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A circular definition is a description that uses the 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:
pragmatic Pragmatism is a philosophical movement. Pragmatism or pragmatic may also refer to: *Pragmaticism, Charles Sanders Peirce's post-1905 branch of philosophy * Pragmatics, a subfield of linguistics and semiotics *'' Pragmatics'', an academic journal i ...
, lexicographic and linguistic. 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.


Approaches to characterizing circular definitions


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. Here are some examples: * Suppose we define " oak" as a
tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...
which has
catkin A catkin or ament is a slim, cylindrical flower cluster (a spike), with inconspicuous or no petals, usually wind-pollinated (anemophilous) but sometimes insect-pollinated (as in '' Salix''). They contain many, usually unisexual flowers, arrang ...
s and grows from an acorn, and then define "acorn" as the 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.


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. 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.


Mathematical

Formal approaches to characterizing circular definitions are found in
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...
,
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
and in
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
. 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 Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
allows for procedures to be defined by using
recursion Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematic ...
. Such definitions are not circular as long as they terminate.


Circular lexicographic (dictionary) definitions

Dictionary entries are often given as examples of apparent circular definitions. Dictionary production, as a project in
lexicography Lexicography is the study of lexicons, and is divided into two separate academic disciplines. It is the art of compiling dictionaries. * Practical lexicography is the art or craft of compiling, writing and editing dictionaries. * Theoreti ...
, should not be confused with a mathematical or logical activity, where giving a definition for a word is similar to providing an
explanans An explanandum (a Latin term) is a sentence describing a phenomenon that is to be explained, and the explanans are the sentences adduced as explanations of that phenomenon. For example, one person may pose an ''explanandum'' by asking "Why is the ...
for an
explanandum An explanandum (a Latin term) is a sentence describing a phenomenon that is to be explained, and the explanans are the sentences adduced as explanations of that phenomenon. For example, one person may pose an ''explanandum'' by asking "Why is there ...
in a context where practitioners are expected to use a deductive system. While, from a
linguistic prescriptivist Linguistic prescription, or prescriptive grammar, is the establishment of rules defining preferred usage of language. These rules may address such linguistic aspects as spelling, pronunciation, vocabulary, syntax, and semantics. Sometimes i ...
perspective, any
dictionary A dictionary is a listing of lexemes from the lexicon of one or more specific languages, often arranged alphabetically (or by radical and stroke for ideographic languages), which may include information on definitions, usage, etymologie ...
might be believed to dictate correct usage, the
linguistic descriptivist In the study of language, description or descriptive linguistics is the work of objectively analyzing and describing how language is actually used (or how it was used in the past) by a speech community. François & Ponsonnet (2013). All a ...
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.Philip Seargeant, "Lexicography as a Philosophy of Language". ''Language Sciences'', 33:1-10 (2011). 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. While a dictionary might produce a "circle" among the terms, "oak", "catkin", and "acorn", each of these is used in different (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. () 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.


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" : mountain - "1a: a landmass that projects conspicuously above its surroundings and is higher than a hill" Merriam-Webster's online dictionary provides another example of a circular definition with the words "condescending" and "patronizing:" : Main Entry: condescending : Function: adjective : 1 : showing or characterized by condescension : patronizing From "condescension": : Main Entry: condescension : 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"patronizing"
Merriam-Webster. Retrieved January 17, 2013.
: 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 :


See also

*
Begging the question In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: ') is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion, instead of supporting it. For example: * "Green is t ...
* Circular reasoning * Fallacies of definition *
Genus–differentia definition A genus–differentia definition is a type of intensional definition, and it is composed of two parts: # a genus (or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are consider ...
*
Infinite regress An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. In the epistemic regress, for example, a belief is justified bec ...
*
Lexicography Lexicography is the study of lexicons, and is divided into two separate academic disciplines. It is the art of compiling dictionaries. * Practical lexicography is the art or craft of compiling, writing and editing dictionaries. * Theoreti ...
* Lexical definition *
Meta-circular evaluator In computing, a meta-circular evaluator (MCE) or meta-circular interpreter (MCI) is an interpreter which defines each feature of the interpreted language using a similar facility of the interpreter's host language. For example, interpreting a lamb ...
*
Self-reference Self-reference occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philoso ...
* Self-refuting idea * Recursive definition * Revision theory * Tautology *
Vicious circle principle The vicious circle principle is a principle that was endorsed by many predicativist mathematicians in the early 20th century to prevent contradictions. The principle states that no object or property may be introduced by a definition that depen ...


References

{{DEFAULTSORT:Circular Definition Definition Philosophical logic