This article stages a dialogue between cosmopolitanism and multiculturalism in order to think through what is at stake in demands that universities should produce graduates who are sensitive to social diversity and attuned to the contemporary realities of globalisation. The argument is that, although ‘graduate attributes’ are no doubt an effective management tool in a massified higher education system, they can also be used to focus attention on what dispositions it is reasonable and desirable to expect graduates to develop. The arguments about cosmopolitanism of Jeremy Waldron and Martha Nussbaum are considered.