Chain Accounts of Sets and Propositions

Iterative accounts of e.g. sets and propositions face one of two problems. Either they fail to resolve Russellian paradoxes, or they are subject to Benacerrafian too-many-candidates problems. I propose chain accounts of sets and propositions as an alternative. Chain accounts have two main pillars. First, target entities like sets and propositions must be wellfounded. This wellfoundedness represents a form of ontological foundationalism. Second, their formation principles are subject to a limitation of size constraint that is partially motivated by the wellfoundedness constraint. I argue that those drawn to iterative accounts to explain which sets and propositions exist would be better served by adopting chain accounts instead.