Abstract
Metaphysicians disagree about whether there are cases of coextension thus defined. This chapter is about this metaphysical dispute in the context of thing nominalism, namely this version of nominalism that rejects tropes alongside universals. Since whether there are genuine cases of coextension is contested, I shall use the phrase “alleged cases of coextension” to refer specifically to these situations in which it is disputed whether both Nonidentity and Coextension are true. Roughly, alleged cases of coextension correspond to situations in which a realist about universals would claim that there is a case of coextension. Here are some examples of alleged cases of coextension:
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