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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit String pairs Date: Sun, 3 Nov 2024 13:19:55 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <1d3df3e5f92cc2dd7bf73d976f1d404c2f1bb755@i2pn2.org> References: <592109c757262c48aaca517a829ea1867913316b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 3 Nov 2024 18:19:55 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="786503"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Bytes: 6041 Lines: 113 On 11/3/24 8:15 AM, olcott wrote: > On 11/3/2024 3:16 AM, Mikko wrote: >> On 2024-11-02 11:09:06 +0000, olcott said: >> >>> On 11/2/2024 3:37 AM, Mikko wrote: >>>> On 2024-11-01 11:50:24 +0000, olcott said: >>>> >>>>> On 11/1/2024 3:44 AM, Mikko wrote: >>>>>> On 2024-10-31 12:19:18 +0000, olcott said: >>>>>> >>>>>>> On 10/31/2024 5:34 AM, Mikko wrote: >>>>>>>> On 2024-10-30 12:16:02 +0000, olcott said: >>>>>>>> >>>>>>>>> On 10/30/2024 5:02 AM, Mikko wrote: >>>>>>>>>> On 2024-10-27 14:21:25 +0000, olcott said: >>>>>>>>>> >>>>>>>>>>> On 10/27/2024 3:37 AM, Mikko wrote: >>>>>>>>>>>> On 2024-10-26 13:17:52 +0000, olcott said: >>>>>>>>>>>> >>>>>>>>>>>>> Just imagine c functions that have enough memory to compute >>>>>>>>>>>>> sums and products of ASCII strings of digits using the same >>>>>>>>>>>>> method that people do. >>>>>>>>>>>> >>>>>>>>>>>> Why just imagein? That is fairly easy to make. In some other >>>>>>>>>>>> lanugages >>>>>>>>>>>> (e.g. Python, Javascript) it is alread in the library or as >>>>>>>>>>>> a built-in >>>>>>>>>>>> feature. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> OK next I want to see the actual Godel numbers and the >>>>>>>>>>> arithmetic steps used to derive them. >>>>>>>>>> >>>>>>>>>> They can be found in any textbook of logic that discusses >>>>>>>>>> undecidability. >>>>>>>>>> If you need to ask about details tell us which book you are >>>>>>>>>> using. >>>>>>>>>> >>>>>>>>> >>>>>>>>> Every single digit of the entire natural numbers >>>>>>>>> not any symbolic name for such a number. >>>>>>>> >>>>>>>> Just evaluate the expressions shown in the books. >>>>>>> >>>>>>> To me they are all nonsense gibberish. >>>>>> >>>>>> The books define everything needed in order to understand the >>>>>> encoding >>>>>> rules. >>>>>> >>>>>> Encoding nonsense gibberish as a string of digits is trivial. >>>>>> >>>>>>> How one >>>>>>> can convert a proof about arithmetic into a >>>>>>> proof about provability seems to be flatly false. >>>>>> >>>>>> You needn't. The proof about provability is given in the books so >>>>>> you needn't any comversion. >>>>>> >>>>> >>>>> So you are saying that the Gödel sentence has nothing >>>>> to do with >>>>> >>>>> BEGIN:(Gödel 1931:39-41) >>>>>    ...We are therefore confronted with a proposition which >>>>>    asserts its own unprovability. >>>>> END:(Gödel 1931:39-41) >>>> >>>> Nothing is too strong but the connection is not arithmetic. >>>> That "asserts its own unprovability" refers to a non-arithmetic >>>> interpretation of an arithmetic formula. >>> >>> I want to know 100% concretely exactly what this means, >>> no hand waving allowed. >> >> It means whatever Gödel wanted it to mean. As the sentence is not >> a part of a proof the only clue we have is what Gödel said. >> > > In other words you don't really understand the proof. > You are merely trusting Gödel on faith. No, it shows that YOU don't undetstand Godels proof, and are just refuting a strawman. If you did, you would point out the specific error being made. > >>>>> Making arithmetic say anything about provability >>>>> seems like making an angel food cake out of lug nuts, >>>>> cannot possible be done. >>>> >>>> Numbers have features and formulas have features. Therefore it is >>>> possible to compare features of formulas to features of numbers. >>> >>> This seems to be a type mismatch error. I need to >>> see every tiny detail of how it is not. >> >> It is possible to compare things of different types. For example, >> chairs are not animals but we can compare the numbers of their legs. >> > > I am not convinced that Gödel proved that there > is any number that cannot be derived by arithmetic. > This seems inherently impossible. He must have > been confused. > That isn't what he said. He said he could construct a function that was effectively a proof checker, that could be used to show that there could not be a number to satisfy that function because such a number would prove that such a number doesn't exist.