```Date: Feb 11, 2013 2:53 AM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <i6adnS7u2oO04oXMnZ2dnUVZ_uWdnZ2d@giganews.com>, fom <fomJUNK@nyms.net> wrote:> On 2/10/2013 6:30 PM, Virgil wrote:> > In article <hoqdnWmpiaOtvYXMnZ2dnUVZ_s2dnZ2d@giganews.com>,> >   fom <fomJUNK@nyms.net> wrote:> >> >> On 2/10/2013 4:16 PM, Virgil wrote:> >>> In article> >>> <3a8b891b-172f-415f-b4f6-34f988abae5d@e10g2000vbv.googlegroups.com>,> >>>    WM <mueckenh@rz.fh-augsburg.de> wrote:> >>>> >>>> On 10 Feb., 18:40, William Hughes <wpihug...@gmail.com> wrote:> >>>>> On Feb 10, 10:51 am, WM <mueck...@rz.fh-augsburg.de> wrote:> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> On 9 Feb., 17:36, William Hughes <wpihug...@gmail.com> wrote:> >>>>>> >>>>>>>>> the arguments are yours> >>>>>>>>> and the statements are yours-> >>>>>> >>>>>>>> Of course. But the wrong interpretation is yours.> >>>>>> >>>>>>> How does one interpret> >>>>>>>      we have shown m does not exist> >>>>>>>      (your statement)> >>>>>> >>>>>>> to mean that> >>>>>> >>>>>>>      m might still exist> >>>>>> >>>>>>> ?> >>>>>> >>>>>> TND is invalid in the infinite.> >>>>>> >>>>>> Regards, WM> >>>>>> >>>>> In Wolkenmeukenheim, we can have> >>>>> for a potentially infinite set> >>>>>> >>>>>         we know that x does not exist> >>>>>         we don't know that x does not exist> >>>>>> >>>>> true at the same time.> >>>>> >>>> Is it so hard to conclude from facts without believing in matheology?> >>>>> >>>> The diagonal of the list> >>>> 1> >>>> 11> >>>> 111> >>>> ...> >>>>> >>>> is provably not in a particular line.> >>>> But the diagonal is in the list, since it is defined in the list only.> >>>> Nothing of the diagonal can be proven to surpass the lines and rows of> >>>> the list.> >>>> >>> It is not that the diagonal "surpasses" any particular line, it is> >>> merely that an appropriately defined  "diagonal" is different from each> >>> and every particular line, i.e., does not appear as any line among the> >>> lines being listed.> >>> >> Yes.  And the scare quotes are nice.> >>> >> The problem with singular terms means that> >> "diagonal" is, in fact, a plurality of acts> >> of definition.> >> > The Cantor antidiagonal rule, for an actually infinite list of actually> > infinite binary sequences is a quite finite rule :> >> > If the two possible values are 'm' and 'w', then the nth term of the> > diagonal is to be not equal to the nth term of the nth listed sequence,> > meaning that> >     if the nth term of the nth listed sequence is "m"> >     then the nth listed element of the diagonal is "w"> > and> >     if the nth term of the nth listed sequence is "w"> >     then the nth listed element of the diagonal is "m".> >> > In this way, the constructed sequence differs from the nth listed> > sequences at lest at its nth postion> >> > > Thanks, I do understand that.> > I was referring to WM's position.  There cannot be one> diagonal for him.  Given n, WM must find a diagonal> (note the indefinite article) such that length(dFIS)>n+1> so that comparison with the n-th listed sequence can> be made.> > While there may be other sources for the definition> of "distinguishability", the one I have is in a book> on automata.  Distinguishability is characterized in> terms of finitary "experiments of length k".  Two> "states" are k-distinguishable if there is an experiment> of length k which differentiates them.  Two states> are distinguishable if they are k-distinguishable> for any k.Shouldn't that be "k-distinguishable for some k"?> > Two "states" are k-equivalent if there is no m<=k for> which the given states are differentiated by an experiment> of length m.> > Two "states" are equivalent if for every k they are> not k-distinguishable.  So, equivalence is infinitary.> > This description coincides with your explanation> as the Cantor diagonal is formed specifically to> be k-distinguishable for every k.> > As for WM, definite articles imply representation> with singular terms.  He has a plural multiplicity> of diagonals.No one of which is the real one.--
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