more from Øystein Linnebo

### Single Idea 14091

#### [catalogued under 7. Existence / C. Structure of Existence / 4. Ontological Dependence]

Full Idea

We can give an exhaustive account of the identity of the empty set and its singleton without mentioning infinite sets, and it might be possible to defend the view that one natural number depends on its predecessor but not vice versa.

Gist of Idea

There may be a one-way direction of dependence among sets, and among natural numbers

Source

Øystein Linnebo (Structuralism and the Notion of Dependence [2008], V)

Book Reference

-: 'The Philosophical Quarterly' [-], p.73

A Reaction

Linnebo uses this as one argument against mathematical structuralism, where the small seems to depend on the large. The view of sets rests on the iterative conception, where each level is derived from a lower level. He dismisses structuralism of sets.