Full Idea
Any object can play the role of 3; that is, any object can be the third element in some progression. What is peculiar to 3 is that it defines that role, not by being a paradigm, but by representing the relation of any third member of a progression.
Gist of Idea
The number 3 defines the role of being third in a progression
Source
Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
Book Reference
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.291
A Reaction
An interesting early attempt to spell out the structuralist idea. I'm thinking that the role is spelled out by the intersection of patterns which involve threes.