Full Idea
Structuralism says we study whole structures: objects together with their predicates, relations that bear between them, and functions that take us from one domain of objects to a range of other objects. The objects can even be eliminated.
Gist of Idea
Structuralism focuses on relations, predicates and functions, with objects being inessential
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1)
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.82
A Reaction
The unity of object and predicate is a Quinean idea. The idea that objects are inessential is the dramatic move. To me the proposal has very strong intuitive appeal. 'Eight' is meaningless out of context. Ordinality precedes cardinality? Ideas 7524/8661.
Related Ideas
Idea 7524 Order, not quantity, is central to defining numbers [Dedekind, by Monk]
Idea 8661 The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend]