Real and nominal definition

Definitions usually take the following form:

A puppy is a young dog.

A triangle is a three-sided rectilinear area.

Man is a rational animal.

Knowledge is justified true belief.

The term being defined is known as the defined term or definiendum and the defining formula is also known as the definiens. In the first example above, the term being defined is "puppy" and the defining formula is "young dog".

There are two ways in which you can read a definition. You can read it from left to right or you can read it from right to left. To read a definition from left to right is to treat it as a real or essentialist definition, whereas to read it from right to left is to treat it as an abbreviatory, nominal or verbal definition. Abbreviatory definitions are good and helpful; they are commonplace in science as they replace a (usually) long expression with a shorter one.

Many philosophers think that real definitions are important; they see them as providing the true or genuine meaning of a term. There are many things wrong with real definitions. One is that the terms used in the definiens are rarely easier to understand than the definiendum. Man may well be a rational animal, but is the notion of rationality so well-understood that it doesn't need elucidation? Another problem is that repeatedly replacing definienda with definientia in a sentence leads to increasing longer statements and the process has no natural way of terminating. It is easy to see that a dictionary (of real definitions) for a finite language containing a definition of every noun in that language (and in which each definiens contains at least one noun) must contain circular definitions. This can be illustrated by the following sentence. Click on a highlighted word to replace it with its defining formula.

The cat sat on the mat.

Here the problem arises because "family" occurs in the definiens of "genus" and "genus" occurs in the defining formula of "family". (The definitions I've used come from the 7th edition of Chambers English Dictionary. Although I've used standard dictionary definitions, the same point applies to real definitions.) Further arguments against the usefulness of real definitions in philosophy can be found in chapter 11 of the second volume of Karl Popper's Open Society and in sections 6 and 7 of his intellectual autobiography Unended Quest.