more from Řystein Linnebo

Single Idea 14084

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

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


Řystein Linnebo (Structuralism and the Notion of Dependence [2008], I)

Book Reference

-: '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]