As a result, conservativeness can only be employed to do the required job if we have nominalistic premises to start with (Field 1989, p. 129). As Field points out, it is a confusion to argue against his view by claiming that if we add some bits of mathematics to a body of mathematical claims (not nominalistic ones), we may obtain new consequences that could not be achieved otherwise (Field 1989, p. 128). The restriction to nominalistic assertions is crucial.