Abstract: This chapter aims to determine in exactly what sense we should be ‘realists’ about arithmetic, that is, exactly what kind of arithmetical ‘independence’ from the mind we should be interested in defending. It argues that taking what is called in this chapter ‘modal independence’ as characteristic of realism is a mistake, and that we should instead characterize realism in terms of is called in this chapter ‘essential independence’.

Keywords: independence, modal, essential, mind, quasi-realism,