A circular definition is a type of definition 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, 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.
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 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.
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.
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Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
Le contenu de ce cours correspond à celui du cours d'Analyse I, comme il est enseigné pour les étudiantes et les étudiants de l'EPFL pendant leur premier semestre. Chaque chapitre du cours correspond
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