XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/19/2026 11:29 PM, Richard Damon wrote:   
   >> My system is not supposed to decide in advance whether   
   >> Goldbach is well‑founded. A formula becomes a truth‑bearer   
   >> only when PA can classify it in finitely many steps.   
   >> Goldbach may or may not be classifiable; that’s an open   
   >> computational fact, not a semantic requirement. This has   
   >> no effect on Gödel, because Gödel’s sentence is structurally   
   >> non‑truth‑bearing, not merely unclassified.   
   >   
   > Which shows that you don't understand what logic systems are.   
   >   
   > The don't "Decide" on truths, they DETERMINE what is true.   
   >   
   > Your problem is that either there is, or there isn't a finite length   
   > proof of the statement.   
   >   
   > Semantics can't change in a formal system, or they aren't really semantics.   
   >   
   > Your problem is you don't understand Godel statement, as it *IS* truth   
   > bearing as it is a simple statement with no middle ground, does a number   
   > exist that satisfies a given relationship. Either there is, or there   
   > isn't. No other possiblity.   
   >   
   > You confuse yourself by forgetting that words have actual meaning, and   
   > that meaning can depend on using the right context.   
   >   
   > Godel's G is a statement in the system PA.   
   >   
   > It is a statement about the non-existance of a natural number that   
   > satisfies a particular computable realtionship.   
   >   
   > It is a statement defined purely by mathematics and thus doesn't   
   > "depend" on other meaning.   
   >   
   > It is a mathematical FACT, that for this relationship, no matter what   
   > natural number we test, none will satisfy it, so its assertation that no   
   > number satisfies it makes it true.   
      
   PA augmented with its own True(PA,x) and False(PA,x)   
   is a decider for Domain of every expression grounded   
   in the axioms of PA.   
      
   A system at a higher level of inference than PA can   
   reject any expressions that define a cycle in the   
   directed graph of the evaluation sequence of PA   
   expressions. Then PA could test back chained inference   
   from expression x and ~x to the axioms of PA.   
      
   --   
   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)