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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 Ref
-: '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]
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |