Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: Keith Thompson Newsgroups: comp.theory,comp.ai.philosophy,comp.ai.nat-lang,sci.lang.semantics Subject: Re: Simply defining =?utf-8?Q?G=C3=B6del?= Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Date: Wed, 15 Jul 2020 18:42:40 -0700 Organization: None to speak of Lines: 119 Message-ID: <87a7001bhr.fsf@nosuchdomain.example.com> References: <2tCdnb0urbddzpfCnZ2dnUU7-b_NnZ2d@giganews.com> <87k0z85tt0.fsf@nosuchdomain.example.com> <87d0505kmk.fsf@nosuchdomain.example.com> <5Lmdnehh4P6hLZbCnZ2dnUU7-LdQAAAA@giganews.com> <878sfo5elp.fsf@nosuchdomain.example.com> <87zh820x98.fsf@nosuchdomain.example.com> <87imeo1wov.fsf@nosuchdomain.example.com> Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit Injection-Info: reader02.eternal-september.org; posting-host="02ec520d1b2b3210c7ee6ae74092840a"; logging-data="6855"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19eXs2iYeBq9nJ1Tihec4iC" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux) Cancel-Lock: sha1:29InulH8lVfIVZ9ebdoFirsUcsM= sha1:5bief86bOq7nTiTtlvGlFPnK2Ic= Xref: csiph.com comp.theory:21694 comp.ai.philosophy:22043 comp.ai.nat-lang:2423 olcott writes: > On 7/15/2020 1:04 PM, Keith Thompson wrote: >> olcott writes: >>> On 7/14/2020 1:25 PM, Keith Thompson wrote: >>>> olcott writes: >>>> [...] >>>>> Since everyone here is indoctrinated into believing that Gödel is >>>>> correct I have to use different terms for provability so that people >>>>> will carefully analyze my reasoning and not simply dismiss it >>>>> out-of-hand on the basis of their indoctrination. >>>> >>>> It seems to me that the best way to demonstrate that Gödel is >>>> incorrect would be to demonstrate a flaw in what he actually wrote. >>>> I haven't read everything you've written here, but I don't recall >>>> you ever directly quoting Gödel's proof. >>> >>> Not really. When we refute the enormously simplified key result of his >>> claim: true and unprovable can possibly coexist, then the steps that >>> he used to get to this key result are moot. >> >> You've been asserting that for years, and nobody believes you > https://scholar.google.com/scholar?hl=en&as_sdt=0%2C28&q=%22true+and+unprovable%22+godel&btnG=&oq=%22true+and+unprovable%22 125 results. No, I'm not going to read them. >> Do you think that's going to change if you assert it just one >> more time? What is your goal here? >> >> Whether it's the best way or not, surely *a* way to demonstrate >> that Gödel is incorrect would be to demonstrate a flaw in what he >> actually wrote. Not in some summary of his proof, but in his actual >> proof as he wrote it. Something like "In step 42, Gödel makes use >> of this assumption, but previously in step 23 he showed that that >> assumption does not hold in all cases". (That's a hypothetical >> example, of course.) > > His mistake can only be seen through a refutation of the essence of > his conclusion. Ah, now that's an interesting assertion. Did you really mean "only"? So are you saying that you *cannot* demonstrate that Gödel proof is incorrect by citing a specific error within the proof. It seems to me that that's equivalent to saying that Gödel's proof is correct. I'm sure that's not what you meant. Did you mean specifically that *you* cannot do that? I doubt that that's what you meant either. Are you saying that it's possible for every step of Gödel's proof to be valid, but for the proof as a whole to be invalid, yielding a false conclusion? If so, that's a remarkable assertion from someone who says that a complex system can be complete and consistent. Do you believe there is a specific flaw in Gödel's proof? (This question is not about what that flaw is, just whether you think there is one.) > There is his own conclusion: > > The first incompleteness theorem states that in any consistent formal > system F within which a certain amount of arithmetic can be carried > out, there are statements of the language of F which can neither be > proved nor disproved in F. > > and there are many scholars that interpret what this means: > https://scholar.google.com/scholar?hl=en&as_sdt=0%2C28&q=%22true+and+unprovable%22+godel&btnG=&oq=%22true+and+unprovable%22 > > It is far simpler to refute the scholars interpretation because it can > be shown that true and unprovable cannot coexist and people have a > rational understanding of the terms "true" and provable > > On the other hand apparently if "incomplete" was defined as: > "painted my pickup truck green" most math people would agree that a > formal system is "incomplete" if someone just painted their pickup > truck green because that is the way it has been defined. > >> Are you able to cite a specific flaw in Gödel's proof? If you're >> actually able to do that, I think people would pay attention. >> If you're not able to do that, it just might imply that you're >> wrong about all this. > > If a complex proof have an enormously complex proof with a large > number of steps concludes that 3 > 7 do we need find exactly which > detail of the proof went astray? Once again, I asked you a yes or no question, and your response did not included the word "yes" or "no". Are you able to cite a specific flaw in Gödel's proof? Obviously you've decided that the best way for you to refute Gödel's proof is to refute "the essence of his conclusion". But you know by now that that doesn't convince the other participants in this discussion. If a mathematician published a complex proof that 3 > 7, I personally probably wouldn't bother to find a flaw in it -- but surely it would be possible to find such a flaw. If such a proof had been published nearly a century ago and generally accepted by the mathematics community, the first person to demonstrate a flaw would be famous. If your goal is to repeatedly make the same claims and not convince anyone, keep doing what you're doing. If your goal is to demonstrate to the satisfaction of experts in mathematical logic that Gödel was wrong, I suggest that finding a specific flaw in Gödel's proof is the best way to do that. (To be honest, I don't expect that to be possible, because I think Gödel was right and you're wrong, but I have no rigorous proof of that other than Gödel's proof itself, which as I've said I don't claim to understand in full.) >>>> You seem to assert that provability and truth must be the same thing >>>> because of course they are, and how could anyone believe otherwise? >>>> >>>> I haven't read Gödel's proof myself, and likely wouldn't understand >>>> all of it, but there are plenty of people who have and would. >>>> >>>> [...] -- Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com Working, but not speaking, for Philips Healthcare void Void(void) { Void(); } /* The recursive call of the void */