Intensions

The intension of a referring expression e in a language is a partial function I_e that assigns to a world w the referent I_e(w) of e there, when there is a referent of e in w. Thus, the intension of "the tallest woman" is a partial function that assigns to w the tallest woman in w.

The intension of a unary predicate P is a partial function I_P that assigns to a world w the extension I_P(w) of P at w, i.e., the set of all satisfiers of P there.

Intensions are meant to capture the semantic features of terms, with respect to intensional semantics. Now let e be the referring expression:

• The set of even integers.

Let E be the predicate

• is an even integer.

Then the intension of e assigns to w the set of all even integers, for each w. And the intension of E assigns to w the set of all even integers, too. So I_e=I_E. But e and E are plainly not semantically equivalent, even within intensional semantics. So intensions are insufficient for characterizing the semantic features of expressions, even with respect to intensional semantics.

A longshot: Perhaps something like this led Frege to his weird "The concept horse is not a concept" claim.