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. 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.
A circular definition occurred in an early definition of the kilogram. The kilogram was originally defined as the mass of one liter of water at standard pressure and the temperature at which it is densest (which is about 4 °C). The unit of pressure is the newton per square meter, where a newton is the force that accelerates one kilogram one meter per second squared. Thus the kilogram was defined in terms of itself. Since water is nearly incompressible, this circularity is of no consequence — with each iteration of the "circle," the resulting measure of a kilogram rapidly converges. Even so, to clear up any confusion, the kilogram was later defined as the mass of a certain piece of metal in Sèvres.
A circular definition also 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?"
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.
Dictionaries are sometimes used erroneously as sources for examples of circular definition. 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. While, from a linguistic prescriptivist perspective, any dictionary might be believed to dictate correct usage, the use of dictionaries is not itself expected to be a rule-following practice independent of the give-and-take of using words in context. Thus, the example of a defintion 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 are used in contexts (e.g., those related to plants, trees, flowers, and seeds) that generate an ever-branching network of usages.
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