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A circular definition is one that uses the term(s) being defined as a part of the definition or assumes a prior understanding of the term being defined. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic. ==Approaches to characterizing circular definitions== From a pragmatic point of view, circular definitions may be characterised in terms of new, useful or helpful information: either the audience must already know the meaning of the key term(s), or the definition is deficient in including the term(s) to be defined 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. 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. For another example, we can define "oak" as a tree which has catkins 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. Consequently, many systems of definitions are constructed according to the vicious circle principle in such a way that authors do not produce viciously circular definitions. 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), and may also be involved in circular definitions: "rake: an implement with three or more tines" → "tine: a part of a rake". However, if more specific differences are added, then the 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", also 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 dictionary definitions. From a linguistic point of view, some intuitively circular definitions in the derivation of words can easily be shown to be non-circular. For example, sometimes a definition like "musicality: the quality or state of being musical" (see Figure) is said to be circular. But strictly speaking, the condition "the term(s) being defined as a part of the definition or assumes a prior understanding of the term being defined" is false in this case. The definition chain "musicality: the quality or state of being musical" → "musical: associated with music" → "music: an acoustic art form" is a two-step derivation of the word "musicality" from the root "music", where the chain ends. A definition chain which ends not circular. It may be objected that the term to be defined and one of the difference terms in the definition share the same root; the answer is that the objection requires prior analysis of the terms in order to identify identical parts, yet the terms themselves cannot be reduced to these parts: the meaning of "musicality" is composed of the meaning of "musical" and the meaning of "ity", the meaning of "musical" is composed of the meaning of "music" and "al". In each case, the terms to be defined and the terms in the definition are different. 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. Such definitions are not circular as long as they terminate. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Circular definition」の詳細全文を読む スポンサード リンク
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