Extension (logic)

Refers to the totality of all objects described by a particular term.

For example, the extension of the term “horse” could be defined as follows:

“Horse” describes all animals of the genus Equidae.

In other contexts, the same term may have a different extension:

The term “horse” describes all the chess pieces also known as “knights”.

The opposite term to extension is intension, which describes the definition of a term by its associated meanings.

As the examples above show, the same identifier can describe different sets of terms depending on the context. It is therefore generally important to understand the precise extension of a term in order to avoid possible errors of equivocation.

Ambiguity of the extension of a term can also result from the grammatical structure of a statement (amphiboly). See also: Syntactic ambiguity.

• Intension

• Amphiboly
• Equivocation
• Syntactic ambiguity

• Extensional and intensional definitions on Wikipedia