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Intension vs. extension

In logic, linguistics and the philosophy of language, we make a distinction between intension and extension. On the one hand, intension refers to "the internal content of a term or concept that constitutes its formal definition"(Britannica Encyclopedia). On the other hand, a word's extension refers to the range of objectts which fall under it. For example, examples of the extension of the word "dog" would be "cur," "husky," "malamute," "german shepherd," and so on.

It is important to note, as the Britannica Encyclopedia does, that the distinction between intension and extension does not correspond precisely with the distinction between denotation and connotation. Denotation does denote the formal dictionary definition of a word in a manner comparable to intension, but connotation is not the precise equivalent of extension. "Connotation" has reference more to associations with a word than with concrete examples of concepts which fall under it.

In possible world semantics, "The intension of a word is a function that associates every world with the referent of that word at that world"(Steinhart, p. 100). Steinhart let's "IN" be the intension function. Let's look at his example, keeping in mind that the numbers associated with each word are subscripts:

IN("Allan") = {(w1, A), (w2, A), (w3, A), (w4, A)};

IN("Diane") = {(w1, D), (w2, D), (w3, A), (w4, D)};

Therefore, such and such a thing is true of Allan and Diane at one world, but not at another. Diane might be sad in one world, but happy in another.

Steinhart, Eric. "More Precisely: The Mathematics You Need To Do Philosophy." Broadview Press, 2009.