Cantor Confusion
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From: Lester Zick on 24 Oct 2006 15:36 On 24 Oct 2006 03:21:06 -0700, mueckenh(a)rz.fh-augsburg.de wrote: > >Lester Zick schrieb: > >> On Mon, 23 Oct 2006 02:00:06 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> >> wrote: >> >> >In article <1161518242.756958.103660(a)h48g2000cwc.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: >> >> [. . .] >> >> > Virgils definition, although not wrong, definitions >> >can not be wrong, does not lead to desirable results. >> >> Since when can definitions not be wrong? > >Since they got to now that set teory is correct only by definition. Sure. And since definitions cannot be true set theory cannot be true. (Technically not a theory at all since it can't be true and should be rechristened set analysis comprised of various analytical techniques.) ~v~~
From: Lester Zick on 24 Oct 2006 15:37 On Mon, 23 Oct 2006 22:24:16 -0400, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >MoeBlee wrote: >> mueckenh(a)rz.fh-augsburg.de wrote: >> > If you claim that what you call modern set theory has a deviating >> > definition of infinity, then I am not interested in your theory. >> >> This is not a matter of defining 'is infinite'. And if you're not >> interested in Z set theory, then fine. But then you don't claim that >> your argument about trees in Z set theory? I take it that your argument >> about trees is in your informal understanding of pre-formal Cantorian >> set theory. And I am not interested in your informal understanding of >> pre-formal Cantorian set theory as if your informal understanding of >> pre-formal Cantorian set theory has anything to do with formal >> mathematics. > >That is rather remarkable. On the one hand, Mueckenheim claims standard >set theory is inconsistent, but on the other he makes it clear that what >he calls "set theory" is not standard set theory. Do you think he really >thinks that standard set theory is inconsistent despite admitting that >he hasn't read anything written on the subject since Cantor? Is there not an inconsistency regarding containment in standard set analysis? ~v~~
From: Lester Zick on 24 Oct 2006 15:41 On Mon, 23 Oct 2006 23:23:10 -0400, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >MoeBlee wrote: >> Han.deBruijn(a)DTO.TUDelft.NL wrote: >> > Okay. Define your "identity relation". >> >> If it's primitive, then it's not defined. Usually, in mathematical >> logic, the symbol for identity is the only primitive predicate symbol. >> And it cannot be defined, even if we wanted to, in first order logic, >> which goes along with what I mentioned in my earlier post. >> >> Again, I have to say, it is not efficient for me to answer questions >> going in reverse. That is, if you say, "Why?" or "Define", then you can >> ask "Why?" of "Define" after every of my answers to a previous question >> of "Why?" or "Define". And I can keep answering until I finally arrive >> at the primitives of the theory or even the primitive notions of the >> informal meta-meta-theory. But it is much more efficient for us to >> START with those primitives and then demonstrate theorem by theorem. >> >> Thus, I suggest you just get a book on the subject and learn it like >> anyone else has ever had to learn a technical subject. Then, I hope >> that I could help you with any questions you have along the way. > >Indeed. One cannot learn mathematics by arguing with people on sci.math. One rarely learns anything by arguing period. One can however learn a considerable amount by analyzing arguments posted on usenet groups and elsewhere even if the "arguments" represent nothing but sophistry dressed up like a dog's dinner. ~v~~
From: Virgil on 24 Oct 2006 15:41 In article <1161685266.460059.199900(a)i42g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Lester Zick schrieb: > > > On Mon, 23 Oct 2006 02:00:06 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> > > wrote: > > > > >In article <1161518242.756958.103660(a)h48g2000cwc.googlegroups.com> > > >mueckenh(a)rz.fh-augsburg.de writes: > > > > [. . .] > > > > > Virgils definition, although not wrong, definitions > > >can not be wrong, does not lead to desirable results. > > > > Since when can definitions not be wrong? > > Since they got to now that set teory is correct only by definition. > > Regards, WM Since the ZF ( and ZFC and NBG) axiom system, including all its primitives and standard definitions, has not been shown to be self-contradictory, despite extensive investigations by those much more capable than any here, we may use the system(s) with some confidence. Those who choose to assume things which contradict any of those ZF (or ZZFC or NBG) axioms, or their consequences, deny themselves the right to use any of the conclusions drawn from those axiom sets, at least until the deniers have derived those same results from some other set of axioms which has also not been shown to be self contradictory. So far, those who object to ZF, and ZFC and NBG, have provided nothing satisfactory with which to replace them
From: Lester Zick on 24 Oct 2006 15:44
On Mon, 23 Oct 2006 22:01:25 -0400, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Han de Bruijn wrote: [. . .] >> >> There are many readers here who DO understand Mueckenheim's binary tree. >> And no, binary trees will not be found in Halmos' "Naive Set Theory". >> Because it's too naive, I suppose .. > >You mean all the cranks think they understand it. So this set of all cranks. Would that be those who disagree with you? ~v~~ |