Single Idea 10809

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

Full Idea

In my usage of 'class', there is no such things 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. Rather, that makes it a 'set' that is not a class.

Gist of Idea

We can accept the null set, but not a null class, a class lacking members


David Lewis (Mathematics is Megethology [1993], p.05)

Book Reference

-: 'Philosophia Mathematica' [-], p.5

A Reaction

Lewis calls this usage 'idiosyncratic', but it strikes me as excellent. Set theorists can have their vital null class, and sensible people can be left to say, with Lewis, that classes of things must have members.