[FOM] Questions on Cantor

Arik Hinkis arikhinkis at gmail.com
Sun Jan 27 08:36:01 EST 2013

Cantor, unlike Dedekind (1963 p 45), never explicitly mentioned
extensionality but: he read Dedekind and he defined (1878) the subset
relation for different sets only.

Re foundation: I beieve that Dedekind avoided publishing a third edition to
his monograph because he saw no way to make a set different from its
elements, as is infinite set is. The subject was probably brought up by him
in his meeting with Cantor of September 4, 1899. I believe that Canotr's
1895 definition of set is designed (definite and distinct) to rule out
non-well-founded sets.


On Sat, Jan 26, 2013 at 1:32 PM, Frode Bjørdal
<frode.bjordal at ifikk.uio.no>wrote:

> I have not studied Cantor's texts, but from what I recall I have heard and
> seen conflicting accounts as to how and whether he implicitly presupposed a
> well-founded notion of sets. Could some please
> (1) give textual evidence for him assuming i) well-foundedness, ii)
> non-wellfoundedness and (perhaps) iii) full naivety,
> and
> (2) confirm textually that he presupposed extensionality?
> Best regards from
> Frode
> *********************************************************
> Frode Bjørdal
> Professor i filosofi
> IFIKK, Universitetet i Oslowww.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
> Questions on C
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