 Why might one believe in impossible worlds? One argument is the so-called “argument from ways” (Vander Laan 1997), which is related to the first definition of impossible world given above. This draws on the analogy with  David Lewis’s  notorious argument concerning our quantifying over ways things could have been (see Lewis 1973: 84). The world could have been different in so many ways: Hilary Clinton could have won the 2016 US election, I could be dancing on the ceiling, and Fermat’s Last Theorem could have remained without proof. Our belief in possible worlds is just a paraphrase of our belief that there are many ways the world could have been.