Why Lewis's analysis of modality succeeds in its reductive ambitions

Some argue that Lewisian realism fails as a reduction of modality because in order to meet some criterion of success the account needs to invoke primitive modality. I defend Lewisian realism against this charge; in the process, I hope to shed some light on the conditions of success for a reduction. In §1 I detail the resources the Lewisian modal realist needs. In §2 I argue against Lycan and Shalkowski’s charge that Lewis needs a modal notion of ‘world’ to ensure that worlds correspond to possibilities. In §3 I respond to Divers and Melia’s objection that Lewis needs to invoke primitive modality to give a complete account of what worlds there are. In §4 I ask what it is for a notion to ‘involve’ modality. I conclude that the question is either in bad standing or at best offers little traction on the debate, and propose a different way of assessing when materials are appropriately included in a reductive base