I am using the term 'intensional' in the sense that was defined by Alonzo Church in the following excerpt from his book on lambda calculus:
I would also like to add the point that *every* intensional definition of possible worlds arises from some human intention to create some collection of possible worlds for some purpose.
That means that possible worlds are both intensional (with an S) and intentional (with a T).
MW: At best then we are talking at cross purposes. Intensionality applies to classes, my possible worlds are individuals, i.e. some particular spatio-temporal extent. I do not know how you get possible worlds to be classes, but that is your problem not mine.
MW: Extensionality (as a basis for identity), of course, applies differently to classes and individuals. With classes it means sets with them same membership are the same, with individuals it means individuals with the same (spatio-temporal) extent are the same.
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