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Topic: Matheology § 295
Replies: 24   Last Post: Jun 30, 2013 3:32 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 295
Posted: Jun 30, 2013 3:27 PM
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In article <50612434-27a6-4f1f-9f35-d0fcf2667944@googlegroups.com>,
mueckenh@rz.fh-augsburg.de 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.

--





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