James Adrian

      A formal definition is constructed from meanings that are previously known to the reader or listener. They describe an exact meaning.

      Any statement that is offered as a formal definition (as in science, math, law, and other disciplines) must have all of the following properties:

      A definition must name the term being defined and provide a description of that term.

      Here is an example: A hydrocarbon is a compound consisting only of carbon and hydrogen.

      "A hydrocarbon"is the defined term, and "a compound consisting only of carbon and hydrogen" is the description.

      Other sentence structures are possible, but both the defined term and its description must be somewhere in the statement.

      Other than the term being defined, the meaning of each term used in a definition must be known before that definition is stated.

      The term being defined must not appear in the description of that term. Using the term being defined in the description of that term is circular.

      Consider the following:

      A nice car is a car you like.

      Here, the term being defined is "nice car" and not "car." In order for this definition to be a valid formal definition, the term "car" must have been previously defined.

      The term being defined and the description of that term must be interchangeable. It must be clear that the term and its description have exactly the same meaning.

      A term is well defined if and only if it is described by a statement that has all of the properties required of a formal definition.

      There are many undefined terms that nobody bothers to define in the development of formal definitions. "If," "the," "we," "were," "to," "accept," "this," "as," and "true" are all undefined terms in most formal systems because there is great confidence that the meanings of these terms are know unambiguously to every person reading or hearing them.