A particular that is both F and G is F in virtue of resembling the F-particulars and is G in virtue of resembling the G-particulars. But if the F- and G-particulars are the same, how can a particular have two properties, F and G, in virtue of resembling the same particulars? This is the coextension difficulty. The chapter argues that the most famous examples of coextensive properties — being cordate and being renate — are really not such. Though being cordate and being renate are coextensive predicates, they apply in virtue not of properties but of relations, and not coextensive ones. But since there may well be such coextensive properties, the coextension difficulty needs a solution. The solution advocated in this chapter consists in adopting Realism about Possible Worlds, and making F-particulars be F in virtue of resembling all possible F-particulars. The chapter also discusses the problem posed by necessarily coextensive properties and Resemblance Nominalism's commitment to Counterpart Theory, brought about by its commitment to Realism about Possible Worlds.
Keywords: coextensive properties, being cordate, being renate, Counterpart Theory, Lewis, possible worlds