definition
Information about definition
A definition is a statement of the meaning of a term, word or phrase. 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]
An extensional definition, also called a denotative definition, of a concept or term specifies its extension. It is, a list naming every object that is a member of a specific set.
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 and present Prime Ministers.
One important form of extensional definition is ostensive definition. 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.[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. Enumerative definitions are only possible for finite sets and only practical for relatively small sets.
In classical thought, a definition was taken to be a statement of the essence of a thing. 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.[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. 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. Russell described it as "a hopelessly muddle-headed notion".[9]
More recently Kripke's formalisation of possible world semantics in Modal logic led to a new approach to essentialism. 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.
For instance, we could define natural number as follows (after Peano):
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. Thus we cannot define being, unity and similar concepts.[15] Locke supposes in An Essay Concerning Human Understanding[16] that the names of simple concepts do not admit of any definition. More recently Bertrand Russell sought to develop a formal language based on logical atoms. 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.[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. 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. Saul Kripke pointed to difficulties with this approach, especially in relation to modality, in his book Naming and Necessity.
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. For terms such as these it is not possible to state a definition; rather, one simply comes to understand the use'' of the term.
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Stipulative definitions
Intension and extension
An extensional definition, also called a denotative definition, of a concept or term specifies its extension. It is, a list naming every object that is a member of a specific set.
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 and present Prime Ministers.
One important form of extensional definition is ostensive definition. 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.[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. Enumerative definitions are only possible for finite sets and only practical for relatively small sets.
Definition by genus and differentia
)
Scientific classification of living things uses definition by genus and differentia.
Rules for definition by genus and differentia
- A definition must set out the essential attributes of the thing defined.
- 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.
- 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 no other objects (i.e. not include any things to which the defined term would not truly apply).
- 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).
- 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
In classical thought, a definition was taken to be a statement of the essence of a thing. 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.[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. 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. Russell described it as "a hopelessly muddle-headed notion".[9]
More recently Kripke's formalisation of possible world semantics in Modal logic led to a new approach to essentialism. 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.
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. Normally this consists of three steps:- At least one thing is stated to be a member of the set being defined; this is sometimes called a "base set".
- 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.
- All other things are excluded from the set
For instance, we could define natural number as follows (after Peano):
- "0" is a natural number.
- 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".
- Nothing else is a natural number.
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. 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.[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. Thus we cannot define being, unity and similar concepts.[15] Locke supposes in An Essay Concerning Human Understanding[16] that the names of simple concepts do not admit of any definition. More recently Bertrand Russell sought to develop a formal language based on logical atoms. 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.[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. 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. Saul Kripke pointed to difficulties with this approach, especially in relation to modality, in his book Naming and Necessity.
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. For terms such as these it is not possible 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
Notes
1. ^ OED and www.dictionary.com.
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. 4
8. ^ Posterior Analytics Bk 2 c. 7
9. ^ A history of Western Philosophy, p. 210
10. ^ Claude Lévi-Strauss. "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. [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. 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. 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. 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. iii. 3
21. ^ Philosophical Investigations
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. 4
8. ^ Posterior Analytics Bk 2 c. 7
9. ^ A history of Western Philosophy, p. 210
10. ^ Claude Lévi-Strauss. "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. [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. 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. 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. 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. iii. 3
21. ^ Philosophical Investigations
References
- Copi, Irving (1982). Introduction to Logic. New York: Macmillan. ISBN 0-02-977520-5.
- Joseph, Horace William Brindley (1916 repr. 2000). An Introduction to Logic, 2nd edition. Clarendon Press repr. Paper Tiger. ISBN 1-889439-17-7. (full text of 1st ed.)
- Joyce, George Hayward (1926). Principles of logic, 3d ed., new impression. London, New York: Longmans, Green and co. (contents of 1949 ed.) http://www.amazon.com/dp/B00086LT0G http://catalog.loc.gov/
- McKean, Erin (2001). Verbatim: From the bawdy to the sublime, the best writing on language for word lovers, grammar mavens, and armchair linguists. Harvest Books. ISBN 0-15-601209-X.
- Simpson, John; Edmund Weiner (1989). Oxford English Dictionary, second edition (20 volumes). Oxford University Press. ISBN 0-19-861186-2.
- Wittgenstein, Ludwig (1953/2001). Philosophical Investigations. Blackwell Publishing. ISBN 0-631-23127-7.
External links
- The structure and internal logic of definitions
- Dictionary.com
- Definitions, Dictionaries, and Meanings, Norman Swartz 1997
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In linguistics, meaning is the content carried by the words or signs exchanged by people when communicating through language. Restated, the communication of meaning is the purpose and function of language.
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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 context.
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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.
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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 its definition. The term may also refer to the complete set of meanings or properties that are implied by a concept, although the term
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In metaphysics, extension is, roughly speaking, the property of "taking up space". René Descartes defines extension as the property of existing in more than one dimension. For Descartes, the primary characteristic of matter is extension, just as the primary characteristic of mind
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In logic and mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come that definition, that is, the necessary and sufficient conditions for belonging to the set being defined.
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necessary and sufficient condition of another means that the former statement is true if and only if the latter is true.
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- A necessary condition of a statement must be satisfied for the statement to be true.
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SET may stand for:
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- Sanlih Entertainment Television, a television channel in Taiwan
- Secure electronic transaction, a protocol used for credit card processing,
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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.
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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 implied or suggested by the concept in question.
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object is a thing, an entity, or a being. This may be taken in several senses.
In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all.
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In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all.
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SET may stand for:
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- Sanlih Entertainment Television, a television channel in Taiwan
- Secure electronic transaction, a protocol used for credit card processing,
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A prime minister is the most senior minister of cabinet in the executive branch of government in a parliamentary system. The position is usually held by, but need not always be held by, a politician.
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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 (as with children and new speakers of a language) or because of the
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Ludwig Josef Johann Wittgenstein (IPA: ['luːtvɪç 'joːzɛf 'joːhan 'vɪtgənʃtaɪn]
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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.
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object is a thing, an entity, or a being. This may be taken in several senses.
In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all.
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In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all.
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Fallacies of definition refer to the various ways in which definitions can fail to have merit. The term is used to suggest analogy with the logical fallacies. This is a typical sort of list found in texts used in college logic courses.
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359, 1805–1809. Hofstadter, Douglas. (2007) I Am A Strange Loop. Basic Books. ISBN 978-0465030781 Kane, Robert (1998). The Significance of Free Will. New York: Oxford University Press ISBN 0-19-512656-4 Lawhead, William F. (2005).
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In philosophy, essence is the attribute (or set of attributes) that make an object or substance what it fundamentally is, and that it has necessarily (in contrast with accidental properties that the object or substance has contingently, and without which the substance could have
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Aristotle (Greek: Ἀριστοτέλης Aristotélēs) (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great.
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The Posterior Analytics is a text from Aristotle's Organon containing a classic treatment and discussion of demonstration, definition, and scientific knowledge. The demonstration is distinguished as a syllogism productive of scientific knowledge
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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.
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Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, historian, logician, mathematician, advocate for social reform, pacifist, and prominent rationalist.
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Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke, beginning when he was a teenager.
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possible worlds is used to express modal claims. In philosophy, the term "modality" covers such notions as "possibility", "necessity", and "contingency". Talk of possible worlds is very widespread in contemporary philosophical discourse (especially in the English-speaking world),
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In formal logic, a modal logic is any logic for handling modalities: concepts like possibility, existence, and necessity. Logics for handling a number of other ideas, such as eventually, formerly, can, could
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This article or section may be confusing or unclear for some readers.
Please [improve the article] or discuss this issue on the talk page. This article has been tagged since August 2007.
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Please [improve the article] or discuss this issue on the talk page. This article has been tagged since August 2007.
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non-rigid or flaccid designators, which may designate different things in different possible worlds.
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Proper Names and Definite Descriptions
The notion of rigid designation was first introduced by Saul Kripke in the lectures that became Naming and Necessity..... Click the link for more information.
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