XPost: comp.theory, comp.software-eng, sci.logic   
   XPost: sci.math   
   From: polcott333@gmail.com   
      
   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.   
      
   > G is true and unprovable in F (which means that F is incomplete)   
   > or G is false and provable in F (which means that F is inconsistent).   
   >   
      
      
   --   
   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)