonomy, but should be distinguished from folk taxonomy, which lacks scientific basis. Modern biological classification's eight major taxonomic ranks In biological classification, rank is the level in a taxonomic branched ordering of living things. The most specific level is species, the next most specific is genus, and then family, class, etc. Sometimes (but only rarely) the term "taxonomic category" is used and more often the term "rank" is used -- the ranking, or ordering,, which is an example of definition by genus and differentia. Intermediate minor rankings are not shown. Main article: Genus-differentia definition A genus-differentia definition is one in which a word or concept that indicates a species -- a specific type of item, not necessarily a biological category -- is described first by a broader category, the genus, then distinguished from other items in that category by a differentia. The differentiae of a species are the species' properties that

A new definition can be composed by two parts:

  1. a genus In biology, a genus is a low-level taxonomic rank (a taxon) used in the classification of living and fossil organisms, which is an example of definition by genus and differentia. The term comes from Latin genus "descent, family, type, gender", cognate with Greek: γένος – genos, "race, stock, kin" (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, and a definition can be composed of multiple genera (more than one genus).
  2. the differentia: The portion of the new definition that is not provided by the genera.

For example, consider these two definitions:

Those definitions can be expressed as a genus and 2 differentiae:

  1. a genus: A plane figure.
  2. 2 differentiae:
    • the differentia for a triangle: bounded by 3 straight sides.
    • the differentia for a quadrilateral: bounded by 4 straight sides.

Continuing the process of differentiation:

Importantly, differentiae can include genera. For instance, consider the following:

This definition could be recast as follows:

In other words, a genus of a definition provides a means by which to specify an is-a In knowledge representation and object-oriented programming and design, is-a is a relationship where one class D is a subclass of another class B (and so B is a superclass of D) relationship, and the non-genus portions of the differentia of a definition provides a means by which to specify a has-a In database design and object oriented program architecture, has-a is a relationship where one object "belongs" to (is a part or member of) another object (called the composite type), and behaves according to the rules of ownership. In simple words, has-a relationship in an object is called a member field of an object. Multiple has-a relationship.

When a system of definitions is constructed with genera and differentiae, the definitions can be thought of as nodes forming a hierarchy A hierarchy (Greek: hierarchia , from hierarches, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above," "below," or "at the same level as" one another and with only one "neighbor" above and below each of or—more generally—a directed acyclic graph In mathematics, a directed acyclic graph, also called a DAG, , is a directed graph with no directed cycles; that is, for any vertex v, there is no nonempty directed path that starts and ends on v; a node that has no predecessors It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges is a most general definition; each node along a directed path is more differentiated (or more derived) than its predecessors, and a node with no successors It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges is a most differentiated (or a most derived) definition. When a definition, S, is the tail It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges of all of its successors (that is, S has at least one successor and all of the direct successors It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges of S are most differentiated definitions), then S is often called a species In biology, a species is one of the basic units of biological classification and a taxonomic rank. A species is often defined as a group of organisms capable of interbreeding and producing fertile offspring. While in many cases this definition is adequate, more precise or differing measures are often used, such as similarity of DNA, morphology or and each of its direct successors is often called an individual As commonly used, an individual is a person or any specific object in a collection. In the 15th century and earlier, and also today within the fields of statistics and metaphysics, individual means "indivisible", typically describing any numerically singular thing, but sometimes meaning "a person." . From the seventeenth or an entity An entity is something that has a distinct, separate existence, though it need not be a material existence. In particular, abstractions and legal fictions are usually regarded as entities. In general, there is also no presumption that an entity is animate. Entities are used in system developmental models that display communications and internal; the differentia of an individual is called an identity In philosophy, identity is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from entities of a different type. Or, in layman's terms, identity is whatever makes something the same or different. For instance:

The identity itself (or some part of it) is often used to refer to the entire individual, a phenomenon that is known in linguistics as a pars pro toto synechdoche.

Rules for definition by genus and differentia

Main article: Fallacies of definition

Certain rules have traditionally been given for this particular type of definition.[4][5][6]

  1. A definition must set out the essential attributes of the thing defined.
  2. 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.
  3. 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).
  4. 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).
  5. 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'.

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