[FOM] Cantor's Concept of "Mannigfaltigkeitslehre"

[Alexei E Angelides]

Hao,

In "Beitrag...", from 1878, Cantor describes sets with both the German word
"Menge" and "Inbegriff". But the word "Mannigfaltigkeitslehre" in the title
means literally "theory of manifolds", in Riemann's sense. Cantor's earliest
works, including "Beitrag...", is still connected to its use in the topology
tradition. As far as I can tell, Cantor does not begin using "Mengenlehre",
which is directly translated into "set theory", until the "Beiträge zur
Begründung der transfiniten Mengenlehre," written in 1895-7, which is also
where he first introduces the transfinite numbers. Of course, this does not
by itself rule out the possibility that he was using
"Mannigfaltigkeitslehre" in a more general--set-theoretic--sense in the
earlier works.

But for a very nice discussion of some of the details as well as a complete
bibliography of Cantor's works, see Jose Ferreiros, Labyrinth of Thought
(Birkhauser, 1999). I do not believe the collected works to which you refer
have been translated into English yet.

Alexei Angelides

Quoting hao zhaokuan <zkhao at fudan.edu.cn>:

> Dear FOMer,
>
> When Cantor use "Mannigfaltigkeitslehre"in his paper Ein Beitrag zur
> Mannigfaltigkeitslehre , did he mean "set theory"? Can you help me
> translate this German words into English? And does anybody konw if there
> is an English translation of Gessamelte Abhandlungen mathematischen und
> philosophischen Inhalts.
>
> Best Wishes
>
> Hao Zhaokuan
>