MW: Lewis specifically asserts that possible
worlds actually exist in the sense you mean.
Please note my reply to
Chris M: Lewis also said that a solution that did not assume the
existence of possible worlds would be preferable if it could derive the
same results. Michael Dunn demonstrated such a solution, ...
Short answer: He did not. Dunn came up with a formal semantics for modal languages equivalent to Kripke's. It can be used for the same sorts of formal purposes that Kripke semantics can be used for — proving soundness and completeness results, proving the consistency of certain modal principles, etc. Dunn did NOT provide (nor did he purport to provide) alternatives to the solutions to numerous problems in semantics, philosophy of language, metaphysics, philosophy of mind etc that Lewis propounded in terms of worlds.