In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 26 Feb., 00:13, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 25, 11:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 25 Feb., 16:11, William Hughes <wpihug...@gmail.com> wrote: > > > > > > We both agree > > > > > > There does not exist an m > > > > such that the mth line > > > > of L is coFIS with the diagonal > > > > (here we interpret "There does > > > > not exist" to mean "we cannot find"). > > > > Do you now wish to withdraw this statement? > > No. > > I say > > 1) *Every* FIS of d is a line and every line is a FIS of d.
Then d is the union of all its FISs. But in proper set theories, the union of a family of sets need not be one of the family, and unless the family contains a maximal member, which the family of lines does not, cannot not be member of that union.
So WM is claiming the existence of a maximal set in a family of sets carefully constructed so as not to have any such maximal member.
> 2) Therefore d is completely in the lits. In fact, it *is* the list.
NO, it is the union of the list, but as the list has no maxmal member, that union cannot be either the list or a member of the list.
> 3) We know that everything that is in the list, is in one single line > of the list (by construction and by induction).
If everything in the list is in one line of the list, and each line is a FIS of the next line, then everything must be in a last line, and the list must be actually finite.
> 4) We cannot find the last line and the corresponding last FIS of d. > It does not exists in the sense that we could name it.
Nor in any other sense whatsoever! > >
> Note: We cannot find a "last number" because by this phrase we do not > fix a number. The last number is just that number that has not yet got > a follower in our thoughts.
Outside of WMytheology a number cannot be accepted as a natural unless and until it is known to have a successor.
The existence of a successor is a requirement for membership in the set of naturals.
So numbers not already known to have successors cannot be known to be naturals at all. --