Single Idea 9157

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

Full Idea

Frege regarded the null set as an indefensible entity from the point of view of iterative set theory. It collects nothing. He thought a null entity (a null extension) is derivable only as the extension of an empty concept.

Gist of Idea

The null set is only defensible if it is the extension of an empty concept

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority II

Book Reference

'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.26


A Reaction

Frege is right, if you like sets. Othewise all the other sets are going to be defined simply by their extension, and the empty set has to be defined in a different way, which looks like appalling theory. Empty concepts bother me though!