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.