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.