more from Charles Chihara

Single Idea 9573

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set]

Full Idea

In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it.

Gist of Idea

The null set is a structural position which has no other position in membership relation


Charles Chihara (A Structural Account of Mathematics [2004], 11.6)

Book Reference

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.343

A Reaction

It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set.