  That Lewis's truth conditions for modal statements are themselves free of modality and, hence, that his theory counts as a genuine reduction of modal notions to non-modal is not terribly controversial (albeit not undisputed — see Lycan 1991, 224–27; Divers and Melia 2002, 22–24). Significantly more controversial, and perhaps far more critical to the project, is whether or not his account is complete, that is, whether or not, for all modal statements φ, (i) if φ is intuitively true, then its Lewisian truth condition holds (ii) if φ is intuitively false, then its Lewisian truth condition fails.[21]  The challenge to Lewis, then, is that his account can be considered successful only if it is complete in this sense. 