Full Idea
It is not clear how the view that natural numbers are purely intra-structural 'objects' can be squared with the widespread use of numerals outside purely arithmetical contexts.
Gist of Idea
The structural view of numbers doesn't fit their usage outside arithmetical contexts
Source
B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26)
Book Reference
Hale,B/Wright,C: 'The Reason's Proper Study' [OUP 2003], p.15
A Reaction
I don't understand this objection. If they refer to quantity, they are implicitly cardinal. If they name things in a sequence they are implicitly ordinal. All users of numbers have a grasp of the basic structure.