XPost: comp.theory, comp.ai.philosophy, comp.software-eng   
   XPost: sci.math   
   From: mikko.levanto@iki.fi   
      
   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.   
      
   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.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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