Date: Dec 9, 2012 4:21 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: fom - 01 - preface
On 8 Dez., 23:37, Virgil <vir...@ligriv.com> wrote:

> In article

> <7a354fd9-0c0f-49f8-84b6-3f457d3b2...@10g2000yqk.googlegroups.com>,

>

>

>

>

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 8 Dez., 10:02, Zuhair <zaljo...@gmail.com> wrote:

> > > On Dec 7, 9:45 am, fom <fomJ...@nyms.net> wrote:

>

> > > > Although it is not mentioned frequently

> > > > in the literature, Frege actually

> > > > retracted his logicism at the end of

> > > > his career. His actual statement,

> > > > however, is much stronger. He rejects

> > > > the historical trend of arithmetization

> > > > in mathematics as foundational.

>

> > > > In "Numbers and Arithmetic" he writes:

>

> > > > "The more I have thought the matter

> > > > over, the more convinced I have become

> > > > that arithmetic and geometry have

> > > > developed on the same basis -- a

> > > > geometrical one in fact -- so that

> > > > mathematics in its entirety is

> > > > really geometry"

>

> > > I agree with Frege. Geometry or more generally thought about structure

> > > is what mathematics is all about, number is basically nothing but a

> > > very trivial structure.

>

> > Then everybody should understand that the infinities in the numbers

> > forming the following triangle and the geometrical aspects have a

> > common origin:

>

> > 1

> > 11

> > 111

> > ...

>

> > Height and diagonal have lenght aleph_0. What about the basis?

>

> Aleph_0 is not a length, nor an area, nor a volume.

If it was a whole number or integer, as Cantor insisted, then it could

be used to define a length or an area or a volume etc.

Regards, WM