XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/18/2026 9:56 PM, Richard Damon wrote:   
   > On 1/18/26 10:19 PM, olcott wrote:   
   >> On 1/18/2026 7:24 PM, Python wrote:   
   >>> Le 19/01/2026 à 00:41, olcott a écrit :   
   >>> ..   
   >>>> I already just said that the proof and refutation of   
   >>>> Goldbach are outside the scope of PA axioms.   
   >>>>   
   >>>> Any proof or refutation of Goldbach would have to use   
   >>>> principles stronger than the axioms of PA, because PA   
   >>>> itself does not currently derive either direction.   
   >>>   
   >>> "currently" ? ?  What kind of language is that? PA is what it is, it   
   >>> not changing with time !   
   >>>   
   >>> You could have said that about Fermat's theorem back in the day... It   
   >>> happens not to be the case.   
   >>>   
   >>> You are out of reason, Peter. Not only a liar, an hypocrite, but a fool.   
   >>>   
   >>   
   >> If its truth value cannot be determined in a finite   
   >> number of steps then it is not a truth bearer in PA,   
   >> otherwise it is a truth-bearer in PA with an unknown value.   
   >>   
   >   
   > So, you admit that you don't know how to classify it.   
   >   
   > Thus its truth-bearer status is unknown.   
   >   
   > Thus, your claim that it is outside of PA is just a LIE.   
   >   
      
   No it was a mistake. Here is my correction:   
   If Goldbach's truth value cannot be determined in a   
   finite number of steps then it is not a truth bearer   
   in PA, otherwise it is a truth-bearer in PA with an   
   unknown truth value.   
      
   This has no effect on my claim that I got rid of   
   Gödel Incompleteness.   
      
   When we change the foundation of formal systems   
   to proof theoretic semantics and add my truth   
   predicates then Gödel's claim of applying to   
   every formal system that can do a little bit of   
   arithmetic becomes simply false.   
      
   Every attempt at showing incompleteness  PA   
   has never actually been  PA.   
      
   The satisfaction of external models of arithmetic   
   never has been  PA. These are categorically   
   outside of PA by the definition of proof theoretic   
   semantics thus defined as non-well-founded. This   
   neuters their ability to show incompleteness.   
      
      
   --   
   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)