Sad observation: Cantor/Godel/Turing/Tarski
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From: Bill Taylor on 18 Jun 2010 01:18 On Jun 18, 5:16 pm, Bill Taylor <w.tay...(a)math.canterbury.ac.nz> wrote: WOOPS! I AM A COMPLETE BUFFOON!! > However, I would be interested to know, what are the main > (say 2 or 3) topics that you have had such difficulty with? I just noticed that the original title had these in it! Please forgive the boo-boo, and ignore both these posts! -- Blundering Bill (...ignore them in the appropriate order, OC!)
From: Daryl McCullough on 18 Jun 2010 06:43 Bill Taylor says... >Jun 16, 9:16 am, 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. > >You are very wise not to name names! > >However, I would be interested to know, what are the main >(say 2 or 3) topics that you have had such difficulty with? They are in the subject line. The intractable arguments are about: 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. I keep getting sucked into the chimeric belief that the "dissidents" can be convinced of their errors if only I gave the right argument. But it never happens. There is no argument that can make a dent in their opposition. -- Daryl McCullough Ithaca, NY
From: George Greene on 19 Jun 2010 17:09 On Jun 18, 6:43 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > The intractable arguments are > about: > > 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. #1 is way ahead right now, basically ever since WM showed up. We haven't had as much of a problem with incompleteness for the last 3 years except from Colin Leslie Dean; 1 person arguably doesn't count.
From: Bill Taylor on 20 Jun 2010 02:11 > > 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. Just enlighten me quickly and briefly, whoever is so disposed. But is (4) provable without recourse to (2)? Or is (2) a pretty-much-necessary precursor to (4)? Could (4) have successfully been proved in 1930, all other history being as is? -- Befuddled Bill
From: Bill Taylor on 21 Jun 2010 01:31
Let me set a record by answering my own post, TWICE in the same thread! [While I'm waiting for responses to my queries below.] > > > 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. > > Just enlighten me quickly and briefly, whoever is so disposed. > > But is (4) provable without recourse to (2)? > > Or is (2) a pretty-much-necessary precursor to (4)? > > Could (4) have successfully been proved in 1930, > all other history being as is? Getting back to Daryl's original plea, about Sisyphus and the hill. I have the greatest sympathy; and I am astonished that Daryl has been so public-minded as to try to continue enlightening people about these matters, in the face of so much obstinacy. Nevertheless, I wouldn't have thought the above 4 topics were quite on the same level. 1 & 2, I agree, have become the modern crackpot's playground. What angle trisection and parallel postulate used to be, those have become. There is no hope of ever enlightening anyone on such matters, who has failed once or twice, maybe thrice, to follow a suitable explanation. Number 3, OTOH, i would have thought was sufficiently technical to put off the amateur cranks and crackpots, and fail to generate enough sparks to supply any heat to the debate, such as it might be, on this topic. And number 4, indeed, I would have thought SO technical as to be beyond the comprehension, indeed even the vocabulary, of the typical crackpot. I would NOT expect to have to do a lot of explaining much less defending, of that one. Anyway, thanks for all your efforts Daryl; I will certainly continue to read your remaining posts with avidity! -- Beaming Bill ** Isn't it obvious that it is ridiculous to say something ** is obvious, to someone who does not find it obvious? |