XPost: sci.logic, sci.math, comp.theory   
   From: news.x.richarddamon@xoxy.net   
      
   On 1/10/26 7:16 PM, olcott wrote:   
   > On 1/10/2026 5:19 PM, Richard Damon wrote:   
   >> On 1/10/26 11:19 AM, olcott wrote:   
   >>> On 1/10/2026 3:25 AM, Mikko wrote:   
   >>>> On 08/01/2026 16:18, olcott wrote:   
   >>>>> On 1/8/2026 4:21 AM, Mikko wrote:   
   >>>>>> On 07/01/2026 15:06, olcott wrote:   
   >>>>>>> On 1/7/2026 6:10 AM, Mikko wrote:   
   >>>>>>>> On 06/01/2026 16:02, olcott wrote:   
   >>>>>>>>> On 1/6/2026 7:23 AM, Mikko wrote:   
   >>>>>>>>>> On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:   
   >>>>>>>>>>> Just an external observation:   
   >>>>>>>>>>>   
   >>>>>>>>>>> A lot of tech innovations in software optimization area get   
   >>>>>>>>>>> discarded from the very beginning because people who work on   
   >>>>>>>>>>> them perceive the halting problem as a dogma.   
   >>>>>>>>>>   
   >>>>>>>>>> It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a   
   >>>>>>>>>> provably   
   >>>>>>>>>> true sentence of a certain theory.   
   >>>>>>>>>>   
   >>>>>>>>>   
   >>>>>>>>> ...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   
   >>>>>>>>>   
   >>>>>>>>> F ⊢ G_F ↔ ¬Prov_F (⌜G_F⌝)   
   >>>>>>>>> "F proves that: G_F is equivalent to   
   >>>>>>>>> Gödel_Number(G_F) is not provable in F"   
   >>>>>>>>> https://plato.stanford.edu/entries/goedel-incompleteness/   
   >>>>>>>>> #FirIncTheCom   
   >>>>>>>>>   
   >>>>>>>>> Stripping away the inessential baggage using a formal   
   >>>>>>>>> language with its own self-reference operator and   
   >>>>>>>>> provability operator (thus outside of arithmetic)   
   >>>>>>>>>   
   >>>>>>>>> G := (F ⊬ G)   // G asserts its own unprovability in F   
   >>>>>>>>>   
   >>>>>>>>> A proof of G in F would be a sequence of inference   
   >>>>>>>>> steps in F that prove that they themselves do not exist.   
   >>>>>>>>   
   >>>>>>>>  From the way G is constructed it can be meta-proven that either   
   >>>>>>>   
   >>>>>>> Did you hear me stutter ?   
   >>>>>>> A proof of G in F would be a sequence of inference   
   >>>>>>> steps in F that prove that they themselves do not exist.   
   >>>>>>   
   >>>>>> An F where such sequence really exists then in that F both G and   
   >>>>>> the negation of G are provable.   
   >>>>>>   
   >>>>> G := (F ⊬ G)   // G asserts its own unprovability in F   
   >>>>>   
   >>>>> A proof of G in F would be a sequence of inference   
   >>>>> steps in F that prove that they themselves do not nexist.   
   >>>>> Does not exist because is contradicts itself.   
   >>>>   
   >>>> That conclusion needs the additional assumption that F is consistent,   
   >>>> which requires that the first order Peano arithmetic is consistent.   
   >>>   
   >>> It remains true for any proof system that does not   
   >>> contradict itself.   
   >>>   
   >>>> If F is not consistent then both G and its negation are provable in F.   
   >>>> The first order Peano arithmetic is believed to be sonsistent but its   
   >>>> consistency is not proven.   
   >>>>   
   >>>   
   >>> The point is that after all these years no one ever   
   >>> bothered to notice WHY G is unprovable in F. When   
   >>> we do that then Gödel Incompleteness falls apart.   
   >>>   
   >>> *G is unprovable in F because its proof would contradict itself*   
   >>> *G is unprovable in F because its proof would contradict itself*   
   >>> *G is unprovable in F because its proof would contradict itself*   
   >>>   
   >>>   
   >>   
   >> Right. so you can only have two of the following, and not all three:   
   >>   
   >> 1) Consistent.   
   >> 2) Complete   
   >> 3) Capable of supporting the Natural Numbers.   
   >>   
   >> It seems the logic you can handle can't do the last, so yo are fine   
   >> with your limited, but Complete and Consistant system.   
   >   
   > Not at all. Gödel incorrectly conflates true in meta-math   
   > with true in math. Proof Theoretic Semantics rejects this.   
   > Proof Conditional Semantics is misguided.   
   >   
      
      
   Nope, it weems you think math doesn't work.   
      
   Sorry, all you are doing is proving that you don't actually understand   
   what you are taking about, and that you versio of "logic" allows you to lie.   
      
   G must be true (or all of mathematic is just inconsistant, something you   
   can't just assume) as there can not be a number g that satisfies that   
   relationship.   
      
   If you want to claim that there might be such a number, then you are   
   just assuming that mathematics is inconsistant.   
      
   If you want to claim there is a finite proof of the fact that there is   
   such an number, you have to explain how you can write such a proof and   
   not have it be encodable in a number g that satisfies the relationship.   
   In other words, you are claiming that "writing" is just inconsistatn.   
      
   "Math" isn't "meta", math is math. MEANING can be created by   
   programming, something Godel effectively shows can be recreated in   
   mathematics.   
      
   All you are doing is proving that you think anything you don't   
   understand can't be true, which just proves your stupidity.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)