Full Idea
The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory.
Gist of Idea
The iterative conception has to appropriate Replacement, to justify the ordinals
Source
Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9)
Book Reference
Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.146
A Reaction
The modern approach to axioms, where we want to prove something so we just add an axiom that does the job.
Related Idea
Idea 23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]