Date: Feb 25, 2013 6:11 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 24 Feb., 21:04, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 24, 8:32 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 24 Feb., 15:56, William Hughes <wpihug...@gmail.com> wrote:
>
> > > So, when WM says that a natural number m does not
> > > exist, he may mean that you can prove it exists
> > > but you cannot find it.

>
> > > Suppose that P is a predicate such that
> > > for every natural number m, P(m) is true.

>
> > Example: Every line of the list L
>
> > 1
> > 1, 2
> > 1, 2, 3
> > ...

>
> > contains all its predecessors.
>
> > > Let x be a natural number such that
> > > P(x) is false. According to WM you cannot
> > > prove that x does not exist.  (WM
> > > rejects the obvious proof by contradiction:

>
> > >      Assume a natural number, x, such that P(x)
> > >      is false exists.
> > >      call it k
> > >      Then P(k) is both true and false.
> > >      Contradiction,  Thus the original assumption
> > >      is false and no natural number, x, such
> > >      that P(x) is false exists)

>
> > > We will say that x is an unfindable natural
> > > number.

>
> > > It is interesting to note that WM agrees with
> > > the usual results if you insert the term findable.

>
> > > E.g.
>
> > > There is no findable last element of the potentially
> > > infinite set |N.

>
> > > There is no findable index to a line of L that
> > > contains d.

>
> > > There is no ball with a findable index in the vase.
>
> > > etc.
>
> > > It does not really matter if nonfindable natural
> > > numbers exist or not. They have no effect.

>
> > > I suggest we give WM a teddy bear marked unfindable.
>
> > I suggest, William keeps abd comforts it until he can find the first
> > line of L that is not capable of containing everthing that its
> > predecessors contain.

>
> Every line of L is capable of containing everything that
> its predecessors contain.


And why then do you believe, or at least claim, that something that is
completely in the list must be distributed over more than one line?

> In WM's world, just because you can't
> find something does not mean it does not exists.


That is so in other worlds too.

Regards, WM