more from Øystein Linnebo

### Single Idea 14085

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism]

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 Reference

-: '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]**