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Topic: Peer-reviewed arguments against Cantor Diagonalization
Replies: 156   Last Post: Nov 4, 2012 3:01 PM

 Messages: [ Previous | Next ]
 Arturo Magidin Posts: 796 Registered: 8/24/06
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Oct 28, 2012 11:29 PM

On Sunday, October 28, 2012 10:27:52 PM UTC-5, Hercules ofZeus wrote:
> On Oct 29, 1:14 pm, Arturo Magidin <magi...@member.ams.org> wrote:
>

> > On Sunday, October 28, 2012 10:01:31 PM UTC-5, Hercules ofZeus wrote:
>
> > > On Oct 29, 12:20 pm, Arturo Magidin <magi...@member.ams.org> wrote:
>
> >
>
> > > > On Sunday, October 28, 2012 9:04:41 PM UTC-5, JRStern wrote:
>
> >
>
> > > > > On Sun, 28 Oct 2012 17:41:59 -0700 (PDT), Arturo Magidin
>
> >
>
> > > > > <magi...@member.ams.org> wrote:
>
> >
>
> > > > > >Huh?
>
> >
>
> > > > > >Sorry, but that statement makes absolute no sense
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> >
>
> > > > > >whatsoever to me.  What exactly was the point you
>
> >
>
> > > > > >were attempting to make?
>
> >
>
> > > > > That I am not arguing with the conclusion that Cantor's Theorem is
>
> >
>
> > > > > true, I am questioning whether the diagonal argument is coherent.
>
> >
>
> > > > > How can this be unclear?
>
> >
>
> > > > Because I did not simply state the conclusion. I gave you the "diagonal argument". If you are questioning whether it is "coherent", then you should point to whatever point you find incoherent, rather than simply quote and then give a sentence fragment.
>
> >
>
> > > > The government doesn't like it when I read minds without a warrant, so I try not to do it, you see.
>
> >
>
> > > > I have you a complete proof of Cantor's Theorem; the diagonal argument is embedded in that theorem. What is it that you find incoherent?
>
> >
>
> > > > If there is nothing you find incoherent, then why is it that you continue to "question" its coherence?
>
> >
>
> > > > If you could not even tell that you were presented with the argument in the first place, then perhaps your problems arise much sooner than at Cantor's diagonal argument?
>
> >
>
> > > > If it is a *particular* presentation of the argument that concerns you, then it is incumbent upon you to specify which presentation it is you find yourself having doubts about, and stop nattering about "peer-review", books, and the like.
>
> >
>
> > > > --
>
> >
>
> > > > Arturo Magidin
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> >
>
> > > Are you saying you just proved:
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> >
>
> > > ALL(f):N->R  E(r):R  ALL(n):N  f(n)=/=r
>
> >
>
> > > in 1ST ORDER LOGIC?
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> >
>
> > > i.e. FOL = Quantifiers Over Arguments Not Functions.
>
> >
>
> > In ZF, functions are sets; and the objects of the theory are sets. So the statement above is a perfectly fine first order statement in the language of ZF. Moreover, there is a *set* of functions from N to R, so I'm quantifying over the **objects** that are elements of that set.
>
> >
>
> > But surely, if you know about first order logic, then you knew that?
>
> >
>
> > And if you didn't... well, you are someone else whose problems come from much earlier than any objection you might by trying to raise here; your problem is the same as Sir Richard Phillips's.
>
> >
>
> > --
>
> > Arturo Magidin
>
> >
>
> >
>
>
>
>
>
>
>
> And you see no problem with using a logic composed of predicate
>
> strings (functions) to construct sets to construct functions to range
>
> over ALL functions, and calling it 1st order logic - No Quantifying
>
> over functions here!

The reason I see no problems is because I actually know what I'm talking about.

You should try it some day. Until then, let me know when you are actually willing to pay for my insight. I'm tired of casting pearls before the hercs.

--
Arturo Magidin

Date Subject Author
10/27/12 JRStern
10/27/12 Frederick Williams
10/27/12 JRStern
10/28/12 Tim Little
10/28/12 Peter Webb
10/28/12 JRStern
10/28/12 J. Antonio Perez M.
10/29/12 Michael Stemper
10/29/12 David C. Ullrich
10/29/12 JRStern
10/29/12 JRStern
10/30/12 David C. Ullrich
10/30/12 David C. Ullrich
10/29/12 LudovicoVan
10/27/12 J. Antonio Perez M.
10/28/12 INFINITY POWER
10/28/12 Shmuel (Seymour J.) Metz
10/28/12 Graham Cooper
10/28/12 magidin@math.berkeley.edu
10/28/12 INFINITY POWER
10/28/12 Graham Cooper
10/28/12 Virgil
10/28/12 Graham Cooper
10/28/12 JRStern
10/28/12 magidin@math.berkeley.edu
10/28/12 Graham Cooper
10/28/12 Graham Cooper
10/28/12 magidin@math.berkeley.edu
10/28/12 Graham Cooper
10/28/12 magidin@math.berkeley.edu
10/29/12 Frederick Williams
10/29/12 LudovicoVan
10/29/12 Richard Tobin
10/29/12 LudovicoVan
10/29/12 J. Antonio Perez M.
10/29/12 J. Antonio Perez M.
10/29/12 magidin@math.berkeley.edu
10/29/12 Frederick Williams
10/28/12 Graham Cooper
10/28/12 JRStern
10/28/12 Peter Webb
10/28/12 magidin@math.berkeley.edu
10/28/12 Hercules ofZeus
10/28/12 magidin@math.berkeley.edu
10/28/12 Hercules ofZeus
10/28/12 Arturo Magidin
10/28/12 Hercules ofZeus
10/28/12 Arturo Magidin
10/28/12 Hercules ofZeus
10/29/12 J. Antonio Perez M.
10/29/12 Graham Cooper
10/29/12 JRStern
10/29/12 Frederick Williams
10/29/12 magidin@math.berkeley.edu
10/29/12 Pubkeybreaker
10/29/12 JRStern
10/29/12 magidin@math.berkeley.edu
10/29/12 Graham Cooper
10/29/12 JRStern
10/29/12 magidin@math.berkeley.edu
10/30/12 Graham Cooper
10/30/12 magidin@math.berkeley.edu
10/30/12 Graham Cooper
10/30/12 J. Antonio Perez M.
10/31/12 Peter Webb
10/29/12 Peter Webb
10/29/12 magidin@math.berkeley.edu
10/29/12 Shmuel (Seymour J.) Metz
10/29/12 Virgil
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 Graham Cooper
10/29/12 Peter Webb
10/30/12 Graham Cooper
10/30/12 Peter Webb
10/30/12 Graham Cooper
10/30/12 Peter Webb
10/30/12 Graham Cooper
10/30/12 MoeBlee
10/30/12 Peter Webb
10/30/12 Graham Cooper
10/31/12 Peter Webb
10/31/12 Graham Cooper
10/31/12 Peter Webb
10/31/12 Graham Cooper
11/2/12 Peter Webb
11/1/12 Peter Webb
11/1/12 Hercules ofZeus
11/2/12 Peter Webb
10/31/12 Peter Webb
10/30/12 Richard Tobin
10/30/12 Graham Cooper
10/30/12 MoeBlee
10/30/12 Graham Cooper
10/30/12 MoeBlee
10/30/12 Graham Cooper
10/31/12 Richard Tobin
10/31/12 Graham Cooper
10/31/12 Graham Cooper
10/31/12 Graham Cooper
10/31/12 Richard Tobin
10/31/12 Graham Cooper
10/31/12 Richard Tobin
10/31/12 Graham Cooper
10/31/12 Graham Cooper
10/29/12 Peter Webb
10/29/12 LudovicoVan
10/29/12 J. Antonio Perez M.
10/29/12 LudovicoVan
10/29/12 Peter Webb
10/29/12 LudovicoVan
10/30/12 Peter Webb
10/30/12 LudovicoVan
10/30/12 Peter Webb
10/30/12 LudovicoVan
10/30/12 Peter Webb
10/30/12 J. Antonio Perez M.
10/30/12 LudovicoVan
10/30/12 Virgil
10/30/12 J. Antonio Perez M.
10/30/12 LudovicoVan
10/31/12 Peter Webb
10/31/12 LudovicoVan
10/31/12 J. Antonio Perez M.
10/31/12 Shmuel (Seymour J.) Metz
11/1/12 LudovicoVan
11/1/12 Jesse F. Hughes
11/2/12 Peter Webb
11/2/12 LudovicoVan
11/2/12 Graham Cooper
11/2/12 Shmuel (Seymour J.) Metz
11/2/12 Virgil
11/2/12 Peter Webb
11/2/12 Peter Webb
11/3/12 J. Antonio Perez M.
11/3/12 Shmuel (Seymour J.) Metz
11/4/12 Peter Webb
11/4/12 Virgil
11/4/12 Shmuel (Seymour J.) Metz
11/1/12 Shmuel (Seymour J.) Metz
10/31/12 Shmuel (Seymour J.) Metz
10/31/12 Shmuel (Seymour J.) Metz
10/29/12 JRStern
10/29/12 Shmuel (Seymour J.) Metz
10/28/12 Graham Cooper
10/28/12 J. Antonio Perez M.
10/29/12 David C. Ullrich
10/29/12 JRStern
10/29/12 LudovicoVan
10/29/12 Fernando Revilla
10/29/12 Shmuel (Seymour J.) Metz