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Single Idea 9573

[from 'A Structural Account of Mathematics' by Charles Chihara, in 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

Source

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.