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Full Idea
The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right.
Gist of Idea
For mathematical objects to be positions, positions themselves must exist first
Source
Fraser MacBride (Structuralism Reconsidered [2007], §3)
Book Ref
'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.585
A Reaction
Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others.