XPost: sci.math, comp.theory, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/20/2026 10:04 PM, Richard Damon wrote:   
   > On 1/20/26 4:23 PM, olcott wrote:   
   >> 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.   
   >   
   > No, it becomes inconsistant.   
   >   
   >>   
   >> 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.   
   >>   
   >   
   > But there is no "cycle" in the statement of G. It is PURELY a statement   
   > of the non-existance of a number that satisfies a purely mathematic   
   > relationship (which has no meaning by itself in PA).   
   >   
      
   Even the relationship cannot exist  PA.   
   Instead it is about PA in outside model theory   
      
   > You only can find a cycle when you accept the interpretations in the   
   > meta-math.   
   >   
   > So, do you accept that interpreation (and thus the proof) or do you   
   > reject it, and thus have no grounds to deny the effect of the proof.   
      
      
   --   
   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)