Date: Dec 9, 2012 4:21 AM
Subject: Re: fom - 01 - preface
On 8 Dez., 23:37, Virgil <vir...@ligriv.com> wrote:
> In article
> 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.