```Date: Apr 11, 2013 1:19 PM
Author: William Hughes
Subject: Re: Matheology § 238

On Apr 11, 6:42 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 11 Apr., 18:00, William Hughes <wpihug...@gmail.com> wrote:>>>>>>>>>> > On Apr 11, 5:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > On 11 Apr., 16:42, William Hughes <wpihug...@gmail.com> wrote:>> > > > On Apr 11, 4:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > On 11 Apr., 12:49, William Hughes <wpihug...@gmail.com> wrote:>> > > > > > On Apr 11, 8:28 am, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > > > On 10 Apr., 22:53, William Hughes <wpihug...@gmail.com> wrote:> > > > > > <snip>>> > > > > > > > Thus, the fact that there is no line (along with> > > > > > > > all its predecessors) that cannot be removed> > > > > > > > is not a contradiction.>> > > > > > > It is not a contradiction with mathematics. So far I agree. But it> > > > > > > would be a contradiction in case someone (and there are many here> > > > > > > around) maintained ~P for some d_n if there is a proof of P for all> > > > > > > FISs of d:>> > > > > > I do not claim this.  I claim that the collection of all d_n does> > > > > > not have the property P.>> > > > > That is not in question.> > > > > My claim is this:> > > > > If we have the propositions (with d_n a digit)> > > > > A =  for every n: P(d_n)> > > > > B =  for every n: P(d_1, d_2, ..., d_n)> > > > > Then B implies A.>> > > > > Do you agree?>> > > > Indeed, however, B does not imply>> > > > P(d_1,d_2,d_3....)>> > > That is not required. It is only required that B implies> > > A =  for every n: P(d_n).>> > > > So there is no contradiction is saying that A and B> > > > are true but it it not true that P(d_1,d_2,d_3,...)->> > > So A does not imply P(d_1,d_2,d_3,...) either?>> > correct.>> So you agree that B implies A.yep, but A does not imply C:  P(d_1,d_2,d_3..)>>>Now let P be (can remove the collection without changingthe union of the remaining lines).  We have there is nocontradiction in saying A: for all n, the nth line can be removed.
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