Full Idea
If a particular set-theory is in a strong sense 'reducible to' the theory of ordinal numbers... then we can still ask, but which is really which?
Gist of Idea
If ordinal numbers are 'reducible to' some set-theory, then which is which?
Source
Paul Benacerraf (What Numbers Could Not Be [1965], IIIB)
Book Reference
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.290
A Reaction
A nice question about all reductions. If we reduce mind to brain, does that mean that brain is really just mind. To have a direction (up/down?), reduction must lead to explanation in a single direction only. Do numbers explain sets?
Related Idea
Idea 10687 Maybe we reduce sets to ordinals, rather than the other way round [Hossack]