more from Gottlob Frege

Single Idea 14238

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

Full Idea

A class consists of objects; it is an aggregate, a collective unity, of them; if so, it must vanish when these objects vanish. If we burn down all the trees of a wood, we thereby burn down the wood. Thus there can be no empty class.

Gist of Idea

A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class


Gottlob Frege (Elucidation of some points in E.Schröder [1895], p.212), quoted by Oliver,A/Smiley,T - What are Sets and What are they For?

Book Reference

'Metaphysics (Philosophical Perspectives 20)', ed/tr. Hawthorne,John [Blackwell 2006], p.126

A Reaction

This rests on Cantor's view of a set as a collection, rather than on Dedekind, which allows null and singleton sets.