  However, working realism does not in any obvious way imply platonism. Although working realism says that we are justified in using the platonistic language of contemporary mathematics, this falls short of platonism in at least two ways. As the above discussion of truth-value realism showed, the platonistic language of mathematics can be analysed in such a way as to avoid reference to and quantification over mathematical objects. Moreover, even if a face-value analysis of the language of mathematics could be justified, this would support object realism but not platonism. An additional argument would be needed for the third component of platonism, namely, Independence. The prospects for such an argument are discussed in Section  4.1.