A definition is a statement of the meaning of a word or phrase. This article is about meaning as it is studied in the discipline of linguistics The term to be defined is known as the definiendum (Latin: that which is to be defined). The words which define it are known as the definiens (Latin: that which is doing the defining). ^[1]

Contents 1 Stipulative definitions 2 Intension and extension 3 Definition by genus and differentia 3.1 Rules for definition by genus and differentia 3.2 Essence 4 Genetic definition 5 Recursive definitions 6 Limitations of definition 7 See also 8 External links 9 References 10 Notes

Stipulative definitions

Main article: Stipulative definition

There are two types of definitions:

A descriptive definition provides to a term a meaning which is in general use. A stipulative definition is a type of Definition in which a new or currently-existing term is given a new meaning for the purposes of argument or discussion in a given

A stipulative definition of a term carries a meaning which a speaker wants it to convey for the purpose of his or her discourse. Thus, the term may be new, or a stipulative definition may prescribe a new meaning to a term which is already in use.

A descriptive definition can be shown to be "right" or "wrong" by comparison to usage, but a stipulative definition cannot.

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. A precising definition is a Definition that extends the dictionary definition ( Lexical definition) of a term for a specific purpose by including additional criteria

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. Charles Leslie Stevenson (1908–1979 was an American Analytic philosopher best known for his work in Ethics and Aesthetics. 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

Stevenson has also noted that some definitions are "legal" or "coercive", whose object is to create or alter rights, duties or crimes. ^[2]

Intension and extension

Main articles: Intension and Extension (metaphysics)

An intensional definition, also called a connotative definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set. Not to be confused with the homophone Intention; or the related concept of Intentionality. In Metaphysics, extension is roughly speaking the property of "taking up space" In Logic and Mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come to that Definition Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional 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

An extensional definition, also called a denotative definition, of a concept or term specifies its extension. An extensional definition of a concept or term formulates its meaning by specifying its extension, that is every object that falls under the Definition In any of several studies that treat the use of signs for example in Linguistics, Logic, Mathematics, Semantics, and Semiotics, the It is, a list naming every object that is a member of a specific set. For other uses of Object see Object. In Philosophy, an object is a thing an Entity, or a Being.

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 (; whereas an extensional definition would be simply a list of all past, present and future prime ministers. This article is about the government position For other uses see Prime Minister (disambiguation. This article is about the government position For other uses see Prime Minister (disambiguation. This article is about the government position For other uses see Prime Minister (disambiguation.

One important form of the extensional definition is ostensive definition. An ostensive definition conveys the meaning of a term by pointing out examples 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'. This is the manner in which all children initially learn the names of things. 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. An extensional definition of a concept or term formulates its meaning by specifying its extension, that is every object that falls under the Definition For other uses of Object see Object. In Philosophy, an object is a thing an Entity, or a Being. Enumerative definitions are only possible for finite sets and only practical for relatively small sets.

Definition by genus and differentia

Main article: Genus-differentia definition

Traditionally, a definition consists of the genus (the family) of thing to which the defined thing belongs, and the differentia (the distinguishing feature which marks it off from other members of the same family). 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 Thus 'triangle' is defined as 'a plane figure (genus) bounded by three straight sides (differentia). ^[4]

Rules for definition by genus and differentia

Main article: Fallacies of definition

Certain rules have traditionally been given for this particular type of definition. Fallacies of definition refer to the various ways in which Definitions can fail to have merit ^[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, Locke adds that a definition of a term must not consist of terms which are synonymous with it. This error is known as 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). The question of free will
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'.

Essence

Main article: Essence

In classical thought, a definition was taken to be a statement of the essence of a thing. In Philosophy, essence is the attribute or set of attributes that make an object or substance what it fundamentally is and which it has by necessity 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. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. ^[7]

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,^[8] 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. The Posterior Analytics is a text from Aristotle 's Organon that deals with demonstration, Definition, and Scientific knowledge This led medieval logicians to distinguish between the so-called 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. Analytic philosophy (sometimes analytical philosophy) is a generic term for a style of Philosophy that came to dominate English-speaking countries in the 20th century Russell described it as "a hopelessly muddle-headed notion". Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian ^[9]

More recently Kripke's formalisation of possible world semantics in Modal logic led to a new approach to essentialism. Kripke semantics (also known as relational semantics or frame semantics, and often confused with Possible world semantics) is a formal Semantics A modal logic is any system of formal logic that attempts to deal with modalities. In Philosophy, essentialism is the view that for any specific kind of Entity, there is a set of Characteristics or Properties all of which 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. Philosophy of language]]In Modal logic and the Philosophy of language, a term is said to be a rigid designator when it designates (picks out denotes refers to the same thing

Genetic definition

A genetic definition describes the process or method by which a thing is formed.

"But if you define the circle as a pattern resulting from having a segment of a line revolve around one of its ends, this is a genetic definition because it tells you how to make a circle. "^[10]

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. A recursive definition or inductive definition is one that defines something in terms of itself (that is recursively) albeit in a useful way Normally this consists of three steps:

1. At least one thing is stated to be a member of the set being defined; this is sometimes called a "base set".
2. 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. Recursion, in Mathematics and Computer science, is a method of defining functions in which the function being defined is applied within its own definition
3. All other things are excluded from the set

For instance, we could define natural number as follows (after Peano):

1. "0" is a natural number. In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an In Mathematical logic, the Peano axioms, also known as the Dedekind-Peano axioms or the Peano postulates, are a set of Axioms for the Natural
2. 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".
3. 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. Self-reference is a phenomenon in natural or Formal languages consisting of a sentence or Formula referring to itself directly or Although this sort of definition involves a form of circularity, it is not vicious, and the definition is quite successful. A circular definition is one that assumes a prior understanding of the term being defined

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 leave some terms undefined. In the Philosophy of language, a natural language (or ordinary language) is a Language that is spoken or written in phonemic-alphabetic or phonemically-related English is a West Germanic language originating in England and is the First language for most people in the United Kingdom, the United States If every term of every definiens must itself be defined, where should we stop?^[11] A dictionary, for instance, insofar as it is a comprehensive list of lexical definitions, must resort to circularity. The lexical definition of a term also known as the Dictionary definition is the meaning of the term in common usage The Symbol Grounding Problem is related to the problem of how Words ( Symbols get their Meanings and hence to the problem of what meaning itself really is ^[12][13][14]

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. Scholasticism was the dominant form of theology and philosophy in the Latin West in the Middle Ages, particularly in the 12th 13th and 14th centuries Thus we cannot define being, unity and similar concepts. Disambiguation For the Wigwam album see Being (album, for spiritual or religious beingness, see Ego (spirituality ^[15] Locke supposes in An Essay Concerning Human Understanding^[16] that the names of simple concepts do not admit of any definition. John Locke (29 August 1632 – 28 October 1704 was an English Philosopher. An Essay Concerning Human Understanding is one of John Locke 's two most famous works the other being his Second Treatise on Civil Government More recently Bertrand Russell sought to develop a formal language based on logical atoms. Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian Logical atomism is a philosophical belief that originated in the early 20th century with the development of Analytic philosophy. 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. Philosophical Investigations ( Philosophische Untersuchungen) is along with the Tractatus Logico-Philosophicus, one of the two major works ^[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. John Stuart Mill (20 May 1806 &ndash 8 May 1873 British Philosopher, political economist, civil servant and Member of Parliament, was an influential Individuation (Latin principium individuationis) is a concept which appears in numerous fields and may be encountered in work by Gilbert Simondon, Bernard Stiegler 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. The theory of descriptions is one of the philosopher Bertrand Russell 's most significant contributions to the Philosophy of language. A definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun Saul Kripke pointed to difficulties with this approach, especially in relation to modality, in his book Naming and Necessity. Saul Aaron Kripke (born on November 13, 1940 in Bay Shore New York) is an American philosopher and Logician now Emeritus A modal logic is any system of formal logic that attempts to deal with modalities.

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. This article is about the philosophical term proposed by Ludwig Wittgenstein not about the common observation that offspring resemble parents and one another 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.

See also

• Analytic proposition
• Demonstration
• Fallacies of definition
• Ramsey-Lewis method
• Synthetic proposition
• Indeterminacy

External links

• Gupta, Anil (2008) Definitions, Stanford Encyclopedia of Philosophy
• The structure and internal logic of definitions
• Definitions, Dictionaries, and Meanings, Norman Swartz 1997
• Definitions.net

References

Notes

1. ^ OED and www.dictionary.com. The Oxford English Dictionary ( OED) published by the Oxford University Press (OUP is a comprehensive Dictionary of the English
2. ^ Stevenson, C. L. , Ethics and Language, Connecticut 1944
3. ^ Philosophical investigations, Part 1 §27-34
4. ^ See Genus-differentia definition
5. ^ Copi 1982 pp 165-169
6. ^ Joyce, ibidem
7. ^ Posterior Analytics, Bk 1 c. 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 The Posterior Analytics is a text from Aristotle 's Organon that deals with demonstration, Definition, and Scientific knowledge 4
8. ^ Posterior Analytics Bk 2 c. The Posterior Analytics is a text from Aristotle 's Organon that deals with demonstration, Definition, and Scientific knowledge 7
9. ^ A history of Western Philosophy, p. 210
10. ^ Claude Lévi-Strauss. Claude Lévi-Strauss (klod levi stʁos born 28 November 1908 is a French Anthropologist. "Discussion of Lévi-Strauss's paper 'Social Structure'" ([1952] 1962) in An appraisal of anthropology today. Edited by Sol Tax. University of Chicago Press 1953
11. ^ This parallels the diallelus, but leading to scepticism about meaning rather than knowledge
12. ^ 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. The regress argument (also known as the diallelus) is a problem in Epistemology and in general a problem in any situation where a statement has to be justified The pursuit of lexicography is divided into two related disciplines Practical lexicography is the art or Craft of compiling writing and editing dictionaries [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)
13. ^ 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. John Langshaw Austin ( March 26, 1911 – February 8, 1960) was a British philosopher of language, born in Lancaster and 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. James Opie Urmson (1915-) was Fellow Tutor and Emeritus Fellow in Philosophy of Corpus Christi College Oxford. Sir Geoffrey James Warnock (1923&ndash1995 was a Philosopher and Vice-Chancellor of Oxford University. Oxford: Oxford UP, 1961. 1979. )
14. ^ In the game of Circ, players compete to find circularity in a dictionary.
15. ^ Joyce, G. H. Principles of Logic, Chapter x
16. ^ Essay, Bk III, c. 4
17. ^ See especially Philosophical Investigations Part 1 §48
18. ^ 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. Philosophical Investigations ( Philosophische Untersuchungen) is along with the Tractatus Logico-Philosophicus, one of the two major works 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
19. ^ This theory of meaning is one of the targets of the private language argument
20. ^ Essay III. Philosophical Investigations ( Philosophische Untersuchungen) is along with the Tractatus Logico-Philosophicus, one of the two major works The private language argument is a philosophical Argument introduced by Ludwig Wittgenstein in his later work especially in the Philosophical Investigations iii. 3
21. ^ Philosophical Investigations

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