THE INCOMPLETENESS FILE: Digest of reports!

MONDAY, SEPTEMBER 24, 2018

New chapter starts tomorrow:
What did Godel demonstrate in his "incompleteness theorems?" Are these theorems useful, important, insightful, even coherent?

Can general readers hope to know the answers to such questions? Below, you see links to last week's reports from the incompleteness file:
Tuesday, September 18: Incompleteness meets incoherence! A lucid writer intones.

Wednesday, September 19: What the Sam Hill is a "logical system?" No general reader will know!

Thursday, September 20: What the heck is a "formal system?" Once again, Joe Average won't know!

Friday, September 21: Do Godel's theorems even make snese? Flying spaghetti monsters!
Tomorrow, we start our award-winning "guardians file." To review reports from all previous files, use links provided below:
Monday, September 10: Digest of reports: The Godel file.

Monday, September 17: Digest of reports: The Platonist file.

Monday, September 24: Digest of reports: The incompleteness file.

18 comments:

  1. I am reposting a comment here, because it's relevant to this post.

    RE: Godel - I just received an e-mail from Quora, relevant to a prior thread

    Are there any applications of Gödel's incompleteness theorems to other fields (other than in mathematics)? What are they?
    Michael Hochster
    Michael Hochster, Statistician
    Answered Sep 29, 2010
    Purported applications of Gödel's theorem outside of mathematics are just about always bunk. There is a wonderful book on this topic by Torkel Franzén called Godel's Theorem: An Incomplete Guide to Its Use and Abuse. Amazon link:
    http://www.amazon.com/Godels-The...
    Only part of the book is devoted to debunking; the book also contains lucid explanations of the first and second incompleteness theorems from several different angles.

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    1. A "wonderful" book...it is probably full of "lucid prose" that makes Gödel's theorems "accessible to the general reader". I bet it even has a number of ecstatic positive reviews to sell it.

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  2. Mozart's great G minor symphony went over well the other day. How about his little G minor symphony?

    https://www.youtube.com/watch?v=rNeirjA65Dk

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  3. The question of whether Rebecca Goldstein has succeeded in making Gödel's theorems accessible to the general reader, as is stated on the cover of her 2006 book, is completely different than the question of whether Gödel himself is "coherent", and whether she successfully explains why Gödel is important is different from determining whether Gödel was actually important.

    Somerby the "media critic" seems to be asking both sets of questions. But judging Goldstein's accomplishments is a vastly different question than judging Gödel's accomplishments. And Gödel was not a member of the "media", so his work has to be judged on different terms. And he can't be judged adequately by someone who has no background in mathematics.

    If you want to have a discussion about the difficulty that advanced science or math has in making itself understandable to the general reader, that is another discussion, worthwhile, perhaps. But the complexity of Einstein's or Gödel's achievements and the difficulty of expressing them in simple terms do not by themselves render those achievements incoherent.

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    1. You can't successfully explain and make accessible incoherent, unimportant theorems dumbass.

      Delete
    2. 5:25 said:
      "You can't successfully explain and make accessible incoherent, unimportant theorems "

      This can mean:
      1. Gödel's theorems are incoherent and unimportant, thus they can't be explained or made accessible. Why bother posting about them then?
      2. Gödel's theorems are coherent and important, else the attempt to explain them and make them accessible is doomed to be unsuccessful. So why in this case does Somerby bother to wonder if they are important or coherent?

      Regarding the logic behind 5:25's assertion:
      A theorem that is unimportant can certainly be successfully explained. "Importance" has no bearing on the ability to explain.

      A theorem that is incoherent can be successfully explained as well. The resulting explanation will not yield more coherence than the original theorem possesses. However, an incoherent explanation does not affect the coherence of a coherent theorem; it merely reflects the incoherence of the explicator.

      Are you of the opinion, 5:25, that the importance and coherence of Gödel's theorems is a given, based on Somerby's posts about them?

      Delete
    3. There is no success in an incoherent explanation of an incoherent theorem cuntrag and I guess you could make unimportant theorems accessible to general readers if you really wanted to and were as fucking dumb as you are. Go for it.

      Somerby's posts about Gödel's theorems frame them as unimportant and incoherent. Why I think they are important and coherent based on what he wrote, idiot whore? What the fuck's the matter with you?


      Delete
    4. Yes, he does seem to be framing Gödel's theorems as incoherent and unimportant, but he has gotten schooled on that recently from commenters who know something about mathematics, and his defenders rush to point out that Somerby is just a media critic, and is merely criticizing Goldstein's book and other "made easy" type publications.

      But, if you are correct, on what does Somerby base his assessment of Gödel's theorems as unimportant and incoherent? Somerby is a media critic and not a mathematician. How did he arrive at this conclusion? Accusing Goldstein of failing to explain Gödel is one thing. But accusing Gödel of incoherence...let's just say that that is a fool's errand. It betrays a profound ignorance and arrogance.

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    5. "He does seem to be framing Gödel's theorems as incoherent and unimportant, but he has gotten schooled on that recently from commenters who know something about mathematics, and his defenders rush to point out that Somerby is just a media critic"

      Who gives a shit?

      "But accusing Gödel of incoherence...let's just say that that is a fool's errand. It betrays a profound ignorance and arrogance."

      Great.

      "On what does Somerby base his assessment of Gödel's theorems as unimportant and incoherent?"

      Umnn .. despite the genius anonymous commenters that know something of mathematics, he based it on a known mathematician who said, “most pure mathematicians go through life with only a vague acquaintance his work.” and called the theorems “inconsequential” and “unnecessary”.

      Can't you fucking read? What the fuck is the matter with you?

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    6. 6:48

      You’re absolutely correct, I’m one of the early defenders of Bob as just a media critic, but it became plain that he has larger fish to fry in this series of essays. So far, it’s not that he can’t explain himself in that regard, it’s that he hasn’t. So we have to wait for the next installments, which is cool with me. One of the things Somerby wonders about is the theorems’ social value. In that sense, he’s honing in on something. Guess we’ll have to wait and see what he’s really on about.

      And you’ve been a paragon of restraint in communicating with whatever that pos 6:33 is. I’ve done my share of cussing in these comments, but damn. Such ugly invective is truly disturbing, and has no place anywhere, anytime, for any reason. For that reason, I perhaps need to rethink my own approach. The commenters I appreciate the most never resort to foul language.

      Well, maybe we can ignore it away. It’s the only thing that might work in a forum like this.

      Leroy

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  4. If Somerby had addressed the practical value of Godel's work, he'd be on sounder grounds. Mathematics tends to move to greater abstractness. The natural numbers are useful for counting and a great many other things. The Peano Postulates allow one to develop the natural number axiomatically, just as Euclids' axioms did for geometry. Number theory produces results farther from significant reality, such as Fermat. Does it matter whther or not a^n +b^n = c^n has solutions for n > 2? Then Godel's takes a step toward greater abstraction and less obvious value. Why does it matter whether or not every true number theory statement can be proved? We don't have time to prove them all, anyhow.

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  5. the Stanford Encyclopedia of Philosophy entry on the incompleteness theorems, in case anyone cares... https://plato.stanford.edu/entries/goedel-incompleteness/

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  6. https://www.salon.com/2018/09/17/heres-why-the-allegation-against-kavanaugh-is-credible-hes-smeared-and-attacked-women-before/

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    1. That's all well and fine, but it's not going to sway big government Conservatives (are there any other kind?) from keeping big government Brett Kavanaugh off the Supreme Court.

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