```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 couldbe used to define a length or an area or a volume etc.Regards, WM
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