XPost: sci.math, comp.theory, sci.math.symbolic   
   From: polcott333@gmail.com   
      
   On 1/10/2026 6:35 PM, Richard Damon wrote:   
   > 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.   
   >   
      
   Proof Theoretic Semantics agrees with me you are   
   going by Proof Conditional Semantics.   
      
   --   
   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)