Full Idea
For each stone, there is at least one pattern such that the stone is a position in that pattern. The stone can be treated in terms of places-are-objects, or places-are-offices, to be filled with objects drawn from another ontology.
Clarification
His 'offices' are like offices of government, which can be held by varied persons
Gist of Idea
A stone is a position in some pattern, and can be viewed as an object, or as a location
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 8.4)
Book Reference
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.259
A Reaction
I believe this is the story J.S. Mill had in mind. His view was that the structures move off into abstraction, but it is only at the empirical and physical level that we can possibly learn the structures.