more from Paul Benacerraf

Single Idea 9906

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory]

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?


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]