more from Keith Hossack

Single Idea 23624

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets]

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


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]