Editing Circular definition

{{Short description|Self-referential description of meaning}}
{{Refimprove|date=March 2016}}
[[File:Circular definition of circular definition.png|thumb|Circular definition of "circular definition"|alt=Circular definition: a definition that is circular]]
A '''circular definition''' is a type of [[definition]] that uses the [[Terminology|term]](s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: [[pragmatics|pragmatic]], [[lexicographic]] and [[linguistic]]. Circular definitions are related to [[circular reasoning]] in that they both involve a [[self-referential]] approach.

Circular definitions may be unhelpful if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself.

In linguistics, a circular definition is a description of the meaning of a [[lexeme]] that is constructed using one or more synonymous lexemes that are all defined in terms of each other.<ref name=SIL>{{Cite web |date=2015-12-03 |title=Circular Definition |url=https://glossary.sil.org/term/circular-definition |access-date=2023-03-07 |website=Glossary of Linguistic Terms |language=en}}</ref>

==Approaches to characterizing circular definitions==
===Classical===
In [[Plato]]'s ''[[Meno]]'', several definitions of [[virtue]] are offered, the third of which states that virtue is the power of attaining good justly or with justice, where justice has already been defined as a form or aspect of virtue. [[Socrates]], in response to Meno, states that the process of finding a definition will have to be started again because the wording offered defines virtue as a part of virtue.<ref>Plato, ''Meno'', 79b-c</ref>

===Pragmatic===
From a pragmatic point of view, circular definitions may be characterised in terms of new, useful or helpful information: a definition is deficient if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself. Such definitions lead to a need for additional information that motivated someone to look at the definition in the first place and, thus, violate the principle of providing new or useful information.<ref>Wierzbicka, A., ''Semantics: Primes and Universals''. Oxford University Press: 1996.</ref> Here are some examples:

* Suppose we define "[[oak]]" as a [[tree]] which has [[catkin]]s and grows from an acorn, and then define "acorn" as the [[nut (fruit)|nut]] produced by an oak tree. To someone who does not know which trees are oaks, nor which nuts are acorns, the definition is inadequate.
* If someone wants to know what a [[cellular phone]] is, telling them that it is a "phone that is cellular" will not be especially illuminating. Much more helpful would be to explain the concept of a cell in the context of telecommunications, or at least to make some reference to portability.
* Similarly, defining [[dialectical materialism]] as "materialism that involves dialectic" is unhelpful.

Consequently, when constructing systems of definitions, authors should use good practices that avoid producing viciously circular definitions. In many learner's dictionaries, circular definitions are greatly reduced by writing definitions using only the words in a constrained [[defining vocabulary]].<ref>Bullock, D. 'NSM + LDOCE: A Non-Circular Dictionary of English', ''International Journal of Lexicography'', 24/2, 2011: 226-240</ref>

===Lexicographic===
From a lexicographic point of view, the simplest form of circular definition in a dictionary is in terms of synonyms, and the number of steps for closing the definition chain into a circle is known as the ''depth'' of the circular definition: the circular definition "object: a thing" → "thing: an object" is a circular definition with a depth of two. The circular definition "object: a thing" → "thing: an entity" → "entity: an object" has a depth of three.

[[File:EulerDiagram.svg|thumb|"Four legs" is a simple example of differentia specifica.]]
The classic "genus-difference" dictionary definition is in terms of nearest kind (''genus proximum'') and specific differences (''differentia specifica''). This genus-difference description may be involved in producing circular definitions of part and kind relationships, for example: "rake: an implement with three or more tines" → "tine: a part of a rake". However, if more specific differences are added, then the effect of circularity may disappear: "rake: a gardening implement with a long handle with three or more tines arranged on crossbar at 90° to the handle and the tines at 90° to both crossbar and handle"; in this case, "tine" is most usefully defined with reference to "rake", but with additional differences providing points of comparison, e.g.: "tine: a sharp spike at the end of a rake". In practice, a pragmatic approach is often taken in considering the effects of circularity in dictionary definitions.<ref>Atkins, B. and M. Rundell. ''The Oxford Guide to Practical Lexicography''. Oxford University Press: 2008.</ref>

====Circular lexicographic (dictionary) definitions====
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Dictionary entries are often given as examples of apparent circular definitions. Dictionary production, as a project in [[lexicography]], should not be confused with a [[mathematical]] or [[logical]] activity, where giving a definition for a word is similar to providing an [[explanans]] for an [[explanandum]] in a context where practitioners are expected to use a [[deductive system]].<ref>Michael Silverstein (2006). "[http://www.annualreviews.org/doi/abs/10.1146/annurev.anthro.35.081705.123327?journalCode=anthro Old Wine, New Ethnographic Lexicography]". ''Annual Review of Anthropology'', 35:486-7.</ref><ref name=Seargeant/> While, from a [[linguistic prescriptivist]] perspective, any [[dictionary]] might be believed to dictate correct usage, the [[linguistic descriptivist]] perspective recognizes that looking up words in dictionaries is not itself a rule-following practice independent of the give-and-take of using words in context.<ref name=Seargeant>Philip Seargeant, "Lexicography as a Philosophy of Language". ''Language Sciences'', 33:1-10 (2011).</ref> Thus, the example of a definition of oak given above (something that has catkins and grows from acorns) is not completely useless, even if "acorn" and "catkin" are defined in terms of "oak", in that it supplies additional concepts (e.g., the concept of catkin) in the definition. {{citation needed|date=March 2016}}

While a dictionary might produce a "circle" among the terms, "oak", "catkin", and "acorn", each of these is used in different {{clarify|reason="definition"or "context"?|text=contexts|date=March 2016}} (e.g., those related to plants, trees, flowers, and seeds) that generate ever-branching networks of usages. In another case it might produce a true circle. Taken as a whole, dictionaries are circular because each and every word is defined in terms of words that are also contained within the dictionary. ({{clarify|text=A person could not pick up a (foreign) dictionary and make any sense of it unless they already know the meaning of a minimal subset of a number of words without having the need to refer to the dictionary for said meaning.|date=March 2016}})

{{clarify|reason=needs elaboration; the concept of "circularity" is not evident in this sentence|text=A circular definition crept into the classic definition of death that was once "the permanent cessation of the flow of vital bodily fluids", which raised the question "what makes a fluid vital?"<ref>Tulloch, Gail (2005). ''Euthanasia, Choice and Death'', p.8. Edinburgh University. {{ISBN|9780748618811}}.<!--Quotes or paraphrases [[Peter Singer]].--></ref>|date=March 2016}}

Definitions in lexicography can be broadly or narrowly circular. Narrowly circular definitions simply define one word in terms of another. A broadly circular definition has a larger circle of words. For example, the definition of the primary word is defined using two other words, which are defined with two other words, etc., creating a definitional chain. This can continue until the primary word is used to define one of the words used in the chain, closing the wide circle of terms. If all definitions rely on the definitions of other words in a very large, but finite chain, then all text-based definitions are ultimately circular. [[Extension (semantics)]] to the actual things that referring terms like nouns stand for, provided that agreement on reference is accomplished, is one method of breaking this circularity, but this is outside the capacity of a text-based definition.{{citation needed|date=March 2016}}

====Examples of narrowly circular definitions in dictionaries====
The 2007 [[Merriam-Webster]] dictionary defines a "hill" and a "mountain" this way:

: hill - "1: a usually rounded natural elevation of land '''lower than a mountain'''"<ref>[http://www.m-w.com/dictionary/hill "hill"]. Merriam-Webster. Retrieved January 17, 2013.</ref>
: mountain - "1a: a landmass that projects conspicuously above its surroundings and is '''higher than a hill'''"<ref>[http://www.m-w.com/dictionary/mountain "mountain"]. Merriam-Webster. Retrieved January 17, 2013.</ref>

Merriam-Webster's online dictionary provides another example of a circular definition with the words "condescending" and "patronizing:"

: Main Entry: condescending<ref>[http://www.merriam-webster.com/dictionary/condescending "condescending"]. Merriam-Webster. Retrieved January 17, 2013.</ref>
: Function: adjective
: 1 : showing or characterized by condescension: patronizing

From "condescension":

: Main Entry: condescension<ref>[http://www.merriam-webster.com/dictionary/condescension "condescension"]. Merriam-Webster. Retrieved January 17, 2013.</ref>
: Function: noun
: 1 : voluntary descent from one's rank or dignity in relations with an inferior
: 2 : '''patronizing attitude''' or behavior

To "patronize":

: Main Entry: patronize<ref>[http://www.merriam-webster.com/dictionary/patronizing "patronizing"]. Merriam-Webster. Retrieved January 17, 2013.</ref>
: Function: transitive verb
: 1 : to act as patron of: provide aid or support for
: 2 : '''to adopt an air of condescension toward''': treat haughtily or coolly
From the Oxford Dictionary of English: 

* Punishment – "a ''penalty'' inflicted as ''retribution'' for an offence".
* ''Penalty'' – "a punishment imposed for breaking a law, rule, or contract".
* ''Retribution'' – "punishment inflicted on someone as '''vengeance''' for a wrong or criminal act".
* '''Vengeance''' – "punishment inflicted or retribution exacted for an injury or wrong".

Therefore, a punishment means "a ''punishment imposed for breaking a law, rule, or contract'' inflicted as ''punishment inflicted on someone as'' '''punishment inflicted or retribution exacted for an injury or wrong''' ''for a wrong or criminal act'' for an offence". Obviously, this is not the final result of substitution as this would result in an endlessly long sentence.

==Mathematical theory==
Formal approaches to characterizing circular definitions are found in [[logic]], [[mathematics]] and in [[computer science]]. A branch of mathematics called [[non-well-founded set theory]] allows for the construction of circular sets. Circular sets are good for modelling cycles, and, despite the field's name, this area of mathematics is well founded. [[Computer science]] allows for procedures to be defined by using [[recursion (computer science)|recursion]]. Such definitions are not circular as long as they terminate.<ref>{{Cite web|title=Recursion|url=https://www.cs.utah.edu/~germain/PPS/Topics/recursion.html|access-date=June 18, 2020|website=University of Utah School of Computing}}</ref>

==Linguistics==
Linguistically, a circular definition is a description of the meaning of a [[lexeme]] that is constructed using one or more synonymous lexemes that are all defined in terms of each other.<ref name=SIL />

==See also==
* [[Begging the question]]
* [[Circular reasoning]]
* [[Fallacies of definition]]
* [[Genus–differentia definition]]
* [[Infinite regress]]
* [[Lexicography]]
* [[Lexical definition]]
* [[Meta-circular evaluator]]
* [[Self-reference]]
* [[Self-refuting idea]]
* [[Recursive definition]]
* [[Revision theory]]
* [[Tautology (logic)|Tautology]]
* [[Vicious circle principle]]

==References==
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{{Defining}}

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[[Category:Definition]]
[[Category:Philosophical logic]]