Circular definition

Circular definition of "musicality"

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.

Circular lexicographic (dictionary) definitions

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 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. 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 contexts (e.g., those related to plants, trees, flowers, and seeds) that generate ever-branching networks of usages.

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?"

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

This definition alone is close to suffering from circular definition, but following the definition train:

Main Entry: condescension

Function: noun

1 : voluntary descent from one's rank or dignity in relations with an inferior

2 : patronizing attitude or behavior

Looking up the word "patronizing" then gives us:

Main Entry: patronize

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

In the Oxford Dictionary the word "inspiring" is another example of a circular definition:

Main Entry: inspiring

Function: Adjective

1 : Having the effect of inspiring someone

In short: the two words are used to define each other.

See also

• Fallacies of definition
• Begging the question
• Tautology
• Self-reference
• Meta-circular evaluator
• Recursive definition
• Infinite regress
• Lexical definition
• Lexicography
• Revision theory