Sad observation: Cantor/Godel/Turing/Tarski
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From: Charlie-Boo on 26 Jun 2010 13:07 On Jun 16, 9:03 pm, George Greene <gree...(a)email.unc.edu> wrote: > On Jun 15, 11:24 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > stevendaryl3...(a)yahoo.com (Daryl McCullough) writes: > > > 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. > > > Clearly. But what's so sad about this? > > I'll tell you what's so sad about it: Ignorance KILLS. No, ignorance is bliss. Why is there a fine line between genius and insanity? Because the smart people know the truth - how wrong people are (to talk of what other people are thinking or predicting the future or drawing conclusions without evidence) and how much better things can be if people dropped their pride and prejudices. In any discussion here you will see people use the fact that something was published, or that the person saying it is famous, as evidence of its being true. Every opinion is based on personal preferences regarding the source rather than the content of an idea. This inability to make objective decisions is the definiton of schizophrenia. C-B > Having more people learn more truths > is absolutely necessary to more people achieving their human > potential.
From: Charlie-Boo on 26 Jun 2010 13:15 On Jun 20, 2:11 am, Bill Taylor <w.tay...(a)math.canterbury.ac.nz> 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. > > 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? All of these are simple applications of self-reference to some domain. E.g. (4): If truth were definable in logic, then there would be a sentence that expresses "This is not true." which violates the premise that every sentence is true or false. C-B > -- Befuddled Bill
From: Charlie-Boo on 26 Jun 2010 13:20 On Jun 21, 1:31 am, Bill Taylor <w.tay...(a)math.canterbury.ac.nz> wrote: > 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. Why does someone do something? Because they enjoy the results. Even a failed attempt is better than the inability to try. To try to draw an asymmetry between the person who makes the same arguments repeatedly and the person who gives them the same response repeatedly is pointless. C-B > 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?
From: Barb Knox on 26 Jun 2010 20:22 In article <abbac23c-415d-440c-9498-e914281f4fc4(a)w12g2000yqj.googlegroups.com>, Charlie-Boo <shymathguy(a)gmail.com> wrote: > On Jun 16, 9:03�pm, George Greene <gree...(a)email.unc.edu> wrote: > > On Jun 15, 11:24�pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > > > > stevendaryl3...(a)yahoo.com (Daryl McCullough) writes: > > > > 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. > > > > > Clearly. But what's so sad about this? > > > > I'll tell you what's so sad about it: Ignorance KILLS. > > No, ignorance is bliss. > Why is there a fine line between genius and insanity? It's not symmetric. Most geniuses are arguably borderline crazy, but it is not the case that most crazy people are borderline geniuses. For a local example, consider our currently-most-prolific anti-Cantorian. > Because the smart people know the truth - how wrong people > are (to talk of what other people are thinking or predicting the > future or drawing conclusions without evidence) and how much better > things can be if people dropped their pride and prejudices. > > In any discussion here you will see people use the fact that something > was published, or that the person saying it is famous, as evidence of > its being true. But in addition to all the noise you will also see people discussing PROOFs. You know, actual mathematics. It's a big problem that so many people here have so little appreciation for the value of mathematical argument (versus informal English-language argument). > Every opinion is based on personal preferences > regarding the source rather than the content of an idea. EVERY opinion? See above about proofs. > This inability to make objective decisions is the definiton of > schizophrenia. Not according to DSM. Oh dear, there I go citing an "authority" <slap hand>. > > Having more people learn more truths > > is absolutely necessary to more people achieving their human > > potential. -- --------------------------- | 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: Bill Taylor on 28 Jun 2010 01:39
On Jun 25, 10:30 pm, Barb Knox <s...(a)sig.below> wrote: > 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 .... VERY GOOD INDEED! And, unlike almost all modern spoofy ditties, it *actually scans*!! Most people have great problems with this matter. Barb - you are definitely on my hero(ine) list! -- Beaming Bill ** Haiku's inventor ** Must have had seven fingers ** On his middle hand. Starting at zero, Accumulate where needed: Ordinal heaven! |