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Groups > comp.theory > #135240
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Newsgroups | comp.theory |
| Subject | Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence |
| Date | 2025-11-07 10:21 +0200 |
| Organization | - |
| Message-ID | <10eka64$1ndvh$1@dont-email.me> (permalink) |
| References | (25 earlier) <10edf9g$3r2m1$1@dont-email.me> <10efa37$ashj$2@dont-email.me> <10efdqa$c4n4$1@dont-email.me> <10ehmsu$10gr3$1@dont-email.me> <10ehvj7$12r5g$1@dont-email.me> |
On 2025-11-06 11:08:22 +0000, olcott said: > On 11/6/2025 2:39 AM, Mikko wrote: >> On 2025-11-05 11:52:40 +0000, olcott said: >> >>> On 11/5/2025 4:49 AM, Mikko wrote: >>>> On 2025-11-04 18:05:34 +0000, olcott said: >>>> >>>>> On 11/4/2025 3:56 AM, Mikko wrote: >>>>>> On 2025-11-03 23:45:57 +0000, olcott said: >>>>>> >>>>>>> On 11/2/2025 6:45 AM, Mikko wrote: >>>>>>>> On 2025-11-01 13:54:09 +0000, olcott said: >>>>>>>> >>>>>>>>> On 11/1/2025 4:18 AM, Mikko wrote: >>>>>>>>>> On 2025-10-31 12:20:13 +0000, olcott said: >>>>>>>>>> >>>>>>>>>>> On 10/31/2025 6:15 AM, Mikko wrote: >>>>>>>>>>>> On 2025-10-30 13:03:23 +0000, olcott said: >>>>>>>>>>>> >>>>>>>>>>>>> On 10/30/2025 5:50 AM, Mikko wrote: >>>>>>>>>>>>>> On 2025-10-29 16:25:00 +0000, olcott said: >>>>>>>>>>>>>> >>>>>>>>>>>>>>> On 10/29/2025 5:45 AM, Mikko wrote: >>>>>>>>>>>>>>>> On 2025-10-28 15:12:29 +0000, olcott said: >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> On 10/28/2025 4:58 AM, Mikko wrote: >>>>>>>>>>>>>>>>>> On 2025-10-28 01:22:21 +0000, Richard Damon said: >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> On 10/27/25 5:45 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>> On 2025-10-26 17:57:16 +0000, Richard Damon said: >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> On 10/26/25 7:44 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>> On 2025-10-25 19:57:19 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>> On 10/25/2025 6:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-10-24 17:37:43 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>> On 10/24/2025 2:46 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-10-23 15:39:13 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/23/2025 5:02 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-10-22 12:39:31 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/22/2025 4:23 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-10-21 15:11:19 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/21/2025 4:31 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-10-20 16:24:46 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/20/2025 3:55 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-10-19 15:03:34 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/19/2025 3:44 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-10-18 10:58:15 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/18/2025 4:30 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That is not a sense of "proof". >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That is the correct way to do a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A way to do is not a sense. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The conventional way to do proofs concludes that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> within its rules if the Moon is made from green >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cheese and the Moon is not made from green cheese >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this proves that Donald Trump is the Lord and savior Jesus Christ. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Right, and the empirical falct that nobody has verified all of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1. the Moon is made from green cheese >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2. the Moon is not made from grenn cheese >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 3. Donald Trump is not the Lord and saviour Jesus Christ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> at the same time supports the idea that the conventiona wya to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do proofs is correct and trustworthy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we require that correct reasoning is only semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> logical entailment from basic facts the Principle of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Explosion ceases to exist. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Only if you exclude from "correct reasioning" some reasning that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> actually is correct. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is no counter-example that can possibly exist >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can show there are any gaps in the body of human >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that can be expressed in language that begins >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with a consistent set of basic facts and only applies >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic logical entailment to these facts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is no language that begins with a consistent set of basic facts >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and only applies semantic logical entailment to those facts and can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> express all of human knowledge without any gaps. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>> A subset of formalized English does do this. >>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>> Nobody has ever presented such subset. >>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>> ChatGPT rewords my words into that subset. >>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>> Your words have much less material than all human knowledge without >>>>>>>>>>>>>>>>>>>>>>>>>> any gaps. Therefore it is impossible to verify that you have told >>>>>>>>>>>>>>>>>>>>>>>>>> every necessary word to it. >>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>> Categorically exhaustive reasoning reverse- engineers >>>>>>>>>>>>>>>>>>>>>>>>> the required architecture of the system. Wittgenstein >>>>>>>>>>>>>>>>>>>>>>>>> did this on Gödel https://www.liarparadox.org/ Wittgenstein.pdf >>>>>>>>>>>>>>>>>>>>>>>>> and he was so succinct eliminate the convoluted mess of Gödel >>>>>>>>>>>>>>>>>>>>>>>>> numbers that people mistook his succinct analysis as simplistic >>>>>>>>>>>>>>>>>>>>>>>>> not understanding what Gödel was really saying. >>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>> Yes, an expectable consequence of ignoring essential aspects is >>>>>>>>>>>>>>>>>>>>>>>> not understanding. >>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>> Gödel numbers are merely the ridiculously convoluted >>>>>>>>>>>>>>>>>>>>>>> way that Gödel added the functionality of this simple >>>>>>>>>>>>>>>>>>>>>>> operator: ⊢ to a formal language woefully too inexpressive. >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>> Natural numbers are one of the best understood topics of mathematics. >>>>>>>>>>>>>>>>>>>>>> Therefore restricting the assumptions to natural numbers provdes the >>>>>>>>>>>>>>>>>>>>>> basis for the most interesting result. >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>> Of course one can ask whether one can prove a similar theorem about >>>>>>>>>>>>>>>>>>>>>> finite strings. It is much simpler to express claims and proofs as >>>>>>>>>>>>>>>>>>>>>> fimite strings as thats how they are usually expressed anyway. But >>>>>>>>>>>>>>>>>>>>>> that requires that one first constructs a theory of finite strings. >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> But we can show a direct one-to-one mapping of finite strings in a >>>>>>>>>>>>>>>>>>>>> finite alphabet to natural numbers (it just becomes the notational base >>>>>>>>>>>>>>>>>>>>> for the numbers). >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> That's true, and I would prefer that rather than Gödel's mapping. But >>>>>>>>>>>>>>>>>>>> the proof of Gödel's theorem is simpler if the number of symbols in >>>>>>>>>>>>>>>>>>>> the alphabet is prime even if that would mean that some of the symbols >>>>>>>>>>>>>>>>>>>> are unused. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Godel's Theorem doesn't need the number of symbols to be prime, it uses >>>>>>>>>>>>>>>>>>> prime numbers to number the symbols, and prime powers for the position. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> And consequently Gödel's example of an undecidable formula is more complex >>>>>>>>>>>>>>>>>> than needed. Which doesn't really matter as the complex details can be >>>>>>>>>>>>>>>>>> hidden behind definitions. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> ...We are therefore confronted with a proposition which asserts its own >>>>>>>>>>>>>>>>> unprovability. 15 ... >>>>>>>>>>>>>>>>> (Gödel 1931:40-41) >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> G := (F ⊬ G) // Olcott's Minimal Type Theory >>>>>>>>>>>>>>>>> https://philarchive.org/archive/PETMTT-4v2 // YACC BNF of MTT >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> ?- G = not(provable(F, G)). >>>>>>>>>>>>>>>>> G = not(provable(F, G)). >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> ?- unify_with_occurs_check(G, not(provable(F, G))). >>>>>>>>>>>>>>>>> false. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Gödel, Kurt 1931. >>>>>>>>>>>>>>>>> On Formally Undecidable Propositions of Principia Mathematica And >>>>>>>>>>>>>>>>> Related Systems >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Nice to see that you don't disagree. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> In other words you agree that I proved 1931 Incompleteness is incorrect. >>>>>>>>>>>>>>> Gödel's G when boiled down to its barest essence is simply semantically >>>>>>>>>>>>>>> unsound the same way the Liar Paradox is unsound. >>>>>>>>>>>>>> >>>>>>>>>>>>>> As yousually your "in other words" is a lie. Existence of a simpler proof >>>>>>>>>>>>>> does not make the original one incorrect. >>>>>>>>>>>>> >>>>>>>>>>>>> My words are true within your words: >>>>>>>>>>>>> "Nice to see that you don't disagree." >>>>>>>>>>>>> If you didn't mean that then you should not have said that. >>>>>>>>>>>> >>>>>>>>>>>> I did not say nor mean "you did not disagree with anything". The usual >>>>>>>>>>>> meaning of what I said is that you don't disagree with what I said in >>>>>>>>>>>> my previous message about the complexity of Gödel's sentence. >>>>>>>>>>> >>>>>>>>>>> The complexity of Gödel's sentence is nuts. >>>>>>>>>>> G := (F ⊬ G) Just detect the cycle in this >>>>>>>>>>> and Gödel is refuted. >>>>>>>>>> >>>>>>>>>> Nice to see that you still don't disagree with my comment about the >>>>>>>>>> complexity of Gödel's sentence. >>>>>>>>> >>>>>>>>> Yet I absolutely do disagree. >>>>>>>> >>>>>>>> OK, you think Gödel's numbering scheme is simple. >>>>>>> >>>>>>> ...We are therefore confronted with a proposition which asserts its own >>>>>>> unprovability. 15 ... (Gödel 1931:40-41) >>>>>>> >>>>>>> It totally hides the details that proof his theorem is unsound. >>>>>> >>>>>> You have never revealed any unsound detail of the proof, not even >>>>>> whether it uses a false premise or an invalid inference. >>>>> >>>>> The details of the proof that use Gödel numbers as their >>>>> primary basis hide the underlying semantics about exactly >>>>> what unprovable in F actually means. >>>> >>>> No, they don't. That is very clearly expressed. >>> >>> They don't answer the question why and how is G unprovable in F >>> their answer is that there is some number that some how says so. >> >> That no proof proves G is sufficient to say that G is unprovable. > > If G is semantic gibberish then G would not be provable. That does not follow. G if provable if there is a proof that is valid in the theory and ends with G. If there is not then G is unprovable. Consequently, if G is not in the language of the theory then it is unprovable. But Gödel's G is a sentence of the first order Peano arithmetic and therefore has an arithmetic meaning. Gödel also proved that in its arithmetic meaning G is true. In some non-arthmetic meaning it can be false. -- Mikko
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The halting problem breaks with reality olcott <polcott333@gmail.com> - 2025-10-13 19:37 -0500
Re: The halting problem breaks with reality dart200 <user7160@newsgrouper.org.invalid> - 2025-10-13 19:21 -0700
Re: The halting problem breaks with reality olcott <polcott333@gmail.com> - 2025-10-13 21:26 -0500
Re: The halting problem breaks with reality dart200 <user7160@newsgrouper.org.invalid> - 2025-10-13 19:31 -0700
Re: The halting problem breaks with reality olcott <polcott333@gmail.com> - 2025-10-13 21:48 -0500
Re: The halting problem breaks with reality dart200 <user7160@newsgrouper.org.invalid> - 2025-10-13 19:55 -0700
Re: The halting problem breaks with reality olcott <polcott333@gmail.com> - 2025-10-13 22:02 -0500
Re: The halting problem breaks with reality dart200 <user7160@newsgrouper.org.invalid> - 2025-10-13 20:10 -0700
Re: The halting problem breaks with reality olcott <polcott333@gmail.com> - 2025-10-13 22:17 -0500
Re: The halting problem breaks with reality dart200 <user7160@newsgrouper.org.invalid> - 2025-10-13 20:54 -0700
Re: The halting problem breaks with reality olcott <polcott333@gmail.com> - 2025-10-13 23:37 -0500
Re: The halting problem breaks with reality dart200 <user7160@newsgrouper.org.invalid> - 2025-10-13 22:45 -0700
Re: The halting problem breaks with reality dart200 <user7160@newsgrouper.org.invalid> - 2025-10-13 22:52 -0700
Re: The halting problem breaks with reality Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-14 18:12 +0000
Re: The halting problem breaks with reality Mikko <mikko.levanto@iki.fi> - 2025-10-14 12:53 +0300
Re: The halting problem breaks with reality --- confirmed olcott <polcott333@gmail.com> - 2025-10-14 11:29 -0500
Re: The halting problem breaks with reality --- confirmed Mikko <mikko.levanto@iki.fi> - 2025-10-15 11:49 +0300
Re: The halting problem breaks with reality --- confirmed olcott <polcott333@gmail.com> - 2025-10-15 07:21 -0500
Re: The halting problem breaks with reality --- confirmed Mikko <mikko.levanto@iki.fi> - 2025-10-16 11:38 +0300
The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-16 08:57 -0500
Re: The Halting Problem is Incoherent "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-16 14:07 -0700
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-17 11:32 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-17 10:06 -0500
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-18 12:30 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-18 05:58 -0500
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-19 11:44 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-19 10:03 -0500
Re: The Halting Problem is Incoherent "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-19 12:55 -0700
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-20 11:55 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-20 11:24 -0500
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-21 12:31 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-21 10:11 -0500
Re: The Halting Problem is Incoherent "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-21 13:38 -0700
Re: The Halting Problem is Incoherent Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 22:13 +0000
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-21 20:46 -0500
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-22 12:23 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-22 07:39 -0500
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-23 13:02 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-23 10:39 -0500
Re: The Halting Problem is Incoherent "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-23 11:57 -0700
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-24 10:48 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-24 12:41 -0500
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-25 14:57 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-25 14:53 -0500
Re: The Halting Problem is Incoherent "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-25 13:03 -0700
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-26 13:34 +0200
Re: The Halting Problem is Incoherent "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-25 11:24 -0700
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-24 10:46 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-24 12:37 -0500
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-25 14:59 +0300
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-25 14:57 -0500
Re: The Halting Problem is Incoherent Richard Damon <Richard@Damon-Family.org> - 2025-10-25 21:27 -0400
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-26 13:44 +0200
Re: The Halting Problem is Incoherent Richard Damon <Richard@Damon-Family.org> - 2025-10-26 13:57 -0400
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-27 11:45 +0200
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-27 08:56 -0500
Re: The Halting Problem is Incoherent Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-27 17:15 +0000
Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-27 12:22 -0500
Re: The Halting Problem is Incoherent Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-27 18:54 +0000
Re: The Halting Problem is Incoherent Richard Damon <Richard@Damon-Family.org> - 2025-10-27 21:26 -0400
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-28 11:54 +0200
Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-10-28 10:07 -0500
Re: Gödel's G := (F ⊬ G) Richard Damon <Richard@Damon-Family.org> - 2025-10-28 21:57 -0400
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-10-29 12:43 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-10-29 11:22 -0500
Re: Gödel's G := (F ⊬ G) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-29 12:47 -0700
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-10-30 12:37 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-10-30 07:54 -0500
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-10-31 13:02 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-10-31 07:09 -0500
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-01 11:10 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-01 08:50 -0500
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-02 14:41 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-03 17:40 -0600
Re: Gödel's G := (F ⊬ G) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-04 00:29 +0000
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-03 18:32 -0600
Re: Gödel's G := (F ⊬ G) Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-04 01:59 +0000
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-04 11:51 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-04 11:45 -0600
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-05 12:46 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-05 05:55 -0600
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-06 10:35 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-06 05:03 -0600
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-07 10:14 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-07 07:00 -0600
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-08 10:34 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-08 07:47 -0600
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-09 12:19 +0200
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-04 11:46 +0200
Re: Gödel's G := (F ⊬ G) olcott <polcott333@gmail.com> - 2025-11-04 10:29 -0600
Re: Gödel's G := (F ⊬ G) Mikko <mikko.levanto@iki.fi> - 2025-11-05 12:47 +0200
Re: The Halting Problem is Incoherent Richard Damon <Richard@Damon-Family.org> - 2025-10-27 21:22 -0400
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-28 11:58 +0200
Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-10-28 10:12 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Richard Damon <Richard@Damon-Family.org> - 2025-10-28 21:57 -0400
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-10-29 12:53 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-10-29 11:26 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Richard Damon <Richard@Damon-Family.org> - 2025-10-29 21:46 -0400
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-10-30 12:44 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-10-30 08:01 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-10-31 13:10 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-10-31 07:18 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-01 11:16 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-01 08:52 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-02 14:43 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-03 17:41 -0600
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-04 11:53 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-10-29 12:45 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-10-29 11:25 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-29 12:46 -0700
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-10-30 12:50 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-10-30 08:03 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-10-31 13:15 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-10-31 07:20 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-01 11:18 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-01 08:54 -0500
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-02 14:45 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-03 17:45 -0600
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-04 11:56 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-04 12:05 -0600
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-05 12:49 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-05 05:52 -0600
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-06 10:39 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-06 05:08 -0600
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-07 10:21 +0200
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence olcott <polcott333@gmail.com> - 2025-11-07 07:31 -0600
Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence Mikko <mikko.levanto@iki.fi> - 2025-11-08 10:37 +0200
Re: The Halting Problem is Incoherent Richard Damon <Richard@Damon-Family.org> - 2025-10-28 21:57 -0400
Re: The Halting Problem is Incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-29 12:56 +0200
Re: The halting problem breaks with reality Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-14 18:09 +0000
Re: The halting problem breaks with reality Richard Damon <Richard@Damon-Family.org> - 2025-10-17 12:13 -0400
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