```Date: Feb 26, 2013 5:34 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <49f12b7a-da95-49b3-84ef-f4b0becb8471@j9g2000vbz.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> 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.--
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