I agree that you do not have to use an extensional approach to such things, but with possible worlds you can choose to use an extensional approach. They do not become non-extensional because there are other non-extensional approaches.
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From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of sowa@xxxxxxxxxxx
Sent: 19 July 2011 10:16
Subject: Re: [ontolog-forum] intangibles (was RE: Why most classifications are fuzzy)
It is true that talking about sets of possible worlds has the appearance of being extensional, but possible worlds are not observable. They can only be specified by some intensional axioms or descriptions.
If you specify a set W of possible worlds by some set S of axioms, any results you get from analyzing W could be derived directly from S. The seemingly extensional analysis is nothing but a round about way of using the axioms S to derive your conclusion.
In general, any set of possible worlds used for any version of modal logic (or any other kind of logic that uses Kripke semantics) can be replaced by some set of axioms (or laws) that generate exactly the same results without making any assumptions about possible worlds.
For further discussion of these issues, see