In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 21 Feb., 20:23, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 21, 6:40 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 21 Feb., 14:18, William Hughes <wpihug...@gmail.com> wrote: > > > > > > According to WM > > > > > > i.; > > > > > > A) For every natural number n, P(n) is true. > > > > implies > > > > > that this claim A holds for every natural number from 1 to n, but not > > > necessarily for infinitely many following. > > > > > > B) There does not exist a natural number n such that P(n) is > > > > false. > > In fact we cannot find such a number. Nevertheless we cannot exclude > its existence. Please consider what I wrote about the sets A and B. > We cannot find a last finite number that has left A. Nevertheless it > must exist.
Outside of Wolkenmuekenheim it not only need not exist, it cannot exist.
> > > Every potentially infinite set of natural numbers has a last element. > > > But you cannot identify it.
Then no such set can exist, since in every sane set theory what WM here claims is false. > > > > I do not understand. You made the claim that A implies B. > > For every number from 1 to n.
But not for n+1? > > > Now you seem to be arguing against this. Note that the statement > > in B is that the natural number n does not exist, not that > > the natural number n cannot be identified. I remind you again > > that the words are yours.- > > The statement is that the natural number does not exist between 1 and > n inclusively.
I do not recall that that provision *between 1 and n) was included in the original. > > Find a FIS of d that is not in a line of the list or agree that you > cannot prove that there is no natural number such that line(n) = d.
For each nth line l of lenght n, there is a FIS_(n+1) of d having lenght n + 1. Thus line(n) =/= d.
So unless WM has a list of lines longer than every natural, he loses!!! --