more on this theme | more from this thinker
Full Idea
The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC.
Gist of Idea
Limitation of Size justifies Replacement, but then has to appropriate Power Set
Source
Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9)
Book Ref
Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.147
A Reaction
Which suggests that the Power Set axiom is not as indispensable as it at first appears to be.
Related Idea
Idea 23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |