more from Řystein Linnebo

Single Idea 14090

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique]

Full Idea

If objects depend on the other objects, this would mean an 'upward' dependence, in that they depend on the structure to which they belong, where the physical realm has a 'downward' dependence, with structures depending on their constituents.

Gist of Idea

In mathematical structuralism the small depends on the large, which is the opposite of physical structures


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

Book Reference

-: 'The Philosophical Quarterly' [-], p.68

A Reaction

This nicely captures an intuition I have that there is something wrong with a commitment primarily to 'structures'. Our only conception of such things is as built up out of components. Not that I am committing to mathematical 'components'!