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