Date: Feb 26, 2013 5:15 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
WM <> wrote:

> On 26 Feb., 00:13, William Hughes <> wrote:
> > On Feb 25, 11:37 pm, WM <> wrote:
> >

> > > On 25 Feb., 16:11, William Hughes <> 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.
> 2) Therefore d is completely in the lits. In fact, it *is* the list.

Wrong! There is no line of d which is only a FIS of d and thus a line of
your list.

Each element of d is an element of infinitely many elements of the list,
but that no more makes d a member of your list than it makes the union
of a family of sets equal to one of the sets in the union.

At least not outside WMytheology

> 3) We know that everything that is in the list, is in one single line
> of the list (by construction and by induction).

Which line would that be? And how does that line contain everything in
the infinitely many following lines of which it is necessarily a proper

> 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.

It does not exist in any sense in any list of lines constructed so as
not to have a last line.
> >
> > > > Indeed if we throw findable in
> > > > we agree about a lot of stuff.

> >
> > > > There is no findable largest natural
> > > > number.

> >
> > > > There is no ball with a findable index
> > > > in the vase.

> >
> > > And there is no findable set of natural numbers
> Here you cut my statement and by that changed it.

And changed it for the better, as the changed version can be true
everywhere while the original can only be true in WMytheology.

> I said: And there is
> no findable set of natural numbers that would require more than one
> line.

I know of no piece of paper large enough to make that true.
> >
> > Well there is certainly a potentially infinite
> > set of findable natural numbers.
> > This potentially infinite set contains all the natural numbers
> > I need and use.

> Every natural number is findable. Therefore you claim that not every
> natural number and not every FIS of d is in one single line of the
> list, must be wrong.

For every line of your list there are at least as many elements of d,
the union of all lines, NOT in that line as in it.

> (Because you cannot find any number that is not
> in one line of the list together with every other natural number.)

There is no line of the list which has ANY natural number TOGETHER WITH
> Do you wish to withdraw your statement that not every natural number
> is in one line of the list together with every other natural number?

Hardly! Do you wish to withdraw your statement that every natural number
is in one line of the list together with every other natural number?

Which line would that be that contains, for example, the last number in
the next line?
> Note: We cannot find a "last number" because by this phrase we do not
> fix a number.

Because for every proposed "las number" its successor makes it not the

And outside the confusion of WMytheology, for every natural there is a
successor natural with no limit. This is apaprently denied in

> The last number is just that number that has not yet got
> a follower in our thoughts.

In the thoughts of those not constrained by the idiocies of
WMytheology, every natural, in order to be recognized as a natural, must
have a successor in our thoughts. Things without successors are not
naturals, to least not outside WMytheology.
We cannot imagine a natural without one.

> Yes this property depends on persons,
> their thoughts and it can varywith time. That is the feature of
> potential infinity.

Sets which are time-dependent do not work in any standard set theory,
only in WMytheology.

One can have a function of time whose VAlUES are sets, but that function
is not a time-dependent set.