Coextension and Identity
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Coextension : the F s = the G s (where quantifi cation is intended as unrestricted).
Metaphysicians disagree about whether there are cases of coextension thus defi ned. This chapter is about this metaphysical dispute in the context of thing nominalism, namely the version of nominalism that rejects tropes alongside with universals. Since whether there are genuine cases of coextension is contested, I shall use the phrase ‘ alleged cases of coextension’ to refer specifi cally to these situations in which it is disputed whether both Nonidentity and Coextension are true. 2 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:
• A cordate particular is a particular with a heart. A renate particular is a particular with kidneys. So prima facie by asserting that Kiki is cordate and that Kiki is renate, we are asserting two different things about Kiki. If so, <Kiki is cordate> and <Kiki is renate> appear to be different ascriptions of properties to Kiki. Yet ‘is cordate’ and ‘is renate’ apply to exactly the same particulars.