```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 iscompletely 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
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