XPost: comp.theory, comp.software-eng, sci.logic   
   XPost: sci.math   
   From: polcott333@gmail.com   
      
   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 exist.   
   Does not exist because is contradicts itself.   
      
   Rene Descartes: I think therefore thoughts do not exist   
   is simply incorrect because it contradicts itself.   
      
   > In an F where such sequnénce does not exist G is unprovable by   
   > definition. However it is meta-provable frome the way it is   
   > constructed and therefore true in every interpretation where   
   > the natural numbers contained in F have their standard properties.   
   >   
      
   Self-contradictory gibberish is never true or provable.   
   It is better to reject it as gibberish before   
   proceeding otherwise someone might make an   
   incompleteness theorem out of it and falsely   
   conclude that math is incomplete.   
      
   This sentence is not true:   
   "This sentence is not true"   
   is true because the inner sentence   
   is self-contradictory gibberish.   
      
   This sentence cannot be proven in F:   
   "This sentence cannot be proven in F"   
   is true because the inner sentence   
   is self-contradictory gibberish.   
      
   --   
   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)