 The final distinction, or rather, collection of distinctions, which we’ll introduce here and which needs to be borne in mind when considering the recent debate on relations, concerns the existence and identity conditions for relations. Since Lewis it has become commonplace to conceive relations as either “abundant” or “sparse”: according to an abundant conception there is a relation for every arbitrary pair (or triple, or ...) of things whereas according to a sparse conception there are only as many relations as are required to characterise the relational aspects of likeness and difference (Lewis 1986: 61). But this binary distinction doesn’t do justice to the variety of different conceptions of the existence and identity of relations that have been put forward. Distinguish, on the one hand, an a posterori view according to which relations exist only if they are instantiated and whether they are instantiated is an empirical matter (Armstrong 1978a: 76–77) from, on the other hand, an a priori view according to which their existence is settled by purely logical principles, for example strong comprehension principles whereby every open formula determines a corresponding property or relation (Zalta 1988: 46–7; Williamson 2013: 226–7). Whereas the former view might admit space-time separation as a relation (or family of relations) whose instantiation is confirmed by physics, the latter would affirm the existence of a relation corresponding to the open formula “x is a much funnier anarchist than y”. Between these two extremes are views that allow some relations, for example, relative velocities conceived as relations between different things when one has a certain velocity relative to another, to be uninstantiated for the purposes of rounding out scientific theory (Bigelow and Pargetter 1990: 77) and views that allow logically complex relations (RvS, R&amp;S etc.) insofar as they are built up by logical operations from simple relations (R, S etc.) found in nature (Bealer 1982: 9–10).