```Date: Jan 29, 2013 4:53 AM
Author: William Hughes
Subject: Re: Matheology § 203

On Jan 29, 10:36 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 29 Jan., 10:18, William Hughes <wpihug...@gmail.com> wrote:>>>>>>>>>> > On Jan 29, 10:09 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > On 29 Jan., 09:54, William Hughes <wpihug...@gmail.com> wrote:>> > > > On Jan 29, 9:33 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > "All" and "every" in impredicative statements about infinite sets.>> > > > > Consider the following statements:>> > > > > A) For every natural number n, P(n) is true.> > > > > B) There does not exist a natural number n such that P(n) is false.> > > > > C) For all natural numbers P is true.>> > > > > A implies B but A does not imply C.>> > > > Which is the point.  Even though A> > > > does not imply C we still have> > > > A implies B.>> > > > Let  L be a list> > > >      d the antidiagonal of L> > > >      P(n),  d does not equal the nth line of L>> > > > We have (A)>> > > >    For every natural number n, P(n) is true.>> > > > This implies (B)>> > > >   There does not exist a natural number n> > > >   such that P(n) is false.>> > > > In other words, there is no line of L that> > > > is equal to d.>> > > And how can C be correct nevertheless? Because "For all" is> > > contradictory.>> >    B: There is no line of L that is equal to d>> > does not imply>> >    C: For all n, line n is not equal to d.>> > B correct does not mean "C correct nevertheless"->> But we know of cases where C is correct nevertheless.B correct does not mean "C is incorrect"
```