Sad observation: Cantor/Godel/Turing/Tarski
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From: Barb Knox on 25 Jun 2010 06:30 In article <6ed9b070-f9af-46cf-8974-a174cd455e39(a)z8g2000yqz.googlegroups.com>, Bill Taylor <w.taylor(a)math.canterbury.ac.nz> wrote: > On Jun 18, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > > > 1. Cantor's theorem about the uncountability of the reals. > > 2. Godel's incompleteness theorem. > > 3. Turing's theorem about the unsolvability of the halting problem. > > 4. Tarski's theorem about the undefinability of truth. > > What puzzles me, is why these topics have become > so popular with the intransigent crackpot minority. [SNIP] > And that leaves (1). I cannot for the life of me understand why > this is such a bugbear. In the case of our currently-most-prolific anti-Cantorian, he seems convinced that nothing is bigger than infinity, because that's what "infinity" MEANS. He is so convinced of this that he *knows* that anything which contradicts it (like |2^s| > |s| for infinite sets 's') simply must be wrong, and those who promulgate this wrong are some combination of ignorant, stupid, and/or evil. Note that he couches all his arguments in English rather than in precise mathematical terms, thus it is easy for him to get stuck on imprecise informal meanings of terms like "infinity". IF he would learn some mathematics then he might be cured of this, but short of that I see no prospect of a cure. > Or rather, maybe I can, and maybe > it has something to do with the godlike sound of "uncountable". > It would perhaps have been better if the word "countable" > had early on been replaced by "listable", which is maybe > more accurate. Then the idea that there are unlistable sets > of reals would not be so anathematical! And Cantor's theorem, > that for any given list of reals, one may define a real not on > the list, (i.e. "all the reals" are unlistable), > would not seem so dire. > _ _ _ _ _ > > Oh well, just rambling out loud. Perhaps I'm completely misguided > in my attempted analysis of the crackpot mindset... > > -- Wandering WiIly > > ** I'm a little crackpot short and stout. > ** Don't ask my handle, let me spout. > ** When I get all steamed up then I shout, > ** Snip a poster - flame the lout. Non-Cantorian's Song I am the very model of a modern non-Cantorian, With insights mathematical as good as any saurian. I rattle the Establishment's foundations with prodigious ease, And supplement 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 .... -- --------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum videtur. | BBB aa a r bbb | -----------------------------
From: Daryl McCullough on 25 Jun 2010 11:39 Barb Knox says... >Non-Cantorian's Song > >I am the very model of a modern non-Cantorian, >With insights mathematical as good as any saurian. >I rattle the Establishment's foundations with prodigious ease, >And supplement 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 .... If I ever write an operetta based on sci.logic, I'll definitely include that song. With proper royalties to you, of course. -- Daryl McCullough Ithaca, NY
From: MoeBlee on 25 Jun 2010 12:51 > Barb Knox says... > > >Non-Cantorian's Song > > >I am the very model of a modern non-Cantorian, > >With insights mathematical as good as any saurian. > >I rattle the Establishment's foundations with prodigious ease, > >And supplement 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 .... aspirate? pontificate? luxuriate? (No seriously, I get it ... "to master rate", right? No, wait, "to muster bait"!) MoeBlee
From: Owen Jacobson on 25 Jun 2010 23:17 On 2010-06-25 02:40:57 -0400, Bill Taylor said: > On Jun 18, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > >> 1. Cantor's theorem about the uncountability of the reals. >> 2. Godel's incompleteness theorem. >> 3. Turing's theorem about the unsolvability of the halting problem. >> 4. Tarski's theorem about the undefinability of truth. > > What puzzles me, is why these topics have become > so popular with the intransigent crackpot minority. <snip rather cogent analysis> > Oh well, just rambling out loud. Perhaps I'm completely misguided > in my attempted analysis of the crackpot mindset... If you haven't yet, you should read "An Editor Recalls Some Hopeless Papers" -- it catalogues one professor's experiences with counterarguments specifically to Cantor's diagonalization proof, breaking them down into a few recurring categories. It's a neat read. The original version is at <http://www.math.ucla.edu/~asl/bsl/0401/0401-001.ps>; HTML and PDF versions can be found via google if you can't read postscript. -o
From: Charlie-Boo on 26 Jun 2010 12:51
On Jun 15, 5:16 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > I'm not going to name any names, but I recently found that I was > arguing the same arguments, in the same way, with the same people, > as I argued 4 or 5 years ago. Clearly, this is a pointless endeavor. Maybe if you had something new or original to talk about you could try something different. Remember the definition of insanity? "Doing the same thing over and over and expecting a different result." This reminds me of Gregory Chaitin, who has written dozens of books and articles with the same ramblings about (1) using a different paradox than the Liar produces better results than Godel, and (2) how talking about the general probability that a TM will halt produces better results than Turing. The fact that (1) Godel's results were already improved upon by Rosser (whom Chaitin never mentions) and so it is meaningless to compare results to Godel's instead of Rosser's, and (2) the probability that a TM will halt as a function of its range of inputs does not always converge, so there is no "probability of halting" in general, doesn't seem to bother him. C-B > So I have kill-filed the people and the argument threads. This isn't > because of any hostility towards those people, nor because of disgust > with the topics, but just as a self-discipline measure to try to keep > myself from staying in the same rut forever. I don't want to be > like Sisyphus forever pushing a boulder up a hill, only to have it > roll back down again. > > -- > Daryl McCullough > Ithaca, NY |