Date: Feb 28, 2013 4:29 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<7a458051-4f30-467f-954a-9688dbd98a4d@h11g2000vbf.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 27 Feb., 21:28, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 27, 8:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >

> > > Do you prefer your argument?
> >
> > There is no disagreement over the facts.
> >
> > We both agree that there is a natural number
> > valued function of time, m(t), such that
> > at any time t, m(t) is the index of an existing
> > line which contains all existing FIS of d.
> > We both agree that m(t) is not constant.
> >

>
> Until now I was of the opinion that you accept completed infinity.
> There is no m(t).
>

> > You think that describing this situation as
> >   "there is a line which contains all FISs
> >    of d"
> > is sensible.

>
> Every FIS of d.


In standard languages, including both English and German,
"not all x" and "not every x" both require existence of an x which is
not whatever is under discussion. But in WMytheology this seems not to
be the case.
> >
> > I think that describing this situation as
> >  "there is a line which contains all FISs
> >    of d"
> > is idiotic.
> >
> > I will not defend my position except to point
> > out that many others agree with me,

>
> That is no argument. Many have believed in witches and have even burnt
> the. Many, many more than are presently believing in finished
> infinity.


That WM is in a tiny minority regarding the nature of infiniteness does
not make him right.

Mathematics will simple pass him by and leave him stuck in his useless
backwater.
>
> > think that your claim
> >  "there is a line which contains all FISs
> >    of d"
> > means something else,

>
>
> Not all. Every! Again you fall back into actual infinity.


We fall back on the fact that there is provably no line containing every
FIS of d any more that one containing all FISs of d.

For every line there must either be a successor line longer than it, or
that line is a last line and one has an actual finiteness of lines.

> Up to every n, all n are in line n. And more does not exist until you
> go to n+1. Remember Dedekind: We *create* numbers. They are not
> "there" or somewhere else, because your old position is in
> contradiction with the clear fact that the list cannot contain more
> than is contained in one single line.


In reality, unlike in WMytheology, there is no natural number which does
not have a successor.
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