Full Idea
Structuralism can be distinguished from traditional Platonism in that it denies that mathematical objects from the same structure are ontologically independent of one another
Gist of Idea
Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure
Source
Øystein Linnebo (Structuralism and the Notion of Dependence [2008], III)
Book Reference
-: 'The Philosophical Quarterly' [-], p.66
A Reaction
My instincts strongly cry out against all versions of this. If you are going to be a platonist (rather as if you are going to be religious) you might as well go for it big time and have independent objects, which will then dictate a structure.