I've been studying the SEP article about intensional logic, and I think I have a good grasp of what "intension" means. The intension of a term like "bachelor" would be a function that designates a set of objects in each possible world. So bachelor is defined as unmarried men, and so the intension of "unmarried men" would be the intersection of the set of unmarried objects and the set of men, in each possible world.
So from the Critique of Pure Reason, Kant wrote:
In all judgments in which the relation of a subject to the predicate is thought (if I only consider affirmative judgments, since the application to negative ones is easy) this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case, I call the judgment analytic, in the second synthetic.
I don't understand why we can't just understand concepts contained within concepts as intensions contained within intensions, such that an intension B is contained in intension A, if and only if, in every possible world there is no object that B designates that A doesn't also designate in that world.
Does anyone know why this doesn't work? There seems to be a lot of skepticism about the analytic/synthetic distinction online.