Inextensional

Inextensional is an adjective used to describe something that cannot be extended, or that resists extension in a formal sense. The term is uncommon in everyday language and is mostly found in mathematical and logical discussions about extendability or the preservation of certain properties under enlargement of scope.

In mathematical contexts, inextensional objects or concepts refer to situations where attempting to extend a structure to a larger domain would force a loss of a required property. For example, a function defined on a subset of a space may be described as inextensible if there is no extension of that function to the larger space that preserves a given condition such as continuity or linearity. The notion contrasts with extensible or extendable objects, for which an extension preserving the relevant property is possible.

In philosophy of language and logic, extensionality is a principle about the dependence of truth-values on reference or extension. Discussions sometimes consider inextensional approaches or contexts that do not adhere to extensional criteria. In such uses, inextensional signals a departure from purely extension-based semantics or comparisons.

Because inextensional is a specialized term, it is often replaced by phrases like non-extendable, nonextendible, or nonextendable in ordinary technical writing. The concept remains a descriptive one rather than a standard, widely-used classification, and its precise meaning tends to depend on the specific mathematical or logical framework being discussed.

See also: extensionality, extendable, nonextendable.