XPost: sci.math, comp.theory, sci.math.symbolic   
   From: polcott333@gmail.com   
      
   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.   
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)