Single Idea 15498

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

Full Idea

There is no such class as the null class. I don't mind calling some memberless thing - some individual - the null 'set'. But that doesn't make it a memberless class.

Gist of Idea

We can accept the null set, but there is no null class of anything


David Lewis (Parts of Classes [1991], 1.2)

Book Reference

Lewis,David: 'Parts of Classes' [Blackwell 1991], p.4

A Reaction

The point is that set theory is a formal system which can do what it likes, but classes are classes 'of' things. Everyone assumes that sets are classes, reserving 'proper classes' for the tricky cases up at the far end.