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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]
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 10270 | The main versions of structuralism are all definitionally equivalent [Shapiro] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 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] |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |