Intension and extension,
in logic, correlative words that indicate the reference of a term or
concept: “intension” indicates the internal content of a term or concept
that constitutes
its formal definition; and “extension” indicates its range of
applicability by naming the particular objects that it denotes. For
instance, the intension of “ship” as a substantive is “vehicle for
conveyance
on water,” whereas its extension embraces such things as cargo ships,
passenger ships, battleships, and sailing ships. The distinction between
intension and extension is not the same as that between connotation and
denotation.
Intension
An intensional definition
gives the meaning of a term by specifying necessary and sufficient
conditions for when the term should be used. In the case of nouns, this
is equivalent to specifying the properties that an object needs to have
in order to be counted as a referent of the term.
For example, an intensional definition of the word "bachelor" is
"unmarried man". This definition is valid because being an unmarried man
is both a necessary condition and a sufficient condition for being a
bachelor: it is necessary because one cannot be a bachelor without being
an unmarried man, and it is sufficient because any unmarried man is a
bachelor.
Extension
An extensional definition of a concept or term formulates its meaning by specifying its extension, that is, every object that falls under the definition of the concept or term in question.
For example, an extensional definition of the term "nation of the world"
might be given by listing all of the nations of the world, or by giving
some other means of recognizing the members of the corresponding class.
An explicit listing of the extension, which is only possible for
finite sets and only practical for relatively small sets, is a type of enumerative definition.
The extension of a lexeme is the set of entities which it denotes. The extension of dog includes all collies, dalmatians, dachshunds, mongrels,
etc. that have ever lived or will ever live and every fictitious
creature that is accepted as being a dog. All the things that can be
denoted by the noun lake are the extension of that lexeme. The lexeme Lake Ontario has a single item in its extension, and the
Dead Sea Scrolls has a single collection of items as its extension.
Dead Sea Scrolls has a single collection of items as its extension.
The
intension of any lexeme is the set of properties shared by all members
of the extension. Thus everything that is denoted by lake must be a body
of water of a certain size surrounded by land, and everything denoted
by island is a body of land surrounded by water—but see below for
discussion of some difficulties in applying these definitions.
Extension
has to do with reference, but reference, as we know, is not all of
meaning: the lexemes violin and fiddle have the same extension.
Extension can change while intension remains the same. The extension of
the referring expression the capital of Australia is a single item, the
city of Canberra. The intension of the same term is ‘city in which the
national government of Australia is located.’ If the capital should be
moved at some future time to another city, the extension changes but the
intension remains the same. The Mayor of Chicago or the Prime Minister
of Great Britain always has the same intension but the extension of each
of these changes from time to time.
