Path: csiph.com!eternal-september.org!feeder.eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail From: =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?= Newsgroups: comp.theory,comp.ai.philosophy,comp.ai.nat-lang,sci.lang.semantics Subject: =?UTF-8?Q?Re=3a_Simply_defining_G=c3=b6del_Incompleteness_and_Tarsk?= =?UTF-8?Q?i_Undefinability_away_V24_=28Are_we_there_yet=3f=29?= Date: Fri, 17 Jul 2020 17:09:24 -0600 Organization: Christians and Atheists United Against Creeping Agnosticism Lines: 83 Message-ID: References: <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> <87a7001bhr.fsf@nosuchdomain.example.com> <87sgdrz49w.fsf@nosuchdomain.example.com> <8uCdnfwjFfAZvY_CnZ2dnUU7-TXNnZ2d@giganews.com> Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 17 Jul 2020 23:09:26 -0000 (UTC) Injection-Info: reader02.eternal-september.org; posting-host="49455606e6f93aeaf5db474afb03adb2"; logging-data="16571"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/HhmmjrSaAuOABqbTHLK+p" User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.14; rv:68.0) Gecko/20100101 Thunderbird/68.10.0 Cancel-Lock: sha1:qy7qb3bwxWsQUQ5nak7D8l3oebQ= In-Reply-To: <8uCdnfwjFfAZvY_CnZ2dnUU7-TXNnZ2d@giganews.com> Content-Language: en-US Xref: csiph.com comp.theory:21756 comp.ai.philosophy:22096 comp.ai.nat-lang:2465 On 2020-07-17 16:04, olcott wrote: > On 7/17/2020 6:16 AM, Alan Smaill wrote: >> olcott writes: >> >>> On 7/16/2020 1:46 PM, Keith Thompson wrote: >>>> olcott writes: >>>>> On 7/15/2020 8:42 PM, Keith Thompson wrote: >>>>>> 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. >>>>> >>>>> 125 different people that all believe that Gödel showed that true and >>>>> unprovable formulas exists, and 125 > 0, thus "nobody believes you" is >>>>> proven to be false. >>>> >>>> Wait, what?  Is that really what you meant to say?  Gödel *did* show >>>> that true and unprovable formulas exist.  Did you omit a "not"? >>> >>> OK that is even better. I thought that he only concluded that some >>> formulas are neither provable nor disprovable. >> >> The conclusion of his original proof (as opposed to comments elsewhere) >> is that in the system he looked at, a particular arithmetical statement >> is neither provable nor refutable (ie its negation is not >> provable). >> >> You are disputing that claim, of course, even though it does not >> refer to truth, but only to provability in a given formal system. >> > > Apparently 126 references on Google Scholar seem to think that he proved > more than that: That would be compared to the 19,800 results one gets when searching for Gödel's Incompleteness Theorem or less than 1% of all results. Are these numbers meaningful? Not really, since things found through Google Scholar are hardly a representative sampling of work in this area. If you want an actual answer to the question what did Gödel prove, the obvious way to get this would be to simply read Gödel's paper. Gödel's paper does not include the word "truth" period. If you want to understand the position of those 126 references or other interpretations of Gödel which does make use of 'truth', you simply need to consider the law of the excluded middle. Given some formula φ, either φ must be true or ¬φ must be true. Since Gödel showed that, in the type of system he was concerned with, there must always exists formulas φ such that neither φ nor ¬φ are derivable as theorems, that entails that, if we were to consider the semantics of the system (i.e. to introduce the notion of 'truth'), then there would be true propositions which are not provable. But Gödel was concerned with formal proofs, not with truth, so he does not mention this. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.