Obections to Cantor's Theory (Wikipedia article)
in [Logic]
|
Prev: Derivations
Next: Simple yet Profound Metatheorem
From: Helene.Boucher on 20 Jul 2005 01:20 david petry wrote: > > There is no mention of one historical or living figure who is > > anti-Cantorian, what their objections were > > Hmm, not quite. I did mention Kronecker. Did you miss that? Sorry, you're right, not quite. There is the *mention* of only one historical and no living figure who is anti-Cantorian. Except for a solitary quote, there is no mention of what Kronecker's views actually are and what kind of system he advocated. "The anti-Cantorians see an underlying reality to mathematics, namely, computation." Is Kronecker one of these anti-Cantorians? Is Feferman? Or is it just Petry? So we still have a rant. You're not giving those with anti-Cantorian views a fair shake, and I'm afraid your expose will make them them look ridiculous rather than inviting.
From: Virgil on 20 Jul 2005 01:27 In article <dbkasd$to7$1(a)lust.ihug.co.nz>, Barb Knox <see(a)sig.below> wrote: > In article <7mrqd1liuvhopdetv1mfe7ii498hru8qr4(a)4ax.com>, > G. Frege <nomail(a)invalid> wrote: > > >On 19 Jul 2005 21:02:29 GMT, Chris Menzel <cmenzel(a)remove-this.tamu.edu> > >wrote: > > > >> > >> Pretty clearly, you aren't terribly well-educated in set theory. Don't > >> you think you should understand a field before you try to point out its > >> flaws? > >> > >Isn't that rather typical for a m o d e r n "anti-cantorian"? :-) > > I am the very model of a modern non-Cantorian, > With insights mathematical as good as any saurian. > I rattle the Establishment foundations with prodigious ease, > And populate the counting numbers with some new infinities. > I've never studied axioms of sets all theoretical, > But that's just ted'ous detail; whereas MY thoughts are heretical > And cause the so-called experts rather quickly to exasperate, > While I sit back and mentally continue just to .... Lovely!!!
From: Virgil on 20 Jul 2005 01:31 In article <dbkcr2$1ep$1(a)lust.ihug.co.nz>, Barb Knox <see(a)sig.below> wrote: > In article > <ITSnetNOTcom#virgil-CEB650.19511919072005(a)comcast.dca.giganews.com>, > Virgil <ITSnetNOTcom#virgil(a)COMCAST.com> wrote: > > >In article <MPG.1d4715811811605b989f27(a)newsstand.cit.cornell.edu>, > > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > >> David Kastrup said: > >> > Alec McKenzie <mckenzie(a)despammed.com> writes: > >> > > >> > > "Stephen J. Herschkorn" <sjherschko(a)netscape.net> wrote: > >> > > > >> > >> Can anti-Cantorians identify correctly a flaw in the proof that > >> > >> there exists no enumeration of the subsets of the natural numbers? > >> > > > >> > > In my view the answer to that question a definite "No, they can't". > >> > > > >> > > However, the fact that no flaw has yet been correctly identified > >> > > does not lead to a certainty that such a flaw cannot exist. > >> > > >> > Uh, what? There is nothing fuzzy about the proof. > >> > > >> > Suppose that a mapping of naturals to the subsets of naturals exists. > >> > Then consider the set of all naturals that are not member of the > >> > subset which they map to. > >> > > >> > The membership of each natural can be clearly established from the > >> > mapping, and it is clearly different from the membership of the > >> > mapping indicated by the natural. So the assumption of a complete > >> > mapping was invalid. > >> > > >> > > Yet that is just what pro-Cantorians appear to be asserting, with no > >> > > justification that I can see. > >> > > >> > Uh, where is there any room for doubt? What more justification do you > >> > need apart from a clear 7-line proof? It simply does not get better > >> > than that. > >> > > >> > > >> Is the above your 7-line proof? it makes no sense. > > > >It makes sense to those who have sufficient mental capacity to > >understand it. Those who either cannot or will not understand it, but > >cannot fault it, are irrelevant. > > I like Randall Holmes' sig on that subject: > "And God posted an angel with a flaming sword at the gates of Cantor's > paradise, that the slow-witted and the deliberately obtuse might not > glimpse the wonders therein." > > I like that sig, too!
From: sradhakr on 20 Jul 2005 02:28 george wrote: > david petry wrote: > > I'm in the process of writing an article about > > objections to Cantor's Theory, which I plan to contribute > > to the Wikipedia. I would be interested in having > > some intelligent feedback. > > Don't do it. > That's the most intelligent feedback you're going to get. > > > > While the pure mathematicians almost unanimously accept > > Cantor's Theory (with the exception of a small group of > > constructivists), there are lots of intelligent people who > > believe it to be an absurdity. > > No, there aren't. At least not that YOU know. > The class of people who have led you to this > opinion are uniformly idiots. > > > Typically, these people > > are non-experts in pure mathematics, > > Except for the one bragging about his "REFEREED,PUBLISHED > WORK" on NAFL or something. > [...] I say, George, old boy, you have made my day. Thanks for acknowledging that NAFL exists. Now can you take the next step and understand why I am objecting to Cantor, and in fact, classical/intuitionistic logics? In particular, take a look at math.LO/0506475 and let me know what you think. It is brief and reasonably well-written and self-contained. When I posted a long time ago to this NG, I was told that my work was not published (as though publication were a pre-requisite for discussion of new work in sci.logic). Now your complaint is that I am "bragging". Seems you can't win an argument with the Cantorians, who are in the same class as relativists when it comes to stone-walling. Regards, R. Srinivasan
From: Robert Low on 20 Jul 2005 02:46
Dave Rusin wrote: > Robert Low <mtx014(a)coventry.ac.uk> wrote: >>Tony Orlow (aeo6) wrote: >>>Stephen J. Herschkorn said: >>>>To those who insist there is a smallest positive real number? >>>000...000.000...001 >>And how many 0's are there after that decimal point? N? log_2(N)? N-1? >>N+1? (Whatever the hell any of those answers mean...) > Tsk, tsk, Robert, you've not been paying attention! There are N of > them; the "1" is in the N-th place, i.e. this decimal expansion is > simply of the number 10^(-N). I think I get it now. N is the biggest number, so if you divide 0.0...01 (N 0's) by 10, you actually get zero, not 0.00...01 (N+1 0's). Of course, the naive amongst us might object that this means that 10*0=0.0...01; this is just silly, because it's making the entirely unwarranted assumption that multiplication or real numbers is associative, and there's no reason for that to be true of the infinitely small ones. > Hmm, looks like I haven't been paying attention either... Well, I must be smarter than you, because I've figured it out :-) |