Single Idea 9907

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

If any recursive sequence whatever would do to explain ordinal numbers suggests that what is important is not the individuality of each element, but the structure which they jointly exhibit.

Gist of Idea

If any recursive sequence will explain ordinals, then it seems to be the structure which matters

Source

Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.290


A Reaction

This sentence launched the whole modern theory of Structuralism in mathematics. It is hard to see what properties a number-as-object could have which would entail its place in an ordinal sequence.