Definition

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The definition is a statement of the meaning of the term (word, phrase, or other set of symbols). Definitions can be classified into two broad categories, intentional definitions (which try to give the essence of the term) and the extensional definition (followed by a list of objects described by the term). Another important category of definitions is the ostensive definition class, which conveys the term meaning by showing examples. A term may have many different meanings and many meanings, and thus require some definition.

In mathematics, definitions are used to give the right meaning to a new term, rather than describing a pre-existing term. Definition and axioms are the foundation upon which all modern mathematics is built.

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Terminologi dasar

In modern usage, the definition of is something, usually expressed in words, attached to the meaning of a word or a group of words. The word or group of words that must be defined is called definiendum , and the word, group of words, or actions that define it are called definiens . In the definition of "An elephant is a big gray animal native to Asia and Africa" ​​, the word "elephant" is definiendum , and everything after the word "is" is definiens .

The definiens is not meaning of a defined word, but is something that conveys the same meaning as that word.

There are many sub-types of definitions, often specific to a particular field of knowledge or study. This includes, among many others, lexical definitions , or the dictionary definition of common words is already in the language; the demonstrative definition , which defines something by referring to the example ( "This," [pointing to a large gray animal], "is an Asian elephant." ); and preliminary definitions , which reduces the uncertainty of a word, usually in a special sense ( "'Big," among Asian female elephants, are individuals weighing more than 5,500 pounds. " >).

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Intentional definition vs extensional definitions

The intentional definition , also called the connotative definition, specifies the conditions necessary and sufficient for things that are members of a particular set. Any definition that tries to establish the essence of something, such as by genus and differentia, is an intentional definition.

The extensional definition, also called denotative definition, of a concept or term that specifies its extension. This is a list that names every object that is a member of a particular set.

Thus, the "seven deadly sins" can be defined intensely as chosen by Pope Gregory I as very damaging to the life of grace and charity in a person, thus creating the threat of eternal condemnation. The definition of extensible is a list of anger, greed, idleness, pride, lust, envy, and greed. On the contrary, while the intense definition of "Prime Minister" may be "the most senior minister of cabinet in the executive branch of the government in a parliamentary system", the definition of extensification is unlikely because it is unknown who the future prime minister will be.

Intentional definition class

The definition of genus-differia is a type of intentional definition that takes a large category ( genus ) and narrows it down to a smaller category with distinguishing characteristics (ie differences).

More formally, the definition of genus-differentia consists of:

1. genus (or family): An existing definition that serves as part of the new definition; all definitions with the same genus are considered members of the genus.
2. the differentia : Part of a new definition not provided by the genus.

For example, consider the following genus-dicha definitions:

• a triangle : A plane character who has three straight sides.
• a quadrilateral : A plane character with four straight sides.

These definitions can be expressed as a genus ("plane figure") and two differentiae ("having three straight-lined sides" and "having four tortuous sides", respectively).

It is possible to have two distinct genus-differentia definitions that describe the same term, especially when the term describes the overlap of two broad categories. For example, the two definitions of the "square" genus-differentia are equally acceptable:

• square : a rectangle that is a rhombus.
• square : a rectangular rectangle.

Thus, "square" is a member of the "genus" rectangle and the genus "rhombus".

Extensive definition class

One important form of the extensional definition is the ostensive definition . It gives a term meaning by pointing, in the case of an individual, to the object itself, or in the case of a class, to an instance of the right kind. So one can explain who Alice (individual) by pointing it to the other; or what rabbit (class) is by pointing to some and expecting others to understand. The ostensive definition process itself is critically assessed by Ludwig Wittgenstein.

The enumerative definition of a concept or term is an definition of extension that provides an explicit and complete list of all objects included in the concept or term in question. Enumerative definitions are possible only for limited sets and are only practical for relatively small sets.

Divisio and partitio

Divisio and partitio is the classic term for definition. A partitio is just an intentional definition. A divisio is not an extensional definition, but a complete subset list of sets, in the sense that each member of the "shared" cluster is a member of one of the subsets. The extreme form of divisio lists all the sets that the only members are members of the "shared" set. The difference between this and the extensional definition is that of the list of extensional definitions members , and not subsets.

Nominal definition vs real definition

In classical thinking, the definition is taken as a statement of the essence of an object. Aristotle states that the essential attributes of objects form their "essential properties", and that object definitions must include these important attributes.

The idea that the definition should state the essence of a thing causes the distinction between nominal and real quid rei or "whatness of the thing". (Early modern philosophers like Locke used the English term as "nominal essence" and "true essence"). The name "hobbit", for example, is very meaningful. It has quid nominis . But one can not know the true nature of hobbits, even if there are such things, so the true nature or quid rei of the hobbits can not be known. In contrast, the name "man" denotes the real (men) things that have certain quid rei . The meaning of a name is different from the property that the object must have in order for it to take effect.

This leads to an appropriate difference between the definitions nominal and the real . Nominal definition is a definition that explains the meaning of a word, that is what it says what it means "nominal essence," and the definition in the classical sense as given above. The actual definition, on the contrary, is one that expresses the true nature or quid rei of the object.

The preoccupation with this essence is lost in many modern philosophies. The analytic philosophy is particularly important from the attempt to explain the essence of a thing. Russell describes essence as "a hopelessly chaotic idea".

Kripke's recent formalization of the possibility of a semantic world in the logic of capital led to a new approach to essentialism. As long as the essential nature of a thing is required for it, they are the things it has in all possible worlds. Kripke refers to the name used in this way as a rigid pointer.

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Theoretical Versus Versus Operational Definition

A definition can also be classified as an operational definition or a theoretical definition.

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Terms with multiple definitions

Homonym

Homonyms are, in a narrow sense, one group of words that have the same spelling and pronunciation but have different meanings. So homonyms are homographs simultaneously (words that share the same spelling, irrespective of their pronunciation) and homophones (words that have the same pronunciation, regardless of their spelling). The condition of being a homonym is called homonimi . The homonym sample is a pair of stalk (part of the plant) and stalk (follow/harass someone) and left (past form) i> left (opposite from right). The differences are sometimes made between "true" homonyms, unrelated in origin, such as skate (skating on ice) and skate (fish), and polysemous homonyms, the copyrights, which have originally distributed, such as mouth (river) and mouth (animals).

Polysem

Polysemic is the capacity for a sign (such as word, phrase, or symbol) to have a double meaning (ie, semip or sememes and thus many senses), usually related to the meaning of contact in the semantic field. Thus it is usually regarded as distinct from homonym, where the dual meaning of a word may be unrelated or unrelated.

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In logic and math

In mathematics, the definition is generally not used to describe the existing term, but to give meaning to the new term. The meaning of a mathematical statement changes if the definition changes. The exact meaning of the terms given by mathematical definitions is often different from the English definition of the word used, which can cause confusion for students who do not pay attention to the given definition.

Classification of mathematical definitions

The author has used different terms to classify definitions used in formal languages ​​such as mathematics. Norman Swartz classifies the definition as "stipulative" if intended to guide a particular discussion. The stipulative definition can be regarded as a temporary definition, works, and can only be contradicted by showing a logical contradiction. In contrast, the definition of "descriptive" can be shown as "true" or "false" with reference to common usage.

Swartz defines the preliminary definition as the definition definition of descriptive dictionary (lexical definition) for a particular purpose by including additional criteria. The underlying definition narrows the set of things that meet the definition.

C.L. Stevenson has identified the persuasive definition as a form of definition of a provision intended to express the "true" or "general" meaning of the term, while in fact establishing modified usage (perhaps as an argument for some specific beliefs). Stevenson also notes that some definitions are "legal" or "coercive" - ​​their object is to create or change rights, duties, or crimes.

Recursive definition

The recursive definition, sometimes also called inductive definition, is the definition of the word in itself, so to speak, albeit in a useful way. Usually this consists of three steps:

1. At least one thing is specified as a specified member of the set; this is sometimes called "base set".
2. All things related to other members of the set are also counted as members of the set. This is the step that makes the definition recursive.
3. Everything else is excluded from the
set

For example, we can define the natural numbers as follows (after Peano):

1. "0" is the original number.
2. Each natural number has a unique successor, so that:
   • the natural number successor is also a natural number;
   • different native numbers have different successors;
   • no natural numbers are replaced by "0".
3. 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 replacement, which can be called "2", and so on. Notice that the second condition in the definition itself refers to natural numbers, and therefore involves self-reference. Although this definition involves a form of circularity, it is not malignant, and its definition has been quite successful.

In the same way, we can define ancestors as follows:

1. Parents are ancestors.
2. The ancestral ancestors are ancestors.
3. Nothing else is an ancestor.

Or simply: the ancestors are the parents or parents of the ancestors.

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In medicine

In the medical dictionary, the definition should be as much as possible:

• simple and easy to understand, preferably even by the general public;
• clinically useful or in the related area where the definition will be used;
• specific, that is, by reading the definition alone, ideally impossible to refer to any entity other than definiendum;
• can be measured;
• reflects current scientific knowledge.

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Issues with definitions

Error definition

Certain rules have traditionally been given for definitions (in particular, different-genus definitions).

1. The definition should define the important attributes of the defined thing.
2. Definitions should avoid circles. To define a horse as "a member of the equus species" will not convey any information. For this reason, Locking added that the term definition should not consist of terms identical to it. This would be a circular definition, a circulus in definiendo . Note, however, that it is acceptable to define two relative terms with respect to each other. Obviously, we can not define "preceding" without using the term "consequent", or vice versa.
3. Definitions should not be too wide or too narrow. It should apply to all the things in which the term specified applies (ie not miss anything), and nothing else (ie excluding things that do not really apply).
4. Definitions should not be unclear. The purpose of a definition is to explain the meaning of a term that may be unclear or difficult, using terms that are generally understood and whose meaning is clear. Violation of this rule is known as Latin obscurum per obscurius . However, sometimes scientific and philosophical terms are difficult to define without ambiguity.
5. The definition should not be negative if it can be positive. We should not define "wisdom" in the absence of ignorance, or any healthy thing like anything that does not hurt. Sometimes this can not be avoided. For example, it seems difficult to define blindness in positive terms rather than as "the absence of sight in a normally seen creature".

Definition limits

Given that natural languages ​​like English contain, at any given time, a limited number of words, a complete list of definitions must be circular or dependent on primitive concepts. If every term of each definiens should be self-defined, "where should we finally stop?" Dictionary, for example, as far as it is a comprehensive list of lexical definitions, must use circles.

Many philosophers have chosen to abandon some undefined terms. The scholastic philosophers claim that the highest genera (called ten generalissima ) can not be defined, because the higher genera can not be assigned where they fall. Thus, unity and similar concepts can not be defined. Locke assumes in the Essay on Human Understanding that the names of simple concepts do not recognize any definitions. Bertrand Russell recently attempted to develop a formal language based on logical atoms. Other philosophers, especially Wittgenstein, reject the necessity of any undefined deviation. Wittgenstein points out in his book Philosophical Investigations that what is considered "simple" in one situation may not be done in another. He rejects the idea that any explanation of the meaning of a term requires itself to be explained: "As if explanations hang in the air unless supported by others," claiming otherwise that the term explanation is only necessary to avoid misunderstanding.

Locke and Mill also argue that the individual can not be defined. Names are learned by connecting ideas with sound, so speakers and listeners have the same idea when the same word is used. This is not possible when nobody else knows a certain thing that "falls under our notice". Russell offers his theory of partial descriptions as a way of defining the exact name, the definition given by a definite description that "selects" an individual. Saul Kripke points out the difficulty with this approach, especially in relation to modalities, in his book Naming and Requirement .

There is a presumption in the classic example of the definition that definiens can be expressed. Wittgenstein argues that for some this is not the case. Examples he uses include games , number and family . In such a case, he argues, there is no fixed limit that can be used to define. Instead, items are grouped together because of family resemblance. For a term like this it is impossible and it is not necessary to declare a definition; more precisely, someone just comes to understand the term usage .

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See also

• Analytical proposition
• Definition of circle
• Clear set
• Definitionism
• Extensional definitions
• Error definition
• Uncertainty
• Intentional definition
• The lexical definition
• Operational definition
• Broad definition
• Ramsey-Lewis Method
• Semantics
• Synthetic propositions
• Theoretical definition

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Note

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References

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External links

• Definition, Stanford Encyclopedia of Philosophy Gupta, Anil (2008)
• Definitions, Dictionaries, and Meanings, Norman Swartz 1997
• Guy Longworth (ca. 2008) "Definition: Use and Variety". = in: K. Brown (ed.): Elsevier The Language and Linguistics Encyclopedia , Elsevier.
• Definition and Meaning, a very short introduction by Garth Kemerling (2001).

Source of the article : Wikipedia