In article <email@example.com>, firstname.lastname@example.org wrote:
> On Saturday, 29 June 2013 23:30:13 UTC+2, Virgil wrote: > > > > 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 existed? > > Just the contrary. Cantor knew that natural numbers exist.
Anything he claimed to know must either be assumed by him or proved by him from other assumptions.
> To know that, one > does not need axioms unless being a jerk, Bourbakist, or matheologian, or a > cross-breed of these species.
To know things without evidence or proof of their truth requires one to be either a god, or someone like WM. > > Regards, WM > > > > 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. --