 A second subject in the philosophy of set theory concerns the justification of the accepted basic principles of mathematics, i.e., the axioms of ZFC. An important historical case study is the process by which the Axiom of Choice came to be accepted by the mathematical community in the early decades of the twentieth century (Moore 1982). The importance of this case study is largely due to the fact that an open and explicit discussion of its acceptability was held in the mathematical community. In this discussion, general reasons for accepting or refusing to accept a principle as a basic axiom came to the surface. On the systematic side, two conceptions of the notion of set have been elaborated which aim to justify all axioms of ZFC in one fell swoop. On the one hand, there is the iterative conception of sets, which describes how the set-theoretical universe can be thought of as generated from the empty set by means of the power set operation (Boolos 1971, Linnebo 2013). On the other hand, there is the limitation of size conception of sets, which states that every collection which is not too big to be a set, is a set (Hallett 1984). The iterative conception motivates some axioms of ZFC very well (the power set axiom, for instance), but fares less well with respect to other axioms, such as the replacement axiom (Potter 2004, Part IV). The limitation of size conception motivates other axioms better (such as the restricted comprehension axiom). It seems fair to say that there is no uniform conception that clearly justifies all axioms of ZFC.