[FOM] Questions on Cantor

David Auerbach auerbach at ncsu.edu
Sun Jan 27 10:56:45 EST 2013

The best and most nuanced account of these issues that I know of is Michael Hallett's wonderful *Cantorian set theory and limitation of size*.  Section 1.3 is particularly relevant. (The main, but far from only, Cantor text for that section is: Über unendliche, lineare Punktmannigfaltigkeiten, 5. )
 Without the nuance, Hallett's Cantor is committed to well-foundedness but not "full naivety".  That is, if full naivety and "not every collection is a set" are inconsistent; for Cantor accepted the latter. 
For extensionality, I can't remember where it first comes up in Hallett, but he has Cantor committed to it; it's relevant in the discussion of Frege's criticism of views that take numbers as collections of "unities" (the theory of "ones").

In any case, Hallett is replete with quotes from Cantor.

On Jan 26, 2013, at 6:32 AM, 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 Oslo
> www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
> Questions on C
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David Auerbach                                                      auerbach at ncsu.edu
Department of Philosophy and Religious Studies
Raleigh, NC 27695-8103

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