Full Idea
The 'modal' version of eliminativist structuralism lifts the deductivist ban on modal notions. It studies what necessarily holds in all concrete models which are possible for various theories.
Gist of Idea
'Modal' structuralism studies all possible concrete models for various mathematical theories
Source
Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I)
Book Reference
-: 'The Philosophical Quarterly' [-], p.60
A Reaction
[He cites Putnam 1967, and Hellman 1989] If mathematical truths are held to be necessary (which seems to be right), then it seems reasonable to include modal notions, about what is possible, in its study.
Related Ideas
Idea 14084 Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
Idea 14085 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
Idea 14087 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]