On 2/11/2013 1:53 AM, Virgil wrote: > 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"?
"some" is certainly better
while writing I must have had "any (particular)" in mind
>> >> 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. >
