Page "Circular definition" Paragraph 26

This is a parody on circular references in dictionaries, which are sometimes understood to be explanatory, rather than descriptive.

Jokes often have an element of wisdom: In some cases, dictionary descriptions lead to apparent circular definitions among related words.

However, jokes also can have an element of misunderstanding: This parody is the shortest possible example of an erroneous recursive definition of an object, the error being the absence of the termination condition ( or lack of the initial state, if looked at from an opposite point of view ).

A purer example of circular reference would be " Circle: See ' Circle '".

The parody is also an erroneous example of the activity of giving a definition in a dictionary, where the more general error it makes is in mistaking dictionaries to involve procedures that are found in logical or mathematical contexts.

Dictionaries are not self-contained texts, nor is their use expected to be so contained.

If modeled on the practice of using dictionaries, there would be no circle in an illustration of the activity of looking up a word whose entry provides a definition in terms of that word ( or in terms of another word defined in terms of this word ).

For this joke to be an example of giving a definition as modeled on dictionary usage, the practice of using dictionaries would have to be self-contained, would have to involve a function — say, a " look-up " procedure — that a computer can perform.

If dictionaries were logico-mathematical texts, then so-called circular definition would amount to infinite regress, where one of the steps involved in running the procedure is to run the procedure ; and, in the context of explanation ( as opposed to description in the form of dictionary definition ), this would be a vicious infinite regress.

Newcomers to recursion are often bewildered by its apparent circularity, until they learn to appreciate that a termination condition is key.