 These nominalistic approaches must contend with various issues, of course. At the very least, they have to successfully argue that the tools they use to avoid commitments to abstract objects don’t themselves involve such commitment. For example, Field must argue that space-time regions are concrete entities, while Putnam and Hellman must argue that by relying on logical possibility and modal logic, there is no commitment to possible worlds considered as abstract objects. In general, any nominalist account that makes essential use of set theory or model-theoretic structures must convincingly argue that the very use of such analytic tools doesn’t commit them to abstract objects. (See Burgess &amp; Rosen 1997 for a systematic survey of different proposals about the existence of abstract objects.)