
Re: Peerreviewed arguments against Cantor Diagonalization
Posted:
Oct 28, 2012 11:27 PM


On Oct 29, 1:14 pm, Arturo Magidin <magi...@member.ams.org> wrote: > On Sunday, October 28, 2012 10:01:31 PM UTC5, 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 UTC5, 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 > > > > > >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 "peerreview", books, and the like. > > > >  > > > > Arturo Magidin > > > Are you saying you just proved: > > > ALL(f):N>R E(r):R ALL(n):N f(n)=/=r > > > in 1ST ORDER LOGIC? > > > 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!
Herc

