Date: Dec 9, 2012 12:02 AM
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:
> > 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:
> 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.