intensions as extensions

"I have a problem for those who, like myself, admire intensional formal semantics and think it a key to understanding natural language. We can go to extremes of intensionality, if we like. Semantic rules can be stated entirely in terms of intensions, while extensions go unmentioned. But when we do, it seems for all the world as if we've gone purely extensional instead!"

David Lewis (1974), "'Tensions", Semantics and Philosophy, M. Munitz & P. Unger