In article <email@example.com>, firstname.lastname@example.org wrote:
> On Saturday, 29 June 2013 06:44:33 UTC+2, Virgil wrote: > > > Actually, Cantor did make assumptions, he just didn't call them axioms. > > Actually, Cantor made no assumptions when he constructed the finite cardinals > in his 1895 article. And Cantor often emphasized that he did not need axioms. > (A very sober attitude that I have to applaude to!)
You mean that Cantor did not assume that natural numbers existd? > > But the letter which fom quoted from, Cantor to Hilbert on 27 Jan. 1900, > written from Berlin to Göttingen and extending over several pages, one of the > most remarkable letters to Hilbert and one the most important in the > collection of Cantor letters edited by Meschkowski and Nilson, as they write > themselves on p. 428 of their voluminous book of Cantor letters (Springer, > Berlin 1991), ... this letter contains Cantor's reference to several classes > of axioms. In addition he admits to be in opposition to Gauß and to Dedekind. > > But as we know, this was a time when Cantor has ceased to publish any new > ideas (except some which later generations judged as being without > mathematical value) and had to be in hospital more and more frequently. So I > personally assume that the ideas exptressed in this letter do not illuminate > the original Cantor.
As usual, WM's personal assumptions are of no value to anyone outside of WM's wild weird world of WMytheology, and only of value to WM inside WM's wild weird world of WMytheology. --