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Re: Gödel's G := (F ⊬ G) specifies a cycle in the directed graph of its evaluation sequence

From olcott <polcott333@gmail.com>
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 07:31 -0600
Organization A noiseless patient Spider
Message-ID <10eksc5$1sgnb$1@dont-email.me> (permalink)
References (25 earlier) <10efa37$ashj$2@dont-email.me> <10efdqa$c4n4$1@dont-email.me> <10ehmsu$10gr3$1@dont-email.me> <10ehvj7$12r5g$1@dont-email.me> <10eka64$1ndvh$1@dont-email.me>

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On 11/7/2025 2:21 AM, Mikko wrote:
> 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 := "lksef 34t987n m nk6f9-823t5jkn mhgtr,edgsbm"
try and prove that.

> 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.
> 

G := "this sentence is not true"
That is semantic gibberish because it has a cycle
in its directed graph.

This is what a cycle in the directed graph of
its evaluation sequence looks like:

"this sentence is not true"
What is it not true about?
It is not true about being not true.
What is it is not true about being not true about.
It is it is not true about being not true about being not true.

This sentence is not true: "This sentence is not true"
is true because the inner sentence is gibberish.

> But Gödel's G is a 

convoluted mess that can be succinctly expressed
as this: G := (F ⊬ G)

A the screwy tricks that Gödel used were because
he chose a language with insufficient expressiveness.
If you want to talk about provability then use a
language with a provability operator: ⊢

You want to talk about self-reference then use a language
having a way to directly express self-reference with this
operator :=

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 ...(Gödel 1931:40-41)

Gödel, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf 


When you try to do this in a language lacking these
basic building blocks you are going to have lots of
purely extraneous complexity.

> 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.
> 

G := (F ⊬ G) // Is is true that this G is not provable
because it has a cycle in its evaluation sequence preventing
if from even being evaluated.

Page 254 of Clocksin & Mellish explain this in depth.
https://athena.ecs.csus.edu/~mei/logicp/Programming_in_Prolog.pdf

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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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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