Virgil
Posts:
4,479
Registered:
1/6/11
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Re: fom - 01 - preface
Posted:
Dec 8, 2012 5:37 PM
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In article
<7a354fd9-0c0f-49f8-84b6-3f457d3b295b@10g2000yqk.googlegroups.com>,
WM <mueckenh@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.
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