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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