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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