more from George Cantor

Single Idea 15505

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Set]

Full Idea

Cantor taught that a set is 'a many, which can be thought of as one'. ...After a time the unfortunate beginner student is told that some classes - the singletons - have only a single member. Here is a just cause for student protest, if ever there was one.

Gist of Idea

If a set is 'a many thought of as one', beginners should protest against singleton sets

Source

report of George Cantor (works [1880]) by David Lewis - Parts of Classes 2.1

Book Reference

Lewis,David: 'Parts of Classes' [Blackwell 1991], p.30


A Reaction

There is a parallel question, almost lost in the mists of time, of whether 'one' is a number. 'Zero' is obviously dubious, but if numbers are for counting, that needs units, so the unit is the precondition of counting, not part of it.