Path: ...!news.misty.com!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: Thu, 31 Oct 2024 19:08:53 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <68ff7a758c839f30a941ba4cdb6167ae231b01f6@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: Thu, 31 Oct 2024 23:08:53 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="366200"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 In-Reply-To: Bytes: 4472 Lines: 57 On 10/31/24 10:18 AM, olcott wrote: > On 10/31/2024 8:58 AM, joes wrote: >> Am Thu, 31 Oct 2024 07:19:18 -0500 schrieb olcott: >>> 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. How one can convert a proof about >>> arithmetic into a proof about provability seems to be flatly false. > >> The key is selfreference. There is a number that encodes the sentence >> "the sentence with the number [the number that this sentence encodes to] >> is not provable". >> > > Can you please hit return before you reply? > Your reply is always buried too close to what you are replying to. > > We simply reject pathological self-reference lie > ZFC did and the issue ends. But that isn't "just" what Z-F did. (note ZFC isn't a person, so it doesn't actively DO anything). > >>>>> It might be the case that one number fills 100 books of 1000 pages >>>>> each. >>>> You fill find out when you evaluate the expressions. If you use Gödel's >>>> original numbering you will need larger numbers than strictly >>>> necessary. If you first encode symbols with a finite set of characters >>>> you can encode everything with finite set of characters. >>> A book a trillion light years deep? >> Is finite. >> >>>> Then you can encode those character strings as integers. The number of >>>> digits can be determined from the length of the character strings. >>>> Besides, computations are much faster than with Gödel's powers of >>>> primes. > >