New Anti-Cantor Attack
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From: Jim Burns on 1 Jun 2010 22:01 |-|ercules wrote: > "Jim Burns" <burns.87(a)osu.edu> wrote >> Bart Goddard wrote: >>> Jim Burns <burns.87(a)osu.edu> wrote in >>> news:hu3n56$jvj$1(a)charm.magnus.acs.ohio-state.edu: >>> >>>> I call drawing the conclusion the end of >>>> an argument. I do not know you, Bart Goddard, >>>> but I suspect that you would be insulted >>>> if I claimed that you claimed that Herc's >>>> mathematical arguments were nonsense /because/ >>>> Herc is crazy, not because of some mathemmatical >>>> fault. >>> >>> No, that's exactly what I'm claiming. An insane >>> argument exists, and the cause of its existence is >>> an insane arguer. [...] >> Perhaps you will surprise me, but I strongly >> suspect that you would judge Herc's arguments >> to be invalid even if I had asserted them, >> or David Ullrich had, or Arturo Magidin had >> than if Herc had asserted them. >> >> It seems like common sense, too obvious to >> need mentioning, to say that changing whose >> mouth an argument comes out of does not change >> the quality of the argument -- but that is, >> really, what I am trying to say here. [...] > maybe you should stop being such an obvious > hypocrite and talk about the argument > and stop attacking the person. Am I being a hypocrite by not addressing your argument? I don't think so: I haven't said one word about whether your arguments are good, bad, crazy, sane, or anything else, although I have quoted others. I stopped addressing your arguments, Herc, some years ago, when you flipped out so badly that I became afraid that you might hurt yourself or someone else. I would have enjoyed arguing with you some more about Cantor's diagonal theorem, but I did not want to cause anything like that. I haven't really paid much attention to your mathematical arguments since then. If I did express an opinion about any of your current arguments, then I shouldn't have. It would have been poorly informed. It's possible (I don't remember) that I expressed an opinion about those arguments of years ago, and it sounded like I was referring to today's arguments. If I did, I'm sorry; I did not mean to. > Here is the latest post in the argument so far... I have read the rest of this post now. I have an opinion about the argument you present, and whether you have been taking your pills lately or not is irrelevant to that opinion. In my own opinion, I would rather I and my arguments were called "crazy" than called what my opinion is about them. Anyway, I am not going to share my opinion with you. So, Herc, are you still being prescribed drugs to stop the voices? And are you taking those drugs? (I'm deleting your argument below. I understand how that could be seen as a way of saying it is worthless. I don't mean that, though. Remember that I am perfectly willing to tell you something is worthless, if I think so. I just don't want to talk about it.) Jim Burns
From: Tim Little on 2 Jun 2010 02:01 On 2010-05-30, Charlie-Boo <shymathguy(a)gmail.com> wrote: > The more stupider it is, the easier it is to refute On the contrary, the "more stupider" it is, the harder it is to refute. Greater levels of stupidity are much more immediately apparent to most people. If there are people who don't see what makes it stupid, they are very likely either stupid themselves or not at all familiar with the subject in question. It is difficult to explain anything at all about the subject in either case. A formal mathematical derivation of |N|=|2^N| containing an error is very easy to refute: just point out the error. A reasonable person familiar with the subject will recognise that it is in fact an error: end of discussion. A vague argument based on quoting that Cantor's proof says "Therefore no matter how big P(N) is there is always a new element that can be listed and therefore the size of the set P(N) is bigger than infinity" is *precisely* an example of "an incorrect proof that looks the same to the mathematically incompetent", as Daryl stated. The stupidity of presenting it as a "New Anti-Cantor Attack" is immediately evident to any reasonable and competent person who has even a passing familiarity with what constitutes mathematical proof. So those to whom it is not immediately evident are either unreasonable, incompetent, or totally unfamiliar with the subject. In none of these cases will it be easy to refute to that person's satisfaction. And so this thread will probably run for months and accrue hundreds or thousands of posts. - Tim
From: Marshall on 2 Jun 2010 02:16 On Jun 1, 12:39 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Transfer Principle <lwal...(a)lausd.net> writes: > > And even though Herc/Cooper turned out to be not worth defending in > > the end, that still doesn't mean that I'm going to start defending > > Spight. > > Out of idle curiosity, how would you go about "defending" Marshall? What?! Haven you never seen "Walker, Texas Ranger?" The obvious answer is "roundhouse kick." Marshall
From: David Bernier on 2 Jun 2010 06:07 Tim Little wrote: > On 2010-05-30, Charlie-Boo<shymathguy(a)gmail.com> wrote: >> The more stupider it is, the easier it is to refute > > On the contrary, the "more stupider" it is, the harder it is to > refute. Greater levels of stupidity are much more immediately > apparent to most people. If there are people who don't see what makes > it stupid, they are very likely either stupid themselves or not at all > familiar with the subject in question. It is difficult to explain > anything at all about the subject in either case. > > A formal mathematical derivation of |N|=|2^N| containing an error is > very easy to refute: just point out the error. A reasonable person > familiar with the subject will recognise that it is in fact an error: > end of discussion. > > A vague argument based on quoting that Cantor's proof says "Therefore > no matter how big P(N) is there is always a new element that can be > listed and therefore the size of the set P(N) is bigger than infinity" > is *precisely* an example of "an incorrect proof that looks the same > to the mathematically incompetent", as Daryl stated. > > The stupidity of presenting it as a "New Anti-Cantor Attack" is > immediately evident to any reasonable and competent person who has > even a passing familiarity with what constitutes mathematical proof. > So those to whom it is not immediately evident are either > unreasonable, incompetent, or totally unfamiliar with the subject. In > none of these cases will it be easy to refute to that person's > satisfaction. And so this thread will probably run for months and > accrue hundreds or thousands of posts. [...] Following the discovery of Russell's Paradox, there was a move by Poincare and Weyl towards predicative definitions/constructions. I was reading an article by Feferman: < math.stanford.edu/~feferman/papers/DasKontinuum.pdf > about (mainly) Weyl's _Das_Kontinuum_ (1918). Quoting Feferman on Poincare: "As we saw, Poincare argued that such apparent definitions are improper: an object is to be defined or determined only in terms of prior objects, notions and totalities; only those are predicative." [page 7] Feferman also discusses ACA_0, a theory having to do with arithmetic-sentence based analysis or something like that. It's "nice" to think one can/could introduce every non-primitive object based on combining functions and objects defined previously, starting from N. I've been wondering what Poincare thought of Cantor's diagonal argument. FWIW, once one is used to not bothering about impredicative definitions or constructions (I include myself), it's not so easy telling apart the predicative from the impredicative. David Bernier
From: Transfer Principle on 2 Jun 2010 16:41
On Jun 1, 3:50 pm, Jim Burns <burns...(a)osu.edu> wrote: > Bart Goddard wrote: > > No, that's exactly what I'm claiming. An insane > > argument exists, and the cause of its existence is > > an insane arguer. > The background for my point is someone else > asserting that people who have been labeled > cranks have a harder time getting people to > agree with them -- /because/ they have been > labeled cranks. My position is that it is not > that these people are wrong because they are > cranks; it is that they are cranks because > they are wrong. And of course, I am the poster to whom Burns is referring here. I indeed asserted that if two people posted identical arguments, one under the name of a well-known "crank" and one under that of a newbie, the "crank" would have a harder time getting people to agree with them. > I should also point out that this is not a > universal belief about arguments. Certainly, > it is not true in politics. That sorry excuse > for a debate about (United States) health > care reform saw senators furiously denouncing > Democrats for the same proposals that they > had applauded when they had come out of > Republican mouths. I'm glad that Burns mentioned politics here, since there is another well-known political "argument" that someone used just yesterday right here on sci.math! Yesterday, a poster named Bergman tried to argue that N is isomorphic to C. Then the poster Gerry Myerson questioned the OP's defintion of "is." Then Ostap Bender pointed out the similarity between Myerson's questioning the definition of "is" and former President Clinton's definition of that same two-letter word just over a decade ago. The point I'm trying to make is that plenty of people use the word "is" all the time, but does Myerson ask them to define that word? No, but he asks Bergman to define that word, just because of his low reputation as someone who believes in an isomorphism between the sets N and C. Apparently to Myerson, only those who contradict Cantor have to define their two-letter words, not those who agree with Cantor. So far I can't tell whether Goddard, like Myerson, would treat posters differently based solely on their reputation (including Clintonian hairsplitting against such posters), but Goddard might be leaning somewhat in that direction. Then again, I know that Goddard is one of the foremost advocates of a moderated sci.math group. So if a person like Bergman were to post, Goddard wouldn't need to ask him to define "is" -- all he'd have to do is block the poster. |