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 > > > > > >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 > > > 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!