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Topic: fom - 01 - preface
Replies: 35   Last Post: Dec 16, 2012 12:20 AM

 Messages: [ Previous | Next ]
 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: fom - 01 - preface
Posted: Dec 9, 2012 12:02 AM

On Dec 8, 6:08 pm, 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?
>
> 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

Date Subject Author
12/7/12 fom
12/8/12 Zaljohar@gmail.com
12/8/12 mueckenh@rz.fh-augsburg.de
12/8/12 fom
12/8/12 mueckenh@rz.fh-augsburg.de
12/8/12 Virgil
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 Virgil
12/8/12 fom
12/8/12 ross.finlayson@gmail.com
12/9/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 fom
12/10/12 mueckenh@rz.fh-augsburg.de
12/10/12 Virgil
12/10/12 fom
12/10/12 ross.finlayson@gmail.com
12/11/12 fom
12/12/12 ross.finlayson@gmail.com
12/12/12 Virgil
12/16/12
12/9/12 ross.finlayson@gmail.com
12/9/12 fom
12/9/12 ross.finlayson@gmail.com
12/9/12
12/10/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/8/12 Virgil
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 Virgil
12/9/12 Zaljohar@gmail.com
12/9/12 mueckenh@rz.fh-augsburg.de
12/10/12 Dan Christensen
12/11/12 fom