Date: Feb 4, 2013 5:29 PM
Author: Virgil
Subject: Re: Matheology � 203

In article 
<f24dfa9c-f4f2-44fa-bc0a-139aef3c2262@y4g2000yqa.googlegroups.com>,
 WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 4 Feb., 13:35, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
> > > On 2 Feb., 02:56, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> >
> > >> "The logicist reduction of the concept of natural number met a
> > >> difficulty on this point, since the definition of Œnatural number¹
> > >> already given in the work of Frege and Dedekind is impredicative. More
> > >> recently, it has been argued by Michael Dummett, the author, and Edward
> > >> Nelson that more informal explanations of the concept of natural number
> > >> are impredicative as well. That has the consequence that impredicativity
> > >> is more pervasive in mathematics, and appears at lower levels, than the
> > >> earlier debates about the issue generally presupposed."
> >
> > > I do not agree with these authors on this point.
> >
> > So, on what grounds do you suppose that the notion
> > of natural number is predicative?
> 
> The notion of every finite initial segment is predicative because we
> need nothing but a number of 1's, that are counted by a number already
> defined, and add another 1.

Where did you get the first 1?
> >
.
.
.

> There are no axioms required in mathematics.

Even Euclid knew better than that.

> Mathematics has evolved
> by counting and summing without any axioms, but by comparison with
> reality. And similar to Haeckel's "ontogeny recapitulates phylogeny"
> we can teach and apply mathematics on the same basis where it has
> evolved.

Except that there is considerable reason to doubt 
that "ontogeny recapitulates phylogeny".

http://evolution.berkeley.edu/evosite/evo101/IIIC6aOntogeny.shtml

Thus justifying our at least equal doubts of WMYTHEOLOGY.
--