Date: Dec 9, 2012 12:02 AM
Author: Zaljohar@gmail.com
Subject: Re: fom - 01 - preface
On Dec 8, 6:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

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

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> > 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?

>

> Regards, WM

I was not referring to the particulars, I was referring to the essence

of the matter. A bijection between sets is a kind of isomorphic

relation between sets that are not necessarily relation sets. So the

universal exemplified by all bijective sets which is what we mean by

Cardinal number is 'essentially' a form.

Zuhair