Abstract 

As a matter of ontology, iterative accounts of e.g. sets and propositions are lacking in at least three ways.  First, without supplementation, they do not track key ontological features of the relevant entities, such as relations of ontological dependence.  Second, they are silent about what can be included in the class of urelements.  And third, considerations of how to account for e.g. sets of propositions and propositions about sets suggest that the stages of iterative hierarchies serve a merely representational role.  I offer an alternative to iterative accounts that centers on chains of e.g. membership or aboutness that track relations of ontological dependence.  This account replicates all the best features of iterative accounts, and it also performs well in the respects in which iterative accounts are lacking.