Obections to Cantor's Theory (Wikipedia article)
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From: torkel on 19 Jul 2005 08:15 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. It's open to anybody to introduce any kind of rant into the Wikipedia. Go for it!
From: Han de Bruijn on 19 Jul 2005 08:23 Dave Seaman wrote: > You, on the other hand, have shown that you do not understand the > difference between numerical analysis and mere numerical methods. Hint: > the former includes error analysis. OK, then my expertise is in numerical methods only. Who cares ... On the other hand, I find that the vendors of those big Finite Element packages do call their products NA, not NM. So ... Han de Bruijn
From: Han de Bruijn on 19 Jul 2005 08:42 David Kastrup wrote: > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: >> Non-mathematical background ? Look at yourself ! You claim that you know >> something about Numerical Analysis, while it is quite clear from your >> postings that you don't even have a clue. > [ ... valid counter argument snipped ... ] Allright. Fair enough. I apologize for having responded too quickly, without knowing some facts. On the other hand, you must realize that such error analysis may become rather clueless with for example F.E. analysis in i.e. a Civil Engineering application. I don't want to say that your work has been relatively "easy", but it has been different from that "heavy" kind of number crunching. On the other hand, you shouldn't deny any mathematical background to everybody who disagrees with you on those Cantor issues. Han de Bruijn
From: Alec McKenzie on 19 Jul 2005 08:43 David C. Ullrich <ullrich(a)math.okstate.edu> wrote: > On Tue, 19 Jul 2005 09:34:45 +0100, Alec McKenzie > <mckenzie(a)despammed.com> wrote: > > > "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. Yet > >that is just what pro-Cantorians appear to be asserting, with no > >justification that I can see. > > I once had a person tell me the following, with a straight face: > > (*) "You can't say for sure there's no such thing as a square > circle! I mean just because they haven't found one yet doesn't > mean they won't discover one tomorrow." > > Please choose one of the following replies: > > (i) No, (*) is nonsense. If it's square then _by definition_ > it's not a circle. So they will _never_ find a square circle. > > (ii) Hmm, good point. > > You really should choose one of (i) or (ii), so people know > how to reply to your post. The point: If you say (ii) then > we know that there's no point worrying about anything you > say. Otoh if you say (i) then there's hope - you agree that > we're _certain_ they will never find a square circle, now > we just have to convince you that our assertions about > enumerations of subsets of N are just as certain, for > entirely similar (although slightly more complicated) > reasons. > > So which is it, (i) or (ii? It is (i), of course. But you seem to be suggesting that the proof in question is flawless for similar reasons to its being so _by definition_. That I cannot see. -- Alec McKenzie mckenzie(a)despammed.com
From: Alec McKenzie on 19 Jul 2005 09:15
David Kastrup <dak(a)gnu.org> wrote: > 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. I am not suggesting there is anything 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. I quite agree that it does not get better than that, but I think one must allow some room for doubt, however small, for any proof. Otherwise one is proclaiming infallibility. It has been known for a proof to be put forward, and fully accepted by the mathematical community, with a fatal flaw only spotted years later. -- Alec McKenzie mckenzie(a)despammed.com |