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Full Idea
The 'non-eliminative' version of mathematical structuralism takes it to be a fundamental insight that mathematical objects are really just positions in abstract mathematical structures.
Gist of Idea
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures
Source
Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I)
Book Ref
-: 'The Philosophical Quarterly' [-], p.60
A Reaction
The point here is that it is non-eliminativist because it is committed to the existence of mathematical structures. I oppose this view, since once you are committed to the structures, you may as well admit a vast implausible menagerie of abstracta.
Related Ideas
Idea 14085 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [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] |