Definitions

# Circular definition

A circular definition is one that assumes a prior understanding of the term being defined. By using the term(s) being defined as a part of the definition, a circular definition provides no new or useful information; either the audience already knows the meaning of the term(s), or the definition is deficient in including the term(s) to be defined in the definition itself. 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, nor is defining dialectical materialism as "materialism that is dialectical". 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 not knowing which trees are oaks, nor which nuts are acorns, the definition is fairly useless.

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.

## Examples of circular definitions

See
See "See".

Another, commonly cited example:

Recursion
See "Recursion".

Another one, not so common:

Endless loop
See "Loop, endless"

Once you find "Loop, endless"

Loop, endless
See "Endless loop"

The 2007 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"
This is a common example of a circular definition.