In linguistics, logic, philosophy, and other fields, an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word’s definition often implies an intension. The term may also refer to all such intensions collectively, although the term comprehension is technically more correct for this.

The meaning of a word can be thought of as the bond between the idea the word means and the physical form of the word. Swiss linguist Ferdinand de Saussure (1857–1913) contrasts three concepts:

  1. the signifier – the “sound image” or the string of letters on a page that one recognizes as the form of a sign
  2. the signified – the meaning, the concept or idea that a sign expresses or evokes
  3. the referent – the actual thing or set of things a sign refers to. See Dyadic signs and Reference (semantics).

Intension is analogous to the signified in the Saussurean system, extension to the referent. Without intension of some sort, words have no meaning.

In philosophical arguments about dualism versus monism, it is noted that thoughts have intensionality and physical objects do not (S. E. Palmer, 1999), but rather have extension in space and time.

Note: Intension and intensionality (the state of having intension) should not be confused with intention and intentionality, which are pronounced the same and occasionally arise in the same philosophical context. Where this happens, the letter s or t is sometimes italicized to emphasize the distinction.

Intensional statement

An intensional statement-form is a statement-form with at least one instance such that substituting co-extensive expressions into it does not always preserve logical value. An intensional statement is a statement that is an instance of an intensional statement-form. Here co-extensive expressions are expressions with the same extension. (A statement-form is simply a form obtained by putting blanks into a sentence where one or more expressions with extensions occur—for instance, “The quick brown ___ jumped over the lazy ___’s back.” An instance of the form is a statement obtained by filling the blanks in.)

That is, a statement-form is intensional if it has, as one of its instances, a statement for which there are two co-extensive expressions (in the relevant language) such that one of them occurs in the statement, and if the other one is put in its place (uniformly, so that it replaces the former expression wherever it occurs in the statement), the result is a (different) statement with a different logical value. An intensional statement, then, is an instance of such a form; it has the same form as a statement in which substitution of co-extensive terms fails to preserve logical value. A non-intensional statement is also known as an extensional statement, since substitution of co-extensive expressions into it always preserves logical value. A language is intensional if it contains intensional statements, and extensional otherwise. English, in common with every other natural language, is an intensional language. The only extensional languages are artificially constructed languages used in mathematics or for other special purposes and small fragments of natural languages.

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