[FOM] Cantor and "absolute infinity": a clarification

Arnon Avron aa at tau.ac.il
Mon Feb 20 07:11:09 EST 2006

On Sun, Feb 19, 2006 at 01:29:34PM -0600, William Tait wrote:
> On Feb 18, 2006, at 5:09 PM, Arnon Avron wrote:
> >>  But unfortunately, Cantor buried his remarks about the
> >> absolute infinite in an endnote. Frege refers to Cantor's paper in
> >> such a way that it is clear that he read the description of the
> >> transfinite numbers. One may wonder whether, if Cantor had positioned
> >> his remarks on the absolute infinite more prominently, Frege might
> >> have been saved dome pain and people such as Dedekind, Hilbert and
> >> Weyl would have seen the paradoxes of set theory simply as mistakes.
> >> Maybe the history of foundations in the early 20th century would have
> >> been quite different. (Purkert has suggested that Cantor buried these
> >> remarks in an endnote because he wanted to sell his theory and did
> >> not want people to confront initially the complication of the
> >> absolute infinite. I want that to be false.)
> >>
> >
> > I don't buy this story and speculation.
> >
> My only story is the assertion about the content of an endnote in  
> Cantor's *Grundlagen*, published in 1883. So it is a 'story' only in  
> the sense of a 'history'; it is accurate and I wasn't trying to sell  
> it. Please read the endnote.

I am sorry for expressing myself unclearly. I was not doubting
of course that Cantor wrote that endnote (in fact, I was aware
of them before). The "story" I meant was that Cantor's ideas were
consistent from the start, and that from the very beginning
he made for hinself the distinction between "infinite" and
"absolutely infinite" (a story told mainly by Lavine in his book).

I apologize that it might have understood from what I wrote that
I dont believe the *facts* that you mentioned.

Arnon Avron


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