Choice in the Iterative Conception of Set

Abstract The iterative conception (IC) is arguably the best worked out conception of set available. What is the status of the axiom of choice under this conception? Boolos argues that it is not justified by IC. We show that Boolos’s influential argument overgenerates. For, if cogent, it would imply that none of the axioms of ZFC which Boolos took to be justified by IC is so justified. We furthermore show that, to the extent that they are consequences of a plural formulation of stage theory, all those axioms are justified by IC — axiom of choice included.