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. --
