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Full Idea
The 'deductivist' version of eliminativist structuralism avoids ontological commitments to mathematical objects, and to modal vocabulary. Mathematics is formulations of various (mostly categorical) theories to describe kinds of concrete structures.
Clarification
'Categorical' means they all map onto one another
Gist of Idea
'Deductivist' structuralism is just theories, with no commitment to objects, or modality
Source
Øystein Linnebo (Structuralism and the Notion of Dependence [2008], 1)
Book Ref
-: 'The Philosophical Quarterly' [-], p.60
A Reaction
'Concrete' is ambiguous here, as mathematicians use it for the actual working maths, as opposed to the metamathematics. Presumably the structures are postulated rather than described. He cites Russell 1903 and Putnam. It is nominalist.
Related Ideas
Idea 14084 Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
Idea 14086 'Modal' structuralism studies all possible concrete models for various mathematical theories [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] |