This chapter introduces the most formidable difficulties ever advanced against Resemblance Nominalism, namely Goodman's imperfect community difficulty and companionship difficulty. The imperfect community difficulty arises when there is a class of particulars such that every two of them resemble each other but there is no property common to all of them. So having a property is not just a matter of resembling certain particulars. The companionship difficulty arises when all F-particulars are G-particulars but not vice versa. So resembling all particulars having a certain property is not what makes a particular to have that property. These difficulties can be seen as showing that property classes, that is, classes whose members are all and only particulars having a certain property F, cannot be defined in terms of certain resemblance conditions. In particular, they show that property classes cannot be defined, à la Carnap, as maximal classes of resembling particulars.
Keywords: Carnap, coextension difficulty, companionship difficulty, Goodman, imperfect community difficulty, perfect communities