Date: Feb 4, 2013 5:29 PM
Subject: Re: Matheology � 203
WM <firstname.lastname@example.org> 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 natural 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
Except that there is considerable reason to doubt
that "ontogeny recapitulates phylogeny".
Thus justifying our at least equal doubts of WMYTHEOLOGY.